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Fan
Engineering
FAN
ENGINEERING
An Engineer’s Handbook
On Fans
and
Their Applications
EditedBy
ROBERT JORGENSEN
Eighth Edition
Total Issue 122,250
Published By
BUFFALO
FORGE
COMPANY
Buffalo, New York
©1983 Buffalo Forge Company
Phototypesetting by Printing Prep Inc., Buffalo, New York
Printing by Kenworthy Graphic Services, Buffalo, New York
Binding by Wm. F. Zahrndt & Son Inc., Rochester, New York
1-83-18M
PREFACE
Fan Engineering has always been written as a handbook for engineers who use fans. This, the eighth edition, is no exception. As in
any handbook, data and formulae are emphasized to facilitate problemsolving. However, some topics are dealt with in detail so that the
reader will better understand the limitations of any results obtained.
_ As has been customary, Fan Engineering is organized in four parts.
Part I deals with fundamental topics. Although these topics are generally treated in other handbooks, they are presented here for the
convenience of the reader. Each subject has a bearing on fans or fan
applications.
Part II is about fans. Although there is some discussion of fan design,
both aerodynamical and mechanical, the emphasis is on those topics
which should concern the user. Even those portions which are concerned with design may be valuable to the user, since an understanding of what makes a fan work may lead to better applications.
Part III is concerned with specific fan applications. Here, too, the
convenience of the reader is the main reason for including several of
| these topics. Other handbooks deal with some of these subjects in
| much greater detail.
Part IV is a collection of miscellaneous topics which readers have
found useful.
The major works that were considered in the preparation of this
handbook are listed in an Appendix. Footnote references are given
for each of the tables and charts unless they were specifically designed
for this or previous editions of Fan Engineering. Much of the material can be traced back through previous editions. The first was edited
by Dr. Willis H. Carrier and published in 1914. The next four editions
were written by Richard D. Madison and published in 1925, 1933,
1938, and
1948. The sixth and seventh editions were written by the
| present editor and published in 1961 and 1970.
The eighth edition contains twenty-five percent more material
than the seventh. There are six new chapters and many other chapters
have been expanded significantly. Chapter | on properties of air has
many new examples and some new psychrometric charts. Chapter 2
now examines the laws governing fluid flow in greater detail and
many examples illustrating pressure-loss calculations have been
Se
| added. Chapter 6 on mass-transfer processes and Chapter 7 on partij
_cles
and particle clouds both enlarge on material previously given
J under air cleaning.
Chapter 8 on engineering statistics is new as is
| Chapter 9 on fan terminology. Chapter 12 includes more information
On dimensionless coefficients and the effects of compressibility on the
fan laws. Chapter 13 reflects the new codes and standards on fan testing. Many pressure diagrams have been added to Chapter 14 along
with topics like windmilling, surge, and stall. Chapter 15 is new and
covers many details of fan control. Chapter 16 on fan noise is new
and Chapter 17 on fan mechanics has been enlarged. Chapter 29 on
air cleaning has been reorganized.
Most of the equations have been rewritten so that either U.S.
customary or SI units can be used. Some symbols have been changed
to conform with those generally found in the literature. A chapteroriented numbering system has been adopted.
The author gratefully acknowledges the technical suggestions and
other assistance contributed by many Buffalo Forge Company personnel. Special thanks are due to Melvin W. First, Sc.D., Consultant to
Buffalo Forge Company for contributing the new material in the
mass-transfer processes, particles and particle clouds, and air cleaning
chapters.
ROBERT
Buffalo, New York
September, 1982
JORGENSEN
OUTLINE OF CONTENTS
PART | - FUNDAMENTALS
CHAPTER
1 - PROPERTIES OF AIR AND OTHER GASES
PATIOS
IIE HICIA Te eee
cere Penton: eriincye ee areca nee tate
a
etc 1-1
StAnCanarAtmospmener er cote Let tensteraiere Aveo thealrae ee oer neue eeece bard eee 1-2
SEAM GAC
corescyasch esteneareray sterssacstete Seer
roeAthenote Gee a ean
Rae 1-3
MOLECUIAHVVGIG INieecoensctacmunicacteucrinceaean
ieeeeisttcaci etercacsoe hicerece cgentioes coroae 1-4
BeWMeCCHGASIEQUatIONIOl otateristic
me ctor
ou inerictnra cmtsam seieiiet haeets 1-6
SE CIIICUGav Tycpaeec ¢ teeth
rtelera near autem orice tetee Ai Aeedcsoee sion a veee 1-8
Dry-Bulb, Wet-Bulb, and Dew-Point Temperatures .................-2. 1-10
Partial Pressure, Saturation, and Vapor Pressure..........-.00....000- 1-10
LFULLITAG TINA 2aes ercre sisoen chorion tancts eo Eo aS eR
ETE
RT Oreo 1-13
DEMSMbyandp SPECITICAWVOl Ui E Siena mt cescides sess saedesach lovesiece fotspeucieleteuewamuse
iecaer 1-15
Heat opecific:eat,and Heat.of Vaporization .2c.c. 6 <cnse aoe ease asnae- 1-21
SDE CIC! EMU
AlDace cere seceesthcetoceotard core ete ee aresoestenetlepeat pracheiisieyeteueys Neie neets1-23
ESOC HOHE MILO
[9Varempctses cys eae cterataeee tenia nore conn cerca neve ariats rete aga wonReet oars eae 1-28
ESVCMOIMCLC Al OSsou scatcazecetarsiaucrene ous ueoatehcssie Suse Sno s-onegooyeulfecaie oka ances ae 1-35
sy cinionne
ti ciGiant re ercccesccs char ameanes euseennit secure, ote eres Reyeanndesyeua pieces 1-35
FOR] & cha aeeao teasonee occa
CRNS
Ee Cee
Ce EN
Een ere
ane eee 1-44
Baro mMeticCOnrectlOmSivecse
in. seus eecrets prensa rereteiace sien Sect akerexeucem uelwonnreoedeee 1-44
BaromerhicuviGaSune nents gacrp os tccie cee apserete ia eens
ce ee eae erany gears 1-48
ME MperatlinesMESASULEIME
MIS saeco crectrscete renee caches ptfonsteh seared delat oseect susie are 1-50
BUMGtV
ME AaSUbeIMmenistank..cieicc
ieee melon Cason se ee ey aeraic yom eas 1-52
CHAPTER 2 - FLUID FLOW
PRINCIELES OF ELUIDIFMOW dame cisten connie coe ccm
eal tar 2-1
Mathematical Odel Samana core cive cocina sacarn arte ero cote ersrocie 6.ogelieus ahrowases 2-1
Comunity EquatiOMmStay-s
ticles cans oe
coats aire
binks nitro Anise ieee 2-3
Equations of Motion or Momentum Equations ..............0
eee eee ee 2-5
Genera vENnergViequiatlOmmpprcnmuesee
rune
itn
ben ceeceniniane meena 2-7
Nonunitorimn-Velocity Conrection RactOrse-os
aces aa peye ees ieee ee oie ae 2-9
SpecikicEnengyy Head: amd jPneSSUNC went creas erie
cre ven weer ic 2-9
Incompressible-Flow:Energy Equations: scene. wee eee eee s Hoe oe 2-10
Campressible-FloWiEMergyEGuatiOmS yee. sstrercears alco ua deen ieee
ec 2-15
AVG IMMINEH MDG Tair ccne gareccra-ccaenevary esicone acertie)cGai oat reeeenet totdain ete arate aes 2-19
Temperature Rise DUetOCOMPHESSIOMmsteeanaracr
tre stalatsrateee erestererre ccs 2-19
SLAQH AION; PLOPCLUES re rita 20 etersiate ensuemeneyee:lereticysie scleens ErvesRPNaparsre evacceaecene 2-22
Racial rama NOntexsF OW yn creates tierra otters carrera ara“aatalasaustiana savers svar. weet Appa 2-22
EERECHS: OF VISCOSITY site race ceeraers evasadare ce)a olenconte steer scarier pois osc ent 2-25
FOMG RNC NIMES CNC hl
SKOWIROEINRILENMENS cascneaceondosgnu
sau soe ondouseore 2-25
OMMAMC ING NM
WISCOSIM: « nn damchowavnaoanoocou
wero oy obREdics 2-26
EWAMOICEIN MOE seu oc 6 ou co molbines agorounmn boned bo pou d oN command Sion 2-26
EANSOMIe ana Relatives OUGININESS#aetiarse
ct ae tartans aneteneie ve erence tiecher 2-31
DRONA ATGIeIN REO rg roa oto G00 ddo.s so oco sen ben oo
momD ag yes o Brae 2-32
BRESSURELOSSESIFORIDU GIEEEIMENTS xtra
tctumerceiceraeie 2-35
Errianic elCOmaltion Sumearmenmearecen crrece
ruekectslcniel lenereret srecetetenen senettrre cata 2-36
EXINCONCITIONS
thor nunckn ee raeiairs tera neice aaa puerta sion tcalersal atnenane cian 2-38
SHANG MUBW Goer scadiod arcade Fob oon ens oenD oni 6 G00 CoonoD 40m cota 2-39
viii
— BUFFALO FORGE COMPANY
FAN ENGINEERING
PART | - FUNDAMENTALS
(Cont'd)
ENDOWS? 205. excescrorss ainussoesnseSievers tone aera toratee carota cmano ean aes Eater etcetera 2-48
e nt astro neces eee 2-60
Changes in Duct Section 2.0.0.0 6.0. seme ewer etc
otcnevele
AbruptiEmlargement q.cccy-cyotereteei
atetertte enestolerer ethak-tonal
rer aeetenetel-l=telcre 2-60
PNM ACMU
waceNeocoobascuboemonecunenocesansuoonocooden
yas 2-62
Diffusers and Evasés (Diverging Tapers) .............-22-2eeeeeeeeeees 2-64
TakeontSrand wunctlomS mace
mrerieiette cieicierir escheat
tres 2-72
oocumon
Olesialiotocusrne
Aomamne GuSoLEetemaSaseumero
Sono
nto COCs 2-75
GOmMpressible FlOW ese. me crete wima scelernieleliore o fetsieiiel= olefetotey myapace al-Kelokels parson 2-78
udouo
LOVIN
comsewocndc cbseecentonnonba
mouse aoendocdcmoates
2-79
PRESSURE AND FLOW MEASUREMENT Si seere cect
tear deren aecerntere 2-82
asad 2-82
PRTG
OEIC NARS: oo nea scdoonnccmoudenooneDao
BhopetonewS
Bresstine.Gages:amdlira
SAU CCGSr rye taretenisee fetes ts kent see arerere eesti 2-86
FlowiRateiby Velocity: IGAVENS@S sarc tects tate creterotors eres etna atresia nearer 2-90
etcierr
Average Pressures trom raVGlhSCSiereraten
etter eisicrterrsrsretenertels
ersten araens 2-95
ANEMONESRS cco ee cuaiacere fone ore susuausiovs aceite) suofere fees onere/sliareecaleiiet exeeherspe care eralcigs 2-97
Differential/Pressune| MeGtersi es joreote acess ststetecelerersiayel «evens wi eelsre eperete atolohersrs 2-98
The: Saquiane= Edged Orificer ss. ce cyenc sserencse) sets « sore eit.sseveiesgeueieys evcuomy evenseaers 2-102
Roumadedz Entry Nozzles az ccs «rc caters cresisteseig eve njersioie te eeoisieristonaueriepees 2-106
Conical-Entry Nozzles(Convergingifapers) <i.)ssc1.. ls elec + ieee ere sieieiete 2-108
Re-entrant: PI DOS ser ae cross ssi cetera tru sca erwuoles 8 @iavieces's aa cnoger @arereeauraneir sysaeeems 2-109
Venturi M@ter? a ccinter: sess cei rare areiss mls Cateich Mtareetmesne smneisine atensiaerarareiees 2-109
Compressible-Flow Measurememtsr
crestor rite steer steer rere teaeette ie2-110
CHAPTER 3 - TRANSMISSION AND DISTRIBUTION OF AIR
PRINCIPLES
OF DU GTIDESIGNie reratcrsasteic scoot araoucreehcisnctio cielchetaicietetarcievnerenane 3-1
Duct. DesigmiMethods: sic sisciicscuereratscszane
ateys, setsuetsaberctefaberoie stapegtelereebreeeae 3-4
RouirydiDU cts eraccis cxtac ccarerevseats lata, nape forencusl rele usar tieeiiencier nitse ica)Ae ae eae 3-9
Rectangular iDUcts yo, c.) slecatveosatete svecuserse sharers chepeme axe ure
ie eaten 3-12
Construction Detailsy..
Suse use cers aetomceniercne cons eee oie ick rican
eC
3-20
FRINCIREES OR DISTRIB Wiil@ Nitec erent eters reenie craetiets ean
aes 3-28
ihrow-ofilsothenmalliAinJetsiacsn
serie oceciciaccetien
eitacrrters cinterteen araerars 3-29
Throw of teatediorGooled/Air Jets eas. aon
ae one
eeerereine 3-34
CHAPTER 4 - SOUND
BhySicaliRropenticss sc ceccauve ment arnen tote aracc tee ten eee eee
Meastinementofisound(Properties sc
caiman cae aetna
DOCSIS airs cease ahotetens ove nachna oarnavaarebarors ayoan UTRRITE kee ne Te ee
Determination of Sound Power Levels and Directivity..............000-
4-1
4-7
4-8
4-13
HearingandiNoiseiCritenianmaaserataracctere
eed cracte acre erent ae 4-16
NOiSeHGOm trol cers wcevesuoreeracucater vee evncates toe rseos se terete retoreo
ee ee 4-25
CHAPTER
5 - HEAT TRANSMISSION
MhermaliGonductivity ean ccriy ceca ierr er orcas cara
SteadViGonductionintecteca
taco
eed ete
ete
ee ae ae 5-1
ae oe
5-6
EilimCoetticie
ntsicrrccisc sire eeetcrs ces, crore cele eee ee
5-6
Heating and Cooling Fluids Inside Tubes..............
cee eeeceeeeeee 5-7
Heating and Cooling Fluids Outside Tubes ..............00cceeseeeeeee 5-9
Natural' Convection) 3. sys ncceeentezeter as hier leat ence
te eee ine ae 5-9
Condensing Vapors
OUTLINE OF CONTENTS
PART | - FUNDAMENTALS
(Cont'd)
Dehumidifying and Cooling Air-Vapor Mixtures ..............c.ccc
sees
EV ADOLALN Qui Ul Stam. ge sncsemyemcires ct satecuces uikelexc orn. Maen
eyATA TOS
EXOTN Mao BET LUTFeES ete ap Pe rey er ch IONC IE Gr ORO
Pe
ce eee Ary ree
OveralliCOetiClents -rr.csrad ys Sho a Cer
hee
EO ee
MeaniEffective Temperature Difference <.i.ccn5 cs ciictysi eects nti
s ie
EXTOMCE GS Ua CO ree tecters me stom aN Nets eeecovenciti erSue nach ea
CHAPTER
6 - MASS-TRANSFER
PROCESSES
BDI TUEST OM syPerea eed nas eee ese Megara dhe foecUae aN, RothchoasaKNICH TCE Pate tare ene
Molecular DiffusioniiniGases and Liquids: 22).5.)-\4.
se eeirtins sialic ee
BadviDiifUSlOnuinjiGasesianGlLiquidSimermerinceritrawraerrrricrierier
eee
arANSheniBetweeni PMAaSES Arey rele jeiers sealloss averse) Menborsioxcho wee torerslerse eater
EOUN OTT
eee
eRe
rm roe per ane ae
De
eRe Tce eA
oF
NOOBS
OR PAO IN|Eevorers tettena errenSeke cestrceresreranc nenoralRetebateaeroters Pateected
e
DVN G ONC Cesare eetewesaaah terebwag YaledotstarePakrceafehe fons elona a Conaronctevetakate tcmeee
ee
(ware Gers iil eliGhec anes cnigcratcd ns Sone soo cao aoe GOA, oo Seino
MOLAIMIEAMSTCTAR ALG sen mene iri tercte ceMeee eee iesacresciclaveere oiecs oekeenaeiete
ian Stem WIN es ONCEDL eee ctarceay oteeper ene eaten rete eee otrcerlerecsie meeyeeieeer see
INDYSOVRRUII@I SE calc xara
Cortney aerencieumn tr tee
Ne
MRO
TO EIR
Ona
AASOLDONL LODE Se ears aera orm erin tester ae ewe oreceteseters oie neouaiseer tats
PXOS OUD U ON ISOLM ETN Samccreracestin te chersy cents Gree. alerts aactamietners coomierstane ur
PRESON
PU OM ZONE Sacer mot mere cree tae este aeraace aot Tet no oases Specarmen eee da
MAST GUO MITSiarerter.
eterna rates terstteeta neorate nica atecetatas dueseasels shetetauenals
CHAPTER 7 - PARTICLES AND PARTICLE CLOUDS
Dynamic Behavior of Aerosol Particles in Still Air ................--5-.
Dynamic Behavior of Aerosol Particles in Moving Streams .............
Brownian Motion and Diffusional ProcessesS............-seee
eee eeeee
OpticaliPropertiesio NeEnOSOlSapamcenre
ee seer ete omeeraee ote elieeet preeneteny arenes
CHAPTER 8 - ENGINEERING STATISTICS
CUMBIA) Gaaaanoudease cos cmsoo0) God0d00 60.0 cooecaacree co mcconcap ia
Measurement EnromanadlWiMGentallMty rm acmrersritete
aie ctsrclenetalenal esroiry -tate=
Propagation of Uncertainties into a Result ............eeee
eee eee cece
DESIgiiof EXPenlMMEMUSi eaerstarrpene rset aouere scarereinereteleis less)sselielet olemeelelvcorelene] ores
PART II - FANS
CHAPTER 9 - FAN TERMINOLOGY
FAN ENGINEERING — BUFFALO FORGE COMPANY
x
PART II - FANS (Cont'd)
boanouds
cubaEroOt mnce
(Gans tautomer iaelCs: agagocososconnecococrH
ss
cece eset eters
Application Classifications .............0..
Performance: ClaracteniStlSters
cx ceop-soneneeteio slotspeneteter Uncle oles Retreat Nake op=t
..e2
The Volume-Flow-Rate/Pressure Approach ............eee
reese
The Mass-Flow-Rate/Specific-Energy Approach............+++++000Miscellaneous Performance
CHAPTER
10 - CENTRIFUGAL
FANS
EMENGY MAMSLS Ia rere aro rare evcucesiererai ele Ree rnceter etae seaereer2)= ket ieyaiie eat eee
Pier umommetne
Nate ao do ocoe sen ncnboneoobancodense
don aseoasedbc
Ideal Performance Characteristics
Eosses anciEfficlenciestrrswaserratiie
aetoie emicheater taeaeayenctay eee a aes
Net Performance Characteristics
Overall Design
nV DYCis[ine ee See case micatie Neen
M een omaAR HB caggcda tos pao ons
Impeller Design
GASIMNGIDESIG IM)war wrstesarete scsi avers usu oreier yoseuchas sieseysnmntenstayeniotepan Pandyenremtete
Inlet Guide Vanes
CHAPTER
11 - AXIAL-FLOW
FANS
NomMeNnClatunenacciecceercneendieeonvent
arenes eters anya, haredererecn/a eyecuatro eens
Enengyalita nste (esrneacate cecascate. steerer «appears hoe esityegs, a ureragen Perens ener ran
INCIdemCe aNd DEViatlonitrercccrd
ces cn tess ory eesscoarsucineerenay
crepe
ea
Performance Characteristics
Overall Design
DUG TMG elih Sonora
omtor ROAShC a mC eE tr oo Goanin cp.ccaarson to SEP
Number and Solidity of Blades
Blade Angles
Blade Profile
CHAPTER
12 - FAN LAWS
DITAME MOA increas esenintcion comet oie Cee roa. aor oo ont
en oboe
AppliGationsS arcciesssicic bos nieonie cecal aus ehor cinke Cotes ae tae
Compressibility
EquiivallemCys egret cencecscncrsate crs. orate taney e ove ats, Pavsporae eebavacss us rays ors eee eee
Power Formulae?
5245... oman aee
ioe Seri
eee
ee
Specitic: speediandiSpecificSizegasaasmae:
aoe acters
cite eee eae
Sound Power Level and Specific Sound Power Level
Similarity and Deviations
SIZEEMC CIS ware cisercia carn vate acuem roc en ouc ein ee hone ae
eee
Reynolds Number Effect
Mach Number Effects
OUTLINE
OF CONTENTS
xi
PART Il - FANS (Cont'd)
Diameter Coetlicienitiy
ie .aractresses ae cooeee ciaoicas)sucteo ao i ew
12-27
MIAOU
EM ONCOGILICIER tetetetcrstc rcknt meee aioe rire eg esMehetea ntd aps es or
12-27
Sound Power LevelliCoefficient an. aaacmice + stercle olseloucis.o nse saeereee 12-28
Bimensionless:Pemonmance Curves prny-batssese.
oessl inemon neers 12-29
CHAPTER
13 - FAN TESTING
BEST OGG Sexes tesotis acesaeatessuetknoe tensivecsmeccont bars ehPRA tat Res ee ORE 13-1
FADOTAtOny TESUS STUDSu.rrsgs cbs chareacetarsisestare Re TART Te Sie IoC 13-3
PIE RCMTESES CUD Skeresaneicvereisystston nett ucestas esaeeakes oeccses aloO oie Sous
TI
13-5
Moasuining! Fain RlOwiIRate smi
etnece ced sare ciel9 Seige metic aero Bee13-6
MeaSuningi ran Specie © Utputsevstseiiccc
os eons Ok ete
ee oe 13-7
Meas uningit-aMiMpuLleOowe leita
ac eta aerela a ivelesi oni ieeoeisran 13-8
Measunihg iano peedua
vert tersccred te oe ee
eerste che oie er tee 13-11
Meas uningrAinDensityieqterctmcr
ace
attest itine eee oem eee ieee 13-12
Measuring; sound Powerlevellanva
et estctie tle
ail eisiore ureters 13-12
SAID
ATOMS areteve = onesce e tershesceedacalettionel scare eter sronauth svevalMel user otra ohatedrecsl cue 13-12
MLESIE SUITS pictus arfre crete testo Garret minceNoa celueusn devin haves atercrnenettomenine 13-12
CHAPTER
14- FAN SYSTEMS
Famand system Matching) o.<.rccs pot seetaere oisbits siotegetuareierris asalors
ever 14-1
ERESSULE DIA GFAliNS pws tics aetna span SRA at aa erate hers otnd Raters ee
SVStem ChanracteniStiGiCUIVES wesrsers ce aac snows uae sO NSE pete Aik memes
AMOS EAT OV SON Sats otcinucbsiter nie ient eonev wastes Ganda oleae noe mine EOE
SyStemSiwitiniviass On eat EXchanGe scciecc cere su Aicler- nui s citer ee eit
14-2
14-13
14-14
14-18
COSCO /SYSLEMIS cavers cresemurerasesiom sense ngs eriwicws nema aarergleeamayee alee 14-20
Meitualiintluence of FamandiSVStem iacesecscy-cospeioiagel
eweestepsieres edesieiniceerete 14-21
Second- and Fourth-Quadrant Performance ..............
eee eee eee 14-22
NMFINCHT
INTL [VIG erstarcrexeschadarevane: ove Ghote cvarersvotererete eee telecon ciatecrie'e sucketeseve iors ol 14-24
SITU
Tt Seen entre Nexen neyarcorsnsys rocczars Ger nmeeePaho aie tinesninesshRotieteveuslchavo eusdeleuatoleecenate 14-25
CHAPTER
15 - FAN CONTROL
OPERATING CHARACKERISTLG Sis. csaecutetee
sri siclaeistmieteetee eter 15-1
‘Oumleyeeeyrlaises
come aopsostourc peoud san nctC oe Oar otro mon pamire ters 15-1
nieryoy CDE
eae on cirao.0 dota Sea bood ibid oampbron ude omen eo Gen Dek 6 15-4
MALIA DLeMle ta NC Sie coeusiae ete wastenen ateSeteus ersiclecrsrecate cities c/s.spscorsueteyet sane ciate 15-5
VANIER al oto da-4 oobeo CE ten 5 orn MO auAt cme SIO EEO
aS ae erneno-3 15-6
Meanie) SESS orerete) So oto c bp 6G.c,d RTO. Bane EO OM he OEE IIE Oar cate 15-7
EI RGUELSEUIGS aro eancicteicorots deere OC One 6 OM OMI Mnbr Cee G aE aS. O mroDOIOmaIS 15-9
“FSU UATE fers tea caving eaxccta.chee oct roles Bac eR
OTE OS DecROe COLO Ga SIONS SUED 15-10
STENAT AUP CRVNRACTIERISUINCS aca gcccboconspedoncsiseabanunopboodus 15-11
COntrOllediRESIStAMCO maa cet he, Boers escee teen ote toca cate Riesscreie rscrews 15-12
S@lerioin lee Matee chance avoopooncans poceoe ese enon onden don omn ooomre 15=13
\3 yoyDCRR
Sul: oe aon GOO ee note oe ako anes boniuats sauob cgche 15-14
AME
FeAEDT URAL
EGhillecsces 2 acer ety rene ae neusttenn,» ceever sons Poxsteatecwriay« Careyenase hyelovetomeesermareee 15-15
FANS I Seeks os pond aoc eD Ono Ope Oe coo Oa DOC Oto APO mma om mcm. fs i5an7;
SiS Tal Pencuihs
OU
‘Oxi
accede gan Gouooods Oo OOO DOD ONO Ober nom crn
ERE SAN
IN G Site ysis
stgoo.c6, wa 15-19
tecosterepoicysca) 1 crestor iowa rates olor fo ea pslanevaranatetaiees vee 15-28
DE NOEtH ren aeoeooodec
pera soe
t Oo 8eUs Domi
cama tat
acan nite, 15-33
til CUBeRe DR lesit 2ccitooraacoreon
see aeee pNOD POD dcr OMeCr odo orp.cricct 15-34
xii
FAN ENGINEERING — BUFFALO FORGE COMPANY
PART Ii - FANS (Cont'd)
Variable inlet Va NOS 2 cr evoneiuccetorsre sietaivicnrieretrucreeerate
rensiete crenata error claret totes
Nariable: Pitehitecccs
seccietesiecd eoeies note tatsnsiteesusuovel orcielete Teyaveyenetotel teeters: eteiere ate
Varia blerSpe
ed irrererts rarer totetoreistercrensens ieee ioe ieceiekeratereran etekaerate emt
(Corwen qadsaacecuscuseccoopiocdococtooso
eeoaooKepE Dood gOGOGS
CHAPTER
16 - FAN NOISE
MechanicallyiGeneratediNotse scree trustclevoreie ert ae renter eieeretsssiera irene
Aerodynamically Generated Noise
XO aC)Al
Olea
(ONW o Pa omoumh conto Oo bDC cons O cco en soo MONO to. ooea been
Predicting Sotind|Powenlleevel Siryerietec eset te ote oieteeta tetaeeteter ert retain
Predicting Sound Pressure Levels
CHAPTER
17 - FAN MECHANICS
Torque
TIOUSIMNGYRE STRAITS seas vcore celedese outta epne eee a atokEIEN uray evat-t coe USOT oe
ae
Centrifugal Force and Centrifugal Moments
Be@aningsSinc
tis samaie oc civic Rinoelecraetcis aoitn cis Crane ore eee
ene
Static Stress;otrain, othengthnand Fallline me camse + cae sensieeaetae
Dynamic Stress, Strain, Strength, and Failure
Vibrations and Critical Speeds
Balameimg a syorearercactecsistons Aucin aiemivierst puceusiala ve Weis aawieni cla jme-aeenre crete ree
Vibration Isolation
Mechanical Testing
CHAPTER
18 - FAN MOTORS AND DRIVES
Load Characteristics of a Fan
Prime: Movers wancccame evan seranin nia itate
Integral-horsepowelrelectric MotonSenaunm
Fractional-Horsepower Electric Motors
Transmission Elements
CHAPTER
ieee ee aaa cme hea ere
eae iaeienrinten ier
ee
naieree siete
19 - FAN SELECTION
SpecifyingiRequinementS.yeec
ime
eae
Selecting the Proper Size and Type of Fan
Rating Fans from Test Curves
ee ern
s eee
PART Ill - FAN APPLICATIONS
CHAPTER 20 - VENTILATION
Design Principles
Heat Control
Odor Control
Industrial-Contaminant Control
Night Air Cooling
eee
OUTLINE OF CONTENTS
xiii
——
PART III - FAN APPLICATIONS (Cont'd)
Mutnatonand Natural Wemtilation\e
oe an.-0 0-15 cnc cnre1c-ca create renew
MechanicaliVentilationmmen
ssaacnetn sce ack omen
ano Eee
SDECIC ADDIIGAtl
OMS 7a mMeee mosuiiys san reine COIC ae aw na she nS
CHAPTER
21 - WINTER AND SUMMER
20-15
20-19
20-20
AIR CONDITIONING
DESO MPM MCI PICS misscrserisetern eine eras cinaiers ae ciecerens arsine roe ice imeitcreres 21-1
DESIGNIPRO CEDURE sre avira
co
tenice aan mt
etre 21-2
OMG Nepsuee cate siechr tee BaP T AN OF cine vane Apert etal he Ne eM creel ena te 21-2
HecigniConcditionswes.prtmieie
rel eet
ete on accuse
ee eee 21-4
ABST HeMNo MeZoxe} [nen kere
veSpo sem ona mmodee ponboo seodnevoandoihaccon 21-29
FEI SYS
os Soc o.dbo CeO Mao Ee Cae rice eH
ORI OPRORA Oe ta 21-50
OPERATION ORFAN:SYSIEMBrrarcctrdaieeic
ccc kaart ric oe nae ers eros 21-64
BOMpIe-D
UCT OVSTEMin
user car) rcs cram tiheis Cieee estas Pacer
erer ene 21-64
REM CATOVSteMirae k me eostam eransisae ie cyto Cuearisshe nsoekeaale Mae Eton ae 21-68
Ruimany-Air/ Secondary-Water Systeme.
as.scl. nec
+014 eee aucune 21-69
REN AIH BY PASStoV Stel ems eystaeacvemi catia wae eadlenetel tore crcden rel soon 21-70
BOWIENico ELEEGIILON varteceeesysnerauctevesc¥encye
cielopsielsurserosuscen veretenereaoue teeras 21-73
BRINScat vailspcdofeeGahan veheraSica e wiel Daeear gpQUEM
Ee BIS.IIE atten etelevesials 21-74
BEUINDECH
TLE Sale veysnayetereimeatsis eeeosteo ayar eeraicArehe- susp arey Seal ooorm ue,© ehese ees euagoues TOS 21-77
JAN? WEIGH
628 age ae soe ntsOne a cheno IenS Rete een Dae Re Re Ree
TS 21-77
‘CONS. SGA ey ES ere ree ee PRN
A RPh
a Po ok ei ee ar
RC
21-83
SSravanaltlOMG UlPIVEN toys, cwsyeycnecya areicteseroneyeretavaty
Huereictalsy yale evererera eee met 21-94
RENIN Sectepey=tayaye eyedcccys.aristysuns) avessnava1v7 ave ovas\apetovatalexa abedede Pats aiaaes eassaa haves 21-94
ROOD ENEIN SANTLOINbaeresrceeys erescsr) apsits rede vsvearesey «awa eancakes olSeonetoverer eres ERS 21-94
BSUIFAC COSMIC
NA CUM Cisex cyses searsyavsnsiaysl'avses/atehove
siMeta aiaters Siarstore Araloererea ames 21-96
BENSUH INO MUene eee crea
Ne eta alcretekoeaysrel=sal stavarsyieies panel rorakerateketave yore eee 21-96
CHAPTER 22 - MECHANICAL
DRAFT
SSI
IINCI DLE tenets te ce Menceexe) stares cccekevasuetcisen aahcataneimseussetoce erofouscouesegeyae 22-1
BECOME OM IDUSTIOM rare ete esis cect a revsiras als onselfen bosayeuedenena, eyouolendenc eevee rusliens 22-2
(Ni? SC Ee eo MECN MIST
s tne sonacncopapucosnboapconoaooeon
roo 22-6
ENOSSBINT ECOG Sean Seid ee Oe 2 Ole We EAD DO IA OLBece READ EO RCO Ree CRAPO 22-7
“TOCKWAS CECI MISO > haw como bonaosoe sannccas 0 Ono DAO O ATO Ie 22-8
Bea HOSSESIM IN CHEXIT GASES matte tt ctoiel ceed ete teledetctoceds ieps 'er-tevcver steve Paley 22-12
Dew Font of theiproducts Of COMPUSHO Merrett
ee aierolererese) veleree erento 22-12
VSI CRIQUATRINAIERS o eons ocude Onno OMed Gouda ree GAOMeaO unmet os pGDten 22-12
IACKETECLAG NACUalLDlaltirtiveeiterstle
irate cheeterno ntaleevterer 22-15
BYAlaMOSSCSi Epa tence TEs rake ols
ne HAUN cone rorenoxadersPavoverecapiiverelaedeuedetaate 22-17
SCSI ITC MMipa capes acheteasecFra Festeh saswalKe Meeont ICRTealonsu netsleveraetgbe) scsivevoielsn tenet yee 22-20
(OQORG)
Goddetnadoeeases
Snobs SoaopanUosonDodooneesaDE ohaeRsoos dens 22-22
CHAPTER 23 - LOCAL EXHAUST
TESTU
see oanc ca hnoo oo dos bo ooetlnt o ideo cleianehe a aiaoeo ager 23-1
BIOOCID GSIGilieanaeear ietslsteredtetere kee eerara cette tors olsfelotoleusinleetereteestolaseranere:
areca) 23-8
MGIC DESICHY a5 55 002.c0u 000 ROAD EA Oe Deb h ROD Ato momTaGae Uomoe soit 3 23-10
NOSAGD So gane thea 6 peUscsma rodeo ROD SUAOD BO UBD DOD OUMe Dyer Samira 23-11
CHAPTER 24 - CONVEYING
LSS MAMNO
ES wecuns soos bosououdcuoUnooDnonararracodctoms
ood OoK 24-2
xiv
FAN ENGINEERING — BUFFALO
FORGE COMPANY
PART Ill - FAN APPLICATIONS (Cont'd)
MENTHEIIECEIClinotS cine oonacenceneunomasouumocunsdicqomdacnennaadages 24-5
Byeksforal WelleteleCe oc cor oc nentun conocccnmmbont
scupccenDm Scone eBomooL 24-6
PRESSUTEIEOSSSSy caver tie arcs seteactre eictle,sheleaa rauWena eeeattee etrecmie eget Mie oteliolere 24-7
FANN AMEINOC? Gono acoerepoan uounOedco Re Ge ont ono noo beer Rees. 24-12
SNWAGIM DESI chaccdenaarcop tdbaqpehanonepersaeoaoosbaddoesaee ge Ue 24-15
ARiWic leach SWACHIS caso nadtiopsnnoddonEe
meacuonuccacooanedat oe 24-15
CHAPTER 25 - AIR-COOLED
HEAT EXCHANGERS
BY
HAMCUNES anasocannooubncoonouccmmoncrcan
acy bohob and Guar Gao 25-1
EoolingsRonds-and:SprayiROndS censarte ie acetic crsrertertere eer
25-3
(Cone MOM eGisndcaccagnuecnocten
se aeonoon Gob ocoos GnoDUDomD Ero dcd 25-3
CoolingalowenmFansrama) RuinpSar eyes eats tertetonctcteaeesirtot talae eralteeter re 25-5
ANTIANNia SINC TS aenct choir she.teupaver stan ueltots oat etna ee Taree oyretaes Careers mercer 25-10
PNP AMES
TERE EINO TU oSeanacesandanonsab
dom pebeacon soos eUuotdoE 25-12
DryZAle COGIERS ccad fponctaleteetoncs ses ah aa oiauacn awl vara sie) speed crete eersverevene 25-12
Div-AinCoolemransramdl PRunnoSmenencnscra
cence eats one teenie targemeee cet 25-20
Evaporative! CoolenSanq.wcpe.aecrcrccsita
aya deka neta a ekitel oniene Monk Meine Merionsceamene 25-24
Evaporative-GoolenFans amd RUmpsSieacrsacite
cere crtanerstatahanetdterstnn-oePerstemerers 25-25
CONGDSMS
SKS as goretev aleehence ete ev uate an rallondlMetarea na taeaeat ee Mapa cecteeateesto inane 25-25
CHAPTER 26 - DRYING AND RELATED PROCESSES
DESIQGMIPRINCIDIESyio
cries cierto. ckeects care actrees ars)crel deere
ao 26-1
MoistureContentiofi MatenialS@iven..tacceeroicicr
otu.cieit dette elie tor reer 26-4
BDTV. UGNGURR GCS gaya ste ister, Ststoyoes aacdvncnn cnenretea de aitze(a tase topSE ertepeeke eS 26-5
Psychrometric/Aspectsiof Dryingiwithy Alle soccer)
clo ee renner elec 26-7
FeatiNeededifionDViiNG crtseeccrctctrs oken hetero sickest xsl
ae cc orc Ree 26-9
AinNeededtomDirect Diviimgmecncsie
oie dene eon cie cee eee
eee 26-10
DirectiDrying WithtStealn: c< sacs. o some eisceenen ieaicie eerste ae earnerrene ore26-11
INGIFECHD YING iesctesec cme
iocmaresta crarercio eve cia sureyarene cre aerate 26-12
Evaporators: Single- and Multiple-Effect ..............
00. ccece eee 26-13
SHrAllave Cxotawitere Kel DUNIETAS: ceac ons Geonames BO AOMA: Soe be ooentrateotadas 26-13
EQUIDIDGMtrcgerneromic
crs aan tenaeere ven eacatcice terete eet rae tie igo eee ren eee 26-13
CHAPTER
27 - AIR BLAST AND OTHER PNEUMATIC
DEVICES
Aire Blast (Cooling) casas sist toysteues cosets ore oe en
oe eT
ee
27-1
All BlaStiDiving eecscorey caystazeusts visa Sie caapa mwerstartene a tesic aerornGle o
27-6
Alt-Blastand|VacuvinnGleaninguacacermeceirsiao
eee een teeta 27-6
Xitel GULANINS inceessrsuiserurens cate seat tacoe
ree ae RRR
eee
27-7
PGB ORES geso wvacsrsdoveet arsine (trubic each hetReese AGI
Rae RIT eosSST EES
27-8
ARES UDP Olitartare hictaycstsbs hc eeetecehor en cukede escactee T
e
27-9
Air-Blast and Sharp Freezing (and Cold Storage) ..............-.e0
eee 27-10
CHAPTER 28 - HANDLING
HOT AND CORROSIVE
GASES
Gas Absorpionticcaiconen
cc ener One ore
rE
ee
S Pray COOLING We we verter cece aoe Ricans er eee at
DilUtiomeCooliing ie sccccusc acetates chen merinc et ets Orie fo eet
Hleat-Resistant Matenialsamiraie
meri
ati eer aera ee arr
Corrosion-ResistantMaterialsmenmasricceierete
eee
eee
Erosion-Resistant Construction
28-1
28-1
28-4
28-5
28-6
OUTLINE OF CONTENTS
XV
ons
PART Ill - FAN APPLICATIONS (Cont'd)
Spark
ResistanuGonstnuctOnpeeasnne mieten
ta santa
ee
JU AURID] Dkk renter brarcavcdearsinreranremner asm
CHAPTER
ranirn tah
28-10
sient RN eae pe ate bt oka
28-11
29 - AIR CLEANING
GENERAL TREATMENT OF AEROSOLS AND GAS MIXTURES
......... 29-7
SEPAnall
Olliene ters eew wu yee rane Re ho amc ycto eens al nan eifcrsd ce eite 29-7
NELCMUOMS
cape omte mei se omar earie taconite eee rh tee coreeerti ciate oieeres 29-8
Rarticle;Congitioningeenres
ssn sneer ese
ie atone Tans ae causterenne 29-9
ANR- CLEANING EQUIPMENT EORTAEROSOLES
5254... css
ee ee 29-10
MechamicaliCollectonsuancdaenaccsecerce
core tacit eascimertane ee 29-11
DrvalnentialiCollectorSuuancnaccicceclmuct
reaere ome rece enc eee tee eee 29-12
Senubbersi(VWetranticie: Collectors) ian merece eee en cr29-17
PAIYNNEISINENS cevaromiave srveve: srsirs gael dae agt Aamo ence ey: Esnaky aren eA nmioio tee 29-24
Electrostatic Precipitatons a> sceaacese a ene hie ee
ema over Baeeornes 29-26
Low-Voltage, Two-Stage Electrostatic PrecipitatorS................0055 29-26
High-Voltage, Single-Stage Electrostatic Precipitators ................ 29-28
J
NTGS II eRe reears eats SASS eo
aRORMCR ns RD
IR SRN AR ay ae NO on PRED IeUE 29-30
Nentilation=AimFiltets tancac cence ears see eran coe aes tn sere eee ayees 29-30
AD SOUUTESE MtenS sceccpeete we,Beene ces Ne aes es eRe ao apy esc as oie et cee
29-32
Cleanable-ClotinindustataliRiltenss wasrsasruse fy ssc
cee acetic 29-32
AIR-CLEANING
GasAbsorbers
EQUIPMENT FOR GASES AND VAPORS.............. 29-34
cece:
eh Pee ee ee Beas ees tare has) Laser eh29-35
OGdOWAASONDETS crac ne eee
me
a eee
lapse sce eave Canela aLries emer erereuo as 29-39
Wanorm NGS onbenSiencyrecrcve create coecerorucr seine mare eter octets mest aPetaY eR 29-41
Gas nGimerat
Ons aeccecitaremeecns
ee eeeee easesnee kese sisee oie eater Acta R TS 29-42
SELECTIONIOFIEOUIPRMENTi marca cece aac scence
cbnrarise rian 29-44
Degreeiof Cleaning Requiredte
crm ac cttaccsctei entero toenees ine cteterete)rare state 29-44
Methods of Handling Collected Material...............
0.0 eee eee eee ee 29-45
PART !IV - APPENDICES
APPENDIX A UNITS, DIMENSIONS, AND DIMENSIONLESS
NUMBERS
(UMTS
eden Rasen Pe ad SEO AG GRITS cre A CURA Senn A rene temrS Oo A-1
DIT
SLOMS ter ckeveiee aecorersiarsin uate scat icy eneonayerciecerceatsur sivteceeranesonerere ateA-3
DimensionlessiNumpbersume
centr curcoraceie cei eracrh siete ce cerrerseslone enoepaee: sons A-3
APPENDIX
B - NOMENCLATURE
RONG MSM
ao noc soocnage conse Re Coe ounGnOda BoD Suo bo GomUgUn OO B-1
GreeksSvimbolSimmanticn
reise te terre aiaramrescier ctor erstrister-aaeistaretennns B-7
Abbreviations tor Unitsiof Measurement: arm. ..ect yc
ee ieccracldoe
eon 5 B-9
APPENDIX
C - CONVERSION
FACTORS AND EQUIVALENTS
U.S. Customary, SI, and other metric conversion factors ............... C-1
Temperature Level Equivalentsinnrtcnkccwrackurscrere
yates GOmen) arel ere eet tas: C-18
DecimaliGquivalemts ene seein
cae crete eae ste tetas aver cicisrereieiBiee C-19
APPENDIX D - PROPERTIES OF MATERIALS
(ElPe GAYSLANSSe Cen Pies@uthB 1SGRESe CRO
TN OAS
OOOO
PD RCI IOI Chemie CRO RoR
oD erin
Ca
xvi
FAN ENGINEERING
— BUFFALO FORGE COMPANY
PART IV - APPENDICES
(Cont'd)
Saturated! Steam: sca vas otra ecstacy ete weer
ee oe
renee D-3
(GASCS ote ths es Cede aoa oes coors wage ensue eae gdcea ear naticrceoe) co
Reve hee aaa eee ae D-4
BIYo
[UiTooysomes Siac
acres reek een
RSE enn
Sn Me ICID Doon are Tracey ohne teeD-5
ESY0)
|fokag cee It ae
onnep UNISON Se Aa Cd born hin Tate, oeieriin GAMER oe D-6
Metal svandvAlloysrrrarects
cenerciysten acai ae Nelayarcie rareienatctars ettered ode settee rare D-8
APPENDIX E - METAL PRODUCT
INFORMATION
Sheet Metal and Wire Gages and Weights.................--22000000-
E-2
WeightsofiSteel icr< ccc begs carey eure iou ranphsys crappees tira:aptebeioteraes witleer spared wean E-4
SteeliBeamiand/ ChanmeliDatanscsasceacc
nes cee oem aiteraens rer esr
E-5
Ripesand Pipe: Flange: Datars atrecrsc.cem eneceoia eratistecd cry orto sete oy rae aretevepen tec E-6
Wreitg htsiot iiuboting ce ieers occckays feaccavey sete evtraiyasy aravuptaca rerceretaust onsen sepa Stamey detente E-7
APPENDIX
F - MISCELLANEOUS
DATA
StandarciiwiSteDrilliSizeswyarcnrncsriccs
acne coe ee
ne
F-1
Areasiand/Circum#ferences of GircleSwans.
see cee oes cette
ee teres F-2
MathematicalliDatia>*
sani ate
betes eae e es ene Ome
oe ot aa eet ar F-4
Miscellaneous! Equationsien
an.
aioe heute
ra eel oh coe enor F-7
Miscellaneous Datars.
mertinte coer. cer atts an eeecere shROS
a eer
F-8
Programming: Data tren: a. sesso tapes ert cress cnvenerct cael cece areeasiest
F-9
ARPENDIX<G
SSOELEGIED
APPENDIX H - BUFFALO
PRO
DU Gl:Sccs
setae
AUTO
RBINDEXRGs
BIBEIOGRAREIN
===
FORGE COMPANY
ee ere trae ae ern eee
os nest ca
cree eveew ne
cee
ees
ee
G-1
ee H-1
tera eee ee \-1
Parte
Fundamentals
£
ye
;
j at)
a
(eeveeymid 13
a
Chapter |
Properties of Air and Other Gases
The thermodynamic and transport properties of gases and vapors are
important in fan engineering. This chapter deals with the thermodynamic properties, especially pressure, temperature, humidity, density,
and enthalpy. Transport properties, such as viscosity, thermal conduc-
tivity, and diffusivity, are dealt with in subsequent chapters. The
gaseous materials most frequently encountered in fan engineering are
air and water vapor; accordingly, most of the data are for these substances. Some formulae have been written specifically for these
materials, but most are generalized to accommodate any gas.
Atmospheric Air
Atmospheric air is a mixture ofdry air, water vapor, and impurities.
Dry air is a mechanical mixture of gases, whose principal constituents
are listed in Table 1.1. (The table values may be considered representa-
tive of the composition of normal outdoor air throughout the troposphere.) The amount of water vapor in atmospheric air will depend on
weather conditions. The nature and amount of impurities in the
atmosphere depend on the forces at work in producing and dispersing contaminants. Industrial, urban, rural, seaside, and other areas
have characteristic atmospheres due to differences in impurities.
Table 1.1
Normal Composition of Dry Outdoor Air
Component
Volume Fraction
Mass Fraction
Nitrogen
Oxygen
Argon
0.7809
0.2095
0.0093
07553
0.2315
0.0128
Carbon Dioxide
0.0003
0.0004
Adapted from the data of J.A. Goff: “Standardization of Thermodynamic Properties of Moist Air,”
Trans. ASHVE, vol. 55, 1949, pp. 462-464.
The reference for Table I.1 lists neon, helium, krypton, hydrogen,
xenon, ozone, and radon, totalling less than 0. 0025 percent by volume,
as the residual part of atmospheric air. ASH RAE' also lists methane,
"ASH RAE Brochure on Psychrometry, ASHRAE,
New York, 1977, p. 3.
1-2
FAN ENGINEERING — BUFFALO FORGE COMPANY
eT
nitrous oxide, sulfur dioxide, nitrogen dioxide, ammonia, carbon
monoxide, and iodine, totalling 0.0003 percent by volume, as constituents of normal, clean, dry atmospheric air. ASHRAE considers all
these gases in the calculation of the apparent molecular weight of
clean, dry atmospheric air and obtains a value of 28.9645. Rounding
off and lumping the residuals with the nitrogen, as has been done in
Table 1.1, yields an apparent molecular weight of 28.964. (See the
section on molecular weight.)
Standard Atmosphere
In 1952, the National Advisory Committee for Aeronautics adopted
the International Civil Aviation Organization’s Standard Atmosphere.
Portions of this Standard are given in Table 1.2. (The reference contains much more extensive data in both U.S. and metric units.) Tem-
peratures
¢ are
based
on
15°C
at sea level and
a lapse rate of
0.0065°C/m throughout the troposphere, and they are assumed to be
constant throughout the stratosphere. The tropopause is considered to
be at the level where the temperature becomes —56.50°C. Pressures p
are based on 101.325 kPa at sea level, a gas constant of 287.04 J/kg-K,
and the perfect gas laws. Densities p are based on the temperature and
pressure at the altitude Z and the perfect gas laws. Absolute viscosities
wu, kinematic viscosities vy, and speeds of sound c are based on relatiohships that will be explained in later sections dealing with these
subjects.
Table 1.2
Standard Atmospheric Data vs. Altitude
Ibm/ft3
est
oe
ees
=UWUDMD
WOW
WOOO
MHD
—$
TW
WON
NOW
CDP
WW
OPHPW
WOON
MIOMD
ieee
a
ane
ee
6S
OOOO
=H
CO00
==
o---—
OOOO
wonwwwn
momo
COCO
CO
os
SI
Ct
STOIC)
Y--—O
PRWW
OOO
SY
CHAPTER
Table 1.2
1 — PROPERTIES OF AIR AND OTHER GASES
1-3
Standard Atmospheric Data vs. Altitude (Concluded)
ft
Ae
8 500
9 000
9 500
ieee
28.7
12 000
13 000
14 000
15 000
20 000
25 000
30 000
35 000
40 000
45 000
50 000
55 000
60 000
Ibm /ft?
;
f
8.29
7.58
6.89
3.75
1.10
8.89
7.04
5.54
4.35
3.42
2.69
2.12
1.67
uX 10°
vy X 10°
fa
lbm/ft-s
ft?/s
ft/s
8
5
2
8
1
5
8
1
4
9
4
97
1.940
1.965
1.990
2.015
2.067
2.121
Zalge
2.234
2.294
2.624
3.016
3.486
4.053
5.059
6.434
8.181
10.404
13.230
16.824
1083.8
1081.8
1079.8
1077.8
1073.8
1069.8
1065.8
1061.8
1057.7
1037.3
1016.4
Cas
973.3
968.5
968.5
968.5
968.5
968.5
:
Adapted from the data of NACA: “Standard Atmosphere — Tables and Data for Altitudes to 65,800
Feet,” Report 1235, U.S. Government Printing Office, Washington, D.C., 1955, pp. 66-81.
Standard Air
In fan engineering, standard air is considered to be air with a density
of 1.2 kg/m’ when SI units are employed, or 0.075 lbm/ft* when U.S.
customary units are used. These two values are not exact equivalents,
but they are close enough for most fan engineering purposes. Neither
do these values exactly correspond to the sea level value given for the
Aeronautical Standard in Table 1.2. Atmospheric air of the composition shown in Table 1.1 will have standard density at various combinations of pressure, temperature, and humidity. Two convenient
combinations are shown in Table |.3, one for dry air and another for
moist air. Note that all the combinations listed in Table 1.3 utilize the
standard barometric pressure at sea level.
The concept of standard air is useful in rating fans, ducts, and other
air handling equipment. Often both duct losses and fan capabilities can
be determined from standard air data and used without correction.
Even when the actual density is considerably different from standard
air density, it is frequently more convenient to apply corrections to
standard air data than it would be to publish separate data for each
condition.
A slightly different concept, that of standard temperature and pressure (STP), is sometimes employed in specifications. In fan engineering, the most logical combinations are those given in Table 1.3.
1-4
FAN ENGINEERING
— BUFFALO FORGE COMPANY
ee
However, other combinations are used in other fields of engineering, so
values for standard temperature and pressure should bespecified. If
the gas is not air, the standard gas also should be specified.
Table 1.3.
Property
Standard Air
U.S.
Sl
Pressure
Temperature
Humidity
29.921 in. Hg
70°F (529.7°R)
0%
101.325 kPa
21°C (294.2 K)
0%
Density
0.075 Ibm/ft?
1.2 kg/m
29.921 in. Hg
68°F (527.7°R)
50%
0.075 Ibm /ft?
101.325 kPa
20°C (293.2 K)
50%
1.2 kg/m
Dry Air
Moist Air
Pressure
Temperature
Humidity
Density
Molecular Weight
The molecular weight of a pure substance is the sum of the atomic
weights of the atoms ina molecule of that substance. Water, for instance,
has a molecular weight of 18.015 based on two atoms of hydrogen at
1.008 each and one atom of oxygen at 15.999, all on the carbon-12
scale. Because air is a mechanical mixture of gases, it does not have a
true molecular weight. Dry air of the composition shown in Table 1.1
has an apparent molecular weight of 28.964. The apparent molecular
weight M of any mixture of gases can be calculated either from a
volumetric analysis using
3 (Me fy)
n
Mis
=
-
dX fk
so
or from
a mass
analysis
|
(1.1)
using
M=
yf
Sy
» (fr/Mx)
Poy
where f: is the volume
molecular
weight
constituents,
or mass
fraction
of constituent
x; and
(1.2)
of constituent x: M;, is the
n is the total number
of
CHAPTER 1 — PROPERTIES
=e
OF AIR AND OTHER GASES
eee
1-5
_ Examples |.1 and 1.2 illustrate the use of these equations in calculating the apparent molecular weight of dry outdoor air of the composition shown in Table 1.1.
Example 1.1
Apparent Molecular Weight of Dry Air from Volumetric Analysis
Component
Wes
Nitrogen
0.7809
x
28.013
=
21.875
Oxygen
Argon
Carbon Dioxide
0.2095
0.0093
0.0003
x
x
x
B1R999
39.948
44.010
=
=
=
6.704
0.372
0.013
X(Mxfr)
= — 28.964
Me ee O04
eee
Xfe=
Mx
1.0000
Pe
Apparent Molecular Weight =
1.0000
M,fy
~ 28.964
Example 1.2
Apparent Molecular Weight of Dry Air from Mass Analysis
Component
Ix
Nitrogen
Oxygen
Argon
0.7553
0.2315
0.0128
=
=
ae
28.013
31.999
39.948
=
=
=
0.026 962
0.007 235
0.000 320
0.0004
a
44.010
=
0.000 009
1.0000
X(fx/Mx)
=
eee
OOOO
Apparent Molecular Weight = 0.034526
28.964
0.034 526
Carbon Dioxide
M,
S| My
Yf=
Differences in molecular weights for the same substance usually can
be traced to either rounding off or to differences between the carbon-12
and the oxygen-16 scales. ASHRAE' lists molecular weights on the
carbon-12 scale as 28.9645 for dry air and 18.015 34 for water. The
previously used value of 28.966 for dry air was based on the oxygen-16
scale. Throughout the remainder of this handbook, a value of 28.965
will be used as the apparent molecular weight of dry air.
A mole, abbreviated mol, is the base unit of substance in SI. As such,
it is further defined as the amount of substance that contains as many
elementary entities as there are atoms in 12 grams of carbon-12. In fan
engineering, the elementary entities of interest are molecules, and the
usual units of mass are the kg or the lbm. One kg-mol of air will have a
mass of 28.965 kg. One lbm-mol of air will have a mass of 28.965 lbm.
"ASHRAE
Brochure on Psychrometry, ASHRAE,
New York, 1977, p. 4.
1-6
FAN ENGINEERING — BUFFALO FORGE COMPANY
eee
ee
The unit of molecular weight is the kg/kg-mol in the first case, and the
lbm/Ibm-mol in the second case. The number of molecules ina kg-mol
of any gas is 6.022 52 X 10°°. There are 2.731 77 X 10° molecules ina
lbm-mol of gas. The volume occupied by a mole of gas will depend on
the unit of the mole and on the temperature and pressure. For a gas
constituent, the mole fraction, volume fraction, and pressure fraction
are equal.
Perfect Gas Equation of State
Boyles’ and Charles’ laws' can be combined to give an equation of
state. For perfect gases,”
BS
eR D
Ce
(1.3)
where absolute pressure p, specific volume v, gas constant R, absolute
temperature 7; and conversion factor Cp can be expressed in any
consistent units. Several such sets of units are listed in Table 1.4.
Table 1.4
Units and Values for Equation 1.3
p
v
Pa
kPa
m3/kg
m3/kg
J/kg°K
J/kg°K
1.0
1000 Pa/kPa
Cp
Ib /ft?
in. Hg
in. wg
mm Hg
ft3/Ibm
ft3/Ibm
ft3/lbm
m3/kg
ft-lb/Ibm-°R
ft-lb/Ibm-°R
ft-lb/Ibm-°R
J/kg°K
1.0
70.73 Ib/ft?*in. Hg
5.193 Ib/ft?-in. wg
133.32 Pa/mm Hg
mm wg
m3/kg
J/kg-K
9.790 Pa/mm wg
Absolute pressure p is the barometric pressure py» in free air or the
sum of the barometric pressure and the gage pressure p, for a confined
quantity of air or gas. When all pressures are measured in the same
units,
72) =
1
’
,
Pp
+
c
Dz.
7
(1.4)
.
.
.
Boyles’ and Charles’ laws state that the volume of a perfect gas varies inversely with absolute pressure and directly with absolute temperature.
“The equation of state for real gases can be expressed as:
Pv = RT (1 + Bp + Gp + Dp +...)
where the empirical coefficients (B), C), Dp...) are temperature-dependent and are called
the second, third, fourth, .. . virial coefficients, Another expression of the equation of state for
real gases is:
PpX= ZRT
;
where the compressibility factor Z is dependent upon both pressure and temperature,
CHAPTER 1 — PROPERTIES OF AIR AND OTHER GASES
aA]
ESSE
When
1-7
mixed units are used,
D.— Cy ps + Cz De
(GES)
where conversion factors C; and C, are those given in Table 1.5 for the
combinations listed.
Table
1.5
Units and Values for Equation 1.5
Pp
Ch
Cy
kPa
kPa
0.133 32
3.3864
1.0
13.619
0.009 790
0.248 66
0.073 43
1.0
Absolute temperature 7 is the sum ofthe conventional temperature
measurement /¢ and the appropriate zero adjustment A according to
Table 1.6.
T=t+A
Table 1.6
(1.6)
Units and Values for Equation 1.6
K (kelvins)
°R (degrees Rankine)
For perfect gases,
“M
(1.7)
where the gas constant R for a particular gas and the universal gas constant R, can be expressed in any consistent units. If the molecular
weight M is based on the carbon-12 scale, the value of the universal gas
constant R, is 8314.3 J/kg-mol-K in SI units or 1545.32 ft-lb/lbmmol-°R in U.S. customary units. Based on Equation 1.7, the gas constant for dry air is 287.05 J/kg-K or 53.35 ft-lb/Ibm°°R.
There are no perfect gases; but air, other real gases, and even water
vapor can be considered to behave according to the perfect gas laws in
most fan engineering applications. Deviations from perfect gas law
behavior increase as a gas or vapor approaches the liquid state. The
water vapor in atmospheric air has such a low partial pressure that it
can safely be assumed to be a perfect gas even when near saturation.
However, deviations should be calculated for higher pressures.
The equation of state can be used to compute any one ofthe variables
p, v, R, or
T when
the other three are known.
Numerous
formulae
BUFFALO FORGE COMPANY
— ING
FAN ENGINEER
1-8
es
based on this equation are given in the sections on humidity and
density. A typical fan engineering application is given below.
Example 1.3.
Volume Flow Rate from Mass Flow Rate
Given 45 359 kg/hr, 27.41 kg/kg-mol, 176.7°C, 98.78 kPa barometric
pressure,
and —4.97
kPa
gage
pressure,
find the volume
flow rate
in m/s.
Using Equations 1.4, 1.6, 1.7, and 1.3 with SI units:
Di Piet Pe — 9 82184 97 — 938
KPa,
IP = tie YB? = Wiel == AUS = CLO
ReDre
_
aes ce
a
ek
RT _ 303.33 X 449.9 =
aC he 9i81< 1000" mis
- 45359
3
eee
O = mv = 12.60 X 1.455 = 18.33 m’/s.
Given 100 000 lbm/hr, 27.41 lbm/Ibm-mol, 350° F, 29.17 in. Hg barometric pressure, and —20 in. wg gage pressure, find the volume flow
rate in cfm.
Using Equations 1.5, 1.6, 1.7, and 1.3 with U.S. units:
P = po + 0.07343 pg = 29.17 + 0.07343(—20) = 27.70 in. Hg,
T=1t + 459.7 = 350 + 459.7 = 809.7°R,
=
R=
ae
JRYSSPe
M
RT _
PCp
=
>=
dees
5741
56.38 X 809.7
27.70 X 70.73
m= 400 j00 =
==
.
“8
= 56.38 ft-lb/lbm-°R,
= 23.30 ft*/Ibm,
1666.7 lbm/ min, and
O = mv = 1666.7 X 23.30 = 38 834 cfm.
Specific Gravity
Since air is the gas most frequently involved in fan engineering, it is
convenient to base equations and data on the properties ofair. One of
the properties of air that is used as a common reference is its density.
CHAPTER 1 — PROPERTIES OF AIR AND OTHER GASES
1-9
640
a Wwon
[op)w oO
lop)NRon
0
RELATIVE
OF
DENSITY
VAPOR
WATER
REFERRED
AIR
DRY
TO
(w)
Figure
50
1.1
100
150
200
TEMPERATURE — °F
250
300
350
Relative Densities of Water Vapor Referred to Air
The ratio of the density of any dry gas to the density of dry air at the
same temperature and pressure is called the specific gravity G of the
gas. For perfect gases, specific gravity can be obtained by dividing the
molecular weight M of the dry gas by 28.965, the molecular weight of
dry air, as follows:
‘
ae
M
28.965 ©
(1.8)
For a sample calculation illustrating the use of Equation 1.8, refer to
Example 1.5.
The ratio w of the density of water vapor to the density of dry air
is not constant for any temperature but a function of relative humidity
gy, as illustrated in Figure 1.1. The ratio of the molecular weights
(18.015/28.965) would indicate that w is equal to 0.622, a value that is
suitable for most fan engineering purposes.
For high pressures and
temperatures, Figure I.! should be used: The following formula, which
is accurate to 0.1% in the range of temperatures from 32°F to 400° F,
can also be used:
Gan
w =
0.6214
aie
+ ar VEU
(1.9)
1-10
FAN ENGINEERING — BUFFALO FORGE COMPANY
nn
ee EEE
The vapor pressure of pure water ps can be determined from Table 1.7
opposite the dry-bulb temperature ¢ of the gas. For sample calculations
illustrating the use of the ratio w, refer to Examples 1.5 and 1.6.
Dry-Bulb, Wet-Bulb, and Dew-Point Temperatures
Unless otherwise specified, the temperature of any gas is that temperature which is indicated by any ordinary dry-bulb thermometer.
This dry-bulb temperature / is the temperature of each constituent,
including the dry gases and any water vapor.
A wet-bulb temperature /’ is measured by submerging a water-covered bulb in a moving stream of gas until equilibrium is obtained. The
wet-bulb temperature will be lower than the dry-bulb temperature as
long as evaporation continues.
Wet-bulb depression (t — 1’) is the difference between dry-bulb and
wet-bulb temperatures for a particular state point. The maximum
depression for a given dry-bulb temperature will occur when the gas
is dry. Zero depression will be observed at saturation.
The temperature of adiabatic saturation ¢* of an air-water vapor
mixture is the temperature that a gas-vapor mixture would attain ina
perfect “saturator,” with no loss or gain of heat to the surroundings.
A wet-bulb thermometer, unshielded from radiation, will register a
temperature approximating that of adiabatic saturation of air and
water vapor, if the velocity of air past the bulb is between 500 and 1000
fpm or 2.5 and 5.0 m/s. Appreciable deviations between /’ and /* occur
with gas-vapor mixtures other than air-water vapor. The defining relationship for the temperature of adiabatic saturation is
h+ ht(W* — W) = he®
(1.10)
Enthalpy 4 and humidity ratio W are defined in subsequent sections.
For moist air having a dry-bulb temperature ¢, a humidity ratio W, and
an enthalpy / that corresponds to ¢ and W, the temperature of adiabatic saturation /* is the temperature corresponding to the saturation
properties h*, h*, and W,*. Refer to Example 1.8 for sample calculations using this relationship. (Thermodynamic wet-bulb is another
name for the temperature of adiabatic saturation.)
The dew-point temperature ¢” of a gas-water vapor mixture is the
saturation temperature corresponding to the humidity ratio of that
mixture. (Refer to Equation 1.25 for details.) It is also the temperature
at which condensation begins when the mixture is gradually cooled.
The presence of certain acid-forming gases will considerably raise the
dew-point temperature for moist air. See the chapter on mechanical
draft for a discussion of this phenomenon.
Partial Pressure, Saturation, and Vapor Pressure
The Gibbs-Dalton rule! for perfect gases can be applied to most of
The Gibbs-Dalton rule states that each component of agas mixture exerts a pressure that is determined by the volume and temperature of the mixture regardless of the other components involved.
CHAPTER 1 — PROPERTIES OF AIR AND OTHER GASES
Table 1.7
1-11
Saturation Vapor Pressures p,,;
of Ice’ and Water2
In in. Hg
86.63
89.51
92.45 |93.96 |95.49 |97.03 |98.61
280/ 100.2} 101.8} 103.4 |105.0}
106
10.1} 111.8) 113.6} 115.4
290/117.2| 119.0) 120.8 |122.7}
124.6] 126.5 |128.4] 130.4 | 132.4 |134.4
300] 136.4] 138.5) 140.6 |142.7]
144.8] 147.0} 149.2) 151.4] 153.6 |155.9
310} 158.2} 160.5) 162.8 |165.2
170.0) 172.5) 175.0) 177.5 | 180.0
320] 182.6] 185.2} 187.8] 190.4]
193.1] 195.8 |198.5} 201.3 |204.1 |206.9
330| 209.8] 212.7) 215.6 |218.6]
221.6] 224.6 |227.7) 230.8 |233.9 |237.1
340] 240.3} 243.5) 246.8 |250.1]
253.4] 256.7 |260.1) 263.6 |267.1 |270.6
350) 274.1] 277.7] 281.3 |284.9} 288.6} 292.3} 296.1 |299.9 |303.8 |307.7
360] 311.6} 315.5] 319.5 |323.5] 327.6} 331.7 |335.9) 340.1 |344.4 |348.7
370| 353.0} 357.4) 361.8 |366.2] 370.7 |375.2 |379.8] 384.4 |389.1 |393.8
380] 398.6 |403.4 |408.2 |413.1] 418.1 |423.1 |428.1} 433.1 |438.2 |44
390} 448.6 |453.9]
459.2 |464.6] 470.0) 475.5] 481.0) 486.6 |492.2) 497.9
400/ 503.6) 509.3] 515.1 |521.0}
526.9 |532.9 |538.9} 545.0} 551.1} 557.3
‘Adapted from data of the National Research Council: International Critical Tables, vol. 3,
McGraw-Hill Book Co., Inc., New York, 1928, p. 210.
Adapted from data of J.H. Keenan and FG. Keyes: Thermodynamic Properties of Steam, John
Wiley & Sons, Inc., New York, 1936. These data differ only slightly from the data of J.A. Goff and
S. Gratch: “Thermodynamic Properties of Moist Air,” Trans. ASHVE, vol. 51, 1945, pp. 125-164;
and from corrections thereto by J.A. Goff: “Saturation Pressure of Water on the New Kelvin
Temperature Scale,” Trans. ASH VE, vol. 63, 1957, pp. 347-354.
1-12
FAN ENGINEERING — BUFFALO FORGE COMPANY
a
——————e——————
eee
the gas mixtures encountered in fan engineering, including those with
water vapor as one constituent. Each constituent will exert a certain
pressure called its partial pressure, and the sum of these partial pressures must equal the absolute pressure of the mixture. The pressure
fraction will equal the mole fraction for each constituent; i.e. the
partial pressure of a constituent divided by the absolute pressure of
the mixture will equal the number of moles of the constituent divided
by the number of moles of the mixture.
Saturation is a condition of equilibrium between a liquid or solid and
its vapor. The pressure exerted by a vapor at saturation is called its
saturation vapor pressure or, in short, its saturation pressure. (When
the actual pressure exerted by a vapor is less than its saturation pressure, the vapor is said to be superheated. The temperature of a superheated vapor is higher than the temperature that would exist if that
vapor was at saturation at the actual pressure.) The saturation pressures of water vapor over water and ice are of particular concern
fan engineering. Table 1.7 lists values of saturation pressure versus
temperature. Below the freezing point, the saturation pressures over
sub-cooled water are generally higher than the saturation pressures
over ice. The table lists the latter. Saturation pressures pws’, over a limited range of wet-bulb temperatures t’, can also be determined
approximately from
Pus’ = Cy? + Cat’ + C;
Gls)
using Table 1.8. (The values in Table 1.8 are based on AMCA
210-74.'
Equations yielding greater accuracy over larger ranges can be found
in the ASHRAE
Table 1.7.)
Handbook,
Table 1.8
the Brochure,
or the references for
Units and Values for Equation 1.11
Joey
Range
Gi
(ee
&
Pa
4-32°C
O25
18.6
692
kPa
4-32°C
3.25 x 10%
1.86 x 10?
0.692
in. Hg
40-90°F
2.96 x 10°4
=1.59 x 102
0.41
The partial pressure of superheated water vapor in air py can be
determined approximately for atmospheric temperatures from
epee
Wi
WS
ptt — ¢)
C4
“Laboratory Methods of Testing Fans for Rating,” AMCA
51-75, 1975. pp. 12
&42.
AOIRAS Handbook and Product
p
“ASHRAE
CIS)
Standard 210-74, ASHRAE
Directory — 1977 Fundamentals,
Brochure on Psvchrometry,
New York,
1977, pp. 44-46.
ASHRAE,
Standard
New York, 1977,
CHAPTER 1 — PROPERTIES OF AIR AND OTHER GASES
1-13
or from a similar equation proposed by Carrier!
ae
Pw
Pws
(Pp — Pws'Mt — 0’)
a
awe Chl?
(ale 13)
using the saturation pressure pys’ at the wet-bulb temperature /’, the
absolute pressure p, the wet-bulb depression (1 — t’), and Table 1.9. For
sample calculations illustrating the use of Equations |. 11-1.13, refer to
Examples 1.6 and 1.8.
Table 1.9
Units and Values for Equations 1.12 and 1.13
Humidity
Humidity, in its general sense, is the presence of water vapor in the
air. The amount of water vapor that can be mixed with dry air (or any
gas) may vary from zero to a maximum that is dependent on temperature and pressure. The water vapor displaces an equal number of molecules of dry air, according to Avogadro’s hypothesis.” Thus, moist air
is not the result of adding water vapor to dry air but the result of substituting water vapor for some of the dry air.
The amount of water vapor in moist air or gas can be described in
various ways. ASHRAE, in its Handbook,’ has adopted certain terminology, which with few exceptions, is used here for the sake of uniformity. Previous editions of Fan Engineering used older terms and
definitions.
The relative humidity y of moist air or gas is the ratio of the partial
pressure of the water vapor p, to the saturation vapor pressure pys for
the same dry-bulb temperature:
eae
(1.14)
This is also equal to the ratio of the mole fraction of water vaporf, to
the mole fraction of water vapor that would exist at saturation
fi, for
'W.H. Carrier, “Rational Psychrometric Formulae,” Trans. ASME,
vol. 33, 1911, pp. 1309-1350.
*Avogadro’ $ hypothesis is that the number of gas molecules in any given volume at any given pressure
and temperature is a constant regardless of the gas or gases involved.
“ASHRAE Handbook and Product Directory - 1977 Fundamentals, ASHRAE,
p. 5.2.
New York, 1977,
1-14
FAN ENGINEERING — BUFFALO FORGE COMPANY
the same dry-bulb temperature:
fo
Hat
oes
(1.15)
The humidity ratio W of amoist gas is the ratio of the mass of water
vapor mw to the mass of dry gas Mz:
= Wiis
iii
(1.16)
The specific humidity H of a moist gas is the ratio of the mass of
water vapor m, to the total mass of the mixture my, + Me:
My
Piece ii
(1.17)
The absolute humidity p, of a moist gas is the ratio of the mass of
water vapor my to the total volume of the mixture Q:
ai
— Mw
Tata
(1.18)
This is also the partial density of the water vapor component.
The degree of saturation 6 of a moist gas is the ratio of the actual
humidity ratio W to the saturation humidity ratio Wat the same temperature and pressure:
oO =
W, °
(1.19)
Any consistent units can be employed in the above equations. Relative humidity y, humidity ratio W, specific humidity H, and degree of
saturation 6 are dimensionless parameters.
A number of important relationships can be derived from these equations together with a consideration of the perfect gas laws. The partial
pressure of the vapor py can be expressed in terms of the relative humidity gy and the saturation vapor pressure py, at the same dry-bulb
temperature. From Equation 1.12,
Pw = Pws?-
(1.20)
The humidity ratio W can be expressed in terms ofthe absolute pressure of the mixture p, the partial pressure of the vapor p,, the saturation vapor pressure Pws, the relative humidity y, the density of water
vapor relative to dry air w, and the specific gravity of the dry gas G:
WwW =
(P= P)G ~ (P= Puse)G
eae
=
cade
(1.21)
The specific humidity H can be determined from the same variables
listed preceding the equation for W:
CHAPTER 1 — PROPERTIES OF AIR AND OTHER GASES
a
PwW
Ee
(P — Ppw)G + pww
1-15
Pwspw
(Pp — Pwsp)G + puspw
(1.22)
The degree of saturation 6 can be expressed in terms of the actual
_ mass of water vapor m, and the mass of water vapor at saturation
Mwys (at the same temperature / and absolute pressure p):
= AU
Siege
(Gie28))
This is not quite the same as relative humidity y. The relationship between ¢ and 6 is expressed in
o=
2
Lease"
(
Pws
=
(1.24)
where p,.s is the saturation vapor pressure at the dry-bulb temperature
of the mixture, and p is the absolute pressure.
Substituting Equation 1.20 in Equation 1.21 yields
2G,
Pe
eG
(1.25)
This equation is the defining relationship for dew-point temperature 7”.
There will be only one value for the partial pressure p, for each combination of pressurep, humidity ratio W, specific gravity G, and density
ratio w, regardless of the dry-bulb temperature. The saturation temperature corresponding to p, is the dew-point temperature.
Density and Specific Volume
Density p is the ratio of the mass of a substance to its volume. Specific volume v is the reciprocal of density. Various general relationships
based on the perfect gas laws can be used to determine density. The
method or equation used will depend on what is known about the gas.
If the gas is dry and if its molecular weight M, absolute temperature
T, and absolute pressure p are known,
should
_
MTp
Cea
G6 Fa)
be used together with Table
(1.26)
1.10 to determine density p. By
using the apparent molecular weight, the densities of mixtures, including that of moist air, can be computed using Equation 1.26. However,
the presence of water yaper is specifically taken into account in
Equations 1.28 through 1.39.
The numerical values in Table !.10 are generally considered standard
values for the units chosen. Any other consistent units can be used with
appropriate values. The numerical values can be combined for con-
FAN ENGINEERING — BUFFALO FORGE COMPANY
1-16
en.
—
venience
m*:kPa/kg-mol-K
i.e., Copo/ To is 8.311
of calculation;
or
21.84 ft’-in. Hg/lbm-mol-° R
Table 1.10
p
M
kg/m
kg/kg-mol
Units and Values for Equation 1.26
Po
kg/m3
kg/kg-mol
Ibm/ft3 | Ibm/Ibm-mol
Ibm/ft? | Ibm/lbm-mol
Ibm/ft? | lbm/Ibm-mol
:
kg/m3
kg/m?
é
:
;
:
:
kg/kg-mol
kg/kg-mol
Copo/ To
;
101 300
8311
;
d
:
!
101.3
14.70
29.92
407.5
8.311
10.73
21.84
297.5
760.0
10 350
62.35
849.1
in.
in.
in.
:
:
If the gas is dry and if its specific gravity G, absolute temperature 7,
and absolute pressure p are known,
eee
Ramee
(1.27)
should be used together with Tables 1.10 and I.11 to calculate density p. The adjusted gas constant R, is for air and includes the conversion factor C from Equation 1.3.
Table 1.11
Units and Values for Equations 1.27 to 1.37
Giro
P, Py, & Pw
Wen
=
kg/m3
Pa
dimensionless
287.0
kg/m3
Ibm /ft3
Ibm /ft8
Ibm /ft3
kg/ms
kg/m3
kPa
lb/ft?
in. Hg
in. wg
mm Hg
mm wg
dimensionless
dimensionless
dimensionless
dimensionless
dimensionless
dimensionless
0.2870
53135
0.7543
10.27
2.153
Example 1.4
Density of Dry Gas
Given dry gas, 30.6 kg/kg-mol,
sity of the gas.
176.7°C, and 98.78 kPa, find the den-
Using Equation 1.26 with SI values:
=
Mp"
30:6
X 98.78
P = B311T ~ 8.311 X 449.9 — 9-808 kg/m’.
CHAPTER 1 — PROPERTIES OF AIR AND OTHER GASES
Given dry gas, 30.6 lbm/lbm-mol,
the density ofthe gas.
350°F, and
1-17
29.17 in. Hg, find
Using Equation 1.26 with U.S. values:
=
Mp
30.6 X 29.17
=
3)
® = F1.84T ~ 21.84 X 809.7 — 9-9905 lbm/ ft’.
Given dry gas, 1.0564 specific gravity, 350°F, and 29.17 in. Hg, find
the density of the gas.
Using Equation 1.27 with U.S. values:
:
ae 0564 eo
GP
2
P = 7543T ~ 0.7543 X 809.7 — 9:0505 Ibm/ ft’.
If the gas is moist and if its specific gravity G, absolute pressure p,
dry-bulb temperature /, and relative humidity ¢ are known,
o=
(Dia PisO)G te Picoy
IRed(le se Al)
(1.28)
should be used together with Table I.11 to calculate density p. The
partial densities of the dry gas pg and the water vapor py can also be
determined using
We Cages
—_
_
=
Pws
G
R(t + A)
(1.29)
Pwspw
Sieg eae ie
(1.30)
If the gas is moist and if its specific gravity G, absolute pressure p,
dry-bulb temperature /, and humidity ratio W are known,
ple We)
R(t + A)
Syme1,
WwND
(4+)
/
Ps
=
PT
zp:
and
<
Ww
Pw
~ PT + wy
(1.31)
(1.32)
(133)
should be used together with Table |.11 to calculate density p or partial
densities pg and py. If the specific humidity H is known rather than the
humidity ratio W,
1-18
FAN ENGINEERING — BUFFALO FORGE COMPANY
a
a=Ae,
Le
EEE
eee
R(t
+ A)
Posen
( G +H)
(1.34)
Pg = p(/—H), and
(1.35)
peor
(1.36)
should be used together with Table 1.11 to calculate density p and partial densities pg and pw.
Example 1.5
Density of Moist Gas
Given moist gas, 30.6 kg/kg-mol, 176.7°C, 98.78 kPa, and 0.2 kg water
vapor per kg dry gas, find the density of the gas and its components.
Using Equations 1.8 and 1.31-1.33 with SI values:
G = 30.6/28.965 = 1.0564,
ae
pee)
0.2870(t + 273.7)
TN
G'w
___
98.78 X 1.2_
0.2870 X 449.9 _ 9)
1», eee
bar
oe
1.0564 ° 0.622
be = pF
0.72415 = 0,603 kg dry air/m’, and
Pw = Tw
= 0.72405 = 0.121 kg water vapor/m’.
Given moist gas, 30.6 lbm/lbm-mol, 350°F, 29.17 in. Hg, and 0.2 Ibm
water vapor per Ibm dry gas, find the density of the gas and its com-
ponents.
Using Equations
1|.31-1.33 with U.S. values:
G = 1.0564,
POAAW)
0.7543(1Het+ O22).
459.7
oeGa ad
29 Te
1-2
7543 x ee = 0.0452 lbm/ft’,
0.1343
UE
1.0564 ay 0.622
Si = 0.0452 74; = 0.0377 Ibm dry air/ft’,
.
Pe P=ear P74-qp
and
=
Pw =
PT
We
0.2
ap = 0.0452 7-5 = 0.0075 Ibm water vapor/ft’.
LL
CHAPTER 1 — PROPERTIES OF AIR AND OTHER GASES
1-19
If the gas is moist and if its specific gravity G, absolute pressure p,
dry-bulb temperature #, and wet-bulb temperature /’ are known,
_ (P= Pw)G + paw
ais
should
R(t + A)
be used together with Table
(1.37)
1.11 to calculate density p. The
partial pressure of the vapor p» can be determined from Equation
1.12 or 1.13. Alternatively, if the gas is air, its density can be found in
the psychrometric density chart, Figure 1.2.
If the gas is moist air and if its humidity ratio Wand the volume ofthe
mixture per unit mass ofdry air va are known,
_i+w
we
(1.38)
The values of W and vcan be determined from measurements of ¢and ¢’
by using a psychrometric chart such as Figure 1.6. Most charts are
drawn for standard barometric pressure po, so use of Equation 1.38
will yield a corresponding density po. To determine a close approximation to the actual density p at the actual pressure p,
wos
nae sig
Example 1.6
(1.39)
Density of Moist Air
Given moist air, 28.50 in. Hg, 90°F dry-bulb, and 75°F wet-bulb,
find the density of the air.
Using Equations 1.11, 1.12, and 1.37 with U.S. units:
Dws’ = 2.96 X 10*t”? — 1.59 X 10°t’+ 0.41 = 0.88 in. Hg for t’ = 75,
ae
28.50(90 — 75)
Pw = Pws’ — 7700
Opisks) =
Oe
Pe)
Pe
P ~~ 0.7543(t + 459.7)
—
7700
= 0.72 in. Hg, and
28.50 — 0.72) + 072% 0.022. G,
0.7543(549.7)
p = 0.0681 Ibm/ft’.
Using Figure 1.2:
{—t'=
90 — 85 = 15°F and
p = 0.0681 lbm/ft* from chart.
FAN ENGINEERING
1-20
— BUFFALO FORGE COMPANY
1.05
1.04
1.03
1.02
PSYCHROMETRIC
DENSITY CHART
1.01
its)
+
lop)
lop)
yOLOW4 ALISNIG
Ge)
COR
oa
ao
e}/Wq| — ALISNAG
—!
Oo
-
oO~ N
oO~
.070
.069
f=)
oO
81N-L4IM
So
SF
N
—
Oo
oO
oOo
Figure 1.2
Psychrometric Density Chart
do — NOISSIHd30 81Nd-LIM
oO
do 40
—
NOISS3¥d40
SSE
CHAPTER 1 — PROPERTIES OF AIR AND OTHER GASES
1-21
Ee
ee
EEE
EE
ee
eee
Using Figure 1.6 and Equations
1.38 and 1.39:
W. = 0.0153 Ibm water vapor/|bm dry air from chart for 29.92 in. Hg,
va = 14.18 ft?/lbm dry air from Figure 1.6 for 29.92 in. Hg,
Pe
Oe
aston a0)
Canes Wy
SOARS
tithe 0.0716 lbm/ft’
as
DSeSa\
ENTS
Ds po( 2) = 0.0716 es
3
;
for 29.92 in. Hg, and
3
ee
:
= 0.0682 lbm/ft° for 28.5 in. Hg.
According to Avogadro’s hypothesis,’ moist air is less dense than dry
air at any particular dry-bulb temperature and pressure, because air
molecules are displaced by lighter water vapor molecules. However,
moist air is more dense than dry air at any particular wet-bulb temperature and pressure. This is because the dry-bulb temperature is lower,
and there are more molecules in a unit volume of mixture at the moist
condition.
Heat, Specific Heat, and Heat of Vaporization
Heat is thermal energy. The SI unit for all forms of energy is the joule.
The U.S. customary unit for heat is the British thermal unit, or Btu. A
similar metric unit is the calorie.
Originally, the mean value of the Btu was defined as | / 180 of the heat
required to raise the temperature of a pound mass of water from the
freezing point to the boiling point. Similarly, the mean value of the
calorie was defined as 1/100 of the heat required to raise the temperature of a gram of water from freezing to boiling. Other definitions
were based on a one-degree rise centered on a specified temperature
level, such as 15°C, 20°C, 59°F, and 60°F. Recent standards, however,
are independent of the properties of water. The ASME standards are
based on the International Steam Table values; i.e. one Btu equals
1055.056 J, and one calorie equals 4.186 800 J. The effects of differences
between International Steam Table values and other values are negligible in most fan engineering.
Specific heat is the heat required to raise the temperature of a unit
mass of substance one degree. Specific heat varies with temperature.
For many processes encountered in fan engineering, a single value of
specific heat, such as that at the average temperature, can be used with
satisfactory results. For more precise calculations, the process must be
broken down into a series of smaller steps, and the specific heat evaluated for each step. Typical values for air, ice, water, and water vapor
are given in Table 1.12.
'Avogadro’s hypothesis is
1 that the number ofgas molecules in any given volume at any given pressure
and temperature is a constant regardless of the gas or gases involved.
1-22
FAN ENGINEERING — BUFFALO FORGE COMPANY
Table 1.12
Typical Specific Heat Values
Substance
cgs
Air
1.00 kJ/kg:K | 0.24 Btu/Ibm-°F | 0.24 cal/g-°C
Water Vapor
Water
Ice
1.88 kJ/kg*K | 0.45 Btu/Ibm-°F | 0.45 cal/g-°C
4.19 kJ/kg°K | 1.00 Btu/lbm-°F | 1.00 cal/g-°C
1.97 kJ/kg-K | 0.47 Btu/Ibm-°F | 0.47 cal/g-°C
The specific heat at constant volume c, is the heat required, during a
constant volume process, to raise the temperature ofa unit mass of gas
one degree. A constant volume process does not involve any external
work; therefore, according to the first law of thermodynamics, the heat
required is equal to the change in the internal energy Au. Hence,
Au = cAt
(1.40)
for a given change in temperature Ar assuming that c, is constant.
The specific heat at constant pressure c, is the heat required, during
a constant pressure process, to raise the temperature ofa unit mass of
gas one degree. A constant pressure process involves a change in
both internal energy Au and external work A (pv). Hence, according
to
the first law,
Au +
A(py) _
7
=cpAt
(1.41)
for a given change in temperature Av assuming that c, is constant.
The difference in specific heats is related to the gas constant R;
Sei
By:
(1.42)
The mechanical equivalent of heat J can be obtained from Table 1.13.
Table 1.13
Units and Values for Equations 1.42, 1.55, and 1.56
Con Ci, OCS
R
4
J/kg°K
Btu/Ibm-°R
cal/g:K
J/kg°K
ft-lb/Ibm-°R
J/g°K
1.00 J/J
778.17 ft-lb/Btu
4.1868 J/cal
The ratio of specific heats y is an important quantity, as will become
apparent in subsequent chapters.
y=
Cp
Cy
(1.43)
CHAPTER
1 — PROPERTIES
OF AIR AND OTHER GASES
1-23
This ratio has values of about 1.66 for monatomic gases, 1.40 for
diatomic gases, and 1.30 for polyatomic gases. Values for specific
gases are given in the appendix on properties of materials.
The specific heats of various gases, at constant pressure and various
temperatures, are listed in Table 1.15. Values for dry air are plotted
against temperature in Figure 1.3. (The references for Table 1.15 and
Figure 1.3 contain many more values at different temperatures.) Figure
1.4 plots specific heat for water vapor against temperature, for various
vapor pressures and relative humidities.
The average specific heat for a mixture of dry air and water vapor
expressed per unit mass ofdry air cp~can be calculated from the humidity ratio W and the specific heats ofdry air cp, and water vapor Cp using
Cbs
"Gye ar iGo
(1.44)
This expression is meaningful only if there is no condensation or evaporation over the range of temperatures considered.
The heat of vaporization hj, sometimes called latent heat, is the heat
necessary to evaporate a unit mass of substance at constant pressure
and saturation temperature. Similarly, the heat of sublimation hiw is
the heat necessary to sublimate a unit mass of substance at constant
pressure and saturation temperature. Values for water and ice can
be determined from Figure 1.5. Values for temperatures ¢ within
the air conditioning range can be determined approximately by
using these formulae:
Refer to Table
coefficients.
Table 1.14
hiw =
C7 —
Cst and
(1.45)
hii
Cota
Grol
(1.46)
1.14 for units of measurement and values of the various
Units and Values for Equations 1.45 and 1.46
hiw & hiw
Cio
kJ/kg
0.08
Btu/lbm
cal/g
Specific Enthalpy
Specific enthalpy / is a measure of the total heat content of a unit
mass of substance. Specific enthalpy values are not absolute; rather, the
zero value is assigned to some arbitrarily selected state point. For most
gases, including air, the zero valwe is for zero degrees (either Fahrenheit
or Celsius, depending on the system of units employed) and standard
— BUFFALO FORGE COMPANY
FAN ENGINEERING
1-24
oo
Table
1.15
Specific Heats of Various Gases
In Btu/Ibm-°F
co
He
OR
Temperature
Cr
28.965 |28.013 |31.999 |44.010]
Air
Ne
02
COz
28.010)
2.016
|18.015|
Gases
100
200
300
400
500
| -359.7)
~259.7|
~159.7|
-~§9.7|
40.3]
.2392
.2392 | .2480 | .2173 | .1589]
.2392 | .2480 | .2173 |.1674|
2393 | .2481 | .2174] .1815]
.2396 | .2481 |.2184] .1964]
.2481]
.2481}]
.2482|
2483]
2.7599]
3.0957]
3.2961]
3.3948]
.4411|
4415]
.4421|
4439)
5.454/M
5.162/M
5.072/M
5.032/M
600
700
800
900
1000
1100
1200
1300
1400
1500
140.3]
240.3]
340.3]
440.3}
540.3|
640.3]
740.3]
840.3|
940.3]
1040.3]
.2403 | .2485 | .2206 |.2100|
.2416 | .2491 | .2239 | .2221]
.2434 | .2503 | .2278 | .2326]
.2458 | .2521 | .2321] .2421]
.2486 | .2546 | .2363 | .2507|
.2516 | .2573 | .2404 | .2584]
.2547 |.2603 |.2442 | 2654]
.2579 | .2635 | .2476 | .2716]|
.2611 | .2668 | .2507 |.2773)
.2642 | .2700 | .2534 |].2824]|
.2487) 3.4355} .4473| 5.013/M
2498] 3.4509) 4527] 4.998/M
.2517| 3.4598) 4592) 4.989/M
.2541| 3.4648] 4667) 4.984/mM
.2570] 3.4692) 4748 | 4.981/M
.2603)] 3.4742] 4833) 4.979/M
.2638/3.4811|.4919| 4.978/M
.2673) 3.4906} .5008 |4.977/M
.2707| 3.5025| 5099 |4.975/M
.2741)| 3.5169|.5191|
4.974/M
1600
1700
1800
1900
2000
1140.3]
1240.3}
1340.3]
1440.3}
1540.3]
.2671 | .2731 | .2560 | .2870| .2773)|
.2698 | .2760 | .2583 | .2913]| .2803)|
.2725 | .2789 | .2604 | .2951 | .2830|
.2750 | .2816 |.2622 | 2986] .2856|
.2773 | .2842 |.2638 | 3017] .2881|
3.5352]
3.5560]
3.5789}
3.6032]
3.6290]
H20 | Monatomic
.5285 | 4.973/M
5380) 4.972/M
.5476 | 4.972/M
.5570) 4.971/M
5663) 4.971/M
Adapted from the data of J.H. Keenan and J. Kaye: Gay Tables, John Wiley & Sons, Inc., New York,
1948, pp. 34, 102, 107, 112, 117, 122, 127, and 128.
TEMPERATURE — °F
900
284
1000
1100
1200
1300
1400
1500
1600
1700
1800
282.
280
278
276°
260
258
+256
254
252
250
248
246
244
242
240
274
272
270
268
266
264.
262.
260.
°F
Btu/Ibm
AIR
DRY
OF
(cpa)
HEAT
SPECIFIC
--
300
400
500
600
700
TEMPERATURE - °F
Figure 1.3
Specific Heats of Dry Air
800
238
900
°F
Btu/Ib
AIR
DRY
OF
(Cpa)
HEAT
SPECIF
°
CHAPTER 1 — PROPERTIES OF AIR AND OTHER GASES
1-25
$
on>
VAPOR PRESSURE.
onie)
male a Je
4
“ny
onoO
"PERCENT
RELATIVE HUMIDITY
> co
ULB aRSeeE
TEMPERATURE — °F
Figure
1.4
Specific Heats of Water Vapor
TEMPERATURE - °F
HEAT OF SUBLIMATION OF ICE
o =)2
a oS
(hj.)
WATER
VAPORIZATION
OF
HEAT
Btu/Ibm
-
saaweonsiban
50
wetnnnrpemtenans
1 00
santevnnnsivorstsis 150 wrommbansetere
“90 0 sroprihnsssnt
“250.
schemnavinnesnede 300 yrenaiwnrasivovrt "350
TEMPERATURE — °F
Figure 1.5
Latent Heats of Water and Ice
1-26
FAN ENGINEERING — BUFFALO FORGE COMPANY
atmospheric pressure. For many refrigerants, specific enthalpy is zero
for saturated liquid at —40°. For water, the datum selected is usually the
freezing point and saturation pressure. Other state points can be used
for other substances.
Specific enthalpy is the sum of the specific internal energy wu and the
work necessary to pump the specific volume v of asubstance against its
pressure p, or
=
h=ut
ING
T
(1.47)
While Equation 1.47 is the defining relationship, the following approximate relationships, based on the perfect gas laws, are generally
more useful in fan engineering. The specific enthalpy of air ha can be
determined from the appropriate specific heat cpa and the temperature / using
a
gE
(1.48)
The specific enthalpy of water 4; can be determined from the appropriate specific heat cp), the temperature f, and Table 1.16 using
hi
Coit ae En):
(1.49)
The specific enthalpy of ice h; can be determined from the appropriate
specific heat cpi, the temperature f, and Table 1.16 using
hi = colt — Co).
Table 1.16
(1.50)
Units and Values for Equations 1.48-1.50
kJ/kg
Btu/Ibm
The specific enthalpy of water vapor h, can be determined from the
specific enthalpy of water and the latent heat of vaporization hy, using
hy
=
hit
hw,
(1.51)
or from the enthalpy of ice and the latent heat of sublimation hj, using
ls
=
h; aF hive
(eS)
The enthalpy of moist air per unit mass of mixture A», can be determined from the specific humidity H and the specific enthalpies of the
air and vapor using
hm = (1 — H)ha + Hhy.
E53)
CHAPTER
1 — PROPERTIES OF AIR AND OTHER GASES
1-27
The enthalpy of moist air per unit mass of dry air hg, can be determined
from the humidity ratio W and the specific enthalpies of the air and
vapor using
han = ha + Why.
(1.54)
The equations in this section can be used in combination to calculate
the enthalpy of moist air per unit mass of dry air Aa, as illustrated in
Example 1.7.
Example
1.7.
Enthalpy and Entropy of Air
Given dry air at 68°F and 29.92 in. Hg, find the specific enthalpy and the
specific entropy.
Using U.S. units and Equations 1.48 and 1.56:
ha = Cpat = 0.24 X 68 = 16.3 Btu/lbm, and
Ley) in(68 + 459.7
;
459.7
SAS 55 ( 29.92
778.2 \ 29.92
Sq = 0.033 11 Btu/lbm-°R.
Given moist air at 68°F, 29.92 in. Hg, and 100% relative humidity, find
both the enthalpy and entropy per unit mass ofdry air.
Using U.S. units and Equations I.11, 1.45, 1.49, 1.51, and 1.54:
Pws = 0.6903 in. Hg from Table 1.7 and w = 0.622 from Figure 1.1,
w =
—Pusew_ _ 0.6903 X 1.0 X 0.622 = 0.014 69,
P—Pwse
29.92 — 0.6903 X 1.0
hw = C7 — Cet = 1093 — 0.55 X 68 = 1055.6 Btu/lbm,
hi = cept — Cur) = 1.0(68 — 32) = 36 Btu/lbm,
hy = hit hw = 36 + 1055.6 = 1091.6 Btu/lbm, and
hin = ha + Why = 16.3 + 0.014 69 X 1091.6 = 32.3 Btu/lbm d.a.
Using U.S. units and Equations 1.57, 1.56, 1.58, and 1.59:
Be
Siw oe= igre
“= Fea1055.6
asg 7 = 2.00 Btu/lbm-R,
= 1.001n
s;at
68 + 459.7)
32 + 459.7
— 85.78
778.2
!"\
29.92\
59.99)
_
ce
— 0.07 Btu/lbm:-°R,
Sw = 81+ Sw = 0.07 + 2.00 = 2.07 Btu/lbm:°R, and
Sm = Sat Wsy = 0.03311 + 0.01469 X 2.07 = 0.06352 Btu/lbm-°R.
1-28
FAN ENGINEERING
— BUFFALO FORGE COMPANY
eS
eS
SS
—————
Specific Entropy
Entropy is a property that is related to the second law of thermodynamics. Changes in entropy are useful in comparing actual and ideal
processes. In fan engineering, efficiency considerations may involve
the use of entropy.
Specific entropy s is entropy per unit mass of substance. Specific
entropy values are not absolute; rather, the zero value is assigned
to some arbitrarily selected state point. For most gases, including air,
the zero value is for zero degrees (either Fahrenheit or Celsius, depending on the system of units employed) and standard atmospheric
pressure. For many refrigerants, specific entropy is zero for satu-
rated liquid at —40°. For water, the reference state selected is usually
the freezing point and saturation pressure. Other state points can be
used for other substances. Tables 1.17 and 1.18 list values for dry and
moist air, respectively.
Specific entropy differences can be calculated for any process from
specific heat cp, absolute temperature 7) gas constant R, and absolute
pressurep using
ee
ye
1
ar)
Rin( 2)
t
J
u
Piss
(LESS)
Assuming that specific heat is constant yields
= cyin( 2)
Poe3 = 6 Wig
E RE
ip
ss (2)
Fin \ pgs
(1.56)
Refer to Table 1.13 for appropriate units and values. By setting 7, and
p; at the appropriate values corresponding to the reference conditions,
the value of s; becomes zero, and the value of s> will approximate the
tabulated value for a pure substance, provided that there is no change
of state when compared to the reference state. The entropy of dry airs,
and that of liquid water s; can both be calculated in this manner.
When there is a change ofstate point compared to the reference state,
as is the case for water vapor, the entropy of vaporization s;, must also
be calculated. This can be approximated from the latent heat of vaporization A, and the absolute temperature 7 using
hiw
Sw
=
y Nae
(1.57)
The entropy of water vapor sy can then be obtained from
Sw
= Sice Siw,
(1.58)
where the entropy of the liquid s; is approximated using Equation 1.56.
The entropy of the mixture of dry air and water vapor referred to a
unit mass ofdry air sm can then be calculated using
Si — Sa
Swe
(1.59)
CHAPTER 1 — PROPERTIES OF AIR AND OTHER GASES
Oe
1-35
Psychrometric Tables
Thermodynamic properties of dry and moist air have been tabulated by Goff and Gratch and reproduced in various works. The
ASHVE Transactions,’ the ASHRAE Handbook, and the ASHRAE
Brochure on Psychrometry' all contain these tables, which cover a
range of temperatures from —160°F
to 200°F
at 29.921 in. Hg barometric pressure. These data are computed from equations containing
virial coefficients,
which
in turn
are
based
on
experimental
data.
Table values, therefore, will differ from those predicted by the perfect
gas laws, but only slightly in the normal air conditioning range. The
ASHRAE
Brochure gives complete details of the derivations, sources
of data, and methods of correcting for differences in pressure. Portions
of these data are reproduced in Tables 1.17 and 1.18. Table 1.17 lists
dry air values of specific volume, specific enthalpy, and specific entropy,
which were extracted directly, and density, which was calculated. All
the data for moist air in Table 1.18 was taken directly from the original
listings. Observe that all the moist air data are referred to a unit mass
of dry air. This is the usual practice in air conditioning. The original
tabulations also list the differences between properties at saturation
and properties for dry air to facilitate interpolation for various degrees
of saturation. Thermodynamic properties have been tabulated in SI
units by Raznjevic.*
Psychrometric Charts
Psychrometric charts have been published in many formats. Among
the most common are those that utilize the rectangular coordinates of
humidity ratio versus dry-bulb temperature and those that use the nonrectangular coordinates of humidity ratio versus enthalpy per unit
mass of dry air. Prior to this edition, the charts in Fan Engineering have
always been drawn using rectangular coordinates, as Figure 1.9 still is.
Figures 1.6-1.8, however, are based on the current ASHRAE practice
of using a uniform but slanted enthalpy scale. The use of the rectangular coordinates, humidity ratio versus dry-bulb temperature, leads to
curved wet-bulb temperature lines and a non-uniform enthalpy scale.
The use of the non-rectangular coordinates of humidity ratio versus
enthalpy leads to non-parallel dry-bulb temperature lines. Neither
method of presentation is inherently more accurate for single point
determinations;
however,
the ASHRAE
charts are more accurate for
mixture processes, which are depicted by astraight line. The error in the
'J.A. Goff and S. Gratch, “Thermodynamic
New York, 1945, pp. 144-154.
*74SHRAE
Handbook
and Product
Properties of Moist
Directory — 1977 Fundamentals,
Air,” Trans.
ASHRAE,
ASHVE,
vol. 51,
New
1977,
York,
pp. 6.3-6.6.
‘A SHRAE
Brochure on Psychrometry, ASHRAE, New York, 1977, pp. 23-26.
*K. Raznjevic, Handbook of Thermodynamic Tables and Charts, Hemisphere Publishing Corporation, Washington, 1976.
1-36
FAN ENGINEERING — BUFFALO FORGE COMPANY
eS
other chart usually is negligible in air conditioning work. Most charts
are drawn for one barometric pressure. Lines of constant volume per
unit mass of dry air usually are superimposed on the chart, as are
lines of constant relative humidity. Any system of units can be used.
(Figures 1.10 and 1.11 use SI units.)
The use of the psychrometric chart for air conditioning and other
mass transfer purposes will be discussed in the chapter on mass transfer, The rnechanics of reading a chart are as follows. For any point on
the chart, there is one value each of dry-bulb temperature, wet-bulb
temperature, relative humidity, humidity ratio, enthalpy, and volume.
These values can be determined by interpolating between the appropriate adjacent lines. The dew-point temperature can also be determined by reading the saturation temperature for the same humidity
ratio. Specific humidity, absolute humidity, and degree of saturation
can be calculated using data taken from the chart together with
Equations 1.17-1.19. The density can be calculated using Equation
1.38 and the appropriate data read from the chart.
Psychrometric charts can be constructed for any gas-vapor mixture
or for any absolute or barometric pressure. Various calculation procedures can be used. Example 1.8 illustrates a simplified method that
can be performed rather quickly with a calculator. For more detailed
calculations, a computer routine should be considered.
Example 1.8
Constructing a Psychrometric Chart
Given an altitude of 5000 feet, construct a skeleton psychrometric
chart covering a range of dry-bulb temperatures from 50°F to 100°F.
Choose an appropriate set of coordinates. In this example, dry-bulb
temperature ¢ will be abscissa and humidity ratio W will be ordinate.
Lines of constant wet-bulb temperature /’, constant relative humidity gy,
constant enthalpy h, and constant volume per unit mass of dry air va
will also be drawn. The absolute pressure p will be constant at the
standard value for the altitude taken from Table 1.2,
p = 24.90 in. Hg.
The coordinates of various points on the saturation curve and other se-
lected relative humidity curves can be determined using Equation 1.21
together with values of the relative density of water vapor w from Figure I. and saturation vapor pressures
py from Table 1.7. For example:
t= 50°F.
y=
1.0,
w = 0.6219
__Pws@® 0.3626 X 1.0 X 0.6219 _
lbm wy.
poi = 2490086060 1.08 mele aera
Wp
CHAPTER 1 — PROPERTIES OF AIR AND OTHER GASES
y=
1.0
y=
Ww
,
Curves for
y =
0.5
WwW
Ibm w.yv./lbm d.a.
009 19
.013 32
019 05
026 93
.037 74
052 44
1-37
Ibm w.yv./lbm d.a.
.004 56
.006 59
009 38
FONSMT
018 30
1025513
:
:
:
‘
5
1.0 and ¢ = 0.5 can now be faired in through plotted
points. Curves for other values ofy could also be drawn.
Ideally, lines of constant enthalpy should be drawn for integer values,
but to simplify the calculations, values corresponding to the above saturation curve coordinates will be determined. Using values of heat of
vaporization h;, from Figure 1.5, enthalpy of water A, from Equation
1.49, enthalpy of water vapor A, from Equation 1.51, and enthalpy of
air ha from Equation 1.48, the enthalpy per unit mass of dry air hy
can be determined from Equation 1.54. For example:
t= 50°F,
y=
1.0,
hw = 1065 Btu/lbm
w.yv.,
hi= Cpt — 32)= 1.00(50 — 32) = 18 Btu/lbm w.v.,
hy = hw + hi= 1065 + 18 = 1083 Btu/lbm w.yv.,
ha = Cpat = 0.24 X 50 = 12.00 Btu/lbm d.a., and
hm = ha + hy
W = 12.00 + 1083 X .009 19 = 21.95 Btu/Ibm d.a.
ha
50
60
70
80
90
hig
Th
Btu/lbm d.a.
l
Ne
21.95
28.88
37.58
48.72
63.15
91.5
120.3
156.6
203.0
263.1
81.95
The last column lists values of t,, the temperature ofdry air having the
same enthalpy Am calculated for moist air at saturation shown in the
previous column, based on Equation 1.48. For example:
FAN ENGINEERING — BUFFALO FORGE COMPANY
1-38
SS
eae
SS ee
(D4
= ILS Ie
Straight lines connecting¢ on the saturation curve and /, on the dry air
line can be drawn.
Ideally, lines of constant volume should be drawn for integer values,
but to simplify the calculations, values corresponding to the above saturation curve coordinates will be determined. Since the reciprocal of
Pz is vm, Equation 1.29 can be used. For example:
Va
_ 1 _ Rit +A) _
_0.7543(459.7 + 50)_Es
nate eed QE ONS626, XGIO)
az a
t
Vii
Se
ay,
oe
ho
ChE
Btu/lbm d.a.
50
60
70
80
90
100
15.67
16.09
16.54
17.06
17.67
18.39
ie
21.78
28.51
36.86
47.43
60.96
78.38
The third column lists values of t,, based on Equation 1.27. This temperature is that temperature of dry air which has the same volume vj
previously calculated for moist air at saturation and shown in the preceding column.
bem
a EAE
SR:
For example:
fies 24.90 X 15.67
0.7543
459.7 = 57.6°F.
Straight lines connecting ¢ on the saturation curve and /, on the dry air
line can be drawn.
At saturation, the wet-bulb temperature is equal to the dry-bulb temperature; therefore, the coordinates calculated previously for the saturation curve can be used. The last column ofthe table above lists values
of t,, the temperature of dry air having the same temperature of adiabatic saturation, based on Equations 1.10 and 1.48. For example:
ho = hs* — hi*(W. — 0) = 21.95 — 18 X 0.009 19 = 21.78 Btu/lbm d.a.,
nas lt, 2 PAIRS
and ¢,'= Ten a tiers
.
90582 Fs
Observe that straight lines connecting these points do not deviate very
much from the lines of constant enthalpy previously drawn. Actually,
on rectangular coordinates, the wet-bulb lines are slightly concave in
the upward direction. The coordinates for wet-bulb temperature points
CHAPTER
1 — PROPERTIES OF AIR AND OTHER GASES
1-39
between saturation and dry air can be calculated using Equations 1.13
and 1.21. For example:
1 = 10°F,
1’ = 50°F;
= ey apace BS Pws'(it— U’)
Pw
Pws
CG
=
Gr:
Dw = 0.3626
eS
Oa
= 0.1833 in. Hg, and
WO
= 5400
=U1E33 7= 0.004 61 Ibm wv./Ibm daa,
A plot of this point falls on the straight line previously drawn. However,
for large temperature ranges, intermediate points should be calculated.
>=
o
>
o
Fo: =
>
==> =
‘
200
DRY-BULB TEMPERATURE ~ °F
a r=)
pre
hie
Ses See
weS S
w.v./lbm
—|bm
da
te
° Ss)
o
c=)a —)
RATIO
HUMIDITY
05
5000 FEET
24.90 in. Hg
RATIO
HUMIDITY
w.v./lbm
Ibm
d.a.
—
70
80
DRY-BULB TEMPERATURE — °F
1-40
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Table 1.17
Properties of Dry Air
Barometric Pressure 29.92 in. Hg
A
p
v
h
S
OF | Ibm/ft3 | ft?/lbm | Btu/Ibm |Btu/Ibm-°F
0 |.08637]11.578]
0.000)
1|.08618/11.604)
0.240}
2 |.08599| 11.629} 0.480)
3 |.08581}11.654]
0.721}
4 |08562|11.679|
0.961]
5 |.08543}11.705|
1.201]
6 |08525) 11.730)
1.441]
7 |.08506/11.756|
1.681)
8 |.08488]11.781|
1.922}
9 |.08470}11.806|
2.162]
10 |.08452/11.831)
2.402]
11 | .08434/11.857|
2.642]
12 |.08416|11.882|
2.882)
13 |.08398}11.907|
3.123}
14 |08380) 11.933) 3.363)
15 |.08363}11.958}
3.603}
16 |.08345/11.983)
3.843)
17 |.08327/12.009|
4.083)
18 |08310} 12.034) 4.324]
19 |.08293]12.059|
4.564)
20 |08275) 12.084} 4.804}
21 |.08258/12.110}
5.044}
22 |08241) 12.135] 5.284)
23 |08224) 12.160} 5.525}
24 |.08206) 12.186} 5.765}
25 |08189) 12.211}
6.005}
26 | 08173) 12.236} 6.245]
27 | 08155) 12.262} 6.485}
28 |.08139) 12.287] 6.726}
29 |.08122)12.312|
6.966}
30 |08105) 12.338} 7.206}
31 | 08089) 12.363}
7.446}
32 |08072) 12.388} 7.686)
33 |08056) 12.413} 7.927}
34 | 08040) 12.438} 8.167}
35 | .08023) 12.464) 8407)
36 |08007) 12.489) 8.647]
37 |07991) 12.514] 8.887)
38 |07974) 12.540} 9.128}
39 | 07959) 12.565} 9.368)
40 | 07943) 12.590} 9.608)
41 | .07926/12616)
9.848}
42 | 07911] 12.641) 10.088)
43 |07895) 12.666]10.329)
44 | 07880) 12.691)10.569)
.00000
00052
00104
00156
.00208
00260
.00312
00364
00415
00467
00518
00569
00620
00671
00721
00772
00822
00873
00923
00973
01023
01073
01123
01173
01223
01273
01322
.01372
01421
01470
01519
.01568
.01617
01666
.01715
01764
01812
.01861
.01909
01957
.02005
02053
.02101
02149
02197
t ia p
v
h
Ss
Ibm/ft? | ft?/Ibm |Btu/Ibm |Btu/Ibm-°F
| 45 |.07863/12.717|10.809}
| 46 |.07848)12.742}11.049)
| 47 |.07833/12.767)11.289}
| 48 |.07817/12.792|11.530)
§ 49 |.07802|12.818)11.770|
} 50 |.07786)12.843)12.010}
07771|12.868)12.250}
| 52 }.07756)12.894)12.491|
| 53 |.07741/12.919}12.731|
| 54 |.07726/12.944)12.971|
| 55}.07710}12.970)13.211|
| 56 /|.07695)12.995| 13.452}
| 57/}.07680)13.020)13.692}
| 58/}.07666/13.045/13.932}
| 59 |.07651)13.071)14.172)
| 60 |.07636}13.096/14.413|
| 61 |.07621)13.121)14.653}
| 62 |.07606)13.147|14.893}
| 63 |.07592)13.172|15.134}
| 64|.07577/13.197|15.374}
| 65 |.07563}13.222)15.614|
| 66 |.07549/13.247/15.855)
|} 67 |.07534)13.273|16.095|
| 68 |.07520)13.298/16.335)
| 69 }.07506/13.323)16.576|
| 70 |.07492/13.348)16.816|
| 71 |.07478/13.373}17.056|
| 72 |.07464/13.398]17.297|
| 73 |.07449/13.424117.537|
| 74|.07435)13.449)17.778|
} 75 |.07422/13.474/18.018|
| 76 |.07408}13.499/18.259|
| 77 |.07394/13.525]18.499|
} 78 |.07380}13.550}18.740|
| 79 |.07366/13.575!|18.980}
]| 80 |.07352|13.601}19.221|
]} 81 |.07339|13.626/19.461}
| 82 |.07325)13.651|19.702]
| 83 |.07312/13.676] 19.942]
} 84|.07298]13.702}20.183}
| 85 |.07285]13.727/20.423|
| 86 |.07272|13.752| 20.663}
7 |.07258}13.777| 20.904)
| 88|.07245/13.803)21.144|
| 89|.07232/13.828] 21.385]
02245
.02293
.02340
.02387
.02434
.02481
.02528
02575
.02622
.02669
02716
02762
02809
.02855
.02902
02948
.02994
.03040
03086
03132
03177
.03223
03269
03314
03360
.03405
.03450
03495
03540
03585
03630
03675
03720
03765
03810
03854
.03899
.03943
03987
.04031
.04075
.04119
.04163
04207
04251
Adapted from the data of J.A. Goff and S. Gratch: “Thermodynamic Properties of Moist Air” Trans.
CHAPTER 1 — PROPERTIES OF AIR AND OTHER GASES
Table
1.17
1-41
Properties of Dry Air (Concluded)
Barometric Pressure 29.92 in. Hg
OF
91 |.
92 |.
93 |.
94 |.
95 |.
96 |.
97 |.
98 |.
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
17
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
2OF
954|22.587|
980]
22.827]
‘0
i
71
1
71
2
2
2
28
3
2
3
3
4
‘4
4
4
5
5
5
5
6
6
6
6
9
yl
)
a
8
8
8
8
‘9
940
ASHVE, vol. 51, 1945, pp. 149-150.
.
.
06660 |15.
06648 | 15.
(06637 |15.
0662615.
06615|15.117
06604 | 15.142
06593 | 15.167
06582|
15.192
(06571
115.218
06560)
15.243
06550|
15.268
06539]
15.293
06528
|15.319
06517/15.344
06507|15.369
(06496 | 15.394
06485 | 15.420
06475| 15.445
06464] 15.470
06453] 15.496
06443] 15.521
06433|15.546
(06422|15.571
06411/15.597
06401|
15.622
06391|
15.647
06381|15.672
06370| 15.698
06360
15.723
06350|15.748
06340|
15.773
06330)
15.799
06320
06310
06300) 15.
;
06229
06270
06310
06350
06390
06430
‘06470
06510
06549
06589
06629
06669
06708
06748
06787
(06827
(06866
06906
06945
06984
07023
07062
07101
‘07140
07179
07218
07257
‘07296
07334
07373
07450
07488
(07527
07565
07603
‘07680
07718
07756
(07794
07832
(07870
.07908
FAN ENGINEERING
1-42
1.18
Table
t
oF
Vir
—
— BUFFALO FORGE COMPANY
Properties of Moist Air at Saturation
Barometric Pressure 29.92 in. Hg
hs
Sh
W
ft?/lbm | Btu/Ibm |Btu/Ibm-°F
0
1
2
3
4
0.835]
1.120}
1.408)
1.698]
1.991]
.00192
.00254
.00316
.00379
.00442
006331
006578
006835
007100
007374
5
6
7
8
9
2.286|
2.583]
2.883]
3.188]
3.494]
.00506
.00570
.00635
.00700
.00766
007658
007952
.008256
.008569
008894
10
11
12
13
14
3.803]
4.116]
4.432)
4.753]
5.076}
.00832
.00899
.00966
.01034
.01101
.009229
009575
009934
01030
01069
15
16
17
18
19
5.403}
5.735]
6.071}
6.412]
6.756]
.01171
.01240
.01311
.01382
.01454
01108
1149
1191
1235
01280
7.106}
7.460}
7.820}
8.186}
8.557]
.01527
.01601
.01676
.01752
.01830
01326
01374
01424
01475
01528
8.934]
9.317]
9.706}
10.103}
10.506}
.01908
.01987
.02068
.02149
.02231
01582
01639
01697
01757
01819
LOS15)023i5
11.333}
.02400
11.758}
.02487
12.169}
.02570
12.585}
.02655
01882
01948
02016
02086
02158
13.008}
.02741
13.438 | .02828
13.874]
02917
14.319]
.03006
14.771}
.03096
02233
02310
02389
02471
02555
15.230)
.03188
15.697]
.03281
16.172]
.03376
16.657 | .03472
17.149 | .03570
02642
02731
02824
02919
03017
Adapted from the data of J.A. Goff and S. Gratch: “Thermodynamic Properties of Moist Air.” Trans,
CHAPTER
Table 1.18
1-43
Properties of Moist Air at Saturation (Concluded)
Barometric Pressure 29.92 in. Hg
Vin
OF
1 — PROPERTIES OF AIR AND OTHER GASES
hn
ft?/Ibm | Btu/Ibm
ve
hy
SH
| ft?/lbm |Btu/Ibm|Btu/Ibm -°F
:
eA
pall
mili
119
135|.1308 | 18.122}
136] .1350 | 18.253)
137] .1393 | 18.389]
138] .1439]
18.528)
139] .1485 | 18.671]
178.9]
183.9]
189.0]
194.4]
199.9]
.3233
.3318
.3405
.3496
.3589
14.
95
96
97
98
99
14.802 | 63.32}
14.856 | 64.92}
14.911]
66.55}
14.967]
68.23}
15.023 | 69.96}
.12231
.12519
12815
.13117
.13427
}|140].1534|
18.819] 205.7)
}141].1584|
18.971] 211.6]
}142].1636 | 19.128] 217.7]
|143].1689 | 19.290] 224.1
|144].1745 | 19.457/230.6]
.3686
.3785
.3888
3994
.4104
100
101
102
103
104
15.081]
15.140]
15.200]
15.261]
15.324
.13745
.14071
.14406
.14749
:
|145]|.1803 | 19.629]
|146|.1862]
19.807]
|147].1924|
19.991]
|148].1989 | 20.181]
:
20.
.4218
.4335
.4457
.4583
4713
105
106
107
108
109
15.387
15.452
15.518
15.586
15.654
4848
4987
ayey
5282
5438
110
111
112
113
114
15.724
:
15.796
;
15.869
:
15.944
}
16.020 |102.31
.5599
5768
5943
6125
6314
115
116
117
118
119
16.098
16.178
16.259
16.343
16.428
|104.98
|107.73
|}110.55
|113.46
|}116.46
6511
6716
6930
TASS
7385
120
121
122
123
124
16.516 }119.54
16.605 }122.72
16.696 |125.98
16.790 |129.35
16.886 |132.8
1629
1883
8150
8429
8722
125
16.985 |136.4
9030
126
127
128
129
17.086 |140.1
17.189 |143.9
17.295 |147.8
17.404 |151.8
9352
9691
1.0049
1.0426
17.516 | 155.9
1.083
130].
t
;
;
E
:
WwW
°F | —
90
91
92
93
94
131
132
133
5
:
:
é
Sh
|Btu/Ibm-°F]
71.73}
73.55}
75.42}
77.34]
17.631 |160.3
17.749 |164.7
17.870 |169.3
17.9941} 174.0
ASHVE, vol. 51, 1945, pp. 149-154.
237.4]
244.4]
251.7]
259.3]
1.125
1.169
1.216
1.266
1-44
Neen
FAN ENGINEERING — BUFFALO FORGE COMPANY
ee eee eee
ee ee
eee
ee
TTT
eee
Fog
Fog is a mixture of air, water vapor, and very fine water droplets, all
at the same temperature. The mixture is a mechanical one; the water
vapor is at saturation; and the water droplets are suspended. The fog
region ona psychrometric chart is the area above the saturation curve.
On Figures |.6-1.8, the humidity ratio and enthalpy lines extend partly
into the fog region. They can be extended even further if necessary. To
determine the properties for any point in the fog region, read the humidity ratio W and enthalpy A directly by interpolating between lines.
To determine the temperature, extend wet-bulb lines and interpolate.
The dry-bulb temperature
¢ will equal the wet-bulb
temperature
1’
Since the humidity ratio W is the total mass of droplets and vapor per
unit mass ofdry air, the mass of droplets per unit mass of dry air W,can
be obtained by subtracting the humidity ratio at saturation W at the
same temperature. The density of the mixture p can be determined from
the chart values of the volume per unit mass ofdry air at saturation vy
and the humidity ratio W using Equation
1.38.
Barometric Corrections
Psychrometric data taken from published charts or tables may not be
sufficiently accurate if the actual pressure is different from the pressure
for which the data were prepared. If greater accuracy is required, cor-
rections can be applied as discussed in this section. Alternatively, a
special chart can be drawn, as illustrated in Example 1.8. ASHRAE
has prepared charts for elevations of 5000 feet and 7500 feet.
If only the density is required, Figure 1.2, the Psychrometric Density
Chart, is convenient to use. Density can also be computed using the
equations and examples in the section on density, or even Tables 1.19
and 1.20.
The effect of a change in pressure on the general appearance of a psychrometric chart is to displace the saturation curve and all the relative
humidity lines. The displacement will be upward for a reduction in
pressure. Similarly, the wet-bulb lines will be moved upward resulting
in higher values for humidity ratio and enthalpy.
The change in saturation humidity ratio, or the difference between
the saturation humidity ratio W.,’ at elevation Z and W,,’, that at the
chart elevation, can be determined using the actual pressure p-, the
chart pressure po, the partial pressure of the vapor pws’, and
Wes
re
Ws"
=
Dome
P=
QS
Das
Woy’
:
(1.60)
Note that the prime signifies that properties are at the wet-bulb temperature. This equation is for points on the saturation curve, but it can be
used in the partially saturated region with only slight errors. Figure 1.12
is a graphical representation of Equation 1.60.
The change in enthalpy, or the difference between the enthalpy /.,’at
CHAPTER 1 — PROPERTIES OF AIR AND OTHER GASES
1-45
elevation Zand h,,’, that at chart elevation, can be determined using the
change in saturation humidity ratio from Equation 1.57, the latent heat
Ay, and
lites “ar UE
ames hi ‘(iWee ca
Ws’).
(1.61)
Figure 1.13 is a graphical representation ofthis equation. It is for points
on the saturation curve, but usually only slight inaccuracies will result if
used in the superheated region.
Example
1.9
Barometric
Corrections
Given a barometric pressure of 24.90 in. Hg, a dry-bulb temperature of
70°F, and a wet-bulb temperature of 50°F, find the density, the humidity ratio, and the enthalpy.
Using Figure 1.7:
W, = 0.0031 Ibm w.v./lbm d.a.,
W.;’ = 0.007 65 Ibm w.v./lbm d.a.,
ho = 20.2 Btu/lbm d.a., and
figs’ = 20.3 Btu/lbm d.a.
Using U.S. units and Equations
1.31
ED
ae Po P SO Oe
°
0.3626
—
24.90
ees
Sent
ea
a
i
W..’ —
1.60, 1.61, and
Wos’ = 0.0016 lbm w.v./lbm d.a.,
W, = W.+ (W.s’ — Wos’) = 0.0031 + 0.0016,
W, = 0.0047 |bm w.v./lbm d.a.,
his’ = hos’ = hin’ (W2s’ — Wos’) = 1065 X 0.0016,
h-s’ — hos’ =
1.704 Btu/lbm d.a.,
hz = hho + (hes’ — hos’) = 20.2 + 1.7 = 21.9 Btu/lbm d.a., and
pil + W)
IR3 (((sist Al)
ce z Ww
G
Ww
ee
=
24.90(1 + 0.0047)
OMS
43 (70 G14 5957)
i cf 0.0047
I
aa
0.0621
0.622
Using Figures 1.12 and 1.13 leads to the same results:
W..’ —
Wos’ = 0.0016 Ibm w.v./lbm d.a. and
lia
hoo —
1.7 Btw) lbmidrar:
}
Ibm /ft.
FAN ENGINEERING — BUFFALO FORGE COMPANY
28.0
BAROMETER
Hg
in.
(ps)
Nhi, oO
0
90
100
WET BULB TEMPERATURE (¢’) — °F
Figure 1.12
Barometric Humidity Ratio Corrections
BAROMETER
Hg
in.
(p,,)
i)TS o
20.0
50
60
70
80
90
100
110
WET BULB TEMPERATURE (1’) - °F
Figure
1.13
Barometric Enthalpy Corrections
120
CHAPTER
Table 1.19
1 — PROPERTIES
mae
29.92
29.81
29.70
29.60
29.49
29.38
29.28
29.17
29.07
28.96
28.86
28.75
28.65
28.54
28.44
1-47
Density Factors for Air at Various Elevations
Standard Air at Sea Level and 29.92 in. Hg = 1.00
ft
0} 1.000)
100/0.996)
200/0.993}
300/0.989/}
400)0.986|
500}0.982/
600)}0.979)
700)0.975}
800)0.971}
900/0.968}
1000/0.964|
1100/0.961|
1200/0.957)
1300}0.954)
1400)0.950)
OF AIR AND OTHER GASES
ede
—
|in.Hg]
ft
eax
—
| in. Hg
1500 /0.947) 28.33]3000)0.896|
1600 /0.944) 28.23]3200/0.890)|
1700 /0.940) 28.13}3400/0.883)
1800/0.937)| 28.02]3600)0.877)
1900/0.933|27.92}3800/0.870|
2000) 0.930} 27.82} 4000) 0.864)
2100)0.926}27.72}4200)0.857)
2200)0.923) 27.62}4400/0.851|
2300/0.920| 27.52] 4600) 0.845}
2400/0.916} 27.42} 4800) 0.838)
2500/0.913}27.32]5000) 0.832)
2600/0.909} 27.21|5200)0.826)
2700/0.906} 27.11}5400) 0.820)
2800}0.903| 27.01} 5600) 0.814)
2900/0.899) 26.91}5800)0.807)|
ft
—
| in. Hg
26.82} 6000/0.801)23.98
26.62] 6500)0.786) 23.53
26.42] 7000/0.772)| 23.09
26.23} 7500)0.757/22.65
26.03} 8000)0.743) 22.22
25.84] 8500/0.729)21.80
25.65} $000)0.715) 21.39
25.46} 9500/0.701) 20.98
25.27} 10000 |0.688) 20.58
25.08 |15000 |0.564) 16.89
24.90} 20000) 0.460) 13.75
24.71} 25000/0.371)11.10
24.52] 30000/0.297)
8.89
24.34/35000)0.235}
7.04
24.16}|40000/0.185)
5.54
Calculated from the data of NACA: “Standard Atmosphere — Tables and Data for Altitudes to
65,800 Feet.” Report 1235, Washington, D.C., 1955, pp. 66-81.
Table
1.20
Density Factors for Dry Air at Various Temperatures
t
th
t
OF
a
OF
Standard Air at 70°F = 1.00
-10 | 1.178
-§ | 1.165
Ol
ste
5 | 1.140
10 | 1.128
60
62
64
66
68
15°)
1-116
20 | 1.104
25 | 1.093
30 | 1.082
} 70
| 72
| 74
| 76
35 | 1.071
78
hi
1.019
1.015
1.011
1.008
1.004
t
hi
t
hi
1
h
OF
ae
OF
ae
OF
ae
} 100
| 105
| 110
| 115
| 120
1.000 | 125 | .906 | 250
996 | 130 | 898 } 260
OZ NI S5m
oda
e220
989 | 140 | 883 | 280
985 | 145
40 | 1.060 | 80
42 | 1.056 | 82
982
978
44 | 1.052
46 | 1.047
974 | 160
971 | 165
48
50
52
54
56
| 1.043
| 1.039
| 1.035
| 1.031
| 1.027
84
86
| 88
| 90
| 92
94
| 96
946 } 200 | 803 | 400 | 616
S38
eZtO)
791
e425
e599
930 | 220 | 779 | 450
582
922 | 230 | .768 | 475 | 567
914 | 240 | .757 | 500 | 552
876 | 290
| .747 | 525 | .538
| .736 | 550 | .525
ney 20NeO7 5m ol2
| .716 | 600 | 500
707 | 625 | .488
| 150 | .869 | 300 | 697 | 650 | 477
| 155 | 862 | 310 | 688 | 675 | 467
855 | 320 | 680 | 700 | .457
848 | 330 | .671 | 725 | .447
967 | 170 | 841
964 | 175 | 835
960 | 180 | 828
957 | 185 | .822
953 | 190 | 815
| 340
| 350
| 360
| 370
| 380
| .662
| 654
| 646
| .638
| 631
| 750
| 775
| 800
| 825
| 850
| 438
| 429
| 421
| 412
| 404
1-48
FAN ENGINEERING — BUFFALO FORGE COMPANY
Barometric Measurements
Barometric pressures can be measured with either a Fortin or an
aneroid barometer. A Fortin, or mercurial barometer, consists ofa vertical glass tube with the top sealed and the bottom immersed ina cistern
of mercury. The tube is evacuated, and the mercury rises to a height corresponding to the atmospheric pressure. However, because
of thermal
expansion, the reading at any given pressure will vary slightly with
temperature. Corrections to the standard temperature of reference can
be made using Table !.21. Theoretically, an additional correction for
the difference in gravitational acceleration from the standard value
should also be made using the data of Table I.22. However, such correc-
tions are negligible in most fan engineering work. Even properly designed, built, and maintained mercurial barometers should be checked
periodically against the National Bureau of Standards’ reference barometer. One way to do this is to compare readings with those on the
local weather station barometer, which is checked periodically against
the national standard. Simultaneous readings can be compared via the
telephone, but to eliminate the possibility of local variations in atmos-
pheric pressure, a transfer instrument should be used. An aneroid barometer can be transported to both locations for comparison with both
instruments. An aneroid barometer consists of an evacuated capsule
whose movement under changes in pressure is transmitted to an indicator that is calibrated in units of pressure. Gravity corrections are not
necessary since aneroid instruments are force gages. If the instrument is
temperature compensated, no corrections for temperature deviations
are needed either. Aneroid barometers should be calibrated frequently.
The U.S. Weather Bureau reports barometric pressure converted to
sea level conditions at 45° latitude using the data of Tables 1.22 and
1.23. In order to compare true values with Weather Bureau reports, the
true values should also be converted. Example 1.10 illustrates how
these conversions are made.
Example
1.10
Barometric
Measurements
Givena mercurial barometer reading of 29.10 in. Hg, at 75°F, 600 ft
elevation, and 40° latitude, find the true atmospheric pressure and the
pressure converted to Weather Bureau Standards.
Using Table
1.21, the temperature
correction
is —0.13
in, Hg, and
from Table 1.22, the gravity correction is —0.02 in. Hg, so that the
true atmospheric pressure is 29.10 — 0.13 — 0.02 = 28.95 in. Hg.
Using Table 1.23, the elevation correction is —0.10 in. Hg/ 100 ft ofelevation, or 6 X —0.10 = —0.60 in. Hg, making the converted readi
28.95 — 0.60 = 28.35 in. Hg.
;
LL
ag
CHAPTER 1 — PROPERTIES OF AIR AND OTHER GASES
Table 1.21
1-49
Temperature Corrections for Barometers
(Use in all engineering calculations assuming
brass scale is true at 62°F)
Observed reading of column in in. Hg
28
30
32
o—a—
S99
9590
o-—
ooo
Onton
wnaOno
2°29
990
ooo
Ono
wo—ww
ess
sso
ooo
o-—
onan
of
0. 01
0. 02
0. 02
0. 03
0. 04
0. 05
0. 05
0. 06
0. 07
oOo oO —~s
0. 07
0. 08
0. 09
0. 10
0. 10
et
Cee
=)
ee
ae
eh
oe
ot
a
i
Oo
OS
Oe
a=
Oe:
Oa’
COMOWM
mM
OPW
UND
WrhH—
S29
S99
999
S959
S00
WHY
—|$OW
OOP
OY
WHhH—
S92
S99
SSS
990
See
0S
UO
©
SO
——
O'S
OO
eet
PSP
SOP
See
Se:
©
=00
===
==]
OF
WHY—
CHOMH
J
999
SS
S99
990
PWM
ND
—-OWO
LPw—
WHYSS
999
SS9
Seo
Sooo
TNPW
COnmN
MHOOW
LWP
COUM
SS
S99
S50
SSe9
eymanes
iguana
Gems
Coenen,
YOP
oo
WO
LWP
ODUM
29
S99
S90
999
Se
ee
See
es,
Pe
COW
ODMN
WHO
WOM
cwnr
Adapted from the data of ASME: ASME Power Test Codes, Instruments and Apparatus, Part 2,
Pressure Measurement, ASME PTC 19.2-1964, pp. 25-26.
Table 1.22
Gravity Corrections for Barometers
(Negligible in engineering calculations)
North
Latitude
Degrees
Elevation, ft
Adapted from the data of ASME: ASME Power Test Codes, Instruments and Apparatus, Part 2,
Pressure Measurement, ASME PTC 19.2; 1, 6-1941, pp. 15-16.
FAN ENGINEERING — BUFFALO FORGE COMPANY
1-50
Table 1.23 Elevation Corrections for Barometers
(Use only for comparing personal data with Weather Bureau data.)
Mean
Mean Atmospheric; Temperature,
(o}
°F
Altitude
Ft.
999
S929
oS
nyt
ra
(aa
(m=)
onde
onmw
mom
Adapted from the data of ASME: ASME Power Test Codes, Instruments and Apparatus,
Pressure Measurement, ASME PTC 19.2; 1, 6-1941, pp. 15-16.
Temperature
Part 2,
Measurements
Temperatures can be measured with a variety of instruments. The
most common, liquid-in-glass thermometers, use various liquids depending on the working range:
Material
Mercury
Alcohol
Toluol
Pentane
Working Range in °F
aes
—100
—150
—300
ton925
to 250
to 200
to 70
Calibrated instruments can be read directly with sufficient accuracy for
most engineering work. When only partially immersed, precautions
must be taken to ensure that heat conduction due to the emergent stem
is either negligible or accounted for. Figure 1.14 can be used to determine the necessary correction. In making average temperature determinations, be sure that the sample or samples are representative. Such
determinations in a moving gas stream should be weighted according
to mass flow. If a gas stream and its retaining walls are at different
temperatures, the thermometer should be shielded to eliminate radiation effects.
Resistance thermometers, which determine temperature by measuring the change in resistance of a calibrated wire, can be extremely
accurate and are suitable for temperatures from —400 to 1800°F.
CHAPTER
1 — PROPERTIES OF AIR AND OTHER GASES
1-51
— i)
— Oo
ADDITIVE
CORRECTION
°F-
0
50
100
150
200
250
INDICATED TEMPERATURE MINUS AMBIENT TEMPERATURE — °F
Figure 1.14
Emergent Stem Corrections for Liquid-in-Glass
Thermometers
When two dissimilar metal wires are joined together, as in a thermocouple, the difference in temperature between the junction and the
opposite ends produces an emf, the magnitude of which is a function
of temperature difference. Combinations of metals that give nearly
straight line relationships between emf and temperature are iron-constantan, copper-constantan, chromel-alumel, and platinum-platinum
(87%) /rhodium (13%). Very good accuracy is obtained by measuring
the emf with a potentiometer and reading the corresponding temperature from calibration tables.
For measuring very high temperatures, pyrometers of either the radiation or optical type give reasonably accurate readings.
Wet-bulb temperatures can be obtained in the same manner as drybulb temperatures except that the bulb must be kept wet. As indicated
1-52
a
FAN ENGINEERING — BUFFALO FORGE COMPANY
Ee
——ee
in the discussion on the temperature of adiabatic saturation, both gas
velocity and radiation from surroundings affect wet-bulb readings.
The reading from an unshielded wet-bulb thermometer in an air stream
at 800 or 900 feet per minute is accurate to within about 0.5% according
to Carrier and Mackey.’ A sling psychrometer can easily be whirled at
speeds sufficient to produce this velocity past the bulb. Aspiration
psychrometers that use tiny fans to produce a uniform circulation of
air over the thermometer bulbs are available. Whenever the wet bulb
is shielded, it will yield a temperature slightly lower than the temperature of adiabatic saturation. Usually this can be disregarded, but for
accuracy a correction should be made, the value of which depends upon
the velocity of air over the bulbs. There may be a 5% error in the wet-
bulb depression if the velocity is 800 or 900 fpm. That is, up to 5% of
the wet-bulb depression may have to be added to the observed wet-bulb
reading to obtain the true temperature of adiabatic saturation.
If a thermometer is dipped into water and used to record wet-bulb
temperatures below 32°F, it will first indicate the wet-bulb temperature
over sub-cooled water. When freezing begins, the temperature will return to and remain at 32°F until freezing is completed. The thermometer will then ultimately register the wet-bulb temperature over ice after
equilibrium is obtained and until the ice is all evaporated.
Humidity
Measurements
Humidity is not measured directly; rather, some property related to
humidity is measured and the humidity determined therefrom. Psychrometers, hygrometers, and dew-point detectors are used. The sling
psychrometer and its motorized equivalent were described in the previous section. The relative humidity, humidity ratio, or any of the other
humidity terms previously defined can be determined using a psychrometric chart or the formulae in this chapter. Hygrometers are calibrated to read directly in terms of relative humidity. They utilize the
effects of humidity on various properties, such as the length of an
organic fiber, the electrical resistance of a hygroscopic material, the
weight of an absorbing material, the thermal conductivity of the
moist air itself, and others. Dew-point detectors are calibrated to
read in terms of dew-point temperature. They operate by cooling a
surface to produce condensation, by expanding a gas sample to produce fog, or by passing an electrical current through a salt film to
produce a vapor pressure equal to that of the atmosphere.
'W.H. Carrier and C.O. Mackey, “A Review of Existing Psychrometric Data in Relation to Practical Engineering Problems,” Trans.
ASME, vol. 59, paper PRO-59-1,
1937, pp. 33-47.
Chapter 2
Fluid Flow
Most aspects of fan engineering are concerned in some way with the flow
of fluids. Consequently, many fundamentals of flow will be stated in this
chapter to provide a basis for the detailed discussions in subsequent chapters. The first part of this chapter deals with flow under more or less ideal
conditions. While it does not ignore friction, it does not deal with it directly.
The second part examines the effects of viscosity and other factors that
determine the resistance to flow. The third part gives means for determining
the frictional losses in the various elements of a duct system. The last part
covers the measurement of pressure and flow.
Principles of Fluid Flow
The general principles that govern fluid flow are discussed in the
following sections. Only the integral equations have been developed.
Differential equations are more suitable for examining some flow situations; if this is so, refer to a text on fluid mechanics.
Mathematical Models
A mathematical model is necessary if a flow situation is to be analyzed quantitatively. The model must be capable of representing any
variable that changes significantly during the flow. (Flow variables include the position, velocity, acceleration, pressure, temperature, density,
enthalpy, and entropy of the fluid.) The changes predicted by the model
must be consistent with the physical laws that govern fluid flow.
These laws are:
1) the general law regarding conservation of mass;
2) the first law of thermodynamics regarding conservation ofenergy;
3) Newton’s second law of motion regarding momentum; and
4) the second law of thermodynamics regarding entropy.
In most fluid mechanics
models, the fluid is assumed to be a con-
tinuum. That is, the velocities and other properties are assumed to vary
continuously throughout the fluid. Such an assumption could not be
justified for highly rarefied gas flows, but these usually do not occur in
fan engineering.
In the mathematical formulation of the physical laws governing fluid
flow, coordinates must be assigned to points in space. In one method
of modelling, coordinates that are a function of time are also assigned
2-2
FAN ENGINEERING
— BUFFALO FORGE COMPANY
to identifiable particles (or portions) of the fluid. This Lagrangian approach requires that the two sets of coordinates be distinguished from
each other and leads to complex equations. It is more usual in fluid
mechanics to use the Eulerian approach, which leads to simpler equations. In this method, the flow field is described; that is, the fluid properties are specified at points in space by properly constructed equations.
The properties can vary with time at any point in space, if that is a condition of modelling. And it is not necessary to assign coordinates to
individual portions ofthe fluid.
Any mathematical model that is capable of representing the most
general flow situation will be more complex than necessary for many
fan engineering applications. Accordingly, various assumptions can be
made to simplify the model. However, caution is advisable in using simplified models until the assumptions have been verified for the situation
being modelled. The more common assumptions are discussed below.
1) All real flows are three-dimensional to some extent, but it is not
always necessary to use a three-dimensional model to describe the flow.
It may be possible to analyze some flow situations with either a one-
dimensional or a two-dimensional flow model. In a one-dimensional
flow model, the changes in variables perpendicular to the main flow are
taken into account by using average values. Only one dimension or coordinate is required to establish position along the flow path. Pipe flow,
for example, usually can be treated as one-dimensional by using the
proper averages across the section for the variables. In two-dimensional
flow, just two independent coordinates are required to describe the flow
field. For instance, the flow across a wing can be analyzed on a twodimensional basis by using a correction factor to account for the threedimensional effects at the tips. A three-dimensional model considers
each variable to be a function of three space coordinates and time.
2) All real flows probably have some unsteadiness. That is, the prop-
erties at a point vary with time. However, the time variations may be
small and centered around a constant value for each property. In such
cases, the temporal average values can be used in the model, and the
flow can be called steady. However, in turbulence studies, these variations cannot be disregarded.
3) All flows are influenced by gravitational forces. However, in some
flows, particularly those involving gases, the effects of gravity are negligible compared to the effects of other forces to which the fluid is exposed. If so, the gravity terms can be omitted from the equations in
the model.
4) All fluids are compressible, especially gases. The effects of compressibility on liquids can be ignored, except for situations involving
large or sudden changes in pressure. The effects can also be ignored in
many calculations involving gases when the pressure changes and Mach
numbers are small. Using a compressibility factor may be the most convenient way to deal with compressibility when it cannot be ignored.
Otherwise the appropriate compressible-flow equations must be used.
CHAPTER 2 — FLUID FLOW
2-3
5) All real flows involve friction. Often, however, it is convenient to
consider the flow frictionless or ideal. The analysis of some flows may
be divided into two parts: that in a boundary layer and that outside
such a boundary layer, with the latter considered ideal.
6) Other effects that are almost always ignored in fan engineering
applications are those due to surface tension, buoyancy, and Coriolis
forces.
The number of equations required to model a flow situation must
equal the number of unknowns. Basically, a continuity equation and
one or more equations of motion will be needed. The latter will provide
a mechanical energy balance. If thermodynamic effects are significant,
the general energy equation will be needed. An equation of state will
be required when an explicit relationship among pressure, temperature,
and density is necessary. The equation of state for perfect gases is discussed in Chapter |. Discussions of the equations of continuity, motion,
and energy are given in the next three sections of this chapter. In these
discussions, reference is made to a system, as opposed to a control volume and its associated control surface. A system is a definite mass of
material that can be distinguished from its surroundings. A control
volume is a region in space and is signified by the abbreviation c.v. This
region is usually fixed, but it may be moving in space. The control surface is the boundary of the control volume and is signified by the abbreviation c.s. For the control volume equations, the flow enters the
control volume through the entrance area A, on the control surface and
leaves through the exit area A>. If there is more than one entrance or
more than one exit, the equations must be modified. Each discussion
contains a system equation in differential form to illustrate the underlying physical law and at least one version of a control volume equation
in integral form to provide the basis for the simplified equations that
are commonly used. Vector notation (denoted by symbols with superior
arrows) is used in the general equations to convey the three-dimensional
aspects without necessitating three equations. Vector quantities include
velocity vector V, area vector A, force vector F, surface force vector Fs,
body force per unit volume vector B, radius or position vectorr,and
surface torque vector 7;. Most of the scalar quantities are defined as
they appear; but time ¢, mass density p, and volume W should be noted
here.
In most fan engineering applications, the reader is not expected to
use either the general system equations or the general control volume
equations. These equations, however, do illustrate what has been omit-
ted from the simplified equations derived from them.
Continuity Equations
The general physical law regarding the conservation of mass requires
that the mass m of a particle or system of particles remain constant with
time f. Stated another way, the rate of change of mass dm/dt must be
zero, which leads to the system equation
2-4
(i
ee
G — BUFFALO FORGE COMPANY
FAN ENGINEERIN
Ni
Se
a
ee
teh
dm _
Ties
(2.1)
The corresponding control volume equation states that the net rate of
mass flow through the control surface must equal the rate of change
of mass in the control volume, or
Seay
kak “hy
[[evera {ffet”Y/
(SA
cv.
(22)
This equation, written in integral form with vector notation, is sufficiently general to cover three-dimensional flow that is nonuniform, unsteady, and compressible. In most fan engineering applications, the
flow is steady and the rate of change of mass in the control volume is
zero, leadingto
|fpV-dd=0.
c.S.
(2.3)
For one-dimensional compressible flow with only one entrance and
one exit in the control surface,
piViAi = p2V2A2.
(2.4)
For one-dimensional incompressible flow with one entrance and one
exit,
VA, = V2A2.
(2.5)
Although Equations 2.4 and 2.5 have been derived from one-dimensional considerations, they can be used for nonuniform flow if the
densities and velocities across the section are represented by appropriate averages. For Equation 2.5 (incompressible flow), it is appropriate
to use the area-weighted average of the velocities V across the section.
For Equation 2.4 (compressible flow), it is also appropriate to use the
area-weighted average of the velocities provided that the volume-flowweighted average of the densities p is used. Alternatively, the areaweighted average of the products pV can be used in Equation 2.4.
Remember that both equations are based on the assumption of steady
flow, which may not always be the case. Unsteady flow occurs in fan
engineering during start-up and shut-down, as well as in situations involving pulsation. The equations must also be modified if there is
more than one entrance area A, or exit area Ap.
CHAPTER
2 — FLUID FLOW
2-5
Equations of Motion or Momentum Equations
Newton's second law of motion requires that the sum of the external
forces F acting on a particle equal the mass of the particle m times its
acceleration dV/dt. The corresponding system equation states that the
rate of change of momentum equals the sum of the external forces on
the system, or
a
ee
TRG Bee
(2.6)
Similarly, the control volume equation states that the sum of the surface forces plus the sum of the body forces must equal the net rate of
momentum flow through the control surface plus the rate of change
of momentum in the control volume, or
+ |[[FY = [[ Verat+ arfff"4
cv.
Coe
c.Vv.
(2.7)
This equation, written in integral form with vector notation, is sufficiently general to cover three-dimensional flow that is nonuniform,
unsteady, and compressible, as well as the gravitational and frictional
effects on the flow. However, in most fan engineering applications,
the flow is steady and gravitational effects are negligible, so
FS IfVoda.
(2.8)
C5:
This vector equation also can be written in component form. For instance, for the component F, and for uniform velocities at both A;
and A>,
Fe=m(Va2 — Vas)
(2.9)
where m is the mass flow rate and V, is the velocity component on
the x-axis.
Newton’s second law also requires that the sum of the moments of
the external forces about a point acting on a particle equal the rate
of change of angular momentum
of the particle. The corresponding
system equation for angular momentum is
NP
ay
VEE
ees
AL
(2.10)
2-6
FAN ENGINEERING
— BUFFALO FORGE COMPANY
and the corresponding control volume equation is
[fr dF + [[[7x Bay = [fr Vovuae arihfF* VodY.
GaSe
C25
CS.
Cv
(2.11)
The latter, written in integral form with vector notation, is sufficiently
general to cover three-dimensional flow that is nonuniform, unsteady,
and compressible,
as well as the gravitational and frictional effects
on the flow. Since, in most fan engineering applications, the flow is
steady and gravitational effects are negligible,
ice [fF VoV-dA
as
(2.12)
where 7; is the net surface torque on the control volume. This vector
equation also can be written in component form. For instance, for
the component 7- and for uniform velocities at both A; and A2,
T: = m(r2Vi2 — 11Vin)
(2.13)
where m is the mass flow rate, r is the radius, and V, is the tangential
component of the velocity about the z-axis.
Equations 2.9 and 2.13 are simple and useful, but they do have
limitations. Both are based on uniform flow but can be used for nonuniform flow if the velocities and radii across the section are represented by appropriate averages. For Equation 2.9 (linear momentum),
it is appropriate to use the mass-flow-weighted average of the velocities
V across the section. For Equation 2.13 (angular momentum), it is appropriate to use the mass-flow-weighted average of the product of the
radius and velocity rV. In either case, it would be appropriate to use
the area-weighted-average velocity only if an appropriate momentum
correction factor’ were applied to each average value. Both equations
also assume that the flow is steady, which is not always the case. And
both equations require that the right-hand side be divided by the conversion factor g. if force and mass are assigned independent dimensions, Equation 2.13 is useful particularly in the analysis of fans and
other turbomachines.
The equations of motion can be used to derive various equations
that deal with the mechanical energy balance in a system. These
equations are also called Euler or Bernoulli equations. However, since
the general energy equation, which contains the mechanical energy
balance as well as a thermodynamic
balance, is discussed in the next
section, no detailed discussion is given here.
——_—
le
>
.
See the second section following.
CHAPTER 2 — FLUID FLOW
2-7,
General Energy Equation
The first law of thermodynamics requires that the heat Q added to a
system less the work W done by the system must equal the change in
energy E of the system. Stated another way, the rate of heat transfer
dQ/dt to the system minus the rate of work done dW/drt by the system
equals the rate of change of energy dE/dt in the system, which leads to
the system equation
dE_dQ_
dW
‘dt
dt *
dt
(2.14)
The directions of energy flow indicated in the above statement are
considered positive and dictate the sign convention. The work term
is frequently given the opposite sign in fan engineering, as noted later.
Assuming that electrical, magnetic, chemical, nuclear, and surface
tension effects are negligible,
Vv?
E=U+m
5)
Ree
(2.15)
where U is the internal energy, mV7/2 is the kinetic energy, and gmZ
is the potential energy of position. The corresponding control volume
equation states that the rate of heat transfer to the system minus the
rate of work done by the system must equal the net rate of energy
crossing the control surface plus the rate of energy accumulation in
the control volume, or
“hOGA
apn
soz,
shee
CS.
8
a {ffcot”
(2.16)
CV.
where e is the energy per unit mass or specific energy and is equal to
u+ V’/2+ gZ. It is usual to separate the rate of work done into two
parts, the rate of shaft work dW,/dt and the rate of flow work at the
control surface ffp V-dA, wherep is the pressure, resulting in
c.S.
S.
dQ
dW,
Sens
soy.
o
reas
— [[rrat=
| eoraa+
aff] 04”
CS.
Cade
CV.
(2.17)
This equation, written in integral form with some vector notation, is
sufficiently general to cover three-dimensional flow that Is nonuniform,
unsteady, and compressible, as well as the gravitational and frictional
FAN ENGINEERING — BUFFALO FORGE COMPANY
2-8
effects on the flow. Assuming steady flow and substituting for e results in
dQ
dW, =
ees
dtd
V?
-P + y+ +
+47
8Z)pV-dA.
IG Bee
Malia )e
(2.18)
c.S.
Assuming one-dimensional steady flow and negligible variations in Z
over the entrance and exit areas yields
dQ
dt
dW,
=
dt
P2
Ferme
vy
ging
395 =
Zo
2V2.A
8 )e
:
=a
P1
Vi
= Se hy Ae ==
5 FF eZ)
ViA,.
iA\
(2.19)
Dividing by the mass flow rate and rearranging gives
Pi
ra ela abet
5 DEAL
EPs
I Se
aT
Var
5 + gZ2 + Ws. (2.20)
Equation 2.20 is useful and relatively simple but does have restrictions. First, it assumes that the flow is steady, which may not always
be the case. And second, it is based on one-dimensional
flow, which
means that the proper average values across the section must be used
for each term if the flow is nonuniform. The ge
averages for
the flow work (sometimes called pressure energy), for the internal
energy, and for the potential energy terms are found by using volume-
flow-weighted-average values of pressure and density and mass-flowweighted-average values of internal energy and elevation. Since the
area-weighted-average velocity is appropriate when using the onedimensional continuity equation for nonuniform flows, it would be
desirable to use the same average in the one-dimensional general
energy equation. However, the use of area-weighted average values
for velocity does not yield the proper average kinetic energy terms.
Kinetic energy correction factors’ must, therefore, be applied to each
of the kinetic energy terms to correct for this difference. The effect of
these factors may or may not be significant, depending on the extent
to which the flow is uniform.
‘Grouping the flow work term with the energy terms, as is done in Equation 2.18, has led to the
concept of pressure energy. This concept is not theoretically proper because there is no stored
energy associated with pressure. Nevertheless, the expression is used and does not cause any difficulties in practice.
*See the following section.
CHAPTER 2 — FLUID FLOW
2-9
The equations in this section are dimensionally consistent only if
the dimensions used are force, length, and time or, alternatively, mass,
length, and time. If dimensions are used for both force and mass, each
mass term must be divided by the appropriate conversion factor g-.
Mass is included in the kinetic and potential energy terms. If heat is
used as a dimension, each heat term must be multiplied by the appropriate value of J, the mechanical equivalent of heat. The internal
energy and heat transfer terms are frequently given dimensions of heat.
The general energy equation will be examined further in the sections for incompressible and compressible flow situations.
Nonuniform-Velocity Correction Factors
When the velocity across a section is nonuniform, the area-weighted
average velocity can be used to determine kinetic energy or momentum only if an appropriate correction factor is applied. The kinetic
energy correction factor is usually designated a, and the momentum
correction factor is usually designated 8. Neither factor can be less
than unity, but both factors do approach unity in highly turbulent
flows and, therefore, are frequently ignored in fan engineering.
The
kinetic energy factor is
|
i VidA
ees eee 48
V°A
(2.21)
and the momentum factor is
1 Pies
aka
(2.22)
where V is the local velocity, V is the area-weighted average velocity,
and A is the area.
Specific Energy, Head, and Pressure
Equation 2.20, the general energy equation, is written so that each
term has dimensions of specific energy or energy per unit mass (or
work per unit mass). While these are the most convenient dimensions
for deriving the general energy equation, they are not the usual ones
used in either hydraulics or fan engineering. In hydraulics, head is
usually used instead of specific energy. Head can be obtained from
specific energy by dividing by g, the acceleration due to gravity.
However, heads are seldom used in fan engineering for the following
reasons. First, the units of head are, in SI, the meter of fluid or, in
U.S. customary units, the foot of fluid; this leads to large numerical
FAN ENGINEERING — BUFFALO FORGE COMPANY
2-10
nn
_—_$—$————————
values when air is the fluid. And second, it is difficult to directly
measure heads in air. Therefore, the term usually used in fan engineering is pressure instead of specific energy. Pressure can be obtained
from specific energy by multiplying by the mass density of the fluid.
The usual units of pressure are the pascal in SI and the inch water
gage in U.S. customary units.
Each term in Equation 2.20 can be associated with a particular
kind of energy whether expressed as specific energy, head, or pressure.
The total energy at a section is the sum of the flow work and the
internal, kinetic, and potential energies at that point. The total head
or total pressure at a section is the sum of the corresponding heads
or pressures. Not all of these terms are named, as will be discussed
in the following sections. Some of the terms may be dropped or combined with others to make a new term.
Incompressible-Flow Energy Equations
The general energy equation can be rewritten for steady, one-dimensional incompressible flow as
P2— Pi
VE
avy — aVy fos
p
28
ria
&c
vn —
q)J
(2.23)
where all terms have dimensions of specific energy. The shaft work
term in Equation 2.20 represents the work that could be done by the
fluid in a turbine, and this turbine work is considered positive. In
fan engineering it is convenient to consider the shaft work done on
the fluid (or fan work) as positive, so the sign has been reversed and
the symbol changed to yr. The internal energy and heat transfer
terms, when combined as shown, represent the conversion of mechanical energy into thermal energy for incompressible flow. This term can
be considered the loss of mechanical energy since the heat transfer
and the increase in internal energy are not mechanically useful under
the incompressible assumption. For simplicity, the kinetic energy factors are assumed to be equal to unity in the following discussion.
This and the assumption of steady one-dimensional flow inherent in
Equation 2.23 limit the applicability of the resulting equations.
Dividing Equation 2.23 by g/g. changes the dimensions of each
term to energy per unit weight, or head, and gives
HrIe =
Pima Pi
y
-
Vy —
2g
Ve
am
V4)
Zaieig Hy-2.
(2.24)
The flow work or pressure terms now contain y, the specific weight
of the fluid, and are called pressure heads. The kinetic energy terms
are called velocity heads. And the potential energy terms are called
elevation heads. The loss term is called the head loss term, and it
CHAPTER
2 — FLUID FLOW
2-11
contains all of the losses between / and 2 including the losses in any
fans between those points. The shaft work term is the gross fan head
if the fan losses are left in the head loss term. However, the shaft
work term is the net fan head if the fan losses are subtracted from
the head losses. Heads are not normally used in fan engineering, but
there is some tendency to call pressures “heads,” and vice versa.
Multiplying Equation 2.23 by p changes the dimensions
term to energy per unit volume, or pressure, and gives
PrF=(p2-
pi) +
Vey — VPeet pg(Z2
Z2-Z 2 i
p(V2
28«
&e
of each
ed
(2.25)
The flow work or pressure terms are called pressures. The kinetic
energy terms are called velocity pressures, and the potential energy
terms are called elevation pressures. The loss term is called the pressure loss, and it contains all of the losses between / and 2 including
the losses in any fans between those points. The shaft work term is
the gross fan pressure if the fan losses are left in the pressure loss
term. But the shaft work term is the net fan pressure if the fan losses
are subtracted from the pressure losses.
This last equation can be expressed in terms of gage static pressure
Ps, barometric pressure pz, velocity pressure py, elevation pressure pz,
fan pressure pr, and pressure losses py1-2.
Pr= (ps2 — psi) + (par — Pai) + (pv2 — pri) + (p22 — pa) +pri-2
(2.26)
The sum of the static, barometric, velocity, and elevation pressures
at a point is the total pressure at that point. Often in fan engineering,
the difference in elevation
between
points / and 2 is very small, so
the barometric and elevation terms are dropped and the sum of the
static pressure and the velocity pressure is called the total pressure.
Regardless of whether or not terms are dropped, the fan pressure pr,
the pressure losses Pzi-2, and the total pressures pr; and pr are related
as follows:
Dr= (pr — pr) + pu-2-
(2.27)
This equation will provide the basis for various discussions relating
to fan performance and system performance. Remember, however, that
this equation is based on incompressible, steady, one-dimensional
flow with unity kinetic energy factors. It is also based on negligible
differences in elevation whenever barometric and elevation terms are
omitted. And there can be exceptions to any of these conditions in
fan engineering. Differences in elevation are not negligible when there
is a stack effect.
FAN ENGINEERING
2-12
Table 2.1.
— BUFFALO FORGE COMPANY
Velocities of Dry Air for Various Velocity Pressures
At 70°F and 29.92 in. Hg Barometer
In fpm
Table 2.2
Velocities of Dry Air for Various Velocity Pressures
At Various Temperatures and 29.92 in. Hg Barometer
In fpm
Temperature °F
650°
|
<2
3
4
5
1833
2592
3175
3666
4099
6
|
8
9
4490
4850
5185
5500
1.00
0
2
1.25
1.50
5
1.75
7
5797
6481
7100
7669
2.00
0
Y4
2.25
5
2.50
7]
aks
8198
8696
9166
9613
3.00
0
0
4.00
5.00
0
0
6.00
10040
11590
12960
14200
CHAPTER 2 — FLUID FLOW
2-13
For incompressible flow, the velocity pressure, density, and velocity
are related as indicated by
2
Py
eee
Cea
=
and
V=\/2g8-Cppv/p.
(2.28)
In SI units,py is in Pa, p is in kg/m’, V is in m/s, g- is 1.0 m-kg/N°s’,
and
| Pa=1N/m’,so
re
Uae
"4
or
re
cP) Pe
(2.29)
In U.S. customary units, py is in in. wg, p is in lbm/ft’, V is in fpm,
gis 32.174 ft-lbm/Ib-s’, and | in. wg = 5.193 lb/ft”, so
y
Vays
Ppv= o( a7)
and
A
V=1097\/py/p.
(2.30)
s 4005\/pr.
(2.31)
For standard air, p is 0.075 lbm/ft’, so
By (Zoos)
an
pr=
and
V=
This indicates that for standard air a velocity pressure of one-inch
water gage corresponds to 4005 feet per minute, and vice versa.
Numerous other solutions of this equation are given in Table 2.1.
Table 2.2 gives velocities for various combinations of velocity pressure
and temperature.
Another interesting value is 69.24, the number of ft of standard air
equivalent to | in. wg.
The useful power & delivered by a fan to an incompressible fluid
can be defined using either the net fan work yr, the net fan head Hr,
or the net fan pressure
pr, by means of
Ls vem
=
Hew
a
prO
aCe ana me IGE
(2.32)
where m is the mass flow rate, w is the weight flow rate, and Q is the
volume flow rate through the fan. The value of the constant Cm, Cw,
or Co depends on the units used, as indicated in Table 2.3. In fan
engineering, this useful power has been called the air horsepower or,
more generally, the air power. It is the minimum power required to
move air at the specified rate against the specified resistance and can
be considered the output power of a fan for those conditions. (Note
that density does not appear as a variable in any of the expressions
for air power.) The air power &, divided by the shaft power A
2-14
FAN ENGINEERING
— BUFFALO FORGE COMPANY
gives the incompressible flow efficiency n. See Equation
comparisons with compressible flow efficiencies.
Table 2.3.
Example 2.1
2.42 for
Units and Values for Equation 2.32
Incompressible Flow — Pressure, Power, and Efficiency
Given the diagram and information below, find the net fan pressure,
the velocity pressure at 4, the air power, and the efficiency.
Pss = Pso = O in. weg,
V; =
Vr =
Z1=
22=23=24=25=
Z6= ft,
f=
Vs =
2000
fpm,
Vs —
Ve =
0 fpm,
Pis-\ = Sin. wg, pr2-6 = Sin. weg,
P= 007s lomi it,
Q = 1000 cfm, and
2p =
np:
Using Equations 2.25, 2.30, and 2.32 with Table 2.3:
Pr = (Po— ps) +
OVE Ve)
oa
pr=—0+0+0+5+
5=
=
Vie\
pv4s = o( ae)
-
paler res
ais eet
;
: at DESI
10in. wg,
2000\? _
= 0.095 (a7
= 0.25 in. wg,
EEGs
CHAPTER 2 — FLUID FLOW
2-15
Bp — P#Q
_ 10XOy1000a ad 1.57 hp, and
Gs
jog aa = 0.786
FA,
2.0
“i
P, can also be determined from m and Yr:
pO _ 0.075X 1000
m=
ivi
Cpr
Vr=
3
Biveit
ga
60
=
Cee
S193 10
9075
1692
ssi
G25.
=
1.25 lbm/s,
092 ftlb/Ibm, and
Oe,
where C, is from Table 2.4.
Compressible-Flow Energy Equations
_ The general energy equation can be rewritten for steady, one-dimensional compressible flow as
7p:
Ey , g(Z2— Zi)
(G+) ysgq)+ aVe—aVi
(5, t w2/)eat
y=
(2.33)
where all the terms have the dimensions of specific energy. As in the
previous section, the sign on the work term has been reversed to
make fan work positive. Shaft work can be determined from this
equation if states / and 2 are defined and if the heat transfer from the
surroundings can be determined. If so, it might be appropriate to
combine the pressure and internal energy terms into enthalpy terms.
The terms of Equation 2.33 cannot be transformed into pressure
terms simply by multiplying by the density, as in the incompressible
case of the preceding section, because the density varies. Nevertheless,
pressure terms are usually preferred in fan engineering. It will be
necessary to use approximations if pressures are to be used for compressible flow. Suitable approximations can be obtained in various
ways including the use of a mean density and assumptions about the
process. Some idealized processes are examined below.
There are various thermodynamic processes that can be described
by the expression py’ = constant where p is the pressure, v is the
specific volume, and x is an exponent that depends on the process.
2-16
FAN ENGINEERING — BUFFALO FORGE COMPANY
For the isochoric or constant density process, x = °°. This process
can also be called isometric or constant volume. For an isobaric or
constant pressure process, x = 0. A constant-temperature or isothermal process has x = /. An isentropic process has x = y, where y is
the ratio of specific heats for the gas undergoing the process. This
constant entropy process is reversible and adiabatic; that is, there is
no friction and no heat transfer. A polytropic process can have any
other positive exponent n. Many actual processes can be approxi-
mated by one or more of these mathematically simple processes. In
addition,.these processes can provide standards of comparison for
an actual process.
Although the derivation will not be given here, Equation 2.33 can
be rewritten as below for a reversible process that follows py’ =
constant.
ve
fe a2Vy — aVi sf (Zora 4h)
28
kc
= Sale)
c=
(2.34)
This is reducible to the following for frictionless incompressible flow:
P2—Pi
Vee
ee aVs — a Vi i (ZZ)
p
28
;
Be
(2.35)
The reversible compressible flow case can be expressed in a similar
way by incorporating a compressibility factor K,
Ye
(pP2 rs Pi)Kp
ne Q2 Vy a
ey
28
OU} V; x 2(Z2
am Z1)
Be
(2.36)
where
for reversible isothermal processes,
saw!
oa
a
(2.37)
ay,
(P2
Veoal
Pi
=!
2 iat
for isentropic processes
(a 7 ')
ee
CHAPTER
2 — FLUID FLOW
4
Pp?
nal
Pi
ne /
2-17
?
for reversible polytropic
a,
processes,
ms
(2.39)
K, = | for reversible isochoric processes, and
K, = 0 for reversible isobaric processes.
Note that p,/K, can be considered a mean density.
The shaft work yr obtained from Equations 2.34-2.36 is the work
required to produce flow from / to 2 for an ideal reversible process.
If the fan inlet is at / and the fan outlet is at 2, yr can be considered
the ideal work output of the fan. This work output will vary with the
process as illustrated in Example 2.2. Losses in the fan are not considered since the process is reversible in each case, but an appropriate
amount of heat transfer, depending on the process, is considered.
Multiplying Equation 2.34 by the mass flow rate m yields the ideal
power & for the reversible process pv* = constant:
“Serra
(Coate
c
m
a2V2e
—
a
Vi
28
a
fl VL —
Si)
:
&e
(2.40)
In terms ofthe pressure difference and Kp,
(p> — p1) O1Kp
F, = eee
Ge
+m
~ Pobre —avi’
oe:
| g(Z2.—Z:)
ar
=
.
(2.41)
Both Equations 2.40 and 2.41 contain the volumetric flow rate 01 at
section /. Refer to Table 2.3 for values of Cg for various units.
The efficiency 7 of an actual process can be defined as the ideal
power & divided by the shaft power &, or
1p
(2.42)
Any process can be chosen as the standard of comparison. Using the
isothermal process leads to the isothermal efficiency. Similarly, the
2-18
FAN ENGINEERING — BUFFALO FORGE COMPANY
polytropic process yields the polytropic efficiency. When the isentropic process is used, the efficiency can be called the isentropic or
adiabatic efficiency. And using the isochoric process leads to the isochoric efficiency, which has the same value as the incompressible
flow efficiency.
Example 2.2.
Given
Compressible Flow — Work, Power, and Efficiency
the diagram
and
information
below,
find the work
output,
ideal power, and efficiency for reversible isochoric, isentropic, and
reversible isothermal processes in the fan. Assume that differences in
kinetic and potential energies are negligible.
A=?
Pi: =
hp,
408 in. wg abs.,p2 = 418 in. wg abs.,
“. pr — p: = 10 in. wg or 51.9 Ib/ ft’,
p: = 0.075 lbm/ ft’, and
m = 1.25 lbm/s -. Q, = 1000 cfm.
Using Equations 2.36, 2.41, 2.42, 2.37, and 2.38:
(p2—
ve=
a
pi) Kp = 51.9Kp
07S
(p2—Pi)OiKp
(La)
CY eS
Ge
Co
n
we
Pp =
5
,an
in(
=
(eet
= 092 Ke ft'lb/ Ibm,
— NES
10 X 1000K.
ie
ae
=
-)
P\
ya
ee
1.57 Kphp,
ae
rain
P2
Vinal.
Pi
Y
|
or
Process
reversible isochoric
isentropic
reversible isothermal
1.0
0.9914
0.9
692 ft-lb/lbm
686 ft-lb/lbm
684 ft-lb/Ibm
1.57 hp
1.56 hp
1.55 hp
11.9%
CHAPTER 2 — FLUID FLOW
oS Eee
SE EE SE EE EE EEE
ee
eee
2-19
ee
Mach Number
The ratio of the stream velocity V to the sonic velocity ¢ is called
the Mach number Ma.
wel
ta=-,,
(2.43)
The Mach number is also a measure of the ratio of the inertial force
to the elastic force and a measure of the kinetic energy to the internal
energy, at a point.
Dimensional analyses’ indicate and experimental data demonstrate
that Mach number is an important natural physical variable in compressible flow situations. Refer to the chapter on fan laws for a discussion of dynamic similarity and Mach number effects on fan law
predictions.
The velocity of sound c in a perfect gas is a function of the ratio
of specific heats +y and the state ofthe gas, or
aS
LN
2eWP
15e
Vee RT
(2.44)
wherep is the pressure, p is the density, T is the absolute temperature,
and R is the gas constant. The speed of sound in air is tabulated for
various conditions in Table 1.2. While the sonic velocity is of the
order of 1100 fps or 335 m/s for air, it is four times higher in hydrogen and about five times higher in most common liquids. It is only
about one-fourth of those values in very-high-molecular-weight gases.
Temperature Rise Due to Compression
The temperature at any state can be calculated
from other state
properties using the equation of state as discussed in Chapter |. The
temperature ratio for any two states can be calculated from the pressure ratio using the equation for the particular process if the process
is known. The temperature rise 72 — 7, experienced by a gas during
compression can be calculated using the absolute inlet temperature
T;, the absolute pressure ratio p2/pi, and
P2
Pee ome Th (é
Xai
ae
ee
‘|
Oe
for any reversible process that follows pv" = constant.
The temperature rise can also be expressed in terms of the pressure
rise p2 — pi. This is facilitated by using the compressibility coefficient
'See Appendix A fora discussion of dimensional analysis.
2-20
FAN ENGINEERING
— BUFFALO FORGE COMPANY
K,, which was introduced together with the exponent x in the discussion of the energy equation for compressible flow, and
Bh
Th
Nome,
T= 5 (P2— PvKo( x a
(2.46)
For a reversible isothermal process, x = / and 72 — T, = 0.
For a reversible adiabatic or isentropic process, x = y and
—
h-Th=
Ti
Pi (p2
ee
P)Ko(
ay
~) =
(p2 — P1) KpCp
y
Picpd =
(2.47)
The second equality includes the inlet density p,, the specific heat cp,
and two constants, C, and J, whose values can be determined from
Table 2.4.
For a reversible polytropic process, x = n and
_
Ces
“—)=
Pi We
pidky(
m
.
(p2 — Pi) KpCp
PicpJ Np
(2.48)
where 7p, the polytropic efficiency, is a function of y and n and can
be calculated from
ee
oa
(2.49)
Note that as m approaches infinity (which corresponds to the constant
density or isochoric case) the polytropic efficiency approaches a
constant value, e.g. 0.2857 for air. Experience indicates that the temperature rise in a fan is better approximated by using a value for the
polytropic efficiency that varies with the degree of perfection in the
design. This is still another illustration of the need to examine carefully the effects of simplifying assumptions. The assumption of a
constant density process may serve well in some cases, but it cannot
be used when calculating temperature rise.
Temperature rise can also be calculated from the shaft power Ge
the rate of heat transfer Qy to the fluid, and the mass
flow rate m
as follows
Tr
T=
using units and values from Table 2.4.
cpmJ
(2.50)
CHAPTER 2 — FLUID FLOW
Table 2.4
Units and Values for Equations 2.46-2.50
kg/m3
Ibm/ft3
Example 2.3
2-21
J/kg
Btu/lbm
Temperature Rise
Given the data below, find the temperature rise.
pi = 0.075 lbm/ft® = 1.2 kg/m’,
P2— pi = 10 in. wg = 2.4836 kPa,
K, = 0.9923 and np = 0.780 for a polytropic process,
P= 2.0 hp = 1.4914 kw,
m = 1.25 lbm/s = 0.5670 kg/s, and
Cp = 0.24 Btu/Ilbm-°R = 1005 J/kg: K.
Using Equation 2.48:
ee
Ore KG
eC
Sa
me
10 X 0.9923 X 5.193
=
_2.4836 X 0.9923 X 1000
LD 1005
10 X0.780)
|
007s
0
8 XO
and
ee
_ (a= pi)KpCp _
peop)
2
ZH
Using Equation 2.50 and assuming that On = 0:
BP.Cn+ Ond
mee
cpmJ
BP.Cm+ Ond
EOE
cpmJ
h—T%=
ci
2.0 X 550+ 0
= 4.71
°F and
024195 K 7782
1.4914X 1000
+0
=) 7)(YG,
1005 X 0.5670 X 1.0
The results of using Equations 2.48 and 2.50 are substantially equivalent, although there are small differences due to rounding off. However, the assumption that Qy = 0 may not be appropriate for other
cases, e.g., when calculating temperature rise for a fan at shut-off.
2-22
oe
BUFFALO FORGE COMPANY
— ING
FAN ENGINEER
Stagnation Properties
When a fluid moving along a streamline is brought to rest, an increase in temperature, pressure, and density results. The stagnation
properties can be determined by considering what happens at the
stagnation point. Assuming an adiabatic process, the stagnation temperature 7, can be determined from the free-stream temperature 7o,
the free-stream velocity %, and the specific heat cp using
pace
Decca
(2.51)
Assuming a reversible adiabatic or isentropic process, the stagnation pressure
p; can be determined from the free-stream pressure Po,
the free-stream Mach number Mao, and the ratio of specific heats y
using
esel
=
po= pol1+ Mad] —
(2.52)
This can also be expressed in terms of the free-stream velocity Vo and
the free-stream density po using
ae
a
Van
[1+
Mao
Mao?
i
Oia24
+].
(2.53)
Note that the stagnation pressure
p; is the sum of the static pressure
Po and a term that is reducible to the velocity pressure for incompressible flow when the Mach number is very small.
The stagnation density can be calculated from the stagnation pressure and stagnation temperature using
cco
Pr
ne
(2.54)
where R is the specific gas constant.
Radial and Vortex Flow
There are several flow situations that can be classified as radial
flow or vortex flow. These cases have practical applications in fan
design and other aspects of fluid flow.
Ideally, in the radial flow of air through a device such as that indi-
CHAPTER
2 — FLUID FLOW
cated in Figure 2.1, the radial velocity
varies inversely with the radius R:
2-23
V, assuming uniform flow,
Vale
Re
fon aa
(2.55)
Disregarding friction, the conversion of velocity pressure into static
pressure in a radial diffuser of this type can be determined from
psi
=
TRY
pn[t Ea;
(2.56)
This is equal to the difference in velocity pressures.
The flow at AA must be essentially radial to prevent separation
from the guiding surfaces. Equation 2.56 applies only to frictionless
flow without separation. The flow will be without separation only if
the dimensions are approximately as shown in Figure 2.1. When the
discharge is into the atmosphere, the average pressure within the
radial diffuser will be less than the atmospheric pressure, so that the
confining walls will tend to approach each other in spite of the impingement of the jet.
D
8
A—
SS
Aart
(Sco)
?.
Figure 2.1
Confined Radial Flow
A free jet impinging against a flat plate has the velocity pattern
indicated in Figure 2.2. The central portion slows as it approaches
the plate, producing a corresponding increase in static pressure. This
is followed by a reconversion of static pressure to velocity pressure,
2-24
FAN ENGINEERING — BUFFALO FORGE COMPANY
ee
which in the frictionless case would reaccelerate the flow to the original velocity. This type of flow, when bounded by walls approximating the natural flow boundaries, is an efficient means of turning an
air stream within a very short distance.
1:0,
HOS
Oi
01010
10 10
6 96 96
96
96
82
en
$7
60
O==G6
Figure 2.2.
37,
30
37
60
=
Impingement of a Free Jet on a Flat Plate
The term vortex flow is used to describe the motion of a fluid whenever a whirl exists. A circular vortex is one without a radial component; a spiral vortex is one that has a radial component. The radial
component ofa spiral vortex can be directed inward or outward.
In a free circular vortex, the velocity varies inversely with the
radius according to Equation 2.55, just as for radial flow. If there
were no friction, the velocity at the center would become infinitely
great. In a free spiral vortex, both the radial and tangential compo-
nents of the velocity vary inversely with the radius. Various types of
vortex flow occur in nature as well as in certain fan applications.
Free spiral vortex conditions are approached in the scroll-shaped
housing of centrifugal fans and also in cyclone collectors. The velocity-radius relation, as expressed in Equation 2.55, can be greatly
modified by friction and other forces. The extent of this modification
can be appreciated by noting that, in a frictionless straight-blade
centrifugal fan that produces one kind of forced vortex, the tangential velocity varies directly with the radius, as indicated by
V,
VY
R;
Rr’
(2.57)
The change in static pressure due to such a change in tangential
velocity can be determined from
RY
Aps2-1 = pv [:a (<a) |
:
(2.58)
CHAPTER
2 — FLUID FLOW
2-25
Effects of Viscosity
The flow of any real fluid is resisted by friction forces that arise
because of the viscosity of the fluid. These forces are generated within the fluid wherever there are velocity gradients. They are transmitted
between the fluid and any solid boundary by a layer of fluid that
becomes attached to the boundary. Forces are transmitted between
this fluid and any other fluid by a mixing layer of entrained fluid.
The acceleration of a fluid is also resisted by inertia forces. If flow is
to take place, work must be done to overcome these resistances. The
energy required can be transferred to the fluid by a fan or by some
other means. In a fan system, this mechanical energy is delivered to
the air by the fan (or fans) and that portion which overcomes friction
is gradually converted into thermal energy as resistance is encountered
throughout the system.
Flow Regimes and Boundary Layers
Fluid flow can be laminar, turbulent, or transitional (in a transition
state between these two regimes). Laminar flow, as the name implies,
is considered to proceed in layers between which there is relative sliding motion. It is characterized by the absence of local macroscopic
velocity fluctuations. Shearing stresses are transmitted essentially by
intermolecular forces. Turbulent flow exhibits relatively large-scale
local velocity fluctuations. This results in eddying, mixing, and transport of momentum, which becomes the main shearing-force-transmission mechanism between adjacent portions ofthe flowing fluid.
The presence of a boundary surface in a flowing fluid produces
various phenomena. As the fluid attaches itself to the boundary,
gradually increasing amounts are retarded forming a boundary layer
whose thickness increases in the direction of flow. The flow in this
layer can be laminar or turbulent, depending on the Reynolds number
of the main flow and on the disturbances present. If the boundary is
a closed, uniform conduit of sufficient length, the flow will eventually
become established; that is, the velocity profile will be the same for
all succeeding sections. This condition will not occur if the conduit is
nonuniform or strongly curved. Similarly, with external flow around
an immersed blunt body, the boundary layer may not have sufficient
kinetic energy to overcome the resulting pressure gradients and other
resistances.
In this case, the flow will separate,
causing return
flow
and eddies that form and reform and are swept out into the main
stream.
Unestablished flow may persist for 50 diameters of straight conduit
after a disturbance. With a smooth entrance, flow may be established
in 20 diameters or less, depending on Reynolds number.
Separation does not occur in accelerated flow. In contrast, decelerated flow does promote separation. Since separation leads to eddy
2-26
FAN ENGINEERING — BUFFALO FORGE COMPANY
formation and, ultimately, to energy dissipation, accelerated flow is
usually less troublesome and more efficient than decelerated flow.
Another phenomenon due to the presence of boundaries is secondary flow. This can occur in either unestablished or established flow.
It is the flow-within-a-flow that occurs, for example, at bends or
discontinuities.
Dynamic and Kinematic Viscosity
Dynamic viscosity p, also called absolute viscosity or coefficient
of viscosity, is that property of a fluid which resists the movement
of one layer over another. Mathematically, it is the proportionality
factor relating shear stress r and velocity gradient du/dy (incremental
velocity per incremental distance), or
2
ee
aw
ae
(2.59)
Kinematic viscosity v is absolute viscosity divided by mass density
p, or
Uap
(2.60)
The dimensions' of kinematic viscosity are L’ /T (the dimensions
of kinematics). The dimensions of dynamic viscosity are FT/L’ or
M/TL (the dimensions of dynamics). Various units of measurement”
are used for viscosity, some with special names like poises and stokes.
In addition, the kinematic viscosities of liquids are sometimes reported
as the measurement
of a particular viscosimeter,
e.g. 100 SSU
or 100
seconds efflux time on the Saybolt Universal viscosimeter. Calibration data like that in Figure 2.7 are needed to convert efflux time to
kinematic viscosity.
As illustrated in Figures 2.3 through 2.6, the viscosity of a gas or
a vapor increases with increasing temperature, whereas the viscosity
of a liquid decreases with increasing temperature.
Reynolds Number
The Reynolds number Re at a point in a fluid stream is the ratio
of the inertia force to the viscous shearing force acting on an element
of fluid at that point. It is the dimensionless combination of some
characteristic linear dimension of the boundary surface D, the relative velocity V of the element and that surface, and the physical
properties of the fluid as represented by the absolute viscosity 4 and
See Appendix A for a discussion of dimensions.
“See Appendix C for conversion factors for units.
CHAPTER 2 — FLUID FLOW
0
50
100
150
2-27
TEMPERATURE — °C
200 250 300 350
400
aS
FLUE GAS TYPICAL
450
500
12 g
HYOROGEN
10=
3 =
FS SZ
DOWTHERM VAPOR
40
DYNAMIC
VISCOSITY
(x)
Example: Air at 70°F, 2= 122X107 tbm/it-s
0
100
Figure 2.3.
200
300
400 500
600
TEMPERATURE -
700
800
900
Dynamic Viscosities of Common
1000
Gases
Adapted from the data of G.A. Hawkins, H.L. Solberg, and A.A. Potter: “The Viscosity of Superheated Steam,” Trans.
AMSE, vol. 62, pp. 677-688, 1940, and that of SAE: Aeronautical Information Report No. 24, 1952.
-40
TEMPERATURE — °C
50
0
100
150
140
20
‘o 130
2
&, ve
=
CO2 590 PS!
ae
= 100
co A
18 »
a
oF]
FREON 22
e 110
ie
=
=
Fa
ates
290
So
3.
2
Vs
eee
= 70
z
3B 60
ae=
/ BUTANE
5
ere
0
?
8
etal
“0
Figure 2.4
0
50
Freon-12 at 60°C, =
13.5 Pa
100
150
TEMPERATURE -
200
250
300
6
Dynamic Viscosities of Refrigerant Vapors
Adapted from the data of J.C. Reed and E.E. Ambrosius: “Viscosity of Refrigerants,” Heating,
Piping and Air Conditioning, June, 1930, pp. 455-461, and that of A.F. Benning and W.H.
Markwood, Jr: “The Viscosities of ‘Freon Refrigerants, ” Journal of the ASRE in Refrigerating
Engineering, April, 1939, pp. 243-247.
2-28
FAN ENGINEERING — BUFFALO FORGE COMPANY
a
a
-25
0
25
TEMPERATURE — °C
50
75
100)
sSS
125,715
50.0
40.0
30.0
25.0
20.0
15.0
10.0
8.0
6.0 0a
=
g
Z
4.0
=
5=
5
23.5% SODIUM
lee2
CHLORIDE BRINE
1.18 SP. GR. @ 50°F
2
=
2
a
20
== 001
is
= 0009
S 0008
0007
KEROSENE 0.81 SP. GR.
@ 60°F
He
0005
0004
1.0
8
6
0003
4
0002
0.702 SP. GR.
@ 60°F
50
0
50
Figure 2.5
3
2
100
150
TEMPERATURE — °F
3
=
a
200
250
Dynamic Viscosities of Liquids
Adapted from the data of SAE: Aeronautical Information Report No. 24, 1952.
300
ee
2
=
==
a
a
-10
:
i
a),
CHAPTER 2 — FLUID FLOW
ea
eee
{i
2-29
eae
TEMPERATURE - °C
10 20 30 50 70 100
200
300
500
005
(50
40
003
cy
S
30
ow
002
20
001
10
0007
0005
&
=
u
:4
SY
S
Sy)
Ss
0003
a
S
we
3
Kas”
ger
0002
2
0001
00007
KINEMATIC
VISCOSITY
ft2/s
(v)
-
u
00003
i
00002
2
10°
VISCOSIT
KINEMATI
mm2/s
(v)
x-
00005
00001
.000007
ut
000005
-000004
eG
at70°F,1atm, v = 000163 ft?/s
Examp
Airle:
15 20
Figure 2.6
30 40
60 80100
200
TEMPERATURE — °F
300
500
.03
1000
Kinematic Viscosities of Gases and Liquids
Adapted from the data of SAE: Aeronautical Information Report No. 24, 1952.
5)
un
FAN ENGINEERING — BUFFALO FORGE COMPANY
2-30
Tee
ENGLER DEGREES
20 ae
eee oePIO
oe
ee
mm’/s
VISCOSI
KINEMAT
—
ft’/s
VISCOSITY
KINEMATIC
—
PON
Ww
=
"19°20 30° 50
70100
200300 500 1000 2000
5000 10.000
TIME — SECONDS
Figure 2.7
Conversions from Efflux Time to Kinematic Viscosity
Adapted from the data of TEMA: Standards of the Tubular Exchanger Manufacturers Association,
TEMA, 1959.
the mass density p or the kinematic viscosity v:
= Dyp
Re=
jp
py
~
ip
=
(2.61)
Some characteristic linear dimensions D are: the diameter of the
opening for orifices, the diameter of the exit opening for nozzles,
the inside diameter for a round conduit, and the equivalent diameter
based on the same hydraulic radius for a rectangular duct.
In all these devices, the local Reynolds number across a section
varies from point to point because of the velocity variation. Therefore, it is convenient to use a Reynolds number based on the mean
velocity Vin.
Dimensional analyses’ indicate, and experimental data demonstrate,
that Reynolds number is an important, natural physical variable in
various flow situations. Refer to the chapter on fan laws for a discussion of dynamic similarity and Reynolds-number effects on fan law
"See Appendix A for a discussion of dimensional analysis.
CHAPTER 2 — FLUID FLOW
2-31
predictions. Refer also to the particle dynamics chapter for information on the effects of Reynolds numbers on particle behavior in an
aerosol. The discussions that follow here are concerned directly with
flow in conduits, but the principles apply to many flow situations.
Absolute and Relative Roughness
Any surface, no matter how polished, has peaks and valleys. The
mean distance between these high and low points is the absolute
roughness e. Table 2.5 lists several roughness conditions with typical
surfaces and corresponding absolute roughnesses expressed in feet.
The relative roughness e/D of the surface in a conduit is the absolute roughness divided by the effective diameter. Any consistent set
of units can be used.
Hydraulically, any value of relative roughness can represent either
a smooth or a rough condition depending on the Reynolds number.
A brief analysis of various flow phenomena will explain this.
It has been established that, for all but the most rarefied flow,
there is a molecular layer of fluid firmly anchored to the boundary
surfaces. In laminar flow there is a velocity gradient all across the
stream.
main
In turbulent
stream
flow there are velocity fluctuations,
the average
but in the
velocity profile in a pipe is almost
flat.
However, a turbulent boundary layer is formed across which there is
a definite velocity gradient. There may also be a very thin laminar
sublayer if the absolute roughness is small compared to the boundary
layer thickness. If such a sublayer submerges the high points of the
surface sufficiently, that is, if sublayer thickness exceeds absolute
roughness by a factor of 4, the pipe surface can be described as
hydraulically smooth.
In the wholly rough zone of turbulent flow, the condition of the surTable 2.5
Roughness Information for Various Conditions
Condition
Typical Surface
Average «
Very smooth
Drawn tubing
.000005 ft
Medium smooth | Aluminum duct'?
.00015 ft + |.00010'-.00020’
Average
Galvanized iron duct? | .0005 ft
.00045’-.00065’
Medium rough
Concrete pipe
.003 ft
001’
-.01'
.01 ft
003’ -.03’
Riveted steel pipe
Very rough
1Crimped slip joint every 3’
2Crimped slip joint every 2¥2'
3New steel pipe also typical
4n andc are for use in Equation 2.78 and may be used with any units for pz, L,
V, p, u,g, and D provided they are consistent dimensionally.
Adapted from the data of F.W. Hutchinson: “Friction Losses in Round Aluminum
ASHVE, vol. 59, 1953, pp. 127-138.
Ducts,” Trans.
2-32
FAN ENGINEERING — BUFFALO FORGE COMPANY
face can be described as hydraulically rough. The laminar sublayer
is reduced to about 1/6 or less of the absolute roughness and can be
prevented from forming at all as the roughness increases in comparison
to the boundary layer thickness.
Darcy Friction Factor
The Darcy friction factorf for flow in pipes is a dimensionless
group that relates two other dimensionless groups: the ratio of the
loss of total head between two points Hy, to the velocity head Ay, and
the ratio of the distance between those two points L and some characteristic dimension D that determines velocity.
At
‘Hy =15
a
Pressures
can be substituted
for heads when
(2.62)
the flow is considered
incompressible.
In the laminar zone,
f
64
Re
(2.63)
which appears as a Straight sloping line on the Moody Chart in
Figure 2.8. There is a critical value of Re above which laminar flow
can exist only if the flow remains essentially undisturbed. Since this
condition is quite easily upset, a dotted line is shown for Reynolds
numbers greater than 2100. This critical Reynolds number is for
conduit flow, but for other types of flow the critical values will be
different. For example, for flow between parallel plates, the critical
Reynolds number, based on the distance between plates, is approximately 900.
In the wholly rough zone,
Dee
losaay
a
(2.64)
which produces a series of straight horizontal lines in Figure 2.8. There
is a value of Re for each value of relative roughness, below which the
flow cannot be considered independent of Reynolds number. These
values are indicated by the dashed, curved line in Figure 2.8.
In the transition zone,
1
e/D
2.51
=—2]
of
Nea
CNG
Ref
(2.65)
CHAPTER
2 — FLUID FLOW
100
ears
10
080) xe©ein tere
an
00,2
050
040
=)
010
008
2.2
=e
=
\S_ 8
Cee
020
DARCY
FRICTION
FACTOR
(/) 015
2 io)wo
Sse
eer Sag foe ee AWE
ROUGH ZONE
= Se
Yn,
m7 ($$
sx Loy
hee
Soy
\
ad Dae
$$
Di
—
10°
30
40
50
10°
10°
5. 100
~
10’
REYNOLDS NUMBER Re
Figure 2.8
20
Soo, 60
.
10°
oe —
003 &
~
Ay
15
DIAMETERS
FOR
VELOCITY
ONE
HEAD
LOSS
(NV)
Moody Chart for Darcy Friction Factor
Adapted from the data of L.F. Moody: “Friction Factors for Pipe Flow,” Trans. ASME,
1944, pp. 671-684.
vol. 66, .
This is the Colebrook' equation, which is based on the research of
Nikuradse, von Karman, and others.
For hydraulically smooth pipes,
Vee 0.3164
oeRee
(2.66)
This is the Blasius formula, which can be used for Reynolds numbers
between 3000 and 10°.
Also for smooth pipes,
]
——
nit
This is the Prandtl
2,5]
= -—2log (——).
o8( Rev f
universal
(2.67)
resistance law, which can be used for
Reynolds numbers between 5 X 10° and 3.5 X 10°.
Example 2.4 illustrates the use of the Darcy friction factor in a
pressure-loss calculation.
'C.F. Colebrook,
Turbulent Flow in Pipes with Particular Reference to the Transition
Between Smooth and Rough Laws,” /CE Journal, vol. 11, 1938, pp. 133-156.
Points
2-34
FAN ENGINEERING — BUFFALO FORGE COMPANY
Example 2.4
Pressure Loss Using Re, ¢/D,f,and L/D
Given 100 ft of 12-in. diameter galvanized iron duct with 1000 cfm of
70° F air flowing, find the pressure loss.
Using Figure 2.6, Equation 2.61, and Table 2.5:
y= N63eC 10" tt 1s,
A = 0.7854 ft’ for 12-in. pipe,
V = 1000/0.7854 = 1273 fpm = 21.22 fps,
DV 2 NOPD?
SS
a
= 130200,
ROU
e = 0.0005 ft, and
-€D _ 0.0005
eaes 0.0005.
Using Figure 2.8:
f= 0.020.
Alternatively, using Equation 2.65:
etal oy
Soe
Vif
= —2 log
GL arama
BUY
Rev f
0.0005
3.7
.
wel
oe
130200\/f
ean d
f= 0.020 (computation requires an iteration procedure).
Using Equations 2.30 and 2.62:
=
YONG
Ppv= o( ae
Se
PEAS
= 0.075 (22>
PL =fEpv = 0.020
a= 0.10 in. wg and
2 0.10 = 0.20 in. wg.
CHAPTER 2 — FLUID FLOW
2-35
Pressure Losses for Duct Elements
In fan systems, the flow through each duct element (including
straight ducts, elbows, diffusers, hoods, etc.) can almost always be considered incompressible. Accordingly, the incompressible-flow energy
equation, as expressed in Equation 2.23, can be used to examine the
energy relationships for a duct element. Excluding fans as duct elements, the fan work term yr will be zero. The combined heat transfer
and internal energy term (u2 — u; — q)J can be considered the loss of
mechanical energy. Regardless of whether this equation is expressed
in terms of energy per unit mass, head, or pressure, the loss is equal
to the sum of the three remaining terms. One term results from the
change in static pressure, another from the change in velocity, and
the last from a change in elevation. In other words, the loss of mechanical energy per unit mass yzi-2 for a duct element is equal to the
change in total specific energy across that element. Similarly, the
head loss Hz-2 is equal to the change in total head. Finally, the
pressure loss pzi-2 is equal to the change in total pressure across the
element.
For most duct elements, the change in elevation between / and 2 is
negligible. For many duct elements, the velocity is sufficiently uniform
at both / and 2 to assume that the kinetic energy correction factors
a, and qa are unity. For some duct elements, the kinetic energies at /
and 2 are equal, so the loss on a pressure basis equals the change in
static pressure.
However, this is an exceptional case, and it is best to
consider any losses based on pressure to be equal to the change in
total pressure.
There are many compilations that give data for calculating losses
for duct elements. Perhaps the most complete is that of Idel’chik.'
Since it is far too extensive to repeat here, only data sufficient to
cover
most
cases,
at least
approximately,
are
given
below.
Both
ASHRAE and SMACNA have taken much of their data from this
source.
The total pressure loss for a duct element is a function of the configuration of the element and of the flow through the element. As
noted in the discussion on Darcy friction factor, certain dimensionless
groups can be used to conveniently express these relationships.
These groups include relative roughness, number of diameters, Reynolds number, and Mach number, all previously discussed. A loss
coefficient K, can be defined to relate the pressure loss pz of a duct
element and the velocity pressure pyx at some location x in that
element:
PL
K.=
"LE.
Idel’chik,
Handbook
of Hydraulic
Pyx
Resistance
(2.68)
—
Coefficients
of Local
Resistance and of
Friction, Distributed by National Technical Information Service, U.S. Department of Commerce,
Springfield, Va., AEC-TR-6630, 1966.
2-36
FAN ENGINEERING — BUFFALO FORGE COMPANY
The value of this coefficient for the different duct elements will vary
depending upon the dimensionless parameters listed above. For instance, for straight ducts,
SseperemSy5)
(2.69)
wheref is a function of Re and ¢«/D. Here, it is usually more convenient to usef and L/D directly, but for other elements that are not
so dependent on L/D, Kz is preferred.
Entrance Conditions
On entering a duct system, the air accelerates from zero velocity
in the surrounding atmosphere to the duct velocity. This process
involves the transformation of pressure energy into kinetic energy,
which means that, as the velocity pressure goes up, the static pressure
must go down. In addition, there will be a loss whose magnitude will
depend on the configuration at the entrance, and the total pressure
will also decrease. If the surrounding atmospheric pressure is taken
to be zero gage pressure, the velocity pressure in the duct will be positive, the total pressure will be negative, and the static pressure will
be even more negative. This last quantity is usually referred to as the
static suction in the duct near the entrance, or static suction, or hood
suction for short.
The loss coefficient K, for an entrance condition can be determined
from the data of Figure 2.9 and Figure 2.10. These data are based on
the duct velocity pressure py, so the total pressure loss py is
Pi= Kipw.
(2.70)
Note that the notched entry approximates a bell-mouth; apparently,
the vortex in the notch promotes smooth flow into the duct.
The curves in Figure 2.10 are based on an area ratio of 5 to |. The
peak values need not be reduced more than 4 or 5%, even for an area
ratio of 2 to |. For area ratios in these ranges, the loss around the
outer edge of the hood is quite small compared to that due to contraction in the pipe, so the addition of a flange will not materially
change the loss. Nevertheless, flanges can control the pattern of air
flow and thereby perform a very useful function.
The static suction ps can be used to determine the flow rate Q
entering a duct, by means of
=
ORK
Ps
p
(2.71)
[
th
CHAPTER 2 — FLUID FLOW
1
———————
ae
io
2-37
Re-entrant
|
Flanged
Bell-Mouthed
K. ~0.90
K. ~ 0.73
K,~0.50
K. ~ 0.82
K,~0.05
K.
~ 0.98
S Fontan
> 1
oo
—————
St
Se
MG
1
———
INotched
Converging
K.~0.05
K_= see Figure 2.10
kK. ~ 0.98
K,.= see Figure 2.10
Figure 2.9
Entrance Conditions
1.0,
0
ROUND
sats
a
SQUARE AND
ake
as
>>.
RECTANGULAR
a
=
ve
(on)
w
2
g
a
4g
(=)
iS
3
EFFECT OF THE INCLUDED ANGLE
IN UNFLANGED HOODS
5
a
20
40
60
80
100
120
=140
TOTAL INCLUDED ANGLE BETWEEN SIDES OF HOOD-DEG.
Figure 2.10
160
Coefficients for Converging Entrances (Hoods)
Adapted from data of A.D. Brandt: “Energy Losses at Suction Hoods,” Trans, ASHVE,
1946, pp. 205-236.
180
vol. 52,
2-38
FAN ENGINEERING — BUFFALO FORGE COMPANY
where C, is 1097 for U.S. customary units’ or a
for SI units, K is
the coefficient of entry from Figure 2.9 or Figure 2.10, p is the air
density, and A is the area of the duct.
If the fan is located at the entrance to a duct system, the entrance
loss becomes part of the fan loss and need not be calculated as part
of the system resistance. The exception is a fan that is rated for conditions with an inlet duct and that duct is omitted.
Example 2.5
Entrance and Exit Losses
Given a flanged entry to a 12-in. diameter duct with 1000 cfm of
standard air, find the entry loss, the static suction, the static pressure
in the duct, and the total pressure in the duct.
Pv = 0.10 in. wg (from Example 2.4)
Using Figure 2.9 and Equations 2.70 and 2.71:
K, = 0.50, Ke = 0.82,
pi = Kipv = 0.50 X 0.10 = 0.05 in. wg, and
Ps
SPO
(C.KeA)
S008 S000?
(1097 X 0.82 X 0.7854)?
= 0.15 in. wg.
The static suction is 0.15 in. wg; therefore, the static pressure in the
duct is —0.15 in. wg. The pressure loss is 0.05 in. wg; therefore, the
total pressure in the duct is 0 — 0.05 = —0.05 in. wg.
Given a 12-in. diameter duct with 1000 cfm of standard air, find the
exit loss.
pv = 0.10 in. wg (from Example 2.4)
Using Equation 2.72:
P.= pv= 0.10 in. wg.
Exit Conditions
On exiting from a duct system, the air decelerates from the duct
velocity to zero velocity in the surrounding atmosphere. This process
involves dissipation of the kinetic energy of the air stream. The static
pressure in the issuing stream will be equal to the surrounding atmospheric pressure. If the latter pressure is taken to be zero gage pressure, the total pressure at the exit will equal the velocity pressure py
at the exit, and the exit loss p, (assuming that the kinetic energy fac-
tor @ is unity) will also equal the v@ocity pressure. This is‘the same
"See Equation 2.30.
“See Equation 2.29.
CHAPTER 2 — FLUID FLOW
2-39
as saying that the loss coefficient Kz is unity, or
Pi
Kipv =
pv.
(2.72)
The kinetic energy in the issuing stream can be increased by using
a nozzle at the end of the duct. (This may be necessary to increase
the distance the stream is projected, to promote dispersion, etc.)
Energy can be conserved by using an evasé at the end of the duct.
While the evasé will introduce an additional loss of its own, it is more
than compensated by the reduction in exit loss.
Even if a fan is located at the exit from a duct system, the exit loss
should be calculated as part of the system resistance. The exception
is a fan that is rated in terms of fan static pressure. Energy can
always be conserved by using an evasé when the exit velocity is not
needed.
yr
>
—————f
Straight Duct Exit
:a
—
>
—
Nozzle Exit
Figure 2.11
Evasé
Exit Conditions
Straight Ducts
The resistance to flow through a straight duct, expressed as a pressure loss pr, can be determined using the velocity pressure py, the
length L, and the equivalent diameter D.
For any straight round duct,
Pina) eye
(2.73)
The proportionality factorf,known as the Darcy friction factor, was
previously discussed and can be determined from Figure 2.8. As
noted there, it is a function of Reynolds number and relative roughness. Since there are so many significant factors that influence duct
resistance, it is common practice to draw duct friction charts for an
average relative roughness and to apply roughness corrections if
necessary. A roughness correction chart is drawn in Figure 2.12. The
correction, as read at the right or left, should be applied as a multiplying factor to the values from the appropriate chart.
FAN ENGINEERING — BUFFALO FORGE COMPANY
2-40
VELOCITY — m/s
S)
"
oc
(Spo
Q ~—
140"
=S"S
OO!
CO
i
CHART VALUES — AVERAGE PIPE - ALL SIZES
aes
551.0 eeME DIUM SmooTH
=c
8
VERY SMooRa
J
0800
: FIGURE
2.13
FOR
FACTOR
CORREC
Aue
2
B12” 400
1.25
1.5
200
300
Figure 2.12
500
1,000
2,000
VELOCITY — fpm
5,000
10,000
Roughness Corrections for Ducts
For any straight rectangular duct,
Bey
oy
Ses
eS
The proportionality factorf’ is known as the Fanning friction factor.
It is equal to the Darcy friction factor divided by 4.
The equivalent diameter D for the same mean hydraulic radius M
is 4M. Since the mean hydraulic radius is the cross-sectional area
divided by the wetted perimeter, the equivalent diameter in terms of
duct dimensions x and y is
SAMO
4xy
Ga
2xy
(2.75)
The Darcy friction factor
f can be considered to be the number of
CHAPTER
2 — FLUID FLOW
2-41
velocity pressures lost divided by the number of diameters. Its recip-
rocal N is the number of diameters for a loss of one velocity pressure. After rewriting, Equation 2.65 becomes
tne!
VN =
e/D . 25Ix/N
2loe(5 Waar:
).
(2.76)
Figure 2.13 is a graphical representation of Equation 2.76 for standard air and average roughness. Corrections for other degrees of roughness can be made by using the appropriate factor from Figure 2.12
based on the descriptions in Table 2.5. Corrections can also be made
for kinematic
viscosity, if different from that of standard
air. Since
kinematic viscosity appears in the denominator of the Reynolds
number and velocity appears in its numerator, an equivalent velocity
equal to the actual velocity multiplied by the ratio of standard kinematic viscosity to actual kinematic viscosity can be used together
with Figure 2.13.
The total pressure losses in terms of N for round and rectangular
ducts are
2
Jest
x or 3
BUS NERES al 2xy pr.
(2.77)
Figure 2.14 can be used to determine the equivalent diameter (to be
used with constant velocity) for any rectangular dimensions. This
chart gives the round-duct diameter, which has the same mean hydraulic radius as the rectangular duct. The two do not have the same
cross-sectional areas. This equivalent diameter can be used directly
in Figure 2.13 together with the actual duct velocity to determine the
number of diameters for one velocity pressure loss.
Figure 2.15 is another type of duct friction chart based on standard
air and average roughness. The appropriate factor from Figure 2.12
can be used to correct for other degrees of roughness. However, there
is no simple way of applying a viscosity correction. This limitation is
unimportant in air conditioning but can cause significant error at
high temperatures or for gases other than air. Nevertheless, Figure
2.15 has many useful features including a capacity-velocity-diameter
conversion.
Figure 2.16 can be used to determine the equivalent diameter (to
be used with constant capacity) for any rectangular dimensions. This
chart gives the round-duct diameter, which has the same friction per
foot of length as the rectangular duct, but the two do not have the
same cross-sectional areas. This equivalent diameter can be used
directly in Figure 2.15 together with the actual capacity, to determine
the friction loss per 100 feet.
Equation 2.73 can be combined with the various equations for
FAN ENGINEERING — BUFFALO FORGE COMPANY
2-42
igen
Ge
DUCT DIAMETER — dm
3
5
10,7
20
20,000
| 100
15,000
%
10,000
8,000
2\¢
Fa
gS
ao
\
=
ds
6,000
5,000
50
30
\
4,000
AVERAGE PIPE
4
‘
= 7500
g
E 2,000
S
© 1,500
a
aL
1b
3
— 3,000
=
10%
Ss
%
2
Qs
1,000
=
5
800
600
500
400 \
300.
Q
5
e vA
3
2
YB %
15
2
at
200» LOX
3 4 5678
10
15
20 2530
40 5060
80 100
DUCT DIAMETER — in.
Figure 2.13
Duct Friction Chart in Diameters per Velocity Pressure
Adapted
from the data of R.D. Madison and W.R.
Elliot: “Friction Charts for Gases Including
Correction for Temperature, Viscosity and Pipe Roughness,” ASHVE Journal Section of Heating,
Piping and Air Conditioning, October, 1946, pp. 107-112.
CHAPTER 2 — FLUID FLOW
> wo
10090
80
70.
60
50
40
30
25
N oO
— on
SIDE
LONG
OF
RECTANGULAR
DUCT
4
So
pleat 8 9° 10
15
SHORT SIDE OF RECTANGULAR DUCT
20.
Figure 2.14
Equivalent Diameters for Use With Constant Velocity
«25
FAN ENGINEERING
2-44
— BUFFALO FORGE COMPANY
NY,
9, BUD CEN 7
0% ABACARER
01
02 03.04 .06.08.1
2.
6x8-A-b) oko
Aig
Seraeran'
40,000\ \ .~< 16:Serene
»
30,000¢>s.
rere SKS
8,000; Vs
100-9
aN
:
AN
QO
\
LRA
40
6
SS
NS
20_-S
10.<
01
2
&
B
VSN
02 .03.04 .06.08.1
2 She bab
2.34
FRICTION LOSS — in. wg per 100 ft py
6 sal
Paani
%
%
&73¢336-3
2 22
BRae
@ara:
Figure 2.15
Duct Friction Chart in Inches per 100 Feet
Adapted from the data of D.K. Wright, Jr: “A New
ASHVE, vol. 51, 1945, pp. 303-316.
Friction Chart for Round
Ducts,” Trans.
CHAPTER 2 — FLUID FLOW
.
2-45
~
>
D
z
eo
A
ae
|
y
%
e
iva
y
%
Zz,
oO.
2
:
)
Wt
!
YY
LONG
SIDE
RECTANGULAR
OF
DUCT
15
SHORT SIDE OF RECTANGULAR DUCT
20
“sy
Figure 2.16
Equivalent Diameters for Use With Constant Capacity
SY
2-46
FAN ENGINEERING — BUFFALO FORGE COMPANY
a
Darcy friction factor to produce pressure-drop expressions for each
zone of the Moody chart. The resulting expressions in the wholly
rough and transition zones are rather complex. A compromise expression for turbulent flow is given here. An exact expression for laminar
flow is given later.
For turbulent flow,
cL Ve
PL
pee:
& pi4-"
‘
(2.78)
Any set of units can be used with this expression provided that they
are dimensionally consistent. The coefficient c and the exponent n can
be determined from Table 2.5 opposite the appropriate condition of
roughness. The effect of changes in the exponent 7 more than offsets
the effect of changes in coefficient c so that pressure drop p, increases
with roughness. The rougher the pipe or duct, the more nearly the
pressure drop pz varies as the square of the velocity V, the first power
of the density p, the 1.4 power of the diameter D, and the zero power
of the viscosity yw. It is common practice to determine pressure drops
from charts and tables drawn up for standard conditions, to correct
for density on the basis of a first power relationship, and to ignore
the effect of viscosity. A somewhat more accurate approach is to use
the relationships indicated in Equation 2.78. The most accurate results can be obtained by using equivalent velocity in Figure 2.13 as
outlined in the discussion ofthat chart.
For laminar flow,
selilyin
tis
(2.79)
This expression is correct when used with any set of units that are
dimensionally consistent. The difference between turbulent and laminar flow, as regards losses, is easily ascertained by comparing Equa-
tions 2.78 and 2.79. In laminar flow, the loss p, is independent of
fluid density p. The actual value of roughness has no effect on loss.
As in any kind of flow, the loss is proportionate to length L, but the
relationships with velocity V and diameter D for laminar flow are
different from those for turbulent flow.
Example 2.6
Round-Duct Loss
Given 100 ft of 12-in. round galvanized duct, 1000 cfm of air at 0.075
lbm/ ft" and 1.22 X 10° lbm/ ft+s, find the pressure loss.
_Q_
A
1000
= 1273 fpm = 21.22 fps and
0.7854
py = 0.10 in. wg from Example 2.4.
CHAPTER 2 — FLUID FLOW
2-47
Using Figure 2.13 and Equation 2.77:
N= Sl and
pr— 4 Ep
(57) (Fr) ot
= 0.20in wg.
Alternatively, using Figure 2.15:
pi = 0.2 in. wg/ 100 ft and
ee 202
1005
Ore
Pt= PL 709 = 0.20 100 = 0.20 in. wg.
Alternatively, using Table 2.5 and Equation 2.78:
= 0.16, c = 0.0746,
CL Ess
PL =
1 =
7
are
gepit"
C0746
1001.22
0107S
3) eo
~
(122510)
pi= 1.19 lb/ft’ = 0.23 in. wg.
Refer to Example 2.4 for use of the Moody Chart and the Colebrook
Equation.
Example 2.7
Rectangular-Duct Loss
Given 100 ft of 10-in. X I5-in. rectangular galvanized duct and 1326
cfm of standard air, find the pressure loss.
Oe oma 1d
513260.
ais 1273 fpm and
ee
Pv = 0.10 in. wg (from Example 2.4).
Using Figure 2.14, Figure 2.13, and Equation 2.77:
D = 12 in. (for use with constant velocity),
fib Brg
paso, D= G+
N=
Sl, and
lysd 6 Sa10 15 = 12 in. from Equation 2.75.)
yy (10+ 15)
FAN ENGINEERING — BUFFALO FORGE COMPANY
2-48
ee
ee
ee
Alternatively, using Figure 2.14 and Figure 2.15:
D = 12 in. (for use with constant velocity),
pu = 0.20 in. wg/ 100 ft based on 1273 fpm and 12 in., and
=
PL=PL
ps
90.209=
709
509
0;
0.20
in. wg.
Alternatively, using Figure 2.16 and Figure 2.15:
D = 13.2 in. (for use with constant capacity),
pu’ = 0.20 in. wg/ 100 ft based on 1326 cfm and 13.2 in., and
an
LOO Ne
Dia Pin x = 0.20199 = 0.20 in. we.
All methods should, and do, give the same results.
Elbows
Elbows,
bends,
and
miters
are
used
to guide a fluid
through
a
change in direction of flow. Both shock losses and friction losses are
caused by such devices. The relative amounts of each, as well as the
total resistance, will depend on the abruptness of the change in direction, the Reynolds number, and the roughness.
Elbow
losses can
be expressed
in terms
of a loss coefficient,
an
equivalent length of straight duct, or an extra equivalent length of
straight duct. Using the loss coefficient Kz, the pressure loss py is
obtained from
P.= Kipv
(2.80)
where the velocity pressure py is the average at any section, provided
that there is no change of section throughout the elbow. The size of
the elbow will have very little effect compared with certain other
geometrical considerations. The most significant factors are: the shape
of the elbow, that is, whether round, square, or rectangular; the aspect ratio, if rectangular; the angle of bend; and the radius ratio or
curve ratio.
The curve ratio CR of an elbow is its inside radius R, divided by
its outside radius Rs, assuming concentricity as indicated in Figure
Dali:
Rp
(2.81)
CHAPTER 2 — FLUID FLOW
Figure 2.17
2-49
Hard and Easy Bends
The radius ratio RR of an elbow is its centerline radius R divided
by its width W in the plane of the bend, also assuming concentricity
as indicated in Figure 2.17.
W
(2.82)
The aspect ratio
AR of an elbow 1s its depth D along the axis of the
bend divided by the width W in the plane of the bend, as indicated by
Ww’
(2.83)
For square elbows the depth equals the width W, while for round
elbows depth and width equals the diameter D. For both, AR = 1.0,
and CR and RR are related according to:
DORR=05
Che Reap
sans
(2.84)
RE 05 (5= a)
(2.85)
S
(OAGR
Figure 2.18 can be used to predict the losses for round miters and
for 90° round elbows and bends of various curve or radius ratios.
This figure is based on averages similar to those of Locklin, and
includes both shock and friction losses.
The amount of the loss is not exactly proportional to the angle of
bend, as indicated by Figure 2.19. Determine the factor based on the
— BUFFALO FORGE COMPANY
FAN ENGINEERING
2-50
a
Bi
J.
6
5
RADIUS RATIO (RR)
80.
£
70
= 60
& 50
25
200
1.5
S10
100.
90 SSx
ara
MITER
NO CURVE RATIO
ZERO RADIUS RATIO
K,=115
SR
rex
2 40
wn
S
3 30
20
PIPE
BEND
10 0
0.1
4 PIECE
ELBOW
0.2
0.3
0.4
0.5
0.6
=
0.7
CURVE RATIO (CR)
Figure 2.18
Adapted
Loss Coefficients for 90° Round Elbows and Miters
from the data of D.W.
ASHVE, vol. 56, 1950, pp. 479-502.
Locklin:
“Energy
Losses
in 90 Degree
Duct
Elbows,”
Trans.
appropriate description and angle of bend. Obtain the loss for the
corresponding 90° elbow from Figure 2.18. Then multiply by this
angle-of-bend factor.
Figure 2.20 can be used to determine the losses for square miters
and for 90° square elbows of various curve or radius ratios. It is
based on tests conducted in the Buffalo Forge Company laboratory.
(There is notable agreement between this data and the average data
of several investigators, as compiled by Locklin. ') From this figure,
it is apparent that size effect is negligible except at high-curve ratios
'D.W. Locklin, “Energy
pp. 479-502.
Losses
in 90 Degree
Duct
Elbows,”
Trans.
ASHVE,
vol. 56, 1950,
CHAPTER
2 — FLUID FLOW
14
2-51
ELBOW ONLY
1.2
1.0
ELBOW WITH
ONE SPLITTER
8
6
OF
ANGLE
FACTOR
BEND
A
ANGLE
OF
BEND
1.6.
:
ELBOW FOLLOWED
14,
BY DUCT
1.2;
ELBOW WITH
a
SPLITTER
oe
8
FOLLOWED
BY DUCT
ANGLE
BEND
OF
FACTOR
6
ri
ANGLE
BEND
vei
Ve
ee
ie
120
«150
180
ANGLE OF BEND
Figure 2.19
Angle of Bend Factors for Elbows
Adapted from the data of R.D. Madison and J.R.
Elbows,” Trans. ASME, vol. 58, 1936, pp. 167-176.
Parker: “Pressure
Losses in Rectangular
2-52
FAN ENGINEERING — BUFFALO FORGE COMPANY
RADIUS RATIO (RR)
5
110
100’
6
ere wie olin
Mi:
15
2.
35
4
80
70
Kee
R/W =0
NO CURVE RATIO
;
60
50
R&T W be
RN
7
>| whe
=
x
Y
=
Le
a
5
we
3
30
r
>WK
>We
S
eo
Sp
Ki=220
38
SIDE OUTLET
3
W = 33
4
wate
w”
2
aA
Z\O
es)
e
S. UF 4
\
-
NNG
pa
act
ee
NN
Fi
ees
eS
<
20
4
iy
Pe
yi,
va
Es
ee
/
vA
of
AIR VEL. 800 FPM
6
; 0.
caele
Alten
eS
4
pay
ie
mes:
CURVE RATIO (CR)
Figure 2.20
Loss Coefficients for 90° Square Elbows and Miters
Adapted from the data of R.D. Madison and J.R. Parker:
Elbows,” Trans. ASME, vol. 58, 1936, pp. 167-176.
“Pressure
Losses
in Rectangular
CHAPTER 2 — FLUID FLOW
DD
2-53
eae
ied
20:
ic
=
1.8)
SIGE:
i
:
CURVE - A
S 1.4
19.
a
:
:
ee 8
Eamets!
“ AV. FORELBOWSOF =~
~~ 1.0-3.0 RADIUS RATIO.
—~
_ OR 3.7 CURVE
RATIO
2 1.0
oO.
ra
6
ae
a
CURVES 8
A
~ AV FOR ELBOWS WITH
~ 0 TO .5 RADIUS RATIO
_NONE TO 0 CURVE RATIO
eee
9
0
5)
1.0
185
2.0
2.5
3.0
35
4.0
ASPECT RATIO (AR)
Figure 2.21
Aspect Ratio Factors for Rectangular Elbows
Adapted from the data of R.D. Madison and J.R.
Elbows,” Trans. ASME, vol. 58, 1936, pp. 167-176.
Parker: “Pressure
Losses in Rectangular
where shock losses decrease to the point of insignificance compared
with friction losses.
Figure 2.21 gives aspect ratio factors for rectangular elbows. Determine the factor based on the appropriate description and aspect ratio.
Obtain the loss for the corresponding square elbow from Figure 2.20.
Then multiply by the aspect ratio factor. Note that there is a broad
range of aspect ratios for which no correction is necessary.
The loss in an elbow located at the end of a duct is much higher
than that for a similar elbow followed by a short run of straight pipe.
This is similar to the phenomenon observed with orifices in that there
is a contraction
of the stream,
and unless expansion
is allowed
to
take place before exiting, a considerable amount of kinetic energy is
wasted. The curves of Figure 2.22 illustrate the effect of both aspect
ratio and curve or radius ratio on the pressure loss in a 90° elbow
discharging directly into the atmosphere.
The combined loss of a compound elbow may be quite different
from the sum of the individual losses, as indicated by Figures 2.23
and 2.24. The columns marked “actual” are the loss as measured. The
columns marked “estimated sum” are the sums of the individual loss
coefficients, estimating the loss coefficient for the upstream elbow as
if it were followed by a duct and also estimating the loss coefficient
for the downstream elbow according to conditions as marked. The
ratio of actual to estimated loss is given as “% of est.” The estimated
combined loss coefficient with splitters is usually quite close to its
actual loss.
— BUFFALO FORGE COMPANY
FAN ENGINEERING
2-54
2.20
2.00
0&5 RRO. CR)
1.80
2 1.60
eine
62H ARIECR)...
eolae
75. RR (.2 CR}
& 1.20
S 80
2= 60
1.0 BR (.33-CR)
Peaeeamwnesmns
[fi sewenneery (01 REGGRES
B3.ORR(72CR)
seuunue
20
iy
dene
a
PG
io
AS,
20
ee)
30.
woe
ee
ASPECT RATIO (AR)
Figure 2.22
Loss Coefficients for 90° Elbows and Miters
Discharging to Atmosphere
Adapted from the data of R.D. Madison and J.R.
Elbows,” Trans.
ASME, vol. 58, 1936, pp. 167-176.
Parker:
“Pressure
Losses
in Rectangular
Conventional elbows are those having concentric inner and outer
radii and constant areas of cross section throughout the bend. From
time to time, various special elbows have been proposed incorporating either a change in area or a change in the shape of that area
throughout the bend. For comparable curve and aspect ratios, conventional elbows are superior to special elbows. For the lowest possible loss, conventional elbows with splitters or miters with turning
vanes should be used.
Splitters are curved vanes placed in an elbow concentric with both
the inside and outside radii and extending the full angle of bend from
face to face. Splitters, in effect, divide the flow into parallel channels,
each having a larger curve ratio and a larger aspect ratio than that
of the original elbow. Usually, the change in aspect ratio has much
less effect upon elbow loss than the change in curve ratio. Disregarding the change in aspect ratio then, the ideal locations for splitters
are those that divide the elbow into components, each with the same
curve ratio. For any number of splitters n, the new curve ratio CR’
of each component elbow formed by the splitters can be determined
using the curve ratio CR ofthe original elbow without splitters in
CREACR
Wes
(2.86)
Figure 2.25 gives the radius of each splitter at the intersection of a
straight line drawn between points that represent the inside and out-
CHAPTER 2 — FLUID FLOW
FIRST |SECOND|
ELBOW w | E ELBOW
ELBOWS
ONLY
2-55
eee
Soe
EST.|% OF
EST. |% OF
(1)
3
AG
a
372|.485] 77. |.276].215| 128
3
-
242} .30
|! 410.5]
4
|.245).202/12.1
85 | 135
4
|.162).112]14.5).103)
.85 | 121
(2)
.264).215]
123
(3)
a
(4)
0.5
1.5)
15
1.5 |.25].455].48 |95.
(5)
|.346] 38
(6)
Ferma
Figure 2.23
|) 4
|||
2
Actual and Estimated Losses for Compound Elbows
(3x
12”)
Adapted from the data of R.D. Madison and J.R.
Elbows,” Trans. ASME, vol. 58, 1936, pp. 167-176.
Parker: “Pressure
Losses in Rectangular
FAN ENGINEERING — BUFFALO FORGE COMPANY
2-56
PLAIN
ELBOWS
ONE DIAMETER
BTW. ELBOWS
SPLITTER IN
EACH ELBOW
bate
EST.
EST. |% OF
S|
Stitt
_
Si
eae cae We
(3)
xX
[=]
.
655
75111.00|
.
.
75
.
|.274)|
.
.30 | 94
= /
Aaa
COZ
ESouieS
4
.20
i
| 75
Nh
(6)
=f
=|
ey
Figure 2.24
52
457]
.52 | 88|.205)
NR
.20
Actual and Estimated Losses for Compound Elbows
(12”x 12")
Adapted from the data of R.D. Madison and J.R.
Elbows.” Trans. ASME, vol. 58, 1936, pp. 167-176.
Parker:
“Pressure
Losses in Rectangular
CHAPTER 2 — FLUID FLOW
2-57
100
90
80
70
60
Ries
(=)
i=)
Ss.
‘50
40
N
oi,
a
i=)
(=)
Z
i)oO
i
ae
30
S
5
N
a
(=)
SS
_
N
oS
=>
o
a
&
-
i
=
pad
(=)
20
-
ine)
oO
—
—a
OUTSID
RADIUS
INCHES
IN
INSIDE
RADIUS
ELBOW
OF
INCHES
IN
Yes)
te)
Verh
ST
Kop
(Sip
vA
:
‘ EXAMPLE:
NUMBEROF SPLITTERS
Figure 2.25
Locations of Splitters in Rectangular Elbows
2-58
FAN ENGINEERING
— BUFFALO FORGE COMPANY
SS
eee
ee
side radii of the elbow without splitters. The example drawn on the
chart shows that, for an inside radius of 2 in. and for an outside
radius of 20 in., the radius of the inner splitter should be approximately 4.25 in., and the radius of the outer splitter should be about
9.25 in.
The loss due to a 90° square-section elbow with one, two, or three
splitters can be determined from the curves in Figure 2.20. Splitters
produce appreciable reduction in pressure loss when the original
curve ratio is low, but there is no material reduction when the original curve ratio is high. Although this data is strictly applicable only
to square-section elbows, corrections for aspect ratio can be made
for rectangular-section elbows.
Turning vanes can be used to reduce the loss through a miter of
either round or rectangular section. As indicated in Figure 2.26, the
loss depends upon the type of miter and the type of turning vane.
The estimated values shown are based on a vane depth of approximately six times the spacing and, where thickened vanes are indicated, a value of 0.5 curve ratio between the back of one and the
front of the next. The very considerable reduction in loss coefficient
from a value of 1.15 (see Figures 2.18 and 2.20) to the approximate
values indicated in Figure 2.26 results from the conversion of the
miter into a series of high-aspect-ratio (or easy-bend) elbows.
SP ee
K, = 0.28
Kr =0:25
K,
= 0.40
TURNING VANES IN ROUND DUCTS
Gizats
K, = 0.35
K,= 0.10
TURNING VANES IN SQUARE DUCTS
Figure 2.26
Loss Coefficients for 90° Miters with Turning Vanes
Adapted from the data of L. Wirt: “New Data for the Design of Elbows in Duct Systems,” General
Electric Review, June, 1927, pp. 286-296.
CHAPTER
2 — FLUID FLOW
2-59
As a rule of thumb in the region of 0.5 curve ratio, the equivalent
length of straight duct for a 90° round elbow is about 9 to 10
diameters. Similarly, the equivalent length of a 90° rectangular elbow
is about 6 to 8 equivalent diameters.
When estimating duct friction, it is often convenient to measure
straight lengths as if all elbows were miters. To compensate, elbow
losses are figured on the extra equivalent length basis. Values were
formerly reported on this basis in the Guide.’
Example 2.8
Round-Elbow Loss
Given a 4-piece 90° round elbow with a 12-in. diameter, an 18-in.
centerline radius, and 1000 cfm of standard air, find the loss.
pv = 0.10 in. wg (from Example 2.4)
Using Equation 2.82, Figure 2.18, and Equation 2.80:
iesa8teal
Ki = 0.33, and
Pit= Kipv = 0.33 X 0.10 = 0.033 in. wg.
Example 2.9
Rectangular-Elbow Loss
Given a rectangular elbow with a 12-in. width, a 15-in. depth, a
6-in. inside radius, and 1326 cfm of standard air, find the loss with
and without splitters.
pv = 0.10 in. wg (from Example 2.7)
Using Equation 2.81, Figure 2.20, and Equation 2.80:
CR=
eee.
Ry
18
= 0.33,
K, = 0.22 for no splitters, and
pi= Kipv = 0.22 X 0.1 = 0.02 in. wg with no splitters,
K, = 0.10 for 2 splitters, and
p.= Kipy = 0.10 X 0.1 = 0.01 in. wg with 2 splitters.
Using Equation 2.83 and Figure 2.21:
AR
eat)pap)Som
oy
ou=
1.25, and
aspect ratio factor is 1.01 from curve A and can be ignored.
"ASHRAE Guide and Data Book — Equipment, ASHRAE, New York, 1969, p. 32.
2-60
FAN ENGINEERING — BUFFALO FORGE COMPANY
Changes in Duct Section
Various fittings can be used to connect two ducts that are of different sizes or shapes.
If the downstream duct is of the same shape but smaller than the
upstream duct, a converging cone or a converging pyramid (with total
included angles of convergence less than 15°) can be used. The total
pressure loss pz, which will be a small fraction of the leaving velocity
pressure py2, can be estimated by using the mean values of D andf
in the equation for straight ducts:
es
pr=SpPr-
(2.87)
A considerably larger loss would result if an abrupt contraction were
used. This will be discussed in a subsequent section.
If the downstream duct is of similar shape but larger than the upstream duct, a diverging cone or a diverging pyramid can be used.
Conical and plane diffusers of this kind are discussed in a later section. An abrupt enlargement can also be used. This, too, is discussed
below.
If the downstream duct is not of the same shape as the upstream
duct, a transformation piece can be used. But even if the areas of the
two ducts are the same, the transformation will have elements with
different slopes. If all the elements are converging, the total pressure
loss can be estimated as outlined above for converging cones or pyramids. If all the elements are diverging, the total pressure loss can be
estimated from the data for conical and plane diffusers. However,
should
some
of the elements converge
and others diverge, the total
pressure loss can be determined as if the transformation piece were a
straight duct, but only if the slopes of the diverging elements are very
small. Otherwise, there will be some additional diffuser loss.
If the downstream
duct is not coaxial with the upstream duct, the
data on bends and miters must be used to calculate total pressure loss.
Abrupt Enlargement
In an abrupt enlargement, the fluid flows into a conduit without
contraction but at less than full bore and then expands to full bore.
Not every sudden enlargement of duct section fulfills these conditions.
The conduit must be sufficiently long (at least 3 or 4 diameters) for
the necessary expansion to take place. On the other hand, if a fluid
does enter a conduit with subsequent contraction and re-expansion,
the condition between the plane of the vena contracta and the plane
where the expansion becomes complete can be considered an abrupt
enlargement.
CHAPTER 2 — FLUID FLOW
2-61
RATIO OF INLET TO OUTLET DIAMETER - D,/ D>
x
“
0.
enewdll
= WN
;
eee (0)
i
fs
ee)
=
®
Fy
a
3 A
a
{
wn
rk
=
:
-
|
“A
w
eee
©
SA
So
ost
8
=
;
=
f
oO
:
wu
S 3
th
'
6a
;
‘
‘
;
ances
se
;
ae
at
i
Mel tas
ae
ws
22
we)
t
{
rey HU Ae len Oe IE ees ead eae Rees ees ee et Re Pe
aC)
a
2.
3
4
5
6
ay
8
RATIO OF INLET TO OUTLET AREA - A /A>
Figure 2.27
=Weg
+
tree
9
1.0
Kz,and K, for Abrupt Enlargements
The total pressure loss p, for an abrupt enlargement, or BordaCarnot loss, is a function of the velocity V; in the upstream duct and
the velocity V2 in the downstream duct, as indicated by
(“Ey
Co
meus
Weyer
(2.88)
where p is the gas density and C, is \/2 for SI units or 1097 for U.S.
customary units. This can also be expressed in terms of the velocity
pressure
py; in the upstream duct and the area ratio A\/A2:
y=
Obviously,
(!= 4) pw = Kipn.
As
the bracketed
terms can
(2.89)
be considered a loss coefficient
K,. Values of Kx versus A;/ A? are plotted in Figure 2.27.
Another important quantity for an abrupt, or even a gradual, enlargement is the change in static pressure. Static pressure will increase
in the direction of flow and is, therefore, called static pressure regain
Psr,
or regain for short.
The
regain is the difference
between
the
change in velocity pressure and the total pressure loss, and can also
be expressed in terms of py: and A\/A2:
ih
CY
patetn ee
pse = 2(4°)(1 41)pn = Kepn.
(2.90)
2-62
FAN ENGINEERING — BUFFALO FORGE COMPANY
The coefficient of pressure recovery Ke is not equal to one minus the
total pressure loss coefficient Kz as is often, but erroneously, stated.
Values of Kr are plotted in Figure 2.27.
The loss and regain can be expressed as functions of the change in
velocity pressure Apy by using an effectiveness factor n. This is done
in the section on diffusers.
The ideal case considered above assumes that duct friction is negligible, that the velocity distribution is uniform in the upstream duct,
and that flow is completely turbulent. Corrections for low Reynolds
‘number, nonuniform kinetic energy, and nonuniform momentum
are given by Idel’chik' for various configurations involving abrupt
enlargement.
Example 2.10
Abrupt Enlargement Loss and Regain
Given an abrupt enlargement from an 8-in. duct to a 12-in. duct and
1000 cfm of standard air, find the loss and the regain.
Ay = 0.3491 ©
Ye orgy
_ @_
NT
1000 _
ayo
ewe
Using Equation 2.30:
iy
Vite \ae
pu = o( a)
2365.\ ae
= UNE (re
Bae
= 0.51 in. wg.
Using Figure 2.27 and Equations 2.89 and 2.90:
K, = 0.309,
Kr= 0.494,
Pt= Kipn = 0.309 X 0.51 = 0.16 in. wg, and
Psr = Krpvi = 0.494 X 0.51 = 0.25 in. wg.
Abrupt Contraction
In an abrupt contraction, the fluid flows into a conduit at full bore
but immediately contracts and then re-expands to full bore. Not
every sudden reduction of duct section fulfills these conditions. The
conduit must be sufficiently long for the necessary contraction and
re-expansion to take place. The conditions up to the vena contracta
are the same as for a square-edged orifice with an opening equal to
the cross section of the conduit. The conditions beyond the vena con'Idel’chik, pp. 128-132.
CHAPTER
2 — FLUID FLOW
2-63
RATIO OF QUTLET TO INLET DIAMETER - D2/D,
cle 2e ee4:
9
6
all
8
:
COEFFICIENT
LOSS
Kz,
-
ees
ee,
STA
BO
pera een nieHt
RATIO OF OUTLET TO INLET AREA - 4/A,
Figure 2.28
Kz,for Abrupt Contractions
tracta are the same as for an abrupt enlargement.
The total pressure loss p; of an abrupt contraction is a function of
the shape of that contraction, the upstream area A,, the downstream
area A2, and the downstream velocity pressure py2, as indicated by
A
Joe = IK (!a 4) pn = Kipyv2.
(2.91)
In the square-edged case, Kz’ is approximately 0.5. Values of the loss
coefficient K, versus A2/A, are plotted in Figure 2.28 for high Reynolds number and K,’= 0.5.
Example 2.11
Abrupt Contraction Loss
Given an abrupt contraction from a 12-in. duct to an 8-in. duct and
1000 cfm of standard air, find the loss.
Pv2 = 0.51 in. wg (from Example 2.8)
Using Figure 2.28 and Equation 2.91:
K, = 0.278 and
Pr=
Kipv2 = 0.278 X 0.51 = 0.14 in. wg.
Idel’chik' gives data for calculating Kz, for rounded and beveled
edges, as well as for low Reynolds numbers, in the square-edged case.
"Idel’chik, pp. 98-99.
2-64
FAN ENGINEERING — BUFFALO FORGE COMPANY
Diffusers and Evasés (Diverging Tapers)
A diffuser is a flow passage in which kinetic energy is converted
into pressure energy. For subsonic flow the passage must diverge in
the direction of flow. A diffuser is distinguished from an abrupt enlargement by gradual divergence. When a diffuser is located at the
exit end of a duct, it is known as an evase. A diffuser’on the outlet
of a fan sometimes is called an evasé, even if there is additional ductwork. And frequently the fan is said to be coned even if the cross
sections of the diffuser are not circular. A conical diffuser, however,
does have circular cross sections. Two-dimensional, or plane, diffusers
have rectangular cross sections and two parallel sides. Any other
diverging passage with rectangular sections is called a three-dimensional diffuser.
The performance of a diffuser, like that of an abrupt enlargement,
will vary with inlet velocity pressure py and the ratio of outlet to
inlet area A2/ Aj. In addition, performance will vary with the centerline length L and the total included angle of divergence 20.
In an ideal diffuser, the regain psx would equal the change in velocity pressure Apy, and the loss in total pressure pz would be zero.
However, in a real diffuser, there will always be a loss in total pressure, and the effectiveness 7, which is equal to psr/Aprv, will be less
than unity. Regain is frequently given in percent of inlet velocity
pressure. The dimensionless fraction psr/pv is also known as the coefficient of pressure recovery Kr.
The flow in a diffuser may follow the walls of the passage, or it
may stall and be deflected away from the walls by reverse flow. Figure
2.29, which is drawn for plane diffusers with straight walls, shows the
various flow regimes that might be encountered. It is generally applicable for entrance Reynolds numbers greater than 5 X 10* and for
Mach numbers less than 0.2. The coordinates are area ratio A2/A,
and the ratio of length to inlet width L/W, but the angle of divergence is also shown. The flow in each regime is described in detail in
the reference cited; only brief explanations follow here.
In jet flow, separation from both walls begins near the throat and
covers both walls. In two-dimensional stall, separation begins near
the throat and covers only one wall. This fixed stall will remain there
unless it is diverted to the other wall by a large disturbance at the
inlet or outlet. There is a region between the two zones where either
jet flow or two-dimensional stall can exist. Transitory stall varies
with diffuser geometry but generally begins in the corners, builds
up, and is swept away repeatedly. Note that the lines of maximum
pressure recovery and maximum effectiveness fall into the region of
“some stall.”
Figures 2.30 and 2.31 are also drawn for plane diffusers. Figure
2.30 shows the coefficients of pressure recovery and Figure 2.31 the
effectiveness values, for various geometries. However, these charts
CHAPTER
2 — FLUID FLOW
A2/A;
OUTLET
INLET
TO
AREA
RATIO
—
on
a
Bt
AGAe Ga,10 els 20
L/W, — LENGTH TO INLET WIDTH RATIO
40
60
Figure 2.29
Flow Regimes in Plane Diffusers
Adapted from the data of L.R. Reneau, J.P. Johnston and S.J. Kline: “Performance and Design
of Straight Two-Dimensional Diffusers,’ ASME Paper No. 66-FE-10, 1966.
2-66
FAN ENGINEERING
— BUFFALO FORGE COMPANY
RATIO
AREA
INLET
TO
OUTLET
A2/A;
—
4
ar
"hy yi
Y
1
%7's
Udy
2
vg
&7
Sipe:
%
a
vy
Cmca
\<20
O
15020
30
40
60
L/W; — LENGTH TO INLET WIDTH RATIO
Figure 2.30
Coefficients of Pressure Recovery for Plane Diffusers
Adapted from the data of L.R. Reneau, J.P. Johnston and S.J. Kline: “Performance and Design
of Straight Two-Dimensional Diffusers." ASME Paper No. 66-FE-10, 1966.
CHAPTER
2 — FLUID FLOW
2-67
A2/A,
OUTLET
TO
AREA
INLET
RATIO
—
io 2
yh a 8 10 et
15 20
i=* LENGTH TO INLET WIDTH RATIO
30 40 60
Figure 2.31
Effectiveness Values for Plane Diffusers
Adapted from the data of L.R. Reneau, J.P. Johnston and S.J. Kline: “Performance and Design
of Straight Two-Dimensional Diffusers.” ASME Paper No. 66-FE-10, 1966.
FAN ENGINEERING — BUFFALO FORGE COMPANY
2-68
$0as ai
Senne
30
tee Hep
rae
an
}
/'3/sf
76
|
ii
i
20 br
i
H
i
15|i
i
;i
DS
10}it
i
i'
ees
Lo
t
ect
caer
sreres
oe
rece
6;
i
%
iee
RATIO
AREA
INLET
TO
OUTLET
A/A;
-
Z,
i
Oo
2 Oo
\% \
RhD>
oc
ese
tS
tose
rarer
he oe
a
be
Ri 0 es
L/R; — LENGTH TO INLET RADIUS RATIO
ee
Figure 2.32
Coefficients of Pressure Recovery for Conical Diffusers
Adapted from the data of A.T, McDonald and R.W. Fox: “An Experimental Investigation of
Incompressible Flow in Conical Diffusers,” ASME Paper No. 65-FE-25, 1965.
CHAPTER 2 — FLUID FLOW
2-69
A2/A;
OUTLET
TO
INLET
AREA
RATIO
—
60
me = oe ; ie RADIUS RATIO
Figure 2.33
Effectiveness Values for Conical Diffusers
Adapted from the data of A.T. McDonald and R.W. Fox: “An Experimental Investigation of
Incompressible Flow in Conical Diffusers,” ASME Paper No. 65-FE-25, 1965.
2-70
FAN ENGINEERING
— BUFFALO FORGE COMPANY
ee
SS
EEE
eet
are drawn for only one inlet boundary layer condition: a turbulent
inlet boundary layer such as might be generated if the diffuser were
preceded by several diameters of straight duct and if flow were uniform. Chart values should be reduced as much as 25% when inlet
flow is nonuniform or boundary layers are thicker. Plots for other
conditions are given in the reference.
To determine static pressure regain, use either
PsR =
Kerpvi
or
(2.92)
Psr= nApv.
(2.93)
To determine total pressure loss, use
pi= (1 — n) Apv.
(2.94)
Peak pressure recovery for a given length or a given area ratio can
be determined from Figure 2.30. A line connecting all such points is
drawn on the chart. It is also drawn on Figure 2.29 to illustrate that
peak recovery occurs in the zone of appreciable stall. On the other
hand, maximum effectiveness generally occurs in the “some stall”
zone. Figure 2.31 shows that maximum effectiveness at constant
area ratio will be produced with a plane diffuser angle of approximately 7°.
Figures 2.32 and 2.33 are drawn for conical diffusers using area
ratio A2/A, and length to inlet radius ratio L/R; as coordinates.
These charts can be used if the same way as Figures 2.30 and 2.31 to
determine performance for any geometry or to optimize performance.
These conical diffuser data are for free-jet exit conditions so that
some improvement could be expected, at least for large angles of
divergence, if a discharge duct were used. In contrast to the situation
for plane diffusers, conical diffusers attain peak recovery for a given
length or area ratio before the onset of stall. This probably is due to
the absence of side-wall corners.
The performance of any diffuser can be improved by fairing the
entrance corners. There is some evidence’ that the presence of a resistance at the exit of a diffuser allows the use of greater angles of
divergence for a given total pressure loss and may even prevent the
onset of stall. Wide-angle diffusers can be improved by using splitter
vanes. Diffusers with curved centerlines have lower performance
than straight-walled diffusers.’
'C.H. McLellan and M.R. Nichols, “An Investigation
Duct Systems,” NACA Wartime Report L-329, 1942.
of Diffuser-Resistance
iS Fail, “Vane Systems for Very-Wide-Angle Subsonic Diffusers.” ASME
Combinations
in
Paper No. 64-FE-4,
64.
‘C.J. Sagi and J.P. Johnston, “The Design and
fusers.”” ASME Paper No. 67-FE-6, 1967.
Performance
of Two-Dimensional
Curved
Dif-
CHAPTER
2 — FLUID FLOW
2-71
According to Fox, the coefficients of pressure recovery for conical
diffusers with low angles of divergence increase as inlet Mach number
is increased to about 0.9. Effectiveness appears to decrease rapidly as
the Mach number is increased to about 0.2 to 0.3. However, effectiveness remains relatively constant over the 0.3 to 0.9 Mach-number
range. At Mach numbers above 0.9, both effectiveness and coefficient
of pressure recovery decline rapidly.
Idel’chik® gives data for calculating coefficient of loss K, for conical, pyramidal, plane, transformation, curved, stepped, and annular
diffusers and for the effects of baffles and screens.
Example 2.12
Diffuser Loss and Regain
Given a 36-in. long conical diffuser, an 8-in. to 12-in. diameter,
and 1000 cfm of standard air, find the loss and the regain.
Ar _ 0.7854
A, 0.3491 = 2.25,
Pv = 0.51 in. wg (from Example 2.8),
Pv2 = 0.10 in. wg (from Example 2.4), and
gl 30)
PRie .--4. ee
Using Figures 2.32 and 2.33 and Equations 2.92, 2.93, and 2.94:
Kr= 0.64,
n = 0.80,
Psr= Krpvi = 0.64 X 0.51 = 0.33 in. wg,
Psr= n(pn — pvr) = 0.80(0.51 — 0.10) = 0.33 in. wg, and
Pr= (1 — n) (pm — pr2) = 9.20(0.51 — 0.10) = 0.08 in. weg.
Note that this loss is considerably less than that for an abrupt enlargement as illustrated in Example 2.10.
'R.W. Fox, “Subsonic Flow in Conical Diffusers,” Technical Report FMTR-67-1,
Foundation, Lafayette, Ind., 1967.
*Idel’chik, pp. 166-188.
Purdue Research
2-72
FAN ENGINEERING — BUFFALO FORGE COMPANY
Takeoffs and Junctions
The total pressure losses of takeoffs and junctions are affected by
the ratio of downstream to upstream velocity, by the branching angle,
and by other geometrical relations. Figure 2.34 shows the average
loss coefficient for a divided-flow fitting of round cross section for
both the run of the main K,\-2 and the takeoff Kz:-3. The total pressure loss py1-2 for the run of the main is
Pu-2 = Ku-2pv2 -
(2.95)
The total pressure loss pzi-3 for the takeoff is
Pu-3 = Kui-3pv3 .
(2.96)
Three different branching angles are shown for the takeoff. Its loss
can be reduced considerably by using a converging taper between the
main and the branch pipe. The dotted curve shows the approximate
effect of a generous taper, one side of which makes a branching angle
of approximately 45°.
The above data apply only to takeoffs where one stream is divided
into two. Similar fittings are used at junctions where two streams are
combined into one. The recommended procedure for such a junction
is to join the upstream main with the downstream main by means of
a taper at least two upstream diameters long and to join the branch
to the taper at an angle of 30° with the upstream main. Figure 2.35
gives the coefficients of loss for both the upstream main to downstream main K,)-3 and the branch to downstream main K,2-3 when
the sum of the areas of the upstream main and the branch equals the
downstream main area. Note that the loss can be negative depending
on the ratio of the branch flow to the total flow Q2/Q3. This is due
to the transfer of momentum from one stream to the other.
The total pressure loss pri-s for the upstream
main to the down-
stream main is
Pu-3 = Ki-3py3 .
(2.97)
The total pressure loss pr2-3 for the branch to the downstream main is
P12-3 = K12-3pr2 -
(2.98)
Idel’chik' presents data on calculating the coefficient of loss for
numerous
takeoffs and junctions, including wyes, double wyes, tees,
crosses, and headers.
'Idel’chik, pp. 260-304.
CHAPTER
2 — FLUID FLOW
.
4
<
xo
ne
500
Ree
US
Bee
90° DIRECT TAKEOFF
300
9
Egor
2-73
eg,
Kii-3
60° DIRECT TAKEOFF
200
&
re
Kui-3
“
45° DIRECT OR 90° ELBOW TAKEOFF
espais 100
=
3
=
o>
Oo
2
\
\
:
Eelsae
80
Gt
50
40
oO
mane
30
20
\
Ku-3
90° WITH 45° TAPER
10
al
Z
p
£8
S49.
Se
y
Gopi
WitBere «ied elie eeI
MAIN OR RUN OF FITTING
{3 (Me)
2
ee
ky
Gh
VELOCITY RATIOS - V2/Vi and V3/ VY
Figure 2.34
Adapted
ASHAE,
Pressure Losses for Divided Flow Fittings
from the data of S.F. Gilman:
vol. 61, 1955, pp. 281-296.
Example 2.13
“Pressure
Losses
of Divided-Flow
Fittings,” Trans.
Takeoff Losses
Given a divided-flow fitting with a 12-in. diameter main, an 8-in.
diameter 60° takeoff, and 1000 cfm of standard air divided equally,
find the losses.
Aya As = 0.785410.
A, = 0.3491 ft’,
V, = 1000/0.7854 = 1273 fpm,
V> = 500/0.7854 = 637 fpm,
V; = 500/0.3491 = 1432 fpm,
2-74
FAN ENGINEERING
— BUFFALO FORGE COMPANY
V2
;
a = a
= 0.5, Kr1-2 = 1.5 from Figure 2.34,
V.
:
a = eH = 1.12, Ki1-3 = 0.7 from Figure 2.34.
Using Equations 2.30, 2.95, and 2.96,
ai
6 (j057)
oe
V.
637) =0.03,
0.075 (S37)
2
2
pas allgar = 0.075 (Goa) =
Pu-2=
Ki-2pr2=
1.5 X 0.03 = 0.05 in. wg for the run of the main,
and
Pu-3= Kiui-3pv3 = 0.7 X 0.13 = 0.09 in. wg for the takeoff.
Ki3-3))
Kyo-x
|
:
0.06 /0.10,A,/A;
:
ppt
4
| Kir-s
0.20-A;/A3
:
—
ae ooh
2
mcm
>
OF
Agte
£2-3
033 Ay/Ay
a
bs abeat
Ger
0
and
Ky2-3
COEFFICIENTS
—K1\-3
LOSS
:
-1
Of
02
:
Kits
e
Kus
N038 Ai7Ae
S
pee
Ku-3
O03
04.
08
06
07
FLOW RATE RATIOS - 01/3 and 02/03
Figure 2.35
808m
.09
50
Pressure Losses for Junctions
Adapted from the data of I.E. Idel’chik, Handbook of Hydraulic Resistance — Coefficients of
Local Resistance and of Friction, Distributed by National Technical Information Service, U.S.
Department of Commerce, Springfield, Va., AEC-TR-6630, 1966, p. 268.
CHAPTER 2 — FLUID FLOW
2-75
Obstructions
Various objects can partially obstruct the flow through a duct.
Idel’chik' gives data for many isolated obstructions like pipes, beams,
and trusses; for orifice plates; and for many distributed resistances
like grids, screens, packed beds, and tube bundles. Only a few will
be examined here.
A simplified formula for the loss pz due to an isolated obstruction is
ese
( ane
(2.99)
where A; is the projected area of the obstruction, A; is the area of the
duct, Cp is the drag coefficient for the obstruction (obtained
from
data like that in Table 2.6), and py is the velocity pressure based on
the free area of the duct. Idel’chik includes means for determining the
effects of velocity distribution k; and offset kz. The value of k, is
approximately 1.15 for struts running completely across the duct and
1.30 for objects with three-dimensional flow around them. The value
of kz is unity for zero offset, and it decreases as the object nears the
wall (in the extreme, 0.3 to 0.6). The value of 7 is unity for smooth
objects and approximately 1.5 for objects with sharp edges.
The general formula for the loss pz due to an orifice plate is
p=[«('-4a) (Geer oe
ae
a
<1]
, (2.100)
Doo
where A, is the area of the upstream duct, A2 is the area of the downstream duct, f is the Darcy friction factor, and pyo is the velocity
pressure based on the area Apo of the orifice. The factor k depends on
the shape of the inlet edge of the orifice, ranging from nearly zero for
a well-rounded entry to unity for a re-entrant condition. The factor r
depends on both the shape of the inlet edge and the ratio of the
length Lo of the orifice (thickness of the orifice plate) to its hydraulic
diameter Do, ranging from nearly zero for long passages to 1.4, or so,
for thin orifice plates. This equation is reducible to that for an abrupt
contraction when A>= Ao and to that for an abrupt enlargement
when A; = Ao.
'del’chik, pp. 388-399.
2-76
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Table 2.6
Drag Coefficients
Struts Running Completely Across the Duct
Round-Duct
Cross Section
os
Rae
Type of Strut
,
Flat Strip
Saas
Rectangular-Duct
eee!
Cross Section
Section
Cp
t/d
Re
0
2.4
0
=
\
12
21a
Kb oN
Q
12
0.33
10 | 10°
1.0 |>108
0.3
4.
’&
L
Id
|-beam
6 Aan
Pipe
|-beam
with fairing
0)'c->
Pipe
with fairing
2 Pipes
e
O
()
BOON
Q
:
hal
0.2
z
|>16
0.06
ADS
i= 105
2.06 | 100
| >10°
162° \ 0
1c:
060 | 1
|>108
A perforated plate can be considered a parallel arrangement of
orifices. For a thin plate with square-edged openings, k = 0.5, fLo/ Do
is negligible, and 7 = 1.414. For a uniform duct, A> = A; and Equation 2.100 is reducible to
ti
Ne
m=2d Fi[om ieee ApE+ sey(-2
m
(2.101)
where Ao is the combined area of the openings. A is the duct area,
and py is the velocity pressure based on the free area of the duct.
A woven wire screen can also be considered a parallel arrangement
of orifices. For round wires, t= 2k'” and k = 1.3. For a uniform
duct, Ay = A; and Equation 2.100 is reducible to
CHAPTER 2 — FLUID FLOW
2-77
n= [ii 494(4-D]o aim
where symbols are the same as for Equation 2.101.
The equations given above for plates and screens are for relatively
high Reynolds numbers and low Mach numbers. For low- Reynolds
number and high-Mach number corrections, consult Idel’chik.'
Example 2.14
Obstruction Losses
Given a 3-in. | beam running through a 12-in. round duct with
1000 cfm of standard air, find the obstruction loss when the web
is parallel to the flow and the beam is centered in the duct.
—, FEBS
ise ok 44a
AcmEON94255
rage otesa
2
= 0.1942 ft’,
2112
k, = 1.15 for struts running completely across,
k=
1.0 for zero offset,
7 =
1.5 for sharp objects, and
Pv = 0.10 (from Example 2.4).
Using Table 2.6 and Equation 2.99:
Cp = 1.2 for 1 beams,
As
Di
Cp —
j=
pepe
(ioe
bikapn, and
028) 2 ee
[1 — 1.5(0.2472)]’
1.15 X 1.0
X 0.1 = 0.14
in. wg.
Given a woven wire screen with 40% open area in a 12-in. round duct
with 1000 cfm of standard air, find the screen loss.
Ti,
Eee
and
pv = 0.10 (from Equation 2.4)
'Idel’chik, pp. 321-349.
2-78
FAN ENGINEERING — BUFFALO FORGE COMPANY
Using Equation 2.102:
p= [1300-3ae (4t-1) Jonand
pr=[1.30(1
— 0.4) + (2.5 — 1)°] 0.10 = 0.3 in. we.
Compressible Flow
The flow of any gas is compressible, but as noted previously, the
flow through a fan system can almost always be considered incompressible. The error in ignoring compressibility effects in the computation of pressure variations will be less than one percent for Mach
numbers up to about 0.2 (based on Equation 2.53, using this value
to evaluate the bracketed terms).
The coefficients of friction and loss given in the preceding sections
probably
can be used for Mach numbers even higher than 0.2.
Shapiro states that incompressible friction formulae are applicable
up to Mach numbers of 1.0. Although Benedict, et al” have shown
that, as Mach numbers increase, coefficients of loss for abrupt enlargements
decrease
and those for abrupt contractions
increase, the
changes are significant only for large steps. (Benedict also suggests
that the ratio of exit to inlet total pressure is not affected by compressibility in subsonic flow.)
For uniform ducts, the properties of the gas will vary along the
flow path because of friction. In subsonic adiabatic flow, the pressure,
temperature, and density will decrease while the velocity and Mach
number will increase. In supersonic flow, the opposite variations take
place, and they can be very significant depending on the length of
the duct and the initial Mach number. In fact, there is a maximum
length of duct for a given mass flow rate, or conversely, there is a
maximum mass flow rate for a given length of duct. This choking
effect occurs when the Mach number at the exit becomes unity.
In order to obtain a supersonic velocity in a duct system, there
must be a converging section followed by a diverging section, with
Ma = |.0 at the throat. The diverging section becomes a supersonic
nozzle just as the converging section becomes a subsonic nozzle, with
velocity increasing and pressure decreasing in both. In a supersonic
wind tunnel, such a nozzle combination is located upstream of the
test section. Downstream of the test section, a similar combination
serves as a diffuser. The converging section is the supersonic diffuser,
and the subsequent diverging section is the subsonic diffuser.
'A.H. Shapiro, The Dynamics and Thermodynamics
Press Co., New York, vol. Il, Chapter 28, p. 1131.
*R.P. Benedict and N.A. Carlucci,
York, 1966, pp. 23-26.
Handbook
of Compressible
Fluid Flow, The Ronald
of Losses in Flow Systems,
Plenum
Press, New
CHAPTER
2 — FLUID FLOW
2-79
Liquid Flow
The data for the incompressible flow of air and gases usually can
be applied to the flow of liquids. However, since water at ordinary
temperatures weighs approximately 800 times more than air, elevation
differences are more significant in liquid flow than in air flow. In
addition, under certain conditions of reduced pressure or increased
temperature, the vapor pressure of the liquid may approach the pres-
sure of the liquid. When it does, the vapor and the liquid phases may
exist simultaneously. Then cavitation will result from the alternate
formation and collapse of vapor bubbles in the liquid, producing
noise, wear on parts, and pressure surges. The friction charts for the
flow of air through conduits, Figures 2.13 and 2.15, can be used for
the flow of water provided that the appropriate corrections are made
\\r
Ss
No?
ca
at \\\
oo
5% |
oe
Ws 4h 658 10 1b) oe
oa
PIPE DIAMETER — INCHES
Figure 2.36
6.6
8210).
15.20
Pipe Friction Chart in Diameters per Velocity Head
Adapted from the data of R.D. Madison and W.R. Elliot: “Pressure Losses for Liquid Flow in
Pipes,” Chemical Engineering Progress, vol. 44, September 1948, pp. 703-706.
CHAPTER
2 — FLUID FLOW
CORRECTION
FACTORS FOR
VERY ROUGH
2-81
TS 22S See
\n
al
CORRECTION
FACTOR
1.0
cae Oe
OleOn aitU
125220
3.0 4.0 5.0
WATER VELOCITY — ft/s
Figure 2.38
10.0
15.0
20.0
Roughness Corrections for Pipes
Adapted from the data of R.D. Madison and W.R. Elliot: “Pressure Losses for Liquid Flow in
Pipes,” Chemical Engineering Progress, vol. 44, September 1948, pp. 703-706.
Table 2.7
Resistances of Standard Pipe Fittings
to Flow of Liquids
Equivalent Lengths in Feet
:
Velocity
Valves
Size | Head
in.
(open)
Factor
Check
;
2.1
2.6
3.6
86
131
1.4
119
1.1
1.4
1.8
2.4
2.7
Shi)
4.2
5.8
3.1
40
5.0
7.0
7.0
8.5
3.0
6.0
7.0
9.0
11.0
15.0
4.1
5.3
6.2
78
Dep:
2.9
325
4.0
2.8
3.5
41
ao]
6.8
8.5
11.0
Ws
8.0
0.0
3.0
5.0
8.0
5.0
9.0
5.0
18.0
23.0
26.0
33.0
10.2
5.6
13.0
7.0
16.0
8.0
20.0 | 11.0
7.0
9.0
11.0
14.0
| 16.0
| 21.0
| 25.0
| 34.0
8.0
60.0
73.0
H
44.0
55.0
65.0
85.0
Adapted from the data of Crane Co.: “Flow of Fluids Through Valves, Fittings, and Pipe,” Tech.
Paper No. 110, 1957, p. A-31.
2-82
FAN ENGINEERING — BUFFALO FORGE COMPANY
for differences in kinematic viscosity and roughness. For convenience,
two similar charts, Figures 2.36 and 2.37, have been drawn for 70°
water flowing through clean steel or wrought iron pipes. Figure 2.38
can be used to correct for very rough pipe. Figure 2.36, like Figure
2.13, is particularly useful when differences in kinematic viscosity
must be taken into account. The method, as previously described, is
simply one of maintaining the same Reynolds number by calculating
an equivalent velocity corresponding to the new kinematic viscosity.
Much of the data on elbows and other fittings given for air and
gases was actually determined from tests conducted with water and
other liquids. Additional data on the resistance, in equivalent length,
of certain standard pipe fittings are given in Table 2.7. The second
column in this table gives a factor for converting the loss in equivalent length to the loss in velocity heads. For instance, the equivalent
length of a standard 3”-diameter 90° elbow is 7.8 feet, and the number
of velocity heads corresponding to the loss is equal to 7.8 X 0.067, or
0.52 velocity heads.
Pressure and Flow Measurements
The instruments and methods that are generally used in fan engi-
neering to measure pressure and flow are discussed in this section.
Since the measurement of barometric pressure was examined in Chapter I, only gage pressures will be considered here. Because all the
flow measurement methods described include the use of pressure
measurements, the discussions of pressure and flow are interspersed.
There are two stages of pressure measurement: sensing and indicating. Different sensors must be used depending upon whether they
are intended to respond to total, static, or velocity pressure. These
sensors may be connected to separate indicating gages or transducers.
Alternatively, the indicator may be integrated with the sensor.
Pressure Taps and Probes
A pressure tap is basically a small opening in the wall of a container
or duct. It may be equipped with a fitting for the connection of a
gage or transducer via a hose or other conduit as shown in Figure
2.39. Alternatively, a transducer may be exposed to the pressure to
be measured by being mounted flush with the hole. Pressure taps, or
wall taps as they are frequently called, are used to sense static pres-
sure. If one leg of a manometer is connected to the wall tap and the
other leg is open to the atmosphere, the gage static pressure will be
indicated. Wall taps can be used to sense the static pressure in either a
gas at rest or a moving gas stream. No special precautions are necessary for gases at rest, but impact and aspiration effects must be
avoided for moving gas streams. Wall taps in a duct must be small,
CHAPTER 2 — FLUID FLOW
FLOW (IF ANY)
Net
IMPINGEONHOLE
f
Flow
DUCT WALL
HOSE FITTING
4
Le
#f
2-83
1/2d << <6d
TO INDICATOR
Figure 2.39
Pressure Tap
free from burrs, and sufficiently far from disturbances such as elbows
and internal obstructions so that disturbance effects are negligible.
Theoretically, the holes should be infinitely small with square edges,
but for Reynold
numbers
0.01 duct diameters,
less than
10’ and for hole sizes less than
the error will be less than 0.01 duct velocity
pressures.: Rayle* has shown that failure to remove burrs can result
in a negative error of up to fifteen percent of the velocity pressure.
Wall taps can sense the pressure only in the vicinity of the hole, but
the same pressure should prevail across the duct section if the flow is
reasonably uniform.
SECTION A-A
DUCT WALL
INDICATOR
Figure 2.40
Round Nose Static Pressure Probe
The static pressures across a section can be sensed with a static
pressure probe. This is usually a bent tube with a rounded nose
pointed into the flow and having a series of static taps drilled about
8 diameters from the nose along the 24-diameter stem as shown in
Figure 2.40. At this point the nose effect, which increases tap pressure, compensates for the decrease due to stem effects. Other forms
of static pressure probes require careful calibration to determine the
effects of flow on the reading. Directional probes, discussed below,
can also be used as static pressure probes.
'R.P. Benedict, Fundamentals of Temperature, Pressure, and Flow Measurements,
John Wiley and Sons, New York, 1977, p. 348.
Second Edition,
°R.E Rayle, “Influence of Oritice Geometry on Static Pressure Measurements,” ASME
59-A-234, 1959.
Paper No.
|
FAN ENGINEERING — BUFFALO FORGE COMPANY
2-84
;
hes
d
FLOW —>
a
A
DETAIL A-A
eae
(eer
DUCT
te
HOSE
WALL
DUCT
eee
——_—F
WALL
HOSE
|
|
TO INDICATOR
TO INDICATOR
Figure 2.41
Impact Probe
The total pressure at a point in a moving gas stream can be measured with an impact probe pointed into the flow. The Pitot tube,
which is a bent tube having a hole in the nose as shown in Figure 2.41,
is usually used, but directional probes may have impact taps, too.
The shape of the nose is not important except when the Pitot tube is
combined with a static probe for velocity pressure measurements.
0.40 DIA.
serve
were ces a LEUILLSOS
ee
OD
HEAD SHALL BE FREE
FROM NICKS AND BURRS
30D
RADIUS
le
\
;
—SECTION A-A—
STATIC PRESSURE
ALL DIMENSIONS SHALL
BE WITHIN +2%.
8 HOLES - 0.13 D, NOT TO EXCEED 0.04 IN.
DIA. EQUALLY SPACED AND FREE FROM
BURRS. HOLE DEPTH SHALL NOT BE LESS
THAN THE HOLE DIAMETER.
TOTAL PRESSURE
Figure 2.42
Pitot-Static Tube
The velocity pressure at a point can be measured with a variety of
probes that sense both total and static pressure. The Pitot-static tube,
illustrated in Figure 2.42, is the standard for laboratory measurements. In practice, the total pressure tap is connected to one side of
a manometer, and the static pressure tap is connected to the other
side. Both static pressure and velocity pressure, or total pressure and
velocity pressure, can be measured simultaneously by using a tee connection in the appropriate line and a second manometer.
CHAPTER 2 — FLUID FLOW
2-85
DUCT WALL
——_»
!
=
Figure 2.43
HOSES
TO
INDICATOR
Stauscheibe Probe
A properly constructed and maintained Pitot-static probe is generally considered a prime instrument that does not require calibration.
However, errors will occur if the probe is not properly aligned with
the flow, so a straightener should be located upstream of the measuring section. Errors due to turbulence, velocity gradient, and blockage
are generally negligible.’ Nevertheless, field measurement with a Pitotstatic tube can be troublesome. A bent tube is difficult to insert
through a pipe coupling connection, and the small holes are susceptible to plugging. These difficulties can often be avoided by using a
Stauscheibe, or type-S, probe. This probe, illustrated in Figure 2.43,
has a tube facing forward and also a reverse tube. The differential
pressure across the combined forward-reverse tubes is higher than the
velocity pressure and requires a calibration correction. Both the Pitotstatic and the forward-reverse probes are substantially non-directional
and should not be used if the flow directions are unknown.
Directional probes are generally patterned after the Fechheimer
tube,’ which is a cylindrical probe having two independent holes located
as shown in Figure 2.44. To determine yaw, the probe is inserted
into the stream; the two holes are differentially connected to a manometer; and the probe is rotated until the gage nulls. A line bisecting
the angle between the holes indicates the direction of the oncoming
flow, and the angle between this line and the duct axis is the angle of
yaw. The holes are spaced so that a manometer connected to only
one tap would register the static pressure under ideal conditions. In
practice, however, a calibration is required for different Reynolds
numbers. Although a three-hole probe may have a different shape,
it is operated in the same way. In addition the third hole, which is
located to face into the flow, is used to measure the total pressure. A
"R.P. Benedict, Fundamentals of Temperature, Pressure, and Flow Measurements, pp. 350-370.
C.J. Fechheimer, “Measurement of Static Pressure,” Trans. ASME, vol. 48, 1926, pp. 965-977.
BUFFALO FORGE COMPANY
— ING
FAN ENGINEER
2-86
Flow
A
A
SECTION “A-A”
DUCT WALL
(erzezPPT IITA
———
:
coe
PROBE
STATIONARY
PROTRACTOR
HOSES TO INDICATOR
Figure 2.44
SECTION “B-B”
Fechheimer Tube
five-hole probe has two additional holes located so that a differential
pressure obtained by connecting them to a manometer, together with
the differential from the total and static taps, can be used to determine pitch from a calibration.
Pressure Gages and Transducers
The pressure taps and probes described in the previous section
can serve only as sensors. To measure pressure, an indicating device
is also needed. Various principles can be used to make different pressure gages and transducers.
For instance, the U-tube manometer can be made from 3/16- to
1/4-inch bore glass tubing and a suitable linear scale. In operation,
the gage is partially filled with water or other fluid of known specific
gravity. One leg is then connected to a pressure tap or probe, and the
other leg is connected to some reference pressure. The liquid will be
displaced by the higher pressure and will rise in the other leg as
shown in Figure 2.45. This illustrates the most general case: one in
which the fluid for the reference pressure is different from the fluid for
the pressure being measured. The densities and heights of these fluids
affect the displacement of the manometer fluid in accordance with
n-namb[+(2)(2)- (OED
(2.103)
The pressure difference p; — p2 is the gage pressure relative to the
reference pressure p>. In fan engineering, the reference leg of the
manometer is usually left open to the atmosphere so that the reference
CHAPTE
2 — FLUID
R
FLOW
Figure 2.45
2-87
U-Tube Manometer
pressure is atmospheric pressure. The units of the gage pressures
obtained from Equation 2.103 will depend on the units used for the
density p, of the manometric fluid, the height A» of the manometric
column, the acceleration due to gravity g, and the gravitational correction factor g-. Any consistent units can be used for the terms in
the bracketed factor. If p» is in Ibm /ft', A ap i hi
ii ft/s’ and g- in
it‘Ibm /Ib-s? then pi — P2 will be in lb/ft”. If pm is in kg/m’, A» in m, g
in m/s* and g, in m-kg/s™N, then p; — p> will be in Pa. In fan engineering, it is customary to drop the pmg/g- term and to directly report
gage pressures in terms of the height of the manometric fluid. Actually the pmg/g- term should not be dropped but, rather, replaced by
Pm&/Pmoo Where Pmo is the density of the manometric fluid at standard temperature and g, is standard gravitational acceleration. The
bracketed term is reducible to / — p;/pm if p1 = p2 and h; = h2, which
usually is so in fan engineering. This gas-column-balancing effect is
only about 0.1% and, therefore, is frequently ignored. Rewriting
Equation 2.103 and taking into account the above considerations gives
Dee
Paes2 Gre ta
eign
(2.104)
Values for the densities of water and mercury at various temperatures are listed in Table 2.8. Standard temperature for water gages is
usually 68°F or 20°C, while standard temperature for mercury gages
(particularly barometers) is usually 32°F or 0°C.
In simple U-tube manometers, the height of the manometric column
is determined by reading the level of the fluid in the two legs and
then subtracting the lower from the higher. The scale used for these
measurements should be calibrated and the readings adjusted for any
change in temperature. This temperature adjustment is usually negli-
2-88
FAN ENGINEERING — BUFFALO FORGE COMPANY
Table 2.8
Densities of Water and Mercury
Temperature
(coe
32
35.6
39.2
42.8
46.4
50
53.6
57.2
60.8
64.4
68
71.6
75.2
78.8
82.4
62.4229
Weel?
Mercury
Pm Pmo
848.714 | 13595.1]
848.402
848.096
847.784
847.478
847.172
846.860
846.554
846.248
845.942
845.630
845.324
845.018
844.712
844.407
844.101
Adapted from the data of J.A. Dean, Ed., Lange's Handbook of Chemistry,
Hill Book Company, New York, 1973, p. 10-125.
1.00000
0.99963
0.99927
0.99890
0.99854
0.99818
0.99782
0.99746
0.99709
0.99673
0.99637
0.99601
0.99565
0.99529
0.99492
0.99456
\\th Edition, McGraw-
gible if the gage is used near the calibration temperature.
The manometric fluid will form a miniscus at the surface. For water
in glass the miniscus will be concave upward, while for mercury in
glass the miniscus will be concave downward. The level of the fluid
should be determined at the same point in the miniscus for each leg.
Various adaptations of the U-tube manometer are used to increase
accuracy, to provide the convenience of a single reading, or to
do both.
Precision U-tube manometers are called micromanometers. In one
type of micromanometer, the tubes are both enlarged at the levels
where the readings will be made. As shown in Figure 2.46, the level
is determined by moving a sharp, pointed index into contact with the
surface of the manometric fluid. Contact may be sensed visually or
electrically. The difference between a reference level and a liquid level
is determined by individual micrometers as shown. Other micromanometers use a precision lead screw with a micrometer head. This lead
screw may be motorized to move either leg, one of which has a small
inclined portion in which the miniscus is located precisely.
An inclined manometer is usually constructed as shown in Figure
2.47. In operation, the gage is zeroed, the differential pressure is
applied, and only the deflection of the inclined leg is measured along
the inclined scale. Since the vertical leg deflection is not measured,
that deflection either must be negligible or else the inclined scale
CHAPTER
2 — FLUID FLOW
2-89
must be adjusted to take that deflection into account. The inclined
scale, in effect, magnifies the reading of the manometric deflection.
The degree of magnification depends on the angle of inclination a.
The magnification factor would equal cor a except for the deflection
of the vertical leg. Inclined manometers should always be calibrated
against a micromanometer.
MOVABLE
POINTER
INDEX
LARGE BORE TUBE
CONNECTING TUBE
Figure 2.46
Micromanometer (Micrometer Type)
Figure 2.47
Inclined Manometer
Numerous other pressure transducers can be used for pressure
measurements. There are other manometers such as the McLeod
gage and the Zimmerli type for low absolute pressures. Other mechanical types use Bourdon tubes, bellows, or diaphragms, together with
a mechanical linkage, for a wide range of pressure measurements.
Piezoelectric elements are used to measure sound pressures and other
rapidly fluctuating pressures. Other electrical pressure transducers
use strain gages, potentiometers, capacitors, transformers, and reluctance elements.
2-90
FAN ENGINEERING — BUFFALO FORGE COMPANY
Flow Rate by Velocity Traverses
The flow rate at a particular cross section in a duct can be determined by measuring the local velocities at a sufficient number of
points to establish the distribution and then integrating over the
area. The local velocities can be measured with various anemometers
as discussed in the next section. Or they can be determined by measuring the local velocity pressures with a velocity pressure probe as
discussed in an earlier section. In either case, the number and locations of the measuring points must be established. Various means of
establishing points are discussed below.
The velocity profile in a duct depends on Reynolds number, relative roughness, and upstream disturbances. However, in general, the
flow will be retarded near the walls. Since it is virtually impossible
to measure the flow very close to the walls, assumptions about the
velocity distribution in this region have to be made. The various
methods described below differ in their assumptions about the distribution in the main flow as well as in the boundary flow.
One of the most common ways to establish the locations of the
traversing stations is to divide the duct into a number of equal areas
and then take the measurement at the centroid of each. Figure 2.48
shows these locations for both rectangular and circular ducts. The
sketches are for a particular number of equal areas, but the associated
tables give values for various other numbers of measuring points.
This method does not take into account the retardation of the flow
near the wall, so a positive error nearly always results. All measuring
points are given equal weight in the integrating procedure, which is
described below. In a variation of this method that was used in
AMCA 210-67, the outermost points for the circular duct traverse
were relocated according to the Prandtl 1/7-power law. For a traverse based on five points per radius, the location of the last point
was moved from 0.474 to 0.480.
Another technique, introduced by Winternitz and Fischl' and known
as the log-linear method, is based on the Nikuradse formula for fully
developed flow. Figure 2.49 shows the locations of the traverse points
for both rectangular and circular ducts using this method. Once
again, the sketches are for a particular number of measuring stations,
and the table for circular ducts offers locations for various numbers
of points per radius. The 26-point technique shown for the rectangular duct was presented by Miles, Whitaker, and Jones’ for adoption
as a British standard. The individual points are not weighted equally
in the integration procedure; rather, they are given the weightings
'F.A.L. Winternitz and C.F. Fischl, “A Simplified Integration Technique for Pipe-Flow Measurement.” Warer Power, vol. 9. no. 6, June 1957, pp. 225-234.
*D.J. Myles. J. Whitaker, and M.R. Jones. “A Simplified Integration Technique for Measuring
Volume Flow in Rectangular Ducts.” NEL Report No. 251, National Engineering Laboratory,
East Kilbride. Glasgow, 1966.
‘
CHAPTER 2 — FLUID FLOW
7
F= 1.0 FOR ALL PTS.
5 POINTS/RADIUS SHOWN
F, DIAMETERS SHOWN
F = 1.0 FOR ALL PTS.
Figure 2.48
Centroids of Equal Areas for Rectangular and Circular Ducts
2-91
2-92
FAN ENGINEERING — BUFFALO FORGE COMPANY
F= 1.0 FOR ALL PTS.
Figure 2.49
Log-Linear Traverse Points for Rectangular and Circular Ducts
CHAPTER
2 — FLUID FLOW
2-93
5 ROWS SHOWN
ROWS OR PTS/ROW |DISTANCE FROM CENTERLINE - x/L ORy/M
F=1.0 FORALL PTS.
F= 1.0 FOR ALL PTS.
Figure 2.50
Log-Tchebycheff Traverse Points for Rectangular and Circular Ducts
2-94
FAN ENGINEERING — BUFFALO FORGE COMPANY
shown in the table for the 26-point method. The individual readings
are, however, equally weighted for circular ducts. Various profiles
were explored by Brown,’ which led to the adoption of the 24-point
technique (6 radii, each with four points) in AMCA 210-74/ASHRAE
51-75.
The log-Tchebycheff method postulates a logarithmic distribution
near the wall and a polynomial distribution of velocity elsewhere.
Figure 2.50 shows the locations of the measuring stations for both
rectangular and circular ducts with varying numbers of points per
side or radius. All measurements are equally weighted in the integration procedure. This method is referenced in various international
standards.
Regardless of whether the traversing method is based on the
centroids of equal areas, on the log-linear distribution, or on the logTchebycheff distribution of measuring points, it is essential that the
probe be properly aligned with the flow. Most laboratory standards
call for a calming length and a straightener to ensure that the direction of the flow is parallel with the duct walls across the measuring
plane. This facilitates the use of any non-directional probe provided
that it is properly aligned with the duct axis. Such alignment, however, is not necessarily used in non-laboratory situations. For on-site
testing, a directional probe is recommended. Such a probe should be
used properly aligned with the flow as determined by the nulling feature of such probes, and only the component of velocity along the
duct axis should be used for the calculation of flow rate. It is also
important to check that the duct is clear of obstructions and to determine the inside area accurately. Whenever it is expected that a traverse
will take considerable time to execute, monitor the flow to ensure
against variations with time. This can be done by fixing a second
probe in a suitable location and monitoring its readings.
The integration procedure to find flow rate from centroid-of-equalarea measurements, log-linear measurements, or log-Tchebycheff
measurements is really an arithmetic procedure used to estimate the
integral. First, compute the individual local normal velocities V,;,
apply weighting factors F; as required, and then average arithmetically. This average normal velocity, when multiplied by the cross-sectional area A, gives the volume flow rate Q:
:
jis
SP ieTs SD
(2.105)
The individual velocities can be calculated using Equations 2.28
through 2.31 as appropriate. Note that it is not proper to simply
average the velocity pressures even when the density is constant across
the section. The cited equations can be used to determine the average
'N. Brown, “A Mathematical Evaluation of Pitot Tube Traverse Methods,” ASHRAE
2335, presented at Atlantic City, 1975.
Paper No.
SEE
CHAPTER
2 — FLUID FLOW
EE
EE
eee
2-95
velocity when the density is constant only by using the average square
root of the velocity pressure. The mass flow rate m can also be determined from these measurements using
:
m=A—
ya
> (pF V,
ee
(2.106)
where p; is the local mass density at the various measuring points.
Graphical integration, too, can be used to find flow rate from traverse measurements. This method offers much more flexibility in
selecting the number and locations of the measuring points. For a
rectangular duct, the measurements for each traverse of the probe
should be plotted as ordinate with their normalized locations as
abscissa. The normalized locations are the actual distances from the
duct wall divided by the total distance across the duct. Additional
measurements should be made whenever the distribution appears to
be questionable. Some assumption will be required regarding the
flow at the boundaries. The area under the curve can be determined
by using a planimeter. This area is the mean velocity for the traverse.
A similar procedure is used for all the other traverses, and the result-
ing mean values are then plotted against their normalized locations
in the other dimension of the duct. The area under this new curve is
the mean for the entire cross section of the duct. For a circular duct,
the measurements for each traverse are plotted against the square of
their normalized radial locations, and instead of measuring the area
under each curve, the values on selected circumferences are arithmetically averaged and the averages are then plotted against the square
of their normalized locations. The area under this curve is the mean
for the entire cross section of the duct.
Even when arithmetical methods
are used to find the flow rate, it
may be wise to check the measured distribution graphically. Unusually high or low values should be investigated.
A single reading can sometimes be used to estimate the flow rate.
When the flow is turbulent and the test section is at least forty
diameters downstream from any disturbance, the approximate mean
velocity Vn can be determined from the center-line velocity V. and
the friction factorfusing
!
Vn = VX ——————.
1+ 1.439\/f
(2.107)
Average Pressures from Traverses
In the early portions of this chapter, the fundamental equations of
fluid flow were examined in their one-dimensional form, and appro-
2-96
FAN ENGINEERING
— BUFFALO FORGE COMPANY
priate average values were suggested for use in those equations when
the flow was not one-dimensional. These same average values are
used here, but other types of averages are possible and may even be
desirable in some situations.
In the preceding section, volume flow rate was determined from
an area-weighted average velocity. Similarly, mass flow rate was determined from an area-weighted average product of density and velocity.
These quantities are useful in calculating the average pressures at the
traverse planes. Another useful quantity is the average density p at
the traverse plane, which can be defined as the mass flow rate m
divided by the volume flow rate Q, or
gyal = (pjFjVnj)
n
i
ji
Q@
n
> (ei Vn)
]
j=
n
As =E (FV)
S (FVnj)
(2.108)
n
j=]
where p, is the density and V,,; is the normal velocity at the measuring
point. Note that this equation is entirely consistent with the continuity equation and that the average density is a volume-flow-weighted
value.
The average static pressure ps is also a volume-flow-weighted value:
1
n
2 arr = (Psj FiVnj)
/
2 Cesk) Vnj)
/
/
two
:
A>, & (Filni)
‘ec2 (Fivni)
(2.109)
Note that, since the static pressure is joined with the density in the
flow work term of the general energy equation, it is consistent that
averages for both static pressure and density are volume-flowweighted.
The average specific kinetic energy ex and average specific potential
energy ep are both mass-flow-weighted values. The specific potential
energy is usually negligible in fan engineering, but the average specific kinetic energy can be determined from
~
I
a
n
TA TE (oiF Vn’)
kao
n
BAT > (eiFK)
(has, © (o)Fi Vas’)
=
28
n
eI)
:
(2.110)
CHAPTER 2 — FLUID FLOW
2-97
The average velocity pressure py can be obtained from the average
specific kinetic energy and the average density using
=
PeK
BEC:
(2.111)
where C, is 5.193 in U.S. customary units and 1.0 in SI units.
The average total pressure is simply the sum of the average static
pressure and the average velocity pressure as indicated by:
Pr=pst+pr.
(2a)
Anemometers
The term anemometer is used here to describe those instruments
that can be used to determine local velocities but utilize principles
other than the relationship between pressure and velocity. Included
in this classification are rotating-vane anemometers, swinging-vane
anemometers
(velometers),
turbine
meters,
hot-wire
anemometers,
Kata thermometers, and laser-Doppler meters.
The vane anemometer is a rotating-vane type of instrument that
can be designed either to register velocity or to give a reading over a
timed interval that can then be converted to velocity. Such an anemometer requires frequent calibration because readings are greatly
affected by the condition of the bearings. This instrument is useful in
measuring low velocities at supply-register and exhaust-grill openings
when in-duct measurements are not convenient and high accuracy is
not required.
The operator should move the anemometer slowly and uniformly
over the whole flow area in order to arrive at an average determination. Exhaust capacity Q can be calculated by using the average
velocity V (obtained with the dial of the anemometer facing the grill),
the gross area of the grill Ay, and a correction factor Kg that can be
determined from Table 2.9 in
O = KeVAg.
(2.113)
Supply capacity QO can be determined by using the average velocity
V (obtained with the dial facing the operator), the gross area A, plus
the net free area A,, and a correction factor Ks determined from
Table 2.9 in
O=0.5 KsV(Ag+ Ap.
(2.114)
The turbine meter can be designed for radial flow, axial flow, or
2-98
FAN ENGINEERING — BUFFALO FORGE COMPANY
Table 2.9
Values of Ksand Kzin Anemometer
Formulae
Average Indicated Velocity, fpm
Gril
et
150 | 200
Ks Supply
Ke Exhaust
Se 957
AG |) HZ
Adapted from the data of L.E. Davies, “The Measurement of Flow of Air through Registers and
Grilles,” Trans. ASH VE, vol. 36, 1930, pp. 201-224.
tangential flow, but the axial-flow type is probably most used for gas
metering. It is usually mounted on the end of a probe for traversing
the duct.
The velometer is a direct-reading, air-velocity meter that is operated by the impact of the flowing air against a swinging vane. By
suitably designing the inlet and outlet jets, the instrument can be
adapted to read either high or low velocities. The velocity can be
taken at any point, or an averaging jet can be used to obtain the
average velocity over an area. These instruments have the advantages
that they can be read directly, are easy to use, and require no additional equipment. Occasionally, the meter itself is placed in the air
flow being investigated. If the flow is appreciably different at the two
ends of the meter, such as in front of exhaust hoods, a material error
may result.
A hot-wire anemometer consists of a resistance wire placed in the
air stream and heated by an electric current. The temperature of a
current-carrying Wire in an air stream depends on the current and the
rate of heat loss to the air. Since this heat loss varies with velocity,
air flow can be determined from the relation between the current and
the temperature of the wire, or between the current and the temperature rise of the air over the wire. Wire temperature can be established
in terms of its resistance.
The time required for the reading of a heated Kata thermometer
to fall through a specified interval (usually 100° to 95°) is a measure
of the non-directional air velocity. Heated-thermocouple and heatedthermometer anemometers each use a pair of temperature-sensitive
devices, one heated and the other not. The difference in reading for
a given heating rate is a measure of the air velocity over the elements.
All of the above devices (when properly calibrated) can be used to
measure low velocities with good accuracy. Refer to the earlier section
on flow rate from traverses for traversing patterns and calculation
procedures.
Differential Pressure Meters
Differential pressure meters can be of the orifice, nozzle, or venturimeter types. Each of these devices produces a pressure difference
that can be correlated with the flow rate. These kinds of meters differ
CHAPTER
2 — FLUID FLOW
2-99
from both anemometers and pressure probes in that the whole flow
must pass through the meter, whereas both pressure probes and
anemometers must be traversed across the flow and sample only a
portion at a time.
Given a plate with a hole in it and a pressure difference, fluid will
flow from all directions on the higher pressure side and issue as ajet
on the lower pressure side. The jet becomes substantially uni-directional at a point somewhat downstream from the opening. At this
point, called the vena contracta, the contraction of the jet (which
occurs because of the multi-directional approach and corresponding
directional momentum on the high pressure side) becomes maximal.
That is, the area at the vena contracta
is the minimum
that can be
achieved with such a free jet. When the edge of the opening is perfectly square, the area of the stream at the vena contracta will be very
close to 60% of the area of the opening. The location of the vena
contracta will be one half of an opening diameter downstream of
the face of the opening. Considerable static pressure is transformed
into velocity pressure in producing acceleration by means of an orifice. This conversion is highly efficient, and the loss is amazingly
low. However, the opposite conversion, from velocity to static pressure, requires careful design in order to obtain high efficiencies or
avoid high losses. The pressure loss between the upstream face and
the vena contracta affects the velocity profile at the vena contracta.
The flow coefficients, as defined below, can be used to determine
flow rates and pressure losses for any orifice or nozzle. The subscript
1 will be used to denote the upstream location, whether it be pipe or
plenum, and the subscript 3 to denote the plane of the vena contracta.
The subscript 2 will be used to denote the plane of area A>. For an
orifice, A» is the area of the opening at entrance.
For a nozzle, A> 1s
the area of the opening at exit.
Based on Equation 2.26, the energy balance
flow for any orifice or nozzle can be written:
for incompressible
Psi + pm = ps3 + pv3 + Pi-3
(2a)
in which the pressure loss is denoted by pzi-3.
The coefficient of contraction Cc, which can be defined as the ratio
of the area of the vena contracta to that of the area at entrance to an
orifice or at exit from a nozzle, can be written:
Ge
4
(2.116)
The coefficient of velocity Cy, which can be defined as the ratio of
the actual average velocity at the vena contracta to the velocity that
would be obtained if there were no loss, can be expressed by
2-100
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Pyv3
Cy=
V Pu-3+
pra
;
(2.117)
The coefficient of resistance Cr, which can be defined as the ratio
of the loss of total pressure to the velocity pressure at the vena
contracta, can be written:
Cp
Pui-3
=
S
Disa,
ji
SS
(OV,
= |! -
(2.118)
The coefficient of discharge Cp of an orifice or nozzle can be defined as the product of the coefficients of contraction and velocity, or
Equation 2.5, which is for incompressible flow, can be rewritten:
a)
V3A3
VrA>
ViA,
(2 120)
where volume flow rate QO is in cfm when areas A are in ft? and
velocities V are in fpm. The corresponding SI units are m’/s, m’, and
m/s. Combining this with Equation 2.28 produces
“ee
NGG
Pv3
as
(2.121)
where Cy is 1097 if AeA pressure py is in in. wg and density p is in
lbm/ft*, or Cy is
if SI] units are used. Incorporating the definition
of coefficient of Anes yields
i=
prs
Similarly, using the definition of coefficient of velocity results in
oe
QO = C.CcCvAr~
Pv3 pres
/ eg
TTR
(2.123)
Substituting the coefficient of discharge for its equivalent produces
a
Q=C\CrA2
Pv ar D3
/ a ypReeetey
,
(2.124)
Manipulating Equation 2.115 and making the appropriate substitution
CHAPTER
2 — FLUID FLOW
2-101
in Equation 2.124 gives
a ty
/ pr = Ps3
Q =< Cy CoA 2
p
or
S ined
Pv
+ psi 7
Q ae Cy CpA2
a
ey
(2. 125)
Ps3
ee
P
(2.126)
After removing the approach velocity pressure py; from under the
radical,
wiser
/ Psi — ps3
The true velocity of approach factor for incompressible flow @;
can be found by equating Equations 2.126 and 2.127, or 2.125 and
MNOTYE
bi=
Pv
+ ps) meS3
Psi — Ps3
Es
Pr
— Ps3
Psi — ps3 *
(2.128)
Using the relationships embodied in Equations 2.115 and 2.117,
di =
:
‘
1 — pu /(pv3 + pui-3)
7
:
j= CV (pu/pvs)
(2.129)
The true velocity of approach factor can also be written as a function
of area ratio and coefficient of velocity or discharge:
1 — Cy'(A3/Ai)y?
NOCT Ry
ONES)
A pseudo velocity of approach factor, 1.e. g;’ = JV 1/1 = (A2/Ai))
or one based only on area ratio, is frequently used. In such cases
a pseudo coefficient of discharge, i.e. Cp’ # Cc X Cy or one different from that defined, must be used in Equation 2.127 (and in
Equation 2.136 which is given in the section on nozzles). Note that
pi'Co’
=
hiCo.
For a nozzle or orifice discharging into the atmosphere, the static
pressure at the vena contracta p3 is equal to zero. Thus, it is necessary
only to measure either the average total pressure or the average static
pressure ahead of the nozzle or orifice in order to find the flow rate.
more convenient to measure the average
Since it is usually much
static pressure rather than the average total pressure, Equation 2.127
2-102
FAN ENGINEERING
— BUFFALO FORGE COMPANY
is used even though it does involve the velocity of approach factor.
Also note that for a plenum approach the velocity pressure py: equals
zero, and therefore, the velocity of approach factor ¢; equals 1.0.
Numerous values for the various flow coefficients have been established empirically. Where similar conditions of flow and measurement exist, these data can be used to predict flow rates from pressure
readings. However, if there is any doubt whatsoever about the uniformity of the upstream flow or the conditions of measurement, or
both, an in-place calibration against a Pitot tube should be made.
There are numerous differential pressure devices that can be used
to measure flow. The flow coefficients for some of these devices,
together with the method of pressure measurement and brief details
of construction, are given in the paragraphs below.
The Square-Edged Orifice
The square-edged orifice is a flat plate with a hole in it. The hole
may be of any shape. In the extreme, it may even be a slot with a
very large aspect ratio. The coefficient of discharge with a plenum
approach is about 0.6 regardless of shape. Orifice plates should be
perfectly flat and the holes accurately made for precise area determinations. All burrs must be removed from the inlet edge so that the
air flows over a sharp 90° corner. The thickness of the edge should
not exceed 1/50 of the orifice diameter. Recommended thicknesses
for various diameters are 1/16 in. for up to 6 in., 3/32 in. for up to
12 in., 1/8 in. for up to 24 in., and 3/16 in. for up to 48 in. Thicker
plates, when required for rigidity as in high pressure work, should
be beveled away on the downstream side of the orifice. Table 2.10
lists flow coefficients for square-edged orifices with various ratios of
hole diameter to pipe diameter. The combined velocity-of-approach
factors and coefficients of discharge ¢;Cp represent the averages for
pipe sizes ranging from 1-1/2 in. to 16 in. These data are based on
vena contracta taps and pipe Reynolds numbers of 10° and will give
reasonably accurate results whether flange, radius, or vena contracta
taps are used. Figure 2.51 shows the location of the various types of
pressure taps. Of the remaining coefficients of flow listed in Table
2.10, the coefficient of velocity Cy for orifices in pipes was assumed
to be 0.975, which is the average of values generally listed for orifices
discharging from plenums. The coefficient of contraction Cc was
calculated using the listed values of @:Cp, the appropriate definitions,
and the assumed value for Cy. The coefficient of discharge Cp was
then calculated using the coefficients of velocity and contraction,
and the velocity-of-approach factor determined accordingly.
The pseudo velocity-of-approach factor ¢,’ and the pseudo coefficient of discharge Cp’ are also given. All data are based on the difference in pressure from the upstream location to the vena contracta
location. The static pressure at the vena contracta will be zero only
when discharge is to the atmosphere. Otherwise, the discharge pres-
CHAPTER
2 — FLUID FLOW
2-103
1” FLANGE TAPS
=
D,
KSSSSSSSSSSSSSSSS
KR
phys
MO
qi BSS
wsTE
é (SSSSSSESSS
ZY,
CLLLELET
A
SSS SY |
eee
\
0.3 TO 0.8 D;—>}
VENA CONTRACTA TAPS
| SEE GRAPH BELOW
ea D,
BEVELS 45°
POUL
Lia
D, te
D,—>
RADIUS TAPS
DIAMETER
RATIO
OO)
UF
Os
We
06
sie
07108)
609
10)
1002.13
PIPE DIAMETERS
Figure 2.51
Square-Edged Orifice and Pressure Tap Locations
Adapted from the data of ASME: ASME Power Test Codes, Instruments and Apparatus,
Measurement of Quantity of Materials, PTC 19.5; 4-1959, p. 9.
Part 5,
2-104
FAN ENGINEERING — BUFFALO FORGE COMPANY
Table 2.10
Flow Coefficients for Square-Edged Orifices
—
a
Contractions)
es Plenum
Adapted from the data of ASME:
ASME Power Test Codes, Instruments and Apparatus, Part 5,
Measurement of Quantity of Materials, PTC 19.5; 4-1959, pp. 20-39.
1.0:
0.9
0.8.
ORIFICE
0.7!
0.6
0.5.
0.4
COEFFICIENT
Kz,
LOSS
0.3
VENTURI TUBE WITH
15° RECOVERY CONE
0.2.
0.1:
:
HERSCHEL
TYPE VENTURI TUBE
U0, «0s,
02)
02,0
0Ma
hs BOChORLE
0G
ca
DIAMETER RATIO
Figure 2.52
Pressure-Loss Coefficients for Flow Meters
Adapted from the data of ASME: ASME Power Test Codes, Instruments and Apparatus, Part 5,
Measurement of Quantity of Materials, PTC 19.5; 4-1959, p. 12.
CHAPTER 2 — FLUID FLOW
Table 2.11
2-105
Equivalent Flow Coefficients for Square-Edged Orifices
Formed by a Uniform Downstream Pipe
.861
912
sure must be measured.
An average coefficient of resistance is shown. This value is calculated from the assumed coefficient of velocity. It is nearly equal to
the average usually shown for orifices discharging from plenums. The
contraction loss przi-; can be determined from the coefficient of
resistance Cr and the velocity pressure at the vena contracta py; using
Pu-3 = Crpv3.
(2.131)
When discharge is to the atmosphere, the pressure corresponding to
the velocity at the vena contracta represents an additional loss.
When the orifice is in a uniform pipe, the overall contraction and
re-expansion loss pzi-4 can be determined from the meter differential
ps: — ps2 and the data of Figure 2.52 using
Pu-4 = Ki (psi — ps2) .
(2. 132)
When the square-edged orifice is formed by a uniform downstream
pipe, some of the velocity pressure at the vena contracta is converted
to, or regained as, static pressure, provided that the discharge pipe is
long enough for complete expansion to take place. The minimum
length of pipe usually necessary for this to occur is three opening
diameters.
When
such a configuration is used, the coefficients listed
in Table 2.10 still apply provided that the pressure at the vena contracta is used as indicated. Alternatively, the equivalent coefficients
of discharge Cp* and resistance Cr* given in Table 2.11 can be used
in the following equations:
OC CRAIN
El |
Q =
Pri — Psa
emcees a!
(2.133)
Psi — Psa
CgiCn*A2
Wrap
Pu-4 = Cr*pvs
ee
, and
(2.134)
(2.135)
where the subscript 4 indicates the location at which full flow is established in the downstream pipe. With a short pipe, Psa will be zero.
2-106
FAN ENGINEERING — BUFFALO FORGE COMPANY
Rounded-Entry Nozzles
If the edge of an orifice opening is rounded rather than square,
the coefficient of contraction is increased. In the extreme, when the
opening is rounded to the degree indicated in Figure 2.53, the coefficient of contraction reaches unity. There is no contraction beyond the
nozzle, and the stream issues from the nozzle full bore.
In all real nozzles there is some small loss of energy due to fluid
friction. For accurately made contours, this loss will be less than the
corresponding loss in a free jet issuing from a square-edged orifice.
It increases with roughness but decreases with Reynolds number.
The ASME Power Test Code PTC 19.5; 4-1959 shows a coefficient
of discharge of 0.994 for long- radius, low- ratio nozzles handling air
when the Reynolds number is above 5 X 10°. The coefficient of discharge drops to a value of 0.942 at a Reynolds number of 10° for
long-radius, high-ratio nozzles.
As distinguished from the reference area of an orifice, which is the
opening area or entrance area, the reference area for a nozzle is the
discharge or exit area. When the coefficient of contraction is 1.0, A?
is equal to A;. Accordingly, the capacity equations are often rewritten
using the area of the vena contracta A3:
OmC Crs:
Teme i283
Soy ae
(2.137)
Velocity-of-approach factors, together with combined coefficients us-
ing a coefficient of discharge of either 0.99 or 0.98, are listed in Table
2.12 for various ratios of nozzle discharge area 43 to upstream pipe
area A. The coefficient of velocity can be taken to be equal to the
coefficient of discharge whenever full-bore flow is assumed, that is,
whenever
the coefficient
of contraction
equals
1.0. Accordingly,
the
coefficient of resistance can be taken to be 0.02 for coefficients of
discharge of 0.99, and 0.04 for coefficients of discharge of 0.98. The
loss can be calculated from either Equation 2.131 or 2.132 using Cr
as listed above or K; from Figure 2.52.
A short-radius
nozzle known
as the I.S.A. (International
Stand-
ards Association) nozzle is illustrated in Figure 2.54. According to
ASME Power Test Code PTC 19.5; 4-1940, the combined coefficient
of discharge and velocity-of-approach factor is as listed for various
areas in Table 2.13 for Reynolds numbers above approximately 10°.
Data on the I.S.A. nozzle was omitted from PTC
19.5; 4-1959 pre-
sumably because results obtained with it are not always accurate.
CHAPTER
Table 2.12
2 — FLUID FLOW
2-107
Flow Coefficients for Long-Radius-Flow Nozzles
13)
From
.090 | Plenum
D,
DIA.
PIPE
SY
cal
450
D2/D, > 0.25
OPTIONAL
rie 1/20,
=e) =
rede
NOZZLE
OUTLET
L =0.6 Dz or 1/3 D,
Figure 2.53
Long-Radius-Flow Nozzle (ASME)
Adapted from the data of ASME: ASME Power Test Codes, Instruments and Apparatus,
Measurement of Quantity of Materials, PTC 19.5; 4-1959, p. 13.
Part 5,
Dy
ALTERNATIVE
ARRANGEMENT
FOR LARGE PIPE
USE MINIMUM @
Figure 2.54
Short-Radius-Flow Nozzle (ISA)
Adapted from the data of ASME: ASME Power Test Codes, Instruments and Apparatus,
Measurement of Quantity
of Materials, PTC 19.5; 4-1959, p. 26.
Part ah
2-108
FAN ENGINEERING — BUFFALO FORGE COMPANY
Adapted from the data of ASME: ASME Power Test Codes, Instruments and Apparatus,
Measurement of Quantity of Materials, PTC 19.5; 4-1959, p. 26.
Part 5,
Conical-Entry Nozzles (Converging Tapers)
If the edge of an orifice opening is beveled, performance will fall
between
that of a square-edged
orifice and a rounded-entry
nozzle,
approaching the former as the included angle between sides nears
180°. The effect of the degree of tapering on coefficient of discharge
is illustrated in Figure 2.55 for discharge into the atmosphere. The
three different curves correspond to the three different approach conditions as illustrated in the accompanying sketches. For all three the
jet will continue to contract beyond the discharge of the nozzle producing a vena contracta at a point slightly downstream. The vena
contracta location can be determined experimentally by means of an
impact tube in the center of the stream since it is at that point where
the impact reading is greatest.
.00
ROUNDED
ENTRY NOZZLE
85
DISCHARGE
OF
COEFFICIENT
(C,)
SHORT PIPE
FROM PLENUM
80
0
5 ~~ 10>
15
aS
Sie
oe
20%
"25
3
aMsihaMmoolen
dg @ Scag
TOTAL ANGLE OF CONVERGENCE - DEGREES
Figure 2.55
Discharge Coefficients for Converging Tapers
Discharging into the Atmosphere
CHAPTER
2 — FLUID FLOW
2-109
If a converging taper is used as a nozzle for flow-measuring purposes, Equation 2.125 can be used to calculate flow rate Q. The coefficient of discharge can be obtained from Figure 2.55. The area of
the nozzle exit A2, the density p of the air or gas, and the upstream
total pressure pr; can all be measured. The static pressure at the vena
contracta is zero.
Re-entrant Pipes
The flow nozzle, or rounded-entry orifice, represents one extreme
in orifice construction. The opposite extreme is the re-entrant pipe.
A perfect re-entrant pipe would have an infinitely thin pipe wall and
would be just long enough to ensure completely reversed flow along
the outer surface but would not be so long that the flow would reattach itself to the pipe wall. Re-attachment is generally assumed to
occur between three and four diameters downstream from the opening. Table 2.14 values are all approximate since they are based on
assumed values for Cc and Cy. Flow rates can be determined from
measurements of the upstream plenum total pressure pr and static
pressure at the vena contracta ps; using Equation 2.125 and Cp. Alternatively, Equation 2.133 and Cp* can be used with measurements of
the static pressure at the point where the flow re-attaches ps4. Both
involve the area of the pipe opening A>. Similarly, total pressure
losses can be determined from either Equation 2.131 or 2.135 and the
appropriate coefficients and velocity pressures.
Table 2.14
Flow Coefficients for Re-entrant Pipes
545
545
Separated
Re-attached
.975
975
631
631
052
052
_—
TS)
Venturi Meter
The venturi meter provides a very convenient method of producing
a pressure difference suitable for measurement and convertible to flow
rate.
As
indicated
in Figure
2.56, the venturi
meter
consists
of a
combination of converging and diverging tapers usually connected
by a short, straight pipe known as the throat. For minimum loss the
included angle in the convergent section should be 30° or less, and
the included angle in the divergent section should be 7° to 8°. Suitable pressure differences are obtained with diameter ratios of 1/2 to
1/3 or with area ratios of 1/4 to 1/9. For highest accuracy, the meter
should be calibrated in place; however, for the proportions listed, a
coefficient of discharge equal to about 0.98 can be used in Equation
2.136 where subscript | refers to the upstream pipe and subscript 3
refers to the throat. The pressure loss can be estimated from Figure
2.52 and Equation 2.132.
2-110
FAN ENGINEERING — BUFFALO FORGE COMPANY
UA
yCz77777772
DATUM LINE FOR PRESSURE
Figure 2.56
Venturi Meter and Pressure Graph
Two datum lines are shown in Figure 2.56. The lower datum line
shows positive gage pressures throughout the meter. The higher datum
line illustrates that a negative gage pressure can be developed in the
throat, depending on the upstream gage pressure level.
Compressible-Flow Measurements
The discussions and equations in the preceding sections on pressure
and flow measurement are generally based on the assumption of incompressible flow. As noted in an earlier section on stagnation properties, when a moving fluid is brought to rest there is an increase in
temperature, pressure, and density. If a probe is inserted into a stream,
the fluid will come to rest at some point on the probe. A total pressure, or impact, probe is designed to measure this increased pressure
and does so whether the flow is compressible or incompressible. A
static pressure tap is designed to avoid stagnation whether the flow is
compressible or incompressible. The differential pressure, or velocity
pressure, can be used directly in Equation 2.28 to determine velocity
for incompressible flow. However, as indicated by Equation 2.53, a
somewhat more complicated expression must be used for compressible flow. Such an expression is
pr=ae[p-4
ae v1 (22) |
(2.138)
CHAPTER 2 — FLUID FLOW
2-111
where Ap is the differential pressure, p is the absolute static pressure,
and y is the ratio of specific heats.
When a temperature probe is inserted into a moving stream, the
indicated temperature will be between the static temperature and the
stagnation temperature as given by Equation 2.51. To determine the
absolute static temperature 7s from the indicated temperature 7; and
flow measurements, an expression such as
i —
ers
2)
(2.139)
can be used. The recovery factor Fr will depend on the design of the
temperature probe.
The flow through a well-designed nozzle can be considered isentropic for all practical purposes. The subscript | will be used to
denote the inlet or admission
plane, the subscript 2 to denote the
plane of the throat, the subscript 3 to denote the plane just beyond
discharge or the area into which the nozzle discharges. The weight
rate of flow w can be determined from the absolute static pressures
Pp. and p2 using any consistent set of units in
Pe eco /
=
By (22)'7" |
Y
P2\s_
(2)
\ ay
2a cysemes ( L222
(2.140)
The volume rate of flow at inlet conditions Or can be determined
from the gage pressures Psi and ps in in. wg, area A in ft’, and density
pin lbm/ft* using 1097 for C, in
;
OQ; —
C.dc-CoArw
Psi
— Ps2
a
Sa
:
(2.141)
C, is \/2 for SI units. The velocity of approach factor ¢. for compressible flow can be determined from Figure 2.57, which is based on
bce =
Be veok
(2.142)
The expansion or compression factor y can be determined from Figure
2.58, which is based on
2-112
FAN ENGINEERING
— BUFFALO FORGE COMPANY
VELOCITY OF APPROACH
FACTOR
6.)
RATIG
2/A1)
AREA
(A
(D2/D))
RATIO
DIAMETER
OF
hie
ah2
eS 9 VG he Sul Gen ies
freien]
ABSOLUTE PRESSURE RATIO (p1/p2)
Figure 2.57
Saekoe
Velocity of Approach Factors
(2.143)
The coordinate scales of Figure 2.58 were chosen so that data could
be read directly for expansion processes in which the absolute static
pressure ratios p,/p2 exceed unity. For compression processes in which
the reciprocal pressure ratios p2/p; exceed unity, the compression
factor yw is the reciprocal of the expansion factor w. indicated on the
chart. Similarly, the temperature at the downstream location 7) will
be higher than the upstream temperature 7, after compression,
whereas the reverse is true after expansion. The indicated temperature
ratio is for expansion, so its reciprocal should be used for compression. The product of ¢- and w is usually called Y in compressor test
codes.
Because pressure variations cannot be transmitted through a fluid
at a velocity greater than that of sound through the fluid, a limiting
condition develops when the fluid velocity reaches the acoustic velocity.
CHAPTER
2 — FLUID FLOW
2-113
ABSOLUT
TEMPERA
RATIO
/7>
(7)
Hie
it
Glo mioe ae dhe tO uly 180
ABSOLUTE STATIC PRESSURE RATIO (p:/p2)
Figure 2.58
In the equations
11:9.
220
Expansion Factors
presented above, it cannot
be assumed
that the
pressure at the throat p2 (even with a steadily converging shape) is
always equal to the back pressure p3 into which the nozzle discharges.
There is a critical pressure ratio (p2/p1)c that defines the lowest throat
pressure that can exist for any admission pressure p;. The numerical
value of this critical pressure ratio is about 0.53 for normal air, 0.55
for highly superheated steam, and about 0.58 for saturated steam. It
can be determined from the ratio ofspecific heats y using
(Cae (Ga yo
(2.144)
The critical or acoustical velocity c2 can be determined from
a=
Sch)
———
p2
D2
re) V &cyRT2
(2.145)
using the mass density p and the absolute pressure p, or the gas constant R and the absolute temperature T°
2-114
FAN ENGINEERING
— BUFFALO FORGE COMPANY
The critical value of the throat pressure p2., is the lowest value that
can exist for any given admission pressure pj. p2 will equal p; whenever p3 is equal to or greater than p2.r. For lower p3 values, p2 will
equal p2., and, therefore, will be higher than ps. In the first case, the
maximum possible velocity can be achieved with a purely converging
nozzle. In the second case, an increase in velocity can be achieved
beyond the throat by adding a diverging section. In fact, this is the
only type of nozzle that will produce supersonic velocities.
Chapter 3
Transmission & Distribution of Air
_A fan can be used to deliver air to one or more places, to remove
air from one or more areas, or both. Delivery or removal can be
achieved by connecting the necessary number of branch ducts to a
main duct. In this chapter the principles of fluid flow are applied to
the problem of proportioning the system so that the required flow
will be transmitted through the various duct branches, and to the
equally important problem of achieving the necessary distribution in
the rooms or spaces being served. Additional details of various
systems are given in the chapters dealing with specific applications.
Refer to the chapter on fan systems for information on the relationship of system characteristics to fan characteristics.
Principles of Duct Design
As in any engineering problem, the best duct design is the one that
most economically produces the desired results. More specifically, in
the design of transmission and distribution systems, the flow must be
proportioned as desired, the combined cost of materials and operation
must be minimal, and no undesirable features should develop during
Operation.
The location of the fan in any system will be dictated by the direction of the flow and the desired pressure relations. That is, a supply
fan can be used to pump air into a space, or an exhaust fan can be
used to draw air out of the space. The same through-flow conditions
will be obtained, but the pressure relations will be different. In the
first case there will be a buildup of pressure in the space, and in the
second, a reduction in the space pressure will occur. Both supply and
exhaust fans can be used, in which case the space pressure will depend
on the relative amounts of air handled by each fan; that is, space
pressure will be positive if there is more supply than exhaust, or
negative if there is more exhaust than supply. Assuming the same
capacities and end pressures, the total energy delivered by the fan, or
fans, to the air passing through a given system must be of a certain
value whether a supply fan, an exhaust fan, or both are used.
If one fan is to supply air to several spaces it must
be located
upstream relative to each space. A downstream location relative to
each space is required if a fan is to exhaust air from several spaces.
When there must be several branches, the fan should be as centrally
located as possible so that each particle of air will require approximately the same amount of energy for transport as all others. Only
3-2
FAN ENGINEERING
— BUFFALO FORGE COMPANY
one pressure can exist at a single point whether it is in free space or
in a duct system. This applies at the junction of any two branches
regardless of any differences in branch size, length, or configuration.
Accordingly, the pressure drop along one branch must equal that
along the other. If the branches are not designed to provide equal
pressure drops at the required flow rates, the flow rates will differ
from the design. When the available pressure exceeds that required,
the flow through a branch can be reduced to the design value by
dampering. This is a waste of energy but cannot always be avoided.
Sometimes, however, the sizes of the ducts can be changed to balance
the pressure drops.
It is often said that the fan must be selected for a pressure sufficient
to overcome the total losses based on the flow through the longest
run. This is just another way of saying that the same pressure must
be dissipated by each portion of the air flowing, regardless of the
lengths of the runs. The proper distribution ofairflow can be achieved
only by using balancing dampers or by using appropriate duct sizes
in all branches.
There is an optimum duct size that will produce the most economical balance between owning and operating costs. If owning costs are
proportional to duct weight and operating costs are proportional to
pressure loss, each can be related to velocity. For a given metal
thickness, duct weight is proportional to diameter, which in turn is
proportional to the square root of the velocity ye and pressure
drop is closely proportional to the square of the velocity V>. If these
two costs are totaled at various velocities, a minimum cost will result at the optimum velocity. The optimum velocity Vop;, or that
velocity which will produce the minimum total of operating and
owning costs for a system as just described, can be determined from
Vope
880: g m Pm Gr
ee
1000
Pato
Gn
ae
(3.1)
As expressed by this equation, the optimum velocity is a function of
the metal thickness x» in in., the density of the metal p, in lbm/in.’,
the first cost of the metal cs in $/lbm, the annual owning cost as a
fraction of the first cost F, the Darcy friction factor/, the density of
alr pa in Ibm/ ft’, the annual operating time /, in hr, and the cost of
power C, in $/hp- hr. The annual owning cost as a fraction of the
first cost can be calculated from
1
i
ERE
(3.2)
where / is the annual interest rate and n is the number of years.
The expression, as given, assumes negligible exit loss and perfect
CHAPT
3 — TRANSMISSION
ER
& DISTRIBUTION OF AIR
en
3-3
fan efficiency so that it yields only approximate results even for
simple straight-run systems. For more complex systems it is customary to use different design velocities in the different branches as
required to equalize friction. The inclusion of fittings and other duct
elements such as heaters, etc., which reduce the fraction of the total
system pressure loss due to straight-duct friction, reduces the accuracy
of the results of Equation 3.1.
Usually, the-mains and branches will transmit a constant volume
of air at all times. Whenever a system is expected to handle a variable
volume, the duct sizes should reflect the anticipated operation. The
fan in such cases must be capable of delivering the maximum amount
even if the ducts are sized for some lesser amount.
Another special situation where the optimum duct sizes can be
based on reduced volume is that of a double-duct system. Even
though each space served may receive a constant volume of conditioned air (hot plus cold), the amounts handled by the hot and cold
mains individually may fluctuate. As the number of spaces increases,
there is a decrease in the probability that either main will be required
to deliver the maximum amount of conditioned air at any particular
time. The probability may be even further reduced by using controls
to reset the temperature of the air in one or both mains. According
to Wilson’ some designers take this into account by arbitrarily sizing
the hot mains for 75% of the total possible capacity. The cold mains
are generally sized to handle 100% of the demand in the extreme
downstream section. Successive upstream sections, each with several
branches, can be sized for a progressively smaller percentage of the
demand. Typical values may be 90%, 80%, and 70% for the third,
second, and first quarter sections. The total pressure requirement
must be calculated on the basis of maximum demand through all
sections. The fan and the volume controls must be so designed that
operation under both full and partial load is satisfactory. Refer to
the air-conditioning chapter for a discussion of design and operating
problems.
The optimum velocity based on the owning and operating costs of
the ducts alone is not always the controlling factor in determining
duct sizes. In the so-called conventional systems, which do not use
elaborate sound treatment, duct velocities can be limited to rather
low values by noise considerations. On the other hand, very high
velocities may be justified in cases where the savings in building
costs, etc., due to reduction in duct size more than offset the increase
in power required to move the air through the system.
=e
In the design of high-velocity systems it is important to limit the
use of high velocities to those sections where the saving in space
'C.M. Wuson, “Handbook on High Velocity Air Distribution Design,” Anemostat Corp. of
America, New York, Reprinted from Heating, Piping and Air Conditioning, Chicago, November
1954, pp. 94-108.
3-4
FAN ENGINEERING — BUFFALO FORGE COMPANY
justifies the increase in power requirements. Progressively lower
velocities will probably be indicated after each successive take-off.
The static-regain method is particularly suitable for sizing the main
risers in multi-story building systems. The equal-friction method or
the static-regain method may be indicated for the horizontal mains
oneach floor, depending on the particular layouts.
Ranges of design velocities for conventional and high-velocity
systems are given in Table 3.1.
Table 3.1
Design Velocities for Conventional
and High-Velocity Systems
Conventional
eeued
Main Ducts......
Branch Ducts.....
Residences
Public
Buildings
_| High-Velocity
Industrial
Buildings
|Normal
Commercial
Buildings
Normal
Max.|
Normal
Max.
Max. |Normal
Max.
700
600
1200)
1000}
1000
800
1600 | 1500
1300} 1000
2200}
1800)
2500
2000
6000
4500
Outside Air Intakes
500
800;
500
900;
500
1200)
600
1000
Filtersieen erence
Heating Coils ....
Air Washers .....
Cooling Coils.....
250
| 450
500
450
S00)
500;
500
450
S00
500
S50)
600)
500
500
S50
600
350i Ses SOs
700;
600
500
500
eo
£700
500
500
Adapted from the data of ASHRAE:
1969, p. 38
ASHRAE
Guide and Data Book
- Equipment,
New
York
Although much discussion has been devoted to establishing duct
velocities and duct sizes, the importance of reducing the pressure
losses due to elbows and other fittings cannot be overemphasized.
For maximum economy it is extremely important that the most direct
routes be used in laying out the duct system. Naturally, where exposed
duct work cannot be tolerated, there must be some compromise on
directness. In any case, when elbows or other fittings are necessary,
easy bends, splitters, or turning vanes should be used.
Duct Design Methods
The common design methods for sizing ducts are constant velocity,
velocity reduction, equal friction, and static regain.
The constant-velocity method is applied in simple systems without
branches and in those exhaust systems where the material transported
might settle if the velocity were reduced. This method can also be
used in combination with others. For instance, in high-velocity design
a constant velocity is often used in the mains up to the point where
the friction equals | in. per 100 ft or so.
An approximate optimum velocity can be determined from Equa-
CHAPTER 3 — TRANSMISSION & DISTRIBUTION OF AIR
ee
eee
3-5
eee
tion 3.1. Alternatively, the velocity can be chosen from Table 3.1, or
several trial values can be selected and evaluated if the design effort
can be justified. Duct sizes are determined from the appropriate
capacity and the design velocity using the equation of continuity or
Figure 2.15. Friction losses can be calculated from the data in the
chapter on fluid flow.
The velocity-reduction method can be employed in designing supply
or exhaust systems having numerous branches. For designing supply
systems this method consists of selecting an appropriate velocity as
indicated in Table 3.1 for the first section of main and progressively
decreasing the velocity at each take-off. For designing return or exhaust systems an appropriate velocity is selected for the duct at the
grill or hood and progressively higher velocities are used at each
junction. Subsequently all main and branch sizes are determined
from the appropriate velocity and capacity, using the equation of
continuity or Figure 2.15. Friction losses may be determined from
the data in the chapter on fluid flow.
Since in this method the branch velocity is arbitrarily chosen as a
certain fraction of that in the main, it is necessary to check whether
the available pressure is equal to or greater than the loss for the
design flow. Dampers can be used for balancing when the loss is less
than the available pressure. In case the available pressure at any takeoff or junction is not enough to produce the desired flow in the
branch, either the available pressure must be increased by selecting a
fan for a greater pressure requirement or the loss in the branch must
be decreased accordingly by increasing duct sizes.
The equal-friction method is also used in designing many supply
and exhaust systems. It is most effective for symmetrical systems or
for systems where the lengths of all the various runs are approximately equal. For such systems, balancing is automatically achieved
by designing for equal friction per foot of length. Velocity reduction
in the direction of flow on supply systems is also achieved automatically. Figures 3.1 and 3.2 can be used to size the remainder of
the system after the first section of main is sized. For systems with
some unequal branches, the mains and symmetrical branches can be
designed according to the equal-friction-per-foot-of-length method.
The remaining branches can then be sized in accordance with the
pressure available at the takeoff.
The static-regain method can be used for designing supply or
exhaust systems having numerous branches each connected to a single
relatively long main. This method utilizes the increase in static
pressure (which accompanies any velocity reduction) to provide equal
static pressures at each takeoff or junction. If the length of main
between branches is either very long or very short, this method may
not be practical.
The static-regain method of proportioning duct systems involves
equating the static pressure regain caused by a change in velocity
3-6
FAN ENGINEERING
— BUFFALO FORGE COMPANY
w
oe
a
=
oO
=a
=
oc
a
uw
oO
[as
uw
=
lu
=
=
a
1
2
3
0h
IG
8 Ge
PERCENT CAPACITY
15
20
Figure 3.1
Round Pipe Sizes for the Equa!-Friction-per-Foot-of-Length Method
CHAPT
3 — TRANSMISSION
ER
& DISTRIBUTION OF AIR
3-7
DIAMETER
OF
BRANCH
PIPE
10
%0
30
40
50
60
70
80
90
:
100
PERCENT CAPACITY
Figure 3.2
Round Pipe Sizes for the Equal-Friction-per-Foot-of-Length Method
3-8
FAN ENGINEERING
— BUFFALO FORGE COMPANY
og FOR SIZING DUCTS WHERE REGAIN = FRICTION
Q2|$ CAPACITY OF DOWNSTREAM MAIN IN cfm
V, 1S VELOCITY OF UPSTREAM MAIN IN fpm
45 L7\$ LENGTH OF DOWNSTREAM MAIN
D2\S DIAMETER OF DOWNSTREAM MAIN
40
35
30
FOR RECTANGULAR DUCTS
25
D2tS EQUIVALENT DIAMETER
FOR EQUAL FRICTION/FT LENGTH
BASED ON CONSTANT CAPACITY
INCHES
I\N
D2
20
1,07 2.0
30
40
50
:
Q2/VY
60 70
80
9.0 10.0 11.0 12.0 13.0
50 L21N FEET
ENTER Q2/V
PROCEED VERTICALLY TO Z>
READ D> AT LEFT
OOM
OPZ
OS
OF
O25
OG
07
08
OS)
UO
el
UL
hese
Q2/Vi
Figure 3.3
Static Regain Method of Sizing Pipes
Adapted from the data of R. Jorgensen: “New Chart Sizes Ducts Directly by Static Regain
Method,” Heating, Piping and Air Conditioning, Chicago, October 1958, pp. 107-108.
CHAPTER
3 — TRANSMISSION
& DISTRIBUTION OF AIR
3-9
pressure at a takeoff to the friction loss caused by the subsequent
length of main up to the succeeding takeoff. Assuming a constant
coefficient of friction and a constant coefficient of regain,
_L2
if Dee
a
a
n(Pri — Pr2).
(3.3)
Figure 3.3 is based on this equation using a value of 0.02 for the
coefficient of frictionf and a value of 0.5 for the effectiveness 7 of
the recovery process. The value of 0.5 for the recovery effectiveness
is reasonable for most applications, but the actual value may be as
high as 0.7 or 0.8 under best conditions. The friction coefficient is
also subject to considerable variation, but results obtained by using
this chart are usually sufficiently accurate. When elbows are encountered in any length of main, the appropriate equivalent length of
straight duct can be added to the actual length of straight duct.
Round Ducts
In all methods of design, the equation of continuity can be used
to determine the duct size from the capacity and the velocity. Accordingly, the ratio of duct sizes D,/Db» is related to the capacity ratio
Qa./Q» and the velocity ratio V2/V» by
Da
O; A Vp Ne
Dp
Ov
Va
(3.4)
in which subscripts a and b are used to denote two different sections
of a duct system. In the constant velocity method of system design
the velocity ratio is, of course, equal to unity, and therefore, the
diameter ratio is equal to the square root of the capacity ratio. In the
velocity-reduction method the ratio of velocities is a constant with a
value less than unity when subscript b denotes a location farther
from the fan than that denoted by subscript a.
For turbulent flow through the straight pipe sections, the ratio
Pta/ pu Of the loss in section a to that in section 6 can be determined
from
Pla
(=)
os
|
(i
vieseye
V, Ge
V,
Da
Pb
ey
bb
ie
Coy
(3.5)
The various symbols have their usual meanings, and the values ofn
and c for numerous roughness conditions can be determined from
Table 2.5 in the chapter on fluid flow. This expression yields approximately the same results as the Colebrook equation and is considerably
easier to use. Equation 3.5 is equivalent to Equation 2.78 and further
3-10
FAN ENGINEERING — BUFFALO FORGE COMPANY
states that the coefficient of frictionf is inversely proportional to a
constant times the Reynolds number raised to the n power and the
roughness ratio raised to the 0.4 — 2n power. The velocity pressure
is, of course, proportional to the velocity squared as indicated by
Pra _ (2)
Pvb
Vee
(3.6)
For equal friction per foot of length, the expression p;/L is a constant. For the same gas conditions in branches a and 6, density p and
viscosity uw are both constant. The necessary diameter ratio for equal
friction per foot of length in terms of either the velocity ratio or the
capacity ratio can be determined from Equation 3.5 and written
PIT
Aa
(;)=
(a
ZO)
LOEeVe
en)
=item)
-(£)
(Baz)
The graphical solution of this equation for average roughness conditions (that is,” = .16) is given in Figures 3.1 and 3.2. Similar charts can
be drawn for other values ofn.However, suitable engineering accuracy
can usually be obtained by using these charts. Reasonably accurate
results can also be obtained by reading duct sizes directly from Figure
2.15 along the appropriate vertical line.
Another convenient relation can be derived from Equation 3.5 for
uniform gas composition and equal friction for unequal lengths L of
duct:
re arger) )tkca fae se st ae
lL4-n
2.0-n
$.4-3n
Therefore, the appropriate diameter ratio in terms of length ratio is
(2:)
Di
i
()
(5.4 - 3n)
ON
3
HAW
(=),
Zo
ATS
(3.9)
This equation, of course, is applicable only for turbulent flow. The
approximation involving the 1/5 power usually yields reasonably
accurate results.
An expression giving the diameter ratio in terms ofthe ratio of pressure loss px/Pia for constant capacity and uniform gas composition is
(2:) vi ee
Dp
Pa
ES (4);
Pia)
°
(3.10)
CHAPTER 3 — TRANSMISSION
& DISTRIBUTION OF AIR
3-11
This, too,isappropriate only for turbulent flow, and the final approximation usually gives reasonably accurate results.
The ratio of the pressure losses for any two capacities can also be
found from the appropriate velocity ratios and diameter ratios as
indicated by
Bale)
Dy
en
1.4-n
Pressure losses can also be expressed as a certain number of velocity
heads pz/pv. In Equation 3.11, substituting the velocity pressure ratio
from Equation 3.6 produces
ie
)rs ( V, y (zy
Prb/ Pv
Vp
rs (i
Dy
Dy
cule)
The final approximation should be used only when the velocities are
nearly constant.
Total pressure losses can also be expressed as a per cent or fraction of
a velocity head py/pr. This is the reciprocal of the number of velocity
heads.
For laminar flow
EMail)
Lb
In laminar
Ly
Vp
Dy;
Mb
J
(3.13)
flow the friction factor, or coefficient of friction, varies
inversely with the Reynolds numbers and is independent of roughness
so that Equation 3.13 is considerably simpler than Equation 3.5. The
expressions corresponding to Equations 3.7 through 3.12 are also
simpler for laminar flow. For equal friction per foot of length with
uniform gas composition, the diameter ratio in terms of either velocity
or capacity ratios is expressed by
Cea):
a
For unequal lengths and equal friction, the length and diameter ratios
are related as indicated in
Nie sa
(#2)
VR = (2)
(Jarl 2)
Ds
CG) - (@)
(3.15)
(3.16)
3-12
FAN ENGINEERING
— BUFFALO FORGE COMPANY
For constant capacity and uniform gas composition, diameters and
total pressure losses are related as indicated by
Gass
Ds
Pla
;
(3.17)
For equal lengths and uniform gas composition, the total pressure
loss ratio can be found from velocity and diameter or from capacity
ratios as indicated by
)-(HAA)-QHOD-
aw
The same loss in velocity heads is expressed by
(22 Va ) B
ee)
Pw/Pvo
OF
(3.19)
Equations 3.13 through 3.19 are all for laminar flow and, consequently,
limited in application.
Although Equations 3.5 through 3.19 are based on the flow of air
through straight ducts, some can also be used to proportion systems
involving elbows. For easy bends, where it is safe to assume that the loss
is equal to a certain number of diameters regardless of size, the ratio of
losses for any two such bends can be determined from Equation 3.11. It
is usually even more convenient to add the equivalent length ofstraight
duct for each elbow to the actual length of straight duct in each case
and to proportion the system as if it consisted entirely of straight duct.
When abrupt turns are involved, for which the equivalent lengths of
straight pipe vary appreciably with size, greater accuracy is obtained by
calculating the losses for these turns separately from the straight
sections to which they join. If the loss for one such turn is determined in
velocity heads or per cent velocity pressure, Equation 3.12 or its
reciprocal, respectively, can be used to find the loss for any similar turn
regardless of size.
Rectangular Ducts
All the preceding equations and charts are for round ducts. When
rectangular ducts are to be used, it is necessary to determine the diameter of an equivalent round duct. Two charts, Figures 2.14 and 2.16,
were given in the chapter on fluid flow. Figure 2.14 is based on equal
velocities and equal mean hydraulic radii for the rectangular duct and
its equivalent round duct. It is a graphical solution of the equation
2xy
Pe
tie
(3.20)
CHAPTER 3 — TRANSMISSION
& DISTRIBUTION OF AIR
eaee
Ce
ee ee
SS
ee
3-13
—_— —
aera ms
70
/
i
Lipid
TTL
VV
[=p)o
/
VIVAL
777
LCs3
7/
7 CLLL
S77
Ark
PERCENT
CAPACITY
OF
WIDTH
OF
PERCENT
~~
LE
ZL
jwSo
| | | | || | |
|
| | |
Ay /
||||
da
het
iy
on
A ~)i=)
| d, tke
Lh
if
S
ure
La
gd)
2.0
125
RATIO OF MAIN PIPE SIDES
3.0 4.0
6010.0
Figure 3.4
Rectangular Pipe Sizes for Equal-Friction-per-Foot-of-Length
3-14
FAN ENGINEERING
— BUFFALO FORGE COMPANY
which can be derived by equating the mean hydraulic radii for equivalent
round and rectangular sections.
Figure 2.16 is based on equal capacities and equal friction per foot of
length for the rectangular duct and its equivalent round duct. It is a
graphical solution of the equation
Aga
bo= (=)
AVES Fe
5
Vase ty Ee rica
*
(=)
(x)
34 St
14—n
3.21)
which can be derived from Equations 3.7 and 3.20. Figure 2.16is drawn
for average roughness (that is, = .16). Similar charts can be drawn
for other roughnesses. Equation 3.21 is for turbulent flow. For laminar
flow
=
Line
3/4
2
1/2
Do= (=) (~) ‘fee
:
(3.22)
Figure 3.4 can be used to proportion the width of constant-depth
rectangular ducts for equal friction per foot of length. This figure is a
graphical solution of the expression
(Ou ia a
Or
ee ie (2 + yp \e
~ \ xpys
eq ar Me
‘
(3.23)
using average roughness (that is, = .16) and settingva = yo.
To proportion rectangular ducts by the equal-friction method, Figures 3.1 and 3.2 can be used with the appropriate equivalent diameters
(based on constant capacity as obtained from Figure 2.16) for any case.
For one side constant, Figure 3.4 can be used directly.
To proportion rectangular ducts by the static-regain method, Figure
3.3 can be used with the appropriate equivalent diameters (as determined from Figure 2.16) and the actual areas.
The following examples illustrate many principles of the various
methods of sizing ducts.
Example 3.1
Round-Duct Design for Exhaust System
Given the system sketched below and the problem of determining
duct sizes and fan requirements, we can calculate the theoretical opti-
mum velocity from Equation 3.1 at least approximately by using the
appropriate rates and other factors indicated. For this problem let us
assume that we use 22 ga (0.030 in.) steel (0.283 lbm/in.*’) duct work
costing $4.15 per lbm installed, that the system operates 2200 hours a
year handling standard air (0.075 lbm/ft’), and that the power rate is 4
cents per kilowatt hour. If we assume a life of 10 years and an interest
CHAPTER 3 — TRANSMISSION
& DISTRIBUTION OF AIR
BRANCHES
LENGTH
cfm
MAIN
HOOD, ETC.
pi = 5 IN. WG
ae
500
p.=2.51N. WG
1000
pr. = 2.5 IN. WG
500
p.=2.0 IN. WG
1000
p.= 2.0 IN. WG
LENGTH
cfm
20’
3500
i
20’
|
10’
}
15’
20’
500
3-15
=pr=1.51N. WG
3000
2000
1500
500
\
rate of 15%, the annual owning cost as a fraction ofthe first cost is
eS (QBISyY.
If we further assume an average friction factor of 0.02, the optimum
velocity is 3978 fpm as indicated by
880 X 0.030 XSUE
0.283 X 4.15 Elda
0.20 \"" ae
Vpeas
=
(se
0.02 ACNE
X 0.075 X 2200 X Sa
0.04 X 0.746
a278apm
Here it is not necessary to check the validity of the 0.02 friction factor since we will assume that the material being handled with the air
requires approximately 4000 fpm transport velocity. The duct sizes can
be determined directly from the capacity and the velocity, but as indi-
cated in the table below, this procedure yields odd duct sizes. Practical
duct sizes giving velocities within 10% of the required transport velocity
will generally be satisfactory. The duct friction per 100 ft of length
px/ 100 ft can be found from Figure 2.15.
D for 4000
D practical
7.0
V actual
3800
pr/ 100 ft
ofl
3-16
FAN ENGINEERING
— BUFFALO FORGE COMPANY
The overall pressure drop in in. wg for each of the alternate air paths
can be determined by adding the appropriate individual drops as
indicated in the following table:
Hoods, els, etc.
50
200 | 206 | 250 |:2500
=
Branch duct
Main ducts
Main ducts
Main ducts
Main ducts
Main ducts
Collector, etc.
88
88
eit
18
32
.44
5.00
kOw
iN Si
—
nil
18
oD
.44
5.00
18
2
.44
|_5.00
Overall
cfm
9.71
9.07
500 _| 1000
93
88
By
=
.44
5.00
.44
5.00
—
—
9.26
9.19
500 |. 1000
8.82
500
=
{_ 3500
The calculations for this example have been greatly simplified since
the losses through hoods, elbows, etc. were predetermined. The losses
through the various ducts are based on average friction, but for most
exhaust systems, smooth or medium-smooth duct friction corrections
should be made, depending upon the material and the number ofjoints
used. As is usually so, the longest run has the highest pressure drop.
With enough experience a designer can determine by inspection which
run will have the highest pressure drop. However, when there is doubt,
all pressure drops should be calculated as in this example.
The fan requirements can be stated as 3500 cfm and 9.71 in. wg static
pressure if blast gates can be used to balance the friction loss in the runs
that do not havea loss as great as 9.71 in. wg. If blast gates are not used
and if the fan is selected for 3500 cfm at 9.71 in. wg static pressure, the
actual capacities through the various branches will be different from
the design values. The run with the greatest pressure drop will suffer a
loss in capacity, and the shortest run will handle more air than required.
The exact values for all runs could be calculated by a trial-and-error
procedure, but the differences will generally be negligible. The conservative designer might add 5%-10% to the fan capacity to ensure that the
longest run would not suffer too big a drop in the amount ofair handled.
It is also possible to balance the total pressure losses by reducing the
duct size in those branches with less than maximum pressure drop. In
this problem, for the branch nearest the fan, the overall pressure drop is
9.71 — 8.82, or 0.89 in. wg less than the maximum. The branch loss
could theoretically be 0.89 + 0.88, or 1.77 in. wg. With Equation 3.10,
the diameter required to produce this higher pressure drop can be
calculated to be 4.34 in. as indicated below
V/s
D=
5.0 (4
= 4.34 in.
CHAPTER 3 — TRANSMISSION
& DISTRIBUTION OF AIR
3-17
If the ducts could be sized exactly to the required fractions ofan inch,
the fan could be selected for 3500 cfm@9.71
in. wg Static pressure and,
theoretically, no blast gates would be needed. Blast gates are frequently
used except where they may create great hazards so that the inevitable
discrepancies between actual and theoretical requirements can be balanced out.
Example 3.2
Round and Rectangular Duct Design for Supply Systems
MAIN
BRANCHES
LENGTH
LENGTH
cfm
e i
yal—60’——
||——60 —a
—o | a)
2000 <==
|
5000 <=
LENGTH
cfm
ei
10’
i
9000
10’
16000
10’
23000
15’
30000
—=~ 3000
|
60°
we
cfm
sg
er eS
Bi ee ae
—-~ 3000
‘
ps = 2.0IN.WG
pi=1IN.WG
a
1
}
ie 41000
TERMINAL REQUIREMENT
FOR EACH BRANCH
The optimum velocity for round duct costing $4.00 per Ibm installed
when the power rate is 4.5 cents per kilowatt hour assuming 24 ga (0.024
in.) steel (0.283 lbm/in.’) and 3500 hours annual operation can be
found by means of Equations 3.1 and 3.2:
06
S11 ais"
fi
880 X 0.024 X 0.283 X 4.00 X 0.16)!" _ 599,
Yop = 1000 (0.02 X 0.075 X 3500 X 0.045 X 0.746
ie
A velocity of 2790 fpm is obtained for a 0.02 friction factor and an
annual owning cost equal to 16% ofthe initial installed cost. The latter
is based on anannual interest rate of 15% and a 20-year life. The validity
of the assumed 0.02 friction factor can be determined by calculating the
Reynolds number and referring to Figure 2.8 for the appropriate roughness condition.
3-18
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Because the horizontal branches are of equal length, a well-balanced
system will result if we design them for equal friction per foot of length
and if we design the main risers by the static-regain method so that the
static pressures at each takeoff will be equal. It is impossible to use
either of these methods with constant velocity, so some compromise on
the optimum velocity is required. The procedure followed below utilizes the optimum velocity for the 4000 cfm branches. This establishes
the size and friction loss per 100 ft according to Figure 2.15. The other
branches are then sized for the same friction loss per 100 ft by noting
the corresponding diameters and velocities at the appropriate capacity
on the friction chart.
The first section of main riser can be sized for any reasonable
velocity. The static-regain method produces a considerable reduction in
main-riser velocity so that, for an average riser velocity approaching
the optimum, the velocity in the first section must exceed the optimum.
A value of 3500 fpm requires an area of 11.72 ft’, which roughly
corresponds to a 46-in. diameter and a 0.27-in. wg pressure loss (or
friction) per 100 ft.
The remaining main-riser sizes can be obtained directly from Figure
3.3. The most convenient way of using this chart is to tabulate the
information indicated below using the subscript 2 to indicate the
portion of main riser under consideration and the subscript / to indicate the preceding, or upstream, portion of main riser. For the second
portion of main riser, which must handle 30 000 cfm, we have already
established that the velocity in the upstream portion will be 3500 fpm.
From 30 000 divided by 3500 a figure of 8.57 is obtained and at the intersection of this value of Q2/V, with the appropriate length L> of 15 ft, a
diameter of 42 in. can be read directly from the chart. The velocity ina
42-in. pipe carrying 30 000 cfm is 3120 fpm. Similar calculations are
required for the remaining sections of main riser.
CHAPTER3 — TRANSMISSION & DISTRIBUTION OF AIR
3-19
At this point the design of the transmission system is essentially
completed. For this example the calculations were simplified somewhat
by using predetermined values for the losses in elbows, outlets, etc. The
static pressure required ofthe fan can be determined as indicated by the
following tabulation and calculations.
2.00 in. wg
60/100 X 0.62 = 0.37
(3100/4000)° X 0.52 = 0.31
15/100X 0.27 = 0.04
Terminal Requirement
Horizontal Branches
Takeoff (worst 3500 to 3100)
Main Riser
1.00
Coils, etc.
3.72 in. wg
Overall
The procedure for sizing rectangular ducts is basically the same. The
installed cost of rectangular duct is slightly higher than that of round
duct so that, assuming all other conditions to be the same, the optimum
velocity for rectangular duct costing 10% more would be 2900 fpm as
indicated by
a
1O\""
2810 (T.00
= 2900 fpm .
Once again sizing the 4000 cfm branch for the optimum velocity, the
required area is 1.38 ft?, which can be satisfied with rectangular dimen-
sions of 16 in. x 12.4 in. The equivalent diameter based on constant
friction per foot of length as determined from Figure 2.16 is 15 in., and
the corresponding friction per 100 ft is 0.92 in. wg. The remaining
branches are easily sized by noting the appropriate equivalent diameter
opposite the necessary cfm for the same friction per 100 ft on Figure
2.15. The corresponding rectangular dimensions can be found in Figure
2.16 and the actual velocity calculated as indicated.
Sizing the first section of main for 3800 fpm means that 10.79 ft’ are
needed. This requirement is matched by a 24-in. x 65-in. rectangular
cross section. The equivalent diameter based on constant capacity 1s
approximately 42 in., and the corresponding friction is 0.32 in. wg per
100 ft of length. Using 3800 fpm in the first section of main and 30 000
cfm in the second, the Q2/V,; equals 7.90, and for a 15-ft L2, the
equivalent diameter D> is 39.8 in. From Figure 2.16, this corresponds to
3-20
FAN ENGINEERING — BUFFALO FORGE COMPANY
a rectangular section 24 in. x 59 in., and the actual velocity here is 3050
fpm. Similar calculations must be made for the remaining sections of
main as indicated below.
V,
V2
3800
3050
2650
2180
3050
2650
2180
1860
The fan should be selected for a capacity of 41 000 cfm and a static
pressure of at least 3.97 in. wg as indicated by the following tabulation.
2.00 in. wg
60/100 * 0.92 = 0.55
(3120/4000) X 0.61 = 0.37
15/100 X 0.32 = 0.05
1.00
3.97 in. wg
Terminal Requirement
Horizontal Branches
Takeoff (Worst 3800-3120)
Main Riser
Coils, Etc.
Overall
In both the round- and rectangular-duct examples, the velocities in
some of the horizontal mains exceeded the velocity in the main riser
immediately upstream. This condition is no worse than that caused by
balancing dampers, which would otherwise be required. Also note that
the design velocities are in the high-velocity range of Table 3.1, so some
kind of sound treatment will be needed.
Examples 3.1 and 3.2 both led to the determination of fan static
pressure even though total pressure losses were calculated. This is so
because the kinetic energy loss at the exit or exits was neglected. In
Example 3.1 the exit loss is equal to the fan velocity pressure so the fan
static pressure was calculated exactly. In Example 3.2 the exit loss was
assumed to be equal to the fan velocity pressure but this really should
be verified.
Construction Details
The Sheet Metal and Air Conditioning Contractors National Association has established standards for duct construction based on experience and tests. Table 3.2 lists sheet metal thicknesses and some of the
joint and reinforcing details found in those standards. The joint details
for low-velocity ducts are keyed to the sketches given in Figure 3.5. The
joints indicated provide sufficient rigidity except that additional transverse stiffening is necessary when the length of a duct section exceeds
the centers listed. No special provisions for air tightness are required if
CHAPTER 3 — TRANSMISSION
Table 3.2
& DISTRIBUTION OF AIR
3-21
Construction Details for Ducts
Low Velocity — 2000 fpm max.
Longest
Side
_Low Pressure — 2 in. wg max.
Transverse
Long- ]
Transverse
Sheet Metal
Rect.
Thickness
Galv.
Joints
Cop|Alum. | per
j feel
Hdim.|
Types
Joint
Types
Reinforcing
Angle
Centers
3”-12" |26ga | .020” | 16 0z |A,B,K
ae
N,O,Z
=
13”-18"
|A,B.K
es
B,O,Z
—
—
19"-30" | 24ga |} .025” | 240z | C,E,K
ae
N,O,Z
|1"%x1"x Ve"
5:
317-42" ||22iga\||
-032*)|
32.0z'
43”"-54" | 22ga | .032” | 320z
55”-60" | 20ga | .040” | 36 oz
ue
N,1,Z
N,1,Z
NZ
NONE xVer
WA Xe xX Ver
VA x TVA xX Ve"
ley
5a
Si
N,1,Z
NI
N,|
TV2" x 1%2"
x Ve"
WREXA V2.
x s/he”
PIESCI NES INE
256%
2'6"
2:60
| 24ga | .025” | 240z
||E;GK
|E,.GK
|E,G,K
61”-84" | 20ga
0" 36 oz |F,G,H,J,L
85"-96" | 18 ga} .051” | 480z |H,J,L,M
over 96” | 18ga | .051” | 480z |H,J,L,M
Round
Duct
Diameter
Sie
13-18%
19”-28”
29”-36”
374-52"
Spiral Lock
Seam Duct
28 ga
26 ga
24 ga
22 ga
20ga
_
Galvanized Sheet Metal Thickness
Longitudinal
Round Duct
Seam Duct
Fittings
26 ga
26 ga
24ga
24ga
22 ga
22 ga
20ga
20ga
18ga
18ga
High Velocity — over 2000 fpm
me
Medium Pressure — to 6 in. wg
High Pressure — to 10 in. wg
Bae
Transverse Reinforcing
|
Transverse Reinforcing
Longest | Galv. | Tie
Cen-{ Galv. | Tie
CenSide
_|Sheet |Rods
Angle
ters |Sheet|Rods
(Mee
ters
3"-12"
|24ga}
—
=
—
|22ga}
—
_—
13”-18"
|24ga
1
—
48"
|22ga}
1
—
40”
—
|1"x1"x16ga
48”
—
|{1"x1"x16ga
48"
19”-24"
|22ga
1
—
48" |22ga}
2
=
40"
—
|1"x1"x ve"
48”
Se
il eX Ne XN/a
48"
25-36" |22 gat —
|1"x1"x ve"
Sele gal |
WAS
NWA
SE | SE
37'-48"
49”-60”"
|22ga|
—
|20ga
1
AG
a =
61"-72”"
|20ga
1
|
73-84"
|18ga
1
—
85"-96"
|18ga Ia
over 96”
|18ga|
2
Round
Duct
Diameter
3-8”
O22"
23”-36"
37”-50"
51”-60”
61"-84”"
|1%"x1V%"x ve"
1V¥2" x 1V2" x Ye"
2° x2"
x Va"
12x 12" x Ve”
AEC ONES SACL
TVA" xX. 1Ve" x Yer
|2V2"
x 2V2" xVe"
Me xl Ve xve*
2” x2"
x Ve"
BOO
DAUM
24"
24"
24”
24”
24”
24”
Le gay —
[2"x2" xe"
Olga
madi
|ilk/20 Xu
ote xe/e
— |2"x2" xe"
|20ga]
1
|[1%2" x1" x Ve"
—
[2% x2V2" x he"
118ga|
1
|1%"xK1"¥"x Ve"
_
A
2x ee xaos
2)
N2akicexe/en
Galvanized Sheet Thickness
Spiral Lock
| Longitudinal
| Seam Duct | Seam Duct
26 ga
24ga
22 ga
20 ga
| Round-Duct
Fittings
20ga
20ga
30”
24”
24"
24%
24”
24”
24”
24”
Girth Reinforcing
Angle
—
Centers
=
=
=
=
=
| 1%" x 1%" x Yo"
1%" x 1V4" x Ve"
172" x 12" x Ve"
Adapted from the data of SMACNA: Low- Velocity Duct Construction Standards, Washington,
D.C., Fourth Edition, April 1969, pp. 11-39, and High-Velocity Duct Construction Standards,
Washington, D.C., Second Edition, January 1969, pp. 6, 14-17. Copper data added.
3-22
FAN ENGINEERING
— BUFFALO FORGE COMPANY
So
ST
SS
AIR FLOW
AIR FLOW
(A)
(B)
DRIVE SLIP
(C)
PLAIN “S” SLIP
HEMMED
em (oa a
“’S” SLIP
f=
ee
ENE
AIR FLOW
AIR FLOW
(E)
AIR FLOW
(F)
BAR SLIP
ALTERNATE BAR SLIP
(STANDING “‘S” SLIP)
H
H-%e"
of
ARGOS
(H)
ANGLE SLIP
_
SANDING SEAM
4
AIR FLOW
(G)
REINFORCED
BAR SLIP (CLEAT)
ANGLE REINFORCED
STANDING SEAM
RIVETOR
AIR FLOW
(K)
POCKET LOCK
—7
(L)
ANGLE REINFORCED
POCKET LOCK
GASKET
(M)
COMPANION ANGLES
(CAULK OR GASKET)
—S——
(N)
PITTSBURGH LOCK
Figure 3.5
Adapted
(O)
ACME LOCK-GROOVED
SEAM
from the data of SMACNA:
(2)
BUTTON PUNCH
SNAPLOCK
Low-Velocity Duct Joints
Low- Velocity Duct Gernirne tion Standards,
D.C., Fourth Edition, April 1969, pp. 13 and 15.
Washington,
CHAPTER 3 — TRANSMISSION & DISTRIBUTION OF AIR
——
ee
ee
3-23
the joints are made in a workmanlike manner. Round duct is generally
less expensive but more space-consuming than rectangular duct. A round
duct requires the least metal for a given cross-sectional area and the least
reinforcing
to prevent vibration. Flat, oval duct is frequently used in highvelocity systems because it can be more economical than rectangular
duct and will fit into tighter spaces than round duct. No details are given
in Table 3.2 because the combination of sheet metal thickness and reinforcing will vary with the manufacturer.
The joints in high-velocity systems must be sealed to provide adequate air-tightness. Welded or gasketed flanged joints can be used, and
liquid or mastic sealants can be applied to slip joints and standing
seams. Tapes are not recommended. Tie rods can be used at joints as
well as at intermediate locations. Complete details are given by
SMACNA.
If abrasive action is expected, ducts for industrial exhaust systems
should be made from thicker sheets. A rule of thumb is to use two
gauges heavier for slight abrasive action and four gauges heavier for
greater abrasive action. Round ducts are commonly used.
SMACNA has prepared standards for round, industrial duct construction that contain information on the minimum thicknesses required
for a wide variety of materials, as well as on the reinforcing members
required, the connections, and the anchors and supports.
The usual material in a heating, air-conditioning, or ventilating
system is galvanized steel. However, aluminum or copper can sometimes bejustified. Various materials or protective coatings can be used
on industrial exhaust systems depending on the nature of the gas or
material being handled. The weight per linear foot of galvanized-steel
rectangular ducts, including an allowance for the recommended standing seams, can be determined from Table 3.4. But additions must be
made for any extra reinforcing. For round galvanized ducts, see Table
3.3; for black-steel ducts, consult Table 3.5.
The surface area S of the material in a 90° elbow of either round or
rectangular cross section can be calculated from the cross-sectional
dimensions D, or x and y and the center line radius r as indicated by
S=
SD
= TT (Xie V)«
(3.24)
For the same center line radius, it is immaterial whether the aspect
ratio is x/y or y/x. Table 3.6 can be used together with Tables 3.3
through 3.5 to determine the weight of a galvanized or black-steel
elbow of either rectangular or round cross section. The thickness of
the material in an elbow or other fitting should be equal to or greater
than that of the connecting straight pipe or duct. Under highly abrasive conditions, rectangular-section elbows are generally used since
their wearing surfaces can be replaced more easily.
"Round Industrial Construction Standards, SMACNA,
Vienna, Virginia, 1977.
3-24
FAN ENGINEERING — BUFFALO FORGE COMPANY
Table 3.3
Weights of Galvanized-Steel Round Ducts
In pounds per lineal foot
—
Diam. of
ft? per
Duct
Running ft
26
a U.S.S. Gauge
4
5
6
Tes
1.39
1.65
’
1.65
2.14
7
8
9
1.91
2.18
2.44
1.91
2.18
2.44
2.48
2.83
Salud
10
11
12
2.70
2.96
Se22
2.70
2.96
or22
13
14
15
3.48
3.74
4.01
16
17
18
2.47
:
2.89
:
S19)
3.10
3.82
4.54
2.86
3.27
3.66
3.34
3.81
4.27
4.39
5.01
5.61
5.25
6.00
6.71
3.51
3.85
418
| 4.05
4.44
4.83
4.72
5.18
5.63
6.21
6.80
7.40
7.42
8.14
8.85
3.48
3.74
4.01
4.52
4.86
5.21
522
5.61
6.01
6.09
6.54
7.01
8.00
9.57
8.60 | 10.28
9.22 | 10.86
4.27
4.53
4.87
4.27
4.53
4.87
5.55
5.85
6.33
6.40
6.79
7.30
7.47
9.82 | 11.74
7.92 | 10.42 | 12.45
toute ap MUU AP TKRERTS
19
20
21
5.14
5.40
5.59
5.14
5.40
5.59
6.68
7.02
7.26
UY
8.10
8.39
9100 | 11.80) 7) 14.11
9.45 | 12.42 | 14.85
9.78 | 12:85 | 15.36
22
23
24
5.92
6.18
6.45
5.92
6.18
6.45
7.70
8.04
8.38
8.88 | 10.35 | 13.60 | 16.25
9.27 | 10.81 | 14.40 | 17.00
V67 ee oO
e484
iran
25
26
27
6.71
6.97
1238
6.71
6.97
7.33
8.72 | 10.06
9.05 | 10.45
9.40 | 10.85
28
29
30
7.50
7.75
8.10
7.50
rise | a oeave
SEE Th az ZAs I UL
PAS
AOIOT A WIGS
eS5Se eeSil ezes 0
8.10 | 10.54 | 12.17 | 14.20 | 18.62 | 22.25
31
32
33
8.36
8.62
8.88
8.36 | 10.87 | 12.54 | 14.63 | 19.20 | 23.00
SiG2 ae 122. Oe 289 Si atSOS 584en eeour0
8.88 | 11.56 | 13.34 | 15.56 | 20.42 | 24.40
34
35
36
OAS
9.41
9.67
SS
9.41
S67
MSO
SS
MG OOM 2 1088
2518
| 12.23 | 14.10 | 16.48 | 21.65 | 25.85
257 S14 SON 16:9iliml
922522 5ie26.60
37
38
39
9.93
10.19
10.46
SOS
WUE)
10.46
2.9
a4SONeill A Om e22se4m 2ies0
psy |) UES)
THT IP PAO)
OTH)
| 13.60 | 15.60 | 18.31 | 24.02 | 28.70
| 11.74 | 15.41 | 18.41
| 12.20 | 16.00 | 19.15
| 12.67 | 16.62 | 19.87
+
4
=|
cee
es
=!
SE|
Se
Sea
SSS
KS
Se
ere ee
ee
ly
ed
=
OODDDOO——|
RK
ORK
| SIN
”
RPS
|
|
DONT
RrOTRNNONGD
Gees
| 5)
eee eege ce
ONWoOMecnmoooooooococ]e
ee a
o~r~tor
FOM-DOTM-—NNOMONMOO
al)aosdbs se).seleX
Jf
FINNANNMMMTHTNOMOOOR
lng ye
eeeee
ONHOHOHNONONSONS
CNSR
2]
~DWDODANMMDOO——AN
tTOnTOrnsGroOd
NH
OTR
SCONt+OR
DMAMO
SSeS
Se
CUMS eees
SCDNONONDODOOOOO0O0O00
@
aDmamnDOO-——N
errN|
STS
elielee
betscloeo
OTMMOOmomMoad
NMMMMMOsds
-+tor-storodtr
FKRVIANNMOMMMN
CCO-—MMOOMWO
S|
tJ
z
=)
ical
PREC
o
o~tordsodrero]
NNNOMMOOOdS
”
an
wo
—)
NANNNMMOMOSS
Weights of Galvanized-Steel Rectangular Ducts
In pounds per lineal foot
tOoOnRqdondqnrog|
w
o—Mooem
Veen
|
OntMmHROdROdTRAID|
|N
AOODH
KR
SCOR TON
NNMMOMST
FI
Ge) IGN a
INSSRE
IC
CORSE
OHSOHSOnHSOnONOM
SR ON SR vy)
COIN
SS OD
CONE NSCS
2
eRe
By,
|
||
CDMNONONDOOOCOO0C0O0000
>
arse
OOO
|
Ere
eh eeeSe|| fas| lior5
osoM
eosincers eos
[Ce
|S
PTO
MOTPROTRANNMN
4
recor
c
fmm BS)
=
NNNNMOST
HK
31M)
4
=
SEG
Ei GS
Ce|
Safed
ee
Se
leew
et Bae
hemetlk
mm
NNN
KK HK
M9)
COINSTOT SIN |
me
———
N|
COOK
RK R
DOO— DODD
eK elseolisa ie) oN a SG Crs Ete GNI)
2SB®OMONDDDODOODODOOCOO
|
& DISTRIBUTION OF AIR
eee
ee
OL
me
cee
HOO
Sess SSS
AOD
RK
Kei)
ROC OOR
eee
———4
eeRr
Ro
OOR TON
ST
OLo'S
Oto Ola Ot
eeRe Re
SS
Otn'©
Oto OL) Ola Ot
eat)
io
-
eee
HK Kr e
NNANAe|
|
2a
FER OPMOK—NTHODBDONTLoDOSO
KK
KANNAN
oa
onomoe—ntwo
a
S|
BMNOK—NMTHODBDONDToOMDONTYH
rg
Table 3.4
——
SS
SS
eee
See COOMUMMAND—-NOt
Se
OTH wo]
MMLnanosa
eo}
DODO
K—KKANMOMTTONOOR
NLD
O
DINO
ot
OONMAONINAONIOM
LO
Oon~st+ornstodqcrno
Seowsesoeessssesesso
="
ase
DODODMMOO
RF
CODDODOFR
N]|
NANNNNOOOMS
TH pr]
Rwoenoo—Ma—
| (=)
TGS
Wore
eK Ye
NICKS
he See ||] || ples) Noriao
IN
~tor~soroser.
mOmONTROSFROTR
AW
KKK CORK M1
NANOS
STONOORR
Soo}
OS
SE)SeIE
SEIS
8)b=
OOO
CHAPTER 3 — TRANSMISSION
3-25
3-26
FAN ENGINEERING — BUFFALO FORGE COMPANY
Table 3.4 (continued)
Weights of Rectangular Ducts
In pounds per lineal foot
22 U.S.S. Gauge
8
9
10
11
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
13.00
13.25
13.50
13.75
14.00
14.50
15.00
15.50
16.00
16.50
17.00
17.50
18.00
18.50
19.00
19.50
20.00
20.50
21.00
21.50
22.00
22.50
46
48
50
13.50
13.75
14.00
14.25
14.50
15.00
15.50
16.00
16.50
17.00
17.50
18.00
18.50
19.00
19.50
20.00
:
14.00
14.25
14.50
14.75
15.00
15.50
16.00
16.50
17.00
17.50
18.00
18.50
19.00
19.50
20.00
A
14.50
14.75
15.00
15.25
15.50
16.00
16.50
17.00
17.50
18.00
18.50
19.00
19.50
20.00
20.50
;
15.00
TdeZ9
15.50
15.75
16.00
16.50
17.00
17.50
18.00
18.50
19.00
19.50
20.00
20.50
21.00
15.50
15.75
16.00
16.25
16.50
17.00
17.50
18.00
18.50
19.00
19.50
20.00
20.50
21.00
21.50
4
CHAPTER 3 — TRANSMISSION & DISTRIBUTION OF AIR
Table 3.5
3-27
Weights of Black-Steel Round Ducts
In pounds per lineal foot
U.S.S. Gauge
p
Runningft
4
5
6
13
1.39
1.65
;
1.90
7
8
9
1.91
2.18
2.44
A 7AN |) 0 |) AbUe I ZENO |)
|
al
8.58
7X) |) SHOR | SAO | CRG IP Gre |) Ta |) GENO)
2.80
3:42 | 4:03 |) 5.25>)
6.47
7.80 | 10.98
10
11
12
2.70
2.96
3.22
3.10
3.78 | 4.45
5.80
3.40 | 415 | 488 | 6.36
357 On e425Om eos]
6.91
13
14
15
3.48
3.74
4.01
400 | 488
4.30
523 a
4.61
5.61
Ho 4
Olea
6.61
16
17
18
4.27
4.53
4.87
4.91
524
5.60
5.97
6.35
6.81
72047)
S916)
12971)
13:65 |)19117
7.48 | 9.74 | 12.00 | 14.49 | 20.40
SOSa
O45
12789 eh 51555)
21-90
19
20
21
5.14
5.40
559
5.91
6.21
6.43
7.20 | 8.48 | 11.04 | 13.60 | 16.42 | 23.10
7.56 | 8.90 | 11.60 | 14.30 | 17.26 | 24.30
TSSal
ose2a 2 OOM
4 80n | Mi7esivalezZ oe (0
22
23
24
5.92
6.18
6.45
6.80
7.11
7.41
8.28 | 9.75 | 12.70 | 15.65 | 18.90 | 26.60
8.66 | 10.20 | 13.29 | 16.38 | 19.80 | 27.80
9.04 | 10.63 | 13.85 | 17.08 | 20.65 | 29.00
25
26
27
6.71
6.97
de23
aA
8.01
Seo
9.40 | 11.06 | 14.40 | 17.75 | 21.50 | 30.20
9.75 | 11.48 | 14.96 | 18.41 | 22.30 | 31.30
OM Mer etieSSin mnoeol ey eOal2a ea 3el
0mlpo2.50
28
29
30
7.50
v.75
8.10
8.62 | 10.50 | 12.38 | 16.10 | 19.87 | 24.00 | 33.75
8.91 | 10.85 | 12.78 | 16.67 | 20.50 | 24.80 | 34.90
9.32 | 11.34 | 13.37 | 17.40 | 21.45 | 25.90 | 36.40
31
32
33
8.36
8.62
8.88
DOM
9.92
10.21
eM
SOni
8 O0N
225156265755
1037-60
| 12.07 | 14.25 | 18.52 | 22.83 | 27.60 | 38.80
| 12.45 | 14.66 | 19.10 | 23.50 | 28.40 | 40.00
34
35
36
9.15
9.41
9.67
10.53
10.82
11.11
| 12.81 | 15.10 | 19.68 | 24.43 | 29.30 | 41.20
| 13.18 | 15.51 | 20.20 | 24.90 | 30.10 | 42.30
| 13.54 | 15.95 | 20.78 | 25.60 | 30.90 | 43.50
37
38
39
9.93
10.19
10.46
11.42
11.71
12.03
| 13.90 | 16.40 | 21.38 | 26.30 | 31.80 | 44.70
| 14.28 | 16.80 | 21.90 | 27.00 | 32.60 | 45.80
| 14.65 | 17.27 | 22.50 | 27.74 | 33.50 | 47.10
:
2.31
2:99"
3:62 |) 5.08
:
;
Siete} |] Cb |) feds)
tad || Sieve | Chay) | Gyn}
7.42
7.159)
8:64 | 112515
TBSa
94 7 3331
8.52 | 10.30 | 14.48
eA Bl eeOe2te ito
5:66
CLOSeo SOM
1.4)
116.04
8.61 | 10.61 | 12.83 | 18.03
3-28
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Table 3.6
Weights of Elbows
Multiply value from Tables 3.3-3.5 by factor below
se
et
Center
Line
Radius
Inches
sy
i)
re
aie
es
ee | Be
co
w
oo
M—On
PY—
SOUPAPNVOOWUMH
OIDPY—wo
WONO@O
dH. SOP
MOOI
AaP—Oaos
HOCODH
BN
|
COOnPNO
MOOMNAWNr
SSeS
See
ROMY
UWON—O
RS
Sey
PWrHOONDPwWH=O
—s
oe
ek
is
POHSOIPHRWH-O
Srey
RONQONDRWONO
foeDHNVOOIBHAONO
ot
eed
eh
Ser
OGGHOBMNWNS
AWN
MNYWOPRPODMDNAOHWO
=WooManwn
DON
TRNAS
OODOAN=
ee OONTAN-O
eek
eed
RRS okaan
RO-SOIMNRWH-S
MNVIOWONODNAOF
OCONT
AN
PRS ed
SMWOMOMNIDMOHOM
OMNMYIMOWoOM—MDNC
wuomnm—-DNrowo
HPOMMYIAwWwon—~4
OMOMNYIAWoOn—~4
MOYNWONOODNAOL
Wwom—DNoNwon—
Principles of Distribution
Distribution requirements vary considerably from one application to
another. Some systems may require a concentrated supply of air at high
velocity, but in others, the objective may be uniform distribution without objectionable drafts over a broad area.
Air can be circulated and distributed within a space by utilizing the
kinetic energy of one or more streams of air issuing into the space. This
energy must be supplied, directly or indirectly, by a fan.
As mentioned under “Principles of Duct Design,” supply and exhaust
can be accomplished with a single fan in either position. A supply fan
must develop the necessary total pressure to produce the kinetic energy
required at the duct opening into a room, plus that necessary to
overcome the losses due to friction, etc. in the duct system, plus that
necessary to produce a static pressure in the space sufficient to force air
through the available exhaust openings. An exhaust fan, however, must
develop the necessary total pressure to overcome the losses due to
friction, etc. in the duct system, plus that necessary to create a negative
static pressure in the space sufficient to produce the required kinetic
energy at the duct opening into the room.
Both supply and exhaust openings are necessary for throughcirculation. Air discharging from an opening, like any moving object,
tends to continue at its exit velocity along a straight-line path. Various
effects tend to slow down and deflect the stream. The effects of
entrainment and temperature difference are discussed below. The mutual effect of the supply and exhaust openings may also be important.
Air entering an exhaust opening tends to approach equally from all
directions. For an opening located in the plane of the wall, the velocity
at one-diameter distance from the opening will be approximately 10%
of that at the opening itself. The velocity decreases rapidly with distance
CHAPTER 3 — TRANSMISSION
i
& DISTRIBUTION OF AIR
3-29
so that the effect of an exhaust opening in producing air motion is
limited to the immediate area of the opening.
Short circuits do develop, to the detriment of room circulation, when
supply and exhaust openings are directly in line at relatively short
distances. The seriousness of short circuiting can be greatly reduced by
changing the in-line relationship or by iincreasing the distance. But the
mutual influence of supply and exhaust openings on each other is
usually of far less importance than, for example, the effect of cold
window panes in producing drafts by convection. The effect of opening
a door may also be more severe than short circuiting. Frequently, the
supply and exhaust openings can be located in such a way as to
counteract these effects. Devices combining both supply and exhaust
in a single unit have been successfully used. The location of supply
and exhaust openings is frequently limited by architectural and functional requirements. Whenever uniform distribution is required in a
large space, the use of multiple openings should be considered for
both supply and exhaust.
Throw of Isothermal Air Jets
The kinetic energy of a jet can be utilized to provide air motion at a
considerable distance from the point where the jet originates, to promote mixing of the jet of supply air with the room air, or both. Neither
effect can be achieved to the exclusion ofthe other.
The center line velocity of a jet issuing from a plain round opening
will persist for the first four diameters of throw. This maximum velocity
will decrease as the square root of the distance over the next four
diameters or so, after which the velocity will be inversely proportional
to the distance from the outlet. When the residual velocity falls below
about 500 fpm, the decrease in velocity is more than proportional to the
total throw or distance from the outlet. Room air will be entrained in
gradually increasing amounts.
Similar effects will occur with openings of other shapes. A rectangular opening will produce a jet, the maximum velocity of which will not
change for a throw of about four times the short dimension. Thereafter,
the maximum velocity will decrease as the square root of the total
throw for a distance of about 4 times the aspect ratio times the short
dimension. Even with an aspect ratio of 40 or 50, this stream eventually
will become an expanding cone with a solid angle of 20° to 24°. The
point beyond which the maximum velocity decreases directly with the
increase in total throw is about 20 effective diameters, regardless of the
opening shape. Closely spaced multiple openings produce streams
similar to that of a single opening of the same total area.
The effective area A. of any outlet is the total area at the vena
contracta or the net free area if there is no contraction. The corresponding effective diameter D, is
= 113VAe .
(3.25)
3-30
FAN ENGINEERING — BUFFALO FORGE COMPANY
The effective diameter of any square-edged orifice, whether round,
square, or rectangular, can be found from its basic dimensions using
Figure 3.6.
LENGTH
SLOT
IN.
-
— ROUND AND RECTANGULAR
OPENINGS (PLENUM APPROACH)
1
546) 2 2600) 4 eaheh7 8910) a 1b ned os comme
SLOT WIDTH OR ORIFICE DIAMETER — IN.
Figure 3.6
Effective Diameters of Round and Rectangular Openings
Adapted from the data of R.D. Madison and W.R. Elliot: “Throw of Air from Slots and Jets,”
ASHVE Journal Section of Heating, Piping and Air Conditioning,
108-109.
Chicago, November
1946, pp.
CHAPTER 3 — TRANSMISSION & DISTRIBUTION OF AIR
3-31
This chart is based on a ratio of free area to gross area Ry of 1.00, a
coefficient of discharge Cp of 0.6, and a velocity-of-approach factor ;
of 1.00. For any other conditions the square-edge value D,,5 ¢ must be
modified according to
2)
ERLE
NS
RadiCpo
EE.
(3.26)
The values of R4 and ¢iCp for several typical outlets are given in
Table 3.7.
The effective velocity of the jet issuing from the outlet V, is that at
the vena contracta. This can be calculated from the capacity Q and
the effective area A. using the equation of continuity or from the
gross area A, of the outlet using
papers
o
10
AgRadiCp
A.”
(3.27)
The average residual velocity at any distance from the outlet, beyond
approximately 10 effective diameters, is about |/3 of the maximum
residual velocity. The maximum, or center line, residual velocity V,
relative to the effective velocity at the outlet V, is a function of the
throw X and the effective diameter D.. Conversely, the throw in diameters X/ D, is proportional to the velocity ratio V,/V,. as indicated by
b cpene e 6)
Doty
(3.28)
The proportionality constant K for orifices and nozzles can be
determined directly from Table 3.8. These values should be modified
for other types of outlets as indicated in Table 3.7.
_ The entrainment ratio Ro, or the ratio of the total moving quantity
Q, to the primary or jet quantity Qj, is also a function of the velocity
ratio V,/ V.as indicated by
=)
)
Ro=-S
}
= 0.314
V,
Vo
(1.12 + 0.395K
) |
é
V
ar
(3.29)
Various solutions of Equations 3.28 and 3.29 are presented graphically in Figure 3.7.
;
This chart can be used to find the entrainment ratio and maximum
residual velocity at any distance from a given outlet. It can also be used
to determine the necessary combination of effective diameter and original velocity for a given throw and a specified residual velocity. Example 3.3 illustrates a typical use of this chart.
3-32
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Table 3.7.
Distribution Factors for Various Outlets
Outlet
a, a ae
|
Approx.
= ewsIkea || Oxi |
Rounded-entrance
MHES iaogcaecod
Square-edged
CHIMES seco oats
Plain straight-duct
OPERINGSMEr tae
Barortilesaepreenmemreer:
Banigrillesiternsesceser
Bangnlles saewnaeresese
Perforated panels.....
Perforated panels.....
Perforated panels.....
Effect of high-aspect
(UGE Bantodoamecs
Effect of adjacent wall
parallel to axis
OfitlOWaearsry-eeeeecee
:
Approximatet
K
1.00
0.99
Use Table 3.8 Values Directly
1.00
0.60
Use Table 3.8 Values Directly
1.00
0.84
0.74
0.72
0.40
0.09
0.03
1.00
0.66
0.78
0.78
0.83
0.75
0.79
Multiply Table 3.8 Values by 1.05
Multiply Table 3.8 Values by 0.86
Multiply Table 3.8 Values by 0.72
Multiply Table 3.8 Values by 0.69
Multiply Table 3.8 Values by 0.89
Multiply Table 3.8 Values by 0.64
Multiply Table 3.8 Values by 0.39
—
-
Multiply Table 3.8 Values by 0.86
Multiply Table 3.8 Values by 1.42
Adapted from the data of A. Koestel, P. Hermann, and G.L. Tuve: “Comparative Study of Ventilating Jets from Various Types of Outlets.” Trans,
ASHVE, vol. 56, New York, 1950, pp. 459-478.
*Velocity-of-approach
table.
factors corresponding to 1400 fpm ahead of bar grilles are included in the
+The value of A increases for throw calculations but decreases for entrainment calculations.
Example 3.3
Isothermal Air Jet
Given a 42-in. X 6-in. bar grille discharging 2000 cfm, find the residual
velocity and the total quantity of moving air at a throw of 30 ft.
From Table 3.7,
R4= 0.74,
diCp = 0.78, and
K = Table-3.8 values X 0.72.
From Equations 3.27 and 3.25,
y=
2000
_ 2000 _
175X074 Oe) | Olen ee
De= 1.137 1.01 = 1.14 ft.
From Figure 3.6 and Equation 3.26,
IDs se=
14 ine
lel ft, and
CHAPTER 3 — TRANSMISSION
& DISTRIBUTION OF AIR
3-33
Table 3.8
Proportionality Factors K for Throw from Nozzles and Orifices
2000
Vi. - fpm
fh
RTT)
500 up
400
—
=
3000
5000
6.0
5.8
300
200
100
:
5.3
48
o5
Adapted from the data of G.L. Tuve and G.B. Priester: “Control of Air Streams in Large Spaces.”
Trans.
ASHWE, vol. 50, New York, 1944, pp. 153-172.
0.78
D.= 1.17
Vv0.74 IF) 5s 1.14 ft.
Using Figure 3.7 with
V, = 430.
V = 1980 and X/D,. = a
= 26.3,
(first approximation)
Since Figure 3.7 is based on Table-3.8 values and since Table-3.8
values must be modified for bar grilles, adjustments must also be
made according to Tables 3.7 and 3.8, and Equation 3.28:
V, = 0.72 X 430= 310,
(second approximation)
K = 0.72 X 4.6 = 3.3, and
V, = 3.3% ae = 249.
(final approximation)
The average residual velocity is 1/3 of this value, or 83 fpm.
Using Equation 3.29 and the definition of entrainment ratio,
Ro= 0.314X ao (112+ 0.395X 3.3 X 7.96" —
l=
Ro 5.2)— 1,00= 4.21,
Therefore, the total quantity of air put into motion is
4.21 X 2000 = 8420 cfm.
Note: The successive approximations of V, are required since Figure 3.7
is based on Table-3.8 values of K. Wherever Table 3.8 canbe used
directly, Figure 3.7 can also be used directly.
FAN ENGINEERING — BUFFALO FORGE COMPANY
3-34
THROW OF AIR IN.
EFFECTIVE DIAMETERS
RATIO
ENTRAINMENT
100
200
300
400
500
MAXIMUM RESIDUAL VELOCITY ( V,)
Figure 3.7.
1000
Throw of Air from Openings
Adapted from the data of R.D. Madison and W.R. Elliot: "Throw of Air from Slots and Jets,”
ASHVE Journal Section of Heating, Piping and Air Conditioning, Chicago, November 1946, pp.
108-109.
Throw of Heated or Cooled Air Jets
If the primary air in a jet is heated above the temperature of the air
in the room, the stream will tend to rise as it proceeds away from the
outlet.
The vertical rise Y of the center line of a horizontally projected stream
is a function of the throw X/D., the original velocity V, and temperature 7,, the ambient temperature
indicated by
7,, and the effective diameter D, as
CHAPTER 3 — TRANSMISSION & DISTRIBUTION OF AIR
Ys
= 0.065 (=) (= Z )(4
:
De
D.
07
Ha
1h
Ve
3-35
e
);
(3.30)
Similarly, ifthe primary air is cooled below the ambient temperature,
the stream will fall.
The maximum possible vertical downward projection Xmax of a
heated stream or the maximum upward projection of a cooled stream
can be calculated from
ig
Ximax van,
De
Bs ((ii
Van )
~ 285.
33)
16; )ee
Equations 3.30 and 3.31 are adapted from the data of Koestel', which
also give the results of temperature-distribution studies.
Example 3.4
Heated Air Jet
Given a 1.0 ft? squared-edged orifice with a plenum approach projecting 3000 cfm of 180°F air through ambient air at 70°F, find the
maximum throw for downward projection and the vertical rise of the
center line ofa horizontally projected stream at that same throw.
From Table 3.7,
R,=
1.00,
d:iCp = 0.6, and
K = Table-3.8 values.
Using Equations 3.27 and 3.25 or Figure 3.6 and Equation 3.26,
=
aa x 0.60 = 5000 fpm,
D. = 1.13 V 0.60
= 0.875 ft,
De, sc. = 10.5 in. = 0.875 ft, and
D. = 0.875 V1.0
= 0.875 ft.
Using Equation 3.31,
>
530
5000°
2
gees 951° ( = (a; = sa) (rein Te) 2385)
'A. Koestel, “Paths of Horizontally Projected Heated and Chilled Air Jets,” Trans. ASHVE,
vol. 61, New York, 1955, pp. 213-232, and “Computing Temperatures and Velocities in Vertical
Jets of Hot or Cold Air,” Trans. ASH VE, vol. 60, New York, 1954, pp. 385-410.
3-36
FAN ENGINEERING
— BUFFALO FORGE COMPANY
X max = 0.875 (\/3.4(4.81)(247) — 2.85), and
X max = 53 ft.
Using Equation 3.30,
4
530aN
ae
Lavias
Y = 0.875 X 0.065 (Ses) le )() Se
Chapter 4
Sound
Certain characteristics distinguish one sound from another. Two
such characteristics, loudness and pitch, are commonly used to describe sounds. While loudness is a measure of the quantity of sound
that reaches the listener’s ear, pitch is a measure of the quality of a
pure tone. Some sounds are pure tones; others are a combination of
several tones; but most sounds are neither. Instead, they are best described as broad-band sounds. Even without distinctive tones, these
sounds each have a characteristic quality that identifies the source for
the listener.
Sounds have different characteristics under different environmental
conditions. For instance, rooms are described as live or dead, hard
or soft. A very dead room nearly duplicates outdoor conditions. Increased distance between a source and a listener decreases loudness
in such a free field. However, in a very live room, loudness does not
change with distance except very near the source. The sound at any
point in a hard room consists of both direct and reflected sound. In
the near field, direct sound predominates; in the reverberant field,
reflected sound prevails.
Some sources radiate more sound in one direction than in another.
Some obstructions in the path between the source and the listener are
more effective in keeping out noise than are others.
Noise is sound that is unwanted or disturbing. Noise control can be
accomplished by reducing the amount of noise generated, by altering
the characteristics of the acoustical path, or by protecting the receiver.
Both the quantity and quality are important in determining the undesirability of sound. It is necessary to understand these physical
properties and how they are measured before numerical values can be
assigned
to generated
sound,
acceptable sound, and the reduction
required in a particular situation.
Physical Properties
Sound travels in waves through any elastic medium. In air, sound
waves take the form of alternating condensations and rarefactions.
These changes in density result from particle displacement. They can
be described and measured in terms of pressure change. The effective
sound pressure at a point is the root mean square value ofthe instantaneous sound pressure over a time interval at that point. Even
though the pressure fluctuations are small compared to normal at-
4-2
FAN ENGINEERING — BUFFALO FORGE COMPANY
mospheric pressure, the difference in sound pressure for two sounds
may be several orders of magnitude. The sound pressure of audible
sound may range from 0.00002 to 20 pascal. Both the ear and the
sound level meter respond to the effective sound pressure rather than
to the instantaneous sound pressure. Loudness is largely determined
by sound pressure.
The condensations and rarefactions that produce a pure tone occur
at regular intervals. The time required for one complete cycle is called
a period (the usual unit of which is the second). The number of com-
plete cycles occurring in a unit of time is called the frequency (the
usual unit of which is called the hertz). Pitch is primarily determined
by frequency.
Few sounds are pure tones. For example, most musical sounds are
a combination
of tones and overtones.
In contrast,
most
noises are
broad-band sounds. Each tone (or each portion of the band, in the
case of broad-band sound) exerts its own rms sound pressure. The
square root of the sum of the squares of the individual rms pressures
is the overall rms pressure (at least for sinusoidal waves). It is usually
far more useful to know the individual rms sound pressures for each
tone or partial bandwidth than to know the overall rms sound pressure. Such a statement of individual pressures and frequencies is
called a sound spectrum. The rms sound pressure is also known as
the effective sound pressure or, more simply, the sound pressure.
Various bandwidths can be used in describing spectra. An octave
band is a band ranging from one frequency to twice that frequency.
Standard octave bands have been established, as indicated in Table
1. One-third octave bands have also been standardized.
Narrow
bands, such as 2% of the mean frequency, can be built into measuring
equipment.
Table 4.1
Band Number
Octave
Octave Band facta
eames
[aid
173oet| 18 |21 |24 eina Ta
|tow |45 | 88|177| 354
Frequency — Hz
2828) 5657
Adapted from the data of “American Standard Specifications for Octave, Half-Octave, and ThirdOctave Band Filter Sets,” ASA, S1.11- 1966, pp. Il and 12.
ad ees Ee eee
Weighting-dB ene] -23]-42{-13]-05] 0 [-on]-07
cu
ul ot oncoal
CHAPTER 4 — SOUND
4-3
The distance that a sound wave travels in one period is called the
wave length of the sound A. This can be determined from the frequency
f and the speed of sound c according to
i
(4.1)
The speed of sound in air can be determined from Table 1.2 (opposite the appropriate temperature) or calculated from the temperature 7, the gas constant R, and the ratio of specific heats y of the
medium, as indicated by
C= NSE GIRIT
(4.2)
The product of the mass density p and the speed of sound c is called
the characteristic impedance pc of the medium. The impedance and
the effective sound pressure p are related to the amount of sound
power transmitted per unit area, or to the intensity /, as expressed by
paps
pou
(4.3)
The intensity of sound at any point in space depends on the distance
to the source, the power and directivity of the source, and the nature
of the sound field.
When a non-directional point source of sound radiates in a free
field (that is, a field without
obstructions),
the sound
will radiate
equally in all directions, diverging as it goes. Because of this divergence, the wave front will be spherical. The intensity / at any distance
x can be determined from the sound power W of the source using
ae
4mx°
(4.4)
The average effective sound pressure p and the sound power W are
related, as shown by
0G
41x
ge i
(4.5)
In other words, when there is spherical divergence, the sound pressure varies inversely with distance. This is not true for other wave
front shapes.
At a distance of several diameters from the source, any wave front
in a free field becomes
nearly spherical in shape. Equation 4.5 is,
4-4
FAN ENGINEERING — BUFFALO FORGE COMPANY
therefore, applicable for any non-directional
source
in a free field,
provided that the distance is great enough.
Most sources
are directional; that is, they radiate more
,
sound
in
certain directions than in others. The particular effective sound pressure p in any particular direction can be expressed in terms of the
average effective sound pressure p and the appropriate directivity
factor Q:
p =Qp.
(4.6)
This leads to an expression for the particular sound pressure in a free
field for a directional point source:
>
QWopc
ome nen
(4.7)
Sound waves may be reflected by rigid surfaces, refracted by differences in the medium that change the velocity of sound, or absorbed by either the medium or surface materials. No real surface is
a perfect reflector of sound. The material may be set in motion by the
sound pressure, or a portion of the sound may penetrate the surface,
or both. Either transmission or absorption would then result, and the
reflected energy would thereby be reduced.
When a sound is generated in a live room, the waves radiate, as in
a free field, until they strike an obstruction. They are then reflected
from one obstruction to another, each reflection taking place at reduced strength. Eventually, the total energy of the wave is dissipated
as heat. When a sound is continuously generated, the noise will
gradually build up in a live room until equilibrium results, that is,
until the rate of absorption equals the rate of generation.
The sound at any point in a live room is a combination of direct
and reverberated sound. The effective sound pressure due to direct
sound pq for a point source with directivity is the same as for a free
field:
>» QWoc
PO
dmx ge
(4.8)
The effective sound pressure due to reverberated sound p, can be
determined from the sound power W of the source, the characteristic
impedance of the medium pc, and the characteristics of the room:
Pr
2-_ 4Woc
Rge ©
(4.9)
Se
ee
ee
Table 4.2.
CHAPTER 4 — SOUND
ee
eS
A
mek
Coefficients a
for various frequencies
in.
2
4-5
Sound Absorption Coefficients
of General Building Materials
Material
=
eee
—
125 |250}
——
-
500]
1000}
2000]
4000
ee
Brick wall, unpainted ...........
18 | 0.02}0.02]
0.03} 0.04} 0.05]
0.05
Brickwwallepalnted)...c cvsdetenekewereue
18 | 0.01}0.01]
0.02} 0.02] 0.02} 0.02
Plaster, gypsum, on hollow tile,
plain-onpainted! . ssc. «scsi
« ©
—
0.02]0.02}
0.02} 0.03]
0.04]
0.04
Plaster, gypsum, scratch and brown
coats on metal lath, on wood studs
—
0.04]0.04}
0.04) 0.06]
0.06}
0.03
Plaster, lime, sand finish on metallath|
Ya
0.04/0.05|
0.06} 0.08]
0.04}
0.06
Plaster,on wood wool .........—
0.40/}0.30}
0.20} 0.15]
0.10}
0.10
RlAStetaitbrOUS seers votre icthems
tate telete
2 | 0.35|/0.30}
0.20} 0.55] 0.10] 0.04
Poured concrete, unpainted.......
—
0.01])0.01}
0.02) 0.02]
0.02}
0.03
Poured concrete, painted ........
—
0.01]0.01}
0.01]
0.02]
0.02}
0.02
Wood, solid and polished ........
2
VO
— | 0.05;
—
0.04} 0.04
Wood, paneling, 2 to 4 in. air space
lovsyn Lite Wages Gate Batre. Gece etOrch Ok CLARO ¥e-V2 | 0.30}0.25}]
0.20] 0.17] 0.15] 0.10
Wood platform with large space
DENEUMSb500
My bods Soehs as
—
OLA
OLS
Ol2 a OM
P/,1NOntSsnOul
CERES. sawerg So
od OO nao a Ono. ako
0.04|0.04}
0.03] 0.03} 0.02} 0.02
Floors
ESL LOM GONG aiaie = olelieinica, sihevieviet
ss)
—
0.01}0.01}
0.01]
0.02]
0.02}
0.02
VVOOGIONISONIG Beres-mens jenebereyelia teltels
—
0.04] 0.04}
0.03] 0.03} 0.03] 0.02
Cork, linoleum, gypsum, or rubber
WECM)
cing opal
a oleGla 6 ¥%e | 0.04)0.03}
0.04} 0.04} 0.03] 0.02
Wood block, pitch pine.........
—
0.05] 0.03}
0.06} 0.09} 0.10} 0.22
Carpets:
Wool pile, with underpad .......
%
0.20/0.25}
0.35) 0.40] 0.50} 0.75
Wool pile, onconcrete.........
¥e
0:09) 0:08)
0:21)
0.26)
0,27
)0,37
Draperies and fabrics:
Velour, hung straight
WORT
cyano trole.& omlowyS
—
0.04|} 0.05]
0.11]
0.18} 0.30} 0.35
WACUINCE
coo accnodac
tou’
—
0.05] 0.07}
0.13} 0.22] 0.32} 0.35
RSCPIACES ay Gag Git OO Oh OO
—
0.05|}0.12]
0.35} 0.48} 0.38} 0.36
Velour, draped to half area
(RACIAOR
Goa o op ao OdeoOO
0.07/0.31]
0.49} 0.75} 0.70} 0.60
A SlOZ/VG2 arity wena sitedeich stior eh
a
0.14]}0.35|
0.55} 0.75] 0.70] 0.60
Seats and people:
Coefficients x area (aS) — sq ft per person or seat
Seats
Chair, upholstered back,
TEAtier SEALS a aiewet eo a)eos eis! ee
—
DOW
25
SO) | SHO) || seh(O) | 22)
Chair, theater, heavily upholstered
—
yD!
IaeD
Sey il Sher)
Sir
psi)
Orchestra chairs, wood ........
=
OFM
OMS
OZ
MOlSSi NO:
Salle
Cushions for pews, perperson
...|
1.5 | 1.0 | 1.5
hr,
ey.
1.6
1.4
People
In upholstered seats (add to
leather-seat chair absorption) ..
—
0.7 | 0.6
0.5
les
1.6
2.0
In heavily upholstered seats .....
—
ON7/ | OLS
OSS 4) 3140)" |) KO
1.0
In orchestra seats with instruments
(add to wood-seat absorption)
..
—
AlOM a7 San Wl Om 3:08
13:5.
O!
Child in high school, seated,
INCIUCING!SEAL
fete ole (eens
test
Child in elementary school, Seated,
including seat)...
3. 6. s = «
Standingee
te teen suena
tener
In church pew(no seat cushion)
. .
=
Z2ESIOM
—
_
(ksh |P2Ss WP Pash i) SEA | siey | Z510)
OWS
Sea
4s5) 1 8:0i8 | 4:0
25a
27
eS.
3.3
4 Oy ea
3.8
4.0
ett
3.8
Adapted from the data of L.L. Beranek: Acoustics, McGraw-Hill Book Co., Inc., New York, 1954,
pp. 300-301.
4-6
FAN ENGINEERING — BUFFALO FORGE COMPANY
The room constant R varies with the amount of surface S, the volume
W of the room,
the average sound absorption coefficient a of the
boundary materials, and the energy attenuation constant { for the air:
hoes
Z)
(ara
Zz)
(4.10)
This equation is valid only where the mean free path between reflections is at least 4Y//S, a condition found in most irregularly shaped
rooms. The value of a can be determined from the individual coefficients in Table 4.2 by using a weighted average based on the
amount of surface for each material. The value of { can be determined
from Figure 4.1. Both @ and ¢ vary with frequency, so R will have
different values in different bands. The room constant can also be
determined by measuring the reverberation times 060 for each frequency band:
ay
Shae
(4.11)
68°F
ft"!
CONSTANT
ATTENUATION
(2)
ENERGY
10
20
Figure 4.1
30
40
50
60
RELATIVE HUMIDITY — per cent
70
80
Energy Attenuation Constants for Air
Adapted from the data of V.O. eet
John Wiley& Sons, Inc., 1950, p.
and C.M. Harris: Acoustical Designing in Architecture,
CHAPTER 4 — SOUND
4-7
The value of C; is 0.161 in SI units and 0.049 in U.S. customary units.
The reverberation time of a room is the time required for the intensity
of an interrupted sound to decay 60 dB or to one-millionth of its
original value.
The expression for effective sound pressure in a reverberant field
for a directional point source is
so
is
a
&
Q
=)
jeanne
\4nx
R
&
(4.12)
This equation suggests that, at a sufficient distance x from the source,
the direct sound is negligible compared to the reverberant sound. The
pressure will be uniform in the reverberant field except for standing
wave effects. Each narrow band of frequencies may have numerous
standing waves. The closer these standing waves are to each other, the
more uniform will be the sound pressure in the reverberant field.
Generally, the sound pressure is most uniform in large, irregular rooms.
Equations 4.7 and 4.12 should be used only for point sources of
sound. Other equations must be employed when the source does not
approximate a point. Many sources, because of their size and shape,
may produce plane waves, at least in the near field. The relation of
the effective sound pressurep in a plane wave to the sound power of
the source W, the plane area of the wave A, and the impedance pc is
‘es Woc
ee
(4.13)
This expression can also be used for plane waves traveling down a
duct, if absorption and reflection can be considered negligible.
Measurement of Sound Properties
The properties of a sound are usually measured with a sound level
meter and an octave band analyzer. Other electronic instruments,
including narrow-band analyzers, oscillographs, and tape recorders,
are also useful.
Sound pressure level is measured with a sound level meter. The
sound pressure generates an electrical signal in the microphone, which
is then amplified and transmitted through an adjustable attenuator
to an indicating meter. The sum of the attenuator setting and the
meter reading is the sound pressure level when the frequencyweighting network is set for flat response. This network is usually
designated C, and readings are reported in dBC.
The spectrum of a sound is determined with an octave band analyzer together with a sound level meter. A series of filters is used to
greatly attenuate signal components above and below certain frequencies (see Table 4.1). When the output of a sound level meter is
fed into an analyzer, the sum of the attenuator setting and the ana-
4-8
FAN ENGINEERING — BUFFALO FORGE COMPANY
lyzer meter reading is the sound pressure level for the band of frequencies indicated by the band selector. The sound level meter should
be set for flat response when used with an analyzer.
The accuracy of any sound measurement depends on the acous-
tical response of the microphone and the electrical response of the
meters. Meters should be calibrated often. Microphones are usually
non-directional at low frequencies. When the wave length is comparable to the size of the “mike,” the response varies with wave length
and angle of incidence. For highest accuracy, these effects should also
be determined by calibration.
The A and B networks of the sound level meter attenuate certain
low-frequency components so that the readings on these two scales
are not sound pressure levels. To distinguish them, A and B network
readings are called sound levels and designated in units of dBA and
dBB, respectively. More will be said about this under “Hearing.” An
ear-weighting network with units of dBE has also been proposed.
Note that the measurements made with a sound level meter are all
called levels. The units of these levels are called decibels, abbreviated
dB, and are dimensionless.
For A, B, and C networks,
a reference
level of 20 wPa is implied. The reason for using decibels is basically
numerical convenience, as shown below.
Decibels
Decibels are dimensionless units for conveniently measuring power
(or some other property that is proportional to power) whenever the
range of values is very large. For instance, the sound power of a
whisper may be 0.000000001 watts and that of a jet airplane 100000
watts. With a reference power of | pW, these sound power levels can
be stated as 30 dB and 170 dB, respectively. Although more con-
venient for numerical expression, using the decibel does make it more
difficult to perceive the difference between two sound power levels.
Table 4.3 shows the sound power and the sound power level for sev-
eral typical sources.
For most broad-band sounds, the square of the sound pressure at
any listener location changes directly with the sound power. Sound
pressures in the audible range vary from 0.00002 Pa to 20 Pa. The
corresponding range of sound pressure levels, with a reference pressure of 20 wPa, is 0 dB to 120 dB. Table 4.4 lists the sound pressure
and sound pressure level for several typical sound situations. Note
that the distances are specified where applicable. In the near or free
field of a localized source, sound pressure varies with distance. Sound
pressure may be relatively constant throughout an area having mul-
tiple sources of sound or in an area having highly reflective surfaces.
Power level and pressure level both can be expressed in decibels
simply because they are both levels. Each is a logarithmic expression
of the ratio of the quantity in question to a particular reference
quantity.
CHAPTER 4 — SOUND
Table 4.3.
4-9
Typical Sound Powers and Sound Power Levels
Power
(watts)
Power Level
(dB re 1 pW)
100000
170
10000
160
1000
150
100
140
10
130
1
120
0.1
110
0.01
100
0.001
90
0.0001
80
0.00001
70
0.000001
60
0.0000001
50
0.00000001
40
0.000 000001
30
Source
(long time average)
Jet airplane
Large orchestra
Blaring radio
Shouting
Conversational speech
Small electric clock
Soft whisper
Adapted from the data of C.M. Harris: Handbook of Noise Control, McGraw-Hill Book Co., Inc.,
New York, 1957, p. 2-8.
By definition, the level of a quantity in decibels is 10 times the
logarithm (to the base 10) of the ratio of that quantity (in dimensional units) to some reference quantity (in the same dimensional
units). The only other qualification is that the quantity be proportional to power.
The sound power level Ly corresponding to any value of sound
power Wis
=
W
Lw= 10 logy.
(4.14)
The reference power MW, is universally taken to be | picowatt. This is
the same as 10°” watts.
The sound pressure level L, corresponding to any value of sound
pressurep is
2
Lp = 10 log £ 2 =a AUG
2)
es
(4.15)
4-10
FAN ENGINEERING — BUFFALO FORGE COMPANY
Table 4.4
Pressure
(Pa)
200
Typical Overall Sound Pressures
and Sound Pressure Levels
Pressure Level
(dB re 20 Pa)
140
Source
(long time average)
Distance
(if applicable)
Threshold of pain
—
Threshold of discomfort
—
Automobile horn
20’
Automobile at 40 mph
Inside
¥
Conversational speech
3
130
20
120
110
2
100
90
0.2
80
0.02
60
0.002
40
0.0002
~
70
50
20
f
:
Quiet residence
‘
Inside
Whiisper
5!
Threshold of hearing
—
:
10
0.00002
0
Adapted from the data of C.M. Harris: Handbook of Noise Control, McGraw-Hill Book Co., Inc.,
New York, 1957, p. 2-10.
The reference pressure po is 20 micropascal. This is the same as
0.00002 Pa or 0.0002 microbar.
It is frequently necessary to add the effect of one sound to that of
another or to subtract the effect of one sound from that of a combination of sounds. The procedures for determining these effects must
recognize the logarithmic character of sound power levels and sound
pressure levels.
The total sound power W,+2+..+, of a combination of sounds is
equal to the sum of the individual sound powers W, + W.+..+ W,.
Because of the logarithmic character of sound power levels, the total
sound power level Lyi+2+..+n is not equal to the sum of the individual
sound power levels Ly: + Lyw2 +.. + Lyn. Rather,
Lm + (/0) km10 oe ae cta(Z0) ise10 ).
= 10 log \ (10) My
Lwi+2+..+n
(4.16)
CHAPTER 4 — SOUND
4-11
DIFFERENCE BETWEEN TWO INDIVIDUAL LEVELS - dB
LSet
ei
AS hi
ey
10
7
ADDITIONAL VALUES
DIFF. CORR.
11-12; .3
(Psih
2
t4:19-3--4
= 190
5
4
5
4
NOISE
BACKGRO
CORRECT
dB
-
AMOUNT
OVERALL
EXCEEDS
HIGHEST
dB1
iz
3
4
5
6
7
8
9
10
DIFFERENCE BETWEEN OVERALL LEVEL AND BACKGROUND LEVEL ALONE - dB
Figure 4.2
Corrections for Combined Levels
The total sound pressure pi+2+..+n of a combination of sounds is
equal to the square root of the sum of the squares of the individual
sound pressures Vp: + po +.. +p, atthe point of measurement.
Because
of the logarithmic
character
of sound
pressure
levels, the
total sound pressure level is not equal to the sum of the individual
sound pressure levels Lp; + Lp2 +.. + Lyn. As with sound power levels,
Loisteen =a Olog
a
Vi(10) ©4410)
Ly2
+
0)
Lon
© i
(4.17)
Figure 4.2 can be used in place of Equations 4.16 and 4.17. The
lower curve facilitates adding two sound power levels or adding two
sound pressure levels. If the two levels being combined have the same
value, the combined
value will be 3 dB higher than either. This is
easily verified. Multiplying any two numbers is the same as adding
their logarithms. Adding two equal values is the same as multiplying
one value by a factor of 2. Ten times the logarithm (to the base 10)
of2 equals 3.0.
4-12
FAN ENGINEERING
— BUFFALO FORGE COMPANY
The upper curve of Figure 4.2 facilitates subtracting from the total
a component of the sound power level or a component of the sound
pressure level. This curve is usually used to obtain a background
correction, so the scale is labeled accordingly.
Examples 4.1 through 4.4 illustrate the use of both Figure 4.2
and Equations 4.16 and 4.17.
Example 4.1
Combining Sound Power Levels
Given the sound power level of two sounds as 90 dB and 100 dB, find
the combined sound power level.
Using Equation 4.16:
90
Lwi+2 = 10 log
(10
100°
+ 10 ° J = 100.4 GB.
Using Figure 4.2:
Lw2—
Ly
=
100 —
90 =
10 dB,
Lyi+2 — Lw2 = 0.4 dB from lower curve, and
Lywi+2 = 100 + 0.4 = 100.4 dB.
Example 4.2
Combining Sound Pressure Levels
Given the sound pressure levels of two sounds as 75 dBC and 74 dBC,
find the combined sound pressure level.
Using Equation 4.17:
Lypi+2 = 10 log
75
ik
(10! + 10"° )= 77.5 dBC.
Using Figure 4.2:
Lp: — Lp, = 75 — 74 = 1 dBC,
Lpi+2 — Lp: = 2.5 dBC from lower curve, and
Lpi+2 = 75 + 2.5 = 77.5 dBC.
Example 4.3
Effect of Background Level
Given the sound pressure level of a sound and its background as 60
dBC and the sound pressure level of the background as 55 dBC, find
CHAPTER 4 — SOUND
eerie
eee
a eee ee ee
4-13
SS
the sound pressure level of the sound without the addition of the background noise.
Using Equation 4.17:
60
35
Lyi = 10 log \10'° — 10° )= 58.3 dBC.
Using Figure 4.2:
Lpi+2 — Lp2 = 60 — S55 = 5 dBC,
Lpi+2 — Lp: = 1.7 dBC from upper curve, and
Lpi = 60 — 1.7 = 58.3 dBC.
Example 4.4
Combining Band Pressure Levels
Given band pressure levels of 80, 85, 90, 85, 80, 75, 70, and 65 dBC,
find the overall level.
Using Equation 4.17:
80
Loteye
sn — 10 log
85
(10M
65
10 oe
10"?)= 92.7 dBC.
Using Figure 4.2:
90
wel
D0
=35
5
Oi
UO
eae
=GS
=)
6.2
2A
Sea
ar Ws3
Spl
ar
OA.
ar)!
SPI
SU)
OPT)
a OO
a
=w
OP
75
Th
70
SFT
65
12.4
WAG
BR
Dial!
ANY
Determination of Sound Power Levels and Directivity
Sound
power levels cannot
be measured
directly, but they can be
determined from appropriate sound pressure level measurements.
The sound power level Ly for a sound source in a free field can be
determined from the average effective sound pressure level Ly at a
particular distance x using
Ly=L, +220 log x + Coa.
(4.18)
The correction A for temperature and barometer can be obtained from
Figure 4.3. For a spherical field, the value of C2 is 10.9 dB for x inm
4-14
FAN ENGINEERING — BUFFALO FORGE COMPANY
30 in. Hg
dB
CORRECTION
A-
-50
0
50
Figure 4.3
100
150
TEMPERATURE - °F
200
250
Corrections for Non-Standard Air
Adapted from the data of A.P.G. Peterson and E.E. Gross, Jr.: Handbook
of Noise Measurement,
General Radio Co., West Concord, Mass., 1967, p. 17.
and 0.6 dB for x in ft. For a hemispherical field, the value of C2 is
7.9 dB for x in m and —2.4 for x in ft. The distance x between the
source and the measurements should be large compared to the dimensions of the sound source if this equation, which is based on a point
source, is to be used. (See Equation 4.5.)
The arithmetic average of several measurements of sound pressure
level is always lower than the true average over an area. If the spread
between readings is less than 5 dB, the error in using the arithmetic
average is less than | dB. If the spread is about 10 dB, the error can
be limited to +1 dB by adding | dB to the calculated average. For
best accuracy, several readings should be taken at the center points
of equal area portions of the surface (whether spherical or hemispherical). The coordinates of such points on a sphere divided into
8 or 12 equal areas are listed in Table 4.5.
The sound power level Lw for a sound source in a reverberant room
can be determined from the average effective sound pressure level L,
in the reverberant field using
Lw=L,+
l0logR—C3—A.
(4.19)
The room constant R can be determined from Equation 4 livethe
value of C; is 6.1 dB for R in m’ and 16.4 dB for R in ft”. The average
effective sound pressure level is measured by moving the microphone
through space for about a wave length, so that any standing wave
effects are averaged out. The distance x between source and measurement should be great enough so that the factor //47x° is negligible
compared to the factor 4/ R. (See Equation 4.12.)
CHAPTER
Table 4.5
4 — SOUND
4-15
Microphone Locations for Free Field Tests
Coordinates of the Center Points of Equal Area Surfaces
on a Sphere of Unit Radius
SPHERICAL SURFACE DIVIDED INTO 8 EQUAL AREAS
Note: For a 4-point hemispherical traverse, use only the + values of Z.
SPHERICAL SURFACE DIVIDED INTO 12 EQUAL AREAS
1 and7
2 and 8
3 and 9
4 and 10
5 and 11
6 and 12
+0.45
+0.45
Adapted from the data of A.P.G. Peterson and E.E. Gross, Jr.: Handbook of Noise Measurement,
General Radio Co., West Concord, Mass., 1967, p. 25.
The sound power level Ly for a sound source in a semireverberant
room can be determined
using
with the aid of a calibrated sound source
j
BPE) AAS 2M EEN BHC
(4.20)
The sound power level Ly’ of the calibrated sound source must be
obtained in either an anechoic chamber or a reverberant room. The
average effective sound pressure level in the semireverberant room is
then measured with only the calibrated sound source operating to
obtain L,’, and next with only the uncalibrated sound source running to obtain L,. Measurements should be made with the micro-
phone at a sufficient distance from the source and moving over a
wave length of space as noted above.
The sound power level Lw for a sound source that is connected to
an anechoically terminated duct can be determined from the average
effective sound pressure level L, at a particular cross section with
area A ofthe duct using
Lw=1Ip+ 10logA—Cs—A.
(4.21)
The value of C, is 0.1 dB when A is in m’ and 10.4 dB when A is in ft’.
4-16
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Sound pressure levels can be measured overall or in octave, one-third
octave, or narrow bandwidths. Individual calculations should be
made for each bandwidth.
The directivity factor Q for a sound source in a particular direction
can be determined from the sound pressure level in a free field in that
direction L, and from the average effective sound pressure level L, at
the same distance from the source using
Jol!
Q
Table 4.6
—
102”
(4.22)
Directivity Factors
Non-Directional Sources with Reflective Surroundings
Position
Q
Nearcenteniofiroomi-mreeminsloe.
romiole sae emieieeinetee
Intcentenofone:walll@zmern
ano cese co
ac ernerenaroce
Inicormeriat. center omtwoiwallSimcceree
esate etree eine
Inicornen formed pysthree walls) a-irucicteltecls
osrretis ehain
]
2
4
8
Directional sources will have directivity factors larger than 1 in some directions and
smaller than 1 in other directions.
The directivity factor to be used for positions in the near field of a duct opening are
the same as for non-directional sources when the opening dimensions are about equal
to the wave length of the band being considered. For wave lengths considerably
shorter than the opening dimensions, the directivity factor approaches 8 for a position
directly opposite the opening and 4 for a position at 45° to the plane of the opening.
Adapted from the data of L.L. Beranek: Acoustics, McGraw-Hill Book Co., Inc., New York, 1954,
p. 319.
Hearing and Noise Criteria
The ear responds to effective sound pressures from approximately
0.00002 Pa (0 dB) to 20 Pa (120 dB) over a frequency range of approxrmately 20 Hz to 10000 Hz. The auditory system functions both
as a sound level meter and as an analyzer. Subjective responses to
sound are expressed in terms of loudness, pitch, and quality. Loud-
ness is primarily determined by sound pressure but is also a function
of frequency. Pitch is essentially determined by frequency but is also
affected by sound pressure. The units of pitch and loudness are the
mel and sone, respectively. Another unit, the phon, is used for loudness level.
The mel, sone, and phon are all units of judgment, as distinguished
from units of measurement. It is not wise to ascribe an uncertainty
of less than | or 2 dB to any acoustical measurement. There are re-
CHAPTER
120
4 — SOUND
4-17
120 LOUDNESS
PH ONSLEVELS
ST
teeny)
100 SG
aS AGEN
90
S 80
80
a
60
=" 60
=
50
az 40
40
=
Se ra
30
=
S20
wm
0
20
100
500
1000
5000
10000
FREQUENCY — Hz
Figure 4.4
Loudness Levels of Pure Tones in a Free Field
Adapted from the data of H. Fletcher and W.A. Munson: “Loudness, Its Definitions, Measurement and Calculation,” J. Acous. Soc. Am., vol. 5, 1933, p. 82.
lationships between acoustical judgments and measurements, but,
since they are statistical relationships, large variations can sometimes
be expected.
The loudness level of a pure tone in a free field can be determined
from its frequency and sound pressure level using Figure 4.4. The
loudness of a tone in phons equals the sound pressure level in dBC
of a 1000 Hz tone, which, to the average listener, sounds equally loud.
Figure 4.4 is based on the average subjective response of numerous
individuals. The threshold of hearing, on the average, corresponds
to the loudness contour line marked 0 phons. The thresholds of discomfort and pain are commonly listed as 120 and 140 dBC sound
pressure levels, respectively.
When
two or more
tones combine,
their loudness level is not the
sum of the individual loudness levels. However, the loudness values
for well-separated sounds are additive on the sone scale. The nomograph in Figure 4.5B can be used to determine the loudness ofa pure
tone in sones from its loudness level in phons.
There are several methods of predicting the loudness level of a
broad-band noise from sound spectrum measurements. The ANSI
FAN ENGINEERING — BUFFALO FORGE COMPANY
7 SONES
-PHONS
raced
LOUDNESS INDEX
120
;
110
|
|
~—500-F- 130
400-}
$00 E420
150 Viena
100,
60-.. 100
90.
30
cooOo
|
~o
90
15480
& 70
a oOo
LEVEL
dB
PRESSURE
BAND
-
5
4 60
3
2 = 50
oo
40.
63
125
250
500 1000 2000 4000
FREQUENCY - Hz
30
0.25
20
8000
4.5A
Figure 4.5A
0.5
4.5B
Contours of Equal-Loudness Index
Figure 4.5B
Sones-Phons Conversion
Adapted from the data of ANSI: Procedure
for the Computation of Loudness of Noise, ANSI
Standard S 3.4-1972 (R-1968), p. 9.
CHAPTER 4 — SOUND
method,'
which
is the same
as one
4-19
of the ISO methods,” involves
determining the loudness index / for each band pressure level using
Figure 4.5A. The sum of all such loudness index values, except the
loudest, is multiplied by a factor F and added to the loudest value
Im as indicated by
Sr haar Je! = Ie)
(4.23)
to give the total loudness S,. The factor F has a value of 0.15 for onethird octave band pressure levels, 0.2 for one-half octave band pressure levels, and 0.3 for octave band pressure levels. The loudness level
Lr is related to the total loudness:
Li
= 40 + 10 log2
S:= 40 + 10
InS,
In2~
(4.24)
Most people are not sensitive to a change in sound pressure level
less than about | dB at a loudness level of about 50 phons. Even
larger changes are not perceptible at lower loudness levels.
Masking occurs when one sound is rendered inaudible by the
presence of another sound. With broad-band sounds, the stronger
will mask the weaker if there is a sufficient difference in sound pressure levels. Figure 4.2 shows that a difference of 6 dB or more will
result in an increase above the higher level of 1 dB or less. With pure
tones, the ear becomes more selective and masking becomes more
difficult.
A pure tone can be detected if its sound pressure level exceeds the
rms level of a rather narrow band of the background noise, regard-
less of noise outside that bandwidth. This bandwidth is 50 Hz for
tones below 1000 Hz. At higher frequencies, the level of the tone
must exceed the level of asomewhat wider band to be detectable.
When two tones have nearly the same frequency, beats will occur
because of wave interference. This rising and falling of noise level
can also be produced by two broadband sounds if an appreciable
portion of the energy in each is contained in a narrow band and if
these bands have nearly the same frequency.
The acceptability of a background noise depends on the communication requirements of a listening area as well as on the loudness
spectrum of the noise in that area. Even without background noise, a
room may be acoustically unsuitable for certain kinds of communication. The reverberation time 060 and room volume Y can be used as
criteria of acceptability of that room for a given kind of communica'ANSI, “Procedure
(R-1968), p. 9.
for the Computation
of Loudness
of Noise,” ANSI
Standard
1SO, “Method for Calculating Loudness Level,” SO Recommendation R 532, 1966.
S 3.4-1972
1000 ©
ft?
(R)
CONSTANT
ROOM
-
400°
OPTIMUM ROOM CONSTANTS
WITH NORMAL OCCUPANCY ~
Y
SPEECH. OPERA.
Wf MOTION AeTURE
YY (HIGH DEFINITION).
USIC, CONCERT HALL,
HURCH, SYNAGOGUE...
EDIUM DEFINITION) _
=
10)
2
9
457 10 92 3
ES
ORGAN LBW DEFINITION
8 7 108
2 9
eet
ROOM VOLUME
(7) - ft?
Figure 4.6
Optimum Room Constants
Adapted from the data of L.L. Beranek: Acoustics, McGraw-Hill Book Co., Inc., New York, 1954,
pp. 316 and 426.
Table 4.7
Distance between
talker and listener
ft (m)
0.5 (0.15)
1 (0.3)
2 (0.6)
4 (1.2)
Speech Interference Levels
indBre 20uPa
Talker’s voice effort
Shouting
92
86
80
74
(1.8)
(3.7)
L.L. Beranek, “Criteria for Noise and Vibration in Communities, Buildings, and Vehicles,’ Chapter
Eighteen, Noise and Vibration Control, L.L. Beranek (ed.), McGraw-Hill Book Company, New
York, 1971, p. 559.
CHAPTER 4 — SOUND
ee
tion. Reverberation
time is a function of room
4-21
constant
R, as indi-
cated in Equation 4.11. In Figure 4.6, the optimum room constants
are plotted versus room volume for various kinds of communication.
This chart is based on the specific relationship between surface S and
volume Y, as indicated in the insert. Lines for dead and live rooms
are also shown based on the average absorption coefficients indicated.
Other acoustical criteria include speech interference levels, damagerisk levels, and various other methods based on surveys of acceptability for normal use.
The speech interference level is the average of the octave-band
sound pressure levels in the three bands where most sounds contributing to speech intelligibility occur. Older speech interference levels
were
Newer
based
on the 600-1200,
speech interference
1200-2400,
and
levels are based
2400-4800
Hz bands.
on the 500,
1000, and
2000 Hz bands. Table 4.7 is based on the new bands, and the levels
are for average male voices with the speaker and listener facing each
other and using unexpected word material.
Various damage-risk criteria have been promulgated to prevent
hearing impairment due to noise exposure. Occupational Safety and
Health Act (OSHA) standards include damage-risk criteria. Table 4.8
gives the permissible noise exposures under OSHA. Octave-band
sound pressure levels can be converted to the equivalent A-weighted
sound levels by plotting the spectrum values on Figure 4.7 and noting
the A-weighted sound level that corresponds to the point of highest
penetration into the sound-level contours.
Table 4.8
Permissible Noise Exposures!
Duration per day, hours
Sound level dBA
See
petsvetavereiere sersttechereneyaere crejertice eiccsater a setetoge see.sicce
Gieirisc
neice eres elke see ae tebe ater ste © Suelo arate o\8 avsparie® avas
LN SSeS tO SNR Ty RCO Ca POENCE OBOE CPor On Al TORS EPRI OR
CHEE
GIG Graton OI oe GyBeen ain ath i ren Anat eie cece aA petra PONCE ROSCA
Xe
SSR
OA RROD Ce IO
te in CE Pat cea ae
Ue seecetesspnenet-cderen vaactencecknceeransteroloriele
Scar tacuona mRececacnOar NDE AOI
Ue
MeCN cee Oeer horercimadel estes ici: es die he cise Oreo sete es
WP
clea clic dure eri asicier mcr d suse: CUPuraenen mira ates
VOORIERD Fie eb aoc go 5.6 O68 DO
HCO OC Ose SUCH CUOMO
OOS
90
92
95
97
100
102
105
110
115
‘When the daily noise exposure is composed of two or more periods of noise exposure
of different levels, their combined effect should be considered, rather than the individual effect of each. If the sum of the following fractions: C:/ 7 + C2/ 72... Ca/ Tn
exceeds unity, then the mixed exposure should be considered to exceed the limit
value. C,, indicates the total time of exposure at a specified noise level, and 7),
indicates the total time of exposure permitted at that level.
Federal Register, Vol. 34, No. 96, May 20, 1969, pp. 7949.
130
4 NhOo
eee
on
annie
an
cath
100
-
90
~~ A-WEIGHTED
SOUND
LEVEL
PRESSURE
dB
SOUND
BAND
OCTAVE
FY Pine
Ea
125
Pe
ee
250
LEV L
PaO Ieee, el Ie fet Cana I
50
1000
2000
4000
BAND CENTER FREQUENCY - Hz
ee ret ees
8000
Octave band sound pressure levels may be converted to the equivalent A-weighted
sound level by plotting them on this graph and noting the A-weighted sound level
corresponding to the point of highest penetration into the sound level contours. This
equivalent A-weighted sound level, which may differ from the actual A-weighted sound
level of the noise, is used to determine exposure limits from Table 4.8.
Figure 4.7
Equivalent Sound Level Contours
Federal Register, Vol. 34, No. 96, May 20, 1969, p. 7949.
Example 4.5
OSHA Exposure Limits
Given band pressure levels of 90, 95, 99, 98, 91, 87, 85, and 80 dBC,
determine the maximum permissible exposure time per OSHA.
Plotting the band levels on Figure 4.7, note that the maximum penetration is close to the 95 dBA curve. Referring to Table 4.8, the maximum permissible exposure is approximately 4 hours.
CHAPTER 4 — SOUND
4-23
SOUND
PRESSURE
LEVEL
dB-
OCTAVE BAND CENTER FREQUENCY - Hz
Refer to Table 4.9 for recommended NC number according to application. The sound
pressure levels in the space under normal conditions (except unoccupied) should not
exceed the corresponding curve values in any octave band.
Figure 4.8
Recommended
Adapted from the data of ASHRAE
ASHRAE, New York, 1977, p. 7.7.
Noise Criteria
Handbook and Product Directory - 1977 Fundamentals,
4-24
FAN ENGINEERING — BUFFALO FORGE COMPANY
Table 4.9
Recommended
Noise Criteria
Mass communication without amplification
Goncert: hallSixe.
eats eaerccc, tae orate tonseorohac ross cherey esotekoncueRenonencrs NC 15-25
Legitimateitheaters: cyaverucircirsestsestets
eleleksllekel chesaensiereu vert ats NC 25-30
Conference rOomsiccs
aes css ,cter eos ttekote euereeener ocr once oketenens NC 25-35
Schoolirooms ee. ats. een cuaravetersateede tc Pee
atc erwetere aoe cameron NC 30-40
Churches'and/courtroomS: crsparwtete
oechoca taletererene eacle (eat chaiierore NC 30-40
Mass communication with amplification
Broadcast:studiosicstse
tua.cpotetetere soba cue cietercee oycnereroreperncie ons NC 15-20
Assembly,hallsieivs
icc. coo sxave cceuenavetoiauscore
okeh sei/oyslone aye) auelener ice NC 25-30
Motionspictureitheaterssscwaes
«5 sccm as eee ss eget oc teneyct elegarsr.o NC 30-35
Individual communication
Homes: .apartmentssand Notelsi..:e sicchereetcicte
leis stereo iteneiere rs NC 25-35
Hospitals:and libraries cisvz< cuore cue erere he sleuclo eleaat ovevede oleraiohene NC 30-40
Privatesoffices :.sacteter s,s. - <. eteor onsuar cise od aaebas eraloydeeoket cnet omelets NC 30-40
Generalioffices: Ae vinn soa sheers. seeterhe. cronies .sveae semen oustenece NC 35-45
Restaurants:andidepartmentistores a ..2.. «a. «src as te cieree. 6 NC 40-50
GOliS@UINS! Jyate cis wusconscanemors elonssonelicuchncs, aicuaere valisccmepeuonstraiton enetots NC 50-60
FactOmes sodawerstnt s+avon os: antec
co oho onatooie ohioiarees Teton nekerone te NC 50-70
The recommended noise criteria are given as NC numbers. Corresponding octave band
spectra are given in Figure 4.9. The maximum sound pressure level in any band
should not exceed the indicated value. The NC number also corresponds to the speech
interference level in decibels.
Adapted from the data of ASHRAE
Handbook and Product
Directory - 1976 Systems, ASHRAE,
New York, 1976, p. 35.6.
One of the most widely used noise criteria is that given in the
ASHRAE Handbook, reproduced here in part. The recommended
noise criteria NC for various types of spaces are given in Table 4.9.
The corresponding octave-band spectra are drawn in Figure 4.8.
These criteria are based partly on speech interference level (indicated
by the NC number) and partly on a favorable relation between highand low-frequency components. Recommended band pressure levels
should not be exceeded under normal conditions. (Normal conditions
are those usually encountered at the time of occupancy, except that
measurement at the occupant location requires removing the occupant.) Fans and other equipment serving a space should not produce
a noise spectrum in that space exceeding the recommended NC curve.
Obviously, the acoustical characteristics of the room and the duct
system, as well as of the fan, must be considered. Fan equipment can
also cause objectionable noise at neighboring locations because of
transmission through the atmosphere. The various criteria can be
used to establish the maximum permissible band-pressure levels
under these conditions. In this case the various factors that affect
sound propagation in open air should be considered.
CHAPTER
4 — SOUND
4-25
A rule of thumb for relating sound level measurements to noise
criteria is: dBA will equal NC — 6 within plus or minus 2 dB.
Noise Control
In order to determine whether the noise at a particular listener
location will be acceptable according to one of the criteria discussed
above, it is necessary to study the transmission path over which the
noise will travel from the source to the listener. There may be several
sources contributing to the noise at any one location and several
paths over which each noise may travel from its source to the listener.
Example 4.6
Effects of Different Sound Fields
Given a point source of sound with an overall sound power level of
85 dB, compare the sound pressure levels: in a hemispherical free field
at 10 ft, in a reverberant field of a hard room, and in a 2 ft X 2 ft
duct. Assume standard conditions; therefore, A = 0. Assume the room
constant for the hard room,
the duct.
R = 200 ft”. Assume
a plane wave
in
Using Equation 4.18:
D>— Ly + 20ilog
(x) + C, + A = 85 — 20+ 2.4 + 0 =67.4dB
in a hemispherical free field at 10 ft.
Note: £ = 0.007 at 50% relative humidity and 8000 Hz, and
AL, = 13.24 (x = 13.24 X 0.007 X 10 = 0.93 dB from Equation 4.26.
Therefore, this attenuation can be ignored for short distances.
Using Figure 4.9, enter at x = 10, proceed diagonally to Q = 2,
proceed vertically to R = ©, and read —17.6 dB.
Lp = Lw+
relative sound pressure level = 85 — 17.6 = 67.4 dB.
Using Equation 4.19:
Lp= Lw— 10 log (R) + C3+ A= 85 — 23+ 16.4
+ 0 = 78.4 dB
ina reverberant field (R = 200 ft’) of ahard room.
Using Figure 4.9, enter at x = 10, proceed diagonally to Q = 2,
proceed vertically to R = 200, and read —6.6 dB.
Lp = Lw + relative sound pressure level = 85 — 6.6 = 78.4 dB.
Using Equation 4.21:
Lp = Lw—
10log A + Ca t+ A= 85 —6+ 10.4 + 0 = 89.4 dB
ina2ft
X 2 ft duct.
Note: similar calculations can be performed for individual band levels.
pinteidcderens = ee
rr
—————————
4-26
FAN ENGINEERING — BUFFALO FORGE COMPANY
co
=)
= |
25
om
aaa
ea
<>
an Oe:
ae)
z=
[at
-30
8
zqG
4
S23
8
Bo
1
1
[ow
ce
A
05
4> =6
aie
SS
Wo
05 £2
a
ie
0.1
025.405
‘one 5
* DISTANCE FROM scousnic SOURCE be= oo
Figure 4.9
Sound Pressure Levels Relative to Sound Power Levels
Adapted from the data of L.L. Beranek: Acoustics, McGraw-Hill Book Co., Inc., New York, 1954,
pp. 317-319.
Many of the principles of noise control can be determined by
studying the relations involved in the measurement of sound power.
In a free field the noise level at any location is a function of distance x and directivity Q. For each doubling of distance, the sound
pressure level will be decreased by 6 dB. If a source is highly directional, it may be feasible to aim most of the noise in the least objectionable direction.
In a reverberant field the noise level can frequently be brought
under control by room surface treatment. However, there will be an
area Close to the source where such treatment will do no good.
In either of the above cases the sound pressure level Lp at any
listener location can be determined from the sound power level Ly
and the directivity factor Q of the source together with the room
constant R using
Lp = Lw+
10 log
In a free field the room
9
constant
se=) AGS
R
becomes
(4.25)
infinitely large making
CHAPTER
4 — SOUND
4-27
4/R insignificant compared to Q/47x’. Similarly, in the reverberant
field the distance x must be large enough to make Q/47x° insignificant compared to 4/R. A graphical solution of Equation 4.25 is given
in Figure 4.9. Both the chart and the equation give the sound pressure level in dB relative to the sound power level for a source that
can be considered a point. The value of C, is 0.1 dB when x is in m
and Ris in m’, but it is 10.4 dB when x is in ft and Ris in ft’.
In open air the energy losses in the air itself may become significant for frequencies above 1000 Hz if appreciable distances are involved. The attenuation in dB can be determined from
AL, = 13.246
(4.26)
for which the distance x is in feet and the energy attenuation constant ¢ is obtained from Figure 4.1. Reflections by and absorption at
the boundaries
and
refractions
due to temperature
gradient,
wind,
etc. generally decrease the noise level below calculated levels at any
outdoor location.
When a partition is located between a source and a receiver, a trans-
mission loss occurs. This loss depends on the frequency and the angle
of incidence of the sound and on the construction and materials of
the partition. Transmission losses for various materials are listed in
Table 4.10. The values in this table have been calculated by the plateau
method as given in the reference.
Table 4.10
Transmission Losses for Field Incidence
in dB
Octave Band Center Frequency in Hz
Material Thickness | 63
125| 250
500 | 1k
Aluminum, 0.25 in.
Concrete, 4 in.
Concrete, 8 in.
Glass, 0.25 in.
Lead, 0.06 in.
Plastic, 1.00 in.
Plywood, 0.25 in.
Steel, 12 ga
Steel, 8 ga
Steel, 0.25 in.
Steel, 0.50 in.
Steel, 1.00 in.
20
21
27
19
20
28
6
21
26
29
35
40
29
33
38
27
a
30
18
33
37
40
40
40
Adapted
14
15
21
13
14
22
0
15
20
23
Do
26
27
33
25
26
30
12
27
31
35
40
40
2k
4k
8k
2929)
38 | 38 | 38
38
38
48
2
e220
30)
3 8p e44a
Om
SO
530i e4
8)
199)
20)
39 | 40 | 40
40 | 40 | 40
40 | 40 | 40
40 | 40 | 47
40 | 45
240
| 48
58
40
OO
Onl
9)-30
| 40
| 40
| 47
| 57
from the data of I.L. Ver and C.1. Holmer: “Interaction of Sound
Structures,”
Chapter
pp. 283, 306, 307.
Il, Noise
and
Vibration
Control,
L.L.
Beranek,
Ed.,
Waves with Solid
McGraw-Hill,
1971,
4-28
FAN ENGINEERING — BUFFALO FORGE COMPANY
oe
EEE
SS SS ES
SS EE EE
ee
60.
50
40
30
20
LOSS
dB
TRANSMISSION
SOUND
-
125
250
Figure 4.10
Adapted from the data of ASTM:
mission
Class,”
E413-73,
500
1000
FREQUENCY — Hz
2000
4000
Sound Transmission Class (STC)
“Standard
1/980 Annual
Book
Classification for Determination of Sound Transof ASTM
Standards,
Part
18, Philadelphia,
Pa.,
1980, pp. 984-986.
The transmission loss characteristics of various wall systems, windows, and doors are often given by a single number rating. The sound
transmission class STC, adopted by the American Society for Testing
and Materials, is such a single-number procedure. Figure 4.10 gives
the sound transmission class contours, each of which is labeled according to the transmission loss at 500 Hz. When a wall system or
window is rated, its spectrum of transmission losses for each of the
one-third octave bands is compared to the various contours, and that
contour number is assigned which best matches the test data according to the specified criteria. Northwood, Warnock, and Quirt list
the sound transmission classes for numerous wall systems, windows,
doors, and floors.' The sound transmission class provides a singlenumber means of comparing alternatives and also can be used to
estimate transmission losses in the various bands.
'T.D. Northwood, A.C.C. Warnock, and J.D. Quirt, “Airborne Sound Insulation,” Chapter 22,
Handbook of Noise Control, Second Edition, C.M. Harris (ed.), McGraw-Hill Book Company,
New York, 1979, pp. 22-9 to 22-21.
CHAPTER 4 — SOUND
4-29
Transmission loss can be defined as 10 times the logarithm (to the
base 10) of the ratio of the sound energy incident on a wall to the
sound energy transmitted through that wall. The transmission loss
for a wall constructed of several surfaces, each with a different individual transmission loss, can be determined from
SihrieS2
eee ats On
ACE
=
10 log
S|
So
TL,
i
Sn
TL2
a
TLn
GO) mea 10) ce
(10)
2e5
(4.27)
The transmission loss for a major opening is 0 dB at all frequencies.
The transmission loss of a crack varies with its geometry but is quite
small, so even small openings in an enclosure may have to be treated
to achieve the desired noise control. The noise reduction, or attenuation, AL, across a wall is the difference in sound pressure level at the
two surfaces and can be determined from the transmission loss TL,
the area of the transmitting wall S,, and the room constant R for
the receiving space using
Alp = Ip ~ Lm = TL ~ 10log(— +5).
y|
Si
(428)
In fan engineering most important noise sources are associated with
airstreams, and most of the transmission path is through those airstreams. Nevertheless, it is important to examine the possibility of
mechanical excitation and solid-borne noise.
Much of the sound energy in a duct radiates in the direction of air
movement. The object of most noise control measures is to impede
this flow of noise yet allow the air to pass freely. Some of the energy
is transmitted to the duct material. That which is not absorbed or
dissipated as heat is transmitted to the ambient air surrounding the
duct. The sound pressure level Lp: outside the duct can be determined
from Equation 4.28 and the sound pressure level Ly; inside the duct.
Usually, a further
reduction
is required,
and an additional
barrier
such as a wall or ceiling must be installed. The sound pressure level
on the duct side of this barrier can be determined from the characteristics of the enclosure including the proposed barrier. When the duct
is quite close to the barrier it may be necessary to consider the direct
radiation, in which case a cylindrical wave front can be assumed
to
radiate from the duct. Equation 4.28 can then be used to determine
the sound pressure level on the opposite side of the barrier. Besides
being tedious, these calculations of the various sound pressure levels
due to reflection and absorption effects involve numerous difficulties.
4-30
FAN ENGINEERING — BUFFALO FORGE COMPANY
The sound pressure level L, in the duct in terms of the sound power
level L,, of the source is
Lp=Lw—l0logA+Ci+A,
(4.29)
assuming a plane wave of area A equal to the cross- -sectional area.
The value of C4 is 0.1 when A is in m’ and 10.4 when A is in ft’.
When computing radiation through a duct opening, do not ignore
reflection and absorption. They are the means by which sound control is achieved. Another factor that also must be considered is the
generation of noises in the various duct elements, which always accompanies air flow.
The attenuation of bare ducts and of ducts covered with thermoinsulation is given in Table 4.11. Even in the small sizes there probably will be a net generation of noise rather than a net attenuation
in high-velocity duct designs, that is, around 5000 fpm.
Table 4.11
Attenuation of Bare and Covered
dB/ft
Ducts
Octave Band Center Frequency — Hz
72x72)
250 | 500
8000
0.03 | 0.03
0.10
0.15 | 0.10
0.10 | 0.05
0.10 | 0.10 | 0.05 | 0.01
0.10
0.05
0.01
For ducts covered with thermal insulation, use table values if round or twice table
values if rectangular.
Adapted from the data of
New York, 1976, p. 35.11.
ASHRAE Handbook and Product Directory — 1976 Systems, ASHRAE,
When the inside of a duct is lined with acoustical material and the
major dimension of the section is only a fraction of the liner length
x in ft, the attenuation AL, can be estimated from the perimeter P in
in., the cross section A in sq in., and the absorption coefficient a using
AL, = 106 —-x0.
z
oy
P
1.4
(4.30)
Figure 4.11 gives attenuation values per foot of duct lined with 1/2”
and |” acoustic material based on average center-of-band absorption
coefficients.
CHAPTER
4 — SOUND
4-31
10
9
8
7
6
5
4
3
S
2
a
a=]
3
= 10
s 3
=:
I
—
EG
5
4
3
2)
d
‘A
:
26
NV
;
2
Saas 416-7.8'91.0
P/A FOR ‘in. LINER
pa
4) 5,67.8910
P/A FOR 1 in. LINER
PERIMETER/CROSS SECTION - (P/A)
Figure 4.11
Attenuation Due to Lined Ducts
Duct lining is usually most effective in the middle frequency range.
At high frequencies, the attenuation can be increased by incorporating
elbows or miters in the system. Unlined bends reduce radiation by
reflecting more power toward the source than is generated by the
disturbance. The net attenuation due to lined and unlined elbows
and miters can be estimated from Table 4. 12.
The sound power radiated down a duct divides at any divided-flow
fitting in proportion to the ratio of individual to total branch area
(A\)/(A;
+ Ar +.. + A,). The difference between upstream and down-
stream sound power levels AL w is expressed by
a
ALy=
10 log
aes
A,
st).
(4.31)
4-32
jie
— BUFFALO FORGE COMPANY
FAN ENGINEERING
eee
eee in OT
ee
ee eS
Table 4.12
Type
|
Curved
Bend,
No
ini
Lining
vi
ee
i as
UNDG.
Attenuation of Elbows
dB
cole
Octave Band Center F eeeetes -H z
Size
_[63 [128 |
250 [ soo | 1000 |am 4000|8000
1
BETO Mm HEC LEOAMIMLOFNemn
2
4
Oe
20° | Os O
Wed ie te
fe
IRO NG
SAO
ing — eas
ae
41-80sed | 0 |SE1
Riwideel Lae Oonae
Ge
et
5
ipiedestnO.
eG |) ot 1h 3
7
20wide | 0 | 1
Slt
ak
5
lm
4)0 wider |ediweie6y 2 oT al ofe s
T
ee
Swadesiepr
ino
f i in | wide |0 | 0
|
2
3
3
3
7
5
3
3
3
3
3 ate
5
3
3
8
6
6
gh
MRS esat Sele pee
eon
mt
Tues
5
8
==
3
3
3
3
3
3
3
8
aa
i ie
20wide | 0 | 1
Bele
6
SP
td
1
Me)
do wide 1
S|
8.
oes
Rot
TN
Tt
i——
[=
a
Gwideseo
oe
ito
wd
6
iio
eonte
; cos TOwide. (20. |-0.
Mit e
heees EAT Eel 1m
HOMO
eng
20wide |0 | 1
Sea
Wace pac ed enKiel),
ate
| 4owide |1 | 6 [11 | 10 | 10 | 10 | 10 L 10
iPiee
Bwide:| Ui
sl Omit
Gl)
dni
pee
G
Poctacree (lO wide) 00, Wed)
|My
c6-n| (20)
iden
ites
ete
ae
20wide |0 | 1
Gel tae
ete Wl Veen
18a | oie
| 4owide |1 | 6
[12 | 14 | 16 | 18 | 18 | 18
Curved-bend data for either round or rectangular sections.
Miter data for rectangular sections without turning vanes.
Lining should be 10% of width and extend upstream or downstream at least 2 duct widths.
Lining need only be on sides. Width is between inside faces of lining.
Adapted from the data of
New York, 1976, p. 35.11.
ASHRAE Handbook and Product
Directory - 1976 Systems, ASHRAE,
Not all the power radiated to an opening leaves the duct. Some is
radiated back and called the end reflection loss. This loss can be determined from Figure 4.12. It is a function of frequency, size, and
location relative to a wall as indicated on the chart.
Similar reflections occur at other discontinuities such as sudden expansions and contractions. The transmission loss for an expansion
chamber will vary with the ratio of cross-sectional area of the chamber
to that of the inlet or exit pipe A./A, and the ratio of the chamber
length to wave length as given by Figure 4.13. The study of filters
and mufflers is too broad to be covered here. For a comprehensive
treatment of the subject, see the reference for Figure 4.13.
CHAPTER
4 — SOUND
4-33
30
END REFLECTION LOSS AT THE OPEN END OF SQUARE DUCTS
hy
S
fee)
\
To
MS
Peo
)
‘
\
=
S 15
DUCT END
“CIN FREE SPACE
Ne
:|.
FLUSH WITH WALL
iC
.
a
a
5
OF
0i3)
0/5,07- 1
7p ae
Be Th 1G
20° 730)5
FREQUENCY X LENGTH X 10°? (f2//000) — CPS-INCHES
Figure 4.12
50770
End Réflection Losses
Adapted from the data of ASHRAE Guide and Data Book, Systems and Equipment,
1967, p. 388.
Ne
st
Oe
—ic
[os
co
Nw
=
TRANSMISSION
LOSS
dB
-
ie
ny
Figure 4.13
0.8
1.2
1.6
2.0
27rl./A\ — RADIANS
2.4
2.8
OZ
Attenuation Due to Expansion Chambers
Adapted from the data of C.-M. Harris: Handbook of Noise Control, McGraw-Hill
New York, 1957, p. 21-16.
Book Co., Inc.,
FAN ENGINEERING — BUFFALO FORGE COMPANY
4-34
eee
ee
The attenuation of a lined plenum can be calculated approximately
from
ALw=
10 log
]
jl
Ai (
cos B ve LOL
2rx’
aS
(4.32)
This equation includes the attenuation due to absorption by the
plenum surface S having an acoustic lining with an absorption coefficient a. It also includes the reduction in direct sound transmission,
which is a function of the distance x between inlet and outlet, the
outlet cross-sectional area A, and the angle B between the direct and
normal paths to the outlet.
Example 4.7
Duct System Noises
Given the system sketched below and the sound power level spectrum
in the main duct, find the sound pressure level in the room, 10’ in
front of the opening.
25’ — 2' X 2’ covered duct_|
~ miter with downstream lining
10’ — 2’ X 2’ covered duct
DOSS
branch
duct end flush with wall
room constant 200 ft°
Using Equation 4.31, calculate the difference between the branch and
the main:
ALw=
4
10 log (a
= —3 dB or 3 dB attenuation.
Using Table 4.11, calculate the attenuation of the covered duct:
ALy= dB/ft X ft = 0.10 X 35 = 3.5 dB, say 4.0 dB.
Using Table 4.12, calculate the attenuation of the miter:
ALy=
11 dB.
CHAPTER 4 — SOUND
Ee
i
ee
4-35
ae
Using Figure 4.12, calculate the end reflection loss:
f= 250 Hz, 1 = 24in.,
fl = 250 X 24 = 6000 Hz in., and
ALyw=5dB.
The total attenuation is
LALw—
34-4
ll + 5 = 23'dB.
Assuming that the initial sound power level in the 250 Hz band was
85 dB, the sound power level entering the room will be 85 — 23 = 62 dB.
Using Equation 4.25 and Table 4.6:
Ly = Lw + 10 log ( S- +4) + c.+
41x"
R
af
Lp = 62 + 10 log
aang
2
4
ale Naina O40) = 255.70 B:
4710°
200
Similar calculations can be made for all octave bands.
Note that in the above situation the reverberant sound predominates,
but that at | ft or so in front of the opening the direct sound would
predominate.
In summary, the general procedure that should be followed in
solving any noise control problem is:
the sound power levels and directivity factors of all
_ . Determine
sources of noise by test or from the manufacturer’s data.
2. Determine the various listening areas that might be affected by the
various sources and establish the allowable noise levels at these
locations from applicable criteria.
3. Determine the paths by which the noise will travel to the listener
(or the listening locations) and calculate the noise levels that can be
expected, taking into account divergence, reflection, and absorption.
4. If the expected noise levels exceed what can be tolerated, consider
whether means
of reducing noise at the source, means of altering
the transmission path, or means of otherwise protecting the listener
are available or desirable.
Sound power levels and sound pressure levels, both expected and
allowable, should be determined for each band of the audible spectrum.
Generally, the use of a band width of one octave will be suitably
accurate for problems involving air handling equipment.
4-36
FAN ENGINEERING
— BUFFALO FORGE COMPANY
The most important source of noise in a fan system will usually be
the fan itself. Therefore, the noise characteristics of fans are discussed
in the chapter on fan sound. Aerodynamic noises are also produced
in duct elements. At low velocities, these are often negligible, but at
high velocities part or all of the natural attenuation of both ducts
and bends may be nullified. Noises generated in grills and diffusers
are especially important since duct treatment cannot be used for their
control. Combustion noises and machinery noises may require treatment, too.
Chapter 5
Heat Transmission
Heat can be transferred from one region to another by radiation,
conduction, convection, or various combinations of these three mecha-
nisms. The direction of heat flow will be from the region with the higher
temperature to that with the lower temperature. The region that emits
the energy is called a heat source, and the receiving region is called a
heat sink. Whether one or another of the three mechanisms will predominate ina situation depends on the space relations and the temperature difference between the source and the sink.
Radiation involves the net transfer of radiant energy between separated bodies. Such transfer does not require a connecting medium.
Instead, radiant energy is propagated as a wave motion from all bodies
in all directions. Although there is energy transfer in both directions
between a hot and a cold body, the heat source emits more energy than it
absorbs, and the sink absorbs more than it emits.
Conduction involves the net transfer of molecular energy within a
body by physical contact. Such transfer can also be achieved by bringing together two distinctly separate bodies. The bodies may both be
solids or fluids, or one of each. Conduction
within a single fluid is
accompanied by convection.
Convection involves the net transfer of thermal energy within a fluid
by mixing action. Convection, or mixing, can occur naturally because
of buoyancy, or it can be forced, as with a fan or pump.
In practical applications heat transfer always occurs as some combination of radiation, convection, and conduction, but it is convenient
for both study and computation to separate these effects.
Thermal Conductivity
All solids, liquids, and gases resist the conduction of heat through
them. In general, gases are the poorest conductors and some solids the
best. The thermal conductivity k is a measure of the ease with which
heat will pass through a material by conduction. This quantity varies
significantly with temperature but only a little with pressure. Its variation over a limited temperature range is generally linear; therefore, in
most engineering applications the average value should be taken as
that at the average temperature. If the thermal conductivity k is divided
by the actual thickness x of a material, the result k/x is known as the
thermal conductance of that thickness of material. The reciprocal of
the conductance is knownas the resistancer or x/k of that thickness of
FAN ENGINEERING — BUFFALO FORGE COMPANY
Ore
Table 5.1
Thermal Properties of Metals and Alloys
i
Metal or Alloy
Copper Alloys
ba COPPATaraere
eltiskekecc ei.
Deoxidized copper ........
Commercial bronze........
Red brass: iit.ci Pere te
Muntzimetal ci. cy..secre sretete
NaValibrasSmnnca acess
Admiralty metal..........
Silicon bronze ........
Nickel Alloys
Pireinickel Set jotre
occa c3s
Monell setae
ote
EKAMONE |s crbeiaepstincatar.
Incortel| GOO tes nrsaecers
cco.
Inconel'X750). on Soh.wee
Hastelloy: Bimetns seers tae
Hasteltoy Gi coe. oars a nteeaas
Hastetloy Dime ens cence
Miscellaneous Metals
Plre: lead ie mevoruckeascioteens
lieadiabbitt cme nearer.
Pure magnesium .........
PUrestiNiee
ee recat one
TitANiUM erecta
oe amas eis
t
p
k
Cp
oF
lbm/in?
Btu-in./hr-ft?-°F
Btu/Ibm-°F
71
77
77
Ti
77
77
77
23
P23
23
23
23
23
23
68
68
68
68
68
68
68
68
092
092
09
09
09
09
09
09
77
112
M2
H27
106
103
091
092
109
32-212
32-212
70
70
77
77
77
68-212
68
64
:
031
036
25
32
05
7]
13
Purewinc ssnsetae
see lee
Iron
Wrought” pe cccrenasmnerane
7
091
212
a2
Cast Werseeuttncts heen
212
12
MOOG sere ine reactaetenster
WOOF
aioe mee
ae oe
O40 SS erences
UW) oiieg etomimemen
recat
Stainless Steel
301, 302, a3}
304 5.3)116)Sili7)) eee acne
COSESIO Mess venesMenras
32
932
32
932
115
158
116
155
212
932
212
932
she
hi Hae Cle tecpeneccsetaeenenecteteyse
ea
S16%420) seh ee
RS
Ue
Seen Goan
ears
BO SO2 re ccccron
ca ste
Non-Metals
932
21
93
21
21
12
Rive: RAS
Se he ee
Steel
212
12
Aw
AW
11
1
Insulators: Refer to Table 5.2.
Building Materials: Refer to Chapter 21.
Miscellaneous: Refer to appendix.
Adapted from the data of S.L. Hoyt: ASME Handbook - Metals Properties, McGraw-Hill Book
Company, Inc., New York, 1954.
CHAPTER 5 — HEAT TRANSMISSION
Table 5.2
5-3
Thermal Conductivity k of Industrial Insulation
Form
Typical
Material
Density
Composition
Ibm /ft?
Typical Conductivity k at Mean Temp F
In Btu-in. /hr-ft?-°F
0
BLANKETS AND FELTS
Mineral Fiber
(Rock, slag, or glass)
Blanket, metal-reinforced
Glass
Blanket, flexible, fine-fiber,
organic-bonded
Blanket, flexible, textile-fiber,
organic-bonded
0.26
0.25
0.24
0.22
0.21
0.20
0.28
0.27
0.25
0.23
0.21
Felt, semi-rigid organic-bonded
Laminated and felted
Without binder
Vegetable and Animal Fiber
Hair felt or hair felt plus jute
0.20
|
INSULATING CEMENTS
Mineral Fiber
(Rock, slag, or glass)
With colloidal clay binder
With hydraulic setting binder
LOOSE FILL
Cellulose insulation
(milled pulverized paper
or wood pulp)
Mineral fiber, slag,
rock, or glass
Perlite (expanded)
Silica aerogel
Vermiculite (expanded)
0.23
0.25 |0.32
0.15
0.42
0.38
200|
300)
500]
700
FAN ENGINEERING — BUFFALO FORGE COMPANY
5-4
Table 5.2 (cont.)
Thermal Conductivity k of Industrial Insulation
Form
Material
Composition
Typical
Density
Ibm /ft®
Typical Conductivity A at Mean Temp F
In Btu-in. /hr-ft2-°F
BLOCKS, BOARDS, AND PIPES
Asbestos
Laminated asbestos paper
Corrugated & laminated
asbestos paper
4-ply
6-ply
8-ply
Molded Amosite and Binder
85% Magnesia
Calcium Silicate
Cellular Glass
Diatomaceous Silica
Mineral Fiber
Glass
Organic-bonded, block,
and boards
Nonpunking binder
Pipe insulation, slag or glass
Inorganic bonded-block
Pipe insulation, slag or glass
Mineral Fiber
Resin binder
Rigid Polystyrene
Extruded, Refrigerant 12 exp
Extruded
Molded beads
Polyurethane
Refrigerant 11 exp
Rubber
Rigid, foamed
Vegetable and Animal Fiber
Wool felt (pipe insulation)
Adapted from the data of ASHRAE: Handbook
ASHRAE, New York, 1977, pp. 22.17 & 22.18.
and Product Directory - 1977 Fundamentals,
CHAPTER
5 — HEAT TRANSMISSION
Table 5.3
5-5
Conductance of Air Spaces at Various Mean Temperatures
In Btu per hr-ft?-°F
Mean
Temp.
oF
Width of Air Space in Inches
Ir
128
.250
364
493
| 713
20
30
40
50
60
70
80
90
100
110
120
130
2.300
2.385
2.470
2.560
2.650
2.730
2.819
2.908
2.990
3.078
3.167
3.250
1.370
1.425
1.480
18535)
1.590
1.648
1.702
BAY
1.813
1.870
1.928
1.980
1.180
1.234
1.288
1.340
1.390
1.440
1.492
1,547
1.600
1.650
1.700
1.750
1.800
1.852
1.100
1.148
1.193
1.242
295
1.340
1.390
1.433
1.486
1.534
1.580
1.630
1.040
1.080
15125
1.168
1.210
1.250
(e295
1.340
1.380
1.425
1.467
1.510
1.550
ke9/2
ip
1.00 | 1.50
1.030
1.070
ily
1.152
URE:
1.240
1.280
1.320
1.362
1.402
1.445
1.485
1.530
1.022
1.065
1.105
1.149
1.188
1.228
1.270
1.310
1.350
(ese
1.435
1.475
1.519
dog,
Adapted trom the data of FB. Rowley and A.B. Algren: “Thermal Resistances of Air Spaces,” Trany.
ASHVE, vol. 35, 1929, pp. 165-181.
material. Most of the good heat conductors are metals. Thermal conductivities and other properties for a variety of metals and alloys are
given in Table 5.1.
Poor conductors,
or materials that have high thermal
resistance,
are known as insulators. Thermal conductivity values for a variety of
insulating materials are given in Table 5.2. Notice that the apparent
densities are quite low. These materials are all fibrous or cellular, with
a high percentage of voids. The listed values are for air--filled voids
and can be decreased by using a higher-molecular-weight gas.'
Additional thermal conductivity values can be found in the heat
exchanger chapter, where tables are given for both liquids and gases,
and in the appendix for miscellaneous materials. Conductances for
building materials, built-up walls, etc. are listed in various tables of the
air-conditioning chapter.
The conductances of various air spaces are given in Table 5.3, and
values for various mean temperatures and widths are listed. The reference temperature is the mean temperature of the air between surfaces,
not the mean wall temperature. Increases of over | in. in the width have
very little effect. Not shown are the effects of surface emissivity and
direction of heat flow.
'R.M. Lander, “Gas Is an Important Factor in the Thermal
Materials,” Trans. ASHVE, vol. 61, 1955, pp. 151-168.
Conductivity
of Most
Insulating
5-6
Dee
— BDUFFALY FPUNVEe vue
EE
FAN ENGINEERING
ee
Steady Conduction
The rate of total heat exchange On across a thickness of material x
can be determined from
:
Qu=
kAAt
x
:
(5.1)
The proportionality factor k can be recognized as the thermal conductivity of the material and the fraction &/x as the thermal conductance for thickness x. The area A is that which is normal to the flow
of heat. This area depends on the relative shapes and amounts of inside A; or outside surface area A, as indicated by
A= A;= Apo
for parallel flat surfaces,
(5.2)
A= aa
for concentric cylindrical surfaces, and
(5.3)
for concentric spherical surfaces.
(5.4)
n(Z
A= VAiAo
Approximate results can be obtained for any other shape by using the
average area.
The temperature difference Av must be constant for steady conduction. This is the difference in temperature between points separated by
the thickness x. Where x is the total thickness of the wall, the temperature difference is that between the two surface temperatures.
Film Coefficients
When heat is transferred to a fluid from a solid, or vice versa, the
process is one of conduction plus convection. The total heat transfer rate
can be expressed in an equation similar to that for steady conduction:
Ou=hAAt.
(5.5)
The proportionality factor 4 is known as the local film coefficient of
heat transfer. This factor varies with certain physical properties of both
the fluid and the heat transfer system. The area 4 is that of contact
between the fluid and the solid, and the temperature difference As that
across the film. This temperature difference is the same as the difference
between the surface temperature and the bulk fluid temperature. Dimensional analysis’ of any heating or cooling process that involves a
fluid flowing at a mass velocity G without a change of phase indicates
Refer to Appendix A for a discussion of dimensional analysis.
CHAPTER
5 — HEAT TRANSMISSION
5-7
that the Nusselt number isa function of Reynolds number and Prandtl
number as indicated by
BO
fe
(22) (4),
Nan
ey
ae
(5.6)
The characteristic dimension D of the system is usually a diameter. The
coefficient y and the exponents n and m depend on the temperature at
which the physical properties A, “, and c, are evaluated and on the
geometry of the system, as indicated in the following paragraphs.
When the local temperature varies, the local film coefficient also varies.
Average values are determined for the average condition.
Any consistent set of units can be used in most of the equations that
follow. Specific units are listed for the dimensional equations.
Heating and Cooling Fluids Inside Tubes
If the various physical properties of the fluid are evaluated at the
bulk temperature /,
ADi _ 03(-)
k
8
:
()
mn
k
4
(5.7)
for turbulent flow inside (subscript /) clean tubes. This expression can
be simplified by using the average properties of most gases:
h; —
5G:
dy"
.
(5.8)
Refer to Table 5.4 for units and values for Equation 5.8. The method for
evaluating film coefficients of liquids outlined in the chapter on heat
exchangers is recommended. The variation of film coefficient with
velocity and temperature is shown for water in Figure 5.1 and for air in
Figure 5.2. A comparison of these two figures illustrates the effect of
physical properties.
Table 5.4
h
Units and Values for Equations 5.8, 5.12, and 5.13
G,
W/m?-K
kJ/kg°K
kg/s-m?
Be)
Btu/hr-ft?-°F
| Btu/Ibm-°F
| Ibm/hr-ft?
.36
cal/s-cm?-°C
cal/g-°C
g/s-cm?
FORGE COMPANY
G
— BUFFALO
FAN ENGINEERIN
5-8
TURBULENT FLOW
INSIDE 1.0 IN. 1.0. TUBES
Btu/ft?-hr-°F
COEFFICIENT
FILM
—
1
1.5
2
3
4
Dy aes iGeeet/epie
sO)
VELOCITY - fps
Figure 5.1
Film Coefficients for Water
Adapted from the data of H.J. Stoever: Applied Heat Transmission,
Inc., New York, 1941, pp. 81, 83.
McGraw-Hill
Book Company,
30
TURBULENT FLOW
INSIDE 1.0 IN. 1.D. TUBES
20
Btu/ft?-hr-°F
COEFFICIENT
FILM
—
10
15
20
30
40
50
60
80 100
#4150
200
VELOCITY - fps
Figure 5.2
Film Coefficients for Air
Adapted from the data of H.J. Stoever: Applied Heat Transmission, McGraw-Hill Book Company,
Inc., New York, 1941, pp. 85, 93.
CHAPTER 5 — HEAT TRANSMISSION
5-9
Heating and Cooling Fluids Outside Tubes
If the various physical properties ofthe fluid are evaluated at the film
temperature t;, Equation 5.6 becomes
heDs
=
ky
33( Peon) a
ae
Myr
iff
.
k
(39)
for turbulent flow outside (subscript o) tubes. The film temperature ¢;
can be assumed to be the average of the bulk fluid temperature ¢ and
the surface temperature of the tube wall ¢,, as calculated by
apie
Ja ae
Fas
(5.10)
For fluids in turbulent flow over single tubes, Equation 5.9 can be
simplified to
hoDo
ky
= .24( D.Gby=)\°
(5.11)
Further simplification yields
ho =
CieeG
aly
(5.12)
for gases over single tubes. Similarly, the film coefficient for gases
over a bank of tubes can be obtained from
-_ C3 Cp Gmax
Be
6
aa
(5.13)
Refer to Table 5.4 for units and values for Equations 5.12 and 5.13.
Natural Convection
Whenever a temperature difference Ar exists between a surface and
its surrounding atmosphere, natural convection currents are induced,
and heat transfer occurs by conduction and convection, as well as by
radiation. The film coefficient Ay for air over horizontal pipes or long
vertical pipes of diameter d can be obtained from
+g
At
hy= ole
Se}
(5.14)
FAN ENGINEERING — BUFFALO FORGE COMPANY
5-10
The film coefficient for natural convection in air over flat plates varies
with orientation and heated length /. For heated horizontal plates
facing upward or cooled horizontal plates facing downward,
Ary”
hy= ca
(5.15)
For heated horizontal plates facing downward
plates facing upward,
At
or cooled horizontal
bea)
ad alee
(5.16)
For vertical plates more than about | ft high,
hy = Codt”’.
(5.17)
For heating coils submerged in water,
"
m=
co
AL
|
:
(5.18)
All equations, except Equation 5.17, are based on a laminar boundary
layer. Refer to Table 5.5 for units and values for Equations 5.14 - 5.18.
Table 5.5
Units and Values for Equations 5.14 - 5.18
h
W/m?K
Btu/hr-ft?-°F
m cal/s-:cm?-°C
Condensing Vapors
There are two major kinds of heat transfer involving condensation
of vapors: where only latent heat is transferred on the vapor side, as in
heaters and condensers, and where both sensible and latent heat are
transferred on the vapor side, as in dehumidifiers, discussed below. In
both, latent heat transfer takes place only at the surface unless there is
fogging. The only resistance is that offered by the film of liquid condensate. Equation 5.5 can be rewritten to express the rate of transfer
CHAPTER
5 — HEAT TRANSMISSION
5-11
QO. as
O.=htAAt,
(5.19)
in which Af; is the mean difference between the saturation temperature fsa, and the surface temperature ¢,, of the tube. High liquid-filmcoefficient h; values can be obtained with so-called dropwise condensation, where most ofthe latent heat is transferred directly to the surface.
Somewhat lower values are obtained with film-type condensation,
where all the latent heat must be transferred through the liquid film.
Even with promoters, dropwise condensation is unstable, so designs
usually are based on film-type condensation data. Whether the tubes
are oriented horizontally or vertically does make a difference, as indicated by
k
uC H
(5.20)
for horizontal arrangements, and
h iE
thy
k
Tea 2
& 93 (
Pg
byl vy
33
(5.21)
for vertical arrangements.
The tube loading I can be determined from the mass rate m, of vapor
condensed per tube and the length L or diameter D:
P=,
eee)
Dales
yet
"~~ ¢D°
(5.22)
(5.23)
Typical values of liquid film coefficients are listed in the chapter on
heat exchangers, where a design method based on the above formulae is
also presented.
Dehumidifying and Cooling Air-Vapor Mixtures
Although the transfer of the latent heat of condensation is not resisted by any air film on the vapor side of the tube wall, it is resisted,
however slightly, by the condensate film. Any simultaneous sensible
heat transfer is resisted by both the liquid and air films. Since gas film
resistance is so much greater, the liquid film resistance to sensible heat
BUFFALO FORGE COMPANY
— ING
FAN ENGINEER
§-12
ea
transfer is ignored completely. The assertion in the chapter on air conditioning that there is no resistance to condensation at a surface istrue
only if the surface is continuously condensate-free, but its use yields
completely satisfactory results in’most air conditioning problems. For
the usual dehumidifying coil, the steady state film coefficient h can be
increased by the ratio of total to sensible heat Qu/Qs. Rewriting
Equation 5.5 gives
Ou~ (Sth) av.
(5.24)
in which the film coefficient h, ignoring the liquid film, can be determined from Equation 5.13 and the temperature difference Ar is the
mean difference between the temperature of the wall 7, and that of the
bulk fluid 7.
Evaporating Liquids
As observed in the chapter on properties of air, vapors form over
their liquids or solids until equilibrium is obtained. The rate of evaporation froma water surface m,, as indicated by Figure 5.3 and the following equations, varies with the latent heat of vaporization h;,, with the
nature and velocity V of air flow, and with the degree of saturation as
represented by the difference in vapor pressures Pws — Pw, aS well as
with the amount of exposed water surface S:
m
m=S
ae
v
Cg + CoV
rs
(Pws — Pw) for parallel flow, and
Cio + Civ
7
(5.25)
ac
oe (Pws — Pw) for transverse flow.
(5.26)
To obtain hy and pws read the appropriate values opposite the dry-bulb
temperature in Figure 1.5 and the water temperature in Table-1.7, respectively. To obtain p, read the Table 1.7 value opposite the dry-bulb temperature and multiply by relative humidity, as indicated in Equation
1.20. Refer to Table 5.6 for units and values for Equations 5.25 and 5.26.
Table 5.6
Units and Values for Equations 5.25 and 5.26
V
Ci
kg/s
m/s
kJ/kg
1610
Ibm/hr
ft/min | Btu/lbm
88
cm/s
cal/g
CHAPTER
5 — HEAT TRANSMISSION
5-13
1200
ayoOoOOo
800
600
400
S(Pwa
hit,
Hg
Btu/hr-ft2-in.
Pw)
—
200
0
Figure 5.3.
200
400
600
800
1000
AIR VELOCITY (V) - fpm
1200
1400
1600
Heat Rates for Evaporation from a Water Surface
Adapted from the data of W.H. Carrier: “The Temperature of Evaporation,” Trans.
24, 1918, p. 38.
ASHVE, vol.
Water in contact with air tends to assume the wet-bulb temperature
of the air. Equilibrium at this temperature is achieved quite rapidly in
an air washer or ina similar device where the water is continually mixed
and large amounts ofsurface are exposed to the air. Under such conditions the rate of evaporation is largely proportional to the wet-bulb
depression, since the vapor pressure difference
pws — Pw is nearly proportional to the difference in wet- and dry-bulb temperatures of the air.
A container of water will assume a temperature somewhere between
the wet- and dry-bulb temperatures, the exact value depending upon the
amount of free surface relative to the amount of containing surface.
Equilibrium at the wet-bulb temperature is not achieved because sensible heat is transferred through the container walls, neutralizing some
of the sensible cooling that accompanies evaporation. The rate of
evaporation will be approximately proportional to the difference in
temperatures of the water and the air in contact with the water surface.
5-14
FAN ENGINEERING
— BUFFALO FORGE COMPANY
—————_____
—
0w C ee OCOD
LLL
SKg
Boiling Liquids
Boiling heat transfer can be accomplished with or without a net
generation ofvapor depending on specific conditions. When there is no
net generation of vapor because of recondensation in the cold surrounding liquid, the process is known as local boiling or surface boiling.
Very high heat transfer rates can be produced with submerged heater
surface if local boiling can be achieved. Both nucleate and film boiling
take place with the liquid at the saturation temperature and, therefore,
produce a net generation of vapor. For these cases Equation 5.5 can be
rewritten as
Ou= hgAAts,
627)
in which Avg is the mean temperature difference between the temperature of saturation and that of the wall. This temperature difference is
usually combined with the boiling coefficient and designated as heat
flux density, expressed by rewriting Equation 5.27 as
hgAte
=
Qu ‘
A
(5.28)
Figure 5.4 gives the boiling heat flux density for water versus temperature difference.
108
:
;.._
MAXIMUM FLUX FOR
NUCLEATE BOILING
= 19°
S
&
F
:
:
A-B,
B-C,
C-D,
DEF,
NATURAL CONVECTION
NUCLEATE BOILING
PARTIAL FILM BOILING
FILM BOILING
|
pe
104
B
R
103
0",
10
Figure 5.4
10°;
102
Atg—
mat10°
°F
Boiling Flux Density for Water at 212°F
Adapted from the data of W.H.
Inc., New York, 1954, p. 370.
McAdams:
Heat
Transmissions,
McGraw-Hill
Book Company,
CHAPTER
5 — HEAT TRANSMISSION
5-15
Overall Coefficients
Rewriting Equation 5.5 for the overall heat transfer between two
fluids separated by a wall of area A produces
On— UA
eA AL = UA
AI
(5.29)
The overall coefficient of heat transfer U can be expressed in terms of
outside area (U, for A.) or inside area (U; for Aj) as indicated. The
temperature difference Ar, is the mean difference between the two
fluids. Because the overall coefficient U is the conductance of a wall,
its reciprocal is the resistance of that wall. And the overall resistance
of any wall is equal to the sum of the individual resistances. For flat,
parallel surfaces the overall resistance of a composite wall can be
determined from
/
——
U
+
he
h;
ky
ok>
‘
Ken
(5.30)
For concentric, cylindrical surfaces such as pipes, the overall resistance based on outside surface can be determined from
Un Mig
5h:
te r( Any
(5.31)
For the usual dehumidifying coil where condensation takes place on
the outside surface, the overall resistance relative to outside area can
be determined from
Pe
Uae he
E70:
ae
Lb fAs
Ag
hi () trot af py).
(5.32)
In Equations 5.30-5.32 A, and h; are the outside and inside film coefficients based on the outside and inside areas respectively; ro and r;are the
outside and inside fouling factors, or resistances, based on the outside
and inside areas respectively; A,/A; is the ratio of outside to inside
surface area; and Qs/Qz is the ratio of the sensible heat to the total
heat transferred through the pipe or tube. Equations 5.31 and 5.32 can
be used when an extended surface is employed.
Occasionally, after the overall coefficient U for a wall has been
computed, the effect of an element added to that wall may be desired,
for which the new coefficient U’ can be determined from the added
resistance x/k and
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5-16
a
ie
/
ot at ep
Ce
(5.33)
Calculated values of the overall coefficient for various types of heat
exchangers are listed in Table 5.7.
Table 5.7
Calculated Values of Overall Heat Transfer Coefficient
for Various Types of Heat Exchangers
In Btu per hr-ft2-°F
Type of Exchanger
Heat Source
Water
sence
Convection
Heat Sink
ence
Watlenerncmrcsscrn starter tcc
Wate tiraseas
aeroaverereuerion
Wateranwnyar: cote aoe
Olek
aeithe te heat
aaa
ON ina a herein
be Bae
Oil epecekeleeceercnc
caete, sass
Oilestysts Merccdoxtkc
nie naires
GaSsneuar ckeackororickensseattens
Gastexcgess
evaretrecten
sere
Gasieieracsaaa doers eee
GasBie pice Gite
Condensing vapor .......
Condensing vapor .......
Condensing vapor .......
Condensing vapor .......
Wateraecirer
tts
Oil ees sere s.cteiecn
GaSv cS taupampntecatoretsas
Boiling liquid .........
Watetacd.
srrecen rotates
OP aetna
Gastareeck aihak Oe
Boiling liquid.........
Waletiziasensmansoms
Oil x. aac orotic
CaS dct den ARES oe
Boiling liquid.........
Watetinn.srwotiacacser
Oile cee aera:
GasM. Fee Mc neat ote
| Boiling liquid.........
Natural
[
100
22
2
167
22
12
2
24
2
2
]
2
190
25
2
Forced
|
1000
222
20
667
222
125
18
200
20
18
10
20
1330
236
20
800
Based on zero metal resistance and the following values for / in free and forced convection respectively:
200 and 2000 for water, 50 and 500 for oil, 2 and 20 for gas, 4000 for condensing vapor, and 1000 for
boiling liquid.
Mean Effective Temperature Difference
Whenever one or both of the reference temperatures in a difference
vary, it is necessary to evaluate a mean temperature difference. Where
the overall coefficient U is largely constant, as when a gas side resistance is controlling, the logarithmic-mean overall temperature difference A/,, as determined from
CHAPTER
5 — HEAT TRANSMISSION
5-17
SOK
Atm
SATA,
Af,
n(32)
(5.34)
can be used. The terminal temperature differences Ar, and At) are
At) = ti — to, and
Atz=
tiz =
(5.35)
to2.
(5.36)
For ease of computation the difference at terminal
| should be the
greater number and that at terminal 2, the smaller. Equation 5.34 is
applicable for either parallel flow or counterflow of the two fluid
streams. The difference in A/,, for the two types of flow is best illustrated by an example.
Example 5.1 Parallel Flow MED Af,= 49d Counterflow MED At,—
80
45—
80 60
Miait55
Ee
vies
25
4x
60
Boe 5h = 30=
22
ees Sweeh 1.95
HOS
15.4 = At
P
80
|
wo
60
80 60
55-45
Big
ld
ici
agl0e = 19.6
= Mtn=
eed |
5:
Computations can be simplified by using Figure 5.5. Additional
data on MED for multi-pass and crossflow arrangements are given
in the chapter on heat exchangers.
The mean temperature difference when there is no change of temperature in either fluid under steady-state conditions is
Bl =ncaton
(5.37)
FAN ENGINEERING — BUFFALO FORGE COMPANY
5-18
Nh
OO.
©
Fam
nrnanw
DIFFERENCE
TEMPERATURE
TERMINAL
OTHER
Aty- _ nA
1
152253
4 567810
15 202530
4050 70
100
Ar, — ONE TERMINAL TEMPERATURE DIFFERENCE
Figure 5.5
Logarithmic Mean Temperature Differences
H.J. Stoever, Applied Heat
p. 48.
Transmission,
McGraw-Hill
Book
Company,
Inc., New
York,
1941,
Extended Surface
The overall resistance
can be determined from
1
a
U;
to heat transmission
~(4)+3+
ho \ Ao
h;
A
based
on
(=<)+
(==
ie
NAS
inside area
(5.38)
As seen from this expression, the effect of extending the outside surface A, depends on the magnitude of the outside resistances (//o, ro)
relative to the inside resistances (//hi, ri). The effect of increasing the
external surface is to reduce outside resistance or increase outside
film coefficients. The effectiveness of any additional surface in promoting heat transfer is dependent on the bond between the primary
and secondary surfaces. In air-conditioning coils the major resistance
is usually on the air side, which is the outside of the coil, so external
fins are the rule.
CHAPTER
5 — HEAT TRANSMISSION
5-19
Radiation
Heat transfer problems involving radiation can be conveniently
divided into two groups: those involving two bodies separated by
non-absorbing media and those involving radiation from flames,
gases, and clouds of particles. Analysis of radiant heat transfer is
much more complicated than that of conduction and convection,
since every part of a system affects every other part. In many cases,
including most of those outlined above, the effects of radiation can
be ignored completely, but in others the combined effects of convection and radiation must be considered. The rate of heat transmission
Qu by radiation can be determined from
ma: ic
100
(ac
“9,4
(5.39)
which utilizes the Stefan-Boltzmann constant for black bodies
(C12 X 10°*) and involves the temperature level rather than a simple
temperature difference. This expression can be rewritten in the form
of Equation 5.5 as
Og— iF ANIa,
(5.40)
in which the effective radiation coefficient hr can be determined from
“+[Gor)
100
ee
a le
(= Ny
Ge
(5.41)
The temperature difference Ate is the difference between the temperature of the radiating surface and its surroundings ¢; — f2, and it is
generally assumed that surrounding surfaces are at the ambient air
temperature. An additional proportionality factor F¢ is also involved.
The magnitude of this factor depends on which area A is being evaluated, that is, on whether the emitting area or the absorbing area is
used. As indicated in Table 5.9, this factor also depends on the emissivity of the two surfaces involved. The emissivities € of various
common materials are listed in Table 5.10.
Table 5.8
Units and Values for Equations 5.39 - 5.43
Ou
Ww
Btu/hr
m-cal/s
W/m?-K
Btu/hr-ft2-°F
pcal/s-cm?-°C
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5-20
Table 5.9
Emissivity Factor Formulae
Surface Sizes
Shapes
Ee
Surface 1 small compared to Surface 2 | Any
€|
Surface 1 almost as large as Surface 2 | Any
nde es chy i ]
/
€)
Surface 1 and Surface 2 both infinite
ca
Surface 1 smaller than Surface 2
Concentric
cylinders
Surface 1 smaller than Surface 2
Adapted trom the data of H.J. Stoever:
Inc., New York, 1941, p. 26.
Table 5.10
Material
NATAL
o6 60 oda ar
Blass an tease
Chrommmeemerinecse
Castiron, sau Sao
Steely
rac
ees
Magnesium .........
Nickelete eter ae
Stainless steel .......
€)
I!
ee
ey
<i.
ae ee
=e ae a
1)
Concentric
Oe
spheres
Ssaicig (2) (< = ')
Applied
Heat
Transmission,
TNS
!
fog
McGraw-Hill
Book
Co.,
Emissivities of Various Surfaces
Surface
p= Os
€
Oxidized faeces eters
Gleanedjeawaancccsa.
Polishedipcrr deere
HiGn-DOliSh\annensas esi
aT ee
ee es Pe
530-1520
450-930
212
440-1070
| .63-.26
.22-.16
10
| .04-.06
.61-.59
Wgh-polishicpects «rte as
490-710
.03-.04
Rotisheds tay: o.d2oa8s
Oxidizedetss
We dee.
Rolishedaa naees,.eear:
Oxdizedieetssen ete
Cleanedy.ik strate.
ies
Oxidizedinmmrcerie terete ate
Polisher. aersresteees
Cleaneds.
(6). 0) ere
Polishedteter
op.<teeeet
Polished ae
ee. Ss.
GalVanized meee sae.
100-2000
390-1100
390
390-1110
450-1950
530-1520
440-710
450-1600
450-1920
212
212
| .08-.36
| .64-.78
21
| .79
| .20-.32
| .55-.20
.07-.09
| .57-.66
| .26-.31
07
21
120-660
—————————Se
CHAPTER
5 — HEAT TRANSMISSION
Table 5.10 (cont.)
5-21
Emissivities of Various Surfaces
Material
€
BiCKe Set cezoc etmcen aun ule FROUDE erate a crates con
Glasst.. teen oe
SM OOth Pe. cts estaceercresscis
OU SaaS:
Sete hee
inhickilaverseeaecese eter
LOA cic a5 fo.5.3be
Black or white.........
U3
94
82
.80-.95
Altimintinieereens rience tere
Adapted from the data of W.H. McAdams: Heat Transmission, McGraw-Hill Book Co., Inc.,
New York, 1954, p. 107.
NOTE: Values are for normal (perpendicular) radiation. They decrease with increasing angularity
between surfaces. They are approximately equal to the hemispherical emissivity, except those for
highly polished metal surfaces that are 15-50% lower than hemispherical emissivity.
Table 5.11
Radiation and Convection Coefficients
(For horizontal bore or insulated standard steel pipe of various sizes
and for flat plates in a room at 80°F)
In Btu per hr-ft2-°F
Nom. Pipe
Temperature difference °F from surface to room
Diam., In. =]
“p
1
2
4
8
12
Vertical
500| 600| 700| 800] 900]1000] 1100
2.12} 2.48
2.03 |2.38
1.93 |2.27
1.84 |2.16
;
y
:
;
1.64} 1.93 |2.45} 3.03 | 3.
f
.28|
14.65
14.48
12.46 |14.28
12.27] 14.09
12.10] 13.93
12.03} 13.84
11.90] 13.70
1.82 |2.13] 2.70} 3.30 |4.00 |4.79 |5.70} 6.72 |7.86 |9.18 |10.64 |12.25 |14.06
Horizontal
Faceup
Horizontal
Face down
| 2.00}2.35]2.97|
3.59} 4.31 |5.12
3.61}
4.38
7.07} 8.21} 9.54] 11.01
}12.63}14.45
7.40 8.71 hoas|11.76 |13.57
Adapted from the data of T. Baumeister: Mechanical Engineers’ Handbook,
Company, Inc., New York, 1967, pp. 4-106.
McGraw-Hill
Book
5-22
FAN ENGINEERING
aan Se ea
Bs
— BUFFALO
YE
FORGE
COMPANY
OEE
Combined Convection and Radiation
Sometimes it is necessary to determine the effects of both convection and radiation on the heat transfer rate. Based on the difference
in temperature Arg between the surface and its surroundings, the
expression for rate of heat transfer can be written:
Ou= hrAAte.
(5.42)
The combined coefficient 7 should be determined from
hr=hy+ Fehr.
(5.43)
The combined coefficient for steam pipes in still air and its variation
with temperature difference is illustrated in Figure 5.6. Additional
data on combined coefficients are tabulated in Table 5.11.
Tr
%
re
= 6)
£
|
HORIZONTAL PIPES IN STILL AIR
APPROXIMATELY CORRECT FOR PIPES AN
ANY POSITION
a
= 95
faa)
i}
=f
—
G3
o
Se
(as)
a
= 1
co
=
;
= {i
100
Figure 5.6
Adapted
200
300
400
500
TEMPERATURE DIFFERENCE - °F
600
700
Combined Coefficients for Steam Pipes in Still Air
from the data of R.H.
Heilman: “Heat Losses from Bare and Covered Wrought Iron
Pipe at Temperatures up to 800 Deg. Fahr..” Trans. ASME, vol. 44, 1922, pp. 299-323, and that
of B.N. Broido: “High-Temperature and High-Pressure Steam Lines,” Trans. ASME, vol. 44,
1922, pp. 1199-1242.
Unsteady Heat Flow
In all of the above cases, steady heat flow conditions were assumed
to exist. Such conditions usually prevail in any heat exchanger a
CHAPTER 5 — HEAT TRANSMISSION
5-23
short time after start-up. The most notable examples of transient, or
unsteady, heat flow are examined in the chapters on air conditioning
and air-blast cooling. In air conditioning, solar radiation often contributes the major portion of the cooling load. The relation between
time of maximum solar intensity and time of maximum cooling load
varies considerably for different materials.
It is necessary, therefore,
to take into account this time lag when determining both maximum
cooling load and equipment size. For heavy wall construction the
time lag may be such that the time of maximum cooling load due to
solar radiation occurs after the period of occupancy. A method for
approximately calculating the length of time necessary to cool a hot
body is given in the chapter on air-blast cooling.
Chapter 6
Mass-Transfer Processes
Mass-transfer processes, especially those involving a phase change
to or from the gaseous state, are often encountered in fan engineering. Typically, humidification, dehumidification, condensation, drying, gas absorption, and gas adsorption processes require fans to
move the vapors (before or after the phase change) along with a
carrier gas. In this chapter, certain fundamentals underlying all these
processes are examined. Other aspects of humidification and dehumidification were discussed in the preceding chapter on heat
transfer. Application data on humidification, dehumidification, and
condensation can be found in the air-conditioning chapter. An entire
applications chapter is devoted to drying. And both gas absorption
and gas adsorption are examined further in the air-cleaning chapter.
Mass transfer occurs by diffusion. Although mass transfer is usually thought to involve the change of phase of a material, in a more
general sense, the term can be applied to the simpler process of
mixing a single-phase material within a carrier material. A system
consisting of two or more phases of the same material or of different
materials is called heterogeneous, and the boundary between the
phases is called an interface.
Diffusion
Transfer of materials from one phase to another by diffusion is
basic to the humidification and dehumidification of air, the drying of
materials such as leather and paper, the absorption of pickling-tank
and other vapors, and the adsorption of gases in gas masks, to name
just a few familiar phase transfers that involve interaction between a
gas and a liquid or solid. Almost without exception, mass transfer
involves two distinct processes: 1) movement of the transferred substance within each of two dissimilar phases, and 2) transfer between
the two phases, the intraphase movement being the simpler of the
two processes. Intraphase migration occurs by molecular and eddy
diffusion, whereas interphase transfer occurs only by molecular
diffusion.
Molecular diffusion is the spontaneous intermingling of molecules
that takes place even in quiescent materials. Gaseous molecules intermingle more rapidly than do liquid molecules, and for both, the
process is orders of magnitude more rapid than in solids. Molecular
intermingling is a three-dimensional, random process associated with
6-2
FAN ENGINEERING
— BUFFALO FORGE COMPANY
the thermal motion of the molecules involved. It is accelerated as
temperature rises. Molecular impacts caused by the same random
motion are also responsible for the pressure of a gas on the walls of
its container, a pressure that rises monotonically with increases in
absolute temperature because of greater molecular velocity. So, when-
ever there are regions within a single phase where concentration
differences exist, more molecules will diffuse out of the high-concentration region than will enter from the low-concentration region,
simply because of the concentration difference. The effect of this
unequal exchange is to gradually even out concentration differences
between regions in a single phase until the formerly high- and lowconcentration regions become homogeneous. Visual evidence of
molecular diffusion in a liquid can be produced by carefully lowering
a crystal of potassium permanganate into a beaker of quiescent water.
As the crystal dissolves, the progress of diffusion can be observed in
the spread of purple coloration in all directions, with the darkest
color closest to the crystal and the lightest color most distant. If left
long enough, the color will become uniform throughout the beaker
sometime after the crystal has completely dissolved. This indicates
that the potassium permanganate is now equally distributed throughout the liquid and that as many molecules are leaving as are entering
the former crystal location.
If this experiment is repeated with vigorous stirring, it will be hard
to see any color differences in the beaker even before the crystal has
completely dissolved. The liquid will become uniformly colored very
much more rapidly than when the water was not stirred. Although
molecular diffusion also occurs during stirring, the mechanical action
overshadows the slower molecular process. The rate of diffusion can
also be increased by thermal as well as mechanical agitation. Such
convective mixing is usually more effective for gases than liquids.
Convective mixing is usually called eddy diffusion to distinguish it
from molecular diffusion. Both diffusion processes are important in
mass transfer between phases.
Molecular Diffusion in Gases and Liquids
Experimental evidence shows that the frictional resistance to
molecular streaming by diffusion is proportional to 1) the velocity of
the streaming component past the interfering one (the nondiffusing
component) and 2) the diffusional distance to a region where the
concentration is lower (or zero at the limit). This means that the
resistance to diffusion will be proportional to the number of molecules blocking the path of the diffusing component. Therefore, the
diffusion of component A through a stagnant component B is
given by
NA
a
Dyp
Rae
DA\
— Pa2
casi
(6.1)
CHAPTER 6 — MASS-TRANSFER
PROCESSES
6-3
where WN, is the net rate of transfer per unit area or mole flux density;
Dy is the gas-phase diffusivity; p is the absolute pressure; T is the
absolute
temperature;
R, is the universal gas constant; z is the dif-
fusion distance; p4; and pa are the partial pressures of the A component at its high- and low-concentration points, between which the
diffusion is occurring; and pam is (ps2 — pai)//n (pa2/ pai), the log
mean of the partial pressures pg; and pao of the stagnant gas B at
planes / and 2. N, is also given by
=
Na=
Dyp
Ps2—
Relies
Psi
Pem
;
(6.2)
The explanation for Equation 6.2 is that the pressure gradient of B is
maintained by the diffusion of A. That is, the collision of diffusing A
molecules with nondiffusing B molecules moves some B molecules in
the same direction that A molecules are streaming. This forced migration of B molecules sets up a partial-pressure gradient that causes an
equal number of molecules to diffuse in the direction opposite to that
of the streaming A molecules. A similar expression for molecular
diffusion through the liquid phase is
Di
Na > ze (Cab
Table 6.1
C42)
(6.3)
Diffusivities (typical)
Dy in Air at 32°F
ft?/hr
Dz in Water at 77°F
ft?/hr
Acetic Acid
0.413
0.48 x 10°
Acetone
0.32
Gas
Ammonia
0.836
Benzene
Butane
0.28
0.29
Carbon Dioxide
0.47
Carbon Tetrachloride
0.24
Chlorine
Ethyl Alcohol
0.36
0.37
Methane
Methyl! Alcohol
Oxygen
Sulphur Dioxide
0.61
0.47
0.63
0.40
0.78 X 10%
0.76 X 10°
0.56 x 10°
0.50 x 10°
0.66 < 10°
Adapted from the data of T.K. Sherwood and R.L. Pigford: Absorption and Extraction, McGraw-Hill
Book Company, Inc., New York, 1952, p. 20 and that of P.E. Liley and W.R. Gambil: “Physical and
Chemical Data,” Chemical Engineers’ Handbook, Fifth Edition, R.H. Perry and C.H. Chilton
(Editors), McGraw-Hill Book Company, Inc., New York, 1973, pp. 3-224 to 3-225.
BUFFALO FORGE COMPANY
— ING
FAN ENGINEER
6-4
where c4) and c4 are the molal concentrations of the component A
at its high- and low-concentration points, between which the liquid
diffusion is occurring, and D; is the diffusivity through the liquid.
Table 6.2
Atomic Volumes
For calculating molal volumes at the normal boiling point
itu
are ieeeme eer: sei eiskondks arapaotomeiens:
micastone enoe oe 29.9
NTU Retr
Nee Foc oS Oe e On OOS Een DO ceo oe c 24.2
ASO IG. scatterer stn Sis Baeteciee aitnatyoueyeoltatiaas Soran a eePerehe wets tober 30.5
Bismuth2ctus Seonkoterroaieretseros Bs Norah erevernieie venensh deme do seens 48.0
Brominessk,
<2 eikcs a sue aie Race oon ene
oe Meet avateiey aetetss 27.0
GarDOn fences csic ceonshate nelwiccassieueterm ora ene elcues iteke ere oie heveptios 14.8
Chlorine: terminal; asin R——Clim seen peerter. ctr seus ee eterna rare 21.6
Medial asin: R==_CHGI=—Ritnesetacc
psoas croveue shorteteuetoteeee
rere 24.6
UNGIMMNs
ooo
ceodane ce Ooaoncas pan dooe eal
Gd Son 27.4
FIUOFING Sep. eirey a Rote esethocacuccenctvars cic ouet vaste cee ieceas 8.7
Germanilinba
ccccrceotet wcrmeretrerereae net Oakes cotekenay sae ies dieatoae one 34.5
Hydrogen, incompounds ........ BS
ea
rect Sets Boat gs© Su
inthydrogenimoatectilee.
<6: cv orsrctorssietecntee,
©trea cucters srerers HAS
KC ER (T(NTMANENITES oooeananaassanbnaococconabn: 10.5
IN-SecCONdalyaMINGS we. secawe- Paateeiee ee Gere cee ciel ners 12.0
Oxvgensd OUDIV;DOUnCeanecry-.
enum
ae ene
re cence er 74
coupled to two other elements:
invaldehvdessandiketonesma-usyercecaeucyenererchenstew
nen ewer creacacaee
74
inimethyiesters: 7.65. r wart emaeehdeucts
ove Sra ae aoe
invethviiethersics
cys sactwae. vs vow ReCi slorsasr nee
IORI
in higher esters andethers .......... ae Sars sien
IACI S)s Sree (onsen eee veeroe boro eR wane
ne
eee
WVU OFWItHiS SPAN ERs comec etwrest srckey ceretice icon He ee ee
GIOSPNOTUS Hrceste reec ern chore eos eaete ierotekn ee euey Soener enone
SU CON eevee saleethaccs oc cakera syn ho ue ere
ee
SII
LU Getcha hohe Cero iA
anual ca oe amok Las ae
eee Oe
TIMP etayces ekectortenecoa:aybvSparala,RR toc- oo
ete
ee
Titan UIicieyes rence eve: Cea cPorsretanec esto me een MT
eee
Vandi
creme re Sais. crete
ie eee roe ae het
ie
LINC erect
conta ete PAC
CRCSPCR I et NOR AES eee
9.1
9.9
11.0
12.0
8.3
27.0
32.0
25.6
42.3
$$3)5/)
32.0
20.4
For a three-membered ring, as in ethylene oxide, deduct 6.0.
For a four-membered ring, as in cyclobutane, deduct 8.5.
Fora five-membered ring, as in furan, deduct 11.5.
For a six-membered ring, as in benzene or pyridine, deduct 15.0.
For a naphthalene ring formation, deduct 30.0.
For an anthracene ring formation, deduct 47.5.
Adapted from the data of T.K. Sherwood and R.L. Pigford,
McGraw-Hill Book Company, Inc., New York, 1952, p. 11.
Absorption
and
Extraction,
CHAPTER 6 — MASS-TRANSFER
PROCESSES
6-5
In the above equations, all the values on the right side represent
well-known constants or readily measurable quantities except for D,,
the diffusivity. Diffusivity has dimensions of length squared divided
by time. Diffusivity values have been derived from both the classical
kinetic theory of gases and from empirical measurements. Although
the two do not agree, the differences are not great enough to cause
practical-application problems. Table 6.1 contains values for the dif-
fusivities of several commonly encountered gases and vapors in air
and water. When published diffusivities are unavailable, approximate
values can be calculated from
Py |
v
Te
p(Va’
au Vey
Lae
M4
Mz
,
(6.4)
where My, and Mz are the molecular weights of gases A and B and
V4 and Vz are the molecular volumes of gases A and B. The molecular volumes can be calculated from data like that in Table 6.2. The
value of 6 is 0.0069 when Dy is in ft?/hr, Tis in K, andp is in atm.
Eddy Diffusion in Gases and Liquids
Eddy diffusion is another mechanism for molecular migration within a single phase. It causes much faster mixing than does molecular
diffusion and is usually the result of turbulent flow conditions. The
rate of mixing is associated with the scale of the turbulence eddies,
and, therefore, is directly related to the Reynolds number of the flow.
Turbulence eddies are the irregular velocity fluctuations around the
mean velocity at any point in the path of a moving fluid. Although
eddy diffusion occurs in all directions, the component of eddy dif-
fusion most important for mixing is the one that occurs transverse to
the direction of flow.
Eddy diffusivity E, is defined as the net rate at which the diffusing
substance moves from a region of higher concentration to one of
lower concentration, divided by the concentration gradient. It is
proportional to the product of the Prandtl mixing length L and the
deviating velocity V’ and has dimensions of length squared per unit
oftime:
ae
Be le
(6.5)
The Prandtl mixing length is a measure of the scale of the turbulence,
and the deviating velocity is related to the intensity of the turbulence.
Both Land V’ are difficult to measure.
An approximate empirical equation that defines eddy diffusivity
E, in ft?/hr solely in terms of the density p of the carrier gas in
lbm/ft® and the Reynolds number Re is
6-6
FAN ENGINEERING
— BUFFALO FORGE COMPANY
E,p=6.6 X 10° Re
+ 0.2.
(6.6)
Transfer Between Phases
At a two-phase boundary (as between a gas and a liquid), there
will be a stagnant film of gas in contact with a stagnant film of
liquid, even though the two phases are in motion relative to each
other. As the relative velocity between the phases increases, the stagnant films become thinner but do not disappear entirely. This is
analogous to stagnant films that persist at the walls of a flow channel
while the fluid inside is in turbulent motion. The significance of
stagnant films for mass transfer between phases is that molecular
diffusion alone is the effective mechanism,
and as explained before,
this tends to be a slow process compared to eddy diffusion, even
when the films have been thinned down as they would be at high
Reynolds numbers. (Thinner stagnant films do help to speed interphase transfer.)
Four resistances in series can be identified for a mass-transfer
process like absorption’: 1) the resistance to migration of the diffusing component from the bulk fluid to the gas/liquid interface
1/kgp»; 2) the resistance to molecular diffusion through the gas-phase
stagnant film at the interface //kg;; 3) the resistance to molecular
diffusion
through
the stagnant
liquid
film
at the interface
//kzx;;
4) the resistance to migration of the diffusing component from the
gas/liquid interface to the bulk liquid //kx».
The rate of diffusion in each of these steps affects the overall rate
of mass transfer. And, inasmuch as eddy diffusion for fluids in turbulent flow is much faster than molecular diffusion, the principal resistances to mass transfer occur in the stagnant films at the interface
between phases. Nevertheless, the resistance to eddy diffusion may be
substantial enough that it must be taken into acc6unt. Thus, the over-
all coefficient of mass transfer K is expressed in an equation similar
to that for the overall coefficient of heat transfer U. That is, the
reciprocal of the overall mass-transfer coefficient is equal to the sum
of the individual resistances in the series:
ERIS SN a tet
K~ kes ker kip
ihe,
kup
(6.7)
The resistances, shown in this equation as reciprocals of the individual coefficients, must have identical units. The coefficients vary
with the temperature and the pressure of the system as well as with
the nature of the diffusing substance and the gas or liquid through
which diffusion must take place. Various empirical and theoretical
|
:
é
:
;
;
:
Other processes, like adsorption, do not involve all four resistances. See the following sections on
absorption and adsorption.
CHAPTER
6 — MASS-TRANSFER
PROCESSES
6-7
expressions (details of which are beyond the scope of this chapter)
have been developed to show the relationship between basic properties and the individual resistances. Because obtaining accurate individual resistances is difficult, most published data pertain only to the
overall coefficient of mass transfer for a given system. In fact, most
experimental data are given in terms of the product of the overall
coefficient and the amount of the effective interfacial surface because
the latter is also hard to measure accurately.
It has already been stressed that one or the other of the resistances
in Equation 6.7 may be controlling, that is, so large as to make the
others insignificant. The resistance to mass transfer through a unit
thickness of liquid is much higher than that through a unit thickness
of gas because of the closer molecular spacing of the liquid. However,
the average length of the diffusion path on the liquid side may be
reduced to very small distances in some practical applications, for
example, those involving condensation on a surface where there is no
liquid side or those involving very fast chemical reactions between
the gaseous diffusing substance and the liquid. Although in the latter
example there is a liquid side, the reaction can be considered to take
place on the surface. The resistance on the liquid side always decreases with increasing solubility of the diffusing substance and may
or may not be significant compared to the gas-side resistance.
Equilibrium
The analogy with heat transfer extends to the concept of equilibrium, as well. Just as it is impossible to transfer heat from a cooler
fluid to a hotter one by simple heat exchange, it is equally impossible
to transfer material from a phase at lower concentration to one at
higher concentration by interphasic contact. Equilibrium is reached
in a reversible process when as many molecules of the diffusing component transfer from the liquid phase to the gas phase as transfer in
the reverse direction during the same time interval, for a net transfer
of zero. Thus, if equilibrium between the phases has been reached
with respect to the diffusing substance, it is possible for a masstransfer process to be 100% efficient when, in fact, only half or less of
the diffusing substance leaves the gas phase and enters the liquid
phase. When equilibrium between the phases is not reached during a
finite contact period, the efficiency of transfer can be expressed as a
fractional efficiency Ey known as the Murphree vapor efficiency:
Vil eae
i
2
(6.8)
where 1, 2, and y. are the gas-phase concentrations at the inlet, at
the outlet, and in equilibrium with the liquid leaving the apparatus.
The equilibrium distribution of a component between its concen-
BUFFALO FORGE COMPANY
— ING
FAN ENGINEER
6-8
tration in a gas mixture and its concentration in a liquid in contact
with the gas phase is given by Henry’s law:
ee
(6.9)
where H, is the Henry’s-law coefficient, pe is the partial pressure of
the diffusing gas in the gas phase, and x is the mole fraction of the
diffusing gas in the liquid phase. Henry’s law holds very well when
the diffusing gas is present as only a small fraction of the gas and
liquid phases and when the total pressure does not greatly exceed
one atmosphere. The Henry’s-law coefficient is greatly affected by
temperature, rising rapidly as temperature increases. For example,
the Henry’s-law coefficient for chlorine in water is 4.9X 10°
atm/Ibm-mol fraction at 10°C and 7.9X 10° at 25°C. Henry’s-law
coefficients for many commonly encountered gas/liquid combinations (but by no means all) are found in the /nternational Critical
Tables and in Perry’s and Chilton’s Chemical Engineers’ Handbook.
Figure 6.1 shows Henry’s-law coefficients and the effect of temperature for several common, gaseous compounds.
Example 6.1
Equilibrium Concentration
Find the equilibrium concentration of chlorine in water in contact
with 100 parts per million by volume of chlorine in air at 10°C
The partial pressure is
100
=10ssatm.
10°
pa
The Henry’s-law coefficient from Figure 6.1 is
Ab
al Op atm/lbm-mol.
The equilibrium liquid concentration is
Pe
fi,
49
10*
= 0.204 X 10° Ibm-mol Cl per |bm-mol HO.
10°
Reiterating, this means that (0.204 X 10°) (71) Ibm Cl: will be dissolved in 18 Ibm H2O. If the two phases were in contact at 25°C, the
equilibrium concentration would be
Pew ait
N04
HEATON:
= 0.126 X 10° Ibm-mol Cl per Ibm-mol H20.
——ee_ees—————
CHAPTER 6 — MASS-TRANSFER
PROCESSES
6-9
Just as the Henry’s-law coefficient relates the gas-phase and liquidphase concentrations at equilibrium, so the driving force for mass
transfer, as expressed by the gas-phase concentration difference, can
be related to the difference between the partial pressure of the diffusing gas in the gas phase and the partial pressure of the same gas
that would be in equilibrium with the liquid concentration contacting
it. That is, p — pe where pe = x Hx. Therefore, mass transfer from gas
to liquid can take place only until the gas-phase concentration is in
108 -—
FOR GASES IN DISTILLED WATER
10°
10
S
ATM/MOL
H’.,
FRACTION
102
é
S02
10!
|
oo oe ee
10°/T, K*
Figure 6.1
Adapted from the data of APT,
California 92502.
Henry’s-Law Coefficients
Inc.: Scrubber
Handbook,
APT,
Inc.. P.O. Box 71, Riverside,
6-10
FAN ENGINEERING
— BUFFALO FORGE COMPANY
equilibrium with the liquid-phase concentration. Furthermore, the
rate of mass transfer will be maximal at the start because the driving
force due to concentration difference will be greatest then. It will
subsequently decay to zero as equilibrium is reached.
Gas-phase concentrations can always be expressed in equivalent
liquid-phase-concentration terms by relating them to the liquid-phase
concentrations that would be in equilibrium with the gas phase. By
this means, liquid- and gas-phase concentrations can be expressed in
identical units for use in calculations.
Gas Absorption
Some of the more general aspects of diffusional processes were
examined in the preceding sections. Although the sections that follow
will also contain some information applicable to diffusional processes
in general, the emphasis will be on gas absorption. Because the scope
of gas absorption is too broad to be treated thoroughly in this handbook, the discussions will be limited to relatively low-concentration
applications, such as found in stack-gas cleaning. The terminology
used will generally correspond to that found in the literature. For
instance, the mass-transfer rate will be expressed in mole-flux-density
terms rather than mass-flow terms. The transfer-unit concept will
also be introduced.
Driving Force
Gas absorption is a mass-transfer process wherein the soluble
components of a gas mixture are dissolved in a liquid. As previously
noted, the rate of transfer may be controlled by either a gas-phase
resistance or a liquid-phase resistance. In Equations 6.1 and 6.2, the
mole flux density was shown to be a function of the difference in
partial pressure between the end points along the gas migration path.
Similarly, in Equation 6.3, the mole flux density was given as a
function of the concentration difference along the liquid path. In the
discussions that follow, it will be more convenient to use the difference in mole fraction along either the gas path or the liquid path.
Since mole fractions are proportional to pressure fractions or concentration fractions, the only effect will be to change the units of
measure.
In gas absorption, the gas path will be from the bulk gas stream to
the gas/liquid interface. Correspondingly, the liquid path will be
from the gas/liquid interface to the bulk liquid. The gas and liquid
will be in equilibrium at the interface. The driving force on the gas
side will be »y — y;, where y is the mole fraction of solute in the gas
and y; is the mole fraction of the solute in the gas at the interface.
Similarly, the driving force in the liquid will be x; — x, where x is the
mole fraction of solute in the liquid and x; is the mole fraction of
solute in the liquid at the interface.
CHAPTER 6 — MASS-TRANSFER
PROCESSES
6-11
Both y; and x;, which are related by the equilibrium conditions at
the interface, vary in a complicated way. It is simpler to use an overall driving force based on either gas-phase units or liquid-phase units.
The overall driving force in gas-phase units is y — y. where y, is the
mole fraction in the gas phase that would be in equilibrium with the
main liquid stream. Similarly, the overall driving force in liquid-phase
units 1s xe — x where x, is the mole fraction in the liquid phase that
would be in equilibrium with the main liquid stream.
Overall Coefficients
Equation 6.7 gave an overall coefficient based on local coefficients
for the bulk gas, the gas film, the liquid film, and the bulk liquid.
However, it is usually more convenient to use either an overall gas-
phase coefficient Kg or an overall liquid-phase coefficient K,. Either
Ke or Ky, can be used because a balance must exist between the mass
leaving the gas and that entering the liquid. Even these coefficients
are difficult to determine, as was previously noted for K, but they are
useful for expressing the relationship between mole flux density Nu
and driving force y — ye or Xe — x as shown in
IN = ISGP = spp) = 1a Ce = 39) «
(6.10)
Since the U.S. customary units for N4 are lbm-mol/hr-ft* and those
for y or x are mole fraction, the units for Kg or Kz must be
Ibm-mol/hr:ft*:
mole fraction. It is usual to combine Kg or Kz with
a, which is the amount of interfacial surface per unit volume of
:
:
2
3
absorption apparatus and has U.S. customary units of ft"/ft’. Values
of Kca have been measured for many types of apparatus.
Total Transfer Rate
The mole flux density N4 is the total transfer rate divided by the
interfacial surface area S. The total transfer rate can, therefore, be
represented by N.S. Since, for a given application, the amount of a
gas component removed from the carrier gas must equal the amount
dissolved in the liquid Solvent, the total transfer rate can be expressed
as a function of either gas-phase mole fractions or liquid-phase mole
fractions. If the gas-phase concentration difference is used, it must be
multiplied by the carrier-gas flow rate. But, if the difference in liquid
concentrations is used, it must be multiplied by the absorbing liquid
flow rate. It is common
to use molal velocities, which are designated
Gy and Ly for the carrier-gas and absorbing-liquid flow rates, respectively. Molal velocities are defined as the number of moles per unit
time divided by the superficial face area A. The mole flux is,
therefore,
NaS = GmA (v1 — y2) = Lm A (x2
— &1).
(6.11)
6-12
FAN ENGINEERING
— BUFFALO FORGE COMPANY
U.S. customary units for Gyand Ly are Ibm-mol/hr-ft?,
In most air-cleaning applications, the entering gas concentration );
reis fixed at a predetermined value by the amount of contaminant
leased and the ventilation rate. The value of the leaving concentration
y> can be established only in relation to the proposed method of
treatment and the associated equilibrium conditions. For absorption,
y2 must be established in relation to x2 based on solubility and chemical reactions.
Transfer Unit Concept
The transfer unit is a useful concept for applying countercurrent
packed absorbers and similar equipment. As previously noted, most
experimental data are expressed in terms of Kcga. The amount of
interfacial surface area S can be determined from the amount of
wetted surface per unit volume a, the packed height Z, and the superficial face area A:
S = aZAr
(6.12)
Combining Equations 6.10, 6.11, and 6.12 and rearranging gives
z=( )
Kea
(2 =)
y-yeJ
=( aa (==)
\Kia
Mi eet WN (613)
The Gmu/Kea term is called the height of one transfer unit; the
V1 — y2/v — ye term is called the number of transfer units. The abbreviations HTU and NTU are used, as are the symbols H and N.
Rewriting Equation 6.13,
Z = HocNoc = HotNor,
(6.14)
where the subscript OG stands for overall gas phase and the subscript
OL stands for overall liquid phase. Both Nog and No, are dimension-
less provided that the required overall difference between the entering
and leaving concentrations of the absorbate y; — y2 and the driving
force y — ye are in consistent units. The packed height Z and the
height of a transfer unit Hog or Ho, must also be in consistent units.
These will both be in feet for the units previously specified for Gu,
Kg, anda.
For countercurrent equipment, the transfer unit can also be defined as a change in gas concentration equal to the average driving
force. The depth of packing needed to produce this change is the
height of one transfer unit.
The height of a transfer unit must be determined experimentally
for the solute/solvent system in question, and for the particular type
of packing desired. The effects of different gas and liquid loadings
CHAPTER 6 — MASS-TRANSFER
PROCESSES
6-13
(that is, different values of Gy and Ly) must also be determined so
that the most economical selection can be made.
_ The simple-looking term for the number of transfer units required
in any particular situation is misleading since this quantity varies in a
complicated way throughout a countercurrent absorption apparatus.
That is, the driving force is not a constant but a variable. However,
the average driving force Ay», upon which both the height and the
number of transfer units are based, can be determined for some situa-
tions and used in
Vile
Na
te
(6.15)
When the absorbing solution is sufficiently dilute (that is the concentration of the solute in the solvent
is low), the number
of transfer
units needed to reduce the solute concentration in the carrier gas
from y; to y2 can be determined from relatively simple analytical
expressions when equilibrium data are available, provided that no
complicating heat-transfer effects or gas volume changes occur. Neither is likely to be a factor when dealing with air pollution control
applications.
The average driving force Ay, may be taken as the logarithmic
mean of the terminal potentials in applications (like air cleaning)
involving only dilute solutions and low gas concentrations. The terminal potentials can be based on the mole fraction of solute in the
gas y and the mole fraction of solute in the gas at equilibrium with
the bulk liquid concentration ye. Using the subscripts / and 2 to
denote the two terminals.
AYm =
(ae)
In
mee
(vy a
eee)
Ve)
‘
(6.16)
(Y— ye)2
This expression is theoretically correct when
both the equilibrium
curve and the operating line can be assumed to be linear, as shown in
Figure 6.2. The operating lines are the lines 1-2, 2-3, and 3-4. The
equilibrium curves are labeled and can be established by referring to
data such as those given in Table 6.3 and using the equation of state
and Dalton’s law ofpartial pressures.
Substitutions involving Equations, 6.14, 6.15, and 6.16 yield
7= ( a)
Keg)
(v1 — 2)
Va)
In (vy — Ye)
2 el Vice) 2
(6.17)
This expression can be used to determine the packed height Z for
6-14
FAN ENGINEERING
Figure 6.2
— BUFFALO FORGE COMPANY
Gas-Absorber Performance
CHAPTER 6 — MASS-TRANSFER
PROCESSES
6-15
either a countercurrent stage or a cocurrent stage. Figure 6.2A illustrates the concentration relationships for a countercurrent absorber,
and Figure 6.2B for a cocurrent absorber. The slope of the operating
line depends on the ratio of liquid flow to gas flow Lu/ Gy. Observe
that the operating line approaches, but theoretically never reaches,
the equilibrium curve according to Equation 6.16 because an infinite
packed height would be required if y2 equaled yo.
Practically, the concentration in the leaving gas stream may be so
close to the equilibrium concentration that equilibrium can be said
to exist. If this condition prevails for a cocurrent stage, it can then be
said that the stage produces an equilibrium step.
As in heat transfer, a countercurrent stage is much more effective
Table 6.3.
Equilibrium Data for Ammonia
in Water
Partial Pressure of NH3 - mm Hg
*Extrapolated values.
r
Adapted from the data of R.E. Emmert and R.L. Pigford: “Gas Absorption and Solvent
Extraction,” Section 14, Chemical Engineers’ Handbook, Fourth Edition, R.H. Perry, C.H. Chilton,
and S.D. Kirkpatrick (Editors), McGraw-Hill Book Company, Inc., New York, 1963, p. 14.4.
6-16
FAN ENGINEERING
— BUFFALO FORGE COMPANY
than a cocurrent one. Countercurrent performance can be approximated by using multiple cocurrent stages, as illustrated in Figures
6.2C and 6.2D. The C diagram is for a 3-stage unit in which the fresh
liquid is pumped to the final gas-treating stage and the resultant
liquid, with its increased concentration of absorbate, is pumped to
the second-last stage, and so on. The D diagram is also for a 3-stage
unit, but fresh liquid is pumped to each stage. The diagrams are
scaled to show that more absorbate can be absorbed if all the
absorbent is fresh rather than cascaded.
Whenever the solute is completely neutralized in the liquid, the
equilibrium valuey. becomes zero, and Equation 6.17 reduces to
=
Pps
of ic "Y2
M
Vi
(6.18)
For this situation, the equilibrium curves in Figure 6.2 would all
become horizontal lines through y=0, the driving forces would
increase, and the operating lines would all lengthen.
Table 6.4 was obtained from Equation 6.17 by setting Z equal to
various multiples of Gy/ Kea and solving for y1/y2.
As indicated by Equations 6.17 and 6.18, large values of contact
surface per unit volume are desirable. This can be achieved either by
breaking up the liquid into a fine spray in the gas or by spreading it
over a finely divided material through which the gas is then passed.
Many types of packing material are available commercially. Ideally,
the height of a transfer unit should be determined for the proposed
packing material and for the gas/liquid system involved. Such data
are available but only for a few systems. Test results are usually
plotted as Hog versus G with L as parameter or as Hog versus L
with G as parameter, as illustrated in Figure 6.3. Alternatively, Gas
and Ly could be used. Many more such tests are needed.
Without testing the proposed gas/liquid system, a reasonably close
approximation can sometimes be obtained from other test data by
comparing the Schmidt numbers for the proposed and the tested
systems.
Table 6.4
Effectiveness of Transfer Units
Number of Transfer Units
Percent of Solute Absorbed
CHAPTER 6 — MASS-TRANSFER
grees
ran graninsnanpevaann
annpanpats
giater
; tnerennnennnntnseawtrennongierinen
¢
¥
:
¢
Rarities
PROCESSES
6-17
vinanan asap
: nneennannannaneapann
nayromennmaengestannoramuramngnnngenrrgienipney
L = 1890 |bm/hr-ft?
¢
ee oe
nent
—
$e
en
Hoc
-tt
oS
Sofo>)
oo
200
Sec
cialSee
400
+ «600
1000 7
00s
5000
G - |bm/hr-ft?
USING 4.7 Ibm/ft? FIBERGLASS PADS (FIBERS VERTICAL)
1 0 00.
wanensevns“2000
Aoennerateanenacee “4000
seonbrnvecnnmsconiienses "10.000.
"90.0
00 ~""40,000
L — |\bm/hr-ft?
Figure 6.3.
Absorption of NHs3 in Water from Air
Adapted from the data of A.J. Teller, S.A. Miller, and E.G. Scheibel: “Liquid-Gas Systems,”
Chemical Engineers’ Handbook, Fourth Edition, R.H. Perry, C.H. Chilton, and S.D. Kirkpatrick
(Editors), McGraw-Hill Book Company, Inc., New York, 1963, pp. 18-43.
Ao
6-18
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Table 6.5
Schmidt Numbers For Various Gases and Vapors
Based on diffusivities in air at 77°F and 29.92 in. Hg
Substance
u/pD,
Substance
Aceticyacidvesssmicntsecicaers 1.16
INNO G cogs coGocnar 0.78
Amylalcoholisesnses ees yay |
Aniline’ Ss crcarossocenrctae 2.14
Benzenéinc
ck ccna
sce 1.76
(eBUtYfiCaChdswr-taays stares 1.91
Butylralcohollee sstaace-rar 1.72
SWSAMME cosoocccecs 1.53
ECaproiciacid) aacsnccs
oe 2.58
Carbon dioxide ......... 0.94
Carbon disulfide ........ 1.45
Chloro benzene......... Dale
Chloro toluene ......... 2.38
Diethyl amine.......... 1.47
Diphenyl).fwaceseeacs
cere 2.28
Ethylsaleohollvenrsrerce
ore 1.30
Ethylibenzenex-eray
eo
b/pDy
Bthyliethen ccs. <sncacteverchs 1.66
Orme achai s.\tetene
<ns crore 0.97
Hexyl alcohols =-rer.ot 2.60
Hydrogeni= seven a 0.22
Methanolc-22
5.ceecaree 0.97
Mesitylene:si:<astcperearars Zi
A=Octane ecco narnsreranys 2.58
OXvden saree enuse es 0.75
Propionic acid. ..6.<.20
10 1.56
Propyl alcohol.......... 1.55
Propyl benzene......... 2.62
Propyl bromide ......... 1.47
Propyliodide .......... 1.61
UGE CEs mores 1.84
Valericiacidit
3. tstseerac- 2.31
Water css. 4: Ge tee
0.60
Adapted from the data of A.P. Colburn and R.L. Pigford: “General Theory of Diffusional
Operations,” Section 8, Chemical Engineers’ Handbook, Third Edition, R.H. Perry, C.H. Chilton,
and S.D. Kirkpatrick (Editors), McGraw-Hill Book Company, Inc., New York, 1950, p. 539.
The Schmidt number Sc is a dimensionless ratio relating the viscosity 4 and density p of the gas mixture and the diffusivity D, of
the diffusing gas in the gas mixture:
a
Seay
(6.19)
The Schmidt numbers for various gases and vapors, based on diffusivity in air, are given in Table 6.5.
The height of a transfer unit is approximately proportional to the
square root of the Schmidt number, that is
Lacal.-L eal Css
Kea
Kea
(=)
:
(6.20)
If the height of a transfer unit for gas B is known, the corresponding value for gas A can then be calculated by using the appropriate
values for the Schmidt number in Equation 6.20. Figure 6.3 dia-
grams
the absorption
of ammonia
in water
from
air. The chart
CHAPTER 6 — MASS-TRANSFER
PROCESSES
6-19
values can be used for acetic acid by increasing them 22% that is,
(1.16/0.78)°° = 1.22, based on data for 77°F.
The preceding relationships are limited in their applicability. When
the dispersed material is comparatively insoluble, more sophisticated
methods, such as those found
in Sherwood
and Pigford! are needed
for reasonable accuracy. Also, the Schmidt-number relationships
given in Equation 6.20 should not be used unless molecular diffusion
predominates over eddy diffusion. This will not be so at high
Reynolds numbers.
It is implied throughout all these discussions that the carrier gas
will be relatively insoluble in the liquid. This, as well as the condition
of very low, initial solute concentration in the carrier gas, is necessary
to ensure comparatively constant gas flow and, therefore, constant
gas velocities and diffusions per unit of driving force. The temperature and pressure should also be comparatively constant for the same
reason.
If these conditions
are not satisfied, the effect of variable
diffusivity must be determined by a complicated integration.
Adsorption
Adsorption is a mass-transfer process wherein certain components
of a fluid are deposited on the surfaces of a solid by surface forces.
Atoms on the surface of a solid exhibit unbalanced forces of attraction normal to the surface because, unlike subsurface atoms, they are
not totally surrounded by atoms of the same kind. The balance of
forces for the surface atoms is partially restored by the deposition of
gas molecules from the surrounding air or gas. Whereas in absorption, the gas molecules
diffuse or permeate
into the structure
of an
absorbing liquid or solid, in adsorption, they remain on the surface.
The term sorption is applied when adsorption and absorption occur
simultaneously.
Adsorption of a gas on a solid is a spontaneous process always
accompanied by a decrease in the free energy of the system and,
therefore, an evolution
of heat. In some
interactions
between
a gas
and a solid, a new chemical compound forms between the adsorbed
gas and the solid surface; this process is called chemisorption.
The formation of an adsorbed surface layer of gas molecules by
adsorption can be likened to the condensation of a vapor to form a
liquid film. In both processes, the heat emitted is a specific value for
each substance and of the same order of magnitude. Because physical
adsorption is related to liquification, it usually occurs only at temperatures
and pressures
close to those for condensation.
Similarly,
the physically adsorbed layer (adsorbate) can be removed (desorbed)
'T.K. Sherwood and R.L. Pigford Absorption and Extraction,
New York, 1952, pp. 137-144
McGraw-Hill
Book Co., Inc.,
6-20
— BUFFALO FORGE COMPANY
FAN ENGINEERING
by applying a specific amount of heat. Adsorption, like condensation,
takes place more readily at lower temperatures and higher pressures.
Adsorbent Materials
Adsorbents are characterized by their extremely porous structures,
which provide internal surface areas many times larger than the external surface. Many adsorbent materials have been developed, each
with a special affinity for certain vapors. These vapors diffuse into
the pores and are bound to the internal surface in various ways. In
practice, the gas mixture is passed through a bed of granular adsorbent material to promote rapid diffusion. Then, before the adsorbent
becomes incapable of removing the dispersed material at the required
rate, it is either replaced or regenerated for further use.
Commercial adsorbent materials include molecular sieves (synthetic
zeolites), activated carbon, activated aluminum,
silica gel, and acti-
vated bauxite. The last three are primarily dessicants (that is, they
preferentially adsorb water vapor at normal temperatures), whereas
activated carbon preferentially adsorbs organic vapors and gases including many malodorous ones. Table 6.6 shows the characteristic
properties of several adsorbents. All important adsorbents other than
carbon have better adsorptive properties for polar than non-polar
substances and, for that reason, are more restricted in their range of
application. Synthetic zeolites can be manufactured by heating alumosilicates to remove the water of hydration. This produces highly uniform and controlled pore sizes that give zeolites a unique specificity
for adsorbing molecules of a predetermined size and shape. This
property, more accurately described as crystal-lattice vacancies, has
been used for adsorbing radioactive iodine on silver-substituted zeolites in the atomic energy industry. By contrast, activated carbons
show a wide range of internal capillary dimensions and a uniform distribution of electrical charges on the surfaces. These properties permit
adsorption of a broad spectrum of chemically diverse molecules. The
Table 6.6
Adsorbent Characteristics
Activated
Carbon
Activated
Alumina
Silica
Gel
Surface area (m2/gm)
Surface area (m2/cm?)
Pore volume (cm?/gm)
1100-1600
210-360
300-560
0.80-1.20
210-320
0.29-0.37
520
0.40
Pore volume (cm?/cm3)
0.40-0.42
0.29-0.33
0.28
Mean pore diameter (A)
15-20°
18-20
Molecular
Sieves
800-1000
_—
0.27-0.38
0.22-0.30
“Refers to micropore volume (<25 A diameter); macropores (>25 A) not included.
Adapted from the data of A. Turk: “Adsorption,” Air Pollution, Volume 1V, Third Edition, A.
Stern (Editor), Academic Press, New York, 1977, p. 332.
CHAPTER 6 — MASS-TRANSFER
PROCESSES
6-21
use of silica gel, etc. for dehumidification is discussed in the chapter
on air conditioning; the use of activated carbon for odor removal and
pollution control is discussed in the chapter on air cleaning.
Activated carbon is the most widely used adsorbent for gas treatment. It is produced by first making a charcoal from coconut (and
other nut shells), wood, bituminous coal, or petroleum sludge. Next,
the charcoal is activated by controlled heating in a steam atmosphere
to drive off organic matter and to generate large internal surfaces on
which adsorption can take place. The surface area of activated carbon ranges from 1100 to 1600 m’/g. See Table 6.6 for the ranges for
other common adsorbents.
Adsorbent Properties
The efficiency of an adsorbent is a measure of its ability to remove
an adsorbate from a flowing air stream and is a function of 1) the
degree of activation (if charcoal); 2) the granule size; 3) the residence
time, that is, the contact time between the gas and the carbon in the
adsorber bed; 4) the air-flow velocity through the adsorber bed; and
5) the temperature of the air stream. Efficiency varies inversely with
granule size and temperature and directly with gas-residence time.
The capacity of an adsorbent is its breakthrough capacity, that is,
the amount
of adsorbate that, when charged to the adsorbent
bed,
results in the first appearance of the adsorbate in the effluent air.
Capacity is a function of the surface area of “active sites” in the adsorbent and, therefore, of the depth and area ofthe beds.
The retentivity of a sorbed chemical is characteristically less than
35% of the breakthrough capacity. As long as the quantity held in
the bed is less than the retentivity limit and the bed temperature does
not greatly exceed the adsorption temperature, desorption is not a
significant problem, even if the bed is operated for long periods with
vapor-free air passing through it. However, when a bed is loaded to
the breakpoint, continuous purging with vapor-free air will ultimately
result in the release of some of the vapor previously adsorbed. In this
respect, the adsorption bed behaves just like a gas chromatographic
column, holding up only temporarily the amount of adsorbate that
was retained after the bed exceeded its retentivity point. In practical
air-and-gas-treatment adsorbers, the gas flow is halted when the bed
reaches the breakpoint, and the vapor capacity is usually calculated
to that point. By contrast, the capacity of adsorbent-filled, airpurifying respirator cartridges and military gas-mask canisters is
based on the retentivity point, thereby avoiding the possibility of
vapor migration after prolonged usage.
The adsorptive capacity varies greatly depending on the nature of
the adsorbate, but usually, it increases with increasing molecular
weight and sometimes can reach values as high as one gram of solvent per gram of carbon. Activated carbon is considered satisfactory
6-22
FAN ENGINEERING
— BUFFALO FORGE COMPANY
for substances that give adsorptive capacities only one-tenth or onetwentieth of this value. Although activated carbon can simultaneously
adsorb several substances with widely differing retentivities, substances of greater retentivity can displace (desorb) those of lesser
retentivity when the carbon nears saturation.
Adsorption Isotherms
Although the internal pores of the adsorbent granules represent the
major surface area available for adsorption, deposition may take
place first on the external surface of the adsorbent granules; later, the
surface-adsorbed molecules migrate into deeper regions, freeing the
surface deposition sites for further service. This process may progress
in turn from the largest internal macropores to those of smaller diameter and then to micropores of 5-20 A diameter. Penetrating the
micropore structure is bound to be a relatively slow process, and indeed, one of the most important factors controlling the adsorption
process in highly porous solids is gas-retention time. As the adsorbed
PRESSURE, BAR
0.2
f
i
|
oe
;
n— CaHio
=
i
~ 0.4
=
i
io
nor
i
4
i
i
—~+
&
C3Hs
i
<a
}
A— 0.3 i
4;
So
:
a
a
© 0.2.
acer
i
!
i
es
Plana
oS,
”
i
|
CoH,
=
= 0.1}
oe
C2H2
Ss
=)
3
}
CH,
0
= 100 LParenranevng “300
300.
mane “400.
500.
600
even: “300, Ant
aay
8 00
PRESSURE, TORR
Figure 6.4
Adapted
Adsorption lsotherms
from the data of A. Turk: “Adsorption,” Air Pollution,
A. Stern (Editor), Academic Press, New York, 1977, p. 335.
Volume
IV, Third
Edition,
CHAPTER 6 — MASS-TRANSFER
PROCESSES
6-23
layer is seldom more than a few molecules thick, a very large surface
area is needed in practical applications. This suggests that physical
adsorption (in contrast to chemisorption) is a reversible process driven
by partial-pressure gradients in a way that is analogous to gas absorption in a nonreacting liquid. However, when saturation of the
adsorbent is below the retentivity point, the partial-pressure gradient
can be decreased only by a rise in temperature or a decrease in absolute pressure rather than by an increase of back pressure from the
already absorbed molecules.
Heating a solid adsorbent in an evacuated chamber will cause it to
release all its adsorbed gases. When a pure gas or vapor is readmitted
to the chamber (after cooling) in carefully measured increments, the
amount of gas adsorbed by the initially empty, porous solid after each
addition can be correlated with the resulting increase in pressure of
the previously evacuated chamber. The difference between the pressure increase that would have occurred had the gas volume been
introduced into an empty chamber and the measured pressure increase (after each gas addition) represents the amount adsorbed on
the porous solid. A plot of the amount of pure adsorbate retained at
each pressure (see Figure 6.4) is known as an adsorption isotherm.
Isotherms are unique for each adsorbent-adsorbate pair and change
position on the plot when the temperature changes, the adsorbed
quantity increasing as the temperature decreases. (Adsorption isobars
give similar information at constant pressures.)
Adsorption isotherms give information on the maximum quantity
that can be adsorbed by a particular adsorbent at equilibrium. This is
useful in evaluating the quality of one adsorbent with another, but
equally important in operating systems are the amount of adsorbate
that can be retained at close to 100% efficiency and the amount of
adsorbed material that can be retained after the adsorbate concentration in the carrier gas has been reduced to zero (the retentivity point).
The first appearance of significant penetration is usually called the
breakpoint and, whereas the adsorbent is still capable of retaining a
great deal more of the adsorbate, increasing percentages penetrate
until the adsorbent becomes saturated, that is, reaches the level
predicted by an adsorption isotherm at the operating temperature.
Adsorption Zones
Figure 6.5 shows how adsorption takes place from the initial exposure to an adsorbable gas or vapor until the bed becomes saturated
with this same gas or vapor. In Zone A, little or no detectable adsorbate appears in the gas leaving the adsorption bed. Following the
breakpoint (indicated on the figure), retention of the adsorbate continues (Zone B), but at a constantly decreasing percentage of the inlet
concentration until saturation occurs and, thereafter, the outlet concentration equals the inlet concentration (zero retention). This is
Zone C in the figure. Usually, deep adsorption beds are used, and
— BUFFALO FORGE COMPANY
FAN ENGINEERING
6-24
100:
Ss
E
< 80
fae
RETENTIVITY
POINT
BREAK
POINT
cS)
r=
ra)
= 69
ZONE B ——»=——
ZONE A——>
ZONE C——.
2
je g
(=)
Ss
8
wa AO.
(2=
fee}
a
1
SATURATION
S 29
=m
—_
=
z
fee
0
ne
0
TIME
Figure 6.5
Adsorption Zones
INLET END
OUTLET END
—oOo=}
100. min.
co
a
—(=)
oS
NROo
CONCENTRATION
INLET
OF
PERCENT
RETENTION
—
Gicr
025
O.S0h
O75: ) 100)
alas
hakSlw
aAt6 0 G20e
BED DEPTH
Figure 6.6
Adsorption Waves
Adapted from the data of A. Turk: “Adsorption,” Air Pollution,
A. Stern (Editor), Academic Press, New York, 1977, p. 335.
Volume
1V, Third
Edition,
CHAPTER 6 — MASS-TRANSFER
PROCESSES
6-25
saturation advances through the bed with time. This is illustrated in
Figure 6.6 where each saturation curve represents a different timedependent history of bed performance.
Figure 6.6 shows that successive layers of the adsorbent in the
direction of flow experience breakthrough at a progressively later
time in the history of the bed. It also shows that bed penetration by
the adsorbate does not occur until the very last downstream layer of
adsorbent experiences its breakthrough, even though the upstream
layers of adsorbent have already reached saturation. It is clear from
Figure 6.6 that adsorbent service life can be extended by increasing
bed depth.
Figure 6.6 shows that, after 10 minutes of operation, the adsorbent
grains at the upstream face of the bed are already saturated with the
adsorbate vapors whereas very little vapor has reached the grains
0.25 inches downstream and no vapor has penetrated through the
entire bed. It also shows that, after 40 minutes of operation, every
adsorbent grain in the first 0.25 inches of the bed is now saturated
with vapor and that the adsorbent grains located between 0.25 and
1.00 inches are partially saturated with vapor. However, the layer at
the 1.00 inch depth has just barely reached the breakpoint, and all
the downstream adsorbent is, as yet, untouched by vapor. After 70
minutes of continuous operation, the most downstream layer of
granules has adsorbed vapor beyond its breakpoint and has entered
the operating condition, shown in zone B of Figure 6.3, where a
fraction of the vapor entering the adsorbent bed penetrates through
it. After 100 minutes vapor penetration has reached 50% of the inlet
concentration. Were operation to continue beyond 130 minutes total
saturation of the bed would occur, and operating conditions would
then resemble zone C of Figure 6.5.
Transfer Units
Just as for gas-absorption apparatus, adsorption beds respond to
the effects of eddy diffusion between the interstices of the adsorbent
grains and to molecular diffusion within the grains. The process can
be characterized by the overall number of transfer units and the
height of one transfer unit. The overall number of transfer units can
be expressed in terms of the gas phase or the solid phase in the
following way:
al KcahS
d
Nani ar yere
N
os
(6.21)
KpahS
pi gla
ae
(6.22)
where Nog and Nop are the overall number oftransfer units based on
6-26
FAN ENGINEERING — BUFFALO FORGE COMPANY
the gas-phase and particle-phase, respectively; Kg and Kp are the
fluid-phase and particle-phase adsorption coefficients, respectively,
expressed as volume of vapor or gas per unit surface area per unit
time; a is the interfacial surface area of the particles per unit of bed
volume;
F is the volumetric flow rate; S is the area of the bed cross
section; and h is the bed length in the direction of flow. Equations
6.21 and 6.22 do not appear to contain a driving force term. A close
examination will reveal that the Kga and Kpa terms have net dimensions of reciprocal time while the /S/F term has dimensions of time.
The former can be considered a rate, the latter a residence time.
These equations are applicable only to Zone A of Figure 6.5 where
the backpressure of the adsorbed vapor is essentially zero. The choice
of fluid-phase or particle-phase adsorption coefficient depends on
whether the controlling resistance to mass transfer is associated with
the gas phase or the particle phase. The height of one transfer unit is
defined in a similar way:
a
oC REaSe 8
Pipa
Et
Kea
(6.23)
(6.24)
where Hog and Hop are the height of one transfer unit based on the
fluid-phase and particle-phase adsorption coefficients, respectively.
Usually, the adsorbent material is heat-regenerated for reuse in situ
before it exhibits significant breakthrough. Over a great many cycles,
it becomes degraded, having a little less adsorptive capacity each time
it is regenerated. Ultimately, it must be reprocessed (as by reactivation) to restore its original properties. Although degradation is likely
to be a slow process, it does occur, and the number of transfer units
associated with a new adsorbent bed is not necessarily the same after
a period of use. Therefore, the degradation factor must be taken into
account when dealing with long-used adsorbent granules, and for
accurate predictions of adsorptive capacity, it must be reevaluated
with the same tests used for the new material.
Chapter 7
Particles and Particle Clouds
Small particles are often encountered in fan engineering. In airconditioning applications, the air drawn from the atmosphere can
contain dust and other contaminants, and droplets may be carried
over from humidifiers or dehumidifiers. Local exhaust systems are
used to capture various particles. High concentrations of particles
are moved in pneumatic conveying systems.
Fans and fan systems that are exposed to particles may need spe-
cial design features. Protection against erosion and corrosion is
discussed in various application chapters. Drifting in ducts and increased energy requirements are examined in the conveying chapter.
Separation and retention are discussed in the air-cleaning chapter.
Aerosols
Disperse systems in air have been given the general name aerosol,
analogous
to the older
term,
hydrosol,
which
denotes
a disperse
system in water or other liquid. An aerosol is defined as a stable
suspension of ultramicroscopic solid or liquid particles in air or gas.
This denotes a two-phase system, although the disperse phase alone
(the particles) is often called the aerosol. By common usage, aerosols
have been given names (dust, fume, smoke, fog, mist, etc.) that distinguish them as liquid or solid, as well as by their method of formation and particle size. The size unit used for small particles is the
micrometer, abbreviated um. (The use of the term micron and its
abbreviation pu is discouraged.) The unaided eye’s limit of visibility is
about 50 um, the largest respirable particle is about 10 wm, and the
size of freshly formed tobacco smoke is about 0.5 um.
Dust is formed by reducing earthy materials to small size. Processes such as grinding, crushing, blasting, and drilling produce dust
particles ranging from the submicroscopic to the visible, their composition being the same as that of the parent material. Common
examples are mineral dusts, derived from the disintegration of rock,
and organic dusts, derived from wheat and flour. Particle size is
predominantly above | um for dust.
Fumes are formed by processes such as combustion, sublimation,
and condensation. Typical examples are the fumes of zinc oxide produced by zinc vapor escaping the surface of molten metal. Its particle
size is usually below 0.1 um at formation, but because these very
small particles agglomerate vigorously, their size increases rapidly.
7-2
FAN ENGINEERING — BUFFALO FORGE COMPANY
Smoke presupposes a certain degree of optical density. Generally,
it is of organic origin, such as the smoke from incomplete combustion of tobacco, wood, oil, or coal. Particles of low vapor pressure
that settle slowly under gravity are also often called smokes. Smokes
are characterized by a particle size well below 0.5 um.
Fogs are formed by the condensation of water vapor upon suitable
nuclei, and mists by the atomization of liquids. Droplet size varies
widely depending upon formation conditions: persistent sea fogs are
below 30 um, and sprays range upward from 50 wm.
When a solid or liquid is broken up into finely divided particles
and dispersed in air, two important changes take place: |) the surface
area is greatly increased, and 2) the space occupied by the dispersed
material is expanded many times over the volume of the original
mass. Thus, if | mL of water is dispersed into droplets each | um? in
volume, 10"° particles will be formed with a total surface area of
4.8 m° compared with 0.00048 m’ for the original | mL drop. Assuming a droplet concentration of a billion particles per cubic meter of
air, the | mL of original material will now be dispersed in an air
volume of 1000 m! The enormous expansion in numbers and surface
area of the disperse phase of an aerosol has an important influence
on chemical reactivity, including fire and explosion effects, cloud
opacity, and particle collection in air-cleaning equipment. The most
important characteristics of an aerosol are the size of the suspended
particles and their concentration.
Particle Size
Clouds in which all the particles are the same size are termed
monodisperse, and a single number is adequate to define their size.
Aside from airborne pollens and spores, monodisperse aerosols are
rare in nature and difficult to prepare in the laboratory. Almost
every aerosol contains a range of sizes around a central value (mode,
mean, or median). These aerosols are called polydisperse, and
whereas a single number is adequate to describe a central point of
the distribution (for example, the median), this number fails to
indicate whether the sizes of the other particles are closely clustered
around the central size or are widely spread. This difference is illustrated in Figure 7.1, which shows two particle-size distribution curves
having the same median value (that is, half the particles are larger
and half smaller) but a markedly different size range. Using familiar
statistical terminology, the size range of each of these bell-shaped,
normal-probability distribution curves can be quantified by its standard deviation.
If a plot of size versus frequency, similar to Figure 7.1, were prepared for a foundry-shakeout dust cloud, it would
have the skewed
shape (Figure 7.2) characteristic of most aerosol clouds. Figure 7.2
shows the mean (weighted average) and the median (half larger, half
CHAPTER
7 — PARTICLES AND PARTICLE CLOUDS
7-3
smaller) of the size distribution, neither of which is the same as the
mode (greatest-frequency class interval) plotted in the histogram.
Mathematical treatment of the skewed curve is difficult, but it can
be made manageable by plotting the logarithm of the size instead of
the size. When this is done, the curve is transformed into a bellshaped one, as seen in Figure 7.3. Customarily, particle size is plotted
as a cumulative distribution curve on logarithmic-probability (or
log-normal) graph paper. It gives a straight line when size follows
the likely log-normal distribution. This transformation is shown in
Figure 7.4, where the 50% value is the median size and the ratio of
the median size to the 15.87% size is the geometric standard deviation
of the size distribution.
On a cumulative (or summation)
size plot,
the geometric standard deviation is also equal to the 84.13% size
divided by the 50% size. When sizes are closely clustered around the
central value, the geometric standard deviation will be a small num-
ber, reducing to | at the limit for a monodisperse cloud. Industrialdust clouds commonly have a geometric standard deviation from 2.5
300 ee
{
ea
Gee
a
ene
Ge
}
ao
= oO
FREQUENCY
OBSERVED
PARTICLES
OF
NUMBER
- aoo
PARTICLE DIAMETER — um
Figure 7.1
Histogram of a Normal Probability Size Distribution
Adapted from the data of L. Silverman, C.E. Billings, and M.W.
Industrial Hygiene, Academic Press, New York, 1971, p. 236.
First, Particle Size Analysis in
7-4
FAN ENGINEERING — BUFFALO FORGE COMPANY
to 3.5 and contain particles that range in size over 3 to 4 orders of
magnitude. For example, foundry-shakeout dust clouds contain
particles of from 0.1 to 100 um.
The data from which the size curves of Figures 7.2, 7.3, and 7.4
were derived were obtained by examining a representative sample of
collected dust under the microscope and measuring the diameter of
particles, one by one. This results in an analysis of particle size by
number
(or count),
and
the 50%
point is the count-median
size.
Similar data are derived from widely used, automatic optical (and
laser) single-particle counters and sizers. These devices continuously
conduct part of the aerosol through a small, illuminated sensing
volume in the interior of the device and direct a scattered light signal
onto a sensitive photomultiplier tube from each particle as it passes
through. The intensity of the scattered light signal is proportional to
a well-defined function of particle size. However, the characteristics
of dust collectors and many other devices, such as crushing and
grinding machinery, are rated on a mass rather than a count basis,
so it is necessary to transform size-by-count curves to size-by-mass
curves to properly relate particle size to mass efficiency.
Whenever the cumulative particle-size distribution by count plots
as a Straight line on logarithmic probability graph paper, as in Figure
7.4, the transformation to a mass basis can be easily made by using
the following equation:
log Mm = log M- + 6.9078 log’ o¢,
=
2
ROao
{
, MODE
CLASS
OBSERVED
0-1yum
0
INTERVAL
fos)
220
12...
2-3
3-4
a3
w
4-5
=
BT
7-8
oe
8-2:
O15.
(7.1)
5-6
Set
NUMBER
E%
0
48
56
84
2
14
21
72
18
ay
10
7
56
:
, 103
FREQUENCY
14
28
5
aaa
>
S
1
1
Ww
0.5
S
'
05
o
0
2
4
6
8
10
12
14
;
0.5
'
16
18
PARTICLE DIAMETER - um
Figure 7.2
Histogram of a Skewed Particle-Size Distribution
Adapted from the data of L. Silverman, C.E. Billings, and M.W.
Industrial Hygiene, Academic Press, New York, 1971, p. 237.
First, Particle Size Analysis in
-
CHAPTER 7 — PARTICLES AND PARTICLE CLOUDS
7-5
where M,, and M-. are the 50% size by mass and by count, respec-
tively, and og is the geometric standard deviation. The entire sizedistribution curve by mass can be plotted as a straight line passing
through the mass median size M,, at 50% and parallel to the count
curve. This is because, for the same aerosol, the slopes of both the
mass and count curves will be identical (that is, the geometric stan-
dard deviations will be the same).
When the size-by-count distribution fails to give a straight line on
logarithmic probability graph paper, it is necessary to divide the
curve into small size intervals and construct the mass-distribution
curve by simple iterative calculations using the center point of the
interval (the average size) and the total number within the interval to
calculate total particle mass for the fraction. The mass-median
MEDIAN
:
:
25 |-
san
CLASS
|:
|
|
|
|
20
|
|
eae
FREQ.
INTERVAL,
=
i1-144umi
oa
©
:
2-283
283-4
%
Se| Sk 06)
|
4-5.66
22.0
5.66-8
8-11.2
Fad eotl On
16-22.6
§
10.6 |
| 22.8
21.0
11.2
aomtaes
i
eras
|
|
|
an
|)
|
|
|
|
%FREQUENCY
PARTICLES
COUNT
BY
-
a
|
|
|
|
|
|
2
14. 18 22
PARTICLE DIAMETER — um
Figure 7.3.
Histogram of a Log-Normal Size Distribution
Adapted from the data of L. Silverman, C.E. Billings, and M.W.
Industrial Hygiene, Academic Press, New York, 1971, p. 238.
First, Particle Size Analysis in
74
FAN ENGINEERING — BUFFALO FORGE COMPANY
diameter of a polydisperse aerosol is always larger and usually many
times larger, than the corresponding count-median diameter because
of the dominating influence of the larger particles in a size-by-mass
distribution. For example, for a hypothetical cloud made up of two
spherical particles, one | um and one 10 wm in diameter, 50% of the
particles, by count or number, will be 1 wm
and 50% 10 um. But, by
mass,
mass
the
10-uwm
particle counts
for 1000
units, whereas
the
;
wo
wo
© oom
_ COUNT MEDIAN M. = 4.7m
orOo
|
Cet
MASS MEDIAN M. =5.2 um
SIZE
INDICATED
TO
EQUAL
OR
THAN
LESS
%PARTICLES
COUNT
BY
___GEOM. STD. DEV.0,= 84% SIZE/50% SIZE=1.6
PARTICLE DIAMETER - um
Figure 7.4
Cumulative Particle-Size Distribution Plotted
on Logarithmic-Probability Graph Paper
Adapted from the data of L. Silverman, C.E. Billings, and M.W. First, Particle Size Analysis in
Industrial Hygiene, Academic Press, New York, 1971, p. 240.
CHAPTER 7 — PARTICLES AND PARTICLE CLOUDS
7-7
l-um particle counts for only | mass unit, so the I-uwm particle now
accounts for only 0.1% of the total mass (that is, 100 X 1/(1000 + 1)).
A similar analysis shows that the surface-median diameter, important
in light-scattering and cloud-opacity calculations, will be between the
count- and mass-median diameters.
Dynamic Behavior of Aerosol Particles in Still Air
Small particles follow the speed and direction of the suspending
air unless acted upon by a force that either does not affect the
suspending medium or affects it less. The simplest situation is one
where the air is still and an external force acts on the suspended
particles but not on the air. Just such a situation exists for a small,
spherical particle suspended in still air and experiencing the gravitational sedimentation force F,. In any consistent units,
Sear
where
Almost
m
is the particle mass
immediately
(7.2)
and g is the acceleration
of gravity.
after it starts to settle, air resistance,
or drag,
will balance the gravitational force, and the particle will then settle at
a constant speed known as the terminal or free-fall settling velocity.
The nature of the resisting force was investigated by Stokes in 1851,
and the equation describing the terminal settling velocity of small
particles in still air bears his name.
The drag force Fp on a settling particle is
a
~ Cad pV?
e:
(7.3)
where A is the projected area of the particle in the direction of
motion and pz, is the air density. Drag coefficients Cp for small particles are related to the particle Reynolds number, for which the
characteristic dimension is the particle diameter rather than the duct
diameter, and the characteristic velocity V is the velocity of the particle relative to the velocity of the air rather than the velocity of the
suspending air. Therefore, it is possible for the particle Reynolds
number
to be a very small value, such as less than one, at the same
time that the suspending air has a Reynolds number higher than
100000. The distinction between the particle Reynolds number and
the suspending-air Reynolds number is very important for understanding the dynamic behavior of small particles. The coefficient of
drag Cp as a function of Reynolds number Re is shown in Figure 7.5
for several particle shapes. This chart is correct for smooth particles
but only approximate for particles with rough surfaces. Of the three
zones marked on the figure, the one called the Newton zone, for
7-8
FAN ENGINEERING
— BUFFALO FORGE COMPANY
which the Reynolds-number range is 500 to 200000, is unimportant
in aerosol technology. This is because particles with Reynolds
numbers in this range usually settle so rapidly that most attention
must be given to preventing premature settling or drifting in ducts.
The fact that the drag coefficients for each of the various particle
shapes are very nearly constant in this zone is noted and utilized in
the chapter on conveying.
The Stokes zone, which covers a range of Reynolds numbers from
0.0001 to 2.0, is the only one that applies to the motion of aerosol
particles. The drag coefficients for particles in this zone vary inversely with the Reynolds number. For spherical particles,
=
244
cma
ake
(7.4)
where d, is the particle diameter and p Is the air viscosity.
Because the drag force Fp equals the gravitational force Fz when
the settling particle reaches its terminal velocity (that is, F, = Fp),
mg=
Expanding
these
expressions
CpA
Pa Vv?
2
,
for spherical
(7.5)
particles
where
m=
10?
Co
COEFFICIENT
DRAG
— (=)
icin
sernpetonrntnttcnie
octrarmattrat
stokes 20NE ——
1 “Vw
IPE
eae bom Oot
O16
0
Figure 7.5
7
1
8 Vineet vee be CUR a cman
NG Bee Une Binet Gee tae USeEL
ntMearsOneem
[ie
geele
10?
10°
10
REYNOLDS NUMBER - Re
103
Oe
We
Drag Coefficients for Particles
Adapted from the data of R.H. Perry, C.H. Chilton, and S.D. Kirkpatrick: Chemical Engineers’
Handbook, McGraw-Hill Book Company, Inc., New York, 1963, pp. 5-60.
CHAPTER7 — PARTICLES AND PARTICLE CLOUDS
t=9
(Pp — pa) d’/6 and A = md’/4 and solving for V redesignated V,,
the terminal settling velocity, a familiar form of Stokes’ law results:
ae
g
d’ (pp = Pa)&
18
—
(7.6)
.
For aerosols, the buoyant effect of the air is negligible, so the expression (pp — fa) iS usually simplified to pp.
The part of Equation 7.6 that contains only the particle and air
characteristics is called the Stokes number and is often termed the
relaxation time 7 because it has the units oftime:
To
d’ pp
18pe ~
(7.7)
For example, the relaxation time of a 0.l-~m water droplet is
8.7X 10° seconds. For 1.0- and 10-um particles, it is 3.6X 10°
and 3.1 X 10“ seconds, respectively.
Ina
gravitational field, the local acceleration g can
equal to 32.2 ft/s’. The viscosity of air at ambient
be assumed
temperature
is
1.225 X 10° Ibm/ft-s. The terminal settling velocity V, of a 25-u~m
spherical particle having a density of 150 lbm/ft° according to
Equation 7.6 is
_ (Geom a) Oe
Dame
CIS\CN 225 C10
|
(32.2) = .0147 ft/s.
Because of viscosity, a shear stress is produced in the suspending
air by the velocity gradient. This gradient exists between the layer
of air molecules adhering to the surface of a settling particle (and
settling with it) and those air molecules at rest in the still air surrounding the settling particle. Air viscosity increases at higher temperature but is largely independent of pressure. When particles are
substantially below | um, their size approaches the length of the
mean free path of the air molecules in which they are suspended,
and, as they settle in what, for them, increasingly becomes the equivalent of a noncontinuous medium, they tend to slip between the
suspending air molecules instead of dragging them downward. This
results in a lower drag-coefficient value and more rapid settling than
predicted by Stokes’ law and requires a correction known variously
as the Stokes-Cunningham and the Cunningham-Millikan molecularslip correction factor C., which has the values shown in Figure 7.6 for
ambient air at | atm pressure. For particles greater than | wm, the
correction factor does not differ significantly from unity, but for
7-10
FAN ENGINEERING — BUFFALO FORGE COMPANY
smaller particles, it assumes great importance. For 0.l-um spheres,
the slip correction equals 3, and spheres of this size settle at a rate
three times the value predicted by the uncorrected Stokes’ equation.
For 0.01-um spheres, the slip correction equals 23.
Particles that are not spherical settle at slower rates than predicted
by Stokes’ equation because of the effect that a larger projected area
A in the direction of movement has on particle drag in Equation 7.3.
(That is, a sphere has the least projected area of any geometric shape
containing equal volume.) Spheroidal quartz particles, for example,
settle at a rate that is only 65% that of glass spheres of equal mass.
Mica platelets and asbestos fibers are even less like spheres, and they
deviate even more from the settling velocity calculated from Stokes’
equation. Figure 7.5 gives drag coefficients for disks and cylinders,
but for less regular shapes, empirically derived particle-shape factors
are usually applied to Stokes’ equation to correct for the effect of increased drag. Similar difficulties arise in applying Stokes’ equation
when the particles are not homogeneous and the correct particle
density is hard to determine. Many coal fly-ash particles are hollow
(cenospheres) and, so, of uncertain density. Agglomerates of metalfume particles contain much empty space, and the handbook value
for the density of the metal oxide would greatly exaggerate the density of a loose cluster. Because the geometric dimensions of aerosol
particles are usually of little intrinsic interest compared to their behavior in motion, it is customary to refer to aerosol particles in terms
of their aerodynamic equivalent diameter. This is defined as the
1S)
re
eee
i}
See
= 10'———Si
So
BOP
..t
ite
ea
Sees
Core
p = PRESSURE, em Ha
“y=PARTICLE DIAMETE
:
eee:
aera
oie
fae
=5)
oO
a
H
}
Bed
=
i
anual
5
'
10
%
1072
ane
10°
PARTICLE DIAMETER - um
Figure 7.6
:
“10!
Slip-Correction Factor C,
Adapted from the data of L. Silverman, CE. Billings, and M.W. First, Particle Size Analysis in
Industrial Hygiene, Academic Press, New York, 1971, p. 17.
CHAPTER
7 — PARTICLES AND PARTICLE CLOUDS
7-11
diameter of a homogeneous sphere of unit density (that is, | g/cm*
the density of water) that has an identical terminal settling velocity in
still air. By this definition, a particle of lead shot having a density of
11.3 g/cm? and a diameter of 10 wm has an aerodynamic-equivalent
diameter of 10 \/11.3 = 33.5 wm; that is, the 10-um lead sphere will
behave in all respects like a 33.5-um water droplet when acted on by
forces that do not act equally on the suspending air.
So far only a single, isolated particle in space, that is, unhindered
settling, has been considered. When particle concentration increases
to the point where a hydrodynamic interaction sets in between adjacent particles, substantial entrainment of the surrounding air
occurs, and the entire dust cloud settles as a coherent body at a rate
greater than would be expected for individual particles of the same
aerodynamic equivalent diameter in unhindered settling. This phenomenon is important for clouds settling in still-air conditions but
not for clouds in turbulent motion.
Dynamic Behavior of Aerosol Particles in Moving Air Streams
Stokes’ equation (7.6) has been derived for unhindered
settling of
homogeneous spheres in still air but can also be applied without
serious error to slowly moving aerosols. Although gravitational
sedimentation will occur at largely the rate predicted by Stokes’
equation, the path followed by particles that are simultaneously
conveyed by a moving aerosol cloud will be a combination of the
Figure 7.7.
Diagrammatic Sketch of a Simple Settling Chamber
Adapted from the data of P. Drinker and T. Hatch, /ndustrial Dust: Hygienic Significance,
Measurement and Control, Second Edition, McGraw-Hill Book Company, Inc., New York, 1954,
p. 284.
7-12
FAN ENGINEERING — BUFFALO FORGE COMPANY
sedimentation vector and the aerosol-flow vector. This interaction
can be illustrated by examining settling chambers, once widely used
for removing large particles from industrial-process air streams.
Figure 7.7 is a schematic representation of such a device. Assume a
horizontal aerosol-velocity vector of 60 fpm in the effective-settling
section, a chamber length of 20 ft, and a chamber height of 7 ft.
From these figures and Equation 7.6, it is possible to calculate
the aerodynamic-equivalent diameter of the minimum-size particle
that will just settle into the dust bin after entering the chamber at
the upper surface. (This is the most unfavorable entry position because it requires the longest settling path to reach the dust bin.)
The aerosol retention time inside the settling chamber will be the
length (20 ft) divided by the aerosol horizontal velocity (60 fpm), or
(20/60) X 60 = 20s. Therefore, particles entering at the top have this
maximum time to settle 7 ft into the dust bin and be captured, a rate
of 0.35 ft/s (chamber height divided by retention time). Rearranging
Equation 7.6 to solve for the diameter and substituting the appropriate quantities (in U.S. customary units), the solution is
185Vu
X 1.225 X 10° =|" X 25400
i = [ele
=| 18 X 0.35
TEE
X 12== 189 um.
2
For quartz quarry dust, the higher particle specific gravity (2.65) will
hasten settling and, thereby, reduce the minimum-size particle collected
at 100%, but the nonspherical shape will reduce settling velocity to
65% of the original and so increase the minimum size collected at
100%. Making these corrections in the calculation gives the correct
value for quartz dust:
d
P1826 0.350265) < 1.225
[
62.3 (2.65) X 32.2
10
a
| x 25400
X 12 = 98 um.
The net effect is to decrease the minimum, aerodynamic-equivalent
quartz-particle size that will be 100% collectable to about one-half
the diameter of the minimum collectable water droplet. The settling
time can be increased either by lengthening the gas path or by reducing the gas velocity. For practical reasons, gravitational settling is
not used in air cleaning for particles below 50 um in size.
Aerosol
particles also respond to forces other than gravity, some
much more effective in influencing the differential behavior of airborne particles in motion. The most important include centrifugal,
inertial, and electrical forces.
Centrifugal force. When a small, suspended particle travels in a
circular path, it is acted upon by centrifugal force and moves radially
outward relative to the path. Centrifugal force F. equals the product
of the centrifugal acceleration and the particle mass m. Centrifugal
CHAPTER 7 — PARTICLES AND PARTICLE CLOUDS
7-13
acceleration equals the square of the tangential velocity V, divided by
the radius of turn R:
mV,-
eye
(7.8)
Although the particle may be suspended in a rotating fluid that is in
turbulent flow, it is assumed that radial outward particle movement
is resisted by viscous drag and that Stokes’ equation reasonably approximates this drag. Therefore, the equation of equilibrium motion
for a small, spherical particle in a centrifugal- force field assumes the
following form, whereby centrifugal acceleration V,"*/ R replaces gravitational acceleration g in a new equation to define terminal radial
velocity V,:
em
d’ pp ee
eo ibyats
cao
(7.9)
In a centrifugal-force field, the radial acceleration may be as high
as 80000 ft/s°, which is about 2500 g’s. The radial acceleration for a
tangential gas velocity of 5000 fpm and a radius of curvature of 3
inches 1s
V, _ (5000/60)
R
=
(3/12)
= 27800 ft/s? .
ie
For a 5-um particle in such a force field, the terminal radial velocity
according to Equation 7.9 is
V=
(aaa)
sme)
a x
(18) (1.225 X 10°)
(150) (27 800)
= 5.06 ft/s.
Assuming a |.0-ft-long gas path, the distance X that a 5-um particle
will travel radially can be approximated by
X=
(1.0)
(5.06) _= 0.061 ft.
(5000/60)
This value is only approximate because it is based on a constant
value of R, whereas R actually increases as the particle migrates
radially. A more exact value can be obtained by using a differential
equation and integrating over the entire path length or by an arithmetical method of dividing the path into short incremental lengths,
solving for X, adding this to R, and repeating the process over the
entire path. The total X can then be obtained by summation. When
7-14
FAN ENGINEERING
— BUFFALO FORGE COMPANY
in the same flow field, the trajectories of particles having the same
relaxation time will be identical if they start from the same point.
The radial migration distance of the particle can be increased by
lengthening the gas path, by decreasing the radius of curvature, or by
increasing the gas velocity. For practical reasons, centrifugal separation is not used to capture particles much below 5 wm in size.
Inertial force. Inertia can be considered a special case of centrifugal force because its application always involves the production of
sharply curved streamlines for the conveying air and the migration of
particles across streamlines to impinge on a target around which air
flows. This process is illustrated in Figure 7.8, which shows an
aerosol stream issuing from a round or rectangular nozzle where the
gas velocity is greatly increased. The jet from the nozzle is discharged
against an adjacent flat surface, causing the air to diverge sharply.
The numbers indicate the velocity pattern in the impinging jet flow.
Particles in the airstream have more inertia than the air itself and
tend to continue forward as the air turns off to the sides, causing
particles with the requisite inertia to impact on the surface. Because
the air velocity over the collecting plate is high, the plate must be
coated with a viscous material to prevent particle bounce and reentrainment. The distance from the jet outlet to the stationary plate
governs the sharpness of curvature of the fluid stream and, with jet
velocity, also controls the collection efficiency. This distance is maintained about equal to the characteristic dimension of the nozzle (for
example,
jet diameter) for capturing small particles.
Efficiency of impaction is usually presented as a function of the
square root of the dimensionless impaction parameter /:
ae
)(&
(7.10)
where Dj is the jet diameter for a round jet or the jet width for a
10
Figure 7.8
10
10
10
10
10
1.0 1.0
6
96
96
96
96
96
96
Impingement of a Free Jet on a Flat Plate
CHAPTER 7 — PARTICLES AND PARTICLE CLOUDS
7-15
rectangular jet and /; is the average air velocity at the jet outlet. The
characteristic grouping of d°p,//8u, so prominent in Stokes’ equation, is also clearly visible in this equation. The Cunningham-Millikan
slip-correction factor C. is added because, as jet velocity increases,
smaller and smaller particles cross the streamlines and strike the
collecting plate. When sonic velocity is reached, particles of 0.25 um
and smaller can be collected very efficiently although the energy
expenditure is, necessarily, great. However, since energy expenditure
is only a minor concern for air-sampling instruments, impaction de-
AEROSOL ENTRY
|G
i lm
act! j
i (maral
bi [imaPr Y
g
i;
VACUUM APPLIED
Figure 7.9
Seven-Stage Cascade Impactor
Adapted from the data of ARIES, Inc., Box III, Davis, California 95616.
7-16
FAN ENGINEERING — BUFFALO FORGE COMPANY
vices have been modified for use as particle-size measuring devices.
Characteristically, this is done by arranging several stages with de-
creasing nozzle sizes in series. Such an arrangement, known as a
cascade impactor, is shown in Figure 7.9. As the same air volume
passes through each nozzle stage in turn, See in V; are solely a
function of jet size D;. For a circular jet, Vj = 4.0m De, where QO
equals the air rate in consistent units. For a series ofjets of decreasing
diameter, the square root of the impaction parameter / will change as
iS Square root of V;/Dj; or 40/7 D; changes, that is, inversely as
. Rearranging Equation 7.10 to solve for Dj gives
n= (2B)" ($2) )"
To design an impaction stage capable of removing all particles of
greater than, for example, 5-yzm aerodynamic equivalent diameter, it
is necessary to know the relationship between / and impaction efficiency. This is given in Table 7.1. For 100% collection with a round
jet, 7? must equal 0.56.
Assuming an air-sampling rate of 2.8 Lpm (46.7 cm’/s or 46.7
SCO” ear 8), 10-um (10 X 10° m) particles of.unit density (1 g/cm’ or
1000 kg/m’), and an air viscosity of 1.82 X 10° Pats.
ja (Cee eae
Selle
(4 X 46.7 X 10° ) (2 yy
18 X 1.82 X 10°
0.56
Table 7.1
arenasEfficiencies
if
1/2
Impaction efficiency
Round jet
The experimental values above were determined
dimension of 3.
Rorametet £
Rectangular jet
for a ratio of plate spacing to characteristic jet
Adapted from the data of L. Silverman, C.E. Billings, and M.W.
Industrial Hygiene, Academic Press, New York, 1971, p. 21.
First, Particle Size Analysis in
CHAPTER
7 — PARTICLES AND PARTICLE CLOUDS
7-17
D; = 0.00386 m = 0.39 cm.
The diameter of a jet at the same flow rate that impacts all particles
5 wm and larger would, by an analogous calculation, be 0.244 cm,
and if the smaller jet were placed downstream of the larger, the
aerosol could be fractionated into three particle-size groups: 10 um
and larger, between 5 and 10 wm, and less than 5 um. Cascade impactors often contain as many as 12 coordinated stages that make it
possible to divide aerosol particles into narrow, overlapping size
fractions for accurate analysis of size and size distribution. Classifying a particle cloud into discrete parts by using a cascade impactor
measures aerodynamic diameter directly and, so, makes the cascade
impactor a highly valuable aerosol-characterization device.
Electrostatic force. A particle carrying a charge in the region of
an applied electrical field experiences acceleration in a direction dependent on the polarity of the charge. The magnitude of the acceleration a is the product of the particle charge ne and the strength of the
charging field F:
a=neE,
(7.11)
where v is the number of electron charges on the particle and e is the
charge of one electron (4.8 X 10 '° statcoulomb).
Airborne dusts often become naturally charged by such common
processes as combustion, comminution, and dispersion as well as by
collision with air ions formed by cosmic rays, lightning, and similar
air-ion-producing processes. But, natural charging seldom results in
more than one or two elementary charges per particle, and the proportion of positively and negatively charged particles is usually about
equal. The result is an electrically neutral cloud containing neutral
particles as well as particles containing weak charges of either
polarity. For example, freshly formed, pulverized-coal fly ash contains about 30% positively charged particles, 25% negatively charged,
and 45% neutral, whereas freshly formed, copper-smelter dust contains about 40% positively charged particles, 50% negatively charged,
and only 10% neutral. Both aerosols contain slightly more negative
charges.
When particles larger than about | um in diameter are passed
through a high-voltage corona discharge, they acquire charges from
adsorbed electrons and gas ions in proportion to the square of the
particle diameter d, and the strength of the charging field E,. For
conducting particles, the saturation charge (that is, the maximum
possible number) is
Sindy
REIT
Fe:
(7.12)
7-18
FAN ENGINEERING — BUFFALO FORGE COMPANY
Particles of insulating materials acquire charges of 50 to 60% of this
value.
For particles smaller than about 0.2 um, diffusion charging predominates, and the number of charges acquired by a particle is given
approximately by
n=
2;
in(i+
dpc Noe't
2kT
‘
(E13)
where n is the number of charges on an initially neutral particle after
time ¢; k is the Boltzmann constant, (1.371 X 10 '° erg/molecule:K);
Nj. is the ion density, ions/cm’; c is the ion velocity (root mean
square), cm/s; and J is the temperature, K. Typical charges acquired
by particles of various sizes are shown in Table 7.2. Particles in a
unipolar ion flux acquire 75% of the saturation charge in less than
0.1 s. The migration velocity of a spherical charged particle V. in the
direction of a collecting electrode of the opposite sign can be obtained from the following expression, which utilizes the air-resistance
relationship given by Stokes’ equation:
— ROCEe
< 8x
(7.14)
where E is the field strength in the collecting space (esu/cm) and C,
is the slip-correction factor.
Electrostatic force fields usually produce migration velocities of
about 0.1 ft/s for 1.0-44m particles. Corresponding velocities for both
larger and smaller particles are somewhat higher. For particles larger
than | wm, which can receive a saturation charge ne proportional to
their surface (that is, proportional to the square of the diameter), the
Table 7.2
Particle
diameter
Number of Charges Acquired by Particles
Field charging
Diffusion charging
Exposure time (sec)
0.1
1
Exposure time (sec)
eo
0.01 | 0.1
1
2
2.4
2.5
3
7
11
200
244
250
70}
110}
150
20000 |24400 | 25000 | 1100 | 1500 | 1900)
2300
Note: calculated under the following conditions typical of a wire-in-tube assembly: T= 300° K,
No = 5 X 10° ions/cm’, E, = 2 kV/cm, in air at atmospheric conditions at 40 kV witha discharge
current of 40 wA/ft.
Adapted from the data of L. Silverman, C.E. Billings, and M.W.
Industrial Hygiene, Academic Press, New York, 1971, p. 19.
First, Particle Size Analysis in
CHAPTER
7 — PARTICLES AND PARTICLE CLOUDS
7-19
migration velocity increases directly with the particle size. However,
for particles smaller than | um in diameter, the saturation charge
that can be imposed is proportional to the first power of the diameter.
So, it appears that the migration velocity for particles below | um
should be independent of particle size but, because the slip-correction
factor increases for smaller particles, the velocity actually increases
with a decrease in size. Assuming a I-um particle with a migration
velocity V. of 0.1 ft/s, the migration distance X through air traveling
at 300 fpm along a 2-foot boundary can be determined from
_ (2.0) (0.1)
= 0.04 ft.
(300/60)
This migration distance can be increased by lengthening the gas
path, by increasing the field strength, or by decreasing the gas velocity.
For practical reasons, electrostatic precipitation is not used in air
cleaning unless high efficiencies are required for particles smaller
than | wm in size. Larger particles that may be present will also be
collected.
Brownian Motion and Diffusional Processes
Aerosol particles smaller than 0.1 um in diameter exhibit a significant random movement called Brownian motion due to collisions
with individual gas molecules. Brown first described this random
motion in 1827 in connection with small particles suspended in
liquids, and later it was confirmed for aerosol particles. The average
linear displacement AX in ft of such a particle in a time interval 0
Table 7.3
Particle Displacements in Standard Air Due to Various Force Fields
Particle Diameter
Displacements in 1 sec for Force Field Listed — ft
Brown?
3.28 X 10°
BBX 10"
3.28X 107
3.28 < 10°
024
.000 27
.000 006 9
.000 000 53
'Stokes-Cunningham slip-correction factor — dimensionless.
.0000057
.0000194
.0000972
.000 8540
:
Gravitational force field - downward linear displacements based on 32.2 ft/s’ acceleration.
‘Centrifugal force field - outward radial displacements based on 862 g’s acceleration.
*Electrostatic force field - normal linear displacements based on 7500 volts/in. field strength and
a saturation charge on the particles.
*Brownian movement - random linear displacements based on average values.
SAll data based on 150 lbm/ ft’ of particle density.
FAN ENGINEERING — BUFFALO FORGE COMPANY
7-20
in seconds is a function of the particle size d, in ft and various gas
properties, as indicated by an equation Einstein developed in 1905:
oe (Ss
3mpNdp
(7.15)
in which the universal gas constant R, is approximately 1545 ft-1b/
lbm-mol-° F, the gas temperature 7is in aoe Rankin, the viscosity
is in lbm/ft-sec, and Avogadro’s numberN is 2.76 X 10°°/lbm-mol.
The factor C, is the Cunningham-Millikan slip-correction factor previously discussed.
Brownian motion will lead to diffusion, that is, a net streaming of
particles through the carrier gas in the direction of the lower concen-
tration when a concentration gradient exists. Concentration gradients
are produced when the streaming particles are removed from the gas
at a boundary. Values for the diffusion coefficient Dy (cm’/s) can be
derived from the relationship
Dy=kBT,
(7.16)
where TJ is the absolute temperature. The Boltzmann constant k is
defined as the universal gas constant divided by Avogadro’s number.
It has a value of 1.371 X 10 '° erg/molecule-K and is unaffected by
pressure or gas composition. The particle mobility B is defined as
equal to C./3mdp. Values for the diffusion coefficients of various
sizes of particles are given in Table 7.3.
When the concentration of diffusing particles remains constant
beyond a certain distance from a deposition surface or boundary (as
Table 7.4
Particle
Velocity of Deposition
Velocity of deposition (cm/sec) through boundary layers of thickness 7m
radius | by gravity
by molecular diffusion
pm
10.000 zm
10° | negligible
10% | negligible
0.13
0.7
0.013
107 | negligible
10°
0.0014
0.000 14
0.000022 | negligible
]
10
0.000012}
Adapted
from
the data
Aerosol Science, C.N.
of C.N.
negligible | negligible
0.000012 negligible | negligible | negligible
negligible |negligible |negligible | negligible
Davies, “Deposition
from
Moving
Aerosols,” Chapter
Davies (Editor), Academic Press, London and New York, 1966, p. 409.
XII,
CHAPTER
7 — PARTICLES AND PARTICLE CLOUDS
7-21
by vigorous eddy diffusive mixing) and when the particle concentration decreases from this value to zero within the diffusion boundary
layer (on the basis that all particles contacting the deposition surface
are permanently removed from the aerosol), the rate of deposition is
DEG
R=——ee
(7.17)
where R is the deposition rate per unit area, D, is the coefficient of
diffusion, C is the concentration of particles outside the boundary
layer, and h is the thickness of the boundary layer through which
particle diffusion occurs. The velocity of deposition Vy (the rate of
deposition per unit of area for a unit of airborne concentration) is
R/C and equals D,/h. Table 7.4 shows values of the velocity of
deposition for particles of differing sizes through boundary layers of
graduated thickness.
Thermophoresis. This is another characteristic of particles substantially below | um for which the driving force is the gas-molecule
bombardment of suspended particles. An aerosol particle subjected
to a temperature gradient between a hot and a cold surface will tend
to move toward the colder surface. This motion is caused by a
thermal force arising from differential interaction of the particle with
the gas molecules. Those approaching from the hot side have a higher
average velocity (momentum) than those approaching from the cold
side, producing a net force in the direction of the flux of thermal
energy. Thermal precipitation of dust particles is used to obtain
samples for analysis by light/ optical or electron microscopy but has
not yet been employed for gas cleaning.
Coagulation. Coagulation of aerosol particles occurs continuously
and spontaneously when airborne particles in Brownian motion collide with one another and stick together, forming larger particles in
the process. When the particle size becomes large enough, rapid
gravitational settling occurs, but when small particles are being
formed or added continuously, the aerosol particle size tends to remain constant, that is, larger particles settle out and new agglomerates form to take their place. If no new particles are added, however,
coagulation ceases when the particle growth has produced
particles
too large to have appreciable Brownian motion and when too few
particles remain to make possible frequent collisions. Consequently,
the rate at which particles disappear by coagulation follows a simple
law:
Pippi
(7.18)
where n is the number of particles, / is the time, and k’ is a coagula-
FAN ENGINEERING — BUFFALO FORGE COMPANY
7-22
a
tion coefficient equal to 4k TC./3u. The full expression becomes
dn _ 4kTn’C.
de
Se
(7.19)
Integrating gives the number of particles n; remaining at /:
No
ny
4k TnoCet
me
3p
(7.20)
where np is the initial particle concentration at ¢=0. Turbulence
enhances coagulation by the eddy diffusion it produces within the
aerosol. Eddy diffusion is independent of particle Brownian motion
and enhances it because mechanical mixing increases contact between
particles by improving the chances of collision and by correcting
local regions where particle diffusion (a relatively slow process) has
depleted the airborne dust concentration.
Coagulation is an important phenomenon in particle collection
because an increase in particle size usually results in either greater
efficiency or a lower energy requirement. A special application of
coagulation to fume collection occurs in the smelting industry where
an important fraction of the product coming from the furnaces is in
the form of condensing vapor in a very hot carrier offgas. Before collection by filters or electrostatic precipitators is possible, the temperature must be greatly reduced. This is done by slowly passing the hot,
condensing aerosol through large, steel flues exposed to the air.
Equation 7.19 shows that the coagulation rate is directly related to
the temperature, the number concentration, and the CunninghamMillikan correction factor, which increases as particles become substantially smaller than | «wm. All three factors are greatly enhanced
in the very hot furnace offgases, where freshly formed fume particles
are in the range of 0.01 to 0.05 um and concentrations may exceed
10 g/m*. This produces vigorous coagulation to the point where large
Table 7.5
Rates of Coagulation
No. per cm?
W mg per L
10M
10°
10°
10’
5236
523.6
52.36
5.236
30
300
ft, equals the time required to reduce the number of particles to one-tenth of the initial number.
W equals mg per L, assuming diameter equals | zm, and density equals | g/m
CHAPTER 7 — PARTICLES AND PARTICLE CLOUDS
7-23
flocs form and rapid gravitational sedimentation occurs in the slowly
moving aerosol. As much as 50% of the smelter product is recovered
from the floor of the large cooling flues as a byproduct of gas cooling.
_ The rate at which coagulation occurs at ambient temperature with
increasing particle numbers is illustrated in Table 7.5, which gives
approximate times necessary to reduce the number of particles to
one-tenth of their original number. It is clear from Table 7.5 that the
size characteristics of small-particle concentrations over 10’/cm? will
not be stable, and as a result of coagulation, even monodisperse
aerosols rapidly become polydisperse unless the particle-number
concentration is quickly diluted with dust-free air to below 10’/cm’.
No other method is known to be effective in preventing rapid coagulation in submicrometer-particle clouds.
Optical Properties of Aerosols
Particles as small as molecules and as large as raindrops scatter
light. They comprise a size range of from 10 angstroms to a few
millimeters, or six orders of magnitude. Light scattering also depends on particle shape and orientation with respect to the incident
light and the direction of observation. Most of the theory of light
scattering is limited to spherical particles, as it is impossible to derive
exact solutions for other geometric shapes.
When light is incident on a small particle, it is scattered in all
directions, and if the particle is made of an absorbent material, some
of this light is also absorbed. When the particle ts large compared to
the wavelength of the incident light, the scattering process can be
described by geometrical optics laws, and one can identify individual
light rays that are either reflected from the surface of the particle or
penetrate into it and that emerge from the particle in a direction
different from the incident beam after refraction and internal reflection. The distribution of light around the particle by refraction and
reflection can be obtained by summing the intensities of the individual light rays. When the particle is partially opaque for the wavelength of the incident light, some of the light penetrating into the
particle will be absorbed and converted into other forms of energy,
mostly thermal. Theory predicts and observations confirm that the
scattered light is composed of two, incoherent, plane-polarized components whose planes of polarization are mutually perpendicular.
Figure 7.10 shows the angular distribution of light intensity scattered
by a 0.2-um-diameter water droplet illuminated by unpolarized light
having a wavelength of 0.524 «wm. The “i,”-light-intensity curves in
Figure 7.10 are for light vibrations perpendicular to the plane of
observation; the “i.” curves are for the intensity of light vibrating
parallel to the plane of observation. The forward-scattering component is clearly the strongest. For particles having a diameter larger
than the wavelength of light, the ratio of forward to backward scattering may be 1000 or more. For this reason, forward scattering is
7-24
FAN ENGINEERING — BUFFALO FORGE COMPANY
used in most optical particle counters and sizers, as well as in totalscattering photometers. For particles larger than the wavelength of
the incident light, the scattering pattern will have prominent side
lobes at the 90 and 270 positions.
Equations for single-particle light scattering are extremely complex
and vary with particle size, shape, and composition. Consequently,
r
330°
one
pet
\
™~ R
ye
os
‘
m1 9° nenoreierds
30°
ge
few)
‘
knw
0°
neg
=
=m] =
~
wahronsn
ns
S
movenieer
=
Soe eaenanebanmnoninseeneeeota
180°
in,
sour Beane sn
aneanrconirannn
Shansaan ie snh
PE
\
/
é
w
snare 150°
H
j
“4
ee
Figure 7.10
Angular Distribution of Intensity of Light Scattered
by a Spherical Particle i; and i. vs y
Adapted from the data of D. Sinclair, “Optical Properties of Aerosols,” Chapter 7, Handbook on
Aerosols: Chapters from the Summary Technical Report of Division 10, National Research Committee,
Selected and published by the United States Atomic Energy gy Commissi
i
Die Ges
Commission, Washington,
CHAPTER 7 — PARTICLES AND PARTICLE CLOUDS
7-25
single-particle counting and sizing instruments require calibration
with monodisperse aerosols of known size and refractive index. A
schematic for an aerosol-particle-size analyser is shown in Figure 7.11.
A small sensing volume of the order of | mm’ is illuminated from a
source that may, for the smallest particle-size measurements, be a
laser instead of the visible-light lamp shown. Aerosol particles in the
flowing aerosol pass, one by one, through the sensing volume enclosed
in a thin, outer sheath of air made dust-free to avoid contaminating
the sensing chamber. Scattered light from each particle is then collected by a lens and directed to an electronic photomultiplier tube as
a discrete light pulse. The resultant photocurrent is amplified, and
each pulse is counted and passed through a pulse-height analyser
calibrated to display particle-size units. Using laser and conventionallamp illumination sources, it is possible to measure aerosol particles
in the range of 0.1 to 20 um with reasonable accuracy, but instrumentation for this technique is difficult because the light intensity scat-
tered per particle is about 10 '° to 10'’watt/steradian when the light
FILTER
CLEAN AIR
FLOWMETER
LEGEND
L LAMP
C ACHROMATIC CONDENSER LENSES
D OPAQUE DISKS
A APERTURE
S SCATTERED LIGHT COLLECTING LENS
O ORIFICE
P PHOTOMULTIPLIER TUBE
Figure 7.11
Optical and Sampling Systems of Sinclair-Phoenix
Aerosol Particle Size Analyzer
Adapted from the data of D. Sinclair, “A New Photometer for Aerosol Particle Size Analysis,”
Journal of the Air Pollution Control Association,
Volume 17, Number 2, 1967, p. 107.
7-26
FAN ENGINEERING — BUFFALO FORGE COMPANY
intensity incident on a scattering particle is | watt/cm’. The instruments are relatively insensitive to particle shape, at least in the range
below 5 um.
Other types of optical instruments measure the light extinction of
clouds rather than single-particle scattering. These instruments, called
total-scattering photometers, are widely used for measuring atmospheric haze and for filter testing. They use forward scattering, are of
simple design, and are intended only for relative measurements.
Although they cannot make measurements of absolute concentration,
many of these instruments have a light of fixed intensity that can be
used as an approximate reference point for absolute concentration
measurements. Light scattering by aerosols is complicated by the
response variations produced by changes in particle size, surface
texture, index of refraction, particle color, and wavelength of illuminating light. But, when relative measurements of concentration upstream and downstream of filters are made with light, these effects
are nullified, since they are equal for both, and only changes in
concentration are detected.
PERCENT
PENETRATION
METER
-_-— ~-
_
PHOTOMULTIPLIER
TUBE
CONE OF
DARKNESS
LIGHT STOP
LIGHT
S OURCE
VACUUM
PUMP
FLOW PATH FOR
FLOW PATH
FOR SAMPLING
Figure 7.12
STRAY LIGHT
ADJUSTMENT
TEST
PROBE
FILTER
Flow Chart for a Forward-Scattering Photometer
Adapted from the data of Air Techniques, Inc., 1717 Whitehead Rd., Baltimore, Md. 21207.
CHAPTER 7 — PARTICLES AND PARTICLE CLOUDS
The basic equation
sorption)
for light extinction
by fine-particle clouds
7-27
(total scattering and ab-
is often called the Lambert-Beer
Law and has this general form:
Ir=
where
/r and
Ih ekynax
/, are the transmitted
|
and
(7.21)
incident
light intensities,
respectively; x is the path length through the particle cloud; a is the
projected area of the average particle in the beam; and k, is a particleextinction coefficient dependent on the index of refraction, the surface roughness, and the color ofthe particle.
Figure 7.12 is a schematic showing the essential elements of a total
scattering photometer, called a penetrometer because it is used to
measure filter penetration. When air is drawn through the scattering
chamber by the vacuum pump, the sampled aerosol passes through
the focal point of the cone of light and causes that light to be scattered forward through the dark area. The phototube, which has been
exposed to darkness up to now, is activated by the forward-scattered
light and sends a signal to the amplifier. The amplifier then augments the signal linearly and indicates it on the microammeter.
(Detectable particle sizes range from approximately 0.1 44m to
100, wm.) This photometer has a threshold sensitivity of at least
10° pail for aerosols containing particles with a count-median
diameter of 0.75 wm, and it is capable of measuring concentrations
10° times this value. Its sampling rate is about | cfm for rapid response. In service, a sample of the aerosol mixture is taken from the
upstream side, close to the filter, to measure the concentration of the
challenge aerosol.
With the challenge aerosol flowing through the
scattering chamber,
the apparatus
needle
reading
on the 100%
is then adjusted
of the 100% scale.
Next,
by setting the
a stray-light
adjustment is made to compensate for any signal caused by dark
current or reflections off internal surfaces of the scattering chamber.
The equipment is now ready to read the downstream concentration,
and the result will be the penetration (1 — efficiency) in percent.
Figures 7.13 and 7.14 summarize many of the properties discussed
in this chapter. They have been included here for easy reference to
often-sought information.
7-28
FAN ENGINEERING — BUFFALO FORGE COMPANY
|
0.01
PARTICLE DIAMETER - ym
1
10
100
THEORETICAL MESH
%
(USED VERY INFREQUENTLY)
.
I.
utr isne elMi sH
325
30
1250! 170,
ELECTROMAGNETIC WAVES
beeen
Hi
anit
MICROWAVES
Bee
ETC.)
FARINFRARED
SMOG
|
10,Hee
1,000
ATMOSPHERIC DISPERSOIDS
CLOUDS ANO FOG
-——J
— DRIZZLE
TYPICAL PARTICLES AND GAS DISPERSOIDS
ROSIN SMOKE
++—— DIL SMOKES
TOBACCO SMOKE
METALLURGICAL DUSTS AND FUMES
AMMONIUM
CHLORIDE FUME
CEMENT OUST
Sout MIST
CONCENTRATOR
NTAC
PAINT PIGMENTS
4
ela
FLOTATION-ORES—e4
|
ZINC OXIDE FUME—-1_—s
COLLOIDAL
SILICA
BEACH SAND
————
# INSECTICIDE DUSTS
SPRAY DRIED MILK
ALKALI
FUME ——>
——-AITKEN NUCLEI—>4
ATMOSPHERIC DUST
ke SEA SALT NUCLEI
COMBUSTION
NEBULIZER-DROPS-4
be— HYDRAULIC
-NOZZLE OROPS—>
LUNG DAMAGING
PNEUMATIC
DUST
} ["wozzte oroPs
RED BLOOD CELL DIAMETER (ADULTS): 7.5, + 0.34
BACTERIA
Figure 7.13
he
HUMAN
HAIR >
Particle Characteristics
CHAPTER 7 — PARTICLES AND PARTICLE CLOUDS
7-29
PARTICLE DIAMETER - um
0.01
0.1
1
10
100
1,000
10,000
234
68
MICROSCOPE
ELECTRON MICROSCOPE —— - -—[->4
CENTRIFUGE
ELUTRIATION
-paa
SEDIMENTATION
TURBIDIMETRY
DIFFRACTION
+
VISIBLE TO EYE
PERMEABILITY
|
eee
scanners
LIGHT SCATTERING
—— -—
NUCLEI COUNTER
—— -—
|
MACHINE TOOLS (MICROMETERS, CALIPERS, ETC.)
ELECTRICAL CONDUCTIVITY
TYPES OF GAS CLEANING EQUIPMENT
ULTRASONICS
(VERY LIMITED INDUSTRIAL APPLICATION)
CENTRIFUGAL SEPARATORS
LIQUID SCRUBBERS
CLOTH COLLECTORS
NOS) ef
Oo
COMMON AIR FILTERS
HIGH EFFICIENCY AIR FILTERS— -- >t —
IMPINGEMENT SEPARATORS
THERMAL PRECIPITATION
‘USED ONLY FOR SAMPLING)
— +MECHANICAL SEPARATORS4
ELECTRICAL PRECIPITATORS ~~ — ~ >
TERMINAL GRAVITATIONAL SETTLING *(FOR SPHERES, SP. GR. 2.0)
IN AIR AT 25°C.
REYNOLDS NUMBER
7
-6
fs Lats
OT
pe Oeof
Oe8 raat0)
Oy a10:28
1 ATM
t
SETTLING VELOCITY, cm/sec
10°*
10°
23
5
23
§
23
5
REYNOLDS NONE?
ide
NOB 1078 1p", 10°,
SETTLING VELOCITY, cm/sec
10° 2
5
Lips) 235 0:
PARTICLE DIF
IN AIR AT 25°C. 1 ATM
10%
1 4
32
§3
2
IN WATER AT 25°C
197,
5
43
Figure 7.13 (Cont.)
Adapted
from the data of C.E.
Lapple:
Particle Characteristics
Reprinted
from Stanford Res. Inst. J. in “Nonviable
Particles in the Air,” Air Pollution, Volume I, Second Edition, A. Stern (Editor), Academic
New York, 1968, pp. 50-51.
Press,
FAN ENGINEERING — BUFFALO FORGE COMPANY
7-30
GRAMS PER CUBIC METER
ss
a
See
STL
LER
Ua
LY
10
10?
LOW-PRESSURE PNEUMATIC CONVEYING
EXPLOSIVE CONC. OF AIR BORNE DUSTS SS
10?
SANO & STONE ORYING
STACK
=
=
DUST
—=— cloupBuRst ———~
STORM
+—
MODERATE RAIN
ee
ELYCASH ERELUENT sees
BALTIMORE
ASMESTD —-MILWAUKEE
BLAST FURNACE
OPEN HEARTH
ELECTRIC
|
STEEL
BRASS
FORY
a ee
GREY IRON FOUNDRY.
SMELTERS
aN
10°
+—
DRILLING
+——
MINE AIR
COAL CUTTING
mc
10°
FOG & MIST
+——
TS
103
INDUSTRIAL-DISTRICT AIR
DRIZZLE. ——=
—————
FOUNDRY-WORKROOM AIR
SHAKEQUT
CLEANING = POURING =MOLOING
COTTON-MILL-WORKROOM AIR
BREAKING
PICKING
CAROING
MINE'A —————
MUCKING
HAULING
COA
+——————_
THRESHOLD LIMITS FOR MINERAL DUSTS AND TOXIC METALS
Fe203
10“
INDUSTRIAL-DISTRICT AIR —>
10°*
CITY AIR
<<
=
POLLEN
RURAL & SUBURBAN AIR
AIR-CONDITIONING FILTERS
Sa
eS
VISCOUS FILTERS
EFFLUENT
AIR
INDUSTRIAL CLOTH FILTERS
Sid
SILICATES.
THRESHOLD LIMITS FOR MINERAL DUSTS AND TOXIC METALS
As
[cee or So, al mea
loca
10°
T
Ps__
Cd} Ho CrO3
T
a
Vice en Cnr
a
ET
EFFLUENT
AIR
vr
ee ay aa:
eee
ae Sp
eal
10°
ee
T
v
ar
Fa RU
ge
ELECTROSTATIC PRECIPITATORS
FABRIC FILTERS
|gL
a SR
1077
Seay ea
SP
10*
ea
Se
a}
_-
(PS
as RI
10"
a
A
aa
Riccar
AIR
aa
10°
anes
CELLULOSE
10°
|
s
ae ON) Se
EFFLUENT
102
ASBESTOS
PAPERS
el
10"
101"
THRESHOLD OF ODORS
a a |
Pu
a
Sa
| oe
10°"?
ho
ee
10°
THRESHOLD LIMITS FOR RADIOACTIVE ELEMENTS ——___|
Ra236
1242410
es
GRAMS PER CUBIC METER
Common
Figure 7.14
Particle Dispersions and Methods of Size Measurement
Adapted from the data of M.W. First and P. Drinker, “Concentrations of Particulates Found in
a
oS
, Pp.
38.
of Industrial
Hygiene and Occupational
Medicine,
Volume
5, Number
4, April
Chapter 8
Engineering Statistics
Statistics is concerned with accumulating and analyzing data. Some
of the statistical methods that are useful in fan engineering are discussed
in this chapter. These include: curve fitting, measurement error and
uncertainty, propagation of uncertainties into the result, and design
of experiments.
Curve Fitting
When one variable is dependent upon another, their relationship
can be expressed by drawing a curve. The equation for that curve may
also be useful, particularly for computer applications. The process of
curve fitting can range from nothing more than freehand placement of
a curve among the data (plotted as discreet points on a graph) to
complex computer calculations of numerous curves that fit the data
with varying degrees of success according to pre-established criteria.
The least-squares criterion, one of the most widely used for closeness
of fit, is that the sum of the squares of the deviations be as small as
possible. A deviation (also called a difference, a residual, or an error)
is the difference between corresponding test and calculated values of
the dependent variable. By summing the squares of the deviations,
positive and negative deviations do not cancel each other. Cancellation
could also be avoided
by using absolute values, but the least-squares
technique is generally preferred.
It may be possible to fit a complex curve to the data so that it passes
through each point exactly. However, this may not be the most desirable curve fit. The best curve, as dictated by physical principles, might
be a simpler one, like a straight line, even though it does not pass
through all the points. The inevitable scatter due to testing errors
demands that there be a finite sum ofthe squares.
The method of least squares can be used to find the best-fitting
straight line according to the least-squares criterion. The method can
also be used to find the best parabola, the best cubic equation, or the
best curve of almost any type. Among the most useful types of curves
for fan performance are the various polynomials including the straight
line and the parabola, which are called first- and second-degree
polynomials.
The method involves: establishing the type of curve to be fitted,
writing the equation in coefficient form, preparing a set of normal
equations, and solving those equations for the unknown coefficients. If
8-2
FAN ENGINEERING — BUFFALO FORGE COMPANY
a straight line is selected, the method gives the straight line that best
fits the data. If a polynomial of higher degree is chosen, the method
yields the best polynomial of the selected degree. In general the equation for a polynomial is
y=aotaxt
ax
t+... + anx"
(8.1)
where n is the degree chosen. Obviously, a straight line requires only
the first two terms on the right. The normal equations for a polynomial are:
Sy =aom + aydx + atx +...
tandx",
(8.2)
Exp = aodx + aydx*? + agdx? +... + a,dx"",
(8.3)
Exp = aodx’ + aydxi t+ agdx* +... + andx"”, and
(8.4)
Exp = aoUx"” + ayUx™ + agdx? +... + andx"™.
(8.5)
The first normal equation is obtained from the selected polynomial by
summing both sides over the range of test values. The value of m in
the first term is the number of data points. The second and subsequent
normal equations are formed by multiplying both sides of the selected
polynomial by the variable in the second and subsequent terms and
then summing. The number of normal equations must equal the
number of undetermined coefficients. These simultaneous equations
can be solved by any suitable technique to determine the coefficients.
However, solving for the higher-degree polynomials may be practicable
only with a computer.
When the type of curve cannot be established from physical principles, several types can be compared. If each is the least-squares fit
for its type, the question arises, “Which is the overall best fit?” The
answer is, “The one with the least sum of the squares.” Other statistical measures that can be used to answer the question are the standard
error of estimates ss, and the correlation coefficient r, The former, as
indicated by
ae
Sat awNy
> (y =
m
Wet
,
(8.6)
is based on the sum of the squares ¥(y — yes)” and the number of
data points m. The best least-squares fit will also be the best leaststandard-error-of-estimate fit. The correlation coefficient can be calculated from
(continued on page 8-6)
CHAPTER
8 — ENGINEERING STATISTICS
Example 8.1
8-3
Curve Fitting Fan Performance
Given the following data:
find the lowest-degree polynomial that closely fits.
Spotting the data on a chart, it is obvious that something
than the first degree is required.
Try the second degree. Substituting »for pr and x and QO,
Y=aotayxt
2
ax.
higher
8-4
FAN ENGINEERING
— BUFFALO FORGE COMPANY
The normal equations are:
=
Sp = Gai FP Ae
Fe Cae
2
ee
3
Lx = aodx + aiLx + a2dx , and
2
SP Spas
2
a)
SP Pee
eos
aw CIOS
Calculating the various sums:
388 960
3439.96
Substituting in the normal equations gives
6ao+
72a,+
1144a.=
26.71,
T2ao+
1144a,;+ 20448a.= 260.06, and
1144a0+ 20 448a)+ 388 960 a2= 3439.96.
Solving by any suitable method gives
do= 4.988 598,
ai= 0.290 588 9, and
a.2=—0.021 104911.
(Note that even for this simple example some pocket calculators should
not be used because they lack the necessary precision.)
Substituting and calculating gives:
(= Yea
17.3587
CHAPTER
8 — ENGINEERING
Ge
II
STATISTICS
8-5
ya)
Z(y— yy
\/
ee
ticaatlek
17.3587
= 0.99866
The correlation coefficient looks good, but the deviations are larger
than expected for a fan test. Therefore, a third-degree equation should
be tried. The results are:
do=
5.299 122,
ai=
0.146 796 3,
az = —0.006 365 312, and
a3 = —0.000 409 433 2.
Jest
(y aml Vest)
(vy pix Dee
(v a
5.5639
5.8623
SAM
4.9831
3.4912
1.0881
—0.0039
0.0077
0.0089
—0.0331
0.0288
—0.0081
0.00002
0.00006
0.00008
0.001 10
0.000 83
0.00007
1.2283
2.0116
1.6341
0.2483
0.868 |
11.3684
0.002 16
17.3587
(=
yy
» (y a! Vea
Ss,
SV — ay
\/
!
ae
17.3587
0.999 94
The correlation coefficient and the deviations are considerably better
than the second-degree equation. The fit is quite close, with the worst
deviation (—0.0331) generally acceptable for fan engineering. Both
the second- and third-degree polynomials are plotted below together
with the test points.
FAN ENGINEERING — BUFFALO FORGE COMPANY
8-6
3RD DEGREE POLYNOMIAL
:
2ND DEGREE POLYNOMIAL
&
3
2
1
0
4
8
12
“16
20
24
Q
(8.7)
(8.8)
where y is the data point value, y is the mean of all data points, and
Ves: 1S the estimated or calculated value from the curve fit. In Equation
8.7 the numerator is the variation that can be explained by the leastsquares curve, and the denominator is the total variation. The numerator of the fraction in Equation 8.8 is the unexplained portion of the
total variation. The closer r approaches 1.0 the better the correlation
between the curve fit and the data. Equation 8.7 is sometimes written
Z(vesr— YY (n—- 1)
>
very) oem(bce)
when the number of data points is small.
(8.9)
CHAP
8 — TER
ENGINEERING
STATISTICS
8-7
Measurement Error and Uncertainty
The value x of a measurement will differ from the true value pw of
the quantity by an amount called the error e'. For positive errors the
measurement exceeds the true value, so
e— ie)
Ol —a
(8.10)
An uncertainty e is a possible value that the error might have. The
exact value of the error cannot be determined, but the interval containing most ofthe possible values can and should be estimated closely.
The best estimate of the true value y is the average x of a large
number n of measurements x;.
hae
Sanaa
!
(8.11)
Statistically, the best estimate is obtained through repeated measurements using many different instruments and many different observers.
Of course, both the instruments and the observers should be fully
qualified for the job. If, as is frequently the case, it is not practicable
to use several instruments and observers, the estimate will not be
as reliable.
The probability P that the true value p falls within a given uncertainty interval +e, surrounding the average x can be determined from
statistics and
should
be stated.’ There are several
ways
to make
a
probability statement about measurements. If the standard deviation
o is known, it can be used with the appropriate Z statistic to obtain the
uncertainty interval +e, for a particular confidence level P where
S5y2.,5=3 22
ae
Zo
oe
(8.12)
It can then be stated that the true value is expected to fall within
the interval defined by x + ex; P Values of Z corresponding to the
appropriate probability P can be found in Table 8.1. For a large
number n of measurements, the standard deviation of the distribution
is defined by
'Two types of errors are considered in this section. Random errors (also called precision errors)
are the result of various small influences that cause a measuring system to indicate different
readings when sensing the same value. The distribution of indicated readings caused by random
errors alone usually approaches a normal distribution as the number of readings ts increased.
Systematic errors (also called bias) are generally constant for a given input and cannot be
reduced by increasing
the number of measurements.
*It is correct to assign a probability (also called confidence level) to an uncertainty interval only
if the distribution ofthe errors is known.
8-8
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Table 8.1
Z Statistic for Normal Distribution
Wi,
|?
1.000
2.000
3.000
68.3%
95.5%
99.7%
]
Cima
n
1/2
£8
aw]
:
(8.13)
Sometimes the standard deviation is considered to be known from
experience; then the above treatment can be used. Usually, however, o
is not known and must be estimated, instead. The estimated value s is
defined for a limited number n of measurements by
]
=|
4
n
1/2
fon
:
(8.14)
The value of scan be used with the appropriate ¢ statistic to obtain
the uncertainty interval +e, for a particular confidence level P where
Beane
35Ba
(8.15)
It can then be stated that the true value is expected to lie within the
interval defined by x + ex; P. Values of ¢corresponding to the appropriate probability P can be found in Table 8.2. The degrees of freedom
for this purpose are n-/ (since one degree has already been used to
calculate x).
Example
8.2 illustrates the use of these statistical quantities for
some typical measurements.
Example 8.2
Measurement Uncertainties
Given the following nozzle measurements, which were obtained for
a constant flow rate, calculate the best estimates of the true values
and the uncertainty intervals for 95% probability.
The values of xand s are from Equations 8.11 and 8.14.
Using Table 8.2,
t = 2.776 for 95% probability and 4 degrees of freedom.
CHAPTER 8 — ENGINEERING STATISTICS
Measurements
:
je
es
Ah
7a
ap
(eg
ley
8-9
Calculations
=
i
|(ar— Ay](ap:— apy] (i — BY
1 | 0.801 | 5.01 0.075|
2028174
5:025),01076
3
|0.817 | 4.97 | 0.076
4
|0.770 | 5.04 | 0.074
Se OW S45 | S20
OL078
I
2,
3
4
5
0.000081}
0.000000
0.000625}
0.000100
0.000625}
0.001600
0.000484}
0.000900
0.001 444| 0.000000
>x
|
ea
3,959 |25.05
ON 92" ||" 520i
Me
0.003259]
0.002600
0.028544}
0.025495
From the above table and Equation 8.15:
A = 0.792 ft? and
yee
Leen
2.776 X 0.028544
vn
V5
= +0.035 ft’; 95%,
A, = 5.01 in. wg and
+Fenp=Ht
ts
vn
=
Re 2.776 X 0.025495
v'5
= +0.03 in. wg; 95%, and
p = 0.075 Ibm/ft* and
see =e
ts
Vn
=+
2.776 X 0.001225
v5
j
= +0.002 lbm/ft'; 95%.
The uncertainty in the area measurement is +0.035 ft’, or 4.4% of
the mean. This seems high and might be improved by measuring more
diameters for each determination just in case the duct is dented or
otherwise misshapen. The uncertainty in the differential pressure
measurement is reasonable at +0.03 in. wg, or 0.6%. The uncertainty
in the density also seems high at £0.002 lbm/ft*, or 2.7%, unless the
five runs were spread over a long period.
Instruments should be calibrated against a suitable standard, preferably one that can be traced to an authority such as the National Bureau
of Standards. The best calibration is the average of repeated calibrations
using many different observers and many standards. However, a single
calibration against a single standard by an experienced person will gener-
8-10
FAN ENGINEERING — BUFFALO FORGE COMPANY
Table 8.2
¢ Statistic
t Statistic
ye
for Probability P of
Freedom
90%
95%
99%
1
2
3
4
5
6
7
8
6.314
2.920
2.353
2.132
2.015
1.943
1.895
1.860
12.706
4.303
3.183
2.776
2.571
2.447
2.365
2.306
63.657
9.929
5.841
4.604
4.032
3.707
3.500
3.355
CHAPTER
8 — ENGINEERING
STATISTICS
8-11
ally be sufficient to obtain reliable calibration data. The calibration data
can be presented as a curve, drawn through plotted points of reading vs.
standard, or by means of a curve-fit equation. Any calibration, even if
obtained by repeated measurements, will be only an estimate. Of course,
the reliability of this estimate will be higher for calibrations obtained by
repeated measurements than for calibrations obtained from a single set
of measurements. Statistics can be used to estimate the uncertainty in the
calibration if the calibration is based on repeated measurements. However, Statistics cannot be applied to a single set of measurements so
judgment and experience must be relied on instead to estimate the uncertainty in a single calibration.
Example 8.3 illustrates how repeated calibrations can be used to
determine the calibration correction and the uncertainty interval for a
typical instrument at one setting.
If an instrument is reported to have a certain accuracy, it is implied
that either the instrument was repeatedly calibrated or that a number of
instruments of the same design were calibrated. The accuracy statement
for an instrument should list the positive and the negative error limits for
all possible readings. If the positive and negative error limits are equal
and of opposite signs, the accuracy can be reported as plus or minus so
many percent of full scale, plus or minus so many percent of reading,
or plus or minus some absolute amount such as °F or in. wg. If the
positive and negative error limits are not equal, they will have to be
stated separately.
If an instrument is given an individual calibration, the calibration cor-
rections for the various readings can be presented by plotting the instrument readings vs. the readings for the standard, and fairing a smooth
curve through the data. Alternatively, the calibration function can be
expressed as an equation obtained by some sort of curve-fit process.
Note that these data give only the bias that should be subtracted from
any reading. The uncertainty associated with that bias should also be
determined. The positive and negative error limits, as given by the
instrument supplier or otherwise determined, should be used to define
the uncertainty interval. This will be plus or minus one-half of the algebraic difference of the positive and negative error limits + (e+ — e-)/2. If
the positive and negative error limits are not equal, the mean estimated
error (e+ + e-)/2 should
be added
to the measurement.
Note that the
positive and negative error limits may be of the same or ofdifferent sign.
Example 8.4 illustrates some of the calculations involved in measurements with different kinds of calibrations.
Many measured quantities have an alternating component superimposed on a steady component. If repeated measurements are made over
a sufficient period, a time-weighted average will yield the steady component. This component may have to be corrected for calibration and
ambient conditions, but the temporal average should be determined
before any such corrections are made. Although automated systems are
preferred, an experienced
observer can
mentally estimate the time-
8-12
FAN ENGINEERING
— BUFFALO FORGE COMPANY
weighted average with good results. Of course, there will still be some
error regardless of the method used to obtain the temporal average.
Example 8.3
Calibration
Given the following mV
readings, which were taken during repeated
calibrations when the standard was set at 6.000 mV, find the calibration
correction, the uncertainty of the calibration, and describe the instrument.
Measurement
i
bie
l
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
20
seselh
Calculations
—
se
(a
5.912
5.911
5.909
5.914
5.908
5.910
5.918
5.916
5.907
5.904
5.909
5.910
5.911
5.906
5.906
5.903
3.915
5.914
5.908
5.911
0.002
0.001
—0.001
0.004
—0.002
0.000
0.008
0.006
—0.003
—0.006
—0.001
0.000
0.001
—0.004
—0.004
—0.007
0.005
0.004
0.000004
0.000001
0.000001
0.000016
0.000004
0.000000
0.000064
0.000036
0.000009
0.000036
0.000001
0.000000
0.000001
0.000016
0.000016
0.000049
0.000025
0.000016
0.000004
0.000001
118.202
0.000 300
Using Equation 8.11,
oenN j= ee = 561 (118.202) = 5.9101 mV, say 5.910 mV .
!
The calibration correction or apparent systematic error is
6.000 — 5.910 = +0.090 mV.
x)
CHAP
8 — TER
ENGINEERING
Using Equation 8.14, the estimated
STATISTICS
standard
8-13
deviation
tribution is
]
-
1/2
(.—
Z|
Ss= [er S (Cae)
|
== [
—
19
of the dis-
1/2
(0.000 300) | == 0.003974,
say 0.004 mV. And the estimated standard deviation of the mean is
s
__ 0.003 974
Jn
V20
= 0.000 889, say 0.0009 mV.
For 95% probability, and 19 degrees of freedom,
t = 2.093 from Table 8.2.
Using Equation 8.15, the uncertainty of the mean at this input is
+ 2.093 X 0.0009 = +0.001 884, say 0.002 mV; 95%.
This instrument
has poor accuracy
as reflected
by the large bias
(+0.090) or calibration correction, but it has good precision as indi-
cated by the relatively small uncertainty (+0.002).
If an additional calibration had been attempted for this instrument,
there is a 95% probability that the calibration correction would have
been within +0.009 mV of the mean.
1/2
see
Ets ()=i =)
1/2
= +2.093 X 0.004( a a
= +0.009 mV.
This suggests that a single calibration might have indicated a calibration correction ranging between 0.081 mV and 0.099 mF. Of course,
with a single calibration, there is no statistical way to calculate the
uncertainty. This simply illustrates the superiority of repeated calibrations over single calibrations.
Example 8.4
Using Calibration Data
Given the following accuracy, calibration, and measurement data,
calculate the corrected measurements and the uncertainties
measurements due to the uncertainties of the calibrations.
of the
Case A: A digital voltmeter reading is 5.75 mV. Accuracy is listed as
+1.0% of full scale. Full scale is 10.0 mV. No calibration curve is
provided.
Since there are no calibration data, the corrected
measurement
1s
8-14
FAN ENGINEERING — BUFFALO FORGE COMPANY
5.75 mV. The uncertainty due to calibration is £0.01 X 10.0 = £0.10
mV. The confidence level associated with this kind of accuracy statement is generally taken to be 95% or better.
Case B: A manometer reading is 0.56 in. wg. At zero pressure the
gage reads —0.02 in. wg. No other calibration data are given, but
accuracy is listed as plus or minus 1% of reading.
Assuming a constant systematic error due to the zero setting, the
corrected
measurement
is 0.56 — (—0.02) = 0.58 in. wg. The uncer-
tainty of the measurement due to instrument accuracy is £0.01 X 0.56 =
+0.0056 in. wg. Again, a confidence level of 95% or better can
generally be assumed for this kind of accuracy statement.
Case C: A thermometer reading is 79.5°F. The accuracy for the batch
of thermometers from which this one was taken is listed as £0.5°F.
No other calibration data are provided.
Since there are no calibration data, the corrected reading is 79.5° F.
The uncertainty due to the instrument calibration is simply +0.5°F.
Here. too, it can generally be assumed that the confidence level is
95% or better.
Case D: The reading from a load cell is 24 mV. The calibration
accuracy is 0.25% of the rated output. The rated output is listed as
3mV/V input, and rated capacity is 300 lb. The electrical input, or
excitation, is 12V.
The correct reading is 300 X 24/(3 X 12) = 200 lb. The uncertainty
due to calibration is 0.0025 X 300 = £0.75 lb. The confidence level
can be assumed to be 95% or better.
Only calibration uncertainties have been considered in the above
examples. Additional uncertainties may result from resolution errors,
hysteresis errors, temperature effects, and other systematic errors.
There will also be random errors associated with the measurements.
Propagation of Uncertainties into a Result
A result R may be a function R(V\V2...) of one or more variables
V;, etc. each of which must be measured or otherwise determined.
When a single measurement is used to determine a result, the uncertainty of the result is exactly the uncertainty of that measurement.
When multiple measurements are used to obtain a result, the uncertainty of the result must be some combination of the individual uncertainties. There are several ways of combining uncertainties, but the
recommended! equation is
2
+ter=
=le( oe
CESS ei)
2( dV;
'S.J. Kline and F.A. McClintock, “Describing
Mechanical Engineering, January 1953, pp. 3-8.
Uncertainties
1/2
;
in Single-Sample
(8.16)
Experiments,”
CHAPTER
8 — ENGINEERING STATISTICS
a
8-15
The variables V; should be measured independently, otherwise covariance terms must be included in the combining equation. The uncertainty
+e; for each variable must have the same probability or confidence
level as that desired for the uncertainty +e of the result. The solution
of this equation can be simplified by using the following rules:
for addition
(R = V, + V2)
2
aaa
R
for subtraction (R=
2\1/2
+ e@°)
Vase a
V,; —
V2)
i
oa
*
(8.17)
(en zi en)?
a
vi
TA
ey
(8.18)
for multiplication (R = V, V2)
cree)
(24
|G)
| |
2
for division (R =
2
1/2
(8.19)
V;/V2)
go
(ft) 2 (2
+4 =+((7) +(¥) | ete
2
»
1/2
(8.20)
for exponentiation (R = V;"V2")
ee_[(,,2
[(7) F (™e
7) | :
2
2
1/2
=R =
Example 8.5
(8.21)
Propagation of Uncertainties
Given the information from Example 8.2 and a nozzle coefficient C
of 0.99 with an uncertainty interval of +0.005 at 95%, calculate the
best value of the flow rate and its uncertainty interval using
O = 1097CA
A
ae .
Using Equations 8.17 to 8.21:
a
eG) Ga.
FAN ENGINEERING — BUFFALO FORGE COMPANY
8-16
(<5) —
(9.005) — 9.000 025 508,
0.99
GaN
60.035 \a= 01001 952926,
(S)
=(a F797)
CON
Tare
7)
(2X 5.01
soe
= See
0.002
(=) = (Gone
\_
= 0,000 177778,
eo\?
ec)
Q
4,
eo
= 0.002 165 175,
——=
Q
a
O = 1097 X 0.99 X 0.792
0.046 531 443 ,
5.01
0.075
= 7030 cfm,
+eg = +7030 X 0.0465 = +327 cfm, and
QO = 7030 cfm + 327 cfm; 95%.
This is not a good test since the uncertainty interval is +327 cfm, or
+4.7%.
Most of the uncertainty derives from the area measurement,
which definitely could be improved. The uncertainty in the density
measurement is suspiciously high at 2.7%, but improving this will not
better the results until the area measurement has also been improved.
The individual uncertainties that were propagated into the above
result were a mixture of random and systematic uncertainties. For
instance, the uncertainty in the nozzle coefficient is a systematic uncertainty that cannot be reduced by increasing the number of
measurements. As noted in Example 8.2, the uncertainty in the area
measurement is extraordinarily high. If the dimensions that were
measured to determine the area were selected at random for the five
different runs, the uncertainty certainly could be reduced by taking
more measurements. This, then, could be classified as a random uncertainty, but ordinarily the uncertainty in any geometric measurement of a single object is systematic. The uncertainties in the
differential pressure measurement
appear to be random. The uncer-
tainties in the density measurement, as suggested in Example 8.2, is
large and suggests that conditions may have been changing especially
in view of the pattern shown by the readings. Additional systematic
uncertainties undoubtedly could have been included in this example.
Uncertainties in the calibration of the various instruments. uncer-
CHAPT
8 — ENGINEERING
ER
STATISTICS
8-17
tainties in any table values used to obtain the density from temperature and pressure measurements, as well as resolution and hysteresis
uncertainties could be obtained with a thorough analysis. Whether
these additional uncertainties would seriously affect the overall uncertainty of the result depends on their magnitudes and their sensitivity coefficients. For a thorough explanation, including examples,
of calculating all the various uncertainties and their sensitivity coefficients,
refer to
ISO
5168-1978
titled Measurement of Fluid
Flow-Rate Measurement.
(E), the
International
Flow-Estimation
Standard
of Uncertainty of A
Design of Experiments
In engineering experiments there are usually many independent and
dependent variables. For instance, in the experimental development of
a fan, the independent variables might include such things as cutoff
location, impeller-tip width, and blade angle. The dependent variables
would include the flow coefficient, pressure coefficient, efficiency, and
sound power level. One strategy for experimentation might be to vary
one independent variable (also called a factor) at a time to discover its
effect on the various dependent variables (also called responses). This
strategy can be effective when the experimental error is negligible compared to the individual effects due to various factors and when the
interactions due to two or more factors are negligible. However, when
neither the error nor the interactions are negligible, a different strategy
may be indicated. A statistical-design-of-experiment strategy can often
be used to obtain a satisfactory mathematical model of the effects and
interactions at less cost than the one-factor-at-a-time strategy.
At the heart of any statistically designed experiment is replication.
Some aspects of replication may be obvious while others will more
likely be hidden. Economies are obtained through the use of hidden
replication. For example, refer to the upper left-hand block of Table
8.3. The first four columns and four rows contain all of the possible
combinations for each of two factors at each of two levels. The factors
are designated X; and X> while the low and high levels are designated
by minus and plus signs. For trial |, both factors are at their minus
levels and this puts their interaction X;X2 at a plus level. Note that for
four trials, each of the factors X, and X2 is sampled at its minus value
twice and at its plus value twice. Also note that the combination X,X>
is sampled at its plus value twice and its minus value twice, as well. If
the experimenter knows that the interaction is negligible, he could
substitute a third factor for the interaction and obtain two samples each
for it at its minus and plus values. It is possible, therefore, to sample in
four trials three factors with 100% replication at each level, whereas
it
would take twelve runs to obtain the same replication when examining
one factor at a time.
,
Refer now to the expanded left-hand block that contains the first
FAN ENGINEERING
8-18
Table 8.3
ful
— BUFFALO FORGE COMPANY
Two-Level Factorial Designs
2a
vE
XX
XyM3-X 2X3
Zi
XyX2X
XyMq
XQXq XyX2Xq
XZXq XyX3Xq
XQXZXq MyX2XZXq
1
+
+
=
+
—
=
+
2
+
=
+
+
+
=
=
+
+
_
+
~
+
7
+
+
.
os
3
=
4
*
“pe
5
+
+
+
=
6
+
=
-
Se
-
-
+.
+
i}
+
+
+
=
=
+
=
+
8
of
+
—
ae
—
4
et
+
+
+
9
+
a
+
ee
10
a
a
-
iH
11
+
—ooee
-
12
+
+
+
13
+
2
an
14
+
Soo
—
Roe
15
+
Shee
—
16
+
See
See
+
eo
+
fy
ee
—
=
=
=
=
se
-
3
-
+
+
=
~
-
=
-
+
ot;
=
+
=
-
+
=
-
-
-
-
-
+
~
F
=
-
-
+
a
=
=
+
+
=
=
+
+
-
=
+
+
=
_
fee
—
qe
-
+
-
+
-
+
=
-
=
ake
+
+P
+
-.
ea
+
+
+
+
+
+
+
———————™EEee
eight columns and eight rows. This is the three-factor, two-level factorial design, and it includes the two-factor, two-level design as a part.
This design can be used to examine three factors and all of their interactions, or as in the preceding case, if one or more of the interactions
is known to be negligible, other variables can be substituted. It is possible, therefore, that this design can be used to examine seven separate
effects. In eight trials, each of these effects or interactions would be
sampled four times at each of its minus and plus values. Similar hidden
replication exists for the four-factor, two-level design also shown on
Table 8.3 and for other designs that are even more complicated. Incidentally, this table can be extended by noting the pattern for the main
effects (which are shaded) and by further noting that the interactions
have received the sign that would result by multiplying the corresponding main effects. Also note that the maximum number of main effects
and interactions that can be examined is one less than the number of
trials because one degree of freedom is reserved for the mean as noted
in the first column. This same table can also be used as a guide for
computing the results of the experiment.
As indicated above, there are two replicates for each of the levels for
each factor or interaction in the four-trial run. Similarly, there are four
replicates for each level of the factors or interactions in the eight-trial
run. The number of replicates increases for the higher designs as well.
The standard error of the mean for two replicates will be 71% of the
standard error of a single observation, and the standard error of the
mean for four replicates will be 50% of the standard error of a single
CHAPTER 8 — ENGINEERING STATISTICS
8-19
observation. In other words, the eight-trial run permits the calculation
of mean effects whose standard errors are half of those that would be
calculated from a single observation.
The number of runs required for a full-factorial experiment increases
dramatically with the number of main effects to be determined, if all
interactions are to be determined as well. As noted above, it is possible
to examine more main effects for a given design if the interactions can
be assumed to be negligible. There is the risk, however, that the assumed
negligible interaction is not negligible, and of course, this will confound
the results for any main effect that shares the same column as the interaction. There are experimental designs that permit the study of more
main effects than is possible with a full-factorial design of equal length.
These fractional designs can provide estimates of a large number of
main effects that are clear of two-factor interactions. In some of these
designs, the composite effects of certain groups of two-factor interactions can also be estimated. Both the Plackett-Burman designs and
the fractional factorials have this property. These designs also provide
space for determining the experimental error.
All of the designs noted above are two-level designs. If the response
is not linear, it is essential that three or more levels of the factor be
investigated. Full-factorial designs for three levels would require very
large numbers of runs.
Example 8.6 illustrates in a very general way how design-of-experiment principles can be applied.
Example 8.6
Design of Experiments
Given three factors (inlet box width, shaft diameter, and VIV addition)
to explore, design an experiment to discover the three main effects both
when the interactions are known to be negligible and when they are not
negligible. For convenience, call the factors A, B, and C respectively.
Assuming linear relationships only, a two-level, three-factor factorial
design will yield all the main effects and interactions in 8 runs.
Using Table 8.3
lis
Trial | A | B | AB
Les
+
2
=
3
ee
4
sali)
oot
te
+
=
5
_
+ | 6
i
8
-
= E
++ -
=
ae
eo)
—
eo) (o)
> ie) =)
+
—
—
+
+
+
—
=
=
_
=
se
st
=
+
=
=
nay
> @)
=a
+
—
=
ae
-f
a
aes
|
+—
+
+
8-20
FAN ENGINEERING — BUFFALO FORGE COMPANY
Assuming linear relationships only, a two-level, two-factor factorial
design can be used if the interactions are negligible.
Trial
A
B
G
l
2
3
4
=
ta
=
Te
=
=
sr
ar
=F
=
a
+
For either design the trials should be run in random order. For instance:
3, 4, 2, and
| for the four-trial experiment.
(Trial 3), A would be set at its minus level,
For the first run
B would be set at its plus
level, and C would be set at its minus level. The test would be run
and a certain result achieved. Trials 4, 2, and | would then be run with
A, B, and C at the proper levels.
Individual
results would
be noted.
(The results are the yields or responses.)
The levels chosen for the factors A, B, and C should be separated
widely enough to cover the range of interest without compromising
the assumed linearity. The individual effects should also be of nearly
equal magnitude. Otherwise, interactions will probably be significant.
For this example the minus and plus values are tabulated below.
=
ain
A
B
Cc
1S in.
10 in.
2 ane
8 in.
No VIV
Yes VIV
The calculations for an experiment are facilitated by using the same
data from Table 8.3 as is used to design the experiment. First, copy
the table including the column for the mean, and note the result for
each run in a separate column. Then, for each column, sum all the
results that are opposite a plus sign. Next do the same for those
Opposite a minus sign. (The sum of these two should be the total
sum.) Now subtract the total minuses from the total pluses. Finally,
divide the difference by the number of plus signs. This is the main
effect or the interaction, as the case may be. The first column gives
the mean of all the results since it is the total of all the results divided
by the total number of runs.
Example 8.7 illustrates the calculation of effects for a very simple
eXperiment.
Example 8.7
Calculating Effects and Interactions
CHAPTER
8 — ENGINEERING STATISTICS
_
8-21
Given the design and information from Example 8.6 and the results
indicated below, find the effects and interactions. The results in this
case are fan efficiencies.
Trial | Result
|
2
3
4
5
6
7
8
=
| Mean
90.1
87.6
88.2
84.7
88.4
86.0
85.5
83.3
+ Sum
— Sum
Total
Diff.
Effect
ali
| a|
Sie
te
oe
te
oF
SF
+
3
=
=
==
+
=
=F
=
+
B
AB
===
Cc
Ase
~—
B a ABC
= vt
693.8 | 341.6
0
392.2
693.8
693.8
693.8
10.6
86.725| 2.65
Note that the main effects are all quite a bit larger than the interactions for this example. There are numerical tests for significance,
but they all require iteration or allocation of space for error sampling.
If it were known that certain interactions were negligible, the corresponding columns could be used as a means of error sampling. In this
instance it would almost appear by inspection that the interactions
AB,
AC,
BC, and
ABC
are
negligible and
that each
of the main
effects is significant. The effect of A is the largest, the effect of B the
next largest and the effect of C is the smallest. Each of these effects
carries a minus sign, which indicates that the effect is in the direction
of reducing efficiency.
These same data can be used to supply information for the smaller
design also examined in Example 8.6. In order to do this, we have to
choose the run from the 8 trial design that corresponds to the plus
and minus values for each of the factors. For instance, trial 5 has a
minus for A, a minus for B, and a plus for C; therefore, it can be used
as trial | in the smaller design. The data and its source are listed in
the calculations below.
Trial
| Result
| Mean
A
B
C
(8 run trial)
l
2
3
4
88.4
87.6
88.2
83.3
ae
sr
3F
=f
=
ate
=
=
=
=
ste
ate
aia
=
=
36
(5)
(2)
(3)
(8)
8-22
FAN ENGINEERING — BUFFALO FORGE COMPANY
+ Sum
— Sum
Total
Diff.
Effect
3475-2
vlabnooen
lars)
eave
0
176267
17600
(17538
347.5 | 347.5 | 347.5 | 347.5
SHS a ON Slee
ee
eal
86.875 1 —2.85 |"2.257] — 205
Note that the effects are slightly different, but the order of importance is maintainedat least for this example. One would have more
confidence in using the values from the 8-trial design than those from
the 4-trial design because of the added replication. And the added
information about interactions could be very important.
The data from an experiment can be used to construct a mathematical model of the system that was tested. The predicted response
°° can be obtained for selected values of
the various factors x,’ using
Cape
JO)
See
Duy
:
nigEh Ga
Bec
eeHa Ie
e
eo
OO
The first term on the right is simply the mean value of all the results
and is obtained from the first column of the calculation-tabulation.
The second term is based on the main effects £;, which are also
determined from the calculation-tabulation. Coded values x; for
the various factors must be used as outlined below. The third term
is based on the two-factor interactions £;, which are found in the
calculation-tabulation. Coded values x:x; of the interacting factors
must also be used. Additional terms must be used to account for
higher order interactions. The coded values of the selected factors
should be based on the selected value for the factor x;’, the plus level
x; and the minus level x; of that factor used in the experiment, and
xi = (xi + x7 )/2
xi
(C3) = eye
(8.23)
Similarly, the coded values for interacting factors x,x; can be ob-
tained from the selected values, the plus and minus values used in the
experiment, and
0.0
Xx; =
+
+
2a
Sr ogie = (Oa oo) Tea es
(Kiyo) /2
(8.24)
Example 8.8 illustrates how a mathematical model can be obtained
from experimental data.
CHAP
8 — TER
ENGINEERING
Example 8.8
STATISTICS
8-23
Mathematical Model
Given the results and findings of Example 8.7, when the input
values are those listed below, find the equation that defies the process.
+ Value
— Value
A
B
(C
10 in.
15 in.
8 in.
2 in.
VeseViIV —ia
No VIV=-—I1
Using Equations 8.23 and 8.24 with the data from Example 8.7:
v= 86.725,
E\x; = —2.65 Ante
Ex.x2 = —2.60 eee ,
3
E3x3 = —1.85 v8 5
Ei2x1x2 — —0.20 a
,
Exsxixs = +0.35 ASC)
Ex3.X2x3 = —0.20 a
, and
Fy23.X1X2X3 = +0.45 a
Substituting in Equation 8.22:
a
I
n
]
es
dl
Des ayce 2 @epee Soy
es, Daa ear oe
Z ol ereae ue "
0
p=
86.725
Nigaili2e5
|
+ 5 ( 2.65
75
2.60
Biaas>
3
oe)
3
i
8-24
FAN ENGINEERING
— BUFFALO FORGE COMPANY
=
12.5
al: ; ( 0.20 eR 2 +0.35 eal
++ (Gas
a
0.20 Be
=38
5 _)
}
The response for input values of A= 12, B=4, and
(assuming linear relationships) can be predicted as follows:
C=+]
v° = 86.725 + 1/2 (+0.530 + 0.867 — 1.850)
+ 1/2 (+0.056 + 0.406 — 0.040) + 1/2 (0.188) = 86.804,
say 86.8%, or
v’ = 86.725 + 1/2 (+0.530 + 0.867 — 1.850) = 86.499, say 86.5%.
The predicted efficiency is 86.5% considering main effects only or
86.8% considering main effects plus interactions.
The predicted response is nearly the same whether based on main
effects only or main effects plus interactions. The interaction effects
can be ignored in many calculations.
Part II
Fans
Chapter 9
Fan Terminology
The terminology used in fan engineering is replete with jargon and
synonyms. This chapter defines and discusses many of the terms that
may be encountered. Other terms are defined as they are introduced
in other chapters.
Fan
Any device that produces a current of air by the movement
of a
broad surface can be called a fan. This handbook is concerned with
those types of fans that fall under the general classification of turbomachinery and have a rotating impeller at least partially encased ina
stationary housing. Fans are similar in many respects to pumps and
compressors. All three are turbomachines that transfer energy to a
flowing fluid. It is easy to distinguish between fans and pumps:
pumps handle liquids; fans handle gases. The distinction between
compressors and fans, however, is not so simple. Both handle air and
various other gases. Broadly speaking, the function of a fan is to
propel, displace, or move the air or gas, while the function of acompressor is to increase the pressure, reduce the volume, or compress
the air or gas. However, there is always some fluid movement through
a compressor, and it is debatable whether that function is less important than the others listed. Fans and compressors have also been
differentiated on the basis of compression ratio or density change.
At one time, a 1.1 compression ratio or 7% density change was the
official ASME! demarcation line. However, machines have been built
for higher ratios and were still called fans. Presently, a 1.3 compression ratio is being considered by ISO,” but AMCA® has removed
the upper limit. The choice of name (whether fan, compressor, or
something else) is, therefore, not regulated or standardized. Verylow-pressure-rise machines will probably be classified as fans, and
very-high-pressure-rise machines will be classified as compressors.
Intermediate-pressure-rise machines can be classified as either.
'Test Code for Fans, ASME
Power Test Codes, PTC I1-1946.
Third Draft International Standard on Air Performance Test Methods of Industrial Fans Using
Standardized Airways, International Organization for Standardization Technical Committee
ISO/TC 117 “Industrial Fans,” Sub-committee ISO/TC
Using Standardized Airways,” Paris, September 1976.
117,/SC
1! “Fan
Performance
“s1 aboratory Methods of Testing Fans for Rating.” AMCA
51-75, 1975.
Standard 210-74, ASHRAE
Testing
Standard
BUFFALO FORGE COMPANY
RING
FAN ENGINEE—
9-2
Some
other
names
for fans
and
compressors
are:
ventilator
(generally restricted to a very-low-pressure-rise), exhauster (used to
signify that gases are being removed from something), and blower
(used to signify that gases are being supplied to something).
Fan Parts
The principal parts of any fan are the impeller and the housing.
Various other parts may be necessary or useful in the operation of
the fan. Referto Figures 9.1 and 9.2.
The impeller is the rotating element that transfers energy to the
fluid. An impeller can also be called a wheel, a rotor, a squirrel cage,
a propeller, or a runner. Impeller should probably be preferred as a
general name, but wheel and rotor are also commonly used for all
types. Squirrel cage is restricted to forward-curve centrifugals, and
propeller is restricted to certain simple axials. Runner is used more
frequently for pumps than for fans.
The blades are the principal working surfaces of the impeller. A
blade can also be called a vane, a paddle, a float, or a bucket. Vane
should probably be preferred as a general name, but blade is also
commonly used for all types. Paddle is uSually restricted to an unshrouded type, and float to centrifugals in general. Bucket is more
frequently used for turbines than for fans.
Shrouds may be used to support the blades. A shroud can also be
called a cover, a disk, a rim, a flange, an inlet plate, a backplate, ora
centerplate. Shroud should probably be preferred as a general name,
but cover and disk are also used. Flange, inlet plate, and rim are restricted to members that shroud the blades on the inlet side of a
centrifugal fan. Backplate and centerplate are restricted to members
that shroud the side opposite the inlet on single-inlet and double-inlet
wheels, respectively.
Hubs
may
be used
to support
the blades directly or through
a
shroud to the shaft. A hub can also be called a boss or a disk, but
this terminology seems to be disappearing.
The housing is the stationary element that guides the air or gas
before and after the impeller. A housing can also be called a casing,
a stator, a scroll, a panel, a ring, or a volute. Housing, casing, and
stator are all general. Scroll and volute are both restricted to centrifugal types, whereas panel and ring are restricted to propeller types.
Centrifugal housing components include the side sheets and scroll
sheets. The point of closest approach to the wheel is the cutoff, also
called the tongue. The area over the cutoff is called the blast area.
Axial housing components include the outer cylinder, the inner
cylinder (or bearing tube), the belt fairing (or belt tube), the guide
vanes, and the tailpiece.
The inlet is the opening through which air enters the fan. It can
also be called the eye or the suction. A stationary inlet piece can be
called an inlet cone, an inlet bell, an inlet nozzle, or a venturi.
CHAPTER
9 — FAN TERMINOLOGY
9-3
INLET GUIDE VANES
¥
SIDE SHEET
E
SCROLL
Figure 9.1
INLET
IMPELLER
Exploded View of a Centrifugal Fan
DISCHARGE VANES
A
INNER CYLINDER
OUTLET
BELT FAIRING
ee
Peer
_rBLADES
IMPELLER
STATIONARY INLET
Ss
an
OMITTED)
Ne
INLET BELL
TAILPIECE
(SOMETIMES
OUTER CYLINDER
Figure 9.2
DIFFUSER
Cutaway View of a Vaneaxial Fan
9-4
FAN ENGINEERING
— BUFFALO FORGE COMPANY
ne
The outlet is the opening through which air leaves the fan. It can
also be called the discharge. A diffuser can be provided to transform
kinetic energy to pressure energy. It can also be called a discharge
cone or an evasé. When a diffuser is supplied with the fan, the exit
opening ofthe diffuser becomes the outlet of the fan.
An inlet box may be used to provide side entry or a means
of
keeping the bearings out of the air stream. Another name for inlet
box is suction box. When an inlet box is provided with a fan, the
entrance opening to that box becomes the inlet of the fan.
Stationary vanes may be used to guide the flow. Vanes used upstream of the impeller can be called prerotation vanes or inlet-guide
vanes. Vanes used downstream of the impeller can be called straightening vanes or discharge guide vanes.
For control, the fan may be equipped with inlet-box dampers or
variable inlet vanes. Inlet-box dampers can be called IBDs, and
variable inlet vanes can be called VIVs, or vortex dampers.
The fan may also be equipped with its own shaft and bearings.
The bearings may be supported on or within the housing, on an
attached base, or on independent pedestals. The attached base is
sometimes called a sub-base.
Aerodynamic Fan Types
If fans are classified according to the direction of the flow through
the impeller, there are four distinctive types: axial-flow fans, radialflow fans, mixed-flow fans, and cross-flow fans. See Figure 9.3.
Axial-flow fans are characterized by flow through the impeller
which is generally parallel to the shaft axis, conventionally called the
axial direction. As discussed in a subsequent chapter, the flow cannot
be exactly axial since there must be a tangential deflection by the
blades, but in conventional designs, there is generally an absence of
radial-flow components. Even designs incorporating some meridional
acceleration are considered axial-flow machines. Impeller blades may
be fixed pitch (permanently secured), adjustable pitch (changeable
when the fan is not running), or controllable pitch (movable while
the fan is operating). Axial-flow fans have cylindrical housings and
may be equipped with inlet bells and diffusers. Vaneaxials have stator
vanes, but tubeaxials do not. Propeller fans are the simpler form of
axial-flow fans, usually ring- or panel-mounted.
Radial-flow fans are more generally called centrifugal fans. The
flow through the impeller is radially outward with varying tangential
components depending on the design. The flow must enter the impeller axially, but there is generally an absence of axial components
through the blading in most conventional designs. Even designs with
inducer sections are considered radial-flow machines.
Centrifugal fans have scroll-shaped housings. Such fans with one
inlet are called single-inlet fans, and those with two inlets are called
double-inlet fans. The abbreviations SI (or SISW) and DI (or DIDW)
CHAPTER 9 — FAN TERMINOLOGY
9-5
j= —— = ——— 9
1)
pemeoerh
ge OH
AXIAL FLOW WITH
MERIDIONAL ACCELERATION
‘S ov
RADIAL FLOW WITH
INDUCER SECTION
MIXED FLOW
CROSS FLOW
Figure 9.3.
Aerodynamic Classification of Fans
are also often used. A centrifugal wheel in an axial housing is known
as a tubular-centrifugal or in-line fan.
Mixed-flow fans are characterized by flow that leaves the impeller
with both the axial and radial components. The flow enters the impeller axially and is deflected tangentially by the blades. The housings
are scroll-shaped like those for centrifugal fans.
Cross-flow fans are also known as transverse-flow fans. The flow
enters the impeller at one portion of its outer periphery and proceeds
radially inward. After passing through the blades, it is generally
acted upon by some vortex-inducing device and, thereafter, proceeds
radially outward through the blades, exiting at a section different
from the inlet section. The housings have elongated inlets and outlets
to match the wheel inlets and outlets.
— BUFFALO FORGE COMPANY
FAN ENGINEERING
9-6
2oade
CW-UB
Ccwo
Clockwise
Up Blast
CW-TAU
CW 1-89
Clockwise
Top Angular Up
CW-TH
CW 90
Clockwise
Top Horizontal
CW-TAD
CW 91-179
Clockwise
Top Angular Down
Nw
!
CW-DB
CW 180
Clockwise
Down Blast
CW-BAD
CW 181-269
Clockwise
Bottom Angular Down
CW-BH
CW 270
Clockwise
Bottom Horizontal
CW-BAU
CW 271-359
Clockwise
Bottom Angular Up
CCW-UB
CCW O
Counter-Clockwise
CCW-TAU
CCW 1-89
Counter-Clockwise
CCW-TH
CCW 90
Counter-Clockwise
CCW-TAD
CCW 91-179
Counter-Clockwise
Up Blast
Top Angular Up
Top Horizontal
Top Angular Down
CCW-DB
CCW 180
Counter-Clockwise
Down Blast
CCW-BAD
CCW 181-269
Counter-Clockwise
Bottom Angular Down
CCW-BH
CCW 270
Counter-Clockwise
Bottom Horizontal
CCW-BAU
CCW 271-359
Counter-Clockwise
Bottom Angular Up
:
yA
Down Blast
Figure 9.4
>
Up Blast
Horizontal
Rotation and Discharge Positions
Adapted from the data of AMCA: “Designations for Rotation and Discharge of Centrifugal
Fans,” AMCA Standard 2406-77, 1977.
CHAPTER 9 — FAN TERMINOLOGY
9-7
Arr. 1 SI
Arr. 2 Sl
Arr. 3 Slor Dl
For belt drive or
For belt drive or
For belt drive or
Arr. 4S
For direct drive. Im-
direct connection.
Impeller overhung.
Two bearings
on base.
direct connection.
Impeller overhung.
Bearings in bracket
supported by fan
direct connection.
One bearingoneach
side supported by
fan housing or
peller overhung on
motor shaft. No
bearings on fan.
Motor mounted on
housing.
on independent
pedestals.
base or supported
by fan housing.
Arr. 7 Slor Dl
Arr. 8 SI
Arr. 9 SI
Arr. 10 SI
For belt drive or
direct connection.
Arrangement 3 plus
base for motor.
For belt drive or
direct connection.
Arrangement 1 plus
extended base for
motor.
For belt drive.
Impeller overhung,
two bearings, with
motor outside base.
For belt drive.
Impeller overhung,
two bearings, with
motor inside base.
Arr. 1
Arr. 3
Arr. 4
Arr. 9
For belt drive or
direct connection.
Impeller overhung.
Two bearings on
internal supports.
Drive through inlet.
For belt drive or
direct connection.
Impeller between
bearings that areon
internal supports.
Drive through inlet.
For belt drive.
Impeller overhung
on motor shaft. No
bearings on fan.
Motor on internal
supports.
For belt drive.
Impeller overhung.
Two bearings on
internal supports.
Motor on casing.
Drive through belt
fairing.
Arr. 7
Arr. 8
Arr. 10
For belt drive or
direct connection.
Arr. 3 plus common
base for motor
and fan.
For belt drive or
direct connection.
Arr. 1 plus common
base for motor
and fan.
For belt drive. Arr. 9
except motor is
mounted on separate base.
Figure 9.5
Standard Drive Arrangements
Adapted from the data of AMCA: “Drive Arrangements for Centrifugal Fans,” AMCA
2404-77, 1977.
Standard
9-8
FAN ENGINEERING
— BUFFALO FORGE COMPANY
co &
Top
Intake
o°
Right Angular
Intake From Above
1°-89°
Horizontal
Right Intake
Right Angular
Intake From Below
90°
91C2 1792
Bottom
Left Angular
Horizontal
Left Angular
Intake
Intake From Below
Left Intake
Intake From Above
180°
181°-269°
270°
2712-359°
Figure 9.6
Adapted from the data of AMCA:
2405-77, 1977.
Standard Inlet-Box Positions
“Inlet Box Position for Centrifugal Fans,” AMCA
Standard
Centrifugal
Fan
Propeller Fan
Figure 9.7
Adapted from the data of AMCA:
AMCA Standard 2407-77, 1977.
Axial-Flow Fan
Standard Motor Positions
“Motor Positions for Belt or Chain Drive Centrifugal Fans,”
SS
i
CHAPTER 9 — FAN TERMINOLOGY
a
a
in
ee
ee
9-9
Construction Standards
The fan industry, through AMCA, has devised certain standard
designations for rotation, discharge, inlet-box position, drive arrangement, and motor position.
The method of specifying rotation is to view the fan from the drive
side and indicate whether it is clockwise or counter-ctockwise. The
drive side of a single-inlet fan is considered the side opposite the
inlet, even in those rare cases where the actual drive location may be
on the inlet side. On dual-drive arrangements, it is necessary to spec-
ify which of the drives is used. The rotation of a propeller or axialflow fan is usually immaterial; that is, it is a matter of individual
design and need not be specified. There is no official designation of
drive side for axial fans so that, should it be necessary to specify rotation, the direction from which the fan is viewed must also be specified.
The method of specifying rotation and discharge position is indicated in Figure 9.4. If the fan is to be suspended from the ceiling or a
side wall, the discharge should be specified as if the fan were floormounted. The intended mounting arrangement should also be given.
An angular measure is required for angular positions.
Various drive arrangements have been assigned numbers as indicated in Figure 9.5. The designations for axials are not official but
are consistent with the standards for centrifugals. Fans can be equipped with bearings on the housing or on an attached base, as appropriate. In some arrangements, pedestal-mounted bearings can be
furnished. Arrangements involving a bearing in the inlet should be
avoided for small fans.
The method of specifying inlet-box position is to view the fan from
the drive side (the same as for rotation) and indicate the position of
the intake opening. Angularity can be specified as shown in Figure 9.6.
Various motor positions have been assigned letter designations as
indicated in Figure 9.7.
Application Classifications
Fans are often classified according to their application or the duty
they are expected to perform. For instance, there are ventilating fans,
mechanical-draft fans, industrial exhausters, pressure blowers, and
many special-service fans.
a
Refer to the chapter on fan selection and to the various application
chapters for further information including more specific terminology.
Performance Characteristics
The performance of a fan can be expressed in several ways. Since
the purpose of a fan is to move air or gas, one of the parameters used
must be flow rate. Either the mass flow rate or the volume flow rate
can be used. Since air or gas is compressible, the volume flow rate
will vary depending on the location at which it is measured. This
9-10
FAN ENGINEERING
— BUFFALO FORGE COMPANY
es
necessitates specifying the measurement location when fan performance is given in terms of volume flow rate. A common colloquialism
for flow rate is simply the word “air,” as in “The air and pressure of
theitaniarem.:
The output power of a fan is also an important fan-performance
parameter. Ideally, the total output power should be the same regardless of whether fan performance is given in terms of mass flow rate
or volume flow rate. Total output power divided by mass flow rate
yields a quantity that we call specific energy, while total output power
divided by volume flow rate yields a quantity that we call total pressure. As noted below, only a portion of the total output power may
be of concern, and this leads to further distinctions in performance
parameters.
The input power of a fan is another important parameter. Fan
input power is the power required to drive the fan and any elements
in the drive train that are considered to be within the fan boundaries.
This has also been called the brake horsepower.
The volume-flow-rate/ pressure approach to fan performance is
conventional in the United States and many other countries. Various
test codes, including AMCA Standard 210-74, have taken this into
account. The mass-flow-rate/specific-energy approach is being promoted as an International Standard and will undoubtedly be incorporated in ISO 117 when it is published. ASME PTC II will include
both approaches. The following definitions are given in two groups,
one for each approach.
The Volume-Flow-Rate/ Pressure Approach
Fan flow rate is the volume flow rate at the fan inlet, which is
equal to the mass flow rate divided by the fan gas density. This might
better be called the fan volume flow rate as will be done in ASME
PTC II. Often, the fan flow rate is simply referred to as the CFM, or
the CFM of the fan.
Fan total pressure is the difference between the average total pressure at the fan outlet and the average total pressure at the fan inlet.
Only the component of velocity in the nominal direction of flow is
taken
into account.
The
abbreviation
FTP
(or even
TP)
is often
used, especially in conversation.
Fan velocity pressure is the velocity pressure corresponding to the
average velocity in the nominal direction of flow at the fan outlet.
The abbreviations FVP and VP are common.
Fan static pressure is the difference between the fan total pressure
and the fan velocity pressure. Therefore, fan static pressure is the difference between the average static pressure at the fan outlet and the
average total pressure at the fan inlet. Fan static is a common colloquialism; FSP and SP are also used.
Fan gas density is the total density of the gas at the fan inlet condition. This is usually shortened to simply density or air density.
CHAPTER 9 — FAN TERMINOLOGY
=e
SE
ee
ee
ee
ee
9-11
eee ee
Fan output power is equal to the product of the fan flow rate, the
fan total pressure, and a compressibility coefficient. Air horsepower,
or the more general term air power, is often used instead of fan out-
put power.
The compressibility coefficient is a dimensionless coefficient used
to account for compressibility effects. See the section on compressibleflow energy equations in Chapter 2. Compressibility coefficient has
at times been called compressibility factor.
Fan total efficiency is the ratio of fan output power to fan input
power. Another name for fan total efficiency is total-to-total efficiency.
Fan static efficiency is the ratio of fan output power to fan input
power in which the fan output power is modified by omitting the
power corresponding to the fan velocity pressure. Another name for
fan static efficiency is total-to-static efficiency.
The Mass-Flow-Rate/Specific-Energy Approach
Fan flow rate is the mass of fluid passing through the fan per unit
of time. ASME PTC I! will call this the fan mass flow rate.
Fan specific energy is the work per unit mass that would be done
on the gas in an ideal transition between the actual inlet and outlet
states. It is equal to the average static pressure at the outlet, minus
the average static pressure at the inlet, all divided by the mean density,
plus the difference in specific kinetic energy across the fan. This
might also be called specific work.
Fan mean density is the arithmetic mean of the inlet gas and
outlet gas densities. This frequently will be shortened to density or
air density.
Fan output power is equal to the product of the mass flow rate
and the fan specific energy. This could also be called air power or
output power.
Fan efficiency is the ratio of the fan output power to the fan input
power. It is, therefore, equal to the product of fan mass flow rate and
fan specific energy, divided by fan input power.
Compressibility coefficient is the ratio of fan inlet density to fan
mean density.
Miscellaneous Performance
Point of operation, also called point of rating, is the relative position on the characteristic curve at which a fan happens to be operating. It can be described as the appropriate combination of volume
flow rate and pressure or of mass flow rate and specific energy. It
can also be defined as a percentage of free delivery or even by the
flow rate alone, as long as the performance characteristic is known.
Dimensionless characteristics can also be used.
Free delivery is the point of operation where the fan static pressure
is zero. It is also called wide-open performance.
9-12
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Shutoff is the point of operation where the fan flow rate is zero. It
is also called static no-delivery or blocked-tight performance.
Chapter 10
Centrifugal Fans
Centrifugal fans of various descriptions constitute one of several
types of turbomachinery, which are used to transfer energy to a flowing fluid. Centrifugal fans are similar in many respects to both centrifugal pumps and centrifugal compressors. Of course, pumps
handle liquids and so can easily be distinguished from fans. But,
since fans and compressors both handle gases, their differences are
not very distinct. Machines with very low pressure rises are always
identified as fans, and those with very high pressure rises as compressors. For intermediate pressure rises, either description can be
applied. Even test codes and standards often fail to make a
distinction.
The flow through centrifugal machines is chiefly radial in the
region of energy transfer and is easily distinguished from the flow in
axial-flow machines. Axial-flow fans are discussed in the next chapter, but many of the principles of energy transfer given in this chapter
are applicable to axial-flow as well as centrifugal fans.
The discussions that follow are concerned with the design of centrifugal fans from an aerodynamic point of view. As noted in the
chapter on fluid flow, a mathematical model can be constructed for
any flow situation, and various assumptions can be made to simplify
the model. What is done here can be described as a one-dimensional,
incompressible, steady-flow analysis. The purpose of the discussions
is not to give a complete design method. (More complex models are
needed for that.) Rather, the intent is to show some of the important
considerations in design so that design features can be appreciated in
the application and operation of fans.
Energy Transfer
In the rotor of any turbomachine, the axial, radial, and tangential
components of the forces of the fluid particles on the rotor are associated with axial thrust, radial thrust, and torque, respectively. Refer
to the chapter on fan mechanics for a discussion of thrust. The net
torque (see Equation 2.13) is equal to the time rate of change
in
moment of momentum of the fluid between the rotor inlet (Subscript
1) and the rotor outlet (Subscript 2). The rate of energy transfer, or
power Y,, for a constant rate of mass flow m, is the product of
torque, angular velocity w, and m:
FAN ENGINEERING — BUFFALO FORGE COMPANY
10-2
Pr =F oltVia— ri Vn)=z (UrVa— UVa)
(10.1)
The product of radius r and tangential velocity V, is often called
the fluid whirl. The product of angular velocity and radius is the
linear rotor velocity U.
The tangential fluid velocity and the radial fluid velocity can be
combined vectorially to obtain the absolute fluid velocity V in the
radial plane. Likewise, the linear rotor velocity can be subtracted
vectorially from the absolute fluid velocity to obtain the relative fluid
velocity
W
in the radial
plane.
See
Figure
10.1. The
net energy
transfer per unit weight of fluid, or what is often called the total Euler
head Hz, can be determined from
go as
=
VeoV
cl gar ss
, UH UY , Wee We
a,
Teal
a
Oe
The first portion of this equation states that the head developed by
an ideal rotor depends on the angular velocity and on the change in
whirl between inlet and outlet. In the right-hand side of the equation,
the first term, (V¥.° — V:°)/2g, is the change in absolute velocity head
across the rotor due to kinetic energy change. The second term,
(Uy — U;’)/2g, is the change in pressure head due to centrifugal
forces.
The
third
term,
(Wi? —
W,’)/2g,
is the change
in pressure
head due to the change in relative velocity through the rotor. The
first term, therefore, represents the change of velocity head while the
last two terms combined represent the change of static head.
The various forms of Equations 10.1 and 10.2 are convenient in
analyzing the effect of design changes and the effect of different conditions of operation on an ideal machine. The sign convention used
here is that a positive value of Y or H means that power must be
transmitted te the air or that head is developed by the rotor,
respectively.
Energy transfer to the fluid due to shaft work can take place only
within the impeller. The energy transformation involved in the conversion of velocity to static head, which may take place in the casing
or elsewhere, should not be confused with the process of energy
transfer.
The analysis of certain limiting flow situations may be helpful in
understanding the energy-transfer process. When flow is purely radial
(that is, Vi2=0 and V,; = 0 ), both the net power transmitted to and
the head developed in the fluid must be zero. Equations 10.1 and 10.2
clearly show that this is so. For purely radial entry (that is, for no
inlet whirl), the theoretical
power
and
head
sively by conditions at the discharge or outlet.
are determined
exclu-
CHAPTER 10 — CENTRIFUGAL
FANS
10-3
W,
V2
STRAIGHT
Vi2 =
U;
BLADE
Wy
Viz = Uy
_— CURVED
BLADE
RK
ss
1
NN
|
=
ee
mit
1H
:
SIDE ELEVATION
END SECTION
RADIAL TIP
SIDE ELEVATION
END SECTION
BACKWARDLY CURVED TIP
—f-----
SIDE ELEVATION
END SECTION
FORWARDLY CURVED TIP
Figure 10.1
Blade Design for Backward, Radial, and Forward Tips
10-4
FAN ENGINEERING — BUFFALO FORGE COMPANY
Another limiting situation is that of no flow, that is, 7 —=0. No
net power can be transmitted to the fluid without flow. Similarly, the
relative velocity at either the inlet or the outlet will be zero. However, the linear rotor velocity and absolute fluid velocities will have
finite values and, the absolute fluid velocity must equal the linear
rotor velocity in such situations. The head theoretically developed by
a rotor at no flow will be twice that due to centrifugal forces alone,
namely (U2 — U,’)/g. The kinetic-energy portion is largely transformed,
not
into pressure
energy,
but, rather, into internal energy
because of fluid friction, producing temperature rise rather than
static head.
The density does not appear anywhere in the expression for theoretical head. So, the head an impeller will develop is independent of
density.
Each type of fan uses the various means of developing head in
distinctly different proportions. In axial-flow fans, the particles theoretically flow at constant radii, so U2 = U, and there is no centrifugal
effect. The various types of centrifugal fans are characterized by distinctly different heel-to-tip ratios and tip angles, so the proportion of
developed head due to centrifugal effect varies. Fans with forwardly
curved blades usually have very large heel-to-tip ratios and, so, produce less head due to centrifugal effect than fans with backwardly
curved blades, which usually have much smaller heel-to-tip ratios.
Radial-blade fans are produced with various heel-to-tip ratios, and
the head developed due to centrifugal effect varies accordingly. Mixedflow fans have a limited change in radius and, therefore, produce a
limited amount of head by means of centrifugal effect. Cross-flow
fans use radial inflow and outflow at the same radius, so the positive
and negative centrifugal effects cancel each other.
Prerotation and Slip
The fluid approaching the inlet of a radial-flow impeller will follow the path of least resistance. For each flow rate there will be a
different path and a different value of the least resistance. The least
resistance occurs at the design flow rate. With uniform axial approach, the fluid particles must simply turn radially to enter the impeller at the design flow rate. At any flow rate other than design, the
fluid particles must turn tangentially, as well as radially, in order to
follow the path of least resistance.
The combination of purely radial absolute velocity and tangential
linear rotor velocity produces a relative fluid velocity, the tangential
component of which is directed opposite to the rotation. The relative
fluid angle can be determined vectorially. The heel of the blade
should be curved forward at such an angle that the fluid can enter
between the blades without impact.
The heel angle can be correct for only one flow rate, called the
CHAPTER 10 — CENTRIFUGAL FANS
ee
eee
10-5
design flow rate. At all other flow rates, the fluid must acquire prerotation. There will be some impact loss and some added fluid friction,
but the sum of the two must be the least possible for the actual flow
rate. At flow rates less than design, the prerotation must be positive
with respect to wheel rotation, and at flow rates over design, the
prerotation must be negative with respect to wheel rotation.
Ideally, the theoretical power and head at the design point are as
indicated by Equations 10.1 and 10.2. However, both the head developed by and the power transmitted to the fluid are less than the
theoretical values due to the phenomenon known as slip. The difference cannot be called a loss but, rather, more appropriately, an ineffectiveness or nonutilization, since it would occur even with an ideal
fluid. Various theories predict slip, but none agrees completely with
empirical data, so none is entirely satisfactory. However, the net
result is that the fluid leaves the impeller at a mean relative angle
with the tangential direction, which is less than the blade angle.
Therefore, the impeller does not develop the full theoretical head nor
transmit the full theoretical power. A reduction in head also occurs
due to the real-flow velocity gradients across the impeller channel. It
is much smaller than that due to slip. Again, this is not a loss since it
does not involve any energy input.
Both the spacing and the discharge angle of the blades influence
the amount of slip. For a greater number of blades np», there is
smaller spacing, more guidance is given the flow, and less slip results.
Lower tip angles 82 cause less slip, apparently because the mean path
of the particles more nearly matches the blade shape. The reduction
of head due to slip AH is also a function of flow rate and heel-to-tip
ratio, but for simplicity,
_ Uy ( KrsinB2
iA
rede
(10.3)
This approximate expression includes what is known as the
Stodola correction and is usually valid only for long overlapping
blades. According to Wislicenus,’ the correction factor K for a 90° tip
and 12 blades is about 0.65. For a 40° tip and 16 blades, K is approximately 0.9. The corresponding difference in power transmitted to the
can be obtained by multiplying by the approfluid due to slip A
priate mass flow rate m, as indicated by
VE
'G.F Wislicenus,
1965, p. 280.
Fluid Mechanics
mUy (Ae)
ae
ne
of Turbomachinery,
Dover
(10.4)
Publications,
Inc., New
York,
10-6
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Ideal Performance Characteristics
The ideal performance characteristics of a fan can be derived
from the energy transfer and slip relationships given above. For simplicity, the condition of no inlet whirl (that is, V;;=0) will be
assumed. The effects of controlled inlet whirl will be discussed under
the heading, “Inlet Guide Vanes.”
The expression for theoretical total head can be rewritten as
He= = (w- rc
4 s)
Bling-cor). (10.5)
This expression shows the effect of volumetric flow rate Q and blade
angle B. The area A, through which the fluid must flow, is best described as that which is normal to the radial-velocity component.
The second term (involving conditions at the inlet) is zero, since zero
inlet whirl is assumed. Subtracting the difference in head due to slip
leaves the ideal head H’; taking into account slip but ignoring reduction in head due to real-flow velocity gradients and losses due to skin
friction, turbulence, etc.:
eee
:
KrsinB>
(
Nb
U>QcotB>
)
a,
(10.6)
The first term gives the theoretical shutoff head, including the effect
of slip. Only part of this will appear as static head, the rest appearing
as temperature rise. The second term expresses the effect of changes
in flow rate. For a given speed of rotation and wheel geometry, the
effect of flow rate variation will depend on the curvature of the blade
at the tip. For a 90° tip angle, the ideal head will be constant regardless of capacity, since the cotangent of 90° is zero. For a forwardly
curved tip angle, the ideal head will rise with increasing flow rate,
since, for angles over 90°, the cotangent becomes negative. For back-
wardly curved tip angles, the ideal head will gradually fall with increasing flow rate, since the cotangent of angles below 90° is positive.
See the curves on Figure 10.2 marked H’; for each blade shape.
The variation of ideal power A’, with flow rate can be determined
simply by noting that power is proportional to the product of specific energy and mass flow rate or the product of head and weight
flow rate:
Pe
Pr
o|
Bxeie
mf & (:
Krrsin B2
np
)
Ur Qcot By
aA
‘E
(10.7)
For radial-tip fans, the theoretical power is directly proportional to
the flow rate. But for forwardly curved tips, the theoretical power
rises much more rapidly and, for backwardly curved tips, much less
CHAPTER 10 — CENTRIFUGAL FANS
10-7
rapidly, even to the point where it may fall off with increasing flow
rate. See the curves on Figure 10.2 marked MH’, for each blade shape.
Losses and Efficiencies
The actual power transmitted to the fluid and the actual head
developed will both differ from the ideal because of various losses.
These losses can be classified according to whether they affect head,
power, or flow rate.
Hydraulic efficiency 7, is the ratio of the actual head H to the
ideal head H’c. The hydraulic losses H’s — H result from skin friction
and energy dissipation caused by a change of direction or velocity in
the impeller or in any other part of the machine. Because the main
flow is generally turbulent, the friction losses usually vary as the
square of the velocity and, therefore, of flow rate. Shock losses are
minimal at the design point and increase as the flow rate deviates
from the design value. The hydraulic efficiency is a measure of the
perfection in the design of the flow passages.
:
Volumetric efficiency 7, is the ratio of the net volume flow rate Q
handled by the machine to the volume flow rate handled by the impeller Q;. The leakage volume
flow rate Q; — Q passes through the
clearance spaces between rotating and stationary parts to recirculate
through the impeller. The volumetric efficiency is, therefore, a measure ofthe perfection in the design of the clearance spaces.
Mechanical efficiency 7, is the ratio of the power transmitted to
the fluid A* (and converted into useful output) to the power that is
applied to the shaft @. The mechanical losses A — HP include
the power loss due to disk friction, as well as the mechanical losses in
bearings, seals, etc.
Total efficiency nr is the ratio of the theoretical air power A to
the shaft power #&. The total power losses
A — F are due to the
skin friction, turbulence, leakage, and mechanical friction. Therefore,
NT = NhNm -
(10.8)
Static efficiency ns can be determined from the total efficiency
using the ratio offan static pressure
prs to fan total pressure
per in
=
PFs
tS yaa
(10.9)
The total and static efficiencies give information on overall performance, that is, for the entire fan including rotor, casing, etc. The
difference is that the kinetic energy leaving the fan (as represented by
its outlet velocity head) is considered available in the first case but
disregarded in the second.
10-8
FAN ENGINEERING
— BUFFALO FORGE COMPANY
|
FORWARDLY-CURVED TIP
a
[
my
> jo LEAKAGE
f-4ESIGN
POINT
i
||
id
|
'
——>
(H)
HEAD
LfDESIGN
POINT
——>
(?)
POWER
ae
— \+ LEAKAGE
hy
Co
P-
|
; ———
F
“FLOW RATE (Q)
Figure 10.2
Calculated Performance Characteristics for Centrifugal Fans
CHAPTER 10 — CENTRIFUGAL FANS
(H)——>
HEAD
POINT
DESIGN
——>
POWER
(P)
POINT
“DESIGN
—>
LOSSES
4_
eau es nore
Tee
c
Telesis
ase
Tire au we ee
FLOW RATE (Q)
Figure 10.3
Calculated Performance Characteristics for Centrifugal Fans
10-9
10-10
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Net Performance Characteristics
The net-head/ flow-rate relationship for the no-leakage condition can
be derived from the ideal-head
/flow-rate relationship by subtracting the
appropriate friction and shock losses for each flow rate. The results of
such calculations for each ofthree typical blade-tip angles are illustrated
in Figure 10.2. Similarly, the net-power/ flow-rate relationships can be
derived from the ideal by adding the power losses due to disk friction,
bearings, etc. The effect of leakage in either case is approximately as if
the zero flow-rate line were shifted to the right by a corresponding
amount. This is also shown in Figure 10.2.
The relationships shown for all three types were calculated as if
each were to handle the same amount of air at design and to develop
the same head with equal total efficiencies. To further illustrate the
differences, Figure 10.3 was drawn showing the calculated net heads
superimposed on one chart and the calculated powers superimposed
on another. The variation of the shock and friction losses with flow
rate is also shown. The three types of fans for which these performance characteristics were drawn are not necessarily of the same size
or speed. To produce the results shown, the backwardly curved design
must have the highest tip speed and the forwardly curved design the
lowest tip speed. At the design point and at other points off design,
the most stable operation (as indicated by the slopes of the curves) 1s
obtained with the backwardly curved type. Also, the power at flow
rates greater than design is least for the backwardly curved type. The
power for this type tends to level off, and if low enough tip angles or
appropriate inlet guide vanes are used, the power curve will actually
droop, as shown by the dashed lines. This Limit-Load® type of power
characteristic is very desirable for closely motored fans in systems
where the flow rate may increase because of lower-than-anticipated
resistance. Note that the forwardly curved type shows the lowest
power at shutoff, which is very desirable whenever there is considerable operation at reduced flow rate.
The dashed-line curve at low flow rate indicated on Figure 10.2 for
the backwardly curved blade design, is for the flat, backwardly inclined
blade variation of this fan. The “break” in the curve is the result of a
severe flow separation from a boundary in the blade passage. The solidline smooth curve is for a truly curved blade fan with an identical tip
angle. For equal tip angles, the blade can be curved only by steepen-
ing the heel angle, which in turn, means that inlet guide vanes must
be used as discussed below.
The usual head/ flow-rate characteristic at low flows for forward-
curved designs appears as indicated on Figure 10.2 by the dashed
line. This is probably due to negative inlet whirl produced by back
flow through the inlet of the wheel at these low flow rates.
High relative Mach numbers lead to choking with a resultant loss
of head and efficiency. However, in most fan applications, the relative
CHAPTER 10 — CENTRIFUGAL
Mach number is quite low.
Theoretically, the net performance
FANS
of a fan can
10-11
be deduced
by
considering energy transfer, prerotation, slip, velocity gradient, and
losses. Practically, however, there are so many secondary interactions
that tests must be performed not only in proving a design but also in
developing it. In the following paragraphs only the major considerations in the design of the various fan elements are discussed.
Overall Design
There are two major design objectives: (1) the design of an individual fan for specific requirements and (2) the design of a line or
several lines of fans for a range of requirements. Some aspects of the
second objective will be discussed later, particularly under the headings of specific speed and the fan laws. Only the design of an individual fan will be discussed here.
Forwardly curved tips provide the maximum head for a given
rotor size, and backwardly curved tips the least. Because a high percentage of head is developed as kinetic energy or velocity head at the
rotor outlet of a forwardly curved-blade fan and because converting
velocity head to static head is inherently less efficient than developing
static head by centrifugal force, such fans are inefficient. The highest
efficiencies are usually obtained with backwardly curved tips. Although first costs are usually lower with forwardly curved designs,
operating costs are lower with backwardly curved designs. A compromise (that is, using a radial tip) may often be indicated. Radial blades
have greater strength against centrifugal force and, so, are used extensively in high-pressure applications. They are also simply shaped
and, so, are used in many situations where maintenance due to wear or
imbalance might otherwise be a problem.
Assuming that the general type of centrifugal fan has been chosen,
the next step is to decide on an operating speed of rotation. The
rotational speed may often be specified or limited because the fan is to
be direct connected to a prime mover. Usually, economy due to reducing
the size and improving hydraulic efficiency favors small, higher-speed
units. However, Reynolds-number effects, especially at the lower pressure ratios, favor larger, lower-speed units.
Having established a general type and speed, the design of an individual fan can now be accomplished by estimating reasonable
values of the various losses and the slip effect. Using blade angles
close to the optimum established by experience, a preliminary value
for the rotor diameter can be determined
from the theoretical head/
flow-rate relationships. A method for determining the optimum inlet
diameter will be given below. Once the tip and inlet diameters have
been fixed, the impeller design can be completed by calculating the
necessary blade- heel angles and streamlining the passages, so as to
minimize the losses. Inlet bells or cones should also be streamlined as
10-12
FAN ENGINEERING
— BUFFALO FORGE COMPANY
much as possible for the same reason. The discharge conditions (that
is, any requirement to gather the air for discharge through one or
more openings) and the need for converting energy will determine
the casing design. The various losses can then be re-estimated and
adjustments made in the design as required. Finally, such a design
should be proven by tests.
Inlet Design
The velocity W, relative to the large diameter of the impeller inlet
is the vector sum of the absolute fluid velocity V; at that point and
the linear
rotor
velocity
U;. If no
inlet whirl
exists, the absolute
velocity will be purely axial (that is, V;) = Via), so that
=
Wi=VV
ia 2 FUP ==
40)):
pi
(=p.v)
* (10.10)
There is an inlet diameter D,; for each combination of hub (or other
obstruction) diameter Dy, rotative speed N, and volume flow rate Q
for which this relative velocity is a minimum. This is the optimum
inlet diameter according to Shepherd.’ A simple solution of Equation 10.10 for the optimum inlet diameter can be obtained either
graphically or by trial and error. The optimum inlet diameter must
be adjusted for the appropriate whirl, if any exists. If there is controlled inlet whirl, the minimum relative velocity must be determined
using vector construction.
The design velocity through the impeller inlet will be high. Some
sort of converging passage is needed to avoid a high shock loss at the
entrance. Even when the inlet is not free but has connected duct
work on the inlet side, the approach or duct velocity probably will be
less than that through the impeller inlet.
From the chapter on fluid flow, it can be concluded that the entrance condition having the least coefficient of resistance is bellshaped. The next best coefficient of resistance is obtained with a
converging taper.
Normally, the clearance between the stationary inlet bell (or cone)
and the impeller should be minimal in order to minimize leakage.
However, it is also true that some designs use slightly larger clearances (and greater leakage flow) to improve performance. Sometimes,
it is possible to improve overall efficiency even though the volumetric
efficiency is reduced.
Impeller Design
All the power that is transmitted to the fluid and converted into
'D.G. Shepherd, Principles of Turbomachinery, The Macmillan Co., New York, 1956, p. 227.
CHAPTER 10 — CENTRIFUGAL FANS
10-13
head is transmitted by the rotating blades. To minimize the slip effect,
the number of blades should be large. On the other hand, to minimize
fluid friction, the number of blades should be comparatively smail so
that the mean hydraulic radius of the channels between blades is
nearly maximal.
The widths of the blades at the heel and tip, as they affect the
channel areas A, and Ao, influence the ideal head as shown in Equa-
tions 10.5 and 10.6. The width of the blade at every point from heel
to tip influences the mean hydraulic radius and, therefore, the friction
losses through the impeller.
The effect of varying the tip angle has already been discussed. The
optimum tip angle is given by Stepanoff' as 25°. However, such low
angles are rarely used in fan design. Excellent efficiencies have been
obtained with angles as high as 45°, and the penalty for using 90°
angles (or radial tips) is usually not more than about five points of
efficiency.
The optimum heel angle is that which allows the air to enter the
impeller with minimal loss. The heels of the blades should be curved
forward if they are to meet the air with minimal shock, regardless of
tip curvature. When the inlet is small, very little is sacrificed by using
a radial heel angle. Since the relative velocity varies with flow rate, it
also follows that the heel angle can be correct only for one flow rate
and that losses will increase rapidly at both higher and lower flow
rates.
The shape of the blade should be a smooth curve connecting the
heel with the tip. The flow can be improved by using airfoil-shaped
blades. Reduced losses (especially at the heel) and, therefore, significant increases in efficiency have been achieved this way. The choice
of a suitable airfoil section can be based on single-airfoil theory with
corrections
for cascade
effect or directly on rotating-cascade
tests,
if available.
Usually, structural considerations alone require that the blades be
shrouded. In a fan, the inlet side of the casing is not generally shaped
to conform to the inlet side of the blade with minimum clearance.
So, shrouds are important from a leakage standpoint, too. Except
for secondary flow within a single channel, whatever leakage does
occur is essentially radial from tip to heel through the clearance
between the stationary and the rotating inlets. If losses are to be
minimized, the shape of the shroud on the inlet side should be such
that the fluid can make the turn from axial to radial flow without
separation. If one factor has led to the rapid development of airfoilbladed fans, that is the development of economical, curved-inlet
shrouds. The well-curved inlet shroud makes it possible to realize
the full advantage of using airfoil blades. Before the advent of
‘A.J. Stepanoff, Turboblowers, John Wiley & Sons, Inc., New York, 1955, pp. 66 and 232.
10-14
FAN ENGINEERING
— BUFFALO FORGE COMPANY
economical spinning and pressing to achieve the desired inlet-shroud
shapes, the only fans that successfully used airfoil blades were of
axial-flow design where such shrouds are unnecessary.
Casing Design
The casing of a centrifugal fan must serve two functions. First, it
must collect the air from the periphery of the wheel so that it can be
discharged in the desired direction. Second, since a large part of the
head developed appears at the impeller discharge as kinetic energy,
the casing must also convert part of this velocity head into static
head. Both transforming energy and collecting air, even at constant
velocity. involve losing part of the total energy. The transformation
of energy can be efficiently accomplished in a radial diffuser at the
impeller periphery. It can also take place in a conical diffuser located
beyond the point of discharge after the fluid has already been collected and directed to that point by some sort of scroll-shaped casing.
Both radial and conical diffusers need considerable space, so the
processes of collection and diffusion are often concurrently attempted
in fans. The sacrifice in efficiency involved in such an attempt is least
with backwardly curved designs, since the least amount of energy
transformation is required here. Diffuser vanes are seldom, if ever,
used in fans because they impair efficiency at off-design points and
may even do so at design.
Casings are usually volute or scroll-shaped. Centrifugal-fan casings
generally have straight parallel sides and a spiral-shaped scroll. The
point at which the scroll most closely approaches the impeller periphery is called the cutoff. Ideally, the cutoff should be located at the
diameter of the impeller, the increase in scroll radius should be proportional to the angular displacement from the cutoff, and the discharge plane should extend nearly radially from the point of cutoff.
In practice, however, the point of cutoff is always cut back so that
there will be some clearance over the impeller tip. The cutoff clearance is critical to both noise generation and efficiency. Also in practice, the plane of discharge may be almost tangential to the point of
cutoff so that, in effect, part of the impeller discharges directly into
the outlet. The shape of the volute can be approximated by using a
series of circular arcs rather than a true spiral curve. Some designs
may incorporate what is called a drop outlet. All these features are
illustrated in Figure 10.4. The lower-case letters indicate the scroll
centers, which may be uniform as shown or expanding from a to d.
The various scroll radii R should be chosen so that the circular arcs
merge into each other, forming a smooth, continuous curve. As
shown, the cutoff has been cut back from a point atop the wheel
through an arc of something
just under 90°. The amount of clearance
over the cutoff is about 20% of the impeller diameter. Values as low
as 5% can be used. The drop outlet is certainly less efficient than a
CHA10
PTE
— CENTRIFUGA
R L
Figure 10.4
FANS
10-15
Scroll Design for Ventilating Fans
diverging taper. The difference will approach that between abrupt
and gradual enlargements, as given in the chapter on fluid flow.
The width of the casing is usually much greater than the tip width
of the impeller. It also usually exceeds the width of the impeller at
the heel so that the entire inlet bell can be contained within the width
of the housing.
Inlet Guide Vanes
Either positive or negative inlet whirl can be produced by using
appropriately shaped guide vanes ahead of the impeller. Vanes curved
in the direction of rotation produce positive whirl, which reduces
theoretical head and power. However, counter-rotation vanes produce
negative whirl with the opposite effect. This can be demonstrated by
substituting positive or negative values of tangential velocity in Equations 10.1 and 10.2. For either positive or negative whirl the impeller
blades should be curved forward at the heel to meet the incoming
flow directly and, so, minimize the losses on entering. Smaller heel
angles are needed with counter-rotation vanes, and steeper heel angles
are required when the vanes are curved in the direction of rotation.
A proper heel angle for no inlet whirl falls somewhere in between. If
two impellers (one intended for use with inlet vanes and the other for
use without inlet vanes) are designed with the proper heel angle and
other features so that hydraulic, volumetric, and mechanical effi-
10-16
FAN ENGINEERING — BUFFALO FORGE COMPANY
ciencies are the same, the difference in actual head and power will
equal the difference in theoretical head and power.
See Figure 10.5
illustrating the effect of guide vanes on blade shape.
Neither an open-inlet fan nor one of the same type with fixed inlet
vanes has higher overall efficiency, if both are equally well designed.
However, there are other considerations, especially in backwardly
curved designs. First, an open-inlet fan is simpler in both blade shape
and inlet design. For the heel angle required, a perfectly flat, backwardly inclined blade gives an acceptable tip angle. Second, a fan
with fixed inlet vanes has a curved blade which, with its steeper heel
angle, makes it mechanically stronger than the flat blade. Third, the
inlet vanes serve as mechanical guards and as straighteners reducing
the effect of any adverse inlet whirl that might result from an accidental upstream disturbance. Fourth and most important of all, at
reduced flow rates, the separation that occurs with flat-blade designs
is eliminated and a smooth, unbroken head/ capacity characteristic
results instead. Fifth, at flow rates over design, the Limit-Load®
horsepower characteristic is accentuated when inlet vanes are used.
The overall efficiency of straight-radial-blade fans can be improved
by using inlet vanes to produce positive whirl. The fluid angle then
more nearly matches the heel angle, thus reducing losses and improving efficiency.
With small inlet diameters, the effectiveness of inlet vanes in changing theoretical head and power is limited. Also, inlet vanes are not
usually used to produce negative whirl. The use of such “ramming”
vanes greatly narrows the operating range.
Fixed inlet vanes are usually placed as near to the impeller inlet as
possible. The effective discharge angle from the vane will be somewhat smaller than the actual angle for any finite number of vanes
because of the inertia of the flowing air. As with slip in impellers, the
number and angle of vanes also influence the slip through inlet guide
vanes. The entering edges of vanes should be directed exactly upstream. To achieve the same degree of vane overlap from the center
to the periphery of the inlet, the radius of curvature of the vane is
gradually increased from the center outward, making the vane surface part of a cone.
Variable
inlet vanes
can
be used advantageously
whenever
con-
siderable operation at less-than-design capacity is required. If the fan
is designed for fixed inlet vanes, variable vanes with the same effective curvature can be substituted without any significant sacrifice in
peak efficiency. If, however, the fan is designed with an open inlet,
the variable vanes should be designed to produce the smallest possible
effect on flow in the wide-open position. In either case, gradual
closure of the vanes should direct the flow more and more in the
direction of rotation. The resultant changes in inlet whirl will reduce
both power and head. Since, for a fan operating on a given system,
CHAPTER 10 — CENTRIFUGAL
FANS
ee
Figure
10-17
10.5
Vector Diagram for Ventilating Fans With and Without Inlet Vanes
reductions in head developed must also be accompanied by reductions in flow rate, power requirements at flow rates less than design
are always lower than the power needed at design. Using variable
inlet vanes for flow control leads to a further reduction of power.
This additional reduction will nearly equal the theoretical amount
due to increased inlet whirl at flow rates near design. That is, the
efficiency remains nearly constant for small flow-rate reductions.
Under these conditions, the change in flow rate and the change in
absolute velocity combine in such a way that the change in the direction of the relative velocity is practically negligible. At more greatly
reduced flow rates, however, there is a significant change in the
direction of the relative velocity. Even so, the change is not as great
as if the flow rate had been reduced without increased inlet whirl.
Variable inlet vanes can be used with forward-, radial-, or backwardblade impellers to achieve power reduction at reduced flow rate better
than with dampers, which do not produce inlet whirl. Because ofthe
shapes of their power/flow-rate curves, the greatest reduction is
usually obtained with backwardly curved blades and the least with
forwardly curved blades. For equal design efficiencies, the net power
for reduced flow rates near design should be very nearly the same,
regardless of the type of impeller.
Ze
Chapter I]
Axial-Flow Fans
As the name
implies, the direction of the flow through an axial-
flow fan is predominantly axial, that is, parallel to the axis of rotation. Ideally, there is no velocity component in the radial direction.
But an increase in the tangential component is necessary if energy is
to be transferred from the impeller to the air.
Many of the principles of energy transfer and design, as given in
the previous chapter on centrifugal fans, also apply to axial-flow
fans. There are some points of difference, however, but before discussing them, it is convenient to name certain dimensions. The nomenclature outlined below may differ from that used by some other
authors because there is no general agreement on the method of
specifying angularity. The method used here is to specify angularity
from a tangential reference line, unless otherwise noted. (Some designers prefer to use an axial reference line.)
The discussions that follow are concerned
with the aerodynamics
of axial-flow fan design. As already noted in the chapter on fluid
flow, a mathematical model can be constructed for any flow situation, and various assumptions can be made to simplify that model.
What is done here is similar to the one-dimensional, incompressible,
steady-flow analysis that was made in the preceding chapter on centrifugal fans. Also, some empirical data are given. The purpose of
this discussion is not to provide a complete design method. (More
complex models are needed for that.) Rather, the intent is to show
some of the more important considerations in design so that design
features can be appreciated in the application and operation of fans.
Nomenclature
Figure 11.1 shows a cylindrical section through an axial-flow fan
blade.
Typical vector diagrams
for conditions at the leading (sub-
script |) and trailing (subscript 2) edge planes are also shown.
The distance between the leading and trailing edges is the chord
length x.. The distance along the cylindrical arc between corresponding points on two successive blades is the pitch length xp.
Les
The distance from the chord line to the mean thickness line is the
camber y,. And the camber will vary with chordwise position xp.
The thickness of the blade y, may be constant, or it may vary with
chordwise position x,. The positions of maximum camber and maximum thickness need not necessarily coincide.
BUFFALO FORGE COMPANY
— ING
FAN ENGINEER
11-2
Wi
ie
JVor = Var
Vi=0
U;
Figure 11.1
Blade Design and Nomenclature for Axial Flow Fans
The blade angle 8 at any position along the chord is that between
a line drawn tangent to the mean thickness line and a reference line
drawn in the tangential direction, that is, parallel to the direction of
rotation. The blade setting or stagger angle y is that between the
chord line and a similar reference line.
The fluid angle @ at any position is that formed by the relative
velocity vector W and the linear rotor velocity vector U.
A constant annular area is needed to produce a constant axial
component V, of the absolute velocity, as indicated on the vector
diagrams.
The purely axial absolute velocity on the leading-edge vector diagram implies that no prerotation exists. The tangential component of
the absolute velocity V, indicated for the trailing edge produces a
large amount of fluid whirl. A discharge-vane assembly can be used
to transform this whirl energy into pressure energy.
The various lengths and angles can vary with radial position. The
cylindrical section shown is for only one of many radial positions
between the hub (subscript H) and the tip (subscript 7).
A rotor-blade assembly preceded by or followed by a stator-vane
assembly constitutes a “stage.”
CHAPTER
11 — AXIAL-FLOW FANS
11-3
Energy Transfer
As with centrifugal fans, the axial and tangential components of
the fluid forces on the rotor produce axial thrust and torque, respec-
tively. If no radial-velocity component exists, no radial-force component does either, and there will be no radial thrust. Axial thrust
is discussed in the chapter on fan mechanics. The rate of energy
transfer, or the power Y, involved in the production of torque, is
the same as for a centrifugal fan. Rewriting Equation 10.1 on the
basis of axial flow (that is, no radial components) produces
Pa= So (Va Va) = tre Voleoras— cova). (14.1
.
wr
5
c
r
c
This equation expresses the power transmitted to a fluid flowing
at a particular radius r. Since different parts of the fluid will flow
at different radii, the variation of mass flow rate m and the variation
of the change in tangential velocity V:2— V,; must both be taken into
account. The fluid angles a; and a2 may also vary with radius. But
the angular velocity w and axial velocity V, can usually be assumed
constant. The product wr is the linear rotor speed U.
The net energy transfer per unit weight of fluid, or the Euler total
head Hz for an axial-flow fan, can be derived as
Demet
The theoretical head Hg developed
Rag
TTD)
will be the same
in each por-
tion of fluid only if the change in tangential velocity is inversely proportional to the radius. This relationship is a design criterion but not
the only one possible.
The change in relative velocity produces an increase in static pressure across the impeller equal to the change in energy W, — W»2°/2g
disregarding losses. There is no centrifugal effect without radial flow,
so Us — VU,/2e=0PThe energy transfer is largely due to the change
in absolute kinetic energy V2 — Vi" /2g.
If this. kinetic energy appears as whirl at the rotor exit, stator discharge vanes can be used to transform it into useful pressure energy.
Such a stage is usually designed for axial inlet flow without inlet
vanes.
Negative transformation can be accomplished with stator inlet
vanes to produce inlet whirl. The rotor blades should then be designed so that they provide axial discharge flow.
Vaneaxial fans are usually single-stage machines with either inlet
or discharge vanes. Compressors are generally multistage machines
that do not necessarily use purely axial velocity for any but the first
11-4
FAN ENGINEERING
— BUFFALO FORGE COMPANY
and last stages. Tubeaxial fans are single-stage machines without
guide vanes: any energy transformation must take place without the
benefit of guidance.
In designing a single-stage vaneaxial fan, it is convenient to assume a purely axial velocity on both entering and leaving the stage.
To produce the necessary change in whirl, some sort of vortex flow
must be superimposed on the axial flow through the stage.
The choices available are the free-vortex pattern and various forcedvortex patterns. Fans have often been designed for free-vortex flow,
which produces constant head (that is, the same total head in each
particle regardless of radius, H,; = H,2). However, Stepanoff' advocates the full forced vortex or solid rotation, which produces constant
dimensionless head (that is, the same total head per unit of peripheral
velocity squared in each particle, H,,/Un° = Hp/
U2 °).
Incidence and Deviation
The difference between the fluid and blade angles at the rotor
entrance is called incidence a; — B;. The same difference at the rotor
exit is called deviation B: — ao.
Incidence at the design flow rate is a matter of design, as discussed
below under blade angles. Deviation is a function of the geometry of
the blade as indicated by
Xp
B2—
a2=
K(B2—
Bi)
ie
(11.3)
The value of K, which relates the difference between the leading- and
trailing-edge angles 82 — B, and the pitch-chord ratio xp/x- to deviation, varies with both stagger angle and blade form. Various ways of
estimating K are listed by Shepherd. One of these indicates a value
of 0.26 for circular-are blades with a 30° stagger angle.
Deviation, like slip, is affected by any factor that influences fluid
guidance through the impeller.
When a fluid cannot accommodate itself to the guiding surfaces of
a passage, then separation occurs. The aeronautical term stall is
sometimes also used to describe such a phenomenon in turbomachines. Stall may originate at only one part of a blade when the
incidence exceeds a certain value. Rotating stall passes from one
blade to the next. Pronounced separation is accompanied by appreciable circulatory flow.
'A.J. Stepanoff, Turboblowers, John Wiley & Sons, Inc., New York, 1955, p. 56.
°—D.G. Shepherd, Principles of Turbomachinery, The MacMillan Co., New York, 1956, p. 406.
CHAPTER
11 — AXIAL-FLOW FANS
11-5
Performance Characteristics
The ideal performance characteristics of an axial-flow fan, as shown
in Figure 11.2, can be derived from the various energy-transfer relationships. The theoretical total head He is exactly as given in
Equation 10.5 for centrifugal fans. The ideal total head H’; can be
obtained from this by substituting the actual fluid angles @ for the
blade angles 8. When there is no controlled inlet whirl,
H';,=
U’
U Qcota>
g
Aly
(11.4)
which shows the effect of volume flow rate Q and fluid angle a.
The linear rotor velocity U varies with radial position. The area Ao,
through which the fluid must flow, is the total annulus between hub
and tip corrected for blade thickness. According to Equation 11.4,
the ideal head at no-flow (or shutoff) is U’/g. The corresponding
static pressure is never realized: first, because some of the energy will
appear as temperature rise, and second, because the losses involved
in circulating around the blade, etc. reduce the head developed.
At design the ideal head will be much less than at shutoff. This 1s
DESIGN
POINT
(@)
POWER
&HEAD
(H)
—
FLOW RATE (Q) —
Figure 11.2
Theoretical Performance Characteristics for Axial-Flow Fans
11-6
FAN ENGINEERING — BUFFALO FORGE COMPANY
shown in Equation 11.4 for fluid angles less than 90°. The actual
head will be less by an amount equal to the hydraulic losses.
At flow rates over design, assuming the same fluid angle a2, the
ideal head shown in Equation 11.4 is less than at design. The actual
head is even smaller because of greater losses. Also, flow-rate increases are accompanied by negative prerotation, negative incidence,
or both. Either will lead to a reduction in head.
At flow rates below design, the ideal head increases but only until
stalling occurs. At this point the variation of fluid angle with flow
rate may influence head production more than the decrease in flow
rate. Actual head/ flow-rate characteristics often first dip before rising
to the shutoff head.
The ideal power/ flow-rate characteristics of axial-flow fans roughly
parallel the head/ flow-rate curves, as indicated by
fa
Coles
P'e= in( &
Pg
goAs
)
(11.5)
The decrease in the bracketed term usually outweighs any increases
in mass flow rate m over design, so ideal power ’, decreases. At
flow rates below that needed to prevent stall, the actual flow rate due
to circulation around the blade increases with head far faster than
the net flow rate decreases. This produces a power characteristic that
rises towards shutoff.
Overall Design
As was done with centrifugal fans, the design of only a particular
fan for a specific requirement will be treated here. The design of a
line or several lines of fans for a range of requirements will be discussed in the chapter on fan laws. Also, a single-stage fan using discharge vanes will be assumed.
The first step in design is to decide on a speed of operation. This
may be specified or limited because of a requirement for direct connection to the prime mover. Reynolds-number effects favor large,
low-speed units. Economy due to reduced size favors small, highspeed units.
Once the speed has been chosen, the next step is then to establish
a reasonable trial size based on past experience, a trial-and-error
method, or both. The specific speed, as determined by the required
performance and the rotative speed, is useful in establishing the hub/
tip ratio vy and the number, chordal length, and various angles of
the blades, all of which affect the size needed.
The adequacy of the trial size can be checked conveniently by
establishing the blade geometry at the corresponding mean effective
radius and then comparing the expected performance, based on em-
CHAPTER 11 — AXIAL-FLOW FANS
eee
Ait=7;
pirical data, with the requirements.’ (Empirical data covering many
designs are presented in the following sections. Where possible, data
published by various investigators was used to supplement that of
the Buffalo Forge Company.)
The need for adjusting the trial design can now be established, at
least approximately, by calculating the ideal head/ flow-rate relationship, including an estimated deviation effect, and by correcting for
reasonable hydraulic and volumetric efficiencies.
Following any necessary adjustments, the design at several other
radii from hub to tip, based on the required or assumed velocity distribution, can then be completed.
Finally, an appropriate stator-vane assembly can be designed to
match the flow leaving the impeller. The casing design can be finished
by incorporating the best practical inlet and diffuser geometry.
This procedure is detailed in the following paragraphs on design.
Once a reasonable design has been established, it should then be
proven by testing.
Design Radii
The mean effective radius r,, of an axial-flow fan is that radius
which divides the flow into two equal parts. Assuming a uniform
axial velocity across the section, the mean radius, in terms of tip and
hub radii rr and ry, is
a
aia
rrtry
ea
as rr
Ta)
(11.6)
A special symbol v is used for the hub ratio:
ps
aa
(11.7)
The mean effective radius, as defined above, is used in calculating
the pressure and flow-rate coefficients that appear below. The pressure generated at the mean effective radius equals the total integrated
pressure, whether free-vortex or solid-rotation flow is assumed.
Experience shows that there is an optimum hub-tip ratio v for
each value of specific speed N,. High ratios are needed for highpressure fans; low ratios are required when only low pressures
are to
be developed. The relationship between optimum hub-tip ratio and
'As noted throughout this handbook, fan requirements are usually stated in terms of pressure to
be developed rather than head. The preceding material in this and the previous chapter was given
in terms of head. Subsequent material will be given in terms of pressure. The conversionof head
to pressure requires multiplication by the product of the air density p and the gravitational
acceleration g and division by the appropriate conversion factor gv.
11-8
FAN ENGINEERING
— BUFFALO FORGE COMPANY
nnowo
mn
RATIO
HUB
(v7)|
30
40 50 60
80 100 #4150
200
SPECIFIC SPEED 1000 J, (based on pyr in in. wg)
Figure 11.3.
Optimum
300,05
Hub-Tip Ratios for Axial-Flow Fans
specific speed is illustrated in Figure 11.3. A range of values is shown
since there is also some variation with the number and solidity of
the blades.
_ The specific speed N, can be determined from the required flow rate
Q, the fan pressure pr, and the rotative speed N. (See the chapter on
fan laws.) These values, together with the mean effective radius and
the hub-tip ratio, also determine the pressure and flow-rate coefficients
Vin and
Or
5
Oneal
Styee (ee
DP’,
=
unl
rus)
ZATGUN irs
oe
5
=
47° Nrm
28cPr
"(20
nee
gL
Nem)
3
ye
2
eo) and
(11.8)
cP
2p
N rm
(11.9)
Any consistent set of units can be used to find the values of these
dimensionless groups. (Both ®’,, and W,, include physical factors.
The corresponding coefficients without physical factors are designated
CHAPTER
11 — AXIAL-FLOW FANS
1129
b'm and Wm in the fan-law chapter.) Blockage due to blade thickness
has been disregarded in Equation 11.8.
Preliminary values of these coefficients can be obtained for a trial
value of rm. Equation 11.6 can then be used with the hub-tip ratio
corresponding
and tip radii.
to the required specific speed to determine
the hub
Number and Solidity of Blades
The optimum number of blades np is also a function of specific
speed. The optimum number can be approximately determined from
the hub and tip radii, as shown by
Oru
Oe
ae
Ov
ae
The solidity of the blades, as indicated
(11.10)
by the ratio of the chord
length to the blade spacing x./x,, more or less determines the flow
rate per revolution at design for a given blade angle. The blade
spacing, or pitch, x, is simply the circumference at a particular radius
2mr divided by the number of blades m,. The chord length of the
blade x. is the distance between the leading and trailing edges at the
same radius.
From an aerodynamic standpoint, the chord length should increase
from hub to tip. From a structural standpoint, the reverse is preferred. As a compromise, however, many designers use an almost
constant chord over the entire blade length.
The blade spacing increases from hub to tip. A pitch-chord ratio
near unity is often used at the mean effective radius. But very good
efficiencies have been obtained with pitch-chord ratios of 4:1 or
higher.
The effect of pitch-chord ratio on flow rate is included in Figure
11.4. This chart indicates a preferred value of ®’,(xp/x-)m for each
value of specific speed N;. However, some variation from the preferred value can be tolerated. (The chart was based entirely on the
performance of rather conventional designs of vaneaxial fans without prerotation.) The pitch-chord ratio xp,/x- corresponding to the
required
flow-rate coefficient
® and the chart values of (®xp/xc)m
can be determined by simple algebra.
Figure 11.4 also plots the optimum values of Win(xp/Xc)m VS. specific
speed Ns. The pitch-chord ratio (xp/Xc)m corresponding to the required pressure coefficient and the chart value of Vin(xp/Xc)m Must
agree with that calculated from (®‘nxp/Xc)m. Although some variation can be tolerated without sacrificing efficiency, any large discrepancy between the two calculated values of (xp/Xc)m usually indicates that a different trial value for the mean effective radius should
be investigated.
SPECIFIC SPEED 1000 JN, (based on per in in. wg)
Figure 11.4
Mean
Pressure and Flow-Rate Coefficients for Axial-Flow Fans
Decreasing the pitch-chord ratio (that is, spacing blades more
closely) improves fluid guidance and, therefore, (within limits) increases the pressure. This effect is indicated in Figure 11.4. Relative
guidance is also a function of the discharge-blade angle.
Blade Angles
Axial-flow blade designs are usually based on a uniform axial
component of velocity across the annulus for the entire blade passage. Without inlet guide vanes, there will be no prerotation at the
design point. The blades can be twisted in various ways to produce
different vortex-flow patterns including those necessary to give constant head or constant dimensionless head along the radius.
The leading-edge blade angles 8; should be designed to match the
fluid angles a, at the rotor inlet. Occasionally, a slight positive incidence will be wanted in a fan with a solidity less than unity in order
to get the maximum pressure possible. Small values of negative in-
cidence are sometimes incorporated into the design of a fan with a
solidity greater than unity to reduce the danger of stall.
The linear rotor velocity U varies directly with the radius. There-
CHAPTER
11 — AXIAL-FLOW FANS
ne
11-11
80.
Wn
Figure 11.5
Mean Camber for Axial-Flow Fans
fore, the relative velocity W, increases and the fluid angle a; decreases with the radius from hub to tip. If the blade angles B; are to
match the fluid angles on entering, then the leading edge of the blade
must be twisted accordingly.
The trailing-edge blade angle (82), at the mean effective radius
must be designed to produce the required pressure. This angle can be
determined from the theoretical fluid angle (a2), based on Equation
11.4 and on the expected deviation 82 — a from Equation 11.3. It
can also be determined from experimental] data such as that of Figure
11.5. The value of (B2)m can be obtained, as well, from the chart value
of (B2 — Bi)m and the required value of (8\)m. (Figure 11.5 includes
the effect of fluid deviation, which may explain the spread in camber
values at higher pressure coefficients.) The discharge angles at other
radii can be determined by constructing the appropriate velocity
triangles.
11-12
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Free-vortex design requires that the product of the tangential component of the absolute velocity V, times the radius r be constant
along the blade from hub to tip at both the inlet and the outlet. The
resultant constant change in whirl leads to a constant head H generation at all radii. (Figure 11.5 is based mainly on designs ofthis type.)
Solid-rotation design requires that the quotient of the tangential
component of the absolute velocity divided by the radius be constant
along the radius. The change in whirl and, therefore, the head generation is proportional to the square of the radius. This leads to a constant dimensionless head Y,, at all radii.
Various other designs based on other forced-vortex patterns are
also used.
The performance of a fan can be altered by changing the blade
setting or stagger angle y. Increased stagger produces an equal increase in inlet and discharge angles and, therefore, an increase in
flow rate, without affecting pressure. With limited changes, the efficiency is practically constant. The change in flow rate is proportional
to the change in the tangent of the inlet angle 8).
Blade Profile
The inlet angles 8, discharge angles B2, and the chord length x, at
various radii can be determined from the preceding data.
The mean thickness line of the blade should be a smooth curve
whose tangents form the necessary angles with the direction of rotation at the leading and trailing edges.
Various combinations of circular and parabolic arcs are used for
the mean line. One convenient method of construction is to place the
point of maximum camber (x)max at the same chord-wise position as
the intersection of the two tangents mentioned above. The amount of
the maximum camber (’5)may Should be one-half the displacement of
the intersection above the chord. Many other tangent lines can be
constructed by dividing the edge tangents into a number of equal
segments and then connecting corresponding points by straight lines.
The blade profile should generally be as thin and as polished as
possible. Streamlined, airfoil-shaped sections are usually used, although thin sheets of constant thickness also often give good results.
Most good airfoils have about the same thickness ), variation with
chordwise position. The maximum
thickness is usually about 10% of
the chord; it should be located 30 to 50 percent of the chord from the
leading edge. The leading edge should be rounded to tolerate variation in incidence. Ideally, the trailing edge should be tapered to a
point, but, for structural reasons, this, too, is rounded. The maximum thickness can increase toward the hub for the same reason,
especially if the chord does not decrease toward the tip.
CHAPTER
11 — AXIAL-FLOW FANS
11-13
INLET CONE
DIFFUSER
DIFFUSER GUIDE VANES
Figure 11.6
Casing Design for Fully Streamlined Vaneaxial Fans
Discharge-Vane and Casing Design
The discharge vanes transform the kinetic energy produced by the
impeller in the form of whirl into more useful pressure energy. To
make
this transformation
efficiently,
the
air discharged
from
the
impeller must be guided through a gradual turn until the tangential
component is eliminated. If the resultant axial velocity is still too
high, a diffuser can be used for additional energy transformation.
(The discharge vanes and diffuser are sometimes combined.) The
entrance angles of the discharge or diffuser vanes should match the
fluid angles at the impeller exit within a few degrees. The exit angles
should be 90° (that is, axial) at all radii. And the axial distance
between the blades and the vanes should be, roughly, 10% of the tip
diameter. Closer spacing may be preferred for operation at the design point only. But larger spacings are preferred for operation at
capacities other than design because the wider spacing allows more
time for the air to adjust itself for any difference in fluid and vane
entrance angles. In a good design, the number of vanes and their
length are related. The solidity at the mean effective radius should be
near unity. The number should also be selected to provide a reason-
able hydraulic radius. And vane length at the hub can be somewhat
shorter than at the tip to compensate for the closer spacing.
The casing itself should be cylindrical over the blades. In order to
11-14
FAN ENGINEERING
— BUFFALO FORGE COMPANY
limit leakage, the clearance at this point should be the minimum
practical value. Radial running clearances of about 0.001 inches per
inch of impeller OD are often used where both the impeller and the
housing can be machined. Using larger clearances means sacrificing
some efficiency.
Additional guiding surfaces are needed inside the casing. They
should provide a smooth transition between the annular passage
over the hub and the cylindrical (or other shaped) passages both upstream and downstream. Streamlined, stationary nose pieces, tail
pieces, or both, supported by vanes, can be used to house the bearings or other drive elements. One or the other of these devices can
be incorporated in the rotor assembly.
Depending on inlet and outlet conditions, inlet bells or diffuser
cones may also be required for efficient operation.
Chapter 12
Fan Laws
The fan laws are a particular version of the more general similarity
laws that apply to all classes of turbomachinery. They express the
relationships among the performance variables for any two fans that
have similar flow conditions. The variables include: fan size D, fan
speed N, fan air density p, fan flow rate Q, fan total pressure per, fan
velocity pressure pry, fan static pressure prs, fan input power &, fan
total efficiency m7, fan static efficiency ns, compressibility coefficient
K,, and sound power level Ly. Alternative variables include: fan mass
flow rate m instead of fan volume flow rate Q and fan specific energy
(or fan work) yr instead of the various fan pressures per, Pry, and prs.
The symbols chosen to represent here the various fan performance
variables are a compromise between the simplest and the most clear.
For maximum clarity, each of the symbols should have a subscript F;
however, this has been omitted from many for simplicity. The subscript F is retained as part of the fan pressure symbols to avoid any
possibility of confusion with the pressure at a point. In some works,
the distinction between fan pressure and pressure at a point is made
by using P for the former
and p for the latter.
In this handbook,
however, all pressures are denoted by p. The symbol for power is A
with subscript 7 designating impeller power, subscript s designating
shaft power, and subscript o designating output power.
Derivation
The fan laws, like the similarity laws, can be derived by various
methods of reasoning. Closely examining the momentum equations
will lead to the correct conclusions. Dimensional analysis can also
be used. Various texts present these methods in various ways. The
fan laws can be based on either compressible or incompressible flow.
Although incompressible-flow fan laws are sufficiently accurate for
many fan engineering applications, compressible-flow fan laws should
be used whenever the difference due to compressibility coefficient
exceeds the accuracy desired for the calculation.
Jorgensen and Bohanon' derived compressible-flow fan laws,
which are the basis for the variations listed in Table 12.1. The incompressible versions, which were listed in previous editions of this
'R. Jorgensen and H.R. Bohanon, “Compressibility and Fan Laws,” ASHRAE Paper No. 2333,
presented at Atlantic City, 1975. This derivation is based on an assumed polytropic process
through the fan based on the total pressures, total temperatures, and total densities at the inlet
and outlet. The fan air density is taken to be the stagnation air density at the fan inlet. The fan
flow rate is the volume flow rate based on fan air density.
12-2
FAN ENGINEERING — BUFFALO FORGE COMPANY
handbook, can be obtained by setting the compressibility coefficient
ratio equal to unity. Table 12.2 lists Fan Law | on the basis of mass
flow rate and fan work. Fan Laws 2 through 10 could also be listed
on this basis but are omitted because mass flow rate and fan work
are not yet in general use.
Applications
The fan laws can be used to predict the performance of a fan, provided that certain requirements are satisfied. The basic requirement
is that the performance at the corresponding points of rating for an
homologous fan be known. Two or more fans are said to be homologous when their air passages are geometrically similar. Two or
more homologous fans are said to be operating at corresponding
points of rating if the positions of the operating points, relative to
shutoff and free delivery, are the same.
The fan laws are listed in Table 12.1. Any of the ten variations can
be used to predict the performance of a fan (subscript a) when the
performance of another fan (subscript b) is known. These ten are
simply mathematical manipulations of one fundamental set of relationships. The different variations have different groups of dependent
and independent variables. Density and compressibility coefficients
are always shown as independent variables, but velocity pressure
and sound power level are always dependent variables. Note that an
entire set of dependent variables must be calculated whenever a particular set of independent variables is changed. Also note that efficiency and point of rating are constant for all fan law applications.
Whenever the flow can be considered incompressible, the ratio of
compressibility coefficients can be taken to be unity, thereby simplifying many calculations.
The choice of fan law variation to be used in any particular situation will depend
on the independent
variables.
For instance,
if a
new D and a new N are specified, as is frequently so when drawing
performance curves, then Fan Law | should be used. This is illustrated in Example 12.1. If the performance of a given fan is to be
varied, then D will be constant and must be one of the independent
variables. Fan Law I, 2, 3, or 4 may be used, depending on whether
N, prr, Q, or # is specified, as illustrated in Examples 12.2 and 12.3.
Fan Laws | and 5 lead to some very useful concepts, which are
discussed in the sections on equivalency, power formulae, specific
speed, specific diameter, and specific sound power level.
Different methods of rating fans could be developed using various
combinations of the ten fan law variations. Methods for rating a
particular size of fan can be developed from the first four variations
because diameter is an independent variable.
However,
methods for
determining the size may call for one of the last six variations.
Some of the more common rating methods are described in the
chapter on selection.
CHAPTER
For all fan laws:
Table 12.1
Fan Laws
772 = nm and (point of rating).
No.
Dependent Variables
la
On
12-3
12 — FAN LAWS
(point of rating),
Independent Variables
=i0n
£ Wa
Lw
2a
Ou =O
2d
PFva
2e
L
4a
Qo =O
+
Da
70 ior (
Ds
) 4+
a)
Na
Pa
50 ior ( ) + 20108(
Pb
Np
(
=prvb
X
Lwp
AF
()
Da
20 ior (
Dp
x
) ae
(Pal
) = se a)
( )x
PFTa
PFT».
PFTa
ZB) toe(
PFTb
Pa
Pb
Koa
Koo
y
=<2-4
FAN ENGINEERING — BUFFALO FORGE COMPANY
Table 12.1 (cont.)
Fan Laws
For all fan laws: 772 = 7» and (point of rating). = (point of rating),
No.
Dependent Variables
Independent Variables
Da\%2
4
;
Na
=Npo
X
;
4
——
x
(2
ay
(#
oe)
(Bx
x
4e
Lwa=Lws
— 13.3 log ($e
ba
De De
i
Ne hh
cs
B.=BPxX
(#) x
(22) x
(
st pma=pox
(1)x
(2)x
6:
OX
SD
fra =loew 4
6a
Da
6b
PFT a= PFTb
&
Ph= Px
6d
PFva= PFvb
x
6e
Lwa=Lwo
+ 23.3 log
it
'D, =
Ib
.
1/2
Rae
-1/4
x
(=)
x
PFT
SK
(=
(e
Pb
ste + 20 log ro)+ Olog
X
G
x
Ge
(
N
(Np2
or
3
,=
Q
1/2
AEN\
x
+ 16.6 log
+
(&
Qo
a
A,
@)*&
Cl = PFvb
PFva
=Dp
x
Kpp
4d
)
(£ )
-
x
Pr»
Dex
x
Q%
Gal
aa7,
No
=) + 26.6 lo (i) + 201
aQ
BN,
1/2
Ben) x
(3
3/2
Be) x
(2
Ne
Np
(2%)
Np
t
BPa=Be=Px
Pz
(=)
"x
=
7d
Prva = Prvp X
Tsale—
laa
5/2
x
x
eS
(4)
wh.
BN
9)
po
es
12
Pb
2
1/2
Pa
aja!
Kpa
Pb
s
Kop
be
Sex
Kou
(ae
-3/2
Keay
Kopp
1/2
3/2
CHAPTER 12 — FAN LAWS
Table 12.1 (cont.)
12-5
Fan Laws
For all fan laws: 172 = nm and (point of rating). = (point of rating),
No.
Dependent Variables
Independent Variables
Te
Lve=Ly + 35 log (2) =
PFT
8a
Da =D,
X
)
8c
Prta = Pr
X
(%)
8d
DFVa= Prve X
(#)
ib
8e
Lwa=Lwe
-1/4
ib
20 lor( Ne) — 15 log ee)
Np
a
x
(£)
x
Qe
x
+
x
l ) XK (ke
a
b
x
1) x ( 1 )
50s
+
by
5
10log
Ze)
Da
=D,
X
9b
Na
=No
X
p as
9d
Lwa=Lw»
eo
+
10b
=O. =Qs
X
=
Kpb
10 log
te)"
me
x
5/4
x
2) 3/4
(&)"
Zy
x
aaeay
(l .
x
OV
+
10log
on
a,
+
S
&
Oe
8log
Np
ah
Gay
ee
(= dies
a
tallSR
tas
—
Dl/ld>
|
—
|
(4:)"x
Zey"x
GY
<b
,
es
Re
Z)
x
(x)
x
10d
14 log
ma
m=
Da
Ze)"
prve=prvs X
Olog
een)”
eee)
Lwa=Lw +
Ke :
-1
oe
10e
Kpp
-1
En
PFva= Prve X
9e
Pb
Z) —wn$) = onl)
20 uous
—
-
9a
Kpa\'2
fs) ai n)
Q
1
a\/4
x
Os
1
ib
p
\3/4
+
a)
SEE
SN
|
NS
ES
Ee
6 log
Gay
Pa
Be
Note that an entire set of dependent variables must be calculated whenever a particular set of
independent variables is changed.
12-6
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Table 12.2.
No.
Dependent Variables
la
Ma
=m»
x
1b
Vra
— YFb
x
ie
GA =a,
x
Fan Law 1 Based on mand yr
Independent Variables
[
Gi) »
(
D
obra =r 3 70 10¢( =) 4
solog(**)
+ 2010s(#)
Note that Fan Laws 2 through 10 could also be listed on the basis of mass flow rate m and fan
work or fan specific energy yr.
Example 12.1
Use of Fan Law 1
Given a 36.5-in. diameter fan delivering 10 000 cfm at 1.85 in. wg,
0.075 lbm/ft, 600 rpm, and 3.4 hp, find the corresponding performance of an homologous fan of 73.0-in. diameter at 0.070 lbm/ft’
and 1200 rpm.
Use Fan Law | because the known quantities (independent variables)
are D, N, and p. Assume incompressible flow.
On
=( 7310") x( 1200\ )| x
QO»
36.5
600
Pera
(73.0)
—, (1200)*_,
IO
1200\°*
react (36. 3) x (a)
Ff
Bp,
(1)
0.070"
x (ass)
x(1) = 16.00,
=
x(1) =
14.93, and
0.070)!
\36. 2) x (sou) “ (ang) . (:) =e
QO. = 10000 X
16.00 = 160 000 cfm,
Prra=
1.85 X
14.93=
P=
3.4
27.62 in. wg, and
X 238.93 = 812.4
hp.
Note that the same factors could be applied to other ratings of the
36.5-in. fan, so that sufficient points could be determined for the
73.0-in. fan to facilitate drawing constant speed curves.
CHAPTER
EC
eee
Example 12.2
12 — FAN LAWS
ee
12-7
ee Ae
Use of Fan Law 3
Given a fan delivering 10 000 cfm at 1.85 in. wg, 0.075 lbm/ft*, 600
rpm, and 3.4 hp, find the corresponding performance of the same
fan at 12 000 cfm and 0.075 Ibm/ft*.
Use Fan Law 3 because the independent variables are D and p
(which are to be held constant), and Q. Assume incompressible flow.
=3
iT
|
]
—4
2
1
1
Na = 600 x (1) lec) x(1) x(1) = 720 rpm
PFTa = 1.85
x (1) (Gam)
FP, =3.A4
<(1)
-4
x(1) x(1) = 2.66
in. wg, and
3
= (Ga)
1
2
x(1) x(1) =59
hp.
Note that the fan must operate at the same point of rating, which
will happen only if the system has a characteristic that requires 2.66
in. wg at 12 000 cfm and 0.075 Ibm/ ft’.
Example 12.3.
Use of Fan Law 4
Given a fan delivering 10 000 cfm at 1.85 in. wg, 0.075 Ibm) ft’, 600
rpm, and 3.4 hp, find the corresponding performance of the same
fan at 5.0 hp and 0.060 lbm/ ft’.
Use Fan Law 4 because the independent variables are D (which is to
be held constant), Y, and p. Assume ne aS ae flow.
:
Ou = 10000
PFTa >=
HH
0.060
f
30)" (208) ": x(1 i = 12250 cfm,
(1, x (3
1.85x(1)
SHES
SING
0.060
wee
;
in. wg,
x (32) x (208) (a): = 2.22
and
Nae~
-§/3
600
0.060
(1) x(G
30)"Scio
=]/3
1/3
x(1)
=73735 rpm :
Note that the fan must operate at the same point of rating, which
will happen only if the system has a, characteristic that requires 2.22
in. wg at 12 250 cfm and 0.060 Ibm/ft*.
ee
Ee
a
a
SS
12-8
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Compressibility
The effects of compressibility are accounted for in the fan laws by
the inclusion of a compressibility coefficient K, for each of the two
fans. This coefficient is a function of the polytropic' exponent n, the
absolute total pressure pr at the inlet, and the absolute total pressure
Prat the outlet:
Pn
(12.1)
The polytropic exponent can be evaluated
ponent y and the polytropic efficiency 7p:
n
2
il
using the isentropic ex-
a
-Vieoae ie
(1222)
The polytropic efficiency can usually be considered equal to the fan
total efficiency nr without serious error:
Ae
n—-1
Te
Kp
To =
a
7
=
aann
(12.3)
Equation 12.3 can be solved directly when the point of rating is
given since nr is then known. Otherwise, an iteration procedure is
required. Convergence is quite rapid if a reasonable efficiency is assumed to start.
Figure 12.1 is a graphical representation of Equation 12.3.
Jorgensen and Bohanon have shown that the evaluation of K, can
often be facilitated by the use of a pressure-rise coefficient x, a
temperature-rise coefficient z, and
2
Ee
In(i + x)
ese yarn
(12.4)
Figure 12.2 is a graphical representation of Equation 12.4. The
values of xand z can be determined from Equations 12.6 and 12.7.
'The assumption of a polytropic process between end states that are defined by total pressures is,
of course, only an approximation of the real process through a fan. Nevertheless, the effects of
compressibility are predicted quite well by this “total polytropic” assumption.
CHAPTER
1.04
12 — FAN LAWS
12-9
1.08 1.12 1.16 1.20 1.24 128 132 136 7140
ABSOLUTE PRESSURE RATIO (pr2/pr:)
Figure 12.1
Compressibility Coefficient
The fan laws for compressible flow include the ratio of the compressibility coefficient for the predicted fan Kpa to the compressibility
coefficient for the tested fan K,», raised to various powers. The evalu-
ation of this ratio can also often be facilitated by using the technique
that Jorgensen and Bohanon have developed. They showed that
Koa _
(2a)
Kop
(a) (} (eee i) ( sph
(%6
Ya
peal )
Ye
(12.5)
The pressure-rise coefficient for the tested fan x, is a function of
the fan total pressure prm and the absolute total pressure pri, at the
inlet and can be evaluated from test data:
__
a
PFTb
Prib~
(12.6)
The temperature-rise coefficient for the tested fan zp is a function of
the isentropic exponent yz, the fan input power ,, the fan flow rate
Q», and the absolute total pressure pip at the inlet and can be evaluated using test data:
Mix
(2)
Yb
Qoprib
Zh
A
.
2a)
The conversion constant Cg has a value of unity in SI units and 6354
in U.S. customary units.
0.
‘
80
0.01
0.02
003
Figure 12.2
Adapted from the data of AMCA:
Standard 210-74, 1974, p. 39.
O04
_ 005
0.06
0.07
0.08
0.09
Compressibility Coefficients
Laboratory
Methods
of Testing Fans for Rating,
AMCA
CHAPTER
12 — FAN LAWS
12-11
The procedure for evaluating the pressure-rise and temperature-rise
coefficients for the predicted fan varies, depending on which fan law
is being used.
For instance when using Fan Law 1, the temperature-rise coefficient Za is
-=a(3)
GS) (4) (2) Ga) =.
(12.8)
The pressure-rise coefficient x, for the predicted condition
then be evaluated using
Die)
i
ea) aoe
|
Ihe
“ rae) (eno and
(12.9)
a
—
Zb
Xq
=
elnl + xa)
can
ff
a
a
—
ib
(12.10)
Finally, the ratio of compressibility factor Kpa/K,s can be evaluated:
Tee ie) Ge acme),
(12.11)
The isentropic exponents ya and ys for the two conditions can be
calculated from information about the two gases. If the two conditions are the same, the last two ratios cancel each other.
A similar procedure can be used with Fan Law 8 except that
2B) (5)C2) Ga) Co): (12.12)
A slightly different procedure is required for Fan Laws 2, 5, 7,
and 9. The differences are
=.
PFTa
PTia
r= x0(F) ()
Ind + 20) = ind +2)
(Gey)
iy
}
(em)
(12.13)
(Ge 7) and
(12.14)
12-12
FAN ENGINEERING — BUFFALO FORGE COMPANY
Zag ene
Equation
ee
12.3 can be used with Fan
Laws
(12.15)
3, 4, 6, and
10. If the
point of rating is not known, an iteration procedure must be used.
Example 12.4
Use of Fan Law 1 - Compressible Flow
Given a 36. 5-1
-in. diameter fan delivering 10000 cfm at 1.85 in. wg,
0.075 lbm/ft*, 600 rpm, and 3.4 hp, find the corresponding performance of an homologous fan of 73.0 in. diameter at 0.070 lbm/ft’,
1200 rpm, 29.92-in. Hg inlet pressure and 1.4 isentropic exponent.
Use Fan Law | as in Example 12.1, but correct for compressibility.
Prib = 29.92 X 13.62 = 407.5 in. wg,
ess)
X>= 4075 ~ 0.004540,
Zo
14—1
1.4
6354
3.4
= 0.001 515,
10000 X 407.5
Za = 0.001515 X 14.93 = 0.022619, (14.93 from Example 12.1),
In(1.022619)_
In(I+ xa)= In(1.004540) in(LOOlsi3) = 0.066926,
Fen = COO
| = LNG.
Keapa __ 0.022619
0.004540
= 0.9793.
Ky»
0.001515 0.069216
Qa = 160000 X 0.9793 '= 163 400 cfm,
Prra = 27.62 X 0.9793 |= 28.20 in. wg, and
Pag = 812.4 X 0.9793"! = 829.6 hp.
The errors introduced in Example 12.1 by assuming incompressible
flow are about 2% each at this point of rating for Q, prr, and &.
Example 12.5
Use of Fan Law 3 -
Compressible Flow
Given a fan delivering 10000 cfm at 1.85 in. wg, 0.075 lbm/ ft’,
600 rpm, 29.92-in. Hg inlet pressure, and 1.4 isentropic exponent,
find the corresponding performance of the same fan at 12000 cfm
and 0.075 lbm/ ft’.
Use Fan
Law
3 because the independent
(which are to be held constant), and Q.
variables are D and p
CHAPTER 12 — FAN LAWS
eeee
Prib = 29.92 X 13.62 = 407.5 in. wg,
AEE
X= Fag = 0.004540,
_ 14-1
6354X%34 _
zo"
4
10000
x407,5 — 2-00!515,
— 0.001515 In(1.004540) _
Ko»=~)004540 In(1.001515) > 02°
rp = 10.000X1.85 X 0.9985 _ 9 ass
6354 X 3.4
Prta ~ 2.66 from Example 12.2,
Prra ™ 2.66 + 407.5 = 410.2,
shed (ear
FKORSS _ ‘|
= 0.9978,
410.2
ae |
407.5
Na = 720X
0.9978
= 719.5 rpm,
0.9985
= 2.66 X
DFTa
0.9978
= 2.658 in. wg,
0.9985
Pu =5.9X Gaon
0.9985
—
ia
2
= 5.89 hp, and
12000 X 2.658 X 0.9978
= 0.850.
6354 X 5.89
Since 7 differs from the value used to compute Koa, recalculate:
DFTa —
2.658,
Pra = 410.2, and
Hise [(or32) ors
pa
‘|
= 0.9978.
This is nearly the same value that was obtained using 0.855 so:
12-13
12-14
FAN ENGINEERING — BUFFALO FORGE COMPANY
Na = 719.5,
Prra = 2.658,
Py = 5.89, and
nra = 0.850.
The error introduced
flow is insignificant.
in Example
12.2 by assuming
incompressible
Equivalency
Sometimes the concept of equivalency can be used to facilitate
comparisons or calculations. Two equivalency concepts that are frequently used in fan engineering are equivalent incompressible values
and equivalent total pressure.
Equivalent incompressible values can be defined as the values that
a particular fan, at a particular speed and a particular density, would
have if the fluid were incompressible rather than compressible. Fan
Law | can be used since diameter, speed, and density are independent
variables and can be held constant. It follows that
01= OK,
Divi
PrrKp,
FP, =
Q), peri, and
and
PRK.
(12. 16)
Y, are the incompressible values of flow rate, pressure,
and power. Kp; = 1.0. Q, prr, Y, and K, are the corresponding com-
pressible values. Fan performance data can be reduced to equivalent
incompressible values for comparison purposes. This is one step
toward the development of dimensionless coefficients (discussed below).
Avoid the use of equivalent incompressible values for anything
other than comparisons, since the only real values for a fan are
the compressible values. (The fluid handled by a fan is always
compressible.)
Equivalent total pressure prre is the total pressure developed by a
particular fan, at a particular speed and a particular reference air
density p., which is equivalent to the required fan total pressure per
at the required density p. From Fan Law Ib,
n= oa8) (FE).
PFTe— PFT
(12.17)
The reference density pe will be standard air density if the reference
data are prepared for standard density. This concept is particularly
useful when making selections from published data that have been
CHAPTER
12 — FAN LAWS
12-15
prepared for standard air conditions. (See the chapter on fan selection
for examples.) Often, calculations can be simplified without excessive
loss in accuracy by assuming the compressibility ratio K,/Kpe to be
unity.
Power Formulae
The output power , of a fan is the rate at which useful energy is
delivered to the gas stream. Based on the total polytropic assumption,
.
OP
a
Po
Oprrk,
eee
(gat
(12.18)
This relationship of fan flow rate Q, fan total pressure prr, and compressibility coefficient K, is expressed in Fan Law Sc.
The power input to the impeller & can be calculated from the
power output and the polytropic efficiency np:
P=
OprrKp
NpCo
(12.19)
The fan input power & is the sum of the power input to the impeller and the mechanical losses ofthe drive train, if there is one:
GP.=PGP+F,.
The mechanical
losses of the drive train &, should
(12.20)
be considered
separately because they cannot be predicted by fan laws. When fan
law considerations are not involved,
_ OprrK,
F,
nrCo
(12.21)
where the fan total efficiency nr is the ratio of fan output power to
fan input power. If the kinetic energy leaving the fan is not useful,
Prs and ns can be substituted for prr and nr.
The value of Cg is unity in SI units and 6354 in U.S. customary
units.
Fan total head Hr is proportional to prrKp/y, and weight flow rate
w is Oy, so fan input power is
Conr
where C,, is unity in SI units and 33 000 in U.S. customary units.
(12.22)
12-16
FAN ENGINEERING — BUFFALO FORGE COMPANY
Example 12.6
Output Power and Efficiency
Given a fan handling 163400 cfm, 28.20 in. wg, 829.6-hp power input
to the impeller, 29.92-in. Hg inlet pressure, 1.4 isentropic exponent,
0.070 Ibm/ft*, and 1200 rpm, find the output power and the total
efficiency.
Pri = 29.92 X 13.62 = 407.5 in. wg,
2820
X= Gag 5
_
Sn)
0:00920.
14-1
6354X 829.6 _
tenloS 400) 44 075mm Under
, _ 0.02262
Ky = 9.06920
In 1.06920 _
In 1.02262 pa
es
P, = 163400 X 28.20 x 2:2778
= 709.1. and
6354
Oooh ee
NT= G596 — 0-855.
This is a supplement to Example 12.4.
Specific Speed and Specific Size
Specific speed N, for a given fan at a given rating is the speed at
which an homologous fan would have to operate to produce a fan
flow rate of unity (Q; = 1) and a fan total pressure of unity (prrs = 1),
at unit density (ps; = |) and the same point of rating. From Fan Law 5b,
2
=
NO"?
p4
ss 3/4
1/4 *
prr’ Kp
(12.23)
The unit of specific speed will be the same as that of fan speed N.
The value of specific speed will depend on the system of units used
for fan flow rate Q, fan air density p, and fan total pressure prr.
(Compressibility coefficient K, is frequently omitted.)
Specific size Ds is the size of the homologous fan referred to above.
From Fan Law Sa,
Dprr'!
piso Ke.
(12.24)
The unit of specific size will be the same as that of fan size D. Its
CHAPTER 12 — FAN LAWS
12-17
ho
=
DA
AIRFOIL BLADES.
_L. BACKWARD CURVED BLADES
SPECIFIC
DIAMETER
inches
D,.
—
Hx
RADIAL TIP BLADES ©
MW
RADIAL BLADES—
CB
RADIAL BLADES =~
_ BVS . FORWARD CURVED BLADES |
met EOE SPEED Nse — spel
AXIAL FLOW FANS
MMP
REROLINE!
OPUS
om
a3! ANEAXIALS”
: OPTIMUM BLADE
TER
inches
Dye
— postion) —
2
ees
OR:
_ DECREASINGsoupty
apg
EN
CENTRIFUGAL.
om
SPECIFIC
DIAM
>
NR
,00
SPECIFIC SPEED Ns. — rpm
Figure 12.3
TOTAL
EFFICIE
%-
Scoa
(==)
t woO
Specific Speeds and Specific Sizes for Various Fans
12-18
FAN ENGINEERING — BUFFALO FORGE COMPANY
value also depends on the system of units used. Another version of
specific speed Nee is based on equivalent total pressure prre:
No"?
Dee ae agien
(12.25)
This amounts to dividing Equation 12.22 by pe’, so that for standard
air Nse = 6.978 Ns. Similarly,
Dprte si
Dse =
51/2 p 1/4 *
(12.26)
This is obtained by multiplying Equation
standard air Dse = 0.5233 Ds.
12.23 by p,'*, so that for
Similar,
but
dimensionless,
QO K,’
quantities
are
speed
coefficient
and diameter coefficient, which are discussed under dimensionless
coefficients.
Figure 12.3 illustrates the relationships among specific speed, specific size, and efficiency for various types of fans. These relationships
are useful in both design and selection of all types of turbomachinery.
Since for any design of fan there is only one value of specific speed
at the point of maximum efficiency, that value serves to identify the
particular design. The same is true for specific size. If either specific
speed or specific size can be established from the requirements of an
application, only those designs with corresponding identifying values
need be considered as possible selections.
Sound Power Level and Specific Sound Power Level
The fan laws for sound are given in Table 12.1. Additional fan law
variations could be written with sound power level Ly as an independent variable, but for simplicity, sound power level is always
listed as a dependent variable in this table. Compressibility has been
omitted from the sound laws because compressibility effects are
insignificant compared to the uncertainties in sound measurement.
The relationships embodied in the sound laws have been verified by
Madison and Graham’ in the Buffalo Forge Company laboratory.
The overall sound power level of a fan can be predicted from the
overall sound power level of an homologous fan at the same point
of rating. For reliable predictions, both fans must have good bearings
and must be in good balance.
The sound spectrum for a fan may or may not be predictable by
fan laws from the spectrum for an homologous fan at the same point
of rating. Similarity requires that corresponding frequencies (e.g.
blade-passing frequencies and harmonics) be equal. Spectra will be
'R.D. Madison and J.B. Graham, “Fan Noise Variation with Changing Fan Operations.” Trans.
ASHRAE, vol. 64, 1958, pp. 319-340.
CHAPTER
12 — FAN LAWS
12-19
similar only when fan speeds are equal. Various methods of estimating spectra are discussed in the chapter on fan noise.
Specific sound power level Lys is the sound power level of an
homologous fan when producing a fan flow rate of unity (Q, = /) at
a fan total pressure of unity (per; = /) and the same point of rating.
From Fan Law Se,
Lws = Lw— 10 log (Oprr).
(12.27)
The unit of specific sound power level is the same as that for sound
power level Lw. The value of specific sound power level will depend
on the system of units used for fan flow rate Q and fan total pressure
prr. A similar, but dimensionless, quantity is sound power level
coefficient, which is discussed under dimensionless coefficients.
Similarity and Deviations
The fan laws are based on similarity of flow for the two fans
whose performances are being compared. There must be geometric,
kinematic, and dynamic similarity.
Geometric similarity requires that corresponding linear dimensions
be proportional and corresponding angles be equal, for the various
flow passages of the two fans. The constant of proportionality is the
ratio of any corresponding dimensions (for example, the ratio of
impeller diameters). Theoretically, thicknesses of parts, roughnesses
of surfaces, clearances between parts, etc. should all be proportional.
Fortunately, some variations can be tolerated without invalidating
the fan laws. However, the effects of any compromise in geometric
similarity should be thoroughly investigated, as discussed in the
section on size effects.
Kinematic similarity requires that corresponding magnitudes be
proportional and corresponding angles be equal, for the various fluid
velocities in the two fans. The constant of proportionality is the ratio
of corresponding peripheral speeds of the impeller. The condition of
kinematic similarity leads to the conclusions of Fan Law Ia: that fan
flow rate, being proportional to velocity times area, is, therefore,
proportional to peripheral speed times diameter squared, which itself
is proportional to rotational speed times diameter cubed.
Dynamic similarity requires that corresponding magnitudes be
proportional and corresponding angles be equal, for the various fluid
forces in the two fans. The constant of proportionality is the ratio of
the inertia forces of two similarly located fluid particles. The inertia
force of a fluid on a unit area is proportional to mass density and
velocity squared. One of the conditions of dynamic similarity leads
to the conclusions of Fan Law Ib: that pressure force per unit area
being proportional to inertia force per unit area is, therefore, proportional to mass density times velocity squared. This leads to fan pres-
12-20
FAN ENGINEERING — BUFFALO FORGE COMPANY
sure being proportional to mass density times velocity squared or to
mass density times diameter squared times rotational speed squared.
The other forces in the fluid are those due to elasticity, viscosity,
gravity, and surface tension. The ratio of the inertia force to these
forces leads to the Mach, Reynolds, Froude, and Weber numbers,
respectively. The concept of dynamic similarity requires that, at
corresponding points in the two fans, Mach, Reynolds, Froude, and
Weber numbers be equal. However, surface tension and gravity forces
are not significant in fans, so in practical applications Weber and
Froude numbers can be ignored.
Viscosity can have a significant effect on fan law relationships, so
Reynolds number should be considered, as discussed in the section
on Reynolds number effect. Elasticity can also have a significant
effect as discussed in the Mach number section.
Size Effects
According to Fan Law 1, the performance of a full-scale fan can
be predicted from the test results for a model of different scale. It is
not always practicable to model every feature of the design. However,
the resulting imperfections in geometric similitude may impair the
accuracy of the predictions. For example, the relative thicknesses of
the parts may differ for structural or economic reasons. Fortunately,
such differences can be ignored in all but extreme cases. The relative
clearances between parts can also easily differ. Such differences,
however, can be critical and should be eliminated by careful design
and quality control. If not, sufficient tests will have to be made to
determine the effect of each variation. The relative roughnesses of
the various surfaces may differ, too, simply because the same materials are used for the construction of both the larger and the smaller
fan. Ideally, sufficient tests should be made to determine roughness
effects also, but this may not always be practicable. Unless the surface is hydraulically smooth for both the larger and the smaller fans,
predictions of efficiency for larger fans will generally be conservative
because the effect of decreased relative roughness is to reduce frictional losses. The pressure coefficients for larger fans will generally
increase because of this reduction. (On the other hand, the work of
Varley’ shows that increased roughness can increase pressure coefficients in pumps. In his tests, the increased pumping action apparently
more than compensated for the increased losses.)
Reynolds Number Effect
The Reynolds numbers for the various flow passages of a fan will
differ because of their differing passage dimensions and fluid velocities. It is convenient and customary to define a single Reynolds
'FA. Varley, “Effects of Impeller Design and Surface Roughness on the Performance of Centrifugal Pumps,” Proceedings of the Institution of Mechanical Engineers,
1961, pp. 955-989,
London, vol. 175, no. 21,
CHAPTER
12 — FAN LAWS
12-21
number Re’ for a fan, based on the impeller diameter at the tip D,
the peripheral velocity at the tip ND, and the mass density p and
viscosity yu ofthe fluid at the inlet:
_ ND’ p
Ha ftppt
(12.28)
Although this number is rather arbitrary, it can
establish whether two fans are dynamically similar.
be used to help
One of the conditions of dynamic similitude is that Reynolds
numbers be equal at all corresponding points in the two fans. When
N or D changes, p or p will have to be changed in order to compensate; for some types of turbomachinery, this can be accomplished by
a judicious selection of fluid. With fans, however, it is not generally
practicable. Any resulting imperfections in dynamic similitude may
impair the accuracy of fan law predictions, as discussed below.
Variations in Re can be produced by changing N or D, or both. By
varying N separately, any size effects that might accompany a change
of D can be eliminated. Tests of this kind by Phelan, et al.’ suggest
that there is a threshold value of Re for every fan design below which
occur gradually increasing deviations from fan law behavior. The
indicated threshold value of Re is: 2.0 x 10° for airfoil-bladed centrifugal fans, 1.0 x 10° for backwardly inclined-bladed centrifugal fans,
and 0.8 x 10° for forwardly curved-bladed centrifugal fans. For
radial-bladed centrifugal fans, no significant deviations were observed
at Reynolds numbers as low as 0.4 x 10°. However, pressure coefficient did gradually deteriorate with decreasing Re. Power coefficient
also generally decreased, but not as rapidly, and even increased for
some points, of rating.
Kittredge’
has derived
a general formula
for estimating the effi-
ciency of a prototype from tests of a geometrically similar model.
He also lists many other investigators’ formulae, most of which are
simplifications of the following:
Caan
p ane Hee
d= m')m
fe
S (Re)
i=!
& f(Re')
(12.29)
This and most of the simplified formulae are based on the premise
that a certain fraction s of the hydraulic losses (1 — m)/7n is shock
losses that follow the fan laws and that are independent of Reynolds
number. The remainder is friction losses that are a functionf of the
'J.J. Phelan, S.H. Russell, and W.C. Zeluff, “A Study of the Influence of Reynolds Number on
the Performance of Centrifugal Fans,” ASME Paper No. 78-WA/PTC-1, 1978.
°C.P. Kittredge, “Estimating the Efficiency of Prototype Pumps from Model Tests,” ASME Paper
No. 67-WA
| FE-6, 1967.
12-22
FAN ENGINEERING — BUFFALO FORGE COMPANY
local Reynolds numbers Re; and have to be summed ¥. If the friction
factors for the various flow passages are similar to those for ducts,
their values depend on the flow regime. The tests by Phelan, et al.
seem to support this. For radial-bladed centrifugal fans, performance
was independent of Re, which suggests that flow was in the wholly
rough zone regardless of speed. This is consistent with the fact that
there are few, if any, points where the flow is not highly turbulent
for this simple design. The more sophisticated designs show improvements with Re increasing up to the threshold value. This suggests
that flow was in the transitional region at least until a speed was
reached at which most of the passages became hydraulically rough.
All this demonstrates the difficulty of using any formulation to predict efficiency improvements. The best technique for establishing
performance at different Re is to test sufficient points over the range
to permit interpolation.
Mach Number Effects
The Mach numbers for the various flow passages of a fan will
differ because of their differing fluid velocities. It is convenient to
define a single Mach number Ma for a fan, based on the peripheral
velocity of the impeller tip and on the speed of sound c for the fluid
at the inlet:
—
(12.30)
Although this number is rather arbitrary, it can be used to help establish whether two fans are dynamically similar.
One of the conditions of dynamic similitude is that Mach numbers
be equal at all corresponding points in the two fans. It is highly
unlikely that two fans will have the same Mach numbers unless they
develop the same equivalent pressures. Any resulting imperfections
in dynamic similitude may impair the accuracy of fan law predictions, as discussed below.
Aside from compressibility effects, variations in Ma produce no fan
law deviations unless one of the corresponding values approaches
unity. When the local Mach number at any point does approach unity,
critical conditions develop, as discussed in the fluid-flow chapter.
Because the flow rate becomes limited, such a condition is usually
described as choking. However, critical conditions are not likely to
occur unless the fan requirements approach those of a compressor
or a passage is highly obstructed.
Dimensionless Coefficients
Table 12.3 lists a number of dimensionless coefficients that are useful in fan engineering, and inspecting this table will show that all these
CHAPTER
12 — FAN LAWS
12-23
coefficients are related to the fan laws. Either SI or U.S. customary
units can be used. For SI units, the formulae can be used directly
without prefixes, but when U.S. units are used, the results must be
adjusted by the U.S. factor. Most of the coefficients are interrelated,
and their relationships are also listed.
Some authors in the field of engineering prefer to use coefficients
with more physical significance. For instance, they like the pressure
coefficient to reflect the ratio of pressure produced to the pressure
corresponding to the peripheral speed at the impeller tip. This leads
to a value of the pressure coefficient that differs, by a factor of 2/7’,
from the value calculated using the listed formula. The various physical factors are listed for convenience in comparing data of the two
different types.
All the coefficients except A are based on the compressible-flow
fan laws, as indicated by the inclusion of compressibility factor Kp.
Often, K, can be assumed to be equal to unity resulting in considerably simpler calculations. However, it is important to include K,
whenever these coefficients are used to examine the effects of small
changes.
The conversion factor g- would ordinarily be included in the formulae whenever per, prv, or & appear. It has been omitted because
its value is unity in SI. The U.S. factor takes g. and all other conversions into account for the following units.
Ibm /ft3
DFT
rpm
Prv
ft
F,
—
ft-Ibm /Ib-s?
Flow Coefficients
Flow coefficient ¢, also called the capacity coefficient, is based
on the relationships in Fan Law la. Perhaps more than any of the
other coefficients, @ can be modified to suit the purposes of the
individual fan designer or author. Multiplying by the factor 4/7
yields the ratio of the actual flow rate to a reference flow rate that
corresponds to the product of the peripheral velocity at the tip and
the circular area based on the tip diameter. The value of the reference
flow rate is not important in itself, so the 4/ 7 factor can be omitted.
However, certain geometric ratios have a great influence on flow
rate, so variations in these ratios should be taken into account when
correlating data. These ratios can be incorporated in a modified
flow coefficient, or they can be stated separately.
12-24
FAN ENGINEERING — BUFFALO FORGE COMPANY
nee
Table 12:3
Name
EEEEEEEEEEEEEE EERE
Dimensionless Coefficients
Symbol
SI Formula
Flow Coefficient
db
OK,/ND°
Pressure Coefficient (total)
w
PrrKp/ pN’*D?
Pressure Coefficient (velocity)
by
Drv/ pN’D’
Pressure Coefficient (static)
Us
(prrKp — prv)/ pN’D
Power Coefficient
nN
PK,| pN’D°
Efficiency (total)
nt
OprrKp/ FB
Efficiency (static)
ns
nr(PerKp — prv)/ PrrKp
Speed Coefficient
o
NO'” p*/ per! Kp'"
Diameter Coefficient
6
Dpre |p ORs
Throttling Coefficient
T
O° Kpp/ prrD*
Sound-Power-Level Coefficient
A
Lw— 10 log Oprr’/p°N°D’
For radial-flow fans, particularly narrower types, some prefer to
use a reference flow rate that corresponds to the product of the peripheral velocity at the tip and the circular area based on the inlet
diameter. Multiplying by the geometric ratio (Di/ D2) will take this
into account. We could define a modified flow coefficient ¢; as
@(D,/ D2), or treat @ and (D,;/D2) as individual dimensionless
coefficients.
For cross-flow fans, the flow rate is nearly proportional to the
width of the blading 6. Multiplying by the geometric ratio D/b will
take this into account. We could define a modified coefficient @, as
¢(D/b) or treat @ and D/b as individual dimensionless coefficients.
For axial-flow fans, the flow area is clearly influenced by the hub
ratio v, which is equal to D2/ D,. Multiplying by //(/ — v*) will take
this into account. Furthermore, some prefer to use the peripheral
velocity at the mean effective radius. Multiplying by 2'7/(/ + v°)!”
will take this into account. The 2'” is an additional physical factor,
so it can be omitted. We could define modified flow coefficients ¢’,
dm, and $'n as b/(1 — v), 6/(1 + )'?, and /(1 — 7°) + 1)”, respectively; or we could treat ¢, //(/ — v’), and //(/ + v’)'” as individual
dimensionless coefficients.
The interrelation of ¢, 6, and o states in dimensionless terms what
Fan Law la says in dimensional quantities.
CHAPTER
Table
12.3 (cont.)
12 — FAN LAWS
12-25
Dimensionless Coefficients
U.S. Factor
Interrelation
=
1/80
Physical Factor’
4/1 = 0.4053
X 6.015 X 10°
1/5°o°
2/ 7° = 0.2026
X 6.015 X 10°
¢ D*/2Ay
2/7 = 0.2026
X 6.015 X 10°
wu — wy
2/7 = 0.2026
X 3.822 X 10°
oy/n
8/7* = 0.08213
+ 6354
bu/r
—
_—
bws/X
+ 2.160 X 10°
ob?"
Qe aM? = 21078
X 27.85
wg!”
p=
|
+ 6.015 X 10°
+ 116 dB
¢'/w
Lw— 10 log ow
=
OOS
2 /mr?= 0.8106
10 log 16/ 7° = —18 dB
'The physical factor for each coefficient is explained in the text for that coefficient.
Pressure Coefficients
Total pressure coefficient w, velocity pressure coefficient wy, and
static pressure coefficient ws are based on the relationships in Fan
Law |b and on fan total pressure, fan velocity pressure, and fan static
pressure, respectively. (Pressure coefficient is also called head coefficient.) Multiplying by a factor 2/7” yields the ratio of the actual fan
pressure to the reference pressure that corresponds to the peripheral
velocity at the tip. The value of the reference pressure is unimportant
in itself, so the 2/0 factor can be omitted. However, as with flow
coefficient, there is a preference for using the peripheral velocity at
the mean effective radius as the reference pressure for axial-flow fans.
Multiplying by 2/(/ + v*) will take this into account. The 2 is a physical factor and so can be omitted. We could define a modified pressure
coefficient wm as w/(1 + v’), or treat w and //(/ + v *) as individual
dimensionless coefficients.
The interrelation of w, 6, and o states in dimensionless terms what
Fan Law Ib says in dimensional quantities. Identical interrelationships would follow for wy and ws except for compressibility effects.
The interrelation shown for by, is dimensionless even though it contains the dimensional terms D* and A’. The interrelation listed for
ws follows from the relationship ofprs with per and prv.
12-26
FAN ENGINEERING — BUFFALO FORGE COMPANY
Power Coefficient
Power coefficient A, also called coefficient of performance, is based
on the power input to the impeller and the relationships in Fan Law
Ic. All bearing losses and other drive losses should be deducted from
the fan input power. Multiplying by the factor 8/7 yields the ratio
of actual input power (to the impeller) to the reference power that
corresponds to the flow rate and pressure used as references for @
and w. The value of the reference power is not important in itself, so
the 8/7 factor can be omitted. However, if either @ or w is modified
as outlined above, \ should also be modified. The interrelation of A
with ¢ and w also requires that efficiency be considered.
Efficiency
Efficiency is a dimensionless performance parameter and, therefore, is included among the dimensionless coefficients. Fan total
efficiency nr is the ratio of the output power of the fan QprrK, to the
input power to the impeller F. Fan Law 5c embodies this relationship, as does the interrelation
of 7 with ¢, w, and A. Refer to the
sections on compressibility and power formulae for additional comments on fan total efficiency and fan static efficiency.
Speed Coefficient
Speed coefficient o is based on the relationships in Fan Law 5b.
This coefficient is the ratio of the actual rotational speed to the rotational speed of an homologous fan (operating at unity flow coefficient and unity pressure coefficient) for the same point of rating.
Naturally, if the flow and pressure coefficients incorporate physical
factors, the speed coefficient should also be multiplied by the appropriate factor.
Speed coefficient is a non-dimensional specific speed. Specific
speed has units of rotational speed and is that speed at which an
homologous fan would have to operate to produce a unit flow rate
and a unit pressure (at standard air conditions) for the same point of
rating. The ratio of specific speed Ns. to speed coefficient is 0.871 in
SI] units and 150 600 in U.S. customary units.
Many investigators have shown that the physical proportions of a
fan and its speed coefficient are related. Figure 12.3 illustrates that
narrow radial-flow fans have lower speed coefficients at peak efficiency than wider radial-flow fans. It also shows that axial-flow fans
with high hub ratios have lower speed coefficients at peak efficiency
than those with low hub ratios. The best value of efficiency that can
be obtained depends on the degree of sophistication in the design.
For instance, airfoil-shaped blades exhibit higher efficiencies than
simpler, backwardly curved blades. Figure 12.3 can be used in the
initial stages of selection or design to choose the general type of fan
that might be most suitable.
CHAPTER
12 — FAN LAWS
12-27
Speed coefficient can also be used as illustrated in the chapters on
centrifugal and axial-flow fans to establish the approximate dimensions of a fan on the basis of previously established relationships
between specific physical proportions and speed coefficient.
Once a design has been tested, speed coefficient can be used as an
aid to selecting and rating when Q, per, p, and N are given and D
must be established. (This procedure is described and illustrated in
the chapter on fan selection.) A curve of speed coefficient versus
either flow coefficient or flow rate must be drawn. Spotting the appropriate value of speed coefficient will determine the point of rating.
Diameter Coefficient
Diameter coefficient 6 is based on the relationships in Fan Law
5a. This coefficient is the ratio of the actual diameter to the diameter
of an homologous fan (operating at unity flow coefficient and unity
pressure coefficient) for the same point of rating. Naturally, if the flow
and pressure coefficients incorporate physical factors, the diameter
coefficient should also be multiplied by the appropriate factor.
Diameter coefficient is a non-dimensional specific size or specific
diameter. Specific size has units of length and is that size of an
homologous fan that produces a unit flow rate and a unit pressure
at standard air conditions for the same point of rating. As noted
above, this fan would have to operate at specific speed. The ratio of
specific size Dse to diameter coefficient is 1.0466 in SI units and
1/53.20 in U.S. customary units.
Many investigators have shown that the physical proportions of a
fan and its diameter coefficient are related. Figure 12.3 illustrates that
narrow radial-flow fans have higher diameter coefficients at peak
efficiency than wider radial-flow fans. It also shows that axial-flow
fans with high hub ratios have higher diameter coefficients at peak
efficiency than those with low hub ratios.
Diameter coefficient could be used to establish approximate dimensions in the same way as speed coefficient. It is not done in this
handbook because, once the correlations are made for speed coefficient, there is no need to do the same for diameter coefficient.
|
It is possible to use diameter coefficient as an aid to selecting and
rating when
Q, prr, p, and D are given and N must
However, it is more common
be established.
to use throttling coefficient or one of
its variations.
Throttling Coefficient
Throttling coefficient 7 is based on the relationships in Fan Law
3b. This coefficient is the ratio of a reference velocity pressure to the
fan total pressure. Multiplying by the factor 2°/m makes the area
for the reference velocity pressure equal to the circular area corresponding to the tip diameter. The value of the reference velocity pres-
12-28
FAN ENGINEERING — BUFFALO FORGE COMPANY
sure is not important in itself, so the 2’/m° factor can be omitted.
Sometimes this physical factor is adjusted so that the reference velocity pressure becomes the fan velocity pressure, and the coefficient is
simply called pry/prr. The square root of throttling coefficient can be
referred to as equivalent or relative orifice coefficient. The fourth
root of throttling coefficient is the reciprocal of diameter coefficient.
In previous editions of this handbook, a quantity similar to 7 '? called
unit capacity was discussed.
Throttling coefficient is useful in comparing competing designs.
Plots with 7 as abscissa and 7 as ordinate can be drawn on the same
chart for all designs. Comparison of np values at equal 7 values will
show which design has superior efficiency for the various points of
rating. This approach factors out the effects of speed. That is, the
various designs may have to operate at different speeds to produce
the required Q and prr, but the plot will still show which is the more
efficient.
Throttling coefficient can be plotted as ordinate with ¢ as abscissa
on dimensionless performance curves or with Q as abscissa on con-
ventional performance curves. Fan selection is facilitated when Q,
Prr, p, and D are given and N must be established. An example is
given in the chapter on fan selection.
Sound Power Level Coefficient
Sound power level coefficient A is based on the relationships in
Fan Law Se. This coefficient is the sound power level that an homologous fan would produce when operating at unity flow coefficient
and unity pressure coefficient for the same point of rating. Naturally,
if the flow and pressure coefficients incorporate physical factors, the
sound power level coefficient should also be multiplied by the appropriate factor.
Sound power level coefficient is related to specific sound power
level in the same way that speed coefficient is related to specific
speed. Specific sound power level Lys is equal to Lw— 10 log Qprr
and is the sound power level that an homologous fan would produce,
when operating at unity flow rate and unity pressure, for the same
point of rating.
Both A and Lys are levels, so their values depend on the reference
level used to establish the sound power level Ly. This is universally
taken to be /0'"* watts. The value of A should be the same regardless
of the system of units employed. In Table 12.3, the U.S. factor, when
applied to U.S. units, gives them the same value as SI units. However,
the value of Lys will depend on the system of units used, which,
therefore, should be clearly identified.
When A is plotted against ¢, or Lys against Q, a minimum value
will occur at or very near the point of best efficiency.
Compressibility factor Kp has been omitted from the formulae for
A and Lys because the effect of Kp is insignificant compared to the
CHAPTER 12 — FAN LAWS
————
ee
12-29
inaccuracy of sound power level measurements. In fact, the fan law
relationships involving sound are not universally accepted. The application of sound power level should be limited to the overall sound
produced by the fan, and other rules should be applied when predicting the spectrum. See the chapter on fan noise for rules regarding
centrifugal and axial fans.
Dimensionless Performance Curves
Dimensionless performance curves can be drawn using various coordinates. One combination, as illustrated in Figure 12.4, is very
similar to a conventional constant speed, size, and density plot. Flow
coefficient is used as abscissa; and pressure, power, efficiency, speed,
diameter, and throttling coefficient are plotted as ordinates. It is
tempting to say that such a set of curves fully reveals the performance
of an homologous
series of fans. This is true only up to that point
where fan law deviations become significant. Within these limitations,
dimensionless plots can be used to represent the performance of any
fan in an homologous series, including fans with a control such as
VIV, IBD, or variable pitch. The first of these is illustrated in
Figure 12.5.
Any fan requirement can be plotted as a point on Figure 12.4 or
Figure 12.5, if the fan size and speed are known, simply by calculating
o and w from the appropriate Q and prr. If the point falls within the
range of the fan design, the other variables, such as power and efficiency, can be determined. If the point falls outside the range of the
fan design, another speed or size must be investigated.
~ 1660 DESIGN
on
N
>
Cy
a8
X
a
6 4}
i
als
a
ae
oP
Sar
eee
2
Sg
>
‘YT
TMi
ee
Figure 12.4
ee
Sy a
d
Dimensionless Performance Curves
RE)
12-30
FAN ENGINEERING — BUFFALO FORGE COMPANY
1660 DESIGN
tie
02>
0s
Figure 12.5
0a
05
068
oO?
08
eee
Dimensionless VIV Curves
Mass-Flow-Rate/Specific-Energy Approach
It was noted in the opening paragraph of this chapter that fan
mass flow rate and fan specific energy can be used as performance
variables. Table 12.2 shows Fan Law | based on these variables. The
rest of this chapter, however, deals only with volume flow rate and
fan pressure as performance variables. This is because it is customary
to use the fan-volume-flow-rate/fan-pressure approach in the U.S.
Nevertheless, the alternative approach 1s valid. The following remarks
may be helpful in using this approach.
The alternative to Equation 12.18 is
P=
M VF
Car
(12.31)
The alternative to Equation 12.19 is
a Ciak
where 7; is the impeller efficiency.
(12.32)
CHAPTER
12 — FAN LAWS
12-31
The alternative to Equation 12.21 is
in
Gar
(12.33)
where the fan efficiency 7 is the ratio of the fan output power to the
fan input power.
The value of C,, is unity in S.I. units and 33000 when power is in
hp, specific energy is in ft-lb/lbm, and mass flow rate is in |bm/ min.
The alternatives to Equations 12.23, 12.24, and 12.27 are, respectively,
Nm’?
Nsa =
—
We
Wee
Dyp'4
op?
Dsa = +
Wa
,
(12.34)
, and
(2235)
Lwsa= Lw— 10 log (myer p) .
(12.36)
These are dimensional equations and will yield numerical results different from the originals. For U.S. customary
units, Nya = 5.193 Ns,
Dsa = 0.1926 Ds, and Lwsa = Lws + 14 dB. The reason for the differences is that the reference quantities taken to be unity are ms, Vrs,
and ps rather than Qs, pers, and ps. That is, Nsq and Ds are the
speed and size of the homologous fan required to produce unity ms
and unity yrs with unity ps. All this seems to suggest that we would
be much better off using dimensionless quantities.
The alternatives to the formulae given in Table 12.3 are listed in
Table 12.4.
Almost all the discussions relating to Table 12.3 are also applicable
to Table 12.4. Although the physical factors are identical, the U.S.
factors are different, as shown in the table. The U.S. factors are
based on mass flow rates in lbm/ min and specific energy in ft:lb/lbm;
otherwise, the units are the same as for Table 12.3. The pressure coefficient should probably be called the specific-energy coefficient;
otherwise, all the other names used in Table 12.3 apply.
As noted in the chapter on fan testing, the mass-flow-rate/ specificenergy approach is given as an alternative to the volume-flow-rate/
pressure approach in ASME PTC 11-1983. This is patterned after
the approaches expected to be included in ISO I17.
12-32
FAN ENGINEERING — BUFFALO FORGE COMPANY
Table 12.4
Dimensionless Coefficients
Symbol
SI Formula
d
m/pND*
w
Ver/ N° D
X 1.158 X 10°
d
PI pn’ D
X 3.822 X 10°
n
U.S. Factor
+ 33000
myr/| BP
.
Nm'?
[yp
p'?
5
Dyr'l on 2m
T
m |yep D*
A
Lw— 10 log myr
|p N° D'
2
+ 6278
X 18.45
= FSS <0
+ 101 dB
Chapter 13
Fan Testing
The best way to establish the performance characteristics of a fan
is by testing. Various analytical techniques can be used together with
the physical laws that govern fluid flow to predict performance. But,
even the most sophisticated techniques require using empirically
determined factors. The fan laws can be used, within limits, to predict performance but only after a fan of the same design has already
been tested.
Fan tests usually fall into one of the following categories: 1) tests
conducted during the development of a fan or a line of fans, 2) tests
to provide a basis of rating a fan or a line of fans, and 3) acceptance
tests. Almost all development and rating tests are performed in the
laboratory, although some field verification is desirable. Acceptance
tests can be performed either in the laboratory or in the field, depending on the specifications.
Laboratory tests usually permit testing over the full range of performance
from
shutoff
to free delivery.
Field
tests,
however,
are
usually restricted to a narrower operating range, and sometimes this
range does not include the design point.
Test Codes
Various engineering societies and industry organizations throughout the world have published fan test codes, and several groups are
contemplating new codes.
The Air Movement and Control Association (AMCA), formerly
called the Air Moving and Conditioning Association, publishes a fan
test code entitled Laboratory Methods of Testing Fans for Rating
and designated AMCA Standard 210-74. Since this is a joint standard, it is also designated
ASHRAE
Standard
51-75.
AMCA
also
publishes a sound test code entitled Test Code for Sound Rating
designated AMCA Standard 300-67. Both are laboratory test codes
that provide for simulating many installation and operating variables.
Details regarding instruments and apparatus are specified. Also given
are rules concerning measurement, calibration corrections, reduction
of data, conversion from test to specified conditions, and presentation of results.
AMCA also publishes a Fan Application Manual, Part 3 of which
is entitled A Guide To The Measurement Of Fan-System Perfor-
13-2
FAN ENGINEERING
— BUFFALO FORGE COMPANY
mance In The Field. \t is called AMCA Publication 203 and was
issued in 1976. Although it is only a guide and not a code, AMCA
203 is often used as the basis for field performance measurements. It
contains details regarding instruments and apparatus as well as suggestions concerning measurement, reduction of data, conversion from
test to specified conditions, and presentation of results. Many examples are included illustrating where to take measurements, how to
make calculations, and how to determine the effect of the system on
fan performance. The last takes the form of system-effect factors
usually obtained by referring to AMCA Publication 201.
AMCA 210-74 and AMCA 203 each contain an error analysis.
As noted above, the American Society of Heating, Refrigerating
and Air Conditioning Engineers (ASHRAE) has joined with AMCA
in publishing the fan test code entitled Laboratory Methods of Testing Fans for Rating, ASHRAE Standard 51-75 and AMCA Standard
210-74.
ASHRAE
Standard
36-72,
Methods
of Testing for Sound
Rating, Heating, Refrigerating and Air Conditioning Equipment, can
also be used for fans. This standard does not cover sound radiated
to ducts.
if a consensus is obtained in 1983 as expected.
This is a field test code that provides for testing a fan as installed.
Details regarding instruments and apparatus are specified. Also given
are rules concerning measurement, calibration corrections, reduction
of data, conversion from test to specified conditions, calculation of
uncertainties, and presentation of results.
The
British Standards
Institution
(BSI) has published
a fan test
code entitled Fans for General Purposes: Part 1, Methods of Testing
Performance, numbered BS 848: Part 1: 1980. This code provides for
both tests with standardized airways and site tests. Details regarding
instruments and apparatus are specified. Also given are rules concerning measurement, calibration corrections, reduction of data, conversion from test to specified conditions, calculation of uncertainties,
and presentation of results.
The International Organization for Standardization (ISO) is writing a test code that will provide for laboratory, field, and sound testing. BS 848: Part I: 1980 includes many items that have been under
consideration by ISO, especially those regarding standardized airways. ASME PTC 11-1983 will also contain many items that have
been under consideration by ISO, especially those dealing with the
mass-flow-rate/specific-energy approach to specifying performance.
Test codes are a convenient starting point for performance specifications and contractual agreements. Sometimes, it may be more convenient for all parties concerned if exceptions are taken to certain
code provisions. This is quite legitimate, since fan test codes are not
CHAPTER
13 — FAN TESTING
13-3
instruments of law. However, because most of the provisions of these
test codes are necessary to ensure accurate measuring and reproducible results, caution is advised when contemplating exceptions.
The following discussions of measurements, calculations, and test
setups are based on either AMCA Standard 210-74 or ASME PTC
11-1983, as appropriate.
Laboratory Test Setups
Tests for ratings should be conducted on a setup that meets code
requirements. Acceptance tests should also be set up according to
code requirements, unless both parties agree to exceptions. There are
no rules governing developmental testing.
The test setup should be chosen to allow operation at the intended
point or points of rating. There are two general types of laboratory
test setups: |) those that use an auxiliary fan to provide for operation at or near free delivery, even when the resistances through the
measuring elements are high, and 2) those that do not use an auxillary fan.
The test setup should have a duct arrangement similar to that
intended for the actual installation. Four general duct arrangements
are possible: |) both inlet and discharge ducts, 2) inlet duct only,
3) discharge duct only, and 4) neither discharge nor inlet duct.
When both inlet and discharge ducts are contemplated for the
actual
installation,
the test setup
may
incorporate
a similar duct
arrangement, or an inlet bell fitted to the inlet connection may be
substituted for the inlet duct as shown in Figure 13.1A. (A good inlet
bell will produce the same flow conditions as a straight inlet duct.)
When measurements must be made in both ducts, suitable calming
lengths and straighteners must be provided in each. Inlet ducts
should be sized within +12.5% or —7.5% of the fan-inlet area. Outlet
ducts should be within +5% ofthe fan-outlet area.
If either an inlet duct or a discharge duct is to be used in the actual
installation without the other, the duct arrangement in the test setup
should be similar. The above remarks on duct sizes, calming lengths,
and straighteners also apply. (See Figures 13.1A and 13.1B.)
In any test setup using one or more ducts, performance can be
determined from pressure measurements in those ducts. The point of
rating can be varied by throttling at the end of either duct with a
symmetrical device such as a nozzle, an orifice plate, a perforated
plate, an adjustable cone, or a flat plate.
When no ducts are contemplated for the actual installation, this
condition can be simulated by mounting the fan in the wall of a test
chamber. To change the point of rating, a variable-speed (or variableinlet-vane) auxiliary fan can be used to supply air to the chamber at
different pressures. A suitable pitot-traverse or other flow-measuring
station can be inserted between the supply fan and the chamber. This
arrangement permits measuring performance at or near free delivery,
13-4
FAN ENGINEERING — BUFFALO FORGE COMPANY
FIG. 13.1A TEST SETUP WITH DISCHARGE DUCT ONLY (Pitot Traverse shown)
CL PLANE J
tPLANE 2
]
PLANE 1
{PLANE 5
* PLANE 6
FIG. 13.1D TEST SETUP WITH INLET CHAMBER (Venturi or Duct Nozzle shown)
PLANE 8
-PLANE 1
PLANE 2
AUX.
FAN
ANGLE SUGGESTED
Figure13.1
TestSetups
an
|e
3
Adapted from the data of AMCA and ASHRAE: “Laboratory Methods of Testing Fans for
Rating,” AMCA Standard 210-74, ASHRAE Standard 51-75, pp. 27-36, 1975.
CHAPTER
13 — FAN TESTING
13-5
since the auxiliary fan supplies the energy necessary to overcome the
resistance through the measuring section. Such an arrangement can
also be used
where
only a short
run
of duct connected
to the fan
is contemplated.
The low velocities associated with some ratings cannot always be
measured accurately by pitot-tube tests. Better accuracy can usually
be obtained by using flow nozzles, if substantial exit velocities can be
generated. The pressure needed to produce these velocities can be
supplied by the test fan or by an auxiliary fan if the test fan is incapable. If the fan does develop enough pressure, the nozzles can be
placed at the end of the test duct. Suitable approach conditions must
also be provided. When an auxiliary fan is used, a series of nozzles
can be permanently set up in a chamber as shown in Figure 13.1C.
Variations in point of rating are produced by plugging and unplugging various combinations of nozzles. Alternatively, a single nozzle
or a nozzle Venturi can be inserted into the duct between the auxillary fan and the chamber, as shown in Figure 13.1D.
Figures 13.1A to 13.1D give the chief dimensions for various
laboratory-test setups. Other combinations are possible; for example,
either the pitot traverse or the multiple nozzles can be used with an
inlet chamber. Specific numbers are assigned to various sections or
planes of reference as shown.
If a fan is to be furnished with bearings, it should be tested on its
actual shaft and bearings after a suitable “run in” period. The inlet
and outlet should be unobstructed except for the bearings and supports, and any other appurtenances, such as screens or dampers, that
are specified. Inlet bells and discharge cones, if contemplated, should
also be in place.
Suitable provisions should be made for driving the fan and measuring the input power by using dynamometers, torsion elements, or
calibrated electric motors. If the driver is an integral part of the fan
and helps to determine the airflow passages, it should be either in
place or adequately modeled.
The fan may have to be rotated to provide a suitable discharge
direction on the test block. But, the relative direction of inlet-box
entry to the discharge direction should not be changed, since this
may affect performance.
The room in which the test is conducted should be free from any
air currents that might affect fan performance. Whenever it is necessary to discharge the air into another room, provisions should be
made for makeup air. An adequate, whirl-free supply of uniformdensity air should be available to the fan.
The acoustic properties of the room will determine the type of
sound tests that can be performed.
Field Test Setups
The use of laboratory-type setups in the field is usually impracti-
13-6
FAN ENGINEERING
— BUFFALO FORGE COMPANY
cal. Space may be too valuable to permit using long calming lengths
of duct. Or, energy costs may prohibit using permanently installed
measuring devices having any appreciable pressure drops.
For small fan units, it may be possible to modify the duct work in
order to simulate laboratory-test-block conditions. However, for fans
of any appreciable size, this is not feasible. Similarly, for small fan
units, the driving motor can be removed and replaced by a calibrated
driver. But, for large units, this is not feasible.
Whenever the field installation differs from an ideal laboratory
setup, the effects of the differences should be taken into account. If
this accounting is done at the specification stage, the ratings should
be based on the fan as it is to be installed. This may require that the
vendor derate his laboratory performance or that he conduct special
laboratory tests on models to determine the effects of the differences
in setup. However, if the accounting is done after the fan has been
installed, a tolerance may have to be applied to the vendor’s predicted performance. AMCA' has developed some system-effect-factor
information that is useful for this.
Field noise tests should be very carefully evaluated to take into
account other noise sources and the difficulties of measuring.
Measuring Fan Flow Rate
Fan flow rate can be expressed as either the mass flow rate mr
through the fan or the volume rate of flow Q- corresponding to inlet
conditions. The section on pressure and flow measurements in the
chapter on fluid flow details many aspects of flow measurement.
Refer to this as well as to the information in the appropriate test
code whenever a fan test is contemplated.
If a laboratory test is to comply with the provisions of AMCA
210-74, the flow measurements must be made at the prescribed measuring planes. For pitot-tube traverse measurements, these planes are
in the ducts downstream of the straighteners and the specified calming lengths. When single or multiple nozzles are used, measurements
must be at the prescribed locations. These measurements are not flow
measurements
per se; rather, they are pressure measurements
used
with temperatures and other information to calculate the flow rate.
Many other devices can be used for measuring flow, including orifices and anemometers, both of which are discussed in the chapter on
fluid flow. Some of these are permitted by BS 848: Part 1: 1980. The
parties to a test can agree to any method of flow measurement, but
they should both be convinced that the uncertainties are within
acceptable limits.
AMCA 210-74 specifies a pitot-static-tube type of probe that is
acceptable and may even be preferred when the flow upstream of the
"AMCA, Fan Application Manual: Part | - Fans and Systems, AMCA
Publication 201.
CHAPTER 13 — FAN TESTING
13-7
measuring station is properly conditioned. ASME-PTC 1! specifies a
five-hole or three-dimensional probe because it expects that the flow
will not be conditioned upstream of the measuring station. Equations 2.105 and 2.106 can be used with either code’s measurements to
determine volume flow rate and mass flow rate, respectively. For use
in these equations, point velocities V; can be calculated from Equation 2.28. The normal velocity V,,; will be that indicated by the pitotstatic tube in the AMCA 210-74 test but will require adjustments for
yaw and pitch when using the ASME PTC I] directional probe.
Precautions are necessary to ensure that the mass flow rate at the
measuring station is the same as that passing through the fan.
Appropriate tests for leakage between the measuring station and the
fan should be conducted. The area at the measuring station should
be determined by internal inspection. Internal bracing and accumulations of dust or other materials should not be allowed.
Measuring Fan Specific Output
The fan specific output can be expressed as the total pressure
developed by the fan prr or as its specific energy yr. Discussions of
specific energy and pressure can be found in the chapter on fluid
flow. When output is expressed in terms of pressure, the flow rate
should be expressed in volume-flow-rate terms. However, when output is expressed in terms of specific energy, the flow rate should be
expressed in terms of mass flow rate.
The specific output of a fan is the difference between the pressure
or specific energy at the discharge plane and the corresponding
quantity at the inlet plane. ASME PTC II requires measuring at
these locations. But AMCA 210-74 requires measuring at remote
locations and then correcting for losses.
The quantities actually measured vary depending on code requirements. ASME traverse measurements include static pressures, velocity pressures, yaw angles, and pitch angles, regardless of whether fan
total pressure or fan specific energy is the desired end result. AMCA
traverse measurements omit the flow angles because the flow is preconditioned. Other AMCA setups permit the measuring of static
pressure by piezometer ring in the discharge duct or discharge chamber. AMCA inlet-chamber setups require only a single measurement
of total pressure.
Since the distribution of pressure or energy over the measurement
plane will not necessarily be uniform, it is convenient to use averages
to express the values at the plane. The average static pressure ps can
be calculated from traverse measurements by using Equation 2.109.
Piezometer measurements of static pressure are assumed to reflect
the average across the plane of measurement and can be used directly.
As noted above, the AMCA procedures may require calculating the
pressure loss between the fan and the measuring plane. The ASME
13-8
FAN ENGINEERING
— BUFFALO FORGE COMPANY
procedures do not permit this.
All the AMCA 210-74 setups require calculating fan velocity pressure as the velocity pressure corresponding to the average velocity at
the outlet. The outlet velocity can be calculated from the flow rate,
which,
in turn, is obtained
from a nozzle measurement.
Obviously,
this does not include any distributional effects, so
a= 1.0. ASME
PTC 11 includes these distributional effects regardless of whether fan
total pressure or fan specific energy is the final result, so a ~ 1.0. It
is expected that ISO 117 will include some convention regarding distributional effects: perhaps a = 1.04 at the discharge and a = 1.0 at
the inlet. (See the chapter on fluid flow for a discussion of alpha
factors.)
The average
specific kinetic energy ex and the average velocity
pressure py can be obtained from Equations 2.110 and 2.111, respectively. These include the distributional effects noted above. The average total pressure pris simply the sum of the average static pressure
and the average velocity pressure as indicated by Equation 2.112.
Based on the above definitions and averages, the fan specific
energy \r can be determined from
De
er
Sien DSi
ee
Cent
(13.1)
Correspondingly, the fan total pressure prr is
DEI
Pris
Pri.
(13.2)
Referring to Equations 2.23 and 2.26 will show that the potential
energy terms have been considered negligible, which is usual for fans.
Measuring Fan Input Power
Fan input power& is the power needed to drive the fan impeller
and any drive elements that are considered a part of the fan or are
furnished with the fan. If a fan is supplied with its own shaft and
bearings, then the fan input power should include the bearing losses.
Fan input power does not include any transmission loss resulting
from the use of belt drives, couplings, variable speed, or other
devices, unless the specifications expressly require that these losses
be charged to the fan.
Various prime movers can be used to drive the fan. If properly
calibrated, the input to the prime mover can be measured and its
output determined from the calibration. Unless this is a very good
calibration, it is usually better to use a reaction dynamometer or a
torsion element.
An electric reaction dynamometer is essentially an electric motor
with both its armature and its field mounted so that they will revolve
CHAPTER 13 — FAN TESTING
Table 13.1
13-9
Dynamometer Constants for Convenient Arm Lengths
rs shi
Dynamometer Constant
6.3025
10.5042
12.6050
15.7563
21.0080
31.5126
1/10000
1/6000
1/5000
1/4000
1/3000
1/2000
around the same shaft. An arm is attached to the field and a restraining force applied to the opposite end. If the speed of rotation N, the
restraining force F; and the distance L from the center of rotation to
the point of application of the force are measured, the power input
can be determined from
ae
_ 2nLFN
Ce
(13.3)
The conversion constant Cy has a value of 33000 for power in hp,
distance in ft, force in lb and speed in rpm. For SI units of W, m, N,
and rps, Cy = 1.0. Table 13.1 lists some convenient lengths and the
corresponding U.S. customary values of the dynamometer constant
2 Tels Oye
The restraining force on the arm can be measured with a yardarmtype balance, a dial-type scale, or a suitable force gauge. If the weight
of the arm is not perfectly counterbalanced (by means of an exact
counterweight on the stator), the indicated force F; will have to be
corrected. This correction, called tare F;, can be determined by running the dynamometer, without load, at the proper speed and noting
the scale reading. The corrected force F. may be smaller or greater
than the measured force, depending on whether there is positive or
negative tare, so
F.= Fi+ Fr.
(13.4)
The arm should be in exactly the same position for each reading.
When dial scales are used, the deflection may become so great that
an adjustment will be needed. Such an adjustment is never required
with a yardarm-type balance, which always returns the arm to the
same position.
Calibration tests are not usually needed for electric dynamometers.
By measuring tare at the proper speed, the effects of bearing and
windage losses may be cancelled out. Electrical connections must be
completely flexible, and the bearings should be in good condition
and well lubricated.
13-10
FAN ENGINEERING — BUFFALO FORGE COMPANY
Fan input power can also be found by measuring the electrical
input to a calibrated motor. Calibration tests are made with some
form of absorption dynamometer. If the electrical input is measured
in terms of current / in amps and potential £ in volts and if the corresponding efficiency 7 is determined from the calibration, then the
input power of the fan, if driven by a direct-current motor, can be
calculated from
Bella
F.=
Ke
(13.5)
When alternating-current motors are used, the actual power will
differ from the apparent power indicated by the amps and volts.
Power factor cos 6 is the ratio of actual to apparent power for singlephase or three-phase AC motors.
For single-phase AC motors,
=
EIn cos Ny
SK
(13.6)
For three-phase AC motors,
@=
a
V33 EIncos 6
K
:
(13.7)
The conversion constant K has a value of 746 for power in hp and
1000 for power in kW. A wattmeter can be used to find the actual
power input without having to measure amps, volts, and power factor separately. For three-phase current, either the two-wattmeter
method of measuring power or a polyphase wattmeter should be
used.
If a torsion meter is used, the torque T is obtained from a calibration of the change in resistance for a strain-gage element bonded to
the transmission shaft. A separate prime mover is needed. Fan input
power can be determined from the torque and speed by using
GY = 2aTNa a Cone
(13.8)
The conversion constant C, has a value of 33000 for power in hp,
torque in ft-lb, and speed in rpm. For SI units of W, m:N, and rps,
Gro}
In field testing a fan driven by an uncalibrated prime mover, reasonable values of motor or engine efficiency based on the manufacturer’s tests of similar models should be used. The uncertainty in the
CHAPTER
13 — FAN TESTING
fan input power will, of course,
efficiency values used.
depend
13-11
on the uncertainty
in the
Measuring Fan Speed
Fan performance is quite sensitive to variations in fan speed. The
fan laws indicate that, for a constant point of rating, fan flow rate
varies directly with fan speed, fan output varies directly as the square
of the fan speed, and fan input power varies directly as the cube of
the fan speed. So, fan speed must be accurately determined for each
test point during a fan test.
If the fan is driven by a constant-speed dynamometer or some
other constant-speed prime mover, it is necessary to measure the
speed only enough times to ensure that the uncertainty in the average
speed for any test point is within acceptable limits. For fans driven
by variable-speed dynamometers or other prime movers, the speed
should be regulated so that it will be nearly constant while taking
measurements
for any test point. In the laboratory, controls can be
installed to facilitate speed regulation. In the field, however, the speed
regulator is usually driven by the demand in some process variable
such as furnace draft. It is, therefore, necessary that the controller
be locked in a fixed position so that it is unaffected by changes
in demand.
Rotational speed can be measured with various types of tachometers. An electronic counter, actuated by a magnetic-pulse generator
or a photo-electric pickup, is usually preferred. Slip counting with
stroboscopic light may be acceptable for speeds close to line-frequency synchronous
speeds. Hand
tachometers,
mechanical-revolu-
tion counters, and vibrating-read tachometers are not usually accurate enough for fan-testing purposes.
In the slip method, the shaft must be marked with a reference line
or some other mark that is easily visible under stroboscopic light
flashing at line frequency. The mark will appear to slowly rotate
opposite the shaft rotation and will permit visual observation of the
slip frequency. A stopwatch can be used to measure the time for a
specified number of rotations of the mark. Average slip frequency is
derived by dividing the total number n of mark rotations by the
measured time interval ¢. The fan speed N- is the difference between
synchronous speed and slip frequency. For an electric motor with np
number of poles and a line frequency/,
F
SZ07,
60n
is
fees
(13.9)
This equation will yield fan speeds in rpm for frequencies in Hertz
and time intervals in seconds.
13-12
FAN ENGINEERING — BUFFALO FORGE COMPANY
Measuring Air Density
Fan performance is a function of the density of the air or gas
handled by the fan, so it is necessary that enough measurements be
made to establish the fluid density during a fan test. Values of fluid
density are also needed to calculate the velocity from velocity pres-
sure and various other results of a fan test including conversion calculations.
Density is not measured directly; rather, the thermodynamic properties of temperature and pressure are measured and information
about the composition of the gas is obtained from psychrometric
measurements, gas samples, or process calculations.
Refer to the chapter on properties of air and other gases for information on barometric, temperature, and humidity measurements.
Also included in.that chapter are equations and other information
pertaining to the calculation of molecular weight, gas constant, and
density. Refer also to the various application chapters for information about the gases normally encountered in those applications.
Measuring Sound Power Level
AMCA 300-67 specifies procedures based on using a calibrated
sound source in a semireverberant room. Sound power levels in each
of the eight octave bands (or more detailed spectrum information)
can be determined from appropriate measurements. Various test
setups simulating different types of installations can be used. No
procedures are given for measuring the directivity or pure tones.
Refer to the chapter on sound for discussions on measuring sound
levels, sound pressure levels, and sound power levels. Corrections for
background level, nonstandard air, and end reflection are also given.
Refer also to the chapter on fan noise.
Before noise testing, check the fans for balance and alignment.
Background noises should be eliminated. Motors and bearings sometimes contribute to false readings.
Calibrations
The instruments used in a fan test should be calibrated and the
calibration corrections applied to individual measurements. Measurements at a single point should be temporally averaged before applying the calibration correction. However, calibration corrections must
ie
Test Results
The results of a fan test should be expressed in terms of either the
CHAPTER
13 — FAN TESTING
13-13
fan mass flow rate or the fan volume flow rate, either the fan specific
energy or the fan pressure, and the fan input power. These three
quantities represent the basic performance of the fan. However, performance also depends on the operating conditions, so fluid density
and fan speed, too, should be included in the results. It may be desirable to calculate the fan efficiency and list it with the results. The
uncertainties in each of the results should be calculated from an
analysis of the uncertainties in each of the measurements leading to
that result. Refer to the section on propagation of uncertainties into
a result, which appears in the chapter on engineering statistics.
If the operating conditions differ from the specifications, use the
fan laws and appropriate compressibility corrections to convert actual
results into results corresponding to specifications. Refer to the chapter on fan laws for discussions a
les of the use of the fan
aws and compressibility coefficients.
1
ee
tests are performed at various points of rating, curves can
be fitted using procedures outlined in the chapter on engineering statistics. Flow rate should be plotted as abscissa, and both specific
output and input power should be plotted as ordinates.
Chapter 14
Fan Systems
A fan system may consist of any combination
duct
elements,
heat
exchangers,
air cleaners,
of fans, dampers,
or other equipment
through which all or part of the total flow must pass. Open systems
have at least one intake and one discharge opening. Closed systems
form a loop and have no such openings. Supply and exhaust systems
were described in the chapter on transmission and distribution of air.
Some of the problems of system design and fan selection, such as the
effects of multiple branches, were also discussed there. In this chapter,
additional aspects of fan and system matching will be examined.
Fan and System Matching
Fan performance must match system requirements. The only possible operating points are those at which the system characteristic
intersects the fan characteristic. At such a point, the pressure developed by the fan exactly matches the system resistance, and the flow
through the system equals the fan flow rate. If the actual flow rate
does not equal that specified, either the fan characteristic or the system characteristic must be altered. The fan characteristic can be
changed by varying the speed, the pitch, or the inlet whirl, or by
selecting a different fan. The system characteristic can be altered by
changing the damper settings or by physically changing other system
components.
Graphical methods of determining the points of intersection are
often valuable in analyzing fundamental principles but too tedious
for routine fan selection. The nongraphical selection methods
explained in the fan-selection chapter all take into account the need
for matching the fan and system characteristics.
If two or more fans serve a system, their combined characteristics
determine the flow rate through that system. Techniques for combining the characteristics of two or more fans are discussed in a later
section of this chapter.
In many fan systems, the gas density is nearly constant. However,
when the gas density does vary, it is important that the resistance for
each of the system elements be based on the actual density of the gas
flowing through that element. The overall system resistance for any
particular flow rate will be the sum of the losses throughout the system, including the entrance and exit losses. To properly match a fan
14-2
FAN ENGINEERING
— BUFFALO FORGE COMPANY
to a system, choose those fan characteristics that would exist for the
gas density expected at the proposed fan location.
Pressure Diagrams
When the average total pressure pr, velocity pressure py, and static
pressure ps at each cross section along the flow path is plotted to
scale, the result will be a pressure diagram. Pressure diagrams can be
drawn for individual system elements or for entire systems. Here,
diagrams of several typical elements will be examined first. These
results will then be combined in pressure diagrams for several typical
fan systems.
The air must enter an open system through some fitting or device.
A bell-mouthed entrance is illustrated in Figure 14.1. Observe that
the total pressure, the velocity pressure, and the static pressure are
all zero gauge at some point upstream of the fitting. The air will
accelerate into the fitting, producing a rise in velocity pressure to a
final value that corresponds to the velocity at the fitting’s exit. There
will always be a loss in total pressure because of viscous effects.
0
3
Best
er cciosel
Memes
|
Ree
|
|
|
pee
|
|
|
Sesto
ep sib il
|pe
+p
Cau
—p
Pe
Pie =e)
Figure 14.1.
aie
|
=p
Tien Pie — sss
Pressure Diagram - Entrance
CHAPTER 14 — FAN SYSTEMS
14-3
However, the loss pye is minimal for a bell-mouthed fitting, as illustrated by the very slight drop in total pressure. Other less streamlined
fittings will have greater drops in total pressure. Since the static
pressure is the difference between the total pressure and the velocity
pressure, static pressure will drop below the total by an amount
equaling the magnitude ofthe velocity pressure.
Figure 14.2 illustrates what happens to the pressure in a straight,
uniform duct. For steady flow, the velocity is constant along the
length of the duct. The velocity pressure is, therefore, also constant.
(Incidentally, the velocity pressure is always considered to have a
positive value.) As in any real fitting, there will always be a total
pressure loss pry that causes a decrease of total pressure in the direction of flow. The gauge values of the total pressure at each cross
section will depend on the gauge value at the entrance to the duct. If
the duct is connected to the discharge of the fan, the gauge total
pressures will always be positive as shown. However, if the duct is
located on the suction side of the fan, the gauge total pressures will
always be negative, as will be illustrated later. The gauge static pressure at any point is the gauge total pressure less the gauge velocity
pressure, and since the velocity pressure is always positive, the gauge
static pressure will always be less than the gauge total pressure.
Although this diagram was drawn for a straight duct, many elbows
and other fittings have constant cross-sectional areas too, so this
diagram is also applicable to them.
Figure 14.3 shows a converging conduit or nozzle. Because of the
reduction in area, the velocity and the velocity pressure both increase
FLOW
See
oe
SS
SS
SSS
SS
Pid — Pra
Figure 14.2
SSS
eS
Dr
Pressure Diagram - Duct
Pp
14-4
FAN ENGINEERING
— BUFFALO FORGE COMPANY
in the direction of flow. As in any other fitting, there will be a loss of
total pressure pr» in the direction of flow as shown. The slope of the
static-pressure curve will be even more negative than that of the
total-pressure curve because ofthe increasing velocity pressure.
A diverging conduit, or diffuser, is illustrated in Figure 14.4. The
velocity and the velocity pressure both decrease in the direction of
flow, and there is also a significant loss in total pressure p,. between
the entrance and the exit. The static pressure, however, increases
simply because the change in velocity pressure exceeds the change in
total pressure. This increase is known as Sstatic-pressure regain Psp.
The fitting illustrated here is located where all the gauge pressures
are positive. However, there are other locations where this is not true;
they will be examined later.
Figure 14.5 illustrates what happens at the exit of a system. There
will be a finite velocity at the exit and, therefore, a definite velocity
pressure. The static pressure in the ambient atmosphere surrounding
the exit will be zero gauge. The total pressure at the exit will, therefore, equal the velocity pressure. This, then, represents the exit loss
Pr. \f the kinetic energy of the exit stream cannot be utilized, it may
be wise to add a diffuser to decrease the exit loss. (This will also be
discussed later.) At times, a high exit velocity may be desirable, even
mec
+p
—0
|
hsmil
=
|
|
=
=
Il
+p
-——_)—_--
Pin = PTs — Pre
Figure 14.3
Pressure Diagram - Nozzle
=H)
CHAPTER
14 — FAN SYSTEMS
14-5
though the high kinetic energy increases the fan power requirements.
The system elements previously described can be combined in various ways to form a pressure diagram suitable for most fan systems.
The chief exceptions are systems with stack effect, systems with controlled resistances, and systems that convey materials. Still, it will be
instructive to examine several combinations. Remember that each of
these diagrams was drawn for a particular flow rate. The values of
the losses for that flow rate can be determined from the information
in the fluid-flow chapter.
The pressure diagram in Figure 14.6 is for a fan with an open inlet
and a discharge duct. Note that the total pressure, the velocity pressure, and the static pressure are all zero gauge at some point upstream from the fan inlet. Note also that no inlet loss is shown, even
though the air must be accelerated to some finite velocity. Any losses
associated with this process are charged to the fan. That is, the
standard definitions of fan performance require that specific output
be the net value and not the gross value including the entrance loss.
Pie — PTs — Pro
PsrR — Pso — Ps4
Figure 14.4
Pressure Diagram - Diffuser
14-6
FAN ENGINEERING
— BUFFALO FORGE COMPANY
For this reason, well-designed fans for open-inlet service have very
streamlined inlets. In making this diagram, it is best to begin at the
discharge end. The static pressure there is known to be zero, and the
exit total pressure prs equals the exit velocity pressure pys. The
total-pressure line can be drawn back to the fan, taking into account
the losses calculated for the total length. The static-pressure line will
parallel the total-pressure line for this system because duct area does
not change. It is usual to designate the fan inlet as plane | and the
fan outlet as plane 2. Since fan total pressure prr equals the difference between the total pressure at the outlet pr and the total pressure
at the inlet pm and since pr is zero for an open-inlet fan, the fan total
pressure equals the discharge total pressure pz, as illustrated in the
diagram. The fan static pressure prs is defined as the fan total pressure less the fan velocity pressure pry (which is equal to py2), so as
shown in the diagram, the fan static pressure equals the discharge
static pressure ps2 for an open-inlet fan. The simplicity of this last
relationship explains why fan static pressure has been the basis of
most fan ratings. But, if some combination other than an open-inlet
fan in a simple discharge system is used, a fan-total-pressure method
of rating may be better.
Figure 14.7 is for a fan with an inlet duct but no discharge duct.
This might be called an open-outlet fan. The pressure diagram shows
FLOW
Fey
PLx = Pra
Figure 14.5
Pressure Diagram - Exit
—?pP
“CHAPTER
14 — FAN SYSTEMS
14-7
that, somewhere upstream of the entrance to the duct, the total pressure, the velocity pressure, and the static pressure are all zero gauge.
The entrance condition is not as streamlined as for Figure 14.1, so
the total pressure drops more. The total pressure then continues to
fall throughout the length of inlet duct, finally reaching a value of
pri. Since a constant-area duct is shown, the velocity pressure
remains constant right up to the end, and the static pressure parallels
the total pressure. The value of pr; can be calculated as the sum of
the entrance loss and the duct losses. The velocity at the outlet of the
fan is finite, and since the static pressure ps2 must be zero gauge, the
total pressure at the discharge pr2 must equal the velocity pressure
py. Once again, by definition, the fan total pressure equals the difference in the total pressure across the fan, but this time, there is no
single value of pressure at a point equal to this quantity pr. — pr.
The fan static pressure, which is the difference between the fan
total pressure and the fan velocity pressure, is shown on the diagram
0
]
|
|
|
FLOW
|
|
|
ane
a
a
L| |
|
+p
|
|
f
lpn
al
_} a ae
=p
|
lr
|
eS
Prs
DET
|pss=0 py
:
pf = Pr2
Drv
= Pv2
Drs = Prr—
Prv — P72 —
Figure 14.6
Pia
| Pra = Pra
pf ete
DSO
ame Tle = PS?
Pressure Diagram - Open Inlet
14-8
FAN ENGINEERING — BUFFALO FORGE COMPANY
as ps. — pri. The algebraic derivation is also given. Note that the fan
static pressure does not equal the difference in static pressure across
the fan. Also note that the total pressure requirement can be calculated as the sum of the entrance loss pre, the duct loss pri, and the exit
loss Pry.
A fan having both inlet and discharge ducts can be called “the fan
in the middle.” Figure 14.8 illustrates this. Assuming constant crosssectional-area ducts, the velocity and, therefore, the velocity pressures are constant in both ducts. Once again, there is an entrance
loss, and pr; equals —pr;-. The total pressure continues to fall until it
reaches a value of —pre — pri. And, the static pressure parallels the
total pressure on the inlet side. Since the system discharges to the
oO
|
ae
nnn
Soares
ws
en
Pr2z= Pr
|
DFv |[xn
-0
Pin
Pil
DE
PFv
= Pv2
DES
PET ae DEV
P12 ame DN
a DY
DST
PFs F ps2 Sf
Figure 14.7
Pressure Diagram - Open Outlet
0 prx
CHAPTER
14 — FAN SYSTEMS
14-9
ambient atmosphere, the static pressure at the exit ps; must equal
zero, and the total pressure must equal the velocity pressure at that
point. The total pressure at the fan outlet pm will, therefore, equal
Pix + pra. The only difference between this and the open-outlet case
is the added discharge-duct
loss pry. The fan total pressure can be
calculated as the sum of the entrance loss pre, the inlet-duct loss pri,
the discharge-duct loss pv, and the exit loss pry.
Several interesting and important things happen if we add a diffuser to the system diagrammed in Figure 14.6. As illustrated in Figure 14.9, the exit loss pz, can be greatly reduced. The price that must
be paid for this is an additional diffuser loss pie. However, if the
diffuser is well designed, the sum of the diffuser loss and the new exit
loss will be far less than the original exit loss. This can result in
significant energy savings because the fan total-pressure requirement
DET ae 1
Tl
Prv = Pv2
[DMN OD
Oe
PFs F Dstt PS
Figure 14.8
Pressure Diagram - Fan in the Middle
14-10
FAN ENGINEERING
— BUFFALO FORGE COMPANY
will be reduced. Comparing Figures 14.9 and 14.6 will show that this
is SO.
Another interesting aspect of using a diffuser is its possible effect
on the static pressure along the length of the circuit. Note that in
Figure 14.9 the static pressure is actually negative relative to the
ambient pressure throughout the diffuser and somewhat upstream in
the discharge duct as well. This is simply the result of transforming
kinetic energy to pressure energy in the diffuser.
A similar situation occurs if a diffuser is added to the system diagrammed in Figure 14.7. Note that in Figure 14.10 the fan total pressure is reduced because the sum of the diffuser loss and the new exit
loss is less than the previous exit loss. Note, too, that the static
pressure is negative throughout the length of the diffuser and that,
since the diffuser is connected to the fan directly, the pressure at the
fan outlet is also negative. Although this may sound paradoxical, it
PEL
PR > Df = pm
Drv = Pv2
Prs = Psa
Figure 14.9
ph —) oR)
Pressure Diagram - Exit Diffuser
CHAPTER
14 — FAN SYSTEMS
14-11
is not. Remember that negative gauge pressures are still positive on
the absolute scale.
In Figure 14.10, the diffuser or evasé is considered a part of the
system, and the cone loss p;. must be added to the other losses to
find the fan total-pressure requirement. In Figure 14.11, the cone or
DET
Pr
=> Pr
Prv= Ppv2
Prs'— Psz7— Pr
PFs F ps2 — psi
Figure 14.10
Pressure Diagram - Evasé
14-12
FAN ENGINEERING
— BUFFALO FORGE COMPANY
evasé is considered part of the fan. A loss in the evasé must, therefore, be charged to the fan. And, the output of the fan is, therefore,
reduced, as reflected by the smaller value of fan total pressure. However, the net result is the same as for Figure 14.10. The only difference
is whether the fan is charged for the cone loss. Naturally, the
apparent fan efficiency will be higher if the cone loss is charged to
the system rather than to the fan. If the fans are identical except for
Prr> Pra
Pr
Prv = pvr
(PES at
S2eeme OT
PFs 7 Ps2— Psi
Figure 14.11
Pressure Diagram - Evasé
CHAPTER
14 — FAN SYSTEMS
14-13
whether the cone is separate or built onto the fan, then the input
power will be the same, regardless.
Every system, no matter how complicated, can be illustrated with
a pressure diagram. It is important to do so if there is any question
of how the fan is to be rated. The differences between fan total pressure, fan static pressure, and even static-pressure rise across the fan
can be clearly determined. The pressures to be expected at any point
in the system can also be determined. This could be important if
measurements will be made to check the design. Negative gauge pressures, which might otherwise be unforeseen, can thus be predicted.
System Characteristic Curves
The overall resistance to flow through a system will change with
the flow rate. This variation can be shown graphically by plotting the
pressure-versus-flow-rate characteristics of the system in the same
way that fan characteristics are presented. Figure 14.12 illustrates the
kinds of system characteristics that may be encountered. Figure 14.12A
shows a pressure loss that varies as the square of the flow rate. This
is what is usually assumed for a fan system in which the flow through
each element is believed completely turbulent. However, the flow
through ducts is often in the transition zone, so this assumption may
not be wholly justified. The flow through hard bends or elbows and
through abrupt enlargements will be completely turbulent for most
system velocities. Entrance and exit losses will also vary as the square
of the flow rate.
Figure 14.12B shows how the system characteristic would look if
the flow were laminar throughout. The pressure loss varies directly
with the flow rate in very few system elements. The flow through
some low-velocity fabric filters is completely laminar, but as already
noted, the flow through most other system elements 1s at least partially turbulent.
As shown in Figure 14.12C, there are some elements for which the
pressure loss does not vary at all with flow rate. In any bubbling
device, for instance, flow will not occur until the pressure of the gas
exceeds that of the liquid at that depth where the gas is introduced.
The pressure might also be considered independent of flow rate ina
device where the resistance is controlled at a constant value. This is
very nearly so in certain burners used on large, steam-generating
boilers. The forced-draft fan must often operate on a controlledresistance system similar to that shown in Figure 14.12D. The system
characteristic is usually considered a parabola, but instead of having
the vertex at zero pressure, it occurs at the pressure required by the
controlled-resistance element.
Various system characteristics are examined in later sections in
connection with different fan characteristics. In the chapter on fan
control, system characteristic curves are used extensively in examin-
14-14
FAN ENGINEERING
— BUFFALO FORGE COMPANY
OS Sane
FIGURE 14.12A
-
aay
p=
C, Oo
(COMPLETELY TURBULENT)
FIGURE 14.12B
pr= CQ!
(COMPLETELY LAMINAR)
FIGURE 14.12C
PL
Gs
atys
p=?
(CONSTANT STATIC HEAD)
FIGURE 14.12D
p=O+a0
(CONTROLLED RESISTANCE)
Figure 14.12
System Resistance Curves
ing the start-up and operation of various types of fans having different means of control.
Two-Fan Systems
There are various reasons for using more than one fan in a system:
1) Supply and exhaust fans are used in ventilation systems to avoid
excessive pressure buildup in the space being served; 2) Forced- and
induced-draft fans are used to maintain a specified draft over the
fire; 3) Two smaller fans may fit the available space better than one
large one; 4) Capacity control by means of various fan combinations
may be more economical than other control methods; 5) Multistage
arrangements may be necessary when pressure requirements exceed
the capabilities of a single-stage fan; and 6) Standby fans are often
CHAPTER 14 — FAN SYSTEMS
14-15
needed to ensure continuous operation.
When two fans are used, they may be placed quite far from each
other, or they may be so close as to share a shaft and bearings or
even casings. Double-width double-inlet fans are essentially two
parallel fans in a common housing. Multistage blowers are, in effect,
two or more fans in series sharing the same casing. Fans may also be
in series but at opposite ends of the system. Parallel-arrangement
fans can have almost any amount of their operating resistance in
common. At one extreme, the fans may have common inlet and
discharge plenums. At the other extreme, the fans may both have
considerable, individual duct work of equal or unequal resistance.
Fans in series must all handle the same mass flow of gas, assuming
that no losses or gains occur between stages. The combined total
pressure will be the sum of the individual fan total pressures. The
velocity pressure of the combination is defined as that pressure
corresponding to the velocity through the last-stage outlet. The static
pressure for the combination is the difference between its total and
velocity pressures and, therefore, does not equal the sum of the
individual fan static pressures. The volumetric flow rates will differ
whenever the inlet densities vary from stage to stage. Compression in
one stage will reduce the volume entering the next, if no re-expansion
occurs between the two. As with any fan, the pressure capabilities
are also influenced by density.
The combined total-pressure/volume-flow-rate characteristic for
two fans in series can be drawn by using the volumetric flow rates of
the first stage for abscissas and the sum of the appropriate total
pressures for ordinates. Because of compressibility, the volumetric
flow rates of the second stage will not equal the volumetric flow rates
of the first. The individual total pressures must be chosen accordingly
before they are combined. If the gas can be considered incompressible, the pressures for the two stages can be read at the same flow
rate. Near free delivery, it may be necessary to estimate the negative
pressure characteristics of one of the fans in order to combine values
at the appropriate flow rate.
Fans in parallel must each develop enough pressure to overcome
the losses in any individual duct work, etc., as well as the losses in the
common portions of the system. When such fans have no individual
duct work but discharge into a common plenum, their individual
velocity pressures are lost, so the fans should be selected to produce
the same fan static pressures. In such cases, if the fan velocity
pressures are equal, the fan total pressures will also be equal. When
the fans do have individual ducts but these are of equal resistance
and joined together at equal velocities, then the fans should be chosen
for the same fan total pressures. If the fan velocity pressures are
equal, the fan static pressures will also be equal in this case. But, if
the two streams join together at unequal velocities, energy will transfer from the higher-velocity stream to the lower-velocity stream. So,
14-16
FAN ENGINEERING
— BUFFALO FORGE COMPANY
fans serving the lower-velocity branch can be selected for a correspondingly lower total pressure. The other fan must be chosen for a
correspondingly higher total pressure than would be needed if the
velocities were equal.
The combined pressure/ flow-rate curves for two fans in parallel
can be plotted by using the appropriate pressures for ordinates and
the sum of the corresponding flow rates for abscissas. Such curves
are meaningful only when a combined system curve can be drawn.
Near shutoff, it may be necessary to estimate one fan’s negative-flowrate characteristics in order to combine values at the appropriate
pressure.
Figure 14.13 illustrates the combined characteristics of two fans
with slightly different individual characteristics (A-A and B-B). The
combined characteristics are shown for the two fans in series C-C
and in parallel D-D. Only total pressure curves are shown. This is
ud
oc
—
i?2)
ie)
lu
c
a
4
=—
=)
-
wsaneborta
FLOW RATE
Combined
Figure 14.13
Performance of Fans in Series and Parallel
CHAPTER 14
— FAN SYSTEMS
14-17
always correct for series arrangements but may introduce slight
errors for parallel arrangements. An incompressible gas has been
assumed. The questionable areas near shutoff or free delivery have
been omitted. And, two different system characteristics, E-E and F-F,
have been drawn on the chart. With the two fans in series, operation
will be at point EC or FC if the fan is in system E or F, respectively.
Parallel arrangement will cause operation at ED or FD. Single-fan
operation occurs at the intersection of the appropriate fan and system
curves, provided that the effect of an inoperative second fan is negligible. (For an inoperative fan in series, some sort of bypass is needed,
whereas an inoperative fan in parallel need only be dampered shut.)
Parallel operation yields a higher flow rate than series operation in
system F, but the reverse is true in system E. There is only one series
operating point and one parallel operating point for the fan characteristics shown in Figure 14.13.
An interesting situation develops when the characteristics are of a
more complicated shape. Figure 14.14 is drawn for two, identical
forward-curved-type fans in parallel with a common discharge
plenum. Static pressures are used in this chart. More important,
however, a very complex combined
curve results because of the char-
acteristic dip in the fan pressure curve.
efficiency
characteristics
as
shown
Each fan has pressure and
by the
curves
A-A
and
B-B,
respectively. The combined curve C-C is drawn by plotting all the
possible combinations of flow rate at each pressure value. A single
curve results except in the area just to the left of the peak. This would
be inconsequential except that the multiple curves are very close to
the best-efficiency point. If the system resistance were estimated as in
curve D-D, the expected point of operation would be CD, and the
expected efficiency for the fan would be as indicated by BD. If, for
some reason, the estimate of the system resistance should be wrong
and the actual
system
characteristic
was
as in curve
E-E, then two
points of operation are possible, namely, CE and CE’. Nothing is
wrong with point CE, as indicated by the efficiency at BE. However,
because of slight differences in individual system resistance, the fans
will usually operate to produce the combined performance indicated
at CE’. When this happens, one fan will be overloaded and the other
underloaded, both operating at poor efficiencies, as indicated by the
two points BE’. The imbalance can be easily reversed so that the load
shifts from one fan to the other. But, one or both driving motors
may be damaged if the overload is severe enough.
The combined characteristics for any number of fans of any type
can be constructed using the principles outlined above. Multiple
points of operation will occur at many flow rates whenever the
characteristics of the individual fans have a hump or a hump and a
dip. Some axial-flow fans have more severe dips than that shown in
Figure 14.14 for the forwardly curved fan. Whenever the shutoff
pressure is lower than the peak pressure, the negative-flow charac-
14-18
FAN ENGINEERING
— BUFFALO FORGE COMPANY
PRESSURE
STATIC
FLOW RATE
Figure 14.14
Forwardly Curved Tip Fans in Parallel
teristics of one fan should be considered when drawing the combined
characteristics. Some aspects of operating in this part of the com-
bined characteristics are considered in a later section on stability.
Other aspects, especially those dealing with start-up and operation
with control means, are discussed in the next chapter on fan control.
Systems with Mass or Heat Exchange
Many systems also provide for the exchange of either heat or mass
to or from the flowing gas. When calculating the system requirements, these exchanges must be taken into account. They may also
influence the choice of fan location.
Consider a system with heat exchange. If the air is heated, its
temperature will increase and its density will decrease. Assuming a
constant rate of mass flow, the volume flow rate will increase. The
resistance of any system component upstream of the heater should
be calculated for the higher density and lower velocity corresponding
to the colder temperature. However, the resistance of any element
downstream of the heater should be calculated for the density and
velocity corresponding to the higher-temperature condition. The
resistance of the heater itself should be based on the local densities
and velocities through each portion of the heater. If these resistances
are calculated as pressure drops, the overall system resistance will be
CHAPTER
14 — FAN SYSTEMS
14-19
the sum of the individual resistances along any one flow path. The
system postulated here is relatively simple, since only one upstream
and one downstream condition are assumed. More complicated
systems might involve many temperature changes.
There are two possible fan locations in the simple system discussed
above. It is convenient to refer to them as the cold-fan location and
the hot-fan location. The best position for a fan is the cold-fan
location, because the power needed to drive the fan will be lower
than for the hot-fan location. The hot fan takes more power because
it produces a greater temperature rise. This is a thermodynamic effect
that can be verified by examining Equation 2.46, 2.47, or 2.48. Fora
constant pressure rise p2 — pi, the temperature rise 7> — T\ is proportional to 7\/p,. The variation in absolute pressure p; is usually
very small in fan systems, but the absolute inlet temperature 7, can
vary significantly. The extra energy for the higher temperature rise
requires more power.
Referring to Equation
requires less power
12.21
will also show
that the cold
than the hot fan. The fan input power
fan
&
is
proportional to the fan volume flow rate Q, the fan total pressure
Prr, the compressibility factor K,, and the reciprocal of the efficiency
m. Ignoring compressibility factor and assuming that the same total
efficiency can be achieved regardless of location, the fan input power
is proportional to Qprr. For a given system, the fan total pressure
requirement will be the same regardless of fan location. If this is so,
then the fan input power will vary directly with the fan volume flow
rate, and the power will be least where the flow-rate value is lowest.
This, of course, is the cold-fan location.
If the system reststance is expressed in terms of pressure, the requirement will be constant regardless of the fan location. To verify
this, examine the pressure diagrams in Figures 14.6 through 14.11.
For instance, the entrance losses pre and exit losses prx are identical
in Figures 14.7 and 14.8. The duct loss pz; in Figure 14.7 equals the
sum of the duct losses pra and pz; in Figure 14.8. Because the sums of
the losses are identical, the fan total pressures prr are also identical.
The open-inlet fan diagram in Figure 14.6 appears to contradict the
statement that the pressure requirement is constant regardless of
location. However, the only difference is the absence of an inlet loss
Pie in Figure 14.6. If the systems diagrammed in Figures 14.7 and
14.8 had streamlined inlet bells, the inlet loss would be reduced to
nearly zero, and the fan total pressure requirement would be virtually
the same as that for the open-inlet fan.
If the system resistance is expressed in terms of head or specific
energy, the requirement will vary with fan location. The required
head or specific energy will be lowest where the density is highest.
This, too, is the cold-fan location. Equations 12.22 and 12.33 show
that, for constant weight flow w or mass flow m, the fan input power
GF. willalso be lowest at the cold-fan location.
14-20
FAN ENGINEERING
— BUFFALO FORGE COMPANY
In the above discussion, only heat exchange was considered. If
mass is also exchanged, the situation is more complicated. The mass
flow rate may differ at other locations along the flow path. (Multiple
intakes and outlets have been discussed in the chapter on transmission and distribution of air.) The mass flow rate may also vary
because of a change of state, as when water evaporates into a gas
stream. Conversely, water vapor may condense out of an air/ vapor
mixture. Also, more gas may be generated, as in any combustion
process. In any case, it is necessary to determine the rate of mass gain
or loss for the appropriate physical or chemical process involved.
The resistance of any system element should be calculated for the
mass flow rate through that element. So, if the mass flow rate varies
along the system, the appropriate rate must be used for each element
when calculating system resistance. If the resistance is calculated in
terms of pressure, the total requirement will be the same regardless
of fan location. But, if the system resistance is calculated in terms of
head or specific energy, the total requirement will vary with fan
location. The same general principles apply as described above for
hot- and cold-fan locations. The preferred fan location based on
power will be where the volume flow rate is least. Of course, if there
are branches, the fan must be positioned to serve them.
Closed Systems
In any system, open or closed, the temperature of the air increases
as it passes through the fan. In a closed system, the air circulates
back to the fan so that its temperature rises repeatedly. Eventually,
the losses through the duct walls will exactly balance the energy input
to the system. Under equilibrium conditions, the temperature rise
through the fan equals the temperature drop around the rest of the
system. The equilibrium temperatures can be calculated using the
amount of surface, the surface coefficients, etc. in the appropriate
heat-transfer equations. A similar situation occurs when the dampers
on a fan are completely closed and operation is at the shutoff
condition.
The exact values of pressure are not always determinate in closed
systems. If a major opening to the atmosphere exists, the pressure at
that point will be atmospheric, even if there is no flow through the
opening. The pressures at other locations in the system can then be
figured accordingly. A tightly closed system may have a panel flexible
enough to allow equalization of internal and external pressures. If
not, the pressures will fluctuate so much at any location that measuring becomes difficult or impossible.
Closed systems can be pumped up or down to any pressure by
using an auxiliary compressor or vacuum pump. Fans for circulating
the gas within the system must be chosen for the appropriate density.
The pressures throughout the system can be calculated with reference
to the pressure at the pressurizing connection.
CHAPTER
14 — FAN SYSTEMS
14-21
Mutual Influence of Fan and System
Fan performance data are usually based on tests wherein the air
approaches the inlet with a uniform velocity free of whirl. Ductelement losses, except when noted otherwise, are based on similar
flow conditions. The effects of prerotation on fan performance were
discussed in the chapters on centrifugal and axial-flow fans. The
effects of one elbow on another were listed briefly in the chapter on
fluid flow.
Elbows, unless provided with adequate turning vanes or splitters,
produce uneven velocity patterns that may persist for long distances
in subsequent straight ducts. Nonuniform inlet velocities may, in
themselves, alter fan performance, since different portions of the
impeller will be loaded differently. Nonuniform velocities may produce whirls in the inlet flow that also affect fan performance. To
prevent adverse effects, every reasonable precaution should be taken
to ensure uniform flow from all elbows.
Inlet boxes are special elbows. Their main purpose may be to turn
the air or to protect the bearings from the air stream. If inlet boxes
are to be furnished, fan performance should ideally be based on tests
with the boxes in place. However, this is not always practical. The
total inlet-box loss, which includes the effect on fan performance as
well as the elbow loss, will be of the order of one inlet-velocity head.
The exact value will depend on the design of both the fan and the
box. The relative direction of the inlet-box entry and the fan discharge may also have an effect, especially when forward-curved blade
designs are involved. The highest loss usually occurs when the air
entry is from the direction opposite (180°) that of the discharge. The
least loss usually occurs when the entry is from the same direction
(0°) as the discharge, although an angularity of 90° is not much
worse. A rectangular box with an axial depth of approximately 50%
of the fan inlet diameter and a width of about three times the depth
will be suitable. A splitter plate, in the plane of the shaft, extending
from the closed end of the box out toward the shaft is recommended
to prevent any adverse effects due to whirl. The axial depth can be
tapered gradually to minimize the effects of uneven velocity.
The velocity pattern at the discharge will vary with the fan design.
Performance data are usually based on tests with a straight discharge
duct. If an elbow is placed close to the discharge, some loss in fan
static pressure may occur because of reduced static-pressure regain.
The loss through the elbow may be affected by an uneven velocity
pattern. If the velocity along the inside radius of the elbow is higher
than that along the outside radius, the loss will be higher than
normal.
However,
the loss will be less than normal
if the velocity is
higher along the outside radius than along the inside radius.
The influences of system connections on fan performance have
been termed system effects. System-effect factors are values (usually
14-22
FAN ENGINEERING
— BUFFALO FORGE COMPANY
in terms of pressure) suggested to compensate for these influences, or
system effects. AMCA has published data from which system-effect
factors for various conditions can be determined. Recognizing that
the effect will vary with velocity, AMCA has developed a graph of
system-effect factor in inches water gauge versus air velocity in feet
per minute. It identifies various system effects by a letter code. Additional data suggests the appropriate letter code for various conditions. For instance, different letter codes are suggested for the system
effect of an elbow connected to the inlet of a fan depending on the
length of duct between the elbow and the fan, on the radius ratio of
the elbow, on the number and size of turning vanes, etc. Similar data
are presented for outlet elbows and outlet ducts. The parameters
used are the length of duct between the fan and the elbow, the
relative direction of turn for the scroll and the elbow, and the ratio
of blast area to outlet area. The blast area is defined as the area over
the cutoff of a centrifugal fan and the annular area for an axial fan.
Additional data are given for cabinet enclosures, inlet obstructions,
and other accessories. The AMCA system-effect factors are said to
include only the effect of the system configuration on the fan performance. The pressure loss across the fitting should already be included in the system resistance. Although some of the data have been
obtained from research studies, it is recommended that manufacturers
be consulted about these effects on their individual fan designs and
that judgment based on experience be used when applying these
factors.
Second- and Fourth-Quadrant Performance
Fan performance in the first quadrant is commonly plotted with
flow rate as abscissa and specific output as ordinate. This is usually
volume flow rate and pressure, but it could also be mass flow rate
and specific energy. Power input is also plotted as ordinate with flow
rate as abscissa. Similarly, second-quadrant performance can be
pressure and/or power versus negative flow rate. Typical curves are
shown 1n Figure 14.15.
Figure 14.15 is for a fan operating at constant speed. The parabolic
nature of the pressure characteristic in the second quadrant suggests
that the fan is simply acting as a resistance to flow. In fact, it is very
much like a controlled resistance combined with a variable resistance.
Backward flow never occurs unless enough pressure is available to
overcome a resistance at least equal to the shutoff pressure. This
parabolic characteristic, with vertex at the shutoff pressure, is
probably exhibited by all types of fans driven at constant speed. The
power characteristic shown in Figure 14.14 is for a backward-curvedtype of fan, and the extension into the second quadrant may not be
representative of that for any other fan type. However, extending
the first-quadrant curve into the second quadrant seems natural
enough. And, the eventual upturn also seems inevitable, because
CHAPTER
14 — FAN SYSTEMS
14-23
\
\
\
I
Ww
Figure 14.15
Performance in Quadrants Il and IV
without the driving motor, the fan would tend to windmill in the
opposite direction.
In Figure 14.15 the performance of the fan is extended into the
fourth quadrant. This is probably typical for all fan types. If the
pressure is reduced enough, the flow will increase until a choking
condition develops. Choking could occur even in the first quadrant.
The power characteristic does not extend into the fourth quadrant
for this particular fan type. However, it is conceivable that the power
could drop into the fourth quadrant for some fan types.
Both second- and fourth-quadrant performance can be important
when combining characteristics for two or more fans. In Figure 14.13
the combined performance characteristic D-D was not completed to
shutoff because the second-quadrant performance of A-A was unknown. Since the continuation of A-A into the second quadrant
would probably be a parabola with vertex at the shutoff pressure,
the continuation of D-D to shutoff would involve backflow through
the fan corresponding to A-A.
Also in Figure 14.13, the combined characteristic C-C was not
extended to free delivery because the continuation of the character-
14-24
istic B-B
FAN ENGINEERING
— BUFFALO FORGE COMPANY
into the fourth
quadrant
was
unknown.
If it had
been
known, it would have been easy to extend the curve C-C. But, operating at any of the resultant points would require operating the fan
corresponding to B-B in the fourth quadrant. This would occur
naturally as long as the fan corresponding to A-A operated in the
first quadrant.
Windmilling
If air is blown through a fan and the impeller is not restrained,
that fan will windmill; that is, the impeller will rotate freely. The
direction of this rotation will depend on the direction of the airflow.
If the air is blown through the fan in the normal direction of flow,
the fan will windmill in the normal direction of rotation. This is
certainly true for an axial-flow design, and it is probably true ‘for
most centrifugal fans as well. If the air enters without whirl, the force
exerted on the blades will tend to propel a centrifugal fan wheel in
the proper direction of rotation only if the heel of the blade is curved
forward, as is usual for all but the straight, radial-bladed types. The
latter will not receive any forward impetus from the entering airstream; however, it, and all other types as well, will receive a forward
impetus from the collected airstream near the tip. If the entering air
has a forward whirl, the force in the normal direction of rotation will
be even greater and will tend to move the straight, radial-bladed fan
forward.
However, if the air is blown backwards through a fan, the direction
of rotation will be the reverse of normal; that is, the impeller will
windmill backwards. This will be true for both axial-flow fans and
centrifugal fans, regardless of the blade shape. Any discharge vanes
on an axial-flow fan will tend to accentuate this reverse rotation.
This is because a normal guide vane will produce a whirl in the
reverse rotation direction.
Spin dampers and variable-inlet vanes in their partially closed
positions normally produce whirls in the direction of normal rotation. But, if these or other devices should produce a whirl in the
opposite direction, the tendency to windmill in the normal direction
will be reduced and, in extreme cases, might possibly be reversed.
Windmilling is undesirable: a spinning fan poses a threat to safety,
especially if the rotation is unexpected. Also, fans windmilling in the
reverse direction should be stopped before the driving motor is energized, otherwise physical damage to the shaft or the driving motor
could result. One way of preventing windmilling is to isolate the fan
by using dampers. However, most fully closed control dampers will
leak significantly, so special isolation dampers are often needed to
prevent windmilling. Mechanical devices attached to the shaft can
also be used. These include friction brakes and clutch-type backstops.
The torque these devices must oppose will vary with the rate of back
flow through the fan.
CHAPTER
14 — FAN SYSTEMS
14-25
Stability
Stability, in its general sense, refers to a system’ inherent ability to
regain its equilibrium after a temporary disturbance. For the flow
through a fan system, stability means that the flow rate will return to
its original value without severe excursions once the disturbance has
been removed. It also means that, after a change in control setting,
the flow rate will assume a new value quickly and smoothly. If a fan
system is unstable, the flow rate, the specific output, and the power
input may all fluctuate noticeably.
Actually, the flow through a fan and its system may never be
completely steady. The ordinary performance curves that are plotted
for fans should be interpreted as showing average values. Although
the instantaneous values probably always fluctuate, these fluctuations
are so small and rapid that they can be detected only by sensitive
instruments. Larger or less rapid fluctuations will produce deviations
from
the steady-state
curves
that
will be easy
to detect
or even
impossible to ignore.
Fortunately, unstable operation is usually easy to avoid by following established procedures for selecting and operating fans. The fan
should be selected so that its operating point falls on the negatively
sloping portion of the pressure (or specific-output) curve. An adequate margin should be provided between the peak of the curve and
the operating point so that a disturbance will not force the fan to
operate at the peak. Procedures for starting up and operating with
controls are given in the next chapter.
If the fan is forced to operate on a positively sloping portion of the
pressure (or specific-output) curve, instability may result. This unstable behavior is. variously called surging, pumping, or pulsation.
And the peak of the pressure curve, or a point near it, is called the
surge limit, pumping limit, or pulsation limit. Surging is a periodic
process wherein the flow rate varies dramatically. These flow varia-
tions are accompanied by changes in pressure, power, and noise. The
frequency and amplitude are measurable, and mathematical models
have been constructed to predict these quantities.
:
Figure 14.16 illustrates what happens during surging. The fan
characteristic is shown in both the first and second quadrants.
Assume that there is a damper in the system. With the damper open
a certain amount, operation is on system line OA, and it is stable as
indicated by the negative slope of the fan curve at A. Closing the
damper
in small but finite increments
produces
momentary
condi-
tions under which the damper cannot pass the flow from the fan unless the pressure is increased. The fan responds by producing more
pressure as it backs up the curve. Not only does this satisfy the
damper’ need for more pressure, it also reduces the flow rate, so the
pressure will not have to be increased indefinitely. Because this is
self-limiting, equilibrium will be restored quickly if the damper motion
is stopped.
14-26
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Q
Figure 14.16
Stability and Surge
Closing the damper farther will usually result in stable operation
up to point B. (It may take longer to restore equilibrium as the operating point approaches the peak.) However, closing the damper any
farther than that will produce the potential for unstable operation.
When
the damper is closed beyond
B, the fan cannot respond to
the damper’s need for more pressure without jumping to point D. Of
course, this produces a flow reversal, and equilibrium is even further
disturbed. Actually, this process is not instantaneous, so the pressure
will drop and some point like D’ will result.
Operation at D or D’ cannot be stable, since the damper is now
passing more flow than the fan is delivering. Therefore, the pressure
falls until point E is reached. Although the fan will then tend to
respond by following its characteristic to point C, the usual system
dynamics will not permit this. In a true surge, the flow rate will jump
to point F. Because this is not an instantaneous process either, the
pressure will rise, and some point like F’ will result.
Once again, the fan is delivering more flow than the damper can
pass, and the cycle repeats itself. The frequency and amplitude of
surging depends on: the relationship between the shutoff and peak
pressures, the enclosed volume of the duct between the fan and the
damper, the area of the damper, the pressure level, and various gas
properties.
An old and very simple model’ for predicting pulsation frequency
'W.R. Heath and W.R. Elliot, “Control and Prediction of Pulsation Frequency in a Duct System,”
ASME
Paper No. 46-A-24, 1946.
CHAPTER
14 — FAN SYSTEMS
14-27
considers the system a Helmholz resonator. (A more detailed model
is given by Emmons et al. *) If the system consists of a large-crosssection duct connected to the fan by a small-cross-section duct, the
frequencyfcan be approximated by using
tp
eae
Eee
fee
For such a concentrated-volume
iy
(14.1)
system, the cross-sectional area S
and length L are those of the small connecting duct that can be
likened to the neck of a resonator. The volume V of the large duct
can be likened to the main chamber of a resonator, and it, too, must
be relatively large. The speed of sound c in standard dry air is 1125
fps, so c/27 is 178 fps for this condition.
If the system consists of uniform-cross-section duct, then § should
be based on the fan outlet area and L on the wheel circumference
plus any transformation piece. The frequency for this distributedvolume system will be up to 57% greater than predicted by Equation
14.1, depending on the distribution.
The phenomenon known as rotating stall also influences the
dynamic characteristics of a fan system. Rotating stall occurs when a
disturbance causes the flow to separate from one of the blades, which
results in momentary choking of the flow through the corresponding
blade passage. This, in turn, causes the flow angles to change on
either side of the choked passage, so the following blade tends to
stall and the preceding blade becomes more stable. The stall cell
eventually moves to the next passage and, subsequently, to the one
after that, rotating around the impeller in the direction opposite
rotation. The relative speed of the stall cell varies with the point of
Operation, ranging from zero to approximately one-third of the
impeller rotational speed. The frequency of the stall disturbance,
therefore, ranges from 100% of rotational frequency at inception to
two-thirds of rotational frequency at full stall. If two diametrically
opposite stall cells develop, the stall frequency will be approximately
four-thirds of the rotational speed.
Rotating
stall has been
observed
for many
backwardly
curved
designs of centrifugal fans, especially those with a small number of
airfoil-shaped blades. The stall region on a performance map is
usually limited to flows less than those at maximum efficiency. The
use of variable-inlet vanes tends to inhibit rotating stall, although the
VIV vortex itself can become displaced, causing a disturbance and
producing stall.
The dynamic behavior of a fan system will depend on all the system
*H.W. Emmons
et al., “Compressor Surge and Stall Propagation,” Trans. ASME,
York, Volume 77, Number 4, May 1955, pp. 455-469.
ASME,
New
14-28
FAN ENGINEERING
— BUFFALO FORGE COMPANY
elements, not just the fan. EPRI has funded a large project to study
these interactions in power plants.’
*F.R. Goldschmied
et al., Air/Gas
Dynamics
of Fossil Fuel Power
Plants,
CS-1444,
Research
Project 1651, Prepared by Westinghouse Electric Corporation and Massachusetts Institute of
Technology, Electric Power Research Institute, Palo Alto, California, Report in Five Volumes,
July 1980-October
1981.
Chapter 15
Fan Control
_ The output of a fan can be controlled by using outlet dampers,
inlet-box dampers, variable inlet vanes, variable pitch, variable speed,
or even by varying the number of fans in operation. Each of these
techniques affects flow rate, specific output, stability, turndown ratio,
start-up, and power savings. In this chapter, the effects on the operating characteristics of the fan will first be examined for each technique in turn. Next, the start-up characteristics of various fans will
be considered for different circumstances, for example, single fans
and multiple fans. Finally, the power savings that can be expected at
reduced ratings will be assessed.
Operating Characteristics
The operating characteristics that will be discussed in this section
can all be illustrated on a graph of specific output versus flow rate.
Graphs of pressure versus volume flow rate will be used, but specific
energy versus mass flow rate would be equally acceptable. Both fan
characteristics and system characteristics will be shown on each
graph. An infinite number of system characteristics exist. There are
also an infinite number of performance-characteristic curves for a
fan equipped with a control device. Only a few representative examples will be shown on each graph. The location of the actual
Operating point will depend on the setting of the control device as
well as on the system characteristic.
Outlet Dampers
The operating characteristics of a fan/outlet-damper combination
can be depicted as in either Figure 15.1 or Figure 15.2. In Figure 15.1,
a constant-speed, fan-total-pressure-versus-fan-flow-rate characteristic
is shown together with several parabolic system characteristics all of
which pass through the origin. If we consider the resistance of the
outlet damper to be a part of the system resistance, then each of the
parabolas represent the pressure-versus-flow requirements of the
combined damper and system at various damper positions. For a
typical system, the fan-and-damper combination might operate at
15-2
FAN ENGINEERING — BUFFALO FORGE COMPANY
Figure 15.1
Fan Performance with Outlet Dampers
point A with a wide-open damper. The fan-and-damper combination
would operate successively at points B, C, D, and E with increasing
damper closure. However, it might not be possible to achieve any
lower flow rate than at E because of leakage through the closed
damper. The maximum turndown ratio would be the flow rate at A
divided by the flow rate at E. The operating points D and E are
potentially unstable because the fan characteristic has a positive
slope, as does the system characteristic. However, the fan characteristic has a negative slope for the other operating points, which are,
therefore, expected to be quite stable.
Figure 15.2 shows the same fan-and-damper combination as Figure
15.1 but from a different point of view: the damper is considered part
of the fan, so a different performance curve is given for the fan at
each of the damper positions. The top curve is identical to that in the
CHAPTER 15 — FAN CONTROL
Figure 15.2
15-3
Fan Performance with Outlet Dampers
previous figure, which can only be achieved if the damper loss in the
wide-open position is negligible. Otherwise, the top curve would be
slightly depressed. The dashed curves correspond to several arbitrarily
chosen damper positions. Although they are marked 3/4, 1/2, and
1/4, note that the flow rate is only 3/4, 1/2, or 1/4 if the fan operates
at free delivery. The leakage rate at the fully closed position determines the maximum turndown ratio possible.
The curves shown in Figure 15.2 are only a few of the infinite
number of possible curves. Each should be considered the potential
performance for the corresponding damper setting. And, the entire
system of curves can be considered a map of the potential perform-
ance of the fan-and-damper combination. The performance is only
potential because operation could be at any point on the map. That
point is not fixed until the system characteristic has been established
15-4
FAN ENGINEERING
— BUFFALO FORGE COMPANY
and, of course, until the damper position has been selected. For
instance, assuming a system characteristic such as the line ABCDE,
the performance would be at B for a damper setting corresponding
to the 3/4 position. The system loss would be the vertical distance
from the base line to B, and the damper loss would be the vertical
distance from B to B’. The losses C-C’, D-D’, and E-E’ increase as the
damper is closed farther and farther.
Operation is usually expected to be quite stable wherever the slope
of the fan characteristic is negative and the slope of the system characteristic is positive. The operating points A, B, C, D, and E on
Figure 15.2 are all stable according to this criterion. There is some
evidence that performance with an outlet damper can be evaluated
this way if the principal resistance of the connected system 1s on the
inlet side of the fan. But, if the principal resistance of the system is on
the discharge side of the fan, it is better to revert to Figure 15.1.
There the operating points D and E were considered potentially
unstable because the slopes of both the fan characteristic and the
system characteristic were positive.
Inlet-Box Dampers
Figure 15.3 illustrates the map of potential performance for a fan/
inlet-box damper combination. Postulating a system ABCDE, operation will be at A for the damper in the wide-open position, at B for
the 3/4 position, at C for the 1/2 position, etc. Once again, the
maximum turndown ratio would be the flow rate at A divided by the
flow rate at E. This condition is limited by the leakage through the
damper as represented by the fully closed-position curve. The degree
to which the wide-open-position curve approaches that without any
IBDs depends on the loss of the IBDs in the wide-open position. The
difference between the performance with a wide-open IBD and that
with a particular closure of the IBD can be considered composed of
two parts. One part would correspond to the pressure drop caused
by any resistance and, in this respect, would resemble that caused by
an outlet damper. The other part might be due to any changes in the
flow caused by the IBDs. This, then, affects the flow through the
impeller and, therefore, the output of the impeller. The difference
between B and B” might be due to spin or to other flow-modifying
effects. The difference between B” and B’ might be due to more
ordinary resistance effects. These curves are just typical, and the
actual percentage of one effect versus the other may vary greatly,
depending on the design.
Inlet-box dampers can be considered a part of the fan in much the
same way that outlet dampers were considered a part of the fan in
the previous section. The operating points A, B, C, D, and E on
Figure 15.3 can be expected to be quite stable according to the criterion of opposite slopes for the fan and system characteristics. Experience suggests that, if significant spin effects exist, performance will
CHAPTER 15 — FAN CONTROL
Figure 15.3.
15-5
Fan Performance with Inlet-Box Dampers
be stable. There is some evidence that, even without spin effects,
performance with an inlet-box damper will be stable if the principal
resistance of the connected system is on the discharge side of the fan.
However, if the principal resistance of the system is on the inlet side
of the fan, it is better to consider that the operating points will be at
B’, C’, D’ and E’. The nature of the intersections at D’ and E’ suggests
unstable operation according to the slope criterion.
Variable Inlet Vanes
Figure 15.4 is a potential performance map of a fan with variable
inlet vanes. VIVs are designed to spin the air in the direction of fan
rotation. Like IBDs, VIVs can be considered to have a resistance
effect as well as a flow-modifying effect. However, since VIVs are
15-6
FAN ENGINEERING — BUFFALO FORGE COMPANY
Figure 15.4
Fan Performance with Variable Inlet Vanes
built right into a fan, they are almost always considered a part of the
fan. The performance of the fan/ VIV combination, when connected
to a system ABCDE, would be at points A, B, C, D, or E, depending
on the VIV position. Because the fan and the VIV are so closely
positioned, performance at D’ or E’ is usually considered unlikely,
and so, performance will be at D or E and stable.
As with both outlet dampers and inlet-box dampers, VIVs leak,
and, so, the turndown ratio is limited. The maximum turndown ratio
for this system would be the flow rate at A divided by the flow rate
Auiiee
Variable Pitch
Figure 15.5 illustrates the potential-performance map ofa fan with
CHAPTER 15 — FAN CONTROL
unnees
15-7
comeemenae cammmnenees eemtmeeemen ummm eaememmememe
es
:
forename
oO
Figure 15.5
Fan Performance with Variable Pitch
variable-pitch capability. If we postulate a system characteristic
ZABCDE, performance will be at Z, A, B, C, D, or E, depending on
the pitch setting. As shown, the design setting is usually less than the
maximum setting. The performance at design for this system will be
at A. Higher flow rates can be achieved as at Z, and lower flow rates
as at B, C, D, and
E. The maximum
turndown
ratio would
be the
flow rate at A divided by the flow rate at E for a fan selected for
basic operation at the design position. All points of operation for
this system would be stable because of the positive slope of the
system curve and the negative slopes of the fan curves at the various
pitch-positions. Such fans must be carefully selected to avoid operating at stall, as will be discussed in connection with start up.
Variable Speed
A map of potential performance for a fan with variable-speed capa-
15-8
FAN ENGINEERING
Figure 15.6
bility is shown
— BUFFALO FORGE COMPANY
Fan Performance with Variable Speed
in Figure
15.6. The individual curves are for full
speed, 3/4 speed, 1/2 speed, and 1/4 speed. The full-speed curve will
be identical to the fan curve without the variable-speed device if
no slip exists. However, most variable-speed devices must slip to
transmit torque. For a system such as ABCD, performance will be at
A at full speed, B at 3/4 speed, etc. Because of the fan-law relationship of performance to speed, the performance will be stable at all
speed settings for this particular system. The turndown ratio will be
limited by the minimum speed that the variable-speed device can
achieve.
CHAPTER 15 — FAN CONTROL
Figure 15.7
15-9
Performance of Two Fans in Series
Fans in Series
Figure 15.7 shows the potential performance of two identical fans
in series together with the potential performance of one of the fans
alone. If the fluid can be considered incompressible, the performance
of two identical fans in series is obtained simply by multiplying by
two the pressure for one fan at the pertinent flow rate. This is illustrated by the points A and A’. Point B is the operating point that
would result if there was only one fan in this system.
Two fans in series can be controlled by outlet dampers, inlet-box
dampers,
variable
inlet vanes,
variable
pitch, or variable
speed.
If
each fan is equipped with a control device, then, in general, the
previous discussions pertaining to those devices also apply to fans in
series. One important distinction, especially for high-pressure fans, is
that the absolute pressures in the two fans will differ, and this should
15-10
FAN ENGINEERING
— BUFFALO FORGE COMPANY
x
TWO FANS
ONE FAN a
Figure 15.8
Performance of Two Fans in Parallel
be recognized in their design.
It is common
to use
only one
outlet
damper
or one
inlet-box
damper for two fans in series. Except for the effects on pressure
distribution, the location of the outlet damper on either of the two
fans is immaterial. But, this is not true for an IBD because of the
potential spin or other flow-modifying effects on a fan so equipped.
Fans in Parallel
Figure 15.8 gives the potential performance of two identical fans in
parallel together with the potential performance of one of those fans
alone. The performance of two identical fans in parallel is obtained
CHAPTER
15 — FAN CONTROL
15-11
by multiplying by two the flow rate of one fan at the pertinent pressure. This is illustrated by the points A and A’ on Figure 15.8. Point
B is the operating point that would result if there were only one fan
in this system.
Fans in parallel can be equipped with outlet dampers, inlet-box
dampers, variable inlet vanes, variable pitch, or variable speed for
control. Synchronous control of the parallel fans will lead to the
same kind of results that would be obtained by a single fan. Nonsynchronous
control
is possible, too.
Requirements
might also be
satisfied with only one fan or with one fan at the wide-open position
of the control device and the other fan with a partial opening of the
control device. In a system such as ABO, operation at A is possible
with both fans working in the wide-open control position. But operation at point B requires only one fan in the wide-open control position. Operation between A and B requires either two fans with synchronous control or one fan in the wide-open control position with
the other fan modulated between wide-open and fully closed. Operation between B and O might be accomplished by modulating only
one fan. Figure 15.8 does not show all aspects of the problem that
might have to be considered. For instance, the turndown ratio of the
control device might limit the applicability of a particular control
sequence involving different fans. Even more important is the ability
to bring a second fan on line, which will be discussed separately in
the next section.
Start-up Characteristics
Start-up ofa fan (or getting a fan on line) is usually a very simple
process. Usually, it involves nothing more than pushing the start
button and allowing the fan to come up to speed. Figure 15.9 illustrates what happens when a fan is started up without complications.
Since start-up involves going from standstill to full speed, Figure
15.9 resembles Figure 15.6, which was drawn for variable-speed
operation. Before the start button is pushed, there is no flow and,
consequently, no pressure required, so operation can be considered
to be at point 0. When the fan is turned on, it will gradually accelerate
and eventually will reach the 1/4 speed. If we postulate a system such
as 01234, operation at 1/4 speed will be at point |. Similarly, opera-
tion at 1/2 speed will be at point 2, at 3/4 speed at point 3, and at
full speed at point 4. Obviously, a line drawn through these points
illustrates the rating-point path that is followed during the start-up
process. Each of the points along this path can be considered instantaneously established if equilibrium is also instantaneously estab-
lished. But, the path will be altered if equilibrium is not established
instantaneously. For example, if the attached system has a significant
volume, it may be necessary to pump up the duct, and the path may
1$=12
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Figure 15.9
Start-Up fora Fan ona Simple System
more nearly approach that of 0, 1’, 2’, 3 4. In either case, the intersections between the system curve and the various speed curves are
all stable, and the fan easily comes on line.
Controlled Resistance
Another type of situation is illustrated in Figure 15.10. Here again,
a rather simple fan is accelerated from standstill to full speed during
the start-up process. The difference between this and the previous
case is in the nature of the system resistance. What is postulated here
could be called a controlled-resistance system in which a certain pressure must be achieved before through-flow can begin. Specifically,
the pressure must be raised to X before any gas flows through the
system. If equilibrium is instantly established at each speed, the startup process can be depicted as a straight line from 0 through
1, 2, 3,
CHAPTER 15 — FAN CONTROL
Figure 15.10
15-13
Start-Up fora Fan with Controlled Resistance
and 4 and then a parabola out to 5S. If the duct volume is significant,
it may be necessary to fill up the duct, leading to a path such as 0, 1
2’, 3’, 4, and then on to 5. The point of rating during the filling-up
process starts at free delivery, moves gradually to the left, and in the
case diagrammed, actually reaches shut-off.
Isolation Damper
Still another simple situation is illustrated in Figure 15.11. Here
again, the fan is a simple one accelerating from zero to full speed.
This one, however, is equipped with a leak-free isolation damper.
With the isolation damper closed, the point of operation will always
be at shutoff proceeding from 0 to 1, 2, 3, 4, and 5’. As the damper is
15-14
FAN ENGINEERING — BUFFALO FORGE COMPANY
DAMPER}
WW\-[FAN
Figure 15.11
Start-Up fora Fan with Isolation Dampers
opened, the flow will begin and gradually increase until the damper
is wide-open and the point of operation is at 5. Note that the point of
Operation must go over the hump of the pressure curve and that this
transition may not always proceed smoothly. The difference between
the wide-open fan curve and the parabolic-system curve is the
resistance that must be provided by the damper.
Dip in Characteristic
Yet another start-up situation is illustrated in Figure 15.12. It is
very similar to that diagrammed in Figure 15.9. The difference is that
the fan characteristic has a dip as well as a hump. The fan roughly
represented here could be either a forward-curve fan or a variablepitch fan at one particular pitch setting. As before, the fan must
CHAPTER
15 — FAN CONTROL
|
Figure 15.12
15-15
4.
|
Start-Up fora Fan with a Dip in the Curve
accelerate from standstill to full speed. For a system such as 01234,
there is no problem in bringing the fan on line because the intersections between the system curve and the various fan curves are
all stable.
Variable Pitch
A more complicated situation is shown in Figure 15.13. This is the
same fan that was diagrammed in Figure 15.5 except that the 5/4
pitch position has been omitted and the starting lines (dashed) with
the pitch set at the fully closed position have been added. It is always
recommended that a fan of this type be started with the blades in the
fully closed pitch position. For the assumed system 12345678, the
initial start up corresponding to the acceleration to full speed will
proceed from 0 through 1, 2, and 3, up to point 4. At this point the
15-16
BUFFALO FORGE COMPANY
— ING
FAN ENGINEER
Figure 15.13
Start-Up fora Variable-Pitch Fan
fan has reached full speed, but the pitch mechanism has not been
changed from the fully closed position. The pitch can then be
increased to produce points 5, 6, 7 or 8 or to produce any intermediate points, as required. All the operating points are stable
because the slope of the system curve is positive and the slopes of the
fan curves are all negative. With this particular system, the fan could
be started with the pitch mechanism set at any position. No stall
would be encountered because the system line is low enough. However, this starting procedure is recommended only for the smallest
fans, and then only when the system characteristic is well known.
Figure 15.14 is for the same fan as in the preceding figure, but with
a controlled-resistance type of system. Once again, the fan should be
started at minimum pitch, and after it is on line, then, and only then,
can the pitch mechanism be opened. Note that the points of opera-
CHAPTE
15 —RFAN CONTROL
Figure 15.14
15-17
Start-Up fora Variable-Pitch Fan
tion |, 2, 3, 4, and 5 are all on the right-hand side of the humps of
their respective curves even though the dips appear to penetrate
below the system line. If the fan is isolated by a damper, the start-up
procedure is to bring the fan up to speed with the damper closed and
the pitch mechanism in the fully closed position. After the fan has
come up to speed, the damper can be opened, and then, and only
then, can the pitch be increased. Start up will proceed from 0 to 0’
and then from 0’ to I as the damper is opened.
Fans in Series
When two fans are in series, start up is just like that for a single
fan, if the two fans are started simultaneously. However, if they are
not, the situation can be examined using a diagram like that in
15-18
EE
FAN ENGINEERING — BUFFALO FORGE COMPANY
ee
SS
ee
TWO FANS
vy
%
A+B
YX 3
We
Pvc
=
ONE FAN
Ap 2ND FAN NOT POWERED
0
‘J
Figure 15.15
i
et
ESTE
SE
PI
PL
OR)
|
EPP
EE FEES
Start-Up for Two Fans in Series
Figure 15.15. This is the same as Figure 15.7 but with start-up information added. First, the system 0123 is postulated. Next, it is
assumed that, while the first fan is started, the second fan is at standstill but the flow passes through both fans. Because of the second
fan, the first sees a higher system resistance than the originally postulated one. So, the path of the instantaneous start-up points for the
first fan would be along the line A from 0 to point 4. This fan would
continue to operate here as long as the system and the second fan
stayed unchanged. However, when the second fan is started, the re-
sistance due to that fan, as seen by the first, is gradually reduced.
The first fan’s point of operation moves from point 4 toward point 1.
It reaches | when the point of operation of the second fan reaches
free delivery from some point beyond free delivery. This occurs at a
speed somewhere between standstill and full speed. As the second
CHAPTER 15 — FAN CONTROL
15-19
fan accelerates further, its point of operation ascends its performance
curve while that of the first fan descends its performance curve.
Ultimately, the two identical fans will operate at identical points of
rating and, of course, at identical speeds. These points are 3’ on the
one-fan curve and 3 on the combined curve.
The various portions of the path A and the path A + B are actual
paths so the actual pressures and flow rates can be read on the
appropriate scale. The path B, however, is a relative one. It is shown
on the full-speed curve to illustrate the relative points of operation
on the various part-speed curves of the second fan as it is accelerated.
Actual flow rates can be read for points along path A + B. The pressure for the first fan will be that on the path A, and the pressure for
the second fan will be the difference between that on path A + B and
that on path A.
Fans in Parallel
If two fans in parallel are started simultaneously, the start-up operation will be just like that for one-fan operation. However, if they are
started separately, Figure 15.16 can be used to explain some of the
situations that might develop. This is the same as Figure 15.8, except
that the start-up conditions have been added. Start-up of the first fan
proceeds along the path A from 0 to | if the second fan is isolated
(so there will be no backflow through it). Ignoring the problems of
isolation for the moment, start-up of the second fan would initially
have no effect because the sum of the potential performance of the
second fan and that of the first does not intersect the system characteristic. Only after the second fan has accelerated sufficiently does
the combined characteristic intersect the system characteristic. The
second fan’s relative point of operation at the initial point of intersection will be at shut off for that fan. With further acceleration, the
relative point of operation will move from shut off to the right, as
shown by the path B. Simultaneously, the first fan’s point of operation will gradually move upward from its initial point. Eventually,
when the second fan reaches full speed, the points of operation of the
two fans will be identical. These are depicted as point 3’ on the onefan curve and point 3 on the combined curve. Note that the second
fan’s point of operation has to proceed from shutoff, over the hump,
to the normal operating point. This could cause serious instability
and even graver problems if the fan has a dip in its characteristic.
The various portions of the path A and the path A + B are actual
paths so the actual pressures and flow rates can be read directly on
the appropriate scale. The path B, however, is a relative one. It is
shown on the full-speed curve to illustrate the relative points of
operation on the various part-speed curves of the second fan as it is
accelerated. Actual pressures can be read for points along path A +
B. The flow rate for the first fan will be that on the path A, and the
flow rate for the second fan will be the difference between that on
15-20
FAN ENGINEERING
— BUFFALO FORGE COMPANY
v4
TWO FANS
ONE FAN
Figure 15.16
Start-Up for Two Fans in Parallel
path A+ Band that on path A.
Figure 15.17 can be used to examine some of the problems that
occur in starting up parallel fans that have dips in their characteristic
curves. The characteristics of each fan are approximately the same as
those shown in Figure 15.5, except that a greater turndown capability
has been included and both the 5/4 and Design curves have been
omitted. The map of potential performance for one-fan operation is
shown to the left in the diagram. The map of potential performance
for the second fan has been added on the right-hand side and represents an addition to the performance of the first fan when the first
fan is Operating at the 3/4 position. If we postulate a 100% common-
CHAPTER 15 — FAN CONTROL
Vp
Figure 15.17
15-21
SECOND
FANS
Start-Up for Two Variable-Pitch Fans
resistance system according to 01234567 and if the first fan is on line
Operating at point I, then there will be no difficulty in bringing the
second fan on line. With the blade pitch for the second fan set in the
minimum position, the point of operation will hold at point | until
the second fan develops enough pressure, and then proceed from
point | to point 2 as the second fan continues to accelerate to full
speed. The pitch of the second fan can then be increased from 2
through 3, 4, 5, 6, and on up to 7, if necessary. While bringing the
second fan on line, the point of operation of the first fan must
change because the common resistance increases. For the system
01234567 in Figure 15.17, the point of operation of the first fan
15-22
FAN ENGINEERING
— BUFFALO FORGE COMPANY
;
X
SECOND.
FANT”
y
i
"/p
AS
3/4
Ww,
Z
A
s “
Q
Figure 15.18
Start-Up for Two Variable-Pitch Fans
begins at | when the second fan is first brought on line but reaches 7’
when the second reaches 7.
The situation for the same two fans is different if a system from A
through B, C, D, E, F, and G is postulated as shown in Figure 15.18.
Once again, assuming that the first fan is on line but this time at
point B, note that bringing the second fan up to speed at the minimum blade position will not really add to the performance. (In other
words, the second fan is still not on line.) However,
it can easily be
brought on line by opening the blade pitch enough to shift the point
of operation from B towards C. Continued increase in blade pitch
will produce operation at C, D, E, F, and G without any difficulties
CHAPTER 15 — FAN CONTROL
15-23
_ SECOND.
FAN"
|
|vl%
“%
fa
W
* [we [FAN]
\wereay
Figure 15.19
Start-Up for Two Variable-Pitch Fans
because operation will always be to the right of the hump on whatever performance curve actualizes. If the second fan is started with
an isolation damper closed, the start-up procedure should include
acceleration at minimum blade position followed by an increase in
the blade pitch sufficient to produce a pressure behind the damper
equal to that on the other side, or in other words, a pressure equal to
B. The damper can then be opened without sudden change in operation. Following this, the pitch of the second fan can be increased to
the desired position.
Systems of the type A’ B’ C’ D’ G’ in Figure 15.19 require carefully
controlled start-ups. The first fan could be brought on line satisfac-
15-24
FAN ENGINEERING — BUFFALO FORGE COMPANY
torily by bringing it up to speed and then gradually increasing the
pitch to the 3/4 position for operation at B’ The second fan could
also be brought on line by accelerating it to full speed with the pitch
in the minimum position and then increasing the pitch to produce
operation at, say, C’. Operation at point D’ is even possible, but
beyond that point the potential performance map is empty. Any
further increase in pitch will result in less air flow and the fan will
operate in the stall region of its performance characteristic. Since
operation in stall must be avoided, a different start-up procedure
must be found. Such a procedure involves reducing the pitch of the
first fan enough so that the operating pressure will be below the
minimum stall pressure. A new graph is needed to illustrate this
point, and a slightly different approach will be used to construct this
new graph.
The performance map for one fan can sometimes be used to analyze the performance of two identical fans in parallel without necessarily drawing the combined characteristics. In Figure 15.20 the systems AB and B’G are the same as the system ABCDEFG shown
in Figure 15.18. Note that the AB portion of this system is for one
fan operation and can be used to determine the operating points for
that fan between the fully closed and the 3/4-open pitch position.
The B’G portion is for the second fan if it must be started when the
first fan is on line at B. The situation is exactly the same as that
described in connection with Figure 15.18, and there is no difficulty
in bringing the second fan on line. As the pitch of the second fan is
increased, the operating point of the first fan will move from B to G.
The values of Q read from Figure 15.20 are the flow rates for each
fan, and if there are two fans operating, their flow rates must be
added together to give the total flow rate for two fans in parallel.
Figure 15.20 can also be used to illustrate synchronous start-up of
two fans in parallel. This is shown by the line AG. Note that the
Operating points are higher on the individual pitch-position curves
than for the line AB and that they are lower than the corresponding
point on the line B’G. This facilitates start-up when the controlled
resistance X is so high that operation in stall would result from
starting one fan at a time.
Figure 15.21 is for the same fans and system depicted in Figure
15.19. The curve A’B’ shows the various operating points during the
course of starting the first fan and increasing the pitch to the 3/4
position. The curve B’C’D’G’ shows that the second fan can be
brought on line but that the pitch cannot be increased beyond the
1/6 position without putting the fan into stall. This is only for the
case when the second fan is brought on line after the first is already
operating at the 3/4 position. The two fans could be started synchronously and brought on line without entering stall even with the
high value of Xshown. The path of this process is from A‘ directly to
G’. Note that none of the operating points is close to stall.
CHAPTER 15 — FAN CONTROL
15-25
DESIGN.
Figure 15.20
Start-Up for Two Variable-Pitch Fans
The preceding discussions of fans in parallel are all based on postulated systems having all their resistances common to both fans.
Figure 15.22 is drawn for a situation where part of the resistance is
common to both fans and part is separate. The common resistance
consists of a controlled part at the level of X and a variable part. The
separate resistances are the same for both fans, and the total of the
separate and the common variable resistance is the same as the total
common
variable resistance used for Figure 15.21. The curve A’B’ is
the same as the corresponding curve in Figure 15.21. Both show the
pressure developed across the first fan started. The pressure at B’
would
be measured
by a differential gauge across the points 0 and 2
15-26
FAN ENGINEERING — BUFFALO FORGE COMPANY
SECOND
Figure 15.21
Start-Up for Two Variable-Pitch Fans
on the schematic diagram. Because of the individual resistance between 2 and 3, the pressure at 3 would correspond to that at the
point H’. This is the pressure that would have to be developed by the
second fan at the same point 3 in order for that fan to come on line.
The second fan would, therefore, come on line at the point H”.
Because there is no flow at this point, there is also no pressure drop
across the individual resistance connected to the second fan. This
pressure drop will increase with flow as will that of the common
variable resistance. The path H”G’ can be used to determine the
operating points for the second fan as the pitch is increased to the
3/4 position. As the pressure drop across the common resistance in-
CHAPTER 15 — FAN CONTROL
15-27
SECOND
FAN
Figure 15.22
Start-Up for Two Fans in Parallel
creases due to the added flow of the second fan, the point of operation ofthe first will proceed from B’ to G’. The path H”J’ can be used
to determine the pressure that would be read by a differential gauge
across the points 0 and 3 in the schematic diagram as the blade pitch
of the second fan is gradually increased. Note that the curve H”G’ is
much lower than the curve B”G’ of Figure 15.21. This illustrates that,
as the individual resistances increase compared with the common resistance, the chances of avoiding operation in stall while bringing a
second fan on line are much better. If none of the resistance is
common to both fans, it is necessary only that either fan produce the
pressure at A’ in order to come on line. The operating points for
15-28
FAN ENGINEERING — BUFFALO FORGE COMPANY
either fan would, therefore, fall on the line A’G’ in Figure 15.21.
Most of the preceding discussions were simplified by omitting any
reference to dampers in the system. Dampers are required to keep an
idle fan from windmilling and to prevent the bypass of air around
the rest of the system.
In most
start-ups the damper
on the second
fan should not be opened until the fan has come up to speed and
enough pressure exists behind that damper to ensure that flow will
proceed in the correct direction when the damper is opened.
Power Savings
Figure 15.23
Power Savings with Outlet Dampers
CHAPTER 15 — FAN CONTROL
15-29
Each of the various control devices or techniques can be used to
save power at reduced loads. Just as a map of potential performance
can be drawn with specific output and flow rate as coordinates, a
map of potential performance can also be drawn with input power
and flow rate as coordinates. For each point on the specific output
map, there is a corresponding point on the input power map.
Outlet Damper
Figure 15.23 gives the map of potential power performance for a
fan equipped with outlet dampers. Observe that less power is required as the damper position is changed from wide-open to 3/4, and
Figure 15.24
Power Savings with Inlet-Box Dampers
15-30
FAN ENGINEERING — BUFFALO FORGE COMPANY
still less at the 1/2 and 1/4 positions. This is true only if the basic
power characteristic of the fan is of the type shown, namely, one
with a positive slope. Some fans’ power characteristics have a negative slope over part of the range, and it is obvious that, in these
cases, there will be a power increase rather than a power reduction if
the fan is throttled with an outlet damper. Many axial-flow and
propeller fans have this kind of characteristic, so caution is advisable
when throttling these types of fans.
Inlet-Box Damper
Figure
15.24 shows the power that can be saved when
Figure 15.25
inlet-box
Power Savings with Variable Inlet Vanes
CHAPTER
15 — FAN CONTROL
15-31
dampers are applied to a fan with a positively sloping power characteristic. The spin produced by the IBD not only reduces the output
but also decreases the input more than a simple outlet damper would.
Variable Inlet Vanes
The power characteristics for a fan equipped with variable inlet
vanes are shown in Figure 15.25. Using variable inlet vanes usually
saves more power than using IBDs because the VIVs can be designed
to produce more effective results. (They are usually placed closer to
the impeller.)
Figure 15.26
Power Savings with Variable Pitch
15-32
FAN ENGINEERING — BUFFALO FORGE COMPANY
Variable Pitch
For a properly designed fan with variable-pitch capability, the
power savings can be dramatic, as indicated by Figure 15.26. This
variation in pitch can be achieved in various ways, including manually, pneumatically, and hydraulically. However, the latter two can
be used in automatic systems, and they may require the continuous
application of power to some auxiliary apparatus in order to provide
the necessary force when control is needed. Theoretically, at least,
this additional power should be considered when evaluating the
savings due to variable pitch.
Figure 15.27
Power Savings with Variable Speed
CHAPTER 15 — FAN CONTROL
15-33
Variable Speed
Figure 15.27 shows the power map for a fan with variable-speed
capabilities. The savings are, again, dramatic and predictable according to the fan laws. The variation of speed can be achieved with
several devices, including variable-pitch belt drives, hydrokinetic fluid
drives, hydroviscous fluid drives, AC or DC adjustable-speed electric
motors, and AC adjustable-frequency electric motors. For all these
techniques, the output of the drive will be less than the input to the
drive, and these drive losses, too, should be considered when evaluating the power savings due to variable speed.
Comparisons
Figure 15.28 compares various methods of saving power. As noted
before, the savings resulting from an outlet damper may be substantial, but even greater savings are usually possible with IBDs and
00
IBD
|
viv
Fe
VS,
VS,
VP.
gl
6
Figure
15.28
Comparison of Power Savings
15-34
FAN ENGINEERING
— BUFFALO FORGE COMPANY
VIVs. The very impressive savings that can be achieved with variable
pitch and variable speed are comparable, especially when slip losses
are included in the variable-speed application.
Also, multiple fans can be used to save power, as illustrated in
Figure 15.29. Obviously, only coarse control can be achieved if the
choice of operation is limited to one or two fans, both in the wideopen position. However, fine control by any of the means discussed
(including dampers, vanes, pitch, and speed control) is possible.
ONE
FAN
Figure 15.29
Power Savings with Parallel Fans
Chapter 16
Fan Noise
The sound emitted by a fan is an inevitable by-product of the
energy-transfer process. Because most fan sound is unwanted, it is
classified as noise. The potential for noise production increases with
the normal output of the fan; that is, fan noise increases with both
flow rate and specific output. However, selecting properly, so that the
fan operates at its quieter points of rating, will minimize noise. It can
also be minimized by paying proper attention to design details.
Many of the fundamentals of sound were examined in Chapter 4.
Included there were discussions of physical properties, measurements,
decibels, hearing and noise criteria, and noise control. This chapter
will examine some of the problems associated with predicting the
sound power levels of fans and the sound pressure levels at various
listener locations.
Mechanically Generated Noise
There may be mechanical as well as aerodynamical sources of
noise in a fan. If the mechanical noise predominates, this usually
signifies a mechanical deficiency. For instance, excessive bearing or
belt noise suggests that these components are either overloaded or
failing and that immediate corrective measures should be undertaken.
Similarly, the forces due to rotating unbalance tend to produce
vibrations that can be transmitted mechanically and will, ultimately,
produce noise. Excessive unbalance should be corrected immediately,
and any mechanical-transmission paths should be interrupted with
flexible connections and resilient mounts, as appropriate. The rest of
this discussion will deal exclusively with aerodynamically generated
noise.
Aerodynamically Generated Noise
Fan noise consists of a series of discreet tones superimposed on a
broad-band background. The series of tones, which can be called the
rotational component, can be traced to the energy transfer that also
leads to the development of head. The broad-band background,
which can be called the vortex component, can be traced to the
turbulent-eddy formation that usually leads to losses of head.
16-2
FAN ENGINEERING — BUFFALO FORGE COMPANY
Each time a blade passes a point in the rotational path, an impulse
is delivered to the air at that point. This impulse can be resolved into
a large, steady component and a series of very small, oscillating
components. The steady component produces head; the oscillating
components produce rotational noise at discreet tones. In centrifugal
equipment, the predominant tone of this rotational component of
fan noise is usually that at the blade-passing frequency. But, in very
narrow blade designs, the higher harmonics may be equally intense.
Widening the blades progressively weakens the higher harmonics.
In axial-flow equipment, the predominant tone of the rotational
component may be one of the higher harmonics rather than the
fundamental blade-passing frequency, especially if the fan is used to
develop appreciable pressure.
Doubling the number of blades in any fan theoretically cancels the
odd harmonics and doubles in strength the even harmonics. Insofar
as doubling the number of blades also reduces the size of the fan
required to produce the necessary head, the strength of the even
harmonics will be increased by only one to two times the original
value. (Tests of a one-bladed propeller and the smaller, but equivalent, two-bladed propeller indicate a factor of one. Tests of a 16blade centrifugal and the equivalent 32-blade centrifugal indicate a
factor very close to 2.) Since the odd harmonics will definitely be
eliminated, the sound power level of the fan could be reduced as
much as 3 dB (if the even harmonics are not strengthened at all and
if, originally, they represented one-half of the total intensity) or by as
little as 0 dB (if the even harmonics are strengthened by the full
amount).
Increasing the number of blades usually has more effect on axialfan noise, since the total number of blades is less than for a centrifugal fan. The number of blades should differ from the number of
guide vanes to prevent strengthening the fundamental tone and the
major harmonics, even though this itself creates certain product
frequencies.
Several factors determine the optimum number of blades for each
type of centrifugal fan. These include the effect of blade number on
slip, fluid friction, structural strength, and cost, as well as on noise
output. The net result is that noise considerations seldom dictate the
number of blades.
Vortices can be created at the leading or trailing edges of the
blades, along the sides of the blades, or at locations far from the
blades. Generally, the size, the rate of growth and decay, and the
points of origin and movement of these vortices will be random, and
the resultant noise will have a broad-band spectrum.
Streamlining the leading edges of the blades minimizes vortex formation
at that location.
At the design flow rate, both thin blades
with rounded edges and thick blades with airfoil sections are effective
in reducing vortex formation. However, the airfoil-shaped blade may
CHAPTER 16 — FAN NOISE
16-3
have some advantage, especially when the leading edge does not
match the entering flow angle across the entire width ofthe blade.
Large eddies may form in the blade passages because of flow
separation from a boundary. The greatest advantage to using airfoilshaped blades is reduced separation. However, this is somewhat offset, from a noise standpoint, by the decrease in the optimum number
of blades compared with that for thin blades. Von Karman vortex
streets will be shed from the trailing edges because of their finite
thicknesses. The thickness of the blade trailing edge apparently has
very little effect on centrifugal-fan noise. The effect of trailing-edge
thickness on axial-fan noise is more pronounced. Noise may increase
noticeably if the wake from one blade is cut by succeeding blades.
Whenever two masses of air meet with a finite relative velocity,
turbulence results. The discharge from the impeller and the previously
collected streams join in this way. The degree of turbulence depends
upon the degree of perfection in the design.
The speed of sound so greatly exceeds the air speed in most fans
that noise is propagated equally well both upstream and down. The
acoustical impedances of the inlet and outlet openings are so nearly
equal that, usually, the sound power radiated through the outlet can
safely be assumed to equal that radiated through the inlet. The transmission through the casing walls is so small by comparison that,
when the total sound power output of a fan is measured, the portions
radiated through the outlet and the inlet are each reported as onehalf of that total. Therefore, the corresponding sound power levels
are each 3 dB less than the total sound power level. Other procedures
are necessary to estimate the level of the sound power output through
the casing.
Point of Operation
An experienced listener can tell by the sound of a fan what its
Operating point is. (Even an untrained ear can discern when a fan
stalls because of the rise in noise level and the character of the sound
itself.) This is because the sound power output ofa fan varies with its
point of rating.
A curve of sound power level versus flow rate will exhibit a minimum somewhere near the point of peak efficiency. For centrifuga]
fans, sound power levels usually increase on both sides of the minimum, whereas for axial-flow fans, the level will not change much all
the way to free delivery. The optimum point of rating, from a soundpower-level standpoint, is very close to the point of peak efficiency.
This is best illustrated by a curve of specific sound power level versus
flow rate.
:
The specific sound power level Lws was defined in the fan-law
chapter and can be determined from the actual sound power level
Ly, the flow rate Q, and the fan total pressure prr for any point of
rating by using
16-4
FAN ENGINEERING
— BUFFALO FORGE COMPANY
a
a
TYPE BL - 36.5 IN. DIAM. - 600 RPM - 0.075 LBM/FT?
zs
Se
4
]
a
(=|
=
=2
Ss
52
10
%o
HP
IN
POWER
WG
IN.
IN
PRESSURE
oO.
o'
36
ooo
o
&
&
INCHES
IN
DIAMETER
SPECIFIC
0
2
4
Figure 16.1
6
8
10
»=«12
FLOW RATE IN 1000'S OF CFM
14
16
18
1000'S
SPEED
SPECIFIC
RPM
OF
&
INPERCENT
FFFICIENCIES
IN
Typical Constant Speed Performance Curves
for Centrifugal Fans
150AF — 31.25 IN. DIAM. - 1750 RPM - 0.075 LBM/FT?
co
$3120
}
H
3 =100
n
H
i
SOUND POWER LEVEL
:
‘.
—=
on
WG
IN.
IN
PRESSURE
HP
IN
POWER
Oy 2. Ae 6
8. 10 bel2pc1due
ioe SaeaG
CAPACITY IN 1000'S OF CFM
Figure 16.2
Typical Constant Speed Performance Curves
for Vaneaxial Fans
fC
oN
CHAPTER 16 — FAN NOISE
16-5
Lws = Lw— 10log(QOprr).
(16.1)
Figure 16.1, which shows the performance of a typical centrifugal
fan, and Figure 16.2, which shows the performance of a typical axialflow fan, both contain curves of sound power level versus flow rate
and specific sound power level versus flow rate. The minimum sound
power level does not necessarily coincide with the minimum specific
sound power level because the fan power output is lower for the
point of minimum actual sound power level than it is for the point of
minimum specific sound power level. Comparisons should be based
on equal fan power outputs.
The shape of an actual sound-power-level-versus-flow-rate curve
can be roughly estimated from the shape of the specific-outputversus-flow-rate curve by using Equation 16.1. The actual sound
power level Lw will be proportional to the flow rate Q and the
square of the pressure prr for a constant specific sound power level
Lys. Of course, Lws is not constant, so higher sound power levels
should be expected with greater departure from the point of maximum efficiency. The sound-power-level curve for a centrifugal fan
would be expected to rise from the value at shutoff because both the
flow rate and the pressure increase. However, it would be expected to
fall after the peak of the pressure curve was passed. This fall should
continue until the effects of inefficiency overcome the effect of
rapidly decreasing pressure. This is, in fact, the shape of the curve
in Figure 16.1.
The shape of an actual sound-power-level curve for an axial-flow
‘fan would be expected to gradually fall from the level at shutoff
because the effects of decreasing pressure and increasing flow rate
counterbalance. For any fan that shows a dip in the pressure char-
acteristic, the sound-power-level curve would be expected to rise as
the point of rating enters the dip and climbs to the right. Beyond the
peak of the curve, the sound power level should decrease because the
fan pressure falls. If the fall in pressure is enough, the expected
increase in sound power level due to the decline in efficiency may not
occur.
This is how
the sound-power-level
curve appears
in Figure
lop
Examining the specific sound-power-level curves in Figures 16.1
and 16.2 suggests that the sound-power-level increase is somewhat
proportional to the total-efficiency decrease. Without actual test data,
a value of 4 or 5 dB for every ten points of efficiency may be used to
estimate the specific sound power level of a fan at points other than
at peak-efficiency.
Predicting Sound Power Levels
There
is no satisfactory way to predict fan noise strictly from
theory, so some
experimental
data must
impractical to expect that experimental
be obtained.
However, it 1S
data can be obtained
for
16-6
FAN ENGINEERING
— BUFFALO FORGE COMPANY
every combination of variables for even a single fan line. And, a
family of fans may consist of several sizes built in many arrangements
and equipped with numerous appurtenances. Also, each combination
may operate over a range of speeds, and the operating points on its
characteristic curve may vary widely. Consequently, most fan-noise
ratings are based on the fan laws and other mathematical considerations.
The fan laws, listed in an earlier chapter, include the relationship
of sound power level Ly to fan diameter D, fan speed N, fan density
p, and other independent variables. Fan law le is
Da
Lwa=
Lwp sr 70 log G
a 50lor (Ca) 52 Nie (=) me
Na
a
The coefficients 70, 50, and 20 are the same as those published in
earlier editions of this handbook. Several investigators have developed data suggesting that other coefficients should be used. Instead
of 70, values as low as 60 or as high as 80 have been proposed.
Instead of 50, values as low as 40 or as high as 60 have been
recommended. The coefficients shown in Equation 16.1 will continue
to be used here. However, recognize the possibility that these coefficients may be wrong and that the uncertainty in any result could
be several dB. For instance, for either a diameter ratio or a speed
ratio of 2 and a difference in coefficient of 10, a 3-dB difference will
exist. Most fan-noise measurements cannot be considered any more
accurate than plus or minus 2 dB, so any projections based on those
measurements should be judged in that light.
Sometimes, only the noise associated with the discharge airstream
is relevant; at others,
only the noise associated
with the inlet air-
stream is of interest; in still others, only the noise transmitted through
the casing pertains. In some applications, any two (or even all three)
of these components may have to be examined.
The sound power level of the noise emanating from the inlet, the
outlet, or the casing of a fan Ly, can be estimated from the total
sound power level of the fan Ly by using
Lwn=
Lw—
ALwn,
(16.3)
where ALy, depends on the relevant component. For instance,
ALwn = 3 for either the outlet component of a fan or the inlet
component of a single-inlet fan. For each inlet of a double-inlet fan,
ALwn = 6. These relationships are generally true over the entire
spectrum, so that the values of AL y, can be used for either overall
component levels or spectrum-component levels. By contrast, ALwn
is the transmission loss if the sound power level through the casing is
desired. The transmission loss may vary across the spectrum, so
individual values may have to be applied for each band of interest.
CHAPTER
Table
16.1
16 — FAN NOISE
16-7
Transmission Losses for Fan Casings
Thickness
8 ga and heavier
(Leal 3}
20
Note that these values include adjustments for flanking noise and resonant panels.
Table 16.1 gives typical values of transmission loss for various
thicknesses of material used in fan casings. These values differ somewhat from those previously published in this handbook, reflecting a
more conservative approach to predicting casing-component
noise.
Much higher values of transmission loss can be ascribed to materials
of the same thickness when used in different applications. Experience
suggests that the flanking noises coming through the shaft opening
or vibrations radiating noise from selected panels account for the
lower values in fan applications.
Note that only one value of transmission loss is given for each
thickness of material. In most applications, the transmission loss ofa
barrier varies with the frequency. This is probably true of fan applications, too, but other factors, such as the flanking noises and radiating panels already noted, tend to flatten out the spectrum.
Predicting Sound Pressure Levels
The sound pressure level associated with a fan can vary even for
a constant sound power output. This may result from many things
including the duct arrangement; the directivity of the fan as a sound
source; the nature of the environment
gence,
if the sound
is allowed
(whether hard or soft), diver-
to radiate; reflection, if there are en-
closures or other barriers between the fan and the listener; and
absorption along the path.
The sound pressure level Lyn very close to the source n can be
calculated from the sound power level of the source Ly, and the area
A, associated with that source by using
Lpn = Lwn—
10logAn + Cs.
(16.4)
For instance, the sound pressure level at the inlet of a fan L,; can
be predicted from this expression by using Ly as calculated from
Equation 16.3 and the inlet area A;. Similarly, the sound pressure
level at the outlet of a fan L,2 can be predicted using Ly2 and the
outlet area A>. Either L,; or Lp,2 may pertain if workers are expected
to approach an open-inlet or an open-outlet fan. If both the inlet and
the outlet are ducted, the sound pressure level at the casing Ly. might
be relevant. Predictions based on the full-casing area A, tend to be
optimistic (possibly because of flanking noises and resonant panels).
So, the conservative approach is to use a reduced value for the casing
16-8
FAN ENGINEERING
— BUFFALO FORGE COMPANY
area. One possibility is to use the area of a sphere whose diameter is
that of the impeller. Another is to use only the area facing the listener.
These or other arbitrary techniques will have to be employed until a
more scientific method is developed.
Although
measurements
must
be used to judge compliance
with
specifications, there are certain difficulties in measuring right at the
source. For example, measurements right in the inlet or outlet of a
fan can be seriously affected by wind noise if the microphone is not
properly shielded. Also, it is virtually impossible to measure exactly
on the casing, and even if it could be done, the level would still
probably vary at different locations on the casing. Many specifications call for measurements
at a short distance (like 3 ft) from
the
source. Even these values will be hard to predict because of the difficulties just listed. Nevertheless, the values obtained from Equation 16.4
are probably the best that can be predicted if the distance is short
and divergence Is negligible.
Other specifications call for measuring at a greater distance from
the source. To determine the sound pressure level Lp, at a distance x
from the source, use
fey wae iolog (4-+ Re)Gis
Age
where Ly, is the sound power level as determined from Equation
16.3. This simple expression can be used to approximate the sound
pressure level in a free field, a semireverberant field, or a reverberant
field. In a free field, the 4/R; term becomes negligible, whereas in a
reverberant field, the //A, term can be ignored. However, both terms
must be used in a semireverberant field. The area A, is that area
containing all the points where L,, could be measured. For a nondirectional point source of sound, this area would be the surface of a
sphere at radius x or 47x°. In many practical applications, however,
the area will be irregular, especially if it is not too far from the source.
The effects of directivity can be accounted for by estimating the area
A, over which Lp, would be uniform. If this is done, A, becomes an
isobaric surface. Alternatively, @,/A, can be substituted for //Ax,
where Q, is the directivity factor and A, is the area at a constant
distance x from the source. Refer to the chapter on sound for information on directivity factor Q, and on room constants such as Rg
The value of C4 is 0.1 dB when A, is in m’ and R is in m’, but it is
10.4 dB when
A, is in ft’ and Ris in ft’.
If the fan is enclosed, it will develop a certain sound pressure level
Lpx within its enclosure. Equation 16.5 can be used to calculate this
value. For closefitting enclosures, the room constant must be based
on the net volume. However, this calculation will almost certainly be
wrong because of the interaction between the source and the small
enclosure. Ignoring this error, calculate the sound pressure level Lp,
CHAPTER
16 — FAN NOISE
16-9
just outside the enclosure by using
/
Sie
Lpy = Lpx + 10 log (eyat R ) = 1MEs.
(16.6)
where R, is the room constant for the space surrounding the enclosure, S, is the area of the enclosure walls, and TL, is the transmission loss of the enclosure walls. Transmission-loss values for
various materials can be obtained from the data in the chapter on
sound. Sound-pressure-level predictions at more remote locations
can be based on appropriate rules for divergence, reflection, and
absorption.
It cannot be overemphasized that the above equations give only
approximate levels. Nevertheless, predictions must be made to judge
the need for noise-control measures.
Refer to the chapter on sound for more information on predicting
sound pressure levels from sound power levels.
Example 16.1
Noise Close to a Fan
Given a single-inlet fan with a specific sound power level of 43.7 dB,
find the sound pressure levels close to the inlet, the outlet, and the
casing, if the fan delivers 30000 cfm at 5 in. wg.
The inlet area of the fan is 18.15 ft”, the outlet area is 11.38 ft”, and the
wheel diameter is 44.5 in. The casing thickness is 0.25 in.
An = Te
An— i 38ittz and
AD
= ele = 43 0
Using Table 16.1:
TL.
=
(AL wc —
(dB:
Using Equations 16.1 and 16.3:
Lw= Lws + 10 log (Oprr) = 43.7 + 10 log (30000 X 5°) = 102.4 dB,
Lwi= Lw— (ALw) = 102.4 — 3 = 99.4 dB,
Lyw2= Lw—
(ALw)2=
102.4 — 3 = 99.4 dB, and
Lwe = Lw—
(ALw)c =
102.4 — 20 = 82.4 dB.
Using Equation 16.4:
Lp: = Lw: — 10 log A, + Cs = 99.4— 12.6+ 10.5 = 97 dB,
16-10
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Lp2 = Lw2— 10 logAr+ Ca = 99.4— 10.6 + 10.5 = 99 dB, and
Lypc= Lwe— 10 log Ar + Ca = 82.4 — 16.4 + 10.5 = 77 GB.
Note that spectrum values can be obtained by using similar calculations. Also, A-weighted values can be calculated from the spectrum
values by applying the appropriate weighting factors. (See the chapter
on sound.)
Example 16.2
Noise Away froma Fan
Given the information in Example 16.1, find the discharge noise at
200-ft distance ina free field. Also, find the casing noise just outside an
enclosure if the enclosure is made of 8-in. concrete 15 ft X 15 ft X 10 ft
and if the surrounding space has a room constant R, of 300 ft’.
Using Equation 16.5 for discharge noise:
Bie = Tye Poon (a4)
PX
Lwn
~Wn
—
Ly
yee
=
99.4
A,
R;
ase
4,
dB,
Ay = 4x" = 41 200° = 502655 ft’
(assuming that 200 ft is far enough to consider the outlet a point
source),
4 = negligible ina
4 =
free field,
10.5 dB, and
Lp200 = 99.4 + 10 log =ep spalOlS
99°45 71-0isi LOS—858 dB:
Using Equation 16.5 for casing noise inside an enclosure:
[Dep
i
hyn ar 10 log (
tr =) se Gal;
Ax
Lyn =
Lwe =
82.4 dB,
Ax = 4(10% 15)
2015
15) = 1050 ft?
(ignoring openings for ducts),
R, = 50 ft’ (approximate from Figure 4.6),
Ca = 10.5, and
CHAPTER
16 — FAN NOISE
— $2.47 10 log (755 0)
1050
16-11
+ 10.5= 82.4— 10.9+ 10.5= 82 dB.
Using Equation 16.6 for noise outside an enclosure:
Lpy =
/
Lpx se ID) log G
+ Ze) —
Syr
TLy,
TL, = 38 dB (from Table 4.10 for the 500-Hz band),
Si = Ax = 1050ft-,.and
yi
O2iais 10 log ( +o
— 38 = 82, 5:7 — 38 = 50 dB.
Note that L,, is based ona value of TLy for the 500-Hz band, so this
value of Lp, is only an approximation of the overall level outside the
enclosure. This has been done merely to demonstrate the method. In
actual practice, always determine values across the spectrum when
evaluating fan noise.
Chapter 17
Fan Mechanics
The various parts of a fan must be designed not only for their aerodynamic function but also for mechanical integrity. Among the mechanical subjects considered in this chapter are: |) torque and thrust,
2) centrifugal force, 3) stresses and strains, 4) bearings, 5) critical
speed, 6) balancing, and 7) vibration isolation. The purpose of these
discussions is not to give a complete design method but, rather, to
show some of the important considerations so that design features
will be appreciated when applying and operating fans.
Torque
The shaft torque 7, delivered to a fan by its driving motor can be
calculated from the shaft power Y, and the fan speed N using
oF
KZ.
are
(17.1)
where K is 63030 for U.S. customary units of lb-in., hp, and rpm or
1000/27 for S.1. units of N-m,
kW, and rps. The fan shaft must
be
able to transmit the shaft torque without twisting excessively. See
Equation 17.28 and the associated discussions on shaft design.
Because of bearing-torque losses 7}, the impeller torque 7; will be
less than 7; if the fan has bearings:
=
I= Tis
(17.2)
The blades and their attachments must be able to transmit the
impeller torque without distorting excessively. A rigorous analysis of
blade distortions requires detailed knowledge of the distribution of
pressure on the blades. Some of the distortions can be predicted by
using a less rigorous analysis based on the center-of-pressure concept.
Recognizing that the impeller torque results from the tangential
forces of the blades on the air, the equivalent tangential force per
blade F; can be calculated from the estimated radius r of the center
of pressure and the number ofblades n using
ahi
teres
(17.3)
17-2
FAN ENGINEERING — BUFFALO FORGE COMPANY
For some fans, the air load on the blades is insignificant compared
with the mechanical loads due to centrifugal force. For others,
especially those with long cantilevered blades, the air load must be
considered when designing the blades and their restraints.
Axial Thrust
The axial components of the pressure distribution on an impeller lead to axial thrust. The distribution of axial pressure on the
various surfaces of the impeller will usually be unbalanced. This
unbalanced force will tend to move the impeller toward the inlet in
both axial-flow and centrifugal fans. Because axial thrust must be
resisted or counteracted, bearings and bearing supports (right down
to the foundation) must be designed to hold the impeller in place.
The total axial thrust produced by an axial-flow impeller, or net
axial force F,, can be approximated from
7 CpprrDr
4
:
(17.4)
The thrust will be in lb if the fan total pressure per is in in. wg, the
tip diameter Dr is in ft, and C, is 5.193. Refer to Table 1.4 for C,
values for other units.
For a single-inlet centrifugal impeller, the axial thrust due to unbalanced pressure forces F, can be approximated using the inlet
diameter D,, the fan static pressure prs, and C, as noted above:
7 CpK prsDi
Fa
4
j
(17.5)
The value of the proportionality constant K can be assumed to be
about I.0 whenever the gage pressure inside the fan housing is positive (blower applications), when the impeller is completely shrouded
(inlet
shroud
and
backplate),
and
when
the
shaft
hole
will allow
some leakage (no stuffing box). If the gage pressure in the housing is
negative, if the shaft hole is tightly sealed, or both, the value of K
can be assumed to be about 2.0. If the impeller is completely open
(paddle wheel), there will be practically no net thrust. If the impeller
has only one shroud (cone wheel), the value of K will be higher than
for a completely shrouded impeller.
Theoretically, a double-inlet centrifugal rotor should have no axial
thrust.
However,
some
thrust-resisting capacity should
be provided
to protect against any unbalanced thrust that might develop because
of uneven flow conditions between the two inlets. This can result
from system blockages or from malfunctioning dampers or variableinlet vanes.
CHAPTER
17 — FAN MECHANICS
17-3
AXIAL THRUST RESULTING FROM
~~ _ UNBALANCED PRESSURE FORCES
GAGE PRESSURES SHOWN
—
oa
oma
oe ()
ees
m
RESTRAINING FORCE AT THRUST BEARING
AXIAL THRUST RESULTING FROM
CHANGE IN MOMENTUM
Vay —
=
=
RESTRAINING FORCE AT THRUST BEARING
RADIAL THRUST RESULTING FROM
-/ UNBALANCED PRESSURE FORCES
RESTRAINING FORCE AT RADIAL BEARING
Figure 17.1
Axial and Radial Thrust on Impellers
17-4
FAN ENGINEERING
— BUFFALO FORGE COMPANY
ed
The change in momentum resulting from the change in direction
of flow (from axial to radial) in a centrifugal impeller also produces
axial thrust. This momentum thrust F,’ tends to move the impeller in
the direction opposite the inlet and can be calculated from the mass
flow rate m and the axial approach velocity V2’ using
poe
VG
Lohse pre
(17.6)
F.’ is negligible compared with the unbalanced pressure thrust F; at
low flow rates. However, Fu’ increases with flow rate and usually
dominates at points of rating toward free delivery.
Axial thrust can be reduced or even reversed by building fins on
the backplate exterior. Such fins can be designed to equalize the
pressure with very little flow and only a small power increase.
Balancing holes in the backplate or a balancing chamber, such as
often used in high-pressure single-suction pumps, could also be in-
corporated but are seldom justified.
The distribution of forces within a fan due to an externally applied
vacuum or pressure may or may not be unbalanced. Usually, this
pressure or vacuum is considered to act only on the cross-sectional
area of the shaft and then only if one end extends through the casing
to a region of atmospheric pressure. The resulting thrust will be
directed toward or away from the inlet depending on the direction
of the shaft extension and on whether a vacuum or pressure exists.
Radial Thrust
Unbalanced radial pressures cause radial thrust. Very little radial
thrust can be expected in an axial-flow impeller, but in a centrifugalfan impeller, the radial-pressure distribution can become distorted,
especially at off-design points of rating. (Volute-type housings usually cause nearly uniform pressure distributions over the impellerdischarge area at design.) Any net unbalance will have to be carried
by the bearings and transmitted to the foundation. The radial thrust
from unbalanced pressures is usually negligible compared with the
radial forces produced by rotating mechanical unbalance.
Housing Restraints
The housing, whether floor-mounted or ceiling-suspended, must
be restrained. Although friction and the weight of the unit will sometimes be enough to keep the fan from moving, more positive restraints should still be used.
If the impeller is supported by bearings on independent pedestals,
the foundation bolts for the pedestals must transmit to the foundation the axial- and radial-thrust forces generated in the impeller. Of
course, the bearings and the bearing bolts have a similar function.
~ CHAPTER 17 — FAN MECHANICS
Figure 17.2
17-5
Housing Restraints
The housing will also be exposed to thrust forces because of a change
in momentum, unbalanced pressure, or both.
For an axial-flow fan housing, the change in momentum, in both
the axial and radial directions, is usually negligible. However, this
will not be so if an appreciable difference exists between the inlet and
outlet areas. For a centrifugal-fan housing, changes in momentum
always occur in both the axial and radial directions. The corresponding momentum thrusts may be reinforced or weakened by any unbalanced pressure forces associated with the housing. The net axial
and radial forces must be transmitted through the foundation bolts.
If the impeller is supported by bearings mounted on the housing,
both the impeller and housing thrusts must be restrained by the
housing’s foundation bolts. The reaction torque at the motor must
also be considered in foundation design.
Centrifugal Force and Centrifugal Moments
Consider a body rotating at constant angular velocity about a
fixed axis. Each element of that body, no matter how small, has an
acceleration toward the center of rotation equal to its linear velocity
squared U’ divided by the radius r. The restraining force exerted by
adjacent elements (called centripetal force), which equals the product
of this acceleration and the mass m, must be directed toward the
center of rotation. The force exerted by the mass on its restraints
17-6
FAN ENGINEERING — BUFFALO FORGE COMPANY
must equal the restraining force and act in the opposite direction.
This force, known as centrifugal force F., can be calculated from
Saye
= fee
(17.7)
For U.S. customary units of lb, lbm, ft, and rpm, Cr is 2934. For S.1.
units ofN, kg, m, and rps, Cris (1/27).
Equation 17.7 can be used to calculate the centrifugal force related
to each of various elements of a rotating structure by using the mass
m of the element and the radius r of its center of gravity. Similarly,
the centrifugal force of the entire rotating structure will be the same
as if the total mass were concentrated at its center of gravity. The
degree to which the structure should be divided into elements will
depend on the purpose of the analysis. For example, the overall
unbalance of a rotor can be expressed in terms of the eccentricity,
the distance between the center of gravity of the whole structure and
the center of rotation. On the other hand, the distribution of centrifugal forces affects stresses within the structure. To accurately calculate such stresses, these distributions must be considered rather than
the resultant centrifugal forces acting on the blades, shrouds, etc. A
classical strength-of-materials approach, or perhaps a finite-element
analysis, may be required.
If, at any radial location, the mass is not distributed uniformly
about the plane of rotation, centrifugal moments as well as centrifugal force will be produced. A spectacular example of this is the
twisting moment about the radial axis of an axial-flow fan blade that
develops because each radial section is set at an angle to the plane of
rotation. The net centrifugal moment M, can be determined by dividing the blade into elements in both the radial and chordwise directions and then calculating the centrifugal force F.; for each using
Equation 17.7. Next, determine the distance x; for each element. This
is measured from the elemental CG to the plane of rotation (passing
through the center of gravity of the entire section at the appropriate
radius). Then, determine the cosine of the angle a; between the radial
line through the elemental CG and the radial axis through the CG of
the appropriate section. Finally, add the products of these factors for
all the elements, as shown in
n
M.=
peaius tiGns
»
lis
ie
(17.8)
Figure 17.3 illustrates how a centrifugal moment is generated by one
elemental mass ona axial-flow blade.
Of course, all centrifugal moments must be resisted by the supporting Structure. For some variable-pitch axial-flow fan blades, the cen-
CHAPTER
17 — FAN MECHANICS
17-7
ELEMENTAL MASS mm;
T oe
SIDE ELEVATION
CG OF SECTION 4- A.
SSS
F.; sin a
SECTION A - A
TOP VIEW
PLANE OF ROTATION
Figure 17.3
NI
XN
Centrifugal Moments
trifugal moments are large enough to require a counterbalance.
Otherwise, the mechanism for varying the pitch would have to
produce very high torques to turn the blades and, so, would require
excessive power.
Bearings
Fan bearings must be able to withstand the loads due to the dead
weight, thrust, and unbalance of the rotor assembly. They must also
be able to operate at the intended speed without overheating. Various
methods are used to estimate the temperature rise in sleeve and antifriction bearings, both of which are used in fans.
When not enough heat is dissipated by natural convection from
the pillow block or other type of bearing housing, some form of
forced cooling is necessary. Small fan wheels, called heat slingers,
mounted on the shaft between a hot fan casing and the bearing
promote cooling by increasing the circulation of air over the bearing
and by providing extended heat-dissipation surface for the shaft. Pillow blocks and some bearing liners can be provided with internal
passages through which cooling water or even cooling air can be cir-
culated. Lubricating oil can be circulated through an external cooler.
Most plain journal bearings are furnished with self-aligning and
17-8
FAN ENGINEERING
— BUFFALO FORGE COMPANY
ring-oiling features. If the bearings are water-cooled, the connections
for the water should be flexible. Even though self-aligning features
are built into the bearings, special precautions should still be taken
to line up the original installation as perfectly as possible. Ring oiling
will be adequate if the proper level is maintained in the reservoir and
if peripheral speeds are not excessive. At high shaft speeds, forced or
drop feed may be advisable. Hydrostatic oil lift is not required if the
bearing material is of good quality, but the material must withstand
running dry for a very short period after the shaft has started from
rest. Various babbits and bronzes have different load capabilities. As
a rule of thumb, the diametral clearance between the journal and the
bearing should be about 0.001 inches per inch of shaft diameter plus
0.002 inches. The axial clearance
in thrust
bearings usually ranges
from 0.008 to 0.012 inches.
The clearance, together with the speed, the load, and the viscosity,
determines the coefficient of friction. With a clearance ratio of
0.001 and a ZN/P of 200, a coefficient of 0.01 can be expected. To
calculate ZN/P, the viscosity Z should be in centipoises, the speed NV
should be in rpm, and the bearing pressure P should be in psi and
based on the projected area. Decreasing the clearance and anything
that increases ZN/P increases the coefficient of friction. In starting
on a greasy surface, the coefficient may range from 0.08 to 0.14. If the
bearing is perfectly dry, the coefficient may range from 0.25 to 0.40.
By contrast, antifriction bearings have a coefficient of from 0.001
to 0.002, exclusive of any rubbing seals. Higher values should be
expected during starting. Antifriction bearings must also be selected
with loads, speeds, and heat dissipation in mind.
Every bearing must be protected from excessive vibration, heat,
dirt, and moisture. Any rotor unbalance will produce vibrations at
the bearings. Bearing supports should be isolated from hot fan
casings. Seals should prevent dirt or moisture from entering and
lubricant from being lost. However, bearings in high-velocity airstreams are subject to large pressure differences that can cause loss
of lubricant.
Static Stress, Strain, Strength, and Failure
Stress is a mathematical concept useful in analyzing the effects of
loads on structures. There are two kinds: normal stress, that stress
normal to the area on which it acts; and shear stress, that stress
along the area. For triaxial stress, the most general case, stresses are
produced in three dimensions with nine components, as shown in
Figure 17.4. Stresses in the third dimension can often be ignored
making possible a simpler analysis. Biaxial stress, as illustrated in
Figure 17.5, has only four components, two of which are equal. The
maximum normal stress 0; and the minimum normal stress o2 are
called principal stresses and can be calculated from
CHAPTER
17 — FAN MECHANICS
=
Ont
ee
Oy
|
(-5*)
i=
17-9
2
ae
2
2
ee
a
(17.9)
The maximum shear stress Tax iS
Pee
2
Eos
(17.10)
The angle ¢@ between the principal axes and the x and ) axes can be
found from
hee
2sNene
Rarer
(17.11)
yb
Oy
Ox
aoe
.
7g,
NORMAL STRESSES
SHEAR STRESSES
Ox
Txy —
Tyx
Oy
Tyz
a
Tzy
Oz
Tzx =
Txz
Figure 17.4
Three-Dimensional Stress Element
17-10
FAN ENGINEERING
— BUFFALO FORGE COMPANY
When the principal stresses are known, the stress og normal to a
plane at an angle ¢ to the plane of maximum principal stress can be
calculated from
+
Gg
Sas
—o
ar “a5 a
cos2¢.
(17.12)
The shear stress rg acting along a plane at an angle ¢ to the plane
of maximum principal stress 1s
Le
Clee
C25"
i cline we
2
(17.13)
oO)
Ox
Li?
Oy
Ox
—.
A
Tyx
Oy
Txy
Ox
Ox
Txy
NORMAL STRESSES
Ox, Oy
Figure 17.5
=
SHEAR STRESSES
Txy =
Two-Dimensional Stress Element
Tyx
CHAPTER 17 — FAN MECHANICS
17-11
Strain ¢ is the linear distortion per unit length due to normal
forces. Shear strain y is the change in a right angle produced by
shear forces. Equations 17.9 through 17.13 have counterparts for
strain. Simply substitute « for o and y/2 for rt, and use the same
subscripts.
For an elastic material, stress is related to strain. In the simplest
case, namely uniaxial tension, stress is proportional to strain, or
o> Ee,
(17.14)
where F is the modulus of elasticity. Similarly,
ree Gay
where G is the shear modulus
Eand G:
(17.15)
of elasticity. Poisson’s ratio v relates
E=2G(1+ »v).
(17.16)
The relationships between stress and strain are more complicated
for biaxial or triaxial stress. For instance, the principal strains for
biaxial stress are:
_ 91_ vor
ff Rye
Vor
(17.17)
LOE
am Ey
Cl
apne
a
vO!
VO2
SS Se SS
Bom
These equations can be combined
terms of strains:
oe
—
Joy
_
02
E(e+
Oe
(17.19)
to give the principal stresses in
ose E(e: Sle Vé2)
0)
(17.18)
and
(17.20)
vei)
(17.21)
which are useful for strain-gage evaluations. Note that, even if the
principal directions are known, both principal strains are needed to
determine the principal stresses.
17-12
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Some even simpler analyses can be useful. The average tensile
stress s in a tension member can be computed from the crosssectional area A at the relevant plane and the force component F
acting along a line perpendicular to that area by using
re
(17.22)
Compressive stresses are also normal stresses but directed opposite
to tensile stresses. Bending stresses in a beam are a particular distribution of tensile and compressive stresses across the section. Such
stresses are of zero magnitude at the neutral axis. This axis may
coincide with the centroidal axis, depending on the curvature of the
beam. The stress in any fiber of a straight beam can be computed
from the bending moment M, the second moment of the cross section /, and the distance c of the fiber from the neutral axis using
LIE
5=—.
I
(17-23)
Shear stresses can be produced by any load parallel to the section.
Direct shear V produces an average stress s, over the cross-sectional
area A of
as
Am
(17.24)
Torque 7 produces shear stresses. For a circular shaft with a polar
moment of inertia /, the stress at any radius r is
Ss
Tr:
a:
(17.25)
Table 17.1 gives A, /,, and J for various sections. The second
moments of area /, are about the horizontal axis x — x. The second
moment of area about any parallel axis at a distance ) is greater by
an amount equal to A)". The second moment
of any composite sec-
tion is the total for all the individual sections about the same axis.
The stresses induced in the part may be due to more than one force.
Table 17.2 gives equations for M and V for various beams.
It was noted above that, in elastic materials, stress is proportional
to strain. Many materials are elastic, at least until the load becomes
too great. Figure 17.6 shows what happens to a material like steel
during a tension test. Hooke’s law applies up to the proportional
limit. The material can be stressed to the elastic limit without any
permanent set. At the yield point, if there is one, the material
CHAPTER
17 — FAN MECHANICS
Table 17.1
Section
17-13
Properties of Sections
i= Pe
A
wd’
7d
:
1d*
64
d*
32
4
m(dy' — d*) | (di — do’) | (dv — dy)
ida
4
(di; + dy’)
16
17-14
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Table 17.2
Shear, Moment, and Deflection Formulae
For Beams with Transverse Loads
or
Support and Loading
Diagrams
Bending Moments and
Maximum Bending Moments
Reaction, Vertical Shears,
and Constraining Moments
Cantilever, end load
M=—Wx
R2=+W
ib
Max M =—
WI(at B)
Riot 3hM"=+5WU-x)
errs
M'=+5Wx
Max M = +4 WI (at B)
ee
Oe.
M=+wex
Max
End supports, unif. load
Y
|
W=wl
w.
/
]
Rivet he Roars
-
M=
M=+ w 2? (ar B)
ly (x-*
4
Max M=
Vi=R,
=I
VS
ola/
al
V"=R-W
NT
ae
M\=75W1
Sd
lies
Vis
Wlx
W = load in Ib
R =reaction in |b
a
a
:
m*=+wtU-x
M =moment in in.-lb
V =vertical shear in Ib
Max
+5 wi(a x==i)
4
27
i
3
poss. M=>55Wiwi( when a=4))
eat}
Nexue
D
u=4w(x-*-11)
mea!
Max M=—
=5WI(at
A& B)
x = distance in in.
/ =Ilength of beam in in.
a = length in in.
b =length in in.
Adapted from data of R.J. Roark and W.C. Young: Formulas
for Stress and Strain, Fifth Edition,
McGraw-Hill Book Co., Inc., New York, 1975, pp. 96-108.
CHAPTER 17 — FAN MECHANICS
17-15
Table 17.2 (Cont.)
Shear, Moment, and Deflection Formulae
For Beams with Transverse Loads
Deflections, Maximum Deflections, and End Slopes
Wie aay?3x +27)
ai 6 Er
y=
Max
Se
1We
Ory (at A)
=e 34
the ETT
ALE |
Max
y
\ ane
=nall
Dies hs
(X 1.000
4A)
Beto
—
ea
4 EP
Oy, (at A)
ee
4x)
6
WE
WENA
Foe
Maxy=-4
a
Oe
2
a) 2|
nae (a+ 2b)
aia
HEE (at A)
(X 1.000
for use in Eq. 17.31)
lef
ae24 ap
eS i
_
ax Vv=~ Fe" gp (at B)
) jo
LW
El (at A)
(X 0.645
for use in Eq. 17.31)
3
lx
(at A)
for use in Eq. 17.31)
GP
1Wwe
Ey
3a(a+
2b)
a
o=-L
# (o1- BY a A)
(ax= aN [ia(a+ 2b)
ifa>b)
AE
4 ET (at A)
21x? + x’)
6=
3
Max y=
)
Rese
ry a
at x=4i)
Mee
2
48 EI (31x
(X 0.789 for use in Eq. 17.31)
4x)
ie
2a Wwe
ax Y= —~F95 ep (al B)
y= LHe (Gee
bs
DU
;
Bai)
aly
AES Se a Pe SIFU Naas
Vie
a
Px
oa ari (Dil)
:
(X 1.000
for use in Eq. 17.31)
Seis
pi
ive>s)
2
3
Max y=
a
ne (ax=4/)
(X% 0.766
for use in Eq. 17.31)
= deflection in in.; E = modulus of elasticity in psi; 6 = slope in radians; / = moment of section in in.*
Prime means valid from A to B; double prime from B to C. Constraining moments, loads, and reactions
are positive as shown. Bending moments are positive when clockwise. V & are positive when upward.
If the beam is turned end for end, lengths a & can be interchanged.
17-16
BUFFALO FORGE COMPANY
— ING
FAN ENGINEER
0.2% OFFSET YIELD STRENGTH
ULTIMATE
STRENGTH
ELASTIC LIMIT
STRESS
o
PROPORTIONAL LIMIT
"STRAIN «
Figure 17.6
Stress-Strain Diagram
stretches without any corresponding increase in load. The yield
strength corresponds to a small but definite amount of permanent
set, usually 0.2% as shown. Fracture of the test specimen may occur
when the ultimate strength is reached or at a somewhat greater strain.
The problem in applying this information about a material in the
design of a structure is that the actual stresses rarely correspond to
those in a simple tension test.
Many failure theories are used to estimate when a part will fail
based on an analysis of the stresses and strains in it compared with
the stresses and strains in the tensile-test specimen at failure. Of
course, failure itself must be defined. For some parts, failure is considered fracture. For others, failure is inability to perform their
function, which might occur if the elastic deformation exceeds a
certain amount. For still others, some permanent set can be tolerated.
Among the strength theories for static failure are: the maximumnormal-stress theory, attributed to Rankine; the maximum-shear-
CHAPTER 17 — FAN MECHANICS
17-17
stress theory, also called the Coulomb or Tresca theory, or Guest’s
law; the Mohr theory; the maximum-normal-strain theory, often
called Saint Venant’s theory; the maximum-strain-energy theory; and
the maximum-distortion-energy theory, commonly called the von
Mises- Hencky theory.
Each of the static-failure
theories requires certain information
about the static strength of the material, and each is best suited to a
certain type of failure. A complete discussion is beyond the scope of
this work, but briefly, for ductile yielding and ductile fracture, the
von Mises-Hencky theory is usually considered the most accurate.
Use of the Mohr
theory is usually limited by the accuracy of the
available compression and torsion data. And, the more conservative
maximum-shear-stress theory is the basis for many codes. Although
the maximum-normal-stress theory is sometimes used to predict
brittle fracture, the Mohr theory is preferred if data are available.
Static (or steady) stresses are produced in a fan by the steady
components of the forces acting on the various parts. The steady
components of the fan pressure produce static stresses in both the
rotor and stator parts. The steady (or constant-speed) rotation of the
impeller produces static stresses in the rotor due to centrifugal force
and centrifugal moments. External loads may also contribute to the
static stresses.
Static stresses can be calculated from strain-gage measurements
and other experimental techniques. Analytical methods to determine
stresses include finite-element and strength-of-materials techniques.
Although a complete experimental stress analysis is best, it would be
impractical to require such an analysis for every fan made. Similarly,
finite-element analysis will provide much information, but it may not
all be necessary to ensure the integrity of every fan. Both experimental and finite-element analyses will often reveal problem areas
that might have been missed using less rigorous methods of analysis.
So, their use should be considered, especially for new designs. Alternatively, larger safety factors must be used with the less rigorous
methods. A simple finite-element model is illustrated in Figure 17.7.
More complicated models are needed to determine stresses and
strains at highly localized areas.
The stress distribution in a centrifugal-fan rotor can be found, at
least approximately, by examining a few equations. The blades can
be considered beams. Bending moments can be determined from the
equations in Table 17.2 and the corresponding stresses calculated
from Equation 17.23. For blades that are shrouded both front and
back, the beam might be considered fixed at both ends and uniformly loaded. This suggests that the maximum stresses occur at
the fixed ends, which is usually so. In fact, some fan blades are designed to operate at speeds that will produce a small permanent set
at the fixed ends. The shrouds can be considered rotating discs with
central holes. Without any external loads, the radial stresses must be
17-18
— BUFFALO FORGE COMPANY
FAN ENGINEERING
Figure 17.7
Simple Finite-Element Grid
zero at the inner and outer diameters, and the maximum
o, occurs at the radius \/rilo:
max
Kiba
radial stress
See
gel
FON RE (ro?he — rz)
Oss
(17.26)
The maximum tangential stress o, occurs at the inner radius:
max
0; =
E sinew
reaps,
SOM arpaLi)
Pree
(17.27)
Of course, the blades and shrouds do interact, so the simple analyses
above will not give precise values.
The stress distribution in an axial-flow fan blade can also be estimated easily. The blades are tension members relative to centrifugal
force and can be considered
cantilever beams
(or plates) relative to
the axial and tangential components of the pressure forces. Equations
CHAPTER
17 — FAN MECHANICS
1-9
17.22 and 17.23 can be used. The centers of gravity for all the sections
are usually stacked on a common radial line to minimize the bending
stresses. Sometimes, they are deliberately offset to compensate for
the pressure forces. The supporting hub may be a complicated structure consisting of a rim and supporting discs. Blade loads and selfgenerated loads must be considered.
Dynamic Stress, Strain, Strength, and Failure
The discussions in the preceding section dealt with the effects of
static loadings. But, dynamic loadings must also be considered. These
are usually classified as either impact or cyclic.
Fans may be subject to impact loads during quick starts and stops,
earthquakes, explosions, etc. Stress impact factors based on experience are used in design. The size of the factor depends on the relationship between the rapidity of the loading and the structure’s natural
frequencies of vibration. If the time between zero and maximum
load is more than three times the period of the lowest natural frequency, then the dynamic effects are insignificant and the factor is
1.0. The factor will definitely be greater than 1.0 if the loading time is
less than one-half the period of the lowest natural frequency of the
structure.
The design of shafts is an example of the use of impact factors.
The design equation is usually expressed in terms of the section
modulus //r or its equivalent 7d*//6 and the maximum
allowable
shear stress max Ss:
wd
J
Ka MY + (Ka
Joma
tis a
MAX Ss
The steady-state bending moment
must
be adjusted
for any
‘
(17.28)
M and the steady-state torque
possible shock
T
or impact. The bending
moment impact factor Ky ranges between 1.5 and 3.0 and the torque
factor Kr between |.0 and 3.0, depending on how suddenly the load
is applied. Values of rd’*//6 are listed in Table 17.3. Other parts of
the fan should be analyzed similarly.
Failure modes for impact loading resemble those for static loading;
that is, the part may fracture or it may deform too much, either
elastically or plastically. Notches and stress raisers should be avoided.
Some parts perform better if material is strategically removed.
Fans may be subject to cyclic loads due to frequent starts and
stops, to surging or other aerodynamic phenomena, to resonant conditions, etc. Such loads can produce premature fatigue failures if
they are not considered in the design of the fan. Fatigue cracks
typically originate at points of high stress concentration and propagate until detected or fracture occurs. Low-cycle and high-cycle
fatigue are both possible in fans.
17-20
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Table 17.3.
Values of 7d’//6 for Shafts
in ins
Sree
MEM
Sa
ei
re
re
3/5
0 | 0.196}
Ye |0.236)
% | 0.280)
rs |0.329]
1.571}
1.723}
1.884]
2.055]
Yq | 0.384 | 2.236]
She |0.444) 2.428)
¥% | 0.510) 2.630}
The |0.583 |2.843)
ee
wis
eee
ARE
5.301) 12.57 |24.54) 42.41 |67.35 |100.5 |143.1 | 196.4
5.639] 13.16 |25.47 |43.75}
—
=
=
5.992] 13.78 |26.43 |45.12 |71.02 |105.3 |149.2] 203.8
6.359 | 14.42 | 27.41] 46.51 | —
—
—
_—
6.740) 15.07 |28.41 | 47.93 |74.82 |110.3 |155.4]
7.136) 15.75] 29.44) 49.39)
—
—
—
7.548 | 16.44 | 30.49 |50.87 |78.76 |115.3 |161.8}
7.975] 17.16 |31.56 |52.38)
—
—
—_
211.4
—
219.3
—
Y% |0.663| 3.068] 8.416 |17.89 |32.66 |53.92 |82.83 |120.6 |168.3 |227.3
Se |0.749 |3.304} 8.877 | 18.65 |33.79 |55.49
5 | 0.843] 3.551 | 9.352 | 19.42 |34.94 |57.09 |87.04 | 126.0 |175.1 |235.5
As | 0.944 |3.811} 9.845 | 20.22 |36.12 |58.72}
—
—
—_
—
% | 1.052 |4.083)
376 |1.169 |4.368}
™e | 1.294| 4.666)
"6 |1.428 |4.977]
10.35 |21.04 |37.33 |60.38 |91.39 |131.5 |182.0) 243.9
10.88 |21.88 |38.56 | 62.08
11.42 | 22.75 |39.82 |63.80 |95.89 | 137.3 |189.1 |252.5
11.99 |23.63 |41.10 |65.56 | —
—
=
—
A material’s ability to withstand cyclic loads is indicated by its
endurance limit §,. Endurance limits are usually determined from
tests of standard specimens. However, actual parts will have different
surface finishes, sizes, or stress distributions and, so, will not perform
exactly the same as the test specimens.
The design of fans that are subject to impact or cyclic loads requires consideration of many more factors than can be discussed
here. Among the important fracture-mechanics topics are: mean
stress, alternating stress, stress concentration, toughness, crack initiation, crack propagation, transition temperature, and residual stresses.
Environmental factors also greatly influence the life of a fanv
Creep, creep rupture, stress-corrosion cracking, corrosion fatigue
and any other effects of temperature or gas composition must be
considered.
Vibrations and Critical Speeds
There are two types of vibrations: forced and free. An elastic body
will vibrate freely at one or more of its natural frequencies if its
equilibrium is momentarily disturbed by an external force. The
motion will gradually die down because of damping. If an external
force is applied repeatedly, an elastic body will vibrate at the frequency of the external excitation, whether this coincides with a
CHAPTER 17 — FAN MECHANICS
17-21
natural frequency or not. Resonance occurs when the excitation frequency coincides with one of the natural frequencies. Some sources
of excitation contain components at several frequencies. Large amplitude vibrations accompany resonance unless there is considerable
damping in the system, but they can also be caused by large excita-
tion forces even when the damping is high.
The free vibrations of an elastic body can consist of an infinite
number of particle motions. Among these various modes of vibration
are certain principal ones wherein all the particle motions are at the
same frequency and follow a precise amplitude pattern. The most
important principal modes of vibration are those that occur at the
lowest frequencies. It is convenient to classify these modes of vibration according to their numerical order and the direction of vibration
relative to the principal axis of the part or member. The direction of
oscillation may be longitudinal, lateral, or angular. Longitudinal
vibrations are seldom serious in fan parts. Lateral vibrations cause
bending. Angular vibrations lead to torsion. The first bending mode
may have a higher or lower frequency than the first torsional mode,
depending on the geometry and material of the part. The various
plates and beams that comprise a fan all have natural frequencies.
The lowest natural frequencies usually occur with cantilever beams.
Unshrouded impeller blades fall into this category. Shrouding may
raise the natural frequency to several times the unshrouded value.
The lowest natural frequency/, of a uniform cantilever beam can
be calculated from the modulus of elasticity E of the beam material,
the second moment / of the beam cross section about the principal
axis, the length / of the beam, and its mass per unit length w using
a2
"On
gEI
whe
(17.29)
The lowest natural frequency of an identical beam fixed at both ends
(instead of one) is 6.4 times higher than indicated by Equation 17.29.
The lowest natural frequency of a ring with radius r is
ey
laine
eae
wrt
(17.30)
Equations 17.29 and 17.30 can be used to estimate the lowest
natural frequencies of certain fan parts, such as blades and rings.
Calculations are more complicated for more complicated shapes.
Modal analysis testing, as described in a later section, can be used to
find mode
shapes and frequencies
for even the most
complicated
structures. Fan parts can be excited by periodic aerodynamic forces.
And, detuning may be necessary to avoid resonance.
A fan, like any rotating elastic structure, will have certain operating
17-22
FAN ENGINEERING
— BUFFALO FORGE COMPANY
speeds at which objectionable vibrations are likely to occur. These
critical speeds correspond to the various natural frequencies of the
system. Since it is virtually impossible to perfectly balance a fan,
there will always be an excitation force with a frequency corresponding to the operating speed. If one of the system’s natural frequencies
coincides with the rotational frequency, resonance results.
Figure 17.8 shows the relationships between the nondimensional
response MX/me and the frequency ratio f/f, for the forced vibration of a system resulting from rotating unbalance. The total vibrating
mass M includes the rotating mass m, which has an eccentricity e.
The system amplitude is X, and the phase angle is ¢. Note that, as
the operating frequency f approaches the natural frequency /,, the
response increases. This increase depends on the damping factor (,
where c is the actual damping and ¢, is the critical damping. Note
also that the phase angle @ changes with frequency ratio. Figure 17.8
is for a single-degree-of-freedom system. A more typical spectrum
for a fan that has many degrees of freedom is shown in Figure 17.9.
Critical speeds are often erroneously considered a property of the
shaft only. This is not so; the bearings, supports, foundation, and soil
all contribute to the elastic properties of the system. Special terminology has been suggested to convey this idea. However, we will
continue to use the term critical speed to indicate coincidence between
, 180°;
eee.
3.0.
3
i_a
DB
i 4
x
=
>
ws
LO
2.044306
84.08 5.0
FREQUENCY RATIO ///;,
a.
wn
co
FREQUENCY RATIO
///;,
Figure 17.8
Response to Rotating Unbalance
CHAPTER
17 — FAN MECHANICS
17-23
the operating speed and a natural frequency. The nature of the supporting portion of the system should be specified whenever a critical
speed is calculated. For instance, if details of the foundation and soil
are not known, the critical speed might be calculated for a fan as if it
were on a rigid foundation. If this is done, a considerable margin
between the operating speed and the calculated critical speed should
be provided so that the reduction due to foundation and soil flexibilities will not place the actual critical speed too near the operating
speed.
Complex computer programs are available for calculating critical
speeds. These include the effects of the bearings, the supports, the
foundation, and the soil. Also, gyroscopic and impeller flexibility
effects can be included when appropriate. Detailed response calculations are also possible. That is, the motions at various locations can
be calculated for a given excitation force.
Approximate values of critical speed can be predicted from some
fairly simple equations. For a simple system, the maximum static
deflection y, as determined from the equations in Table 17.2, can be
used in
Jy
(17.31)
to determine the critical speed M,. The /87.7 factor corresponds
to speeds in rpm and deflections in inches. For SI units, substitute
| /27 instead.
AMPLITUDE
(mV.)
——>
FREQUENCY (Hz.) —>
Figure 17.9
Typical Fan Vibration Spectrum
17-24
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Equation 17.31 is appropriate for those systems in which the mass
can be considered concentrated at a single point and the static deflection is calculated at that point. The factors listed in Table 17.2 should
be used to convert deflections for uniform loads to equivalent deflections. If there is more than one concentrated load, approximate
results can be obtained by totalling the deflections under each load.
Do not include any unidirectional deflection, such as that due to
belt pull.
Accuracy can be improved in the more complicated cases by using
Rayleigh’s method, which involves the equation
my,
Ney= 187.7
ws
+ m2y2+..
+ Mayn
ae
mir + myx .. MaVn
(17.32)
When using this method, determine the total deflections under each
load. These deflections result not only from the load at that location
but from all other loads as well. The first approximation
based on
static loads m7 etc. is usually within 1% of the correct value. This can
be improved by using dynamic load m, 5ie etc:
Dunkerley’s equation can also be used:
1
Neo
1
1
oe
Ne’ Ne
1
=)
Nee
(17.33)
In this equation, the actual critical speed N., is given in terms of
the critical speed N,, etc. for each mass m7, etc. in the absence of
all others.
The primary critical speed is excited by unbalance. A secondary
critical speed can be observed at one-half the speed of the first. This
is caused by unbalance in conjunction with gravity or, more likely, by
a nonuniform flexibility of the shaft resulting from a keyway or a
flat spot on the shaft. Many other resonances can occur, some of
them at speeds below the operating speed. During startup, the fan
must accelerate through these speeds. With normal damping, a wellbalanced fan will easily pass through such criticals, whereas an unbalanced fan may not.
The natural frequency/, of a simple torsional system can be calculated from the modulus of rigidity G, the polar moment of inertia /
of the shaft cross section, the length / of the shaft, and the mass
moments of inertia /,, of the concentrated masses. When two comparable masses are connected by a uniform shaft,
predi
va eeo TT
SU (age ie)
(RES
(17.34)
CHAPTER
17 — FAN MECHANICS
17-25
but when one of the masses is so large compared with the other that
the corresponding end of the shaft can be considered fixed,
pyOr
AS
I"
lik
(17.35)
Torsional critical speeds rarely coincide with operating speeds in
fans. When they do, the easiest way to alter the critical speed is to
change the coupling flexibility. Some coupling designs provide increased damping, too.
Balancing
Fan rotors must be balanced; otherwise, vibrations that could
damage the bearings or other parts will be produced. Balancing is
accomplished by redistributing the mass so that the principal inertia
axis more nearly coincides with the axis of rotation. Because perfect
balance is never achieved, specifications usually list the permissible
unbalance. This can be stated in terms such as ounce-inches, which
reflect the size and radius of a balancing mass that would bring the
rotor into balance. Also, eccentricity, the distance between the principal inertia axis and the axis of rotation, can be specified. Specific
unbalance, or unbalance divided by rotor mass, can be specified, too.
However, the most common specifications deal with the vibratory
effects of unbalance. That is, a limit is placed on the displacement,
velocity, or acceleration that can be measured on a vibrating part.
The amount of unbalance that can be tolerated varies with the
speed and mass of the rotor, the sturdiness of the bearings and the
supporting structure, etc. Table 17.4 lists the vibrations usually associek
Vz
ZZ
D
Ze
c
B
A
Figure 17.10
Static and Dynamic Unbalance
17-26
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Table 17.4
Vibration Limits for Fans (Bearing Measurements)
Vibration Severity’
Velocity? - in./s
peak
rms
025
040
.018
8.028
LOO
OVA
062
.26
18
40
28
62
44
1.00
Hh
(56
rigid®
044 |9°°
1611
Ties
Displacement‘ - mils peak to peak
Quality?
d
for various fan speeds® - rpm
flexible’
good
satisfactory
entail
Nel 900)
unsatisfactory
unacceptable
ieee
720 | 600
01 | 0.3]
OFZ
0:4
04]
Os6
0.5) 07) 08
OFS | malatalentcs
OSS Hs 1a
edeOne Zale tes s2
1.0]
1.3] 1.6] 20
33] ale
41| 50 om
03 | 16] 25]
unsatisfactory a
Pee
1800
0.3 | 0.7]
satisfactory
:
aie
| 3600)
ea
20S
Dil)
£4220
3:36
T
t
6r3
t
6.6ulee 93S
SA
Ooh
oot
loss Oca
2a6
ORT
-|
G15) |98
5.3 |10.6 | 15.9
|21.2] 26.5 |31.8
| 8.3 | 16.6 |24.8
|33.1]| 41.4 |49.7
"Vibration severity is classified by ranges of rms velocities. Each range is identified by its highest value
in mm/s (not shown).
“Most portable balancing machines indicate peak (not peak-to-peak) velocity.
‘Balancing qualities listed are ISO judgements. Alarms are often set at 0.3 in./s and shut down at
0.45 in./s.
*Most portable balancing machines indicate peak-to-peak displacements. Table values correspond
to single-frequency components.
‘Filters should be tuned to the fan speed when measuring vibration severity.
“Rigid support means that the fundamental natural frequency of the machine/ support system is
higher than its main excitation frequency. Flexible support means that the machine/ support
system's fundamental natural frequency is lower than the main excitation frequency.
Adapted from the data of ISO: “Mechanical Vibration of Large Rotating Machines with Speed
Range from 10 to 200 rev/s — Measurement and Evaluation of Vibration Severity in situ,” International Organization for Standardization, ISO-3945-1977, corrected and reprinted-1978-03-01.
ated with certain operating descriptions for several rotative speeds.
Shown are both displacements in mils and velocities in in./sec.
It is important to distinguish between static and dynamic unbalances. In Figure 17.10, a rotating impeller is idealized as two
axially separated discs on a shaft between bearings. Centrifugal forces
are shown as vectors. Portion A of the figure depicts a statically unbalanced condition. The vibration will be greater at the left-hand
bearing than at the right-hand bearing, assuming equal support stiffness.
If the impeller were
not rotating, it would
position with the unbalanced
can
be corrected
tend to assume
a
mass at the bottom. Static unbalance
by adding a single balancing mass
at the proper
distance on the opposite side of the impeller, as in portions B and C
of the figure. The method shown in portion B is best, as will soon be
evident. Portion C of the figure depicts a dynamically unbalanced
CHAPTER 17 — FAN MECHANICS
17-27
condition. If the impeller is statically balanced as shown, the vibrations at the two bearings will be of the same magnitude but in
opposite directions. Dynamic unbalance can only be corrected by
adding a balancing couple as shown in portion D ofthe figure.
Some balancing situations have not been pictured in Figure 17.10.
For instance, static unbalance can be corrected out of plane without
introducing a dynamic couple: half the balancing mass could be
added to each of two planes on either side of the unbalance. Dynamic
unbalance can be corrected out of plane also. The balancing couple
can have any moment arm. Such out-of-plane corrections will work
only if the rotor behaves rigidly. However, if it behaves flexibly and
distorts when it rotates, multiplane balancing may be necessary.
Fortunately, most fans can be balanced with two-plane corrections.
Balancing will reduce only those vibrations caused by unbalance.
Vibrations caused by looseness between parts, coupling misalignment, mismatched belts, or other external sources must first be cor-
rected before balancing is attempted. The effects of a bent shaft can
sometimes be balanced out but only if the bend is slight.
Most fans are balanced before shipping. Machines like that shown
in Figure 17.11 are used extensively. The impeller is mounted on a
mandrel and spun at relatively low speed in very flexible bearings.
Every impeller design can be calibrated for very quick and accurate
balancing. However, when the impeller is placed on its own shaft and
bearings, etc., the mounting may differ from that used for balancing,
so a trial run should be made and the balance touched up if necessary.
Figure 17.11
Shop Balancing of an Impeller on a Mandrell
17-28
The
FAN ENGINEERING
— BUFFALO FORGE COMPANY
impeller can
also be balanced
on
its own
shaft
in a shop
balancing machine like that shown in Figure 17.12. Here, too, the
rotor is balanced at low speed, and accuracy is possible because of
the machine’s built-in sensitivity. Touch-up balance may also be
needed
after erection.
This
is especially
true
for highly
stressed
wheels and for high-temperature
jobs.
In the field, fans are usually balanced with the aid of a portable,
electronic balancing machine. Such machines can indicate the vibration amplitudes in terms of displacement, velocity, or acceleration.
They can also indicate frequency and, with the aid of a strobe light,
phase angle, too. Most use a seismic-type velocity probe and can
filter out all frequencies outside the narrow band of interest. During
balancing, the filter is tuned to the rotating speed. Balancing machines are also useful for diagnosing other problems that cause
vibration. Table 17.5 lists some diagnostic clues. Procedures for using
electronic balancing machines are furnished
Vector diagrams can be used advantageously.
with
the apparatus.
Balancing is also possible without a machine. The amounts and
locations of the required balancing masses can be determined with
a piece of chalk, an assortment of detachable weights, a good sense
of touch, and a little patience. Any unbalance will displace the shaft,
which can usually be observed by chalking the shaft. This displacement will be fixed with reference to the rotor and, so, will rotate with
reference to a fixed point in space. If a piece of chalk (or the like) is
held at a fixed point so that it just touches the rotating shaft, it will
leave a mark at the high spot. If the fan is balanced, the mark will
=
Figure 17.12
Shop Balancing of an Impeller and Shaft
CHAPTER
17 — FAN MECHANICS
Table 17.5
Amplitude
17-29
Diagnostic Clues
Frequency
Phase
Possible Cause
T
Steady radial largest
1 X rpm
Steady single reference
mark
Axial largest
lor2 X rpm
2 0Te3
reference marks
Misalignment or bent
shaft (Check with dial
indicators.)
Unsteady
1 X rpm
Unsteady
Resonance (Check for
impeller or other
flexibility using modalanalysis techniques.)
Unsteady
2
2 reference marks
Unsteady
rpm + 2
Unsteady
Oil whip (uncommon
for fans)
Low
60 or 120 Hz
1 or 2 rotating
marks
Electrical
Erratic
many
Erratic
Faulty antifriction
bearings
Erratic
1 or 2 X belt rpm | Unsteady
rpm
rpm
Unbalance (See text
for clues to correcting.)
| Looseness (Check
bolts, keys, etc.)
Defective belts
(Check by freezing
with strobe.)
Low
blade-passing
Steady
Aerodynamic (Check
cutoff clearance.)
extend all the way around. The greater the unbalance, the shorter the
mark will be. The center of the line would be at the same angular
position as the unbalanced mass except for lag. The amount by
which the mark lags behind the unbalance will vary, depending on
the ratio of operating speed to critical speed and the amount of
damping in the system. For operation well below the critical speed,
the angle of lag will be 0°. For operation closer and closer to critical,
the angle of lag will gradually increase becoming 90° at critical.
Above the critical speed, the angle of lag continues to increase until
it becomes 180°. For most fans, the angle of lag will be between 15°
and 4S°.
When a fan is statically out of balance, as shown in Figure 17.10,
the chalk marks at both bearings will be at the same angular position
17-30
FAN ENGINEERING — BUFFALO FORGE COMPANY
relative to some point on the rotor. The displacement amplitudes,
indicated by the lengths of the marks, will be equal only if the unbalance occurs midway between the bearings. The correct angular
and lateral position for a trial mass can be estimated from an analysis
of the chalk marks. If the estimated angular position is correct but
the trial mass is too small, rechalking will produce a longer line in
the same angular position. If the trial mass is too large, the center of
the line will shift 180°. If the trial mass is just right, the line will
extend all the way around the shaft. However, if the angular position
is not quite correct, the center ofthe line will shift accordingly.
To correct dynamic unbalance, two trial masses should be used.
Usually, they are placed on or near the inlet shrouds for a doubleinlet impeller or on the flange and backplate for a single-inlet impeller. The correct angular position for each trial mass can be estimated from the chalk mark at the nearest bearing for Arrangement-3
fans. If the fan is not statically unbalanced, these marks will be 180°
from each other and about equal in length.
If the chalk marks extend all the way around the shaft but a considerable vibration on the bearings persists, the trouble can usually
be traced to weak supports or inadequate foundations. Reinforcing
the supports, adding mass, or both may be required.
3.0
TRANSMISSIBILITY
TR
-
0
by
se10 nswe
Re 20 Ra
en
eee
30° eee eae ae ie?
FREQUENCY RATIO ///,
Figure 17.13
Transmissibility
ao
pore serrererres 50
CHAPTER
17 — FAN MECHANICS
17-31
Vibration Isolation
Vibrations are induced in a fan by unbalanced centrifugal forces
and by aerodynamic forces. Some net force will be transmitted to the
supporting structure. In fact, the supporting structure forms part of
the vibrating system, as discussed in the critical-speed section. Many
fans can be installed without isolators, but the system must be de-
signed accordingly and good balance must be maintained. Vibration
isolation is necessary whenever the vibrations in the supporting structure must be limited because they are annoying or even destructive.
The amount of force transmitted between members of a vibrating
system depends on the masses, stiffnesses, and damping present. The
ratio of transmitted force to impressed force is called transmissibility
TR and is related to the natural frequency/, of the system as well as
to the disturbing frequencyf. Ignoring damping,
DE aeraa aa
ae
(=) oe
The natural frequency of a fan mounted
mined from the static deflection ) using
In
il
21
i
VE
(17.36)
on isolators can be deter-
(17.37)
Equation 17.36 indicates that the transmissibility will be unity when
the ratio of disturbing frequency to natural frequency equals the
square root of two. Transmissibility will be less than unity for higher
values of this ratio and greater than unity for lower values. The
effects of damping are shown in Figure 17.13. If isolators are to be
used at all, experience suggests that transmissibility, as calculated
from Equation 17.36, should be reduced to 0.20 and preferably to
0.10 or lower.
The materials usually used for vibration mounts are steel springs,
rubber-in-shear, and cork. Cork or a similar material can be used in
sheets under direct loads, since it will compress. Rubber, being virtually incompressible, is usually bonded to two steel parts and loaded
in shear. Steel springs are loaded directly in compression. Snubbers
may be needed to prevent swaying.
Several isolators are usually required for support. These should be
installed according to the distribution of the load, which may be due
to thrust forces as well as to the dead weight of the equipment. If the
fan is to be held level, the deflections must be uniform. This can be
accomplished by varying the durometer of rubber, the sheet area of
cork, or the spring constant of a spring. The deflection should be
17-32
FAN ENGINEERING
— BUFFALO FORGE COMPANY
chosen according to Equations 17.36 and 17.37 to give the proper
natural frequency. Usually, steel springs are required for fan speeds
below about 700 rpm but can be used at any speed. Rubber-in-shear
can be used for speeds above 700 rpm, but steel springs will often be
needed to limit the transmissibility to acceptable values. Cork can be
used above about 1200 rpm witha similar proviso.
It is especially important that a fan and its driving motor be
mounted on a common rigid base. If isolation is required, it should
be provided between the base and the supports so that the base,
rather than the isolators,
must
withstand
any torque
or belt pull.
Although the additional mass of the base will limit the system’s
amplitude of vibration, it will not alter the magnitude of the forces
transmitted. Whenever the vibration mounts must be incorporated in
hangers, a fail-safe design must be used.
Vibratory short circuits must be prevented. Flexible connections
must be used between the fan and any ductwork on either the inlet
or the outlet. Fans used in an air-conditioning cabinet can be isolated
from the cabinet, or the entire cabinet can be isolated from its supports. Steam lines, water lines, power lines, etc. must be flexibly
connected. Inertial masses may be needed to restrict the amplitude of
vibration regardless of whether the fan is mounted on isolators or
not. As a rule of thumb, use a mass of concrete two to three times
the mass of the fan and drive.
Mechanical Testing
Various mechanical tests can be performed on a fan or its parts,
either to provide a basis for design calculations or to verify them.
Although destructive tests are occasionally useful, most fan testing is
nondestructive.
Spin tests may be performed to determine the buckling speed of a
blade, the yielding speed of a shroud, or the bursting speed of an
impeller. Nondestructive spin testing may be used simply to prove
that an impeller will be able to operate at a certain speed. That speed
can be the expected operating speed or some higher speed. Overspeed
testing demonstrates that there is a margin of safety at the normal
speed. Overspeeding may also beneficially redistribute static stresses.
A vacuum test pit is convenient for spin testing. The one illustrated
in Figure 17.14 is made of heavy steel and reinforced concrete and
has a vacuum pump that can provide an absolute pressure of fifty
micrometers of mercury (0.050 mm Hg or 0.00197 in. Hg). The power
requirements of the air turbine, ignoring bearing friction, are thereby
reduced to less than I/15000 of that required to drive the impeller at
standard atmospheric pressure. The heavy construction and underground pit arrangement provide protection against flying parts.
In Figure 17.15, a much larger pit is illustrated. Although not
intended for destructive testing, it, too, is underground and has a
CHAPTER
17 — FAN MECHANICS
Figure 17.15
Large Test Pit
17-33
17-34
FAN ENGINEERING
— BUFFALO FORGE COMPANY
very heavy reinforced-concrete cover to protect against flying parts.
Since this pit cannot be evacuated, highly powered drives must be
used for larger impellers at high speeds. (Up to 1500 hp is available
at this facility, and wheels up to 193 in. can be tested.) Impellers can
be mounted on their own shafts and bearings and even in their own
housings, if desired.
Strain gages, brittle lacquers, and photoelastic materials can be
used to measure strains so that stresses can be calculated. Brittle
lacquers and photoelastic materials may be useful in defining strain
patterns, but because of the problems associated with rotating impellers, strain gages are used more extensively for fans. FM transmitters and receivers as well as slip rings have been used to test fans.
Both static and dynamic strains are measured and recorded. Signals
can be recorded during field testing and returned to the laboratory
for processing.
Figure 17.16
Modal-Analysis Test Setup
CHAPTER 17 — FAN MECHANICS
17-35
The vibration characteristics of a fan can be found in various
ways. Natural frequencies can be excited by impact, shaking, or
explosive shock. (Vibration at other frequencies can also be forced
by shaking.) Then, point responses can be measured with accelerometers, velocity sensors, or displacement-measuring devices. From
the point responses and excitation forces, mode shapes can be deduced. Sometimes, if the structure is flexible enough, the mode shape
can be estimated simply from visual or tactile observation, but
usually, computer solution is required.
Figure 17.16 shows a computer-based, modal-analysis test setup.
The test fan is a simple propeller type. The geometrical grid shown
on the CRT was derived from the measured three-dimensional coordinates of selected points on the fan. During the test, the fan is
excited with a hammer blow at one of the points. The response at
each of the points is then measured with an accelerometer. Since the
hammer is equipped with a force gage, the excitation force can also
be measured. The output from the accelerometer gives the response
at all frequencies resulting from the hammer blow. This time-domain
data is transformed by the computer into frequency-domain information for both the responses and the excitations. (The resulting frequency spectra are called Fourier transforms, and the computer
calculations fast-Fourier-transform
analyses.) Transfer functions are
then formed for each response/ excitation pair. Peaks will occur defining the various natural frequencies. To determine mode shapes
and damping ratios, the computer extracts amplitudes for all pertinent frequencies from the transfer functions for all the pairs. This
information can then be used to animate the geometrical grid at any
frequency. This kind of analysis, which yields mode shapes as well as
frequencies, can be very useful in design and development.
An impact-response test (bump test) will give frequency information but not mode shapes. Figure 17.17 shows the kind of equipment
needed. During the test, the fan is bumped, and the response is
measured with an accelerometer. As with the previously described
modal analysis, a frequency spectrum of the response is then formed.
No frequency spectrum can be formed for the excitation because the
excitation force is not measured. The frequency-domain information
is then displayed on a CRT. Although limited, this information is
still useful in design and development.
Shaker tests are performed either by mounting the fan on the
shaker or by suspending the fan elastically so that it can be moved
by the shaker. The excitation frequency is controlled. Although the
excitation force can be measured, it is more common to measure the
vibration amplitudes of the table. Point responses can be sensed with
an accelerometer and a frequency spectrum formed as for impactresponse testing. Or, transfer functions can be formed as for the
modal-analysis testing previously described.
Another use for shaker tests is seismic qualification. In this kind of
17-36
FAN ENGINEERING
— BUFFALO
Figure 17.17
FORGE COMPANY
Impact-Response Testing
testing, the fan must show that it will continue to perform its function
after exposure to a specified shaking pattern. Specifications vary,
especially concerning wave form. But, usually, a frequency sweep is
required, and amplitudes are defined.
Shock tests are specified to demonstrate that a fan will continue to
perform after exposure to a certain shock. Shock-testing machines
administer the shock by dropping a heavy mass through a prescribed
arc to strike the structure on which the test unit is mounted. Shock
tests can also be performed by mounting the test fan on a barge and
detonating measured charges in the water at specified distances from
the barge.
Chapter 18
Fan Motors and Drives
Most fans are driven by an electric motor either directly, through a
flexible coupling, or indirectly, through a V belt. Other types of prime
movers or other types of transmission elements may be more suitable
for a particular application. Some of the more important aspects of a
fan as a load are considered below, after which prime movers and
transmission elements are briefly discussed.
Load Characteristics of aFan
A suitable motor and drive can often be chosen for a fan based
only on the full-load power and speed. However, it is also wise to
examine the starting characteristics of the fan/drive combination.
Breakaway torque, speed/ torque relations, flywheel effect, acceleration time, temperature effects, and other considerations may be
important.
From Fan Law No. Ic, the air power of a fan varies as the cube of
the speed if the density and the point of rating remain constant. So,
the torque needed varies as the square of the speed. Except for
bearing friction, the torque requirement would be zero at standstill,
increasing gradually with increasing speed. This is a very desirable
load characteristic, since all the motor torque is available for starting
at standstill and a very large percentage is available for acceleration
at other speeds.
The breakaway torque 7, is usually only a very small percentage of
a fan’s full-load torque. The numerical value for a journal bearing of
radius r can be calculated from the coefficient of static frictionf, and
the normal force F on the bearing by using
To
oliiee
(18.1)
Refer to the discussions on bearings in the fan-mechanics chapter for
the range of values for the dimensionless coefficient of static friction.
Any consistent units can be used for the other variables. For a con-
stant normal force, the friction torque will gradually decrease as
journal speed increases until the coefficient of friction equals the
equilibrium value for sliding friction. Figure 18.1 shows a typical
speed/torque curve for a fan. The comparative values of breakaway
and full-load torque will vary with the design.
18-2
FAN ENGINEERING
— BUFFALO FORGE COMPANY
TYPICAL
MOTOR CURVE ,
FAN CURVE
Figure 18.1
Typical
Speed/ Torque Curves
Comparatively high normal forces can be produced by belt drives,
so some low-starting-torque motors are limited to direct drives, as
the discussion on fractional-horsepower motors will point out.
The flywheel effect of a fan rotor is its mass moment of inertia
about the axis of rotation. This polar moment of inertia is commonly
expressed in weight units and designated Wk. The moment of
inertia of a particle is the product of its mass and the square of its
distance from the axis. The moment of inertia of a group of particles
is the algebraic sum of the individual moments of inertia. The square
root of the combined moment of inertia divided by the square root
of the total mass is the radius of gyration K of the combined mass.
Table 18.1 lists the polar moments of inertia and the radii of gyration
for some common bodies. Most fan elements can be considered
composed of one or more ofthe bodies listed.
A fan rotor’s radius of gyration is usually between 65% and 75% of
the tip radius.
By comparison,
a solid disk’s radius of gyration is
70.7% of its outer radius.
The energy E in ft-lb stored in a rotating body is related to the
flywheel effect WK° in lb-ft’ and to the rotative speed N in rpm,
according to
CHAPTER
18 — FAN MOTORS AND DRIVES
18-3
ee Baa
5868
(18.2)
For SI units, substitute m for W and 27° for 5868; then, E will be in
J for min kg, K inm, and N inrps.
A corresponding amount of energy must be supplied by the driving
motor in accelerating a fan rotor from rest to the speed N. The same
amount of energy must be dissipated in decelerating a fan rotor from
the speed N to rest. The time required to accomplish acceleration or
deceleration is often important. This time ¢ in sec can be calculated
Table
18.1
SiN
ivge
Flywheel Effects for Cylinders and Prisms
RADIUS OF
FLYWHEEL
r
mr'lpg
V2
28:
WEIGHT W’ | GyRATION K E EFFECT WK?
ri
(ro — rv )lpg
rotry
nro — ri)lpg
&
2,
22
bhipg
b+h
(bh + bh )lpg
&
12
12g,
ht
12
bh” ak, bhx
pg
&
18-4
FAN ENGINEERING
— BUFFALO FORGE COMPANY
from the initial and final speeds N; and N>2 in rpm, the appropriate
flywheel effect WK in lb-ft’, and the torque 7 in lb-ft available for
acceleration or deceleration, as the case may be, using
W K°(N, — Nd)
307.27
(18.3)
For SI units, substitute m for W and 27 for //307.2; then, ft will be
ins for minkg, Kinm, Ninrps,and7inm:N.
If the driving (or retarding) torque is produced at the same speed
as that at which the fan rotates, the WK* can be calculated about
either the driver or the driven axis with equal results. However, if the
speeds differ, the results must also differ, since a given amount of
energy is involved regardless of which axis is used for reference. The
equivalent flywheel effect of the rotor referred to the motor axis
WK? can be determined from the flywheel effect of the rotor referred to its own axis WK’; using the ratio of fan to motor speeds
squared (N-/ Nyy)*, as indicated by
o)
ANS
Mi
a
eS
Nr
Ks(<*)
Nu
:
:
(18.4)
Both the torque needed by the fan to move the air and any frictional torque present are retarding torques. In starting, the torque
developed by the motor at any speed must exceed the retarding
torque if the rotor is to accelerate. The speed/torque curves of different motors vary greatly. If the speed/torque curves for the motor
and load (air and friction), both referred to the same axis, are drawn
to the same scale as in Figure 18.1, the average available torque can
be estimated as the average distance between them, over the range
from zero to full speed or over whatever other speed range might be
contemplated. The area between the two curves divided by the length
along the speed axis will yield the average torque available for
acceleration.
Acceleration time may be an important factor in motor design.
Also, acceleration and deceleration times may be important in flow
control.
If, in deceleration, the retarding torque is considered to be produced exclusively by the air load (that is, no friction or external
braking), the decelerating time can be computed from
_
WK
[2]
1.614 X 10°
NP,
(18.5)
And if, besides that produced by the air load, a retarding torque rt,
CHAPTER
18 — FAN MOTORS AND DRIVES
18-5
is also imposed by bearing friction, then
=a
where
re= [er (Calan uals i=
~)|
Cy. =
(18.6)
NV
ee
\/ 5252 P
(18.7)
If an additional braking torque is applied, it can be included in the
retarding torque in Equation 18.7. All three equations are based on
U.S. customary units: W is in lb, K in ft, N in rpm, P in hp and +
in ft-lb. For SI units, substitute m for W, (27) for 1/1.614 X 10°,
and /000 for 5252; then, t will be in s for m in kg, K in m, N in rps, P
in kW, and vin m-N. Arc tangent is based on radians.
Example 18.1
Acceleration and Deceleration Time
Given a fan witha WK° of 1912 lb-ft? and the speed-versus-torque data
in Figure 18.1, find the acceleration and deceleration times.
Nx
poss
rpm
rpm
t(Motor) | r (Fan)
lb-ft
lb-ft
|/7.(Avail.) |tx + ty-1/2 | ¢
lb: ft
Ib: ft
ial
2001
200
400 | 200
600}
200
800}
200
1000]
200
1200!
200
1400|
200
16001
200
1700 | 100
1780
80
| 1200
1250
1300
1370
1440
1530
1660
1950
2850
3510
1260
60
20
10
140
250
400
570
780
1020
1150
1260
1140
1230
1230
1230
1190
1130
1090
1170
1830
2360
0
=
ain
1185 | 1.05
1230 =| 1.01
bey
ia
TO
103
1160 | 1.07
me
we
W308
110
1500
{0.83
2095
10.30
1180
0.42
8.94
sec
Select a series of speeds, as in the first column of the above table. Next,
calculate the increments, as in the second column. Then, read both the
available motor torque and the required fan torque from Figure 18.1, as
in the third and fourth columns. The difference is the net available
torque, as in the fifth column.
Now, calculate the average available
torque for the speed increment, as in the sixth column. Finally, calculate
the acceleration times for each increment using Equation 18.3, and add
them together to obtain the total starting time. This whole procedure
can be summarized in equation form:
BUFFALO FORGE COMPANY
— ING
FAN ENGINEER
18-6
pee
vc=IL
ene
153.6 (ty + Tx-1)
which is an adaptation of Equation 18.3.
Calculate the deceleration time, using Equations 18.5 and 18.6. Assume
a retarding torque of 10 lb-ft. The air power corresponding to 1260 1b:ft
at 1780 rpm is
A,
_— 271780 X 1260
= 427 hp,
33000
Ny
10 X 1780°
===
=
tice
W K-
5252 X 427
tan '
~
1.614 X 108 Be
=
1912
1780°
;
1.614X 10° 427X 158.6
on
=
= ji
ay)
ran (
an
158.6,
, and
2,70
tan : ) = 146.2s.
158.6
Note that, without the additional retarding torque, the fan would continue to rotate indefinitely because, for N2 = 0, ¢ is infinite according
to Equation 18.5.
Sometimes, a fan may be expected to handle relatively hot gas
under normal operating conditions but relatively cold gas during
start-up. As indicated by the fan laws, the power requirements of a
fan increase in proportion to any increase in fluid density, if the fan
and system are otherwise unchanged. The motor and drive must be
selected accordingly. With a centrifugal fan, it may be possible to
damper back towards shutoff, reducing the power requirements during cold operation. With an axial-flow fan, a bypass can sometimes
be used to move the point of rating nearer free delivery, reducing the
power requirements during a cold start.
Ambient air conditions must also be considered in motor and
drive selection. These may differ from the conditions of the air
handled by the fan. High temperatures can considerably limit the
load-carrying ability. High velocity in some air-over applications
makes possible higher outputs.
Prime Movers
Various heat engines and other devices can be used to drive a fan.
Electric motors are usually employed, unless a more economical
source of energy than electrical power is available. Steam-engine
CHAPTER
18 — FAN MOTORS AND DRIVES
drives
are
largely
obsolete.
And,
air and
gas turbines
18-7
have
very
limited fields of application.
Portable and emergency
fan units are often driven by an internal
combustion engine, but not all fans are designed for this kind of
service. The torque pulses are usually more severe than for any other
type of prime mover.
Certain fans for emergency use, such as those installed in bomb
shelters, can be operated by pedals or hand cranks. Human-powered
drives are also often used on blowers for charcoal grills and backwoods forges.
Steam-turbine drives have various fields of application. One of the
best turbine-drive situations occurs when high-pressure steam is available but low pressure steam
is needed
for heating or processing. A
turbine can then be used as a reducing valve. A turbine drive may
also be the only practical solution when high-speed operation is
required. Speed reducers are usually needed in low-speed applica-
tions, since turbines are essentially high-speed machines. Speed control is easily achieved by throttling the steam supply.
Electric motors are most conveniently discussed under two headings: fractionals and integrals. In either, the characteristics of the
power supply must be determined. Usually, the power will be of the
alternating-current type, and the voltage, the frequency, and the
number
of phases should
be specified. If direct current is available,
the voltage should be checked. The characteristics of the load (the
fan and any drive elements), together with power-company restrictions on starting current as well as economic considerations, will all
determine the type of motor and control that should be selected.
Integral-Horsepower Electric Motors
Polyphase (usually three-phase) alternating-current motors are
almost always used in fan applications requiring more than one
horsepower. Direct-current motors are used in some fan applications.
Single-phase motors are available only in the smaller ratings.
There are several types of polyphase motors, but only two are
generally used for driving fans: the non-synchronous, induction
motors known as the squirrel-cage and the wound-rotor types. Both
are self-starting, but in many applications, special starting controls
are needed to limit the starting time to an acceptable value. Both
types also operate with very little slip at the rated load.
Slip can be defined as the difference between the synchronous
speed and the operating speed. Percent slip is usually calculated with
synchronous speed as the reference value. Synchronous speed Nyyn 1s
a function of the current frequency f and the number of poles Npoies,
as indicated by
(18.8)
18-8
FAN ENGINEERING
— BUFFALO FORGE COMPANY
The squirrel-cage type is named for its rotor construction. Among
the various standard designs, Design B is usually used for fan loads.
This is the “production” motor, suitable for continuous operation at
the rated load. Although the starting current is relatively low (about
600% of full load), frequent starts should
be avoided.
The starting
torque (100% of full load or higher) is more than adequate for most
fans, but the WK capability should be checked against the
requirements.
Squirrel-cage motors are essentially constant-speed machines, but
multiple-speed operation is possible if a special winding or windings
are used. A single “consequent-pole” winding can be reconnected to
give two speeds in the ratio of 2:1. The lower of the two speeds is
obtained by reversing the connections to alternate poles, which, as a
consequence, induces additional intermediate poles. Generally, a 4:3
or 3:2 speed ratio will be more suitable than a 2:1 ratio. Two separate
windings are needed for the 4:3 and 3:2 ratios, but even this is usually
less expensive than an adjustable-speed motor or drive. Multi-speed
motors with variable torque characteristics will usually be capable of
handling fan loads if sized for the high-speed power requirement,
since motor horsepower varies as the square of the speed and fan
horsepower varies as the cube of the speed in most systems.
Wound-rotor motors are also known as slip-ring motors. The
general-purpose or continuous-rated type (as distinguished from the
intermittent-rated type) is used chiefly when an adjustable-speed
motor is desired. Reducing speed below 50% is usually not recommended, since the fan load falls off so fast and control at low loads is
difficult. The polyphase winding of the rotor is connected to an
adjustable, external resistance through slip rings and brushes. The
top speed and efficiency are about the same as for a squirrel-cage
motor, but the cost is higher. Starting torque and starting current can
be controlled by adjusting the external resistance.
Adjustable-speed a-c and d-c motor drives that provide stepless
speed control are available. Speed range, efficiency, and cost should
all be carefully considered. High slip at full load will lower the
efficiency to unacceptable values.
The National Electrical Manufacturers Association (NEMA) has
adopted many standards concerning dimensions, ratings, enclosures,
insulation, and other design data. These standards promote interchangeability, which facilitates motor specification and application.
In the integral-horsepower ratings, frame sizes are given as threedigit numbers. The first two digits are four times the shaft center-line
height in inches of a standard foot-mounted motor. The last digit is a
code number for certain mounting dimensions of the foot itself. The
suffixes U, 7; and S indicate certain shaft dimensions. The letters C
and D indicate face- and flange-mounted types, which will also have
feet unless round frames are specified. Table 18.2 lists standard
NEMA dimensions for polyphase-induction motors. Refer to Figure
CHAPTER
18 — FAN MOTORS AND DRIVES
Figure 18.2
Standard NEMA
Adapted from the data of Motor Standards, NEMA,
18-9
Dimensions
1969, p. 18.
18.2 for lettered dimensions of foot-mounted motors.
The power ratings that can be built into any particular frame vary
with the characteristics of the power source (volts, etc.), the design of
the motor (Design B, etc.), the number of poles (or speed), the type
of enclosure, and other factors. Table 18.3 lists the standard NEMA
ratings for a few combinations.
Motor enclosures fall into two broad categories: open and totally
enclosed. Drip-proof and splash-proof machines are open motors
with varying degrees of protection, as indicated by their names.
However, they should not be used if the ambient air contains anything that might be harmful to the interior of the motor. Weatherprotected machines and machines with encapsulated windings better
protect the windings against adverse atmospheric conditions. Both
are open motors. There are also various subclassifications for totally
enclosed motors. Although enclosures prevent the free exchange of
air between the inside and the outside, they are not airtight. Totally
enclosed, fan-cooled (TEFC) machines have an integral-cooling fan
outside the enclosure but within a protective shield that also directs
the air over the enclosure.
Totally enclosed,
non-ventilated
(TENV)
machines do not have an integral fan, so a much larger frame is
needed except in air-over applications or in some of the smaller
ratings even without air-over. Air-over motors (TEAO) have not
been assigned
frame sizes but, in effect, utilize standard
higher-than-standard
ratings.
Totally
enclosed
frames
motors
can
for
be
furnished with special features for severe-duty applications, for
example, cast-iron construction instead of aluminum or steel.
The National Electric Code classifies various fire and explosion
hazards by divisions, classes, and groups. Explosion-proof
and dustignition-proof motors are available for hazardous environments.
18-10
FAN ENGINEERING
— BUFFALO FORGE COMPANY
———
Table 18.2
Standard NEMA
Frame
No.
143T
145T
182T
104T
213T
215T
254T
256T
Key
| %sx ex 1%
| ex ex 1%
| % xe xl%
| 4 xa x 1%
| %sx Sex 2%
| sx sx 2%
| %x%e x2’
| ¥x%x2%e
A
B
max | max
i
6
if
6
9
Br
9
Th
| 10'%
Th
| 10% | 9
| 12'2 | 10%
{12%
112%
284T
284TS
286T
286TS
3247
324TS
326T
SZOTS
| 2 x'h x3%
| %e x%e xi
| 2 xr x3%
| % x%exi%
| 2x2 x38
| 2 xh x2
Ya xh x 3%
e/2) Xe/20Xe2
| 14
| 14
| 14
| 14
116
16
| 16
16
364T
me x%e x 4a
| 18
i)
32
32
| 4h
| 42
5%
5M
| 6%
| 6%
| 2%
| 24s
| 3%
| 3%
| 4a
| 41/4
|5
|5
ee |p TI
5',
UPS || TF
52
14
ia
5%,
EN as 7
5%
14
8
6%
14
8
6%
15% | 8
6%,
15% | 8
6%
15%
9
if
364TS | 2 xh x2
18
365T | % x%e x4 | 18
365TS | 2 x'h x2
18
404T | % x% x 5% | 20
404TS | 2 x'h x2% | 20
405T | % x% x 5% | 20
405TS | 2 x'e x2% | 20
444T | % xh x6% | 22
444TS | %x% x3
22
445T | % x" x6% | 22
445TS | % x
x3
22
447T | % xh x6% | 22
447TS | % x% x3
22
182
Asx ex le | 9
1SV4a
9
7
16% | 9
7
16% | 9
7
16% | 10
8
16% | 10
8
17% | 10
8
173% | 10
8
18% | 11
9
18% | 11
3
20% | 11
9
20% | 11
9
24
11
9
24
11
9
62 | 4% | 3%
184
Vex Asx 1%
9
Th
213
215
Mx
x2
Va xa x2
10% | 72 | 5% | 4%
DEON
OVA
|e.S
BYa iAVa le SVe)
254U
| Asx Sex 2% | 12% | 10%
256U | ex hex 2%
284U | % x%e x 3%
286U | % x% x 3%
324U | 2 xh x4%
324S | *%x% xi
326U | 2 xh x4%
3268S | %x%xi%
364U | 2 x'h xd
364US | '2 x'h x2
365U | 2 xh x5
365US | 2 x'h x2
112%
| 14
| 14
| 16
| 16
| 16
| 16
18
18
18
18
404U | % x*% x5'% | 20
404US | '2 x'h x 2% | 20
405U | % x%x5'% | 20
405US | '2 x'h x2% | 20
44QU
| x% x7
22
444US | ‘2 x'2 x 2% | 22
Dimensions
:
112%
PAN
14
14
14
152
152
164
15%
16%
16%
4
| 3%
6% | 5
| 2a | 25% | M2)
2s
254 | 23/4 | 3/2]
2%
SMES \ S|)
3}
32 | 34213
4%, | 4's in
3%
| 6% | 5
5
4a | "2 | 3%
a
5¥e | 4% | 454 | "Ae | 47
7
Bie | BY | 4% | Veo)
44
8
6% | 54 | 5% | 252]
5%
8
6%,
5Ye | Bia. |2tee
Sab
| 8
6% | 6
54 |Vee | 55
| 8
6% | 6
5% ie
3%
| 9
i
5% | 5% | 22)
6%
| 9
7
5% | 5% | "2 | 3%
| 9
7
6% | 5% | 221
6%
| 9
7
6% | 5% | 22}
3%
16% | 10
16% | 10
173% | 10
17%
1812
18'
8
8
8
8
s)
9
9
9
6% | 6%
61% | 6%
67 | 6%
Te
4%
7%
4%
8%
4%,
85%
4"
| 1% | 5% | 1%
Te
ks
nh
| 1% | 534 || 12
| 1% | 3
\'h
| 2%
| 1%
| 2%
| 1%
|2
| 2%
| 2%
| 2%
| 274
| 2%
| 274
Adapted from the data of NEMA: “Motor Standards,” Washington, D.C., 1969, MGI-I1.3la.
2"
2"
CHAPTER
18 — FAN MOTORS AND DRIVES
Table 18.3
Standard NEMA
18-11
Frame Assignments
Polyphase, 60 Hertz, 575 Volts or Less
|
RPM
ae
RPM
HP | 3600 | 1800| 1200| 900
HP [ 3600 | 1800 |1200| 900
Design B Squirrel-Cage Open
Class B Insul. - 1.15 Service Fac.
ih
1431
Vy
—
1
—_—
1% | 143T
2
145T
3
145T
5
182T
Th | 184T
10
15
20
25
30
40
50
60
75
100
—
143T
145T
1457
182T
184T
213T
143T | 145T
145T | 182T
182T | 184T
184T | 213T
2131
2157
215T | 254T
254T | 256T
213T
215T
256T | 2847
Zion
2547
284T | 286T
2547
256T
286T | 324T
256T
284T
324T | 326T
284TS | 286T
326T | 364T
286TS | 324T
364T | 365T
324TS | 326T
365T | 404T
326TS | 364TS* | 404T | 405T
364TS | 365TS* | 405T | 444T
365TS | 404TS* | 444T | 445T
125 | 404TS | 405TS* | 445T
150 | 405TS | 444TS*
=
200 | 444TS | 445TS*
=
250 =| 4457S
=
=
HP
1
HP
| 213
12 | 182
2
184
184
184
184
213
213
215
3
184
|)
ils
T' | 215
213
AAS
254U
254U
256U
284U
286U
3248
3268
364US
365US
215 | 254U
254U | 256U
256U | 284U
| 256U
284U | 286U
| 284U
324U | 326U
| 286U
326U | 364U
| 324U
364U | 365U
326U
365U | 404U
364U
404U | 405U
| 365U*
405U | 444U
| 404US" | 444U | 445U
75
100
125
404US | 405US* | 445U
405US | 444US*
—
444US | 445US*
—
is)
a45US
1
—
Wh | 182
2
213
215
10
15
20
25
30
40
50
60
75
100
Design B Squirrel-Cage Open
184
[oe
—
=
—
Design B Squirrel-Cage TENV
i182
184
23
215
184
213
PEIMN5
254U
|—
=
1
=
WA | 143T
2
1457
3
182T
5
184T
PA
2137
125
150
200
250
182
HP
“f{ —
Yq
| —
=
=
=
_
10
15
20
25
30
40
50
60
Design B Squirrel-Cage TEFC
Class B Insul. - 1.00 Service Fac.
1
215T
2547
256T
2847S
286TS
324TS
326TS
364TS
365TS
405TS
—
143T
145T
145T
182T
184T
213T
a
ee
143T
145T
182T
184T
2137
215T
254T
| 145T
| 182T
| 184T
| 213T
| 2157
| 254T
| 256T
215T
256T | 284T
254T
284T | 286T
256T
286T | 324T
| 284T
324T | 326T
| 286T
326T | 3647
| 324T
364T | 365T
| 326T
365T | 404T
| 364TS* | 404T | 405T
| 365TS* | 405T | 444T
| 405TS* | 444T | 445T
| 4447S | 4447S" | 445T | —
| 4457S | 445TS*
=
—
| 447TS | 447TS*
—
=
| 4477S | —
=
=
besa B Squirrel-Cage TEFC
—
182
184
| 213
1% | 182
2
184
184
184
184
213
213
215
3
184
Seles
T' | 215
213
215
254U
215 | 254U
254U | 256U
256U | 284U
10
254U | 256U
284U | 286U
15
256U | 284U
324U | 326U
20
286U | 286U
326U | 364U
25
324U | 324U
364U | 365U
30
326S | 326U
365U | 404U
40
364US | 364U
404U | 405U
50 |365US | 365US" | 405U | 444U
ia HP
General-Purpose Wound-Rotor
1
1
2 :
25
54
254
TY
224
225
ey Wieap
eee
254 | 284
5
=
254
284
324
326
365
404
405
*When motors are to be used with V-belt drives, the correct frame size is that shown but with the
suffix S omitted. (§ indicates a short shaft for direct-coupled service.)
Adapted from the data of NEMA: “Motor Standards,” NEMA, Washington, D.C., 1969, pp. 16-17.
18-12
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Explosion-proof motors are designed to withstand an internal
explosion without rupturing and to prevent the ignition of vapor
surrounding the motor by quenching any flames before they can pass
through the sealing joints. Dust-ignition-proof motors are designed
to exclude ignitable amounts of dust and to prevent the ignition of
accumulations on or near the motor. Both are totally enclosed.
Motor winding insulation systems are classified according to the
highest temperature at which normal service life can be expected.
Table [8.4 lists the maximum temperatures for which the various
classes of insulation are suitable. The maximum temperature is the
sum of the ambient temperature, the measurable temperature rise
above the ambient, and the hot-spot allowance. The last varies with
enclosure type. Should the winding temperature exceed the
maximum, the insulation system will deteriorate prematurely.
Table 18.4
Temperature Standards for Continuous-Duty
Polyphase, Induction Motors
y
Class of
R
Faclacure
Insulation
Service |Ambient |beteeerarrs eee
Maximum
Factor | Temp. |Max. Meas. | Hot-Spot |Temperature
by Resist. |Allowance
Open | 115° | 40cc | goecty |
occ | 130°C
B
TEFC
TENV
1.00
1.00
40°C
40°C
80°C
socG
10°C
5o¢
Open
nthe?
40°C
iS 2G
OLE
155oc
F
TEFC
1.00
40°C
105°C
10°C
155°C
TENV
1.00
40°C
110°C
526
[5ooG
H
|
130°C
130°C
Open
—
—
—
—
—
TEFC
TENV
1.00
1.00
40°C
40°C
12526
185°C
1526
5oG
180°C
180°C
*1.15 service factor or higher based on
HP
1/20-1/8
1/6-1/3
1/2
3/4
1-1/2-200
HP and RPM:
1200 |900
1.40
1.35
1.15
1.18
1.18
Adapted from the data of NEMA: “Motor Standards,” NEMA,
Washington, D.C., 1969, p. 12.
CHAPTER
18 — FAN MOTORS AND DRIVES
The temperature
rise can be measured
18-13
by a thermocouple, etc. or
by resistance. The resistance method involves determining the
winding resistance at two distinctly different conditions of thermal
equilibrium. The “cold” resistance R. can be measured whenever the
motor has been at rest long enough to ensure equilibrium. (The
ambient temperature ¢, at that time must also be measured.) The
“hot” resistance R,; should be measured immediately after the motor
has been shut down from a loaded run ofsufficient duration to ensure
equilibrium. The ambient temperature f, at the time of shutdown
must also be measured. Because of the unavoidable delay involved in
disconnecting power lines and connecting measuring instruments, the
hot resistance is usually obtained by graphical extrapolation using
several measurements and their delay periods. The temperature rise
AT can be determined after the ambient temperature measurements
t- and ¢, have been converted to inferred absolute temperatures 7.’
and 7)’ using
NT
Rh
Ts(tee) ellie
R.
(18.9)
Because the linear relationship between the resistance and the temperature does not extend all the way to absolute zero, inferred
absolute temperatures
must be used. For 100% conductivity copper,
Te’ = 234.5 + t. and Ty’ = 234.5 + th, when all temperatures are in
°C. The temperature of inferred zero resistance for 100% conductivity
copper is —234.5°C. Resistance measurements yield only an average
temperature rise, so a hot-spot allowance is necessary to prevent
overheating. But, thermometer measurements usually yield even lower
temperature rises than resistance measurements.
If the motor is expected to operate at high altitudes, the allowable
temperature rise should be reduced to compensate for the lower
cooling efficiency due to the reduced density. That is, a motor rated
for operation at elevations up to 3300 ft (1000 m) cannot operate at
full load at higher elevations without overheating. However, a motor
selected for a fan rated for sea-level conditions will not overheat at
any higher elevation because the fan power requirement decreases
faster than the motor capability (unless the point of operation is
changed).
The
standard
(104° F). However,
ambient
temperature
if the actual ambient
for
motor
temperature
design
is 40°C
is expected to
exceed 40°C, the temperature rise should be reduced a corresponding
amount by appropriate design measures such as additional cooling or
by derating. That is, a motor rated for operation in a 40°C ambient
temperature cannot be operated in higher temperatures at full-load
without overheating. However, a motor selected for a fan rated for
the same air temperature as the motor ambient will not overheat at
18-14
FAN ENGINEERING
lower temperatures
— BUFFALO FORGE COMPANY
because the motor’s capability increases faster
than the fan load (uniess the point of operation is changed). This
may be important if cold starts are required. Consider providing
overload protection that is directly responsive to winding temperature.
Such inherent overload protection will allow the motor to start a
cold fan yet will prevent overheating at all temperatures. The alternatives include amperage limiting, which might restrict cold starts or
compromise overheating protection.
The open, drip-proof motor with a service factor greater than 1.0
can be overloaded continuously. If it is operated at the name-plate
voltage and frequency, the horsepower ratings can be exceeded by
15% or more, as indicated by the service factors in Table 18.4. When
overloaded, the speed, the efficiency, and the power factor may be
different from those at the rated load. The starting torque and the
starting current will be the same.
NEMA standards provide that a motor will operate successfully
even if the combined variation from rated voltage and frequency is
plus or minus 10% (provided that the frequency variation does not
exceed plus or minus 5%). The effects of supply variations on certain
operating characteristics are given in Table 18.5. Standard voltages
for motors at 60 Hz are 200, 230, 460, and 575 volts and, at 50 Hz,
220 and 380 volts.
Table 18.5
Effects of Voltage Variation on Operating Characteristics
90% Voltage
110% Voltage
Starting torque
-19%
-19%
+ +23%
Starting current
-11%
-11%
+11%
+11%
Full-load speed
-1%
-1%
Hh%
H1h%
Full-load current
+11%
-2%
-6%
+7%
Temp. rise at FL
+6°C
-5°C
-3°C
+10°C
Efficiency — FL
— Yq FL
- FL
-1.2%
-0.7%
+0.4%
+1.0%
+1.5%
+3.0%
+0.4%
-0.2%
-1.0%
-2.0%
-3.5%
-5.0%
Power factor — FL
-—%4 FL
+1%
+3%
+8%
+8%
-3%
-5%
-8%
-8%
Characteristic
illinois
Magnetic noise
2-&4-pole
| 6-pole
al) 17s
decrease slightly
&up | 2- & 4-pole
6-pole & up
+23%
Sp iovee) |eect eee
increase slightly
These data are for general-purpose, induction motors and are only approximate.
CHAPTER 18
— FAN MOTORS AND DRIVES
Table 18.6
Standard NEMA
V-Belt Limitations
Horsepower at Full-Load Speed
Frame
V-belt Sheave
Synchronous RPM
1200
Number
3600
1800
143T
145T
182T
182T
184T
184T
184T
213T
215T
2155,
254T
254T
256T
256T
284T
284T
286T
324T
326T
364T
364T
365T
365T
404T
404T
404T
405T
405T
405T
444T
444T
444T
444T
445T
445T
1%
2-3
3
ie
—
5
7%
72-10
10
AS
15
20
20-25
—
—
—
—
—
—~
_
—
—
—
_
1
1-2
3
Yq
1
1%”
1
—
2
1%
~-
3
5
2
3
_—
—
—
=
—
_
—
—
_—
—
100
_
100
125
=~
_—
—
—
125
150
—
5
7,2
=
10
—
15
—
20
—
25
30
40
50
—
60
—
75
—
900
Va
¥a
TV
=)
_
10
7%
—
—
15
10
~
_—
20
25
30
40
15
20
25
30
_
—
—
—
_
_
—
-
50
40
—
—
60
—
50
_
—
_
—
7S
60
_
—
100
~
75
—
—
_
_
125
a
100
—
_
_—
—
Adapted from the data of “Motor Standards,” NEMA,
18-15
Min.
Max.
Diam.
Width
PAI
2.4"
2.4”
2.0:
aa
2:6"
3.0”
310
305
S80)
Som
4.4”
4.4"
4.6”
4.6”
SO
5.4”
6.0”
6.8”
6.8”
7.4"
8.2”
9.0”
9.0"
9:0”
10.0”
10.0”
10.0”
11,5"
11.0”
1ONSZ
1100"
4V"
4a"
54”
5%"
5a"
5%"
54"
6%"
6%"
62"
T%4"
7TY¥a"
T¥4"
Ts"
9”
97
9”
10%"
10%”
11%"
11%"
11%"
11%"
14%"
14%"
1444"
14%,
14V4'
14%
16%"
16%4”
16%4'
164"
16%"
16%"
i225
12:5-
1960, p. 13 and 1969, MG1-14-43a.
18-16
FAN ENGINEERING
— BUFFALO FORGE COMPANY
As shown in Table 18.6, NEMA limits the minimum pitch diameter
and the maximum width of sheaves that can be mounted on a motor.
There are no published limits to the size and weight of a fan rotor
that can be mounted directly on a motor shaft. If the weight of the
impeller W in lb and the distance / in in. from the edge of the motor
bearing to the center of gravity of the impeller are specified, the
motor manufacturer will be able to properly size the motor shaft. An
approximate, rule-of-thumb solution for the size of the motor shaft d
in in. for a 3600-rpm, Arrangement-4 fan is
d=0.24(WP)'".
(18.10)
NEMA had adopted certain values of effective load WK that
large standard motors should be able to accelerate without causing a
damaging temperature rise. Rule-of-thumb values for smaller motors
are 2.25 lb-ft’ per horsepower rating for 3600-rpm motors, 13.5 Ib-“ft?
per horsepower rating for 1800-rpm motors, 37.5 lb-‘ft? per horsepower for 1200-rpm motors, and 80.0 lb-ft* per horsepower for
900-rpm motors. These rules give the maximum allowable load WK
in lb-ft° referred to the motor axis. If these values are not exceeded,
the motor should be capable of restarting immediately after a false
start or power interruption. Enough time must be allowed before any
subsequent starts so that the motor temperature can return to the
rated temperature. Theoretically, the thermal capacity of any motor
should be checked against the corrected WK. Practically, however,
motors built in frame 447T or smaller are always capable of starting
a normal fan load without overheating. Abnormal, or unusually high
WK’, fan loads may occur if the fan handles very light gas or is very
much oversized. Safe-stall times for large (that is, 4,000-hp to 250-hp)
induction motors are about four to twenty seconds and vary with the
design. Safe acceleration times are longer because ventilation is better
than that for a motor at standstill.
Starters for induction motors can be classified as either fullvoltage, reduced-voltage, or part-winding types. All must provide
overload protection as well as a means of energizing and de-energizing
the motor circuits.
Full-voltage or “across-the-line” starters are the simplest and least
expensive. Most motors can tolerate the application of full-voltage at
standstill, and most fans are designed to tolerate the corresponding
acceleration forces. Unfortunately, these starting currents are often
high enough to produce voltage drops that cause lights to flicker or
magnetic devices to drop out. Power companies, therefore, restrict
the size of motors that may be started across the line.
Reduced-voltage starting lowers both the starting current and, as
indicated in Table 18.5, the starting torque. There are various
methods (including auto-transformer, resistance, and reactance
methods)
that can
be used
to start
squirrel-cage
motors.
Wound-
CHAPTER
18 — FAN MOTORS AND DRIVES
18-17
rotor motors can be started with very low current if the resistance
during starting has been properly selected. Where current restrictions
are strict, several circuit switchings may be required for either type
of motor.
Part-winding starting of motors built for dual-voltage operation
may be possible. Such motors have two similar sections of winding
in each phase. Low-voltage operation requires that the sections be
connected in parallel; high-voltage operation requires a series connection. A standard, dual-voltage motor can be used with the proper
connection for part-winding starting on the lower voltage. Special
internal connections are needed for part-winding starting on the
higher voltage. In part-winding starting, full-voltage power is connected to either 2/3 or 1/2 of the windings. Subsequently, full voltage
is applied to the rest of the windings. During starting, current inrush
is limited by the higher resistance that results from using only part of
the windings. Whether a fan will be accelerated to full speed on the
first step depends on the torque characteristics of the fan and motor
and the inertia of the fan. Higher starting torques are available from
2/3 part windings than from 1/2 part windings. If full acceleration is
not achieved on the first step, another current inrush will occur on
the second step. This will equal the full-voltage starting current corresponding to the motor speed.
Fractional-Horsepower Electric Motors
Single-phase, alternating-current motors are almost always used in
fan applications that require less than one horsepower. Although
polyphase and direct-current motors are also available in this range,
they are rarely used.
Four types of single-phase motors are suitable for driving fans.
These are designated shaded-pole, permanent-split capacitor, splitphase, and capacitor-start motors. All are single-speed motors, but
with suitable internal or external modifications, operation at two, or
even more, speeds is possible. Each type uses a squirrel-cage rotor, a
main field winding, and some sort of auxiliary winding. But, their
rotor designs differ, contributing to differences in locked-rotor torque
and slip at normal operating speeds. Four-pole main windings are
usually used, but two-, six-, and even eight-pole designs are also
available. Auxiliary windings are needed to make the motor selfstarting. Such a winding may be deactivated after it performs the
starting function, or it may remain active at all speeds.
Various physical and mechanical modifications or alternatives are
possible for each type. The standards for frame size, mounting
arrangement, and enclosure all parallel those for integral-horsepower
motors. Fractional-frame sizes are sixteen times the shaft center-line
height of a standard foot-mounted motor. Because single-phase
motors develop a pulsating torque, resilient mountings are often
preferred. Sometimes, a footless motor is chosen so as to minimize
18-18
FAN ENGINEERING
— BUFFALO FORGE COMPANY
the air resistance. In any air-over application, a totally enclosed
motor should be used to prevent gumming the windings. Total
enclosure is especially important in those types that use a centrifugal
switch. Some are called definite-purpose, fan-and-blower motors.
Many general-purpose motors can also be used in fan applications.
Some fans are equipped with special-purpose motors designed for the
precise requirements of the application, taking into account the
cooling effect of any air passing over the motor, the number of starts,
the hours of operation, etc.
Shaded-pole motors are the least expensive of the four types
usually used to drive a fan. These machines inherently have very low
efficiency (about 30%), high slip (about 14%), low locked-rotor
torque (about 60% of full-load torque), and comparatively high
starting current. Starting is achieved by inducing a current in the
short-circuited auxiliary winding, which is angularly displaced from
the main winding. Two such windings are needed if the inotor must
be reversible. The starting winding is energized at all speeds leading
to low efficiency and low power factor. Relatively high-resistance
rotors are needed to develop as much starting torque as these motors
do. This promotes high slip, so the rated speeds of four-pole and
six-pole, 60-Hz motors are 1550 and 1050 rpm, respectively. This
type of motor usually is not used if the fan requirements exceed 1/6
or 1/4 horsepower, since low efficiency leads to high operating
currents and, therefore, to large wire sizes, high heat generation, and
high operating costs. Motors of all ratings are usually built in NEMA
frame 42 or 48, or their equivalents. Because the starting torque is
not enough to overcome the breakaway torque of a belt-driven fan,
these motors are limited to reasonably light, direct-connected fans.
The speed can be adjusted by reducing the effective voltage. This is
done by winding extra coils and taps into the main field or by adding
impedance externally, as with a series choke. In either case, three or
four speed steps can be controlled with a simple selector switch.
Permanent-split capacitor motors are slightly more expensive than
shaded-pole motors. They have medium efficiency (about 50%), fairly
high slip (about 10%), low starting torque (about 60% of full-load
torque), and relatively low starting and running currents compared
with shaded-pole motors. Both the main winding and the starting
winding are distributed, whereas in shaded-pole motors, salient-pole
windings are usually used. The magnetic field used by the auxiliary
winding is angularly displaced by incorporating a capacitor in series
with the auxiliary winding. This starting circuit is in parallel with the
main winding and is energized at all speeds, but with the proper
capacitor, reasonable efficiency and a good power factor are
achieved. The rated speeds of four-pole and six-pole, 60-Hz motors
are 1625 and 1075 rpm, respectively. However, this type of motor
usually is not used if the fan requirement exceeds about 1/3 horsepower. Motors for all ratings are usually built in the equivalent of
CHAPTER 18
— FAN MOTORS AND DRIVES
>
18-19
NEMA frame 42 or 48. The low starting torque of these motors
limits their use to direct-connected fans. Two-speed operation can be
obtained by incorporating two windings in the motor and using a
double-pole, double-throw switch. Three or four speed steps can be
controlled with a selector switch and a series choke or witha tappedwound motor arrangement. The direction-of rotation can be reversed
by reversing the leads.
Split-phase motors are also built with distributed main and auxiliary windings. The starting field is angularly displaced by using a
very-high-resistance auxiliary winding. To prevent this winding from
burning out, it must be deactivated as soon as possible after the
starting function is achieved. A centrifugal switch is usually used to
open the starting circuit at about 75% of the rated speed. No capacitors are used. These motors have a comparatively high efficiency
(about 65%), low slip (about 4%), medium starting torque (about 100
to 275% of full-load torque), and comparatively high starting currents
(about 600% of full-load current). Comparatively low-resistance
rotors are employed, promoting low slip. Rated speeds for two-,
four-, six- and eight-pole, 60-Hz operation are about 3450, 1725,
1140, and 850 rpm, respectively. This type of motor is generally used
for fan requirements of up to I/2 horsepower, and is usually built in,
the equivalent of NEMA frame 48 or 56. Its starting torque 1s
adequate for most belt-driven fans. The four-pole motor is usually
selected for belt-driven applications. Two-speed motors standardized
for four-pole/six-pole speeds are controllable with a single-pole,
double-throw switch.
:
Capacitor-start motors are sply-phase motors with a capacitor in
series with the starting winding. The starting current is greatly limited
by the use of the capacitor, so considerable starting torque (about
250 to 400%
of full-load
torque)
can
be built
into these
motors.
Although the excess starting torque is usually unimportant for a fan
load, this type of motor must often be used to aie light flickering,
etc. Capacitor motors are usually used for 1/2- to 3/4-horsepower fan
requirements. They are built in NEMA frame 56, or its equivalent.
The slip nearly equals that for the split-phase motor, and the efficiencies are equal or higher. The capacitors themselves are generally
mounted in a box, usually in a piggyback position atop the motor.
Just as in the split-phase motor, the starting circuit is de-energized by
means of a centrifugal switch.
Transmission Elements
Various machine elements can be used to transmit mechanical
power from the prime mover to the fan. If the motor speed matches
the fan speed, some form of direct connection may be warranted.
But, if the motor speed differs from the fan speed, an indirect connection through belts, chains, or gears is indicated. Variable-speed
prime movers can be used in either case. Alternatively, the transmis-
18-20
FAN ENGINEERING
— BUFFALO FORGE COMPANY
sion may include a variable-speed device.
Shaft couplings serve several purposes. They provide for disconnection as well as connection. They may also provide enough
flexibility to protect shafts and bearings against misalignment, shock
loads, and torsional vibration. Special designs may include slip or
over-running features to protect one shaft or the other against overload. Variable-speed designs are also available.
Rigid couplings are rarely used because slight lateral and angular
misalignment is almost unavoidable.
Flexible couplings are built in a variety of designs. Flexibility can
be achieved
by using 1) flexible material, such as rubber; 2) flexible
shapes, such as springs; or 3) sliding joints. Every reasonable precaution should be taken to achieve and maintain good alignment even
though a flexible coupling has been used. The extent to which a
flexible coupling will alter vibration characteristics or protect against
shock varies from one design to another. The rating data for a flexible
coupling can be presented in several ways. Torque-transmitting ability
is usually expressed as horsepower per 100 rpm. Speed-and-bore
limitations will also be listed. Service factors for various load/ primemover combinations may be listed separately or incorporated in the
capacity ratings.
Flexible couplings transmit power through parts in mechanical
contact, sometimes cushioned by a film of lubricant. Because the
flexibility permits light oscillations but no further relative rotation,
the driven speed always equals the driver speed.
Hydraulic couplings transmit power without any mechanical
contact of parts. The input power is used to drive the “impeller,” which
applies the force needed to accelerate the fluid. The fluid, in turn,
decelerates in the “runner” applying the forces necessary to drive the
output shaft and the connected load. There is always some relative
rotation or slip between the impeller and the runner. The minimum
slip may range from 2% to 5% of the input-shaft speed. The outputshaft speed can be reduced to about 20% of the input-shaft speed on
fan-type loads. As a practical operating procedure, supplementary
damper control is recommended below about 30% speed because,
otherwise, the response time is rather long when decelerating. Control
is achieved by adjusting the amount of fluid in the working circuit. A
pump delivers fluid from a sump through a cooler to the impeller.
The amount of fluid in the working circuit is usually adjusted by
trimming the level in a rotating chamber with a scoop device. The
power to drive the pump and overcome the bearing friction is usually
called fixed loss ,,,.4, since it remains constant for a constant input
speed. Also, there will be a slip loss Y,,,,, which is a function of the
input Nay and output Ny speeds and of the fan power @,, as indicated by
Op
Pap
Nu
— Nr
Se
Ne
) #.
(18.11)
CHAPTER
18 — FAN MOTORS AND DRIVES
18-21
The fraction represents the slip referred to the fan speed. The slip
power loss as a percent of fan power equals the percent slip.
Maximum slip loss, for loads that vary as the cube of the speed,
occurs at 2/3 speed and is approximately 15% of the full-speed fan
power. Input or motor power “,, is the sum of the load and the
losses, as indicated by
Gy
=a Py
ar Prin a5 Fea
3
(18. 12)
A comparison of various flow-control methods, including speed control, is given in the chapter on fan control.
Also available are variable-speed devices, known as magnetic drives
or eddy-current couplings, that also operate on the slip-coupling
principle. Slip losses can be calculated as shown above. Fixed losses
will be due to windage, etc. in an air-cooled device or to pumping,
etc. in a liquid-cooled machine. Control is achieved by adjusting the
strength of the excitation that produces the magnetic field. This field
is rotated mechanically rather than electrically, but it drives the rotor,
Just as in an induction motor.
In both fluid and magnetic drives, the absence of any mechanical
connection reduces the transmission of torsional vibration and shock
loads. The starting characteristics are also better. Although such considerations are important, the main reason for using a slip coupling
is to provide variable-speed control. The combination of a constantspeed motor and a slip coupling may be more economical than a
variable-speed prime mover.
Hydroviscous couplings are also used as fan drives. They employ a
series of grooved’ disks attached alternately to the driver and the
driven shafts. The output speed is controlled by adjusting the spacing
between the disks. Fan speed can be made equal to motor speed by
forcing the disks together in a “locked up” position. The slip loss
equals that for any slip device, except that it is zero at lock up.
Indirect drives serve several purposes. They permit locating the
motor in various positions relative to the fan. They also allow a wide
choice of fan speeds, even though the selection of motor speeds is
limited.
Most indirect drives are of the V-belt type. (Very few flat-belt
drives are used with fans.) Positive drives of the timing-belt or chainand-sprocket types are used occasionally. The choice is usually based
on the first cost, although the maintenance and operating costs may
also be important. Both chain and belt drives transmit power by
increasing tension in one of the connection legs (and, so, reducing
tension in the other). The net tension force F in lb can be determined
from the power
& transmitted and the belt speed V in fpm, using
p= 33000 Ce
i
V
;
(18.13)
18-22
FAN ENGINEERING
— BUFFALO FORGE COMPANY
For SI units, substitute 1000 for 33000; then, F will be N for H in
kW and Vin m/s.
Ton
Friction drives like the flat- or V-belt types require an initial
tension to prevent the belt from slipping. This produces an additional
load on both the fan and motor bearings at standstill and a consequent increase in breakaway torque. The net tension when transmitting power will equal that for a positive drive with the same pitch
diameter.
The speed ratio of an indirect drive is usually calculated directly
from the pitch-diameter ratio. This calculation gives an exact value
for a positive drive but only an approximate value for a friction
drive, since creep and slip will reduce driven speed. Experimentally
determined values of creep are of the order of 1% to 2%. The reduction in speed due to slip may also be about 1% to 2% on heavily
loaded drives, so the combined speed loss can be as high as 4%. A
corresponding loss of power will result. The frictional force that
must be overcome in pulling a V belt from its groove results in
further power loss, as does any friction within the belt itself. The
overall efficiency of a V belt drive may be about 95%. By comparison, a good quality roller chain may be 98% to 99% efficient,
and silent-chain and flat-belt efficiencies will fall in between.
Rating tables for V belts usually list the allowable power per belt
for various combinations of driver sheave and driven sheave and for
various motor speeds. Correction factors for arc of contact and belt
length are tabulated for standard belt lengths. The smallest sheave
should not be smaller than the minimum value listed for the belt
section involved. This limitation reflects both the short life and poor
efficiency of highly flexed belts. Belt-speed limitations reflect the
need for balancing and the reduced load-carrying ability due to
centrifugal force.
The driver-sheave limits adopted by NEMA and presented in Table
18.6 are based on the fact that belt pull is inversely proportional to
sheave size for constant torque. Although smaller sheaves have lower
first costs and take less space, maintenance and operating costs may
be lower for larger sheaves.
Motor bases should provide take-up and installation allowances
for belt drives. New belts should not be stretched over the sheaves;
instead, the motor should be moved toward the fan when installing
replacements. Moving the motor away from the fan must also be
possible in order to periodically take up the slack produced by
stretching under load.
Variable-pitch sheaves make possible a limited fan-speed adjustment (about 25%). Both stationary and in-motion control types are
available. A variable-pitch sheave will be most economical if chosen
for the high-speed shaft. (In fan applications, this is usually the motor
shaft.) The motor position must be adjustable within the range
required by any adjustable-pitch drive.
Chapter 19
Fan Selection
In most fan applications, it is neither necessary nor desirable to
design a completely new fan for the specific job requirements. Standard designs are available in each of the various aerodynamic types
of fans. Many sizes are offered in arrangements and types of construction suitable for a wide range of duties. Therefore, fan selection
is usually a matter of choosing the best size and type from among
those available.
Fan selection begins with specifying requirements and ends with
evaluating alternative possibilities. Of the many fans that may be
capable of satisfying a particular flow rate and specific output requirement, the best selection is the one that does the job most economically. First costs, operating costs, and maintenance costs must all be
considered.
The methods of rating given in this chapter are based on the fan
laws. Many of the equations have been taken directly from the fanlaw chapter.
U.S. customary units are used in the following examples and discussions, but the equations can be used with S.I. units as well.
Specifying Requirements
A fan specification should give the supplier all the pertinent information regarding performance, service, evaluation, arrangement,
etc. so that the best selection can be offered. Most of the important
items are listed in Table 19.1. Explanations of many of these items
follow in the next few paragraphs.
The number of fans and their aerodynamic type are items that
should be specified only after comparing the various possibilities.
Refer to the chapter on fan systems for discussions on the use of two
fans in series or in parallel. Refer to the chapters on centrifugal and
axial-flow fans for discussions of the various aerodynamic types.
The type of service for which the fan is intended should also be
specified to warn the supplier of any unusual conditions. Sometimes
a duct layout should be included with the specifications. The sizes of
the connecting duct work should always be stated.
The flow rate of the fan must be specified by the system designer.
Either the mass flow rate mr or the volume flow rate Qr can be
19-2
FAN ENGINEERING
— BUFFALO FORGE COMPANY
specified. If a certain flow rate is required at A but the fan is located
at B, any differences due to leakage, heat transfer, mass transfer, or
other fans between A and B must be taken into account. The volume
flow rate at the fan location Q- is related to the mass flow rate mer
and the gas density prat that location:
2
OEE
Ge
cc
(19.1)
The fan gas density or fan air density is the total density at the fan
inlet. Although the fan must be selected for the actual flow rate,
some designers prefer to specify the flow rate based on standard
conditions. There is nothing wrong with this provided that the conditions are adequately specified so that the conversion to actual flow
rate can be made. The standard flow rate Qs and the corresponding
density ps are related to the actual mass flow rate and the actual
volume flow rate, as indicated by
mr= Osps and
=
Or
Osps
pps
(19.2)
(19.3)
If the power requirements are to be evaluated for several ratings,
then the flow rate for each of those ratings should also be specified.
The system designer must also specify the fan output requirements
for each rating. The output (or more properly, the specific output)
can be specified in terms of pressure, head, or specific energy. Pressure is most commonly used, so Table 19.1 and most of the discussions that follow are based on pressure. However, specific energy (or
work per unit mass) is recommended in ISO 117. As noted in the
chapter on fluid flow, head is rarely used in fan engineering.
For a closed system, the fan output must be enough to overcome
the losses caused by the flow through the various system elements. In
an open system, the fan output must also be enough to overcome the
losses of all of the duct elements and, in addition, any difference in
kinetic energy from the system entrance to the system exit. Since
almost all open systems draw from a quiescent region of the atmosphere, the kinetic energy at the entrance will ordinarily be considered zero, and any increase will simply be the value of the exit
kinetic energy. But, if a different pressure is maintained at the exit
than at the entrance, the fan output should be adjusted accordingly.
For instance, if the entrance is pressurized by some device other than
the fan and if the exit is not pressurized, then the fan must do less
work.
Either fan total
pressure per or fan static pressure prs can
be
CHAPTER
19 — FAN SELECTION
Table 19.1
19-3
General Fan Specifications
General
Number of fans
Aerodynamic type
Sizes
Service
Flow Rate for Each Fan — Specify Maximum and Reduced Ratings
Mass flow rate mrin lbm/s
:
Volume flow rate at inlet conditions O-in cfm
Fan Output at Each Flow Rate
Total pressure at outlet p72 in in. wg
Total pressure at inlet p7 in in. wg
Fan total pressure prrin in. wg
Fan velocity pressure pryin in. wg
Fan static pressure prsin in. wg
Gas Composition and Conditions at Each Flow Rate
Name or gas analysis
Molecular weight or specific gravity referred to air
Ambient barometer in in. Hg or elevation in ft
Temperature at inlet in °F
Relative humidity in %
Dust loading through fan
Power-Evaluation Factors
Expected life in yr
Expected operation at each rating in hr/yr
Power rate in $/kw-hr
Demand charge in $/kW or $/hp
Physical Data
Number of inlets
Type of drive
Arrangement number
Direction of entry for inlet boxes
Rotation, discharge, and motor position
Construction Details
Appurtenances
Special materials
Type and mounting of bearings
Motor Data
Electrical characteristics
I
Type
enclosure
2s and eae
aA
Ve
Ps ee LENS WYNS eres Sma
ee
19-4
FAN ENGINEERING
— BUFFALO FORGE COMPANY
nner
EEE
specified. In the chapter on fan systems, several pressure diagrams
illustrated the relationship between the pressure losses of the various
system elements and both the fan total pressure and the fan static
pressure. By definition,
DET
P12 oe DI
and
DES Ps) am Pre
(19.4)
(19.5)
where the subscripts / and 2 refer to fan inlet and fan outlet
conditions.
For an open-inlet fan, pri = 0, so prr= pr2 and, in terms of the
various system losses,
Prr= Pid t Pix,
(19.6)
where pra is the sum of the losses for any straight duct, elbows,
nozzles, diffusers, or other elements connected to the fan and prx is
the exit loss. Whenever the exit loss is very large, consider adding a
diffuser at the exit to reduce the value of przx and, so, conserve
energy. Of course, the diffuser itself will have a loss pr-, which must
be added to pra, but if properly designed, this loss will be less than
the gain achieved by reducing pry.
Also, for an open-inlet fan, prs = ps2, since pri = 0. Although fan
static pressure does equal the static pressure at the discharge, this
relationship is misleading. It has undoubtedly led to the common
practice of specifying fan static rather than fan total pressure. The
pressure loss through a uniform duct, or even an elbow with the
same inlet and outlet area, does, indeed, equal the change in static
pressure. However, the pressure loss through a nozzle or diffuser is
not the same as the change in static pressure. Nevertheless, the fan
static pressure does equal the sum of the changes (both positive and
negative) in static pressure across each element for an open-inlet fan.
This is not true, however, for a fan with any duct work connected to
the inlet.
For an open-outlet fan, pr = —pre — pri and pr2 = py2 = pix where
Pre 1S the entrance loss; where pz; is the sum of the losses for any
straight duct, elbows, nozzles, diffusers, or other elements connected
to the fan inlet; and where pry is the exit loss. Based on this,
PET Dia DlenseDiir
(19.7)
Again, energy can be conserved by adding a diffuser at the exit to
reduce the value of prx.
Also, for an open-outlet fan, prs
= —pn, since pr2 = py2 = prv.
Note that the fan static pressure does not equal any simple static-
CHAPTER 19 — FAN SELECTION
See
19-5
pressure quantity; rather, it equals a total pressure quantity. Neither
does fan static pressure equal the sum of the changes in static pressure across each element for an open-outlet fan.
For a fan with both inlet and outlet duct work,
[ie
[Dial ar [Dix AF Dee
Dit
(19.8)
where the symbols represent the same quantities listed above. To
conserve energy, streamline the entrance fitting as much as possible
to minimize pre, consider a diffuser at the exit to minimize pzx, and
use the fewest elbows and the largest possible ducts to minimize both
Pu and pra. Equation 19.8 can be considered the general equation
relating system losses to fan-pressure requirements. since either
Equation 19.6 or Equation 19.7 can be derived from it.
A general equation for the fan static pressure prs is
PFs = Pid
Pix
Pre + Pri— Pry,
(19.9)
where pry is the fan velocity pressure. It is tempting to simplify this
equation by eliminating both pzx and pry, since they are usually
about the same value. But, this is unwise because the two values may
not be the same and, even more importantly, because the energyconservation potential will be obscured if no p,x term is given.
The sum of the total pressure losses for the system should include
an allowance for any elements needed to connect the fan to the
system. This will be a negligible amount unless the size of the fan
opening differs greatly from the size of the connected duct work.
The performance of a fan is a function of the density of the air or
gas at the fan inlet. The inlet density not only determines the volumetric flow rate for a specified mass flow rate but also the pressure
the fan is able to develop. The factors that affect density and should,
therefore, be specified are: the barometric pressure, the temperature,
and the relative humidity at the inlet, as well as the gas or its composition. The ambient barometric pressure and the gage pressure at the
fan inlet may be specified instead ofthe inlet barometer.
The composition of the gas and information about any entrained
material (dust loading, etc.) should be specified so that the fan supplier can offer the best selection based on previous experience.
Whenever the gas composition and conditions are not specified,
the fan supplier assumes air at standard conditions. Standard conditions for the fan industry are dry air at 70°F and 29.92 in. Hg. The
density corresponding to these conditions is 0.075 lbm/ft.. Other
industries have different standards. (See the preceding discussion on
standard flow rate.)
If the power requirements will be evaluated by the user (as they
should be to obtain the best selection), then the fan supplier should
be advised of the evaluation method used. The usual method is to
19-6
FAN ENGINEERING
— BUFFALO FORGE COMPANY
reduce the expected cost of power during the useful life of the equipment to the present value of an annuity sufficient to yield the annual
expenditure. The annual expenditure will depend on the cost per unit
of energy C and the expected operating schedule (annual operating
times ¢; at each of k operating points), as well as on the power
requirements
at the various operating conditions. The size of the
hypothetical investment / will depend on the expected life m and the
rate of interest i that could be obtained. Accordingly, the cost of the
expected operation reduced to its present value / can be determined
from the energy rate C and the expected annual power consumption
+ At, by using
k
fhe
l=C SS Bp) ———
= Pal
i
(19.10)
The bracketed factor, which is the present value of an annuity expected to yield one dollar annually for n years if invested at ij rate of
interest, can be determined from any standard interest table. Example
19.1 uses Equation 19.10.
Inefficiency can be penalized by charging the fan a flat amount for
each horsepower or kilowatt needed. In the power-generating industry, such a demand charge, which reflects the loss of power available for sale at peak load, may be added to the operating charge,
which is based on fuel cost.
The operating costs, as determined by Equation 19.10 or some
other method, should be added to the first costs and the expected
maintenance costs for each possible selection. The best selection is
that fan having the lowest total cost. Maintenance costs are not as
easily determined as first and operating costs. Often, maintenance
costs can be assumed equal for the alternative selections. However,
all pertinent engineering factors should be examined to justify any
such assumptions.
The items listed under Physical Data and Construction Details
should be specified because the user is usually better able to decide
such issues than the supplier. Some of these items, like rotation and
discharge, do not influence cost. Others, like the arrangement number
and appurtenances, may greatly influence the first cost but not the
size and type of fan that should be selected. Still other items, like the
number of inlets and the type of drive, largely determine the size and
type of fan that should be selected. Refer to the chapter on fan terminology for construction standards.
If there is no inlet-side duct work, either a single- or double-inlet
fan can often be used. In such cases, the first cost is usually lowest
for the double-inlet fan, especially when relatively large flow rates
and low pressures are involved. Double fans need less head room but
more floor space than a single-inlet fan for the same rating. However,
CHAPTER 19
— FAN SELECTION
19-7
single-inlet fans are usually preferred for high-pressure, low-flow-rate
ratings. The advantages of providing only one inlet connection rather
than two are obvious. If direct-connected speeds are required, the
type of fan that can be offered will depend on whether a single or
double inlet is specified.
Direct-drive specifications limit the fan speeds to available motor
speeds, and this, in turn, limits the number of possible fan selections.
It is unlikely that a standard-size fan will be able to exactly satisfy
performance requirements at a direct-connected speed. Accordingly,
either the requirements must be relaxed or a nonstandard
fan must
be used. The performance of a standard fan can sometimes be
changed sufficiently by modifying the wheel diameter or width. At
other times, an odd-size fan can be furnished. When warranted, an
entirely new
maintenance
drives.
fan can be designed. Direct drives usually need less
and involve less power-transmission loss than belt
Belt-drive specifications make possible a large choice of fans. Any
standard-size fan can be used. The most economical motor can usually be employed, even if its speed does not match that of the fan.
Should requirements be altered slightly after installation, it will usually be easy and inexpensive to change the belt drive. The total first
cost of the fan motor and drive generally favors belt drives below
about 200 hp and direct drives above that figure.
The standard designations for arrangement number, direction of
entry for inlet boxes, rotation, discharge, and motor position are
given in the chapter on fan terminology. Arrangements with the impeller mounted between bearings are usually less expensive than
those with overhung impellers. In smaller-size fans, arrangements
with bearings in the inlet are usually avoided because a closely
situated bearing may block much of the inlet. Overhung-impeller
arrangements are often used to protect the bearings when the fan
must handle hot, dirty, or corrosive gas. The alternative is to use
inlet boxes and increase the center distance between the bearings
accordingly. Overhung pulleys or sheaves are preferred for easy
maintenance, but jack shafts may be needed in some larger drives.
Various appurtenances may also be required, including vibrationisolation bases, belt guards, drains, access or inspection doors,
flanged connections, inlet screens, stack bracing, evases, stuffing
boxes, shaft seals, heating slingers, outlet dampers, and variable-inlet
vanes.
Standard fans are usually steel-plate products. However, some
standard lines are cast-iron housed, and aluminum is used extensively
in axial-flow impellers. Under certain conditions, special materials or
methods of construction may bejustified. Where corrosion resistance
is required, the construction materials should be specified by the user,
if possible. Several classes of spark-resistant construction are generally available. Because abrasion resistance is very difficult to achieve
19-8
FAN ENGINEERING
— BUFFALO FORGE COMPANY
in a fan, additional thicknesses of the regular material, special materials, or both may be specified. Center-line support may be needed to
maintain alignment when high-temperature gases are handled. And,
special materials may be required to prevent rapid oxidation at high
temperatures. Refer to the chapter on hot and corrosive gas handling.
Certain fan lines are routinely furnished with antifriction bearings,
others with sleeve bearings. Any preference should be specified together with details on the lubrication system, the cooling media, and
the type of mounting.
The type of motor, its enclosure, etc. should also be specified,
especially if furnished by the user. The electrical characteristics should
always be listed.
Selecting the Proper Size and Type of Fan
Theoretically, almost any size fan of any type could be used to
satisfy the maximum requirements of a particular job. However,
practical engineering and economic considerations reduce the possibilities to a relatively narrow range of sizes and just a few types.
The suitability of a particular type of fan depends more on the
relationships between the various performance requirements than on
their exact values. This is especially true if the speed is specified. In
such cases, the specific speed can be calculated, and the types of fans
that are reasonably efficient at this condition can be determined
from a chart such as Figure 12.3.
Certain types or designs of fans are designated according to their
usual field of application: ventilating fans, mechanical-draft fans,
industrial exhausters, and pressure blowers, each with subclassifi-
cations.
Ventilating fans are designed for clean-air service at normal temperatures. Some heavy-duty ventilating fans can be used for more
severe conditions. Both centrifugal and axial designs are available.
Centrifugal types may have either backwardly or forwardly curved
blades. Maximum efficiencies are obtained with backwardly curved
blades, especially when they are airfoil-shaped. Forwardly curvedblade types are used when space and price are more important than
efficiency. Since belt drives are routinely used, any rating can be
obtained with a standard-size fan. Axial-flow fans will usually be
much smaller and less expensive than centrifugals. But, some of
these advantages may be lost if noise prevention demands extensive
treatment. Propeller fans are usually designed for free-delivery opera-
tion but may sometimes be used for up to one inch static pressure.
Mechanical-draft fans are those designed for forced draft, induced
draft, gas recirculating, primary air, or similar service. Mechanicaldraft fans are usually similar to heavy-duty ventilating fans. Other
features are incorporated as specified by the utility companies and
other users. Because direct connection is usually specified, many
basic designs are required in order to provide maximum efficiency
CHAPTER
19 — FAN SELECTION
199
over the wide range of specific speeds normally encountered. Temperatures and dust loadings may be comparatively high.
Industrial exhausters are designed for various kinds of industrial
service. Usually, some efficiency is sacrificed for simplicity and durability. Belt drives are generally used. In many highly erosive or corrosive applications, the impellers and other parts are considered
expendable.
In others, great effort is made to extend the life of such
parts by using special materials. Whenever stringy material must be
passed through the fan, a centrifugal fan with a cone or open wheel
should be used. The heels of the blades should be shaped so that
material will slide off because of centrifugal force, and there should
be no shrouds to prevent this. When sticky materials must be handled,
the amount of internal surface should be minimized, as is done in
axial fans designed for spray-booth duty.
Pressure blowers must be designed to withstand the high tip speeds
needed to produce high pressures. The impeller is often mounted
directly on the motor shaft. If not, some other form of direct drive is
usually used. Therefore, many designs are needed to provide maximum
efficiency at all ratings.
After determining the type or types of fans that are suitable for an
application, next, find the best size fan in each type. Only one size
fan in each type will operate at the point of maximum efficiency for
any given rating. This optimum-size fan must operate at a certain
speed to produce the required rating. A smaller-size fan that would
have to operate at a higher speed could also be selected, as could a
larger-size fan that would have to operate at a lower speed. In either
case, the efficiency would be lower than that for the optimum size.
Fans that rate to the right of peak efficiency can be called under-
sized; those that rate to the left of peak efficiency can be called oversized. “To the left” means having a lower flow rate, and “to the right”
means having a higher flow rate on the base curve. Oversized fans
are hard to justify unless future increases in flow rate are contemplated. Occasionally, the required operating speed of an oversized
fan will match a motor speed. But, usually, slightly undersized fans
are chosen because the optimum sizes are rarely standard ones.
Ratings slightly to the right of the peak efficiency are usually more
stable, that is, have steeper slopes than those at or to the left of the
best choice. In such cases, the additional costs caused by the lower
efficiency must be offset by the savings in first cost or by some other
engineering or economic factor.
Rating Fans from Test Curves
A fan rating is a statement of fan performance at one point of
operation. A complete rating includes all the variables that enter into
the fan laws: flow rate, specific output, gas density, fan size, speed,
input power, sound power level, and efficiency.
19-10
BUFFALO FORGE COMPANY
— ING
FAN ENGINEER
Rating a fan can be any procedure based on the fan laws that
permits the determination of some of the above variables if others
are given. For instance, rating a fan may involve calculating speed,
input power, and sound power level for a given size of fan at a given
flow rate, specific output, and gas density. In another instance, rating
a fan may involve calculating fan size, input power, and sound power
level for a given combination of speed, flow rate, specific output, and
gas density.
Two methods of rating fans for a given flow rate, specific output,
and density are outlined below. The first, which can be called the
equivalent-air method, starts with a given (or assumed) fan size and
leads to the determination of the corresponding speed and input
power. The second, which can be called the specific-speed method,
starts with a given (or assumed) fan speed and leads to the determina-
tion of size and input power.
In both methods, it is necessary to have a test curve for a fan of
the same type as that being considered. If the density p, for which
this base
curve
was
drawn
differs
from
the actual
density
p. for
which the fan is being selected, the rated fan total pressure prr must
be converted into equivalent fan total pressure ppre:
ati ny
DFTe — PFT
pas
Da
.
(19.11)
Alternatively, equivalent static pressure can be calculated if the rating
is given in terms of fan static pressure.
If the equivalent-air method is used and if the size D, of the fan
being rated differs from the base size D», then the actual flow rate
Qr must be converted into equivalent flow rate Ore:
Ore= or($).
(19.12)
The next step in the equivalent-air method is to find the point of
rating on the base curve. The point-of-rating flow rate On and the
point-of-rating fan total pressure prrp can be determined by trial and
error from the following relationship:
DFTe
PFTp
a2 (
aye
Orp
(19.13)
A slide rule can then be used to establish the point of rating. Set
the hairline over the value of Q-. on the D scale. Adjust the B scale
until the proper value of prre is also under the hairline. Maintaining
this relationship between the B and D scales, now move the hairline
until the values on the B and D scales correspond to a point on the
CHAPTER 19 — FAN SELECTION
19-11
Or versus prr base curve.' This is the point of rating. To determine
the rated speed Na, insert the base speed N, into
a
nol ge) (>
(19.14)
To find the actual input power &,, note the static efficiency 7, at
the point of rating and insert it into
Bn
_ OrprrKp
Conti
(19.15)
where Cg is 6354 in U.S. customary units and unity in S.I. units.
Example 19.1 illustrates the equivalent-air method of rating using
Figure 19.1 as a base curve. This example is based on fan static
pressure, but the same
were used.
Example 19.1
principles would apply if fan total pressure
Equivalent-Air Method of Rating
Given the base performance for a specific design according to
Figure 19.1, pick a standard fan to deliver 30000 cfm of air against
5 in. wg static pressure. Standard wheel diameters for this design
include 361/2 in., 40'/4 in., 44/2 in., 49 in., and 54/4 in. Conditions at
the fan inlet are 100°F dry-bulb, 70°F wet-bulb, and 29.5 in. Hg
barometer.
First, calculate the input density and the equivalent static pressure,
Note that the base curve is drawn for standard air with 0.075 lbm/ft’
density.
Pa = 0.0693 lbm/ft* from Figure 1.2 and
0.075
0.0693 = >°4! in. wg from Equation 19.11.
Die = B25 Fram
Second, select a trial size, calculate the equivalent air, and determine
the point of rating. Note that the base curve is drawn for a 36'/2 in.
wheel diameter.
Daz = 44'/2-in. trial size,
'A calculator can also be used to establish the point of rating by trial and error. Calculate and
store pre! Ore. Select trial values of Onn then square, and finally, multiply by the recalled
value of prre| Ore. If the resulting value does not match prry on the curve at Qrp, select new trial
values of Q¢, until a match is obtained.
—_
SE
“=
=o
wo”
oc
as
”
win
oS
=
oe
S
S
ae
=
a
=e
=>
Sa
CO
=
o
7)
0:
oO
)
'
ema
=
fee
OF
=
cats
em
aa 4
2212 F
—
::
oc
0330
>
wi
= 1 Q-i
uw
Ue=
SS BRST
in
6
Q\-0;
oc
BY
more
4ESRae
TEE
ae
iminet td
eet
hee
=
o.,
a
720 =1
ese
a
4
0
92
uw
2! 3 45
tel nk tal aie
—
0225
Oo
“10
S
:
wes
2
4
6
8
10
12
FLOW RATE IN 1000'S OF CFM
Figure 19.1
5
14
16
18
Typical Fan Test Curves - BL
V>\2
Ore = 30000 (Fr
= 20200 cfm from Equation 19.12, and
Or at Prsp = 10900 cfm at 1.57 in. wg from the base curve.
Third, calculate the speed and the input power. Note that the base
curve is drawn for 600 rpm and that the static efficiency at the point
of rating is 77%.
&
Na = 600
P=
20200
cen
ee
coun) ( 7) = 911 rpm from Equation 19.14 and
30000 X 5
$3540.77 ~ 30.7 hp from Equation 19.15.
Finally, select the next smaller and larger sizes for trial and determine
their ratings:
Da = 40"/s-in. trial size,
CHAPTER 19 — FAN SELECTION
3
1
19-13.
2
Ore = 30000 (2 7) = 24700 cfm,
Orp at Prsp = 12150 cfm at 1.31 in. wg,
Na
Pa~
My
24700
3602\ee
= 1105 rpm, and
600 (Een) Ge
_ 30000
X5
6354
X .715 = 33.0 hp.
D, = 49-in. trial size,
Ore = 30000 seh) - 16750 cfm,
Orp at prsp = 9630 cfm at 1.80 in. wg,
Na
Pa~
=
16700
Bone)
\e
600 ( 9630 )(3 ) = 775 rpm, and
_ 30000 X 5 = 29.6 hp.
6354 X .797
Note that the larger fan must run slower and the smaller fan faster
than the original trial size. The power requirements are all fairly
close to 30 hp. Even allowing for a 3% power loss in the belt drive,
the 401/s-in. fan could be driven by a 30-hp motor without exceeding
the normal service factor of a 1.15-SF motor (1.03
33.0= 34.0,
1.15 X 30.00 = 34.5). The cost of the extra power and the reduction
in motor life should be evaluated against the savings in first cost for
the smaller fan.
Assuming that the fan is expected to operate 7500 hr/yr for 20
years and that the energy costs will average 4c¢/kW/hr while interest
rates
average
15%,
the present
value
of the difference
in cost
for
power to drive the 33.0-hp and 30.7-hp fans can now be determined.
Assuming equal motor and drive efficiencies, the power difference is
0.746 (33.0 — 30.7), or 1.72 kilowatts. Assuming 7500 operating hours,
the cost of the extra power for one year is 0.04 X (1.72) (7500), or
$516.00. The present value of an annuity that would yield this amount
for 20 years if invested at 15% can be determined, using interest tables
or Equation 19.10, as $516.00 (6.26), or $3230.16.
The savings in power alone will more than pay for the difference
in the first cost of the fans, without even considering the reduction
in motor life.
The
first step in the specific-speed
equivalent
total
pressure
by using
method
Equation
is to calculate
19.11.
the
Alternatively,
19-14
FAN ENGINEERING
— BUFFALO FORGE COMPANY
equivalent fan static pressure can be used. The next step is to calculate the value of the specific speed N, corresponding to the required
speed Na, flow rate Or, and equivalent total pressure pre:
Dries
(19.16)
The point of rating can be determined directly if a specific-speed
curve is drawn on the base curve. Simply read the point-of-rating
flow rate Qr, corresponding to the value of specific speed for the
required conditions.
The required size D, can be determined by inserting the base size
D, and the base speed N, into
Or
Dai Di
Np )
ere
Ory
Na
‘
(19.17)
Alternatively, the required size can be found by reading the value
of the specific size D, for the point of rating and inserting it into
Or 2
Da= Dse
: PFTe 1/4 °
(19.18)
To determine the rated power &,, note the total efficiency n, and
insert it into Equation 19.15.
Example 19.2
Specific-Speed Method of Rating
Given the same base performance curve, pick a fan for the same
requirements and conditions as in Example 19.1 except that the fan is
to be direct-connected to a squirrel-cage, 60-Hz induction motor.
First, calculate the inlet density and the equivalent static pressure as
before. From Example 19.1,
Pa = 0.0693 and psre = 5.41 in. wg.
Second, select a trial motor speed, and calculate the corresponding
specific speed for the requirements:
N, = 1170 rpm trial value and
(30000)!
N, = 1170 ———— = 57100 from Equation 19.16.
(5.41)*4
CHAPTER
19
— FAN SELECTION
19-15
Determine the point of rating on the base curve, and evaluate the
suitability of the trial speed:
Osp = 12500 cfm from the base curve.
Since the static efficiency at this point is only 69.5%, try the next
lower motor speed, which will result in a bigger fan and, so, will
move the point of rating to the left:
Na = 880 rpm trial value,
N, = 880
(30000)'”
= 42900 from Equation 19.16, and
(64177
Qrp = 10600 cfm from the base curve.
The static efficiency at this point is 78%, which is high enough to
warrant further investigation.
Next, determine the corresponding size and input power. Note that
the base curve is drawn for 600 rpm and a 36//2-in. wheel diameter:
1/3
Da = 3642
_
Fy
OO
10600
451/2 in. from Equation 19.17 and
880
30000 X 5
= 30.3 hp from Equation 19.15.
6354 X .78
Finally, select the next lower motor speed for trial, and determine the
size and the rating:
Na = 700 rpm trial value,
N; = 700
(30000)'”
= 34200 from Equation 19.16,
(5.4) )2"
Ory = 8600 cfm,
1/3
Dr 33 61)
_
8600
x eS
700
52/2 in. from Equation 19.17, and
30000 X 5
= 29.5 hp from Equation 19.15.
Pa
6354 X .80
Evaluating on the same basis as in Example 19.1, the present value
of the savings in operating costs would be 0.746 (30.3-29.5) (0.04)
(7500) (6.26), or $1120.79. This probably will not be enough to pay
for the difference in first cost because both the fan and the motor
will be more expensive for the low-speed rating.
19-16
i
Se
FAN ENGINEERING — BUFFALO FORGE COMPANY
ee
ee
ES
eee
eee
If the point of rating on the base curve has been determined by
either the equivalent-air or the specific-speed method, the corresponding sound power level Lys can be read from the base curve. Fan
law le, as rewritten below, can then be used to calculate the actual
sound power level Lya:
be!
Lwa= Lwy + 70 log
De
Na
+ 50 log a
Pa
+ 20 log.
(19.19)
Alternatively, the specific sound power level Lw; can be read directly
at the point of rating and used in
Lwa= Lws+ 10 log (Qrprr’) .
(19.20)
In either case, the distribution of sound power level in the various
octave bands can be approximated by using data similar to that
shown in Table 19.2. Such data should be obtained by actually testing the type of fan involved.
Example 19.3
Given the same
19.2, determine
examples.
Overall Noise Rating
base performance curve as for Examples 19.1 and
the noise ratings for the fans selected in those
First, read the sound power levels on the base curve at the point-ofrating flow rate for each fan. (For instance, for the 441/2-in. fan, Lw»
is 88.0 dB.)
Then, calculate the actual sound power level:
i
4412
911 + 20 logio(0.0693"
are)
Lwa= 88.0 +70 logo ($67) + 50 logio a
Lwa = 88.0 + 70 (0.085) + 50 (0.181) + 20 (—0.033) , and
Lwa= 88.0 + 6.0 + 9.1 — 0.7 = 102.4 dB from Equation 19.9.
Tabulating for all the fan selections:
De
442in.
40'/2in.
49 in.
45/2 in
2 2ane
Lwa
Size corr.
88.0 dB
6.0 dB
88.1 dB
2.9dB
88.7dB
8.9 dB
88.1dB
6.7 dB
89.4dB
11.0dB
Speed corr.
Ol dBY
Weiiclss
w13:3:dB
—O7/Glss)
5.5 dB
=Os/clis
8.3dB
3.3dB
Sf ald. yobs
102.4dB
102 dB
103.6dB
104 dB
102.4dB
102 dB
102.4dB
102 dB
DY
Lwa
Say
KOde
103.0dB
103 dB
CHAPTER 19 — FAN SELECTION
Alternatively, read the specific sound
19-17
power levels at the point-of-
rating flow rate for each fan on the base curve. (For instance, for
the 441/2-in. fan, the point of rating Lws is 83.7 — 40, or 43.7 dB.)
Next, calculate the sound power level:
Lwa = 43.7 + 10 logio (30000 X 5’),
Lwo = 43.7 + 10(5.87), and
Lwa = 43.7 + 58.7 = 102.4 dB from Equation 19.20.
Tabulating for all the fan selections:
Da
441/2 in.
40/4 in.
49 in.
45/2 in.
52/2 in.
Lws
Corr.
43.7dB
58.7 dB
44.9dB
58.7dB
43.7dB
58.7dB
43.6dB
58.7 dB
44.4dB
58.7 dB
Lwa
Say
102.4dB
102 dB
103.6dB
104 dB
102.4dB
102 dB
1023dB
102 dB
103.1dB
103 dB
Table 19.2
Octave-Band Distribution of Sound Power Level for Type-BL Fans
Table values are the corrections to be applied to overall sound power level
Blade
Octave Band - Center Frequency Hz
Frequency
Range in Hz
75 to 150
150 to 300
300 to 600
,
Blade Frequency in Hz =
Example 19.4
N X number of blades
60
Octave-Band Ratings
Given the octave-band distribution in Table 19.2, determine the
octave-band distribution of the sound power level for the 44'/2-in.
fan selected in Example 19.3 if it had 16 blades.
Read the appropriate octave-band distribution factors from Table
19.2, and apply them to the overall values to determine the soundpower-level spectrum:
x
Blade frequency = ate = 243 Hz.
19-18
FAN ENGINEERING
— BUFFALO FORGE COMPANY
Freq.
E
Octave Band
4000 |8000
Overall level
Dist. corr.
Band level
102
—=29
1S
Rating Fans from Published Data
Rating data is usually published in the form of tables or charts for
each size fan of a given type. Most users find such presentations
more convenient to use than test curves of a single size. Illustrated
below are some typical methods of presenting rating data and
examples oftheir use.
Multirating tables are probably the most common type of published data. Portions of three pages from a typical multirating table
are shown in Figure 19.2. Such tabulations are almost always based
on standard air. To use such a table, enter with the required flow
rate, listed in the CFM column, and with the required equivalent
static pressure, incremental values of which are tabulated across the
page as S.P. Then, read the speed and input power on the appropriate
line in the applicable columns marked RPM and BHP. If the requirements do not exactly match the listed values of CFM or S.P, linear
interpolations will give sufficiently accurate results. The table value
of RPM is the required operating speed. To obtain the required
operating power, multiply the table value of BHP by the ratio of the
actual density to the standard density. Example 19.5 illustrates the
use of such tables.
Example 19.5
Selection Using Multirating Tables
Given the multirating table for a specific design according to Figure
19.2, pick a fan to deliver 30000 cfm of air against 5 in. wg static
pressure.
Conditions
at the fan inlet are 100°F dry-bulb,
75°F wet-
bulb, and 29.5 in. Hg barometer.
First, calculate the inlet density and the equivalent static pressure.
(Note that the tables are for standard air.)
Pa = 0.0693 lbm/ft* from Figure 1.2, and
Pe,
0.075 _
;
:
Prse= 5 X 0.0693 > 5.41 in. wg from Equation 19.11.
Next, select a trial size, and determine the rating.
Examine the table for size 805. Note that interpolations are required
between 5 and 51/2 in. wg and between 29824 and 30756 cfm:
CHAPTER
19 — FAN SELECTION
19-19
SIZE
[eos [22] Buffalo
ea
HyPe “BL” Fans
Wheel Diameter 40 Yr",
Outlet Area 9.32 aq. ft. inside,
390
Buffalo [intied
eh
de “BL” Fans
R.P.M.
Limit Load H.P. = 44.2 x ( 1000
Wheel Diameter 4412”.
390
Outlet Area 11.38 sq. ft. inside.
BHPIRPM
BESES|EESSE
#82
s
SIZE
980
;
‘nur | Buffalo
Wheel Diameter 49”.
BS
=
a
Jimit - |oad
SIZE
Type “BL” Fans
Limit Load H-P. = 71.1 x (ia
980
Outlet
Area 13.81 eq. ft.inside.
28238
> *3/8
iagaglesseg|
ASESS
SESER|E
Ratings are at 70°F, and 29.92” barometer.
Figure 19.2
Typical Multirating Table - BL
ESSER
EEBEEI
19-20
FAN ENGINEERING — BUFFALO FORGE COMPANY
1076 + Cae) (1102 — 1076) = 1076 + 21 = 1097,
1095 + Ce
(1120 — 1095) = 1095 + 20= 1115, and
1097 + arene) (1115 — 1097) = 1097 + 3 = 1100 rpm.
33.3 + eer, (35.8 — 33.3) = 33.3 + 2.1 = 35.4,
34.9 + =)
35.4 +
(37.3 — 34.9) = 34.9 + 2.0 = 36.9, and
30000 — 29824
=e
iy
he
=
|(36.9 — 35.4) = 35.4 + 0.3 = 35.7 hp.
The required operating power is less than the table value, since the
operating density is less than the standard density for which the table
was prepared:
Bik Cama
= 33.0hp.
0.075
Making similar interpolations for the other
Figure 19.2 and tabulating the results yields:
two
sizes shown
Size 805
1100 rpm
Size 890
990 rpm
Size 980
773 rpm
35.7 hp@ 0.075
33.0 hp @ 0.0693
33.2 hp@ 0.075
30.7 hp @ 0.0693
31.9 hp @ 0.075
29.5 hp @ 0.0693
in
These results agree to within a fraction of 1% with those obtained by
the equivalent-air method, as they should since Figure 19.2 is based
on the data in Figure 19.1. Refer to Example 19.1 for an evaluation
of these selections.
Various other types of multirating tables can also be compiled.
Some list the pressures and input powers for various flow rates at
one or more direct-connected motor speeds. (Figure 19.3 shows such
a table for three sizes of one particular fan design.) Others list the
flow rates and speeds for various pressures with fully loaded motors.
(Figure 19.4 illustrates this type of table for three sizes of another
particular fan design.)
Various types of multirating curves can also be constructed. One
type, illustrated in Figure 19.5, shows the performance of only one
CHAPTER 19 — FAN SELECTION
19-21
Static Pressures at
70° F. & 29.92” Bar.
‘a fs
S.P. in Inenes
of Water
88Din
NN Nw ye
$8ao
38wx wre
83Ne
Si
Roe
—
SS
) 5)
Md
aneo RSow
mo
aS
ab)
= A]
wo ore
oe aS~o
im
woo
2hvo —eowoo 23nO
Figure 19.3
Typical Multirating Table - RE
24" Design = Belt-Air
Pentvate [en feare Pexieelm [owive im [owfoeo
i/4 ||$390 795] oe | ano] roses TT
ifs [ssoo niofect [ s1ao| yoolene| apan|yasfaxo tt}
—
|750}
930] 667 ||
6,200
| 915] 682 [|
5,920]
soo} sea [14620 |
aroloza
| [|
a/a {| 7,760|1,060]
49.5 "7.220 |1.050/70.6 [|7,050 [1,040 [70.9 |]6,120 [i020 [715 [| 4750 | 900 [70.4
[|e470 [1,170]
717 | 8,000 [1,140 [72.3 | 7.050 [1,135 [72.5 |]7.120 [1,130 [735 ||4.000 [7,090 [73.0
| 9.680 |1,930|
74.5 ||9,300 |1,325[77.3 ff9,180 [1,920 [75.2 [[8,670 |v.310 [763 || 7.750 |1,280|
2 tel Pee
Re
es Ga a
ee
30" Design 53 Belt-Air
1/4 pS
ia
a
ES
i
Ti
ai is
!
[soot eno]ose[7900 saLor[7.480 |620 [67.4 |
3/4 frosso| 737[sa| esto|720[700[ooo |violrea[emo {aolaa fT
ere
(10,200 |7e0[71.9 [e480 |770 [722 [| |
Hiasoo| 923[73217300 |900[740 frz00|900[74aFos |ootess| 9300| Tht
es
or Od
re ge
Dall ne
Gia igh FCA 792
Figure 19.4
Typical Multirating Table - Belt-Air
19-22
FAN ENGINEERING
— BUFFALO FORGE COMPANY
prorocemonenennasoucroarecensonenensnnersecnnreennemeneenrenrs
nincnpearnnsnnnnenteninanninnonnnannonnoneNroarnnnennen AONE
INNO
BUFFALO FORGE CO.
TYPE P SPRAYBOOTH VANEAXIAL FAN
SIZE 36
WHEEL DIAMETER 36”
CONE OUTLET AREA 10.08 SQ. FT.
RATINGS ARE AT 70°F AND 29.92” BAROMETER
j
~YVELOCITY'AT CONE OUTLET-FTPERMIN'
Ries
Re rs i rare WCE UE ae
wrgrentenrmmernipenerenes
{
STNG
g
i)
RO
HORSEPOWER
=
Le
oe)
re
Oe
~{ 19
ii
i
“4
Hi
—co
al~
;Hii
Jcahainedneoncsensenedneameva
RPM
OF
HUNDRE
IN
SPEED
fo)
——s
16
<
18 90
iesSeam
Se
ae.
oR
sensor erennenne
CAPACITY IN THOUSANDS OF CFM
Figure 19.5
Typical Multirating Chart - P Spray Booth
CHAPTER
19 — FAN SELECTION
19-23
Pressures at 70° F.
& 29.92" Bar.
Figure19.6
Typical Multirating Chart — CB
FAN ENGINEERING — BUFFALO FORGE COMPANY
19-24
i
i i i i t fi i
| iii{
80 ee
doh
“lu
$.0001
“/
-
aaaact
980-—
CH =) i
pas eer te
ett
+
0-
j
~
i eT
SauerA
a
ae my
of
0.075
—
arinictosternenreae
i i 4
440 430 520
Figure 19.7
Typical Multirating Chart - BA
i
CFM - 1000'S
4
ay
1 mee
Dar
Rey
eter
aad
Seco
cely a
aa40 80 120 ret160Weer cied200thaental240|ePe 280
320 360 400
‘OMSIHINIA — *S2d
a
haar gaa
ee
os i i r wo
uwoccas +
A nee
| AC
a
i
~ pi
‘aM S3HONI/S — ssid JNo,
:
wo
aa =
CHAPTER 19
— FAN SELECTION
19-25
size of fan. Similar charts must be constructed for any other sizes for
which the performance is to be published. To use a chart of this type,
find the intersection of the required flow rate and the pressure in
each group of curves. Then, read the speed opposite the lower inter-
section and the input power opposite the upper intersection. Finally,
correct the input power for density, as in the example on multirating
tables.
Various other types of multirating curves can be constructed to
show the performance of one or more sizes of fans of a given type.
Figure 19.6 shows part of a single-speed, zone-type, multirating
chart. Each zone is marked with the size of fan that could be used to
satisfy any of the ratings within the boundaries of the zone. The
upper and lower curved boundaries are, respectively, the performance
curves of the largest and the smallest impellers that can be employed
in each size. To use such a chart, enter with the rated flow rate and
the equivalent static pressure, and note the fan size. Also note the
position of the equivalent rating with respect to the various horsepower lines. The required horsepower can be determined by multiplying the interpolated chart value by the ratio of the actual density to
the standard density. The required speed is that for which the chart
is drawn.
Figure 19.7 shows another type of multirating chart that can be
used to determine the rating for any standard-size fan in the particular line for which the chart is drawn. To use the chart, locate the
point corresponding to the actual flow rate and the square root of
the equivalent static pressure. Then, draw a straight line through this
point and the origin. Note the intersection with the various horizontal
lines for each size. Also note the values of f, and 7s on the vertical
line passing through that intersection. Now, insert these values into
the appropriate speed and power formulae also given on the chart.
(Example 19.6 illustrates the use ofthis chart.)
Example 19.6
Selection Using a Multirating Chart
Given the multirating chart for a specific design according to Figure
19.7, pick a fan to deliver 300000 cfm of gas against 20 in. wg static
pressure. Conditions at the fan inlet are 300°F, 29.0 in. Hg, and
1.04 SG.
First, calculate the inlet density, the equivalent static pressure, and
the square root of the equivalent static pressure. Note that the chart
is drawn for standard air.
Pa = 0.075 (1.04) (ey) (an
=
0.075
Prsa = 20.0 (Gace
\_
= 28.5, and
= 0.0527 Ibm/ft’,
19-26
\/ Prsa
FAN ENGINEERING
— BUFFALO FORGE COMPANY
= 5.34.
Next, spot the point corresponding to 300000 and 5.34. Draw a
straight line between the spotted point and the origin. Note that this
line intersects several size lines. Also, note that the 1615-size line is
intersected almost directly below the point of maximum efficiency
(actually 87.0%). Similarly, note the value of the speed factor directly
above the intersection (7.550X 1000). Finally, calculate the speed
and power:
Na =
z
Tai
Qo
7550 X 1615 X 28.5
300000
= 1158 rpm and
300000 X 20.0
reasas ey
—— _
a OS nD:
=
Part I]
Fan Applications
Chapter 20
Ventilation
The purpose of any general ventilation system is to promote the
health, comfort, and well-being of the occupants of the space served.
This is accomplished by controlling the thermal conditions, the
amounts
of contaminants,
or both, in the atmospheric environment.
Human occupancy itself produces chemical vitiation, sensible and
latent heat, odors, and organisms. Industrial or other activity within
a space may also produce gaseous or particulate contaminants’as
well as undesirable thermal conditions.
The methods of ventilating discussed in this chapter can all be
classified broadly as dilution methods. This principle of ventilation
simply involves removing an amount of heated, or otherwise contaminated, air and substituting an equal amount of relatively uncontaminated, or “fresh,” air.
Ventilation is a part of air conditioning, and the principles given
here apply to systems that can be described by either name. Similarly,
the term industrial ventilation is often used broadly to cover both
dilution and local-exhaust systems. Refer to subsequent chapters for
further data on air conditioning,
for information
on local exhaust,
and for details on blast cooling of equipment and products.
Design Principles
The
human
body
has a fortunate
tolerance
to limited
amounts
of contaminants, no matter how toxic. Because of this tolerance, a
wide range of contaminating substances can be controlled economically by applying the principle of dilution. The cost of equipment is
roughly proportional to the volume rate of air flow required for ventilation. Also, whenever winter outdoor air is used, tempering provisions must be made to prevent drafts, freeze-up of equipment, etc, For
these reasons, the designer should evaluate auxiliary methods, which
may range from purifying recirculated air to medically screening out
more susceptible persons. Whenever dilution ventilation is used, one
must recognize variations among individuals. The air-conditioning
engineer strives to satisfy the largest possible percentage of occupants;
the industrial hygienist attempts to prevent ill effects in any worker.
Nevertheless, in the first case, some occupants may complain of being
too hot or too cold, no matter how well designed the air-conditioning
system. Similarly, in the second case, it is likely that a small percent-
20-2
FAN ENGINEERING
— BUFFALO FORGE COMPANY
age of workers will not be able to tolerate even small concentrations
of contaminants that are unnoticed by the vast majority.
The principle of dilution is easy to comprehend in the case of a
single gaseous or particulate contaminant. If the tolerance limit is one
part in one hundred, then one hundred parts of fresh air must be
supplied for each part of the contaminant released into the space.
For instance, if a contaminant were generated at the rate CGR of 100
units per minute, and if the limit of human tolerance, or maximum
allowable concentration, MAC, were 2 units per 1000 ft’, then the re-
quired ventilation rate QO would be 100/2, or 50 times 1000, or 50 000
cfm. A formula expressing the dilution principle can be given as:
O= CGR
MAC"
(20.1)
The various quantities must be in consistent units. When two or more
contaminants are released simultaneously, the one with the greatest
ventilation requirement should be used as the basis of design.
Heat, odors, and bacteria, as well as industrial contaminants, can
be controlled by dilution ventilation. Sometimes, other air-conditioning or industrial-ventilation procedures may be more appropriate, as
discussed below.
Heat Control
The sources of heat in a space, besides whatever heat is intentionally supplied, are the occupants themselves and any mechanical,
chemical, or other processes that may be carried on there. The metabolic process yields an amount of heat dependent on the size and
body structure of the individual, his physical activity, age, sex, health,
nutrition, and climate. Table 20.1 lists total, sensible, and latent heat
dissipation rates for various activities. Additional energy may be expended as useful work. Thermal efficiency for humans ranges from
20 to 30%. The total energy liberated as heat from any mechanical or
chemical process can be derived from a knowledge of fuel consumption, efficiencies, etc. And heat gains or losses from external sources,
by whatever means, should also be reckoned.
The physiological response of the human body to thermal stimuli
affects both the subjective feeling of comfort and the health and wellbeing of the individual. Although the human body can adapt to a
diverse range of environmental conditions, as well as physical activities, for both comfort and health, the temperature of the deep-body
tissues must be maintained at relatively constant values. The processes by which heat is dissipated from the body include evaporation,
convection, and radiation. Evaporation can involve insensible perspiration or perceptible sweating. Convection and radiation regulation
are accomplished by variations in skin temperature resulting from
CHAPTER 20 — VENTILATION
Table 20.1
20-3
Heat Dissipation Rates
in Btu/hr
ap
padi
Metabolic
Rate
Basa linger ay celibate
Ns eee ee
291
Sealed atest,
seminar. ace
ae
384
Reading aloud (seated) .............
420
Standingrarrestamn mane
Nae teee eeor
43]
Hand sewing (seated) ..............
44]
Knitting 23 stitches per minute........
462
Dressing and undressing ............
468
allo Gaaecacase steccentric
ree
482
SUNG ING cerns ener eset everett uepe crate se
486
Office work (moderately active) .......
490
Lightiwork:(Standing) 1.4.20.) «2.2110 0
549
Typewriting rapidly ................
558
lroningiwith: 5-|bi iON) cy. «).1e<
pee soc 26
570
Dishwashing — plates, bowls, cups .....
600
Standing at counter (moderately active)
600
Bookgbindingepancuncicssstersseenat
etter:
626
Shoe makingiegesset cess: cect neecctees ers
661
Sweeping bare floor, 38 strokes/min. ...
672
Pool playing eactse
oe steele
680
Walking 2 mph., light dancing ........
761
Light metal working (at bench) ........
862
Painting of furniture (at bench)........
876
GarenteriiGnemccea wacoeee tec c.
954
HestaliranuSenving) eacvecr merce occ
1000
BU ING UWEIGNitrsregon cen masyaicge axe ee revers oe
1041
Walking: im phieee cue cutttesee
fsy cues
1050
Walking 4 mph., active dancing, skating
1390
Walking downstairs ..............-1444
SLONCLMASONING escresewsrvek sopra cksraus
1490
BOW!
iiiGivers curator
vectosnloxsrevsrsyeows
1500
SHAME MENS coc oaecoeoneoo
1800
SUMMING PEAR eset uae Rtas atoratetane
1986
RENDINGLO Sim PN wepetetenetod-cseen decelerate
2268
Walking: Sim phitesapaessrseeciersicr-te
1) telate
2330
Walking very fast (5.3 mph.) .........
2580
Walkinglupistalrsie atartetartetels
cerscskerst ts
4365
Maximum exertion (different people