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~
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FLO
OF FLUIDS
~
THROUGH
~
~
VALVES, FITTINGS, AND PIPE
~
~
By the Engineering Division
~
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Copyright, 1969-Crane Co;
.~"
All rights reserved: This publication is fully protected
~
by copyright and nothing that appears in it may be reprinted, either wholly or in part. without special permission .
;::::)
.
~:::::)
.=:,)
:::::)
:::::::)
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CRANE CO.
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Direct inquiries to
4100 S. Kechi. Aven'ue
Chicago, Illinois 60632
Executive Office
300 Park Avenue
New York, N.Y. 10022
::::::l
~
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Technical Paper No. 410
Price $2.50
PR1~TED
(rw~lfth
IN U. S. A.
Print.ing-1972)
~""
TablE~ of Contents
CHAPTER 2 •_ .....- -_ _.
- - - - - CHAPTER
Theory of Flow in Pipe
page
flow of fluid:$
Through Valves and Fittings
Introduction ............... _.. _................................. _.... _....... _.. 1-1
Physical Properties of Fluids_....... _..._... __ .... __ ..... _. __ .....
Viscosity .. '" ...... _.............................. _. __ .. _._ ... _.. _..........
VV' eigh t density ....................................._........ _.........
Specific volume .................. _.....................................
Sped fic gra \' ity ......................... _.............__ ...............
1-3
1-3
Nature of Flow in PipeLaminar and TurbulenL ................. _.... _.... _... ___ ._ ..... _.. _.
IIIean velocity of flow ..................... _.. _......... _...........
Reynolds number ............. _.......... _........ ___ ....._........ _...
Hydraulic radius ................................ _.....................
1-4
1-4
1-4
1-4
1-2
1-2
1-3
General Energy EquationBernoulli's Theorem ......................................... _._ ........ 1-5
Measurement of Pressure.......... _................................... 1-5
Darcy's FormulaGeneral Equation for Flow of Fluids..................... _.. 1-6
Friction factor _............... _......................................... 1-6
Effect of age and use on pipe friction .................. 1-7
Principles of Co:npressible Flow in Pipe.._...............
Complete isothermal equation .. _.............................
Simplifiedcornpressible flowgas pipe line formula .. _._ ..................... _....._.........
Other commonly used formulas for
compressib:.e flow in long pipe lines ........ _.......
Comparison of formulas for
compressible flow in pipe lines ............ _... _._ .......
Limiting flow of gases and vapors ....... _................
Introduction ...........__ .............................. _........................
Types of Valves and Fittings
Used in Pipe Systems ........._..._.........__...................._...... 2-2
Pressure Drop Chargeable
to Val ves and Fittings........... _...................................'" 2-2
Crane Flow Tests ............................ _.................. _........ ; 2-3
Relationship of Pressure Drop
to Velocity of Flow.. _.... _............. _............................_... 2-7
Resistance Coefficient K, EquivalentLength
LID, and Flow.Coefficient Cv ••••••-••••••••••••••••••••••••••••••• 2-8
Relationship of Equivalent Length LID
and Resistance Coefficient K to the
.
Inside Diameter of Connecting Pipe ............. _............ Z-lC
Valves with Gradually Increased Ports ....._..:........ _.. 2.:..iD
Effect of End Connections ......._.... _..................... _... _... 2-1C
Laminar Flow Conditions.. __........_.... _... _........._............ 2'-11
1-7
1-8
Basis for Design of Charts for Determining
Equivalent Length, Resistance CoeffiCient,
and Flow Coefficient_............................ _.. _........_............ 2_11
1-8
Resistance of Bends ............ _... _..... _............................,., 2-12
1-8
1-8
1-9
Steam-General Discussion ._.......................... _...... _.... 1-10
Other Resistances to Flow...._..............~ ......:_................ 2-13
Flow Through Nozzles and Orifices_...........____.......... 2..lJ
Liquids, gases, and vapors ........................... _......... _Z-1:l
Maximum flow of compressible:,
fluids in a nozzle......................... _..... _... _.............. 22..15
Flow through short tubes .............._............_._ ......... 2-15
Discharge of Fluids Through
Valves, Fittings, and Pipe
Liquid flow ..._....._.......... _........... _._._ ....._.... _... _... _...... 2-15'
Compressible' flow ._ ................_............. __...... _~ ........ _. 2~15
- - - - - - CHAPTER 3
Formulas cmd Nomographs for Flow
Through Valves, Fittings, and Pipe
1 - - - - - - - CHAPTER 4
Examples of Flow Problems
page
Introduction ........... _............ _.............._................. _....... _ 3-1
Summary of Formulas.. _...................... _............ 3-2 to 3-5
Formulas and Nomographs
for Liquid Flow
V e10ci ty ...................................................... _......... _.....3-6
Reynolds number; friction factor for
clean steel and wrought iron pipe.................... 3-8
Pressure drop for turbulent flow ..... _.: .................... 3-10
Pressure drop for laminar flow .......... _................... 3-12
Flow through nozzles and orifices................ _....... 3-14
;f"~".
10
. -"
'-~""-:l
I
.
Formulas and Nomographs
for Compressible Flow
Velocity ............................................. _.......................
Reynolds number; friction factor for
clean steel and wrought iron pipe ....................
Pressure drop .......................................................... _.
Simplified flow f.ormula ............................................
Flow through nozzles and orifices ........................
I9';ge
Introduction ._ .................................._........... _.................. _ 4'-1
Reynolds Number. and' Friction Factor for
Pipe Other than Steel or Wrought Iron .................... 4-1
Determination of Valve Resistance in L, .
LID, K, and Flow Coefficient C•........ _....................... 4-:2
Check Valves-Determination of'Size...................... 4--3
Laminar Flow in' Valves, Fittings, and Pipe, ......... _.. 4-4
Pressure Drop and Velocity
in Piping Systems .............. __......................................... ~
Pipe Line Flow Problems ..... _...................................... 4-10
3-16
3-18
3-20
3-22
3-24
Discharge of Fluids from Piping Systems................ 4-:1'2
Flow Through Orifice MeterL .. _............................... 4-15
Application of Hydraulic'Radius
to Flow Problems .......................................................... 4-:11
Determination of Boiler ~.apacity ..... - ... -... -............··· 4-:18
APPENDIX A ------------~-----------
APPENDIX B
Engineering Data
Physical Properties of Fluids
and Flow Characteri'stics of
Valves, Fitfings, and Pipe
page
E-I
Introduction
page
Introduction ............................................... ~.................. A-I
Physical Properties of Fluids
Viscosity of steam
.................................. A-2
Viscosity of \vater ................................................ A-3
Viscosity of liquid petroleum products .............. A-3
Viscosity of various liquids ............................... A-4
Viscosity of gases and hydrocarbon vapors ...... A-5
Viscosity of refrigerant vapors .......................... A-5
Physical properties of water.. .................................. A-6
Specific gravity-temperature
relationship for petroleum oils ....................... A-7
Weight density and specific
gravity of various liquids ................................. A-7
Physical properties of gases ................................... A-8
Volumetric composition and
specific gravity of gaseous fuels ........................ A-8
Steam-values of k .................................................. A-9
Weight density and specific
volume of gases and vapors ............................... A-lO
Equivalent Volume and 'Weight
Flow Rates of Compressible Fluids.......................... B.,..2
Equivalents of Viscosity
Absolute ............................................................ ;....... B-3
Kinematic ................................................;................ B-3
Kinematic and Saybolt UniversaL ......... :............ B-4
Kinematic and' Saybolt FuroL. ............................. B'-4
Kinematic, Saybolt Universal,
.
Saybolt Furol, and Absolute ............................ B-5
Saybolt Universal Viscosity CharL ......................... B-6
!
Equivalents of Degrees API,
Degrees Baume, Specific Gravity,
Weight Density, and Pounds per Gallon ................ B-1
,I
Steam Data
Boiler capacity .....................................................:... B-8
Horsepower of an engine.......................................... B-8
Ranges in steam consumption
by prime movers ................................................. B-8
Properties; saturated steam, saturated water _________ A-12
Properties; superheated steam ............................... A-16
Properties; superheated steam, compre,osed water ..... A-19
Vlow Characteristics of
)zzles and Orifices
Flow coefficient C for nozzles .................................
Flow coefficient C for
square edged orifices ........................................
Net expansion factor Y
for compressible flow ........................................
Critical pressure ratio, rc
for compressible flow ........................................
A-20'
A-20
A-21
A-21
Flow Characteristics
of Pipe, Valves, and Fittings
Net expansion factor Y for compressible
flow through pipe to a larger flow area ........ A-22
Relative roughness of pipe materials and
friction factor for complete turbulence ............A-23
Friction factors for
any type of commercial pipe ............................ A-24
Friction factors for clean
commercial steel and wrought iron pipe ........ A-25
Resistance in pipe due to
sudden enlargements and contractions............ A-26
Resistance in pipe
due to pipe entrance and exit.. ........................ A-26
Resistance of 90 degree bends .............................. A-27
Resistance of miter bends ....................:................. A-27
Types of valves (sectional ilJustrations) ............ A-28
Schedule (thickness) of steel pipe used
in obtaining resistance of valves and
tittings of various pressure classes ................ A-30
Representative equivalent length ( LID) in
pipe diameters of valves and tittings .............. A-30
Equivalent lengths L and LID
and resistance coefficient K .............................. A-31
Equivalents of resistance coefficient K
and flow coefficient C,...................................... A-32
Power Required for Pumping..................................... B-9
Equivalents (General)
Measure ...........................................................:...........
vVeight ...............................................................:.......
Velocity ......................................................................
Density ........................................................................
B-J 0
B::..! ()
B-IO
B-IO
Physical constants ................................................... 13-10
Temperature ............................................................... B-IO
Pretixes ........................................................................ B-IO
Liquid measures and weigh t3................................... B-11
Pressure and head ....................................................... B-II
Four-Place Logarithms to Base 10............................ B-12
Flow Through Schedule 40 Steel Pipe
Water .......................................................................... B-14
Air ................................................................................. B-15
Commercial Wrought Steel Pipe. Data
Schedules 10 to 160 ................................................. B-16
Standard, extra strong,
and double extra strong...................................... B-18
Stainless Steel Pipe Data
Schedules 55, lOS, 40S, and 80S ............................ B-19
APPENDIX C
page
Bibliography
C-l
Nomenclature ........................................... 5ee next page
1
I
1
\
Nomendature---------·--~---Unless otherwise stated, all symbols used
in this book are defined os follows:
A
a
B
C
Cd
Cv
cross sectional area of pipe or orifice, in
square feet
cross sectional area of pipe or orifice, in
square inches
rate of flow in barrels (42 gallons) per hour
flow coefficient for orifices and nozzles
= discharge coefficient corrected for velocity of approach = Cd / " I-(do/d.)'
discharge coefficient for orifices and nozzles
flow coefficient for valves: expresses flow
rate in gallons per minute of 60 F water
with 1.0 psi pressure drop across valve
=
D
d
,t
!,,
,
t
e
/
g
H
h
f
f
r
h,
hL
h",
K
k
Lm
M
MR
n
P
P'
length of pipe, in feet
equ;\'a:ent length of a resistance to flow,
in pipe diameters
length of pipe, in miles
molecular weight
univer~al gas constant = 1;44
exponent in equation for polytropic change
.(p' \! ~ = constant)
pressure. in pounds per square inch gauge
pressure, pounds per square inch absolute
(see page 1-5 for diagram showing relationship betu:een gauge and absolute pressure)
p'
Q
q
q'
q'.
q' •
q ..
,
q ..
individual gas constant
I
s
s.
T
Q v pi (6q!:::.P)
internal diameter of pipe, in feet
internal diameter of pipe, in inches
base of natural logarithm = 2.718
frictio:::! factor in formula hL =/Lv'/D2g
acceleration of gravity = 32.2 feet per
second per second
total head, in feet of fluid
static pressure head existing at a point, in
feet of fluid
total heat of steam, in Btu per pound
loss of static pressure head due to fluid
flow, in feet of fluid
static pressure head, in inches of water
resista:.'lce coefficient or velocity head loss
in the formula, hL = KV'/2g'
ratio of specific heat at constant pressure
to specific heat at constant volume =
cJ)/c~
L
L/D
R
pressure, in pounds per square foot absolute
rate of flow. in gallons per minute
rate of flow, in cubic feet per second at
flowing conditions
rate of flow. in cubic feet per second at
standard conditions (14.7 psia and 60F)
rate of flow. in millions of standard cubic
feet per day, MMsefd
rate of flow. in cubic feet per hour at standard conditions ('4.7 psia and oaF), scfh
rate of flo\\', in cubic feet per minute at
flowing conditions
rate of flow, in cubic feet per minute at
std. conditions (14.7 pSia and 6oF), sefm
v
Va
v
v,
Wi
W
Wa
x
Y
Z
AfR.'1
544/M
Reynolds number
hydraulic radius, in feet
critical pressure ra[;o for compressible flo'.'
specific gravity of liquids relative to wate:both at standard temperature (60 F)
specific gravity of a gas relative to air =
the ratio of the molecular weight of ct."
gas to that of air
absolute temperature. in degrees Rankine
(460 + t)
temperature, in degrees Fahrenheit
specific volume of fluid, in cubic feet pc:-.
pound
mean velocity of flow, in feet per minute
volume. in cubic feet
mean velocity of flow, in feet per second
sonic (or critical) velOCity of flow of a gas.
in feet per second
rate of flow, in pounds per hour
rate of !low, in pounds per second
weight, in pounds
percent quality of steam = 100 minus pe,
cent of moisture
net expansion factor for compressible flow
through orifices, nozzles, or pipe
potential head or elevation above reference
level, in feet
Subscripts
indicates orifice or nozzle conditions unless
otherwise specified
(I)
indicates inlet or upstream conditions
unless otherwise specified
(2) . indicates outlet or downstream conditions
unless otherwise specified
(100) . refers to 100 feet of pipe
(0)
Greek LeHers
L.lta
f:"
differential between two points
Epsilon
•
absol ute roughness or effective height ot
pipe wall irregularities, in feet
Rho
P
p'
weight density of fluid, pounds per cubic ft.
density of fluid, grams per cubic centimeter
Mu
,
J1. ,
v
,
v
absolute (dynamic) viscosity, in centipoise
absolute viscosity in pound mass per foot
second or pou~dal seconds per sq foot
absolute viscosity. in slugs per foot sec~mc:
or pound force seconds per square 100!
kinematic viscosity, in centistokes
kinematic visc9sity, square feet per secon<.i
1 .1
Thec,ry of Flow
~
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lin Pipe
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CHAPTER 1
.~
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The most commonly employed method of transporting fluid from one point to another is to force the
fluid to flow through a piping system. Pipe of circular section is most frequently used because that
shape offers not only greater structural strength, but
also greater cross sectional area per unit of wall surface than any other shape. Unless otherwise stated,
the word "pipe" in this book will always refer to a
closed conduit of circular section and constant
internal diameter.
Only a few special problems in fluid mechanics ....
laminar flow in pipe, for example .... can be entirely
solved by rational mathematical means; all other
problems require methods of solution which rest, at
least in part, on experimentally determined coefficients. },,1any empirical formulas have been proposed
for the problem of flow in pipe, but these are often
extremely limited and can be applied only when the
conditions of the problem closely approach the
conditions of the experiments from which the formulas were derived.
.=:3
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Because of the great variety of fluids being handled
in modern industrial processes, a single equation
which can be used for the flow of any fluid in pipe
offers obvious advantages. Such an equation is the
Darcy* formula. The Darcy formula can be derived
'rationally by means of dimensional analysis; howevrer, one variable in the formula . . . . the friction
factor .... must be determined experimentally. This
foimula has a wide application in the field of fluid
mechanics and is used extensively throughout this
paper.
·Thc Darcy formula is also known as the \Veisbach formula or the DarcyWcisbach formula; also, as the Fanning formula, sometimes modified
so thal~ the friction factor is one-fourth the Darcy friction factor.
1-2
CHAPTER 1 - THEORY OF flOW IN PIPE
CRANE
Physical Properties of Fluids
The solution of any flow problem requires a knowl- second and is equivalent to 100 centistokes.
edge of the physical properties of the fluid being
•
•
_ J.<
(centipoise)
handled. Accurate values for the properties affecting
v (centlstokes) - '(
')
p
grams
per cu b
IC cm
the flow of fluids ... namely, viscosity and weight
density ... have been established by many authori- By definition, the specific gravity, S, in the foreties for all commonly used fluids and many of these going formula is based upon water at a temperature
data are presented in the various tables and charts .of 4 C (39.2. F), whereas specific gravity used
in Appendix A.
throughout this paper is based upon water at 60 F.
In the English system, kinematic viscosity has
Viscosity: Viscosity expresses the readiness with dimensions of square feet per second.
which a fluid flows when it is acted upon by an external force. The coefficient of absolute viscosity Factors for conversion between metric and English
or, simply, the absolute viscosity of a fluid, is a system units of absolute and kinematic viscosity are
measure of its resistance to internal deformation or given on page B-3 of Appendix B.
shear. Molasses is a highly viscous fluid; water is
comparatively much less viscous; and the viscosity The measurement of the absolute viscosity of fluids
of gases is quite slY.all compared to that of water. (especially gases and vapors) requires elaborate
equipment and considerable experimental skill. On
Although most fluids are predictable in their vis- the other hand, a rather simple instrument can be
cosity, in some, the viscosity depends upon the used for measuring the kinematic viscosity of oils
previous working of the fluid. Printer's ink, wood and other viscous liquids. The instrument adopted
pulp slurries, and catsup are examples of fluids as a standard in this country is the Saybolt Universal
possessing such thixotropic properties of viscosity.
Viscosimeter. In measuring kinematic viscosity
with this instrument, the time required for a small
Considerable confusion exists concerning the units volume of liquid to flow through an orifice is deterused to express viscosity; therefore, proper units mined; consequently, the "Saybolt viscosity" of the
must be employed whenever substituting values of liquid is given in seconds. For very viscous liqUids,
viscosity into formulas. In the e.G.S. (centimeter, the Saybolt Furol instrument is used.
gram, second) or metric system, the unit of absolute
viscosity is the poise which is equal to 100 centi- Other viscosimeters, somewhat similar to the Saybolt
poise. The poise has the dimensions of dyne seconds but not used to any extent in this country, are the
per square centimeter or of grams per centimeter Engler, the Redwood Admiralty, and the Redwood.
second. I t is believed that less confusion concerning The relationship between Saybolt viscosity and
units will prevail if the centipoise is used exclUSively kinematic viscosity is shown on page B-4; equivaas the unit of viscosity. For this reason, and since lents of kinematic, Saybolt Universal, Saybolt Furol,
most handbooks and tables follow the same pro- and absolute viscosity can be obtained from the
cedure, all viscosity data in this paper are expressed chart on page B-5.
in centipoise.
The ASTM standard viscosity temperature chart for
The English units commonly employed are "slugs per liquid petroleum products, reproduced on page B-6,
foot second" or "pound force seconds per square is used to determine the Saybolt Universal viscosity
foot"; however, "pound mass per foot second" or of a petroleum product at any temperature when the
"poundal seconds per square foot" may also be en- viscosities at two different temperatures are kno\\TI.
countered. The viscosity of water at a temperature The viscosities of some of the most common fluids are
given on pages A-2 to A-5. It will be noted that.
of 68 F is:
with a rise in temperature, the viscosity of liquids
o.ol poise'
decreases, whereas the viscosity of gases increases.
I centipoise* =
0.01 gram per cm second
lo.ol dyne second per sq cm
The effect of pressure on the viscosity of liquids and
perfect gases is so small that it is of no practical
(0.000 672 pound mass per foot second
interest in most flow problems. Conversely, the
lO.OOO 6j2 poundal second per square foot
viscosity of saturated, or only slightly superheated.
I
_
{o.ooo 0209 slug per foot second
vapors is appreciably altered by pressure changes, as
p., 0.000 0209 pound force second per square ft
indicated on page A-2 showing the viscosity of steam.
Unfortunately, the data on vapors are incomplete
Kinematic viscosity is the ratio of the absolute vis- and, in some cases, contradictory. Therefore, it is
cosity to the mass density. In the metric system, expedient when dealing with vapors other than
the unit of kinematic viscosity is the stoke. The steam to neglect the effect of pressure because of [he
stoke has dimensions of square centimeters per lack of adequate data.
f
,
1
1
.~
\
• Actually the viscosity of water at 68 F is 1.005 centipoise.
..:;;='3
"'J~
CRANE
CHAPTER I - THEORY Of flOW IN PIPE
,;;:::3
Physical Properties of Fluids -
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Weight density,
specific volume, and specific gravity: The weight
density or specific weight of a substance is its weight
per unit volume. In the English system of units,
this is expressed in pounds per cubic foot and the
symbol designation used in this paper is p (Rho).
In the metric system, the unit is grams per cubic
centimeter and the symbol designation used is p'
(Rho prime).
The specific volume V, being the reciprocal of the
weight density, is expressed in the English system
as the number of cubic feet of space occupied by one
pound of the substance, thus;
V
=
::::;)
:::::»
~::::)
":::::.')
I
p'
::.:::::)
.::::)
.::::)
:.::::»
,~
"~
The variations in weight density as well as other
properties of water with changes in temperature are
shown on page A-6. The weight densities of other
common liquids are shown on page A-i. Unless
very high pressures are being considered, the effect of
pressure on the weight of liquids is of no practical
importance in flow problems.
The weight densities of gases and vapors, however,
are greatly altered by pressure changes. For the socalled "perfect" gases, the weight density can be
computed from the formula;
p
=
144
P'
f[T'
The individual gas constant R is equal to the universal gas constant, AiR = 1544, divided by the molecular weight of the gas,
R
=
In steam flow computations. the reciprocal of the
weight density, which is the speCific volume, is commonly used; these values are listed in the steam
tables shown on pages A-12 to A-19. A chart for de~
termining the weight density and specific volume of
gases is given on page A-II.
Specific gravity is a relative measure of weight density. Since pressure has an insignificant effect upon
the weight density of liquids, temperature is the
only condition that must be considered in designating the basis for specific gravity. The specific gravity of a liquid is its weight density at 60 F (unless
otherwise specified) to that of water at standard
temperature, 60 F.
p
Computations in the metric system are not commonly referred to in terms of specific volume; however, the number of cubic centimeters per gram of a
substance can readily be expressed as the reciprocal
of the weight density, that is;
=:)
~
.~
1544
M
Values of R, as well as other useful gas constants,
are given on page A-8. The weight density of air
for various conditions of temperature and pressure
can be found on page A-ID.
continued
S =
p
p
any liquid at 60 F,
l
{unless otherwise specified!
(water at 60 F)
,
!
I"!
A hydrometer can be used to measure the specific
gravity of liquids directly. Three hydrometer
scales are common in this country .... the API scale
which is used for oils .... and the two Baume scales,
one for liquids heavier than water and one for liquids
lighter than water. The relationship between the
hydrometer scales and specific gravity are:
For oils.
S(60F/60F)
I)!.;
+deg.API
For liquids lighter
than water,
S (60 F/60 F)
140
1)0 + deg. Baume
For liquids heavier
than water.
S (60 F/60 F)
145
145 - deg. Baume
For convenience in converting hydrometer readings
to more useful units, refer to the table shown on
page B-7 .
The specific gravity of gases is defined as the ratio
of the molecular weight of the gas to that of air, and
as the ratio of the individual gas constant of air to
that of the gas.
S = R (air) _ M (gas)
• R (gas) - M (air)
:=}
i
j
1·4
CHAPTER 1 - THEORY Of flOW IN PIPE
Nature of Flow in Pipe -
CRANE
Laminar and Turbulent.
-.--"'-'-.-~---~------
'... Flgu ....
1~11
Figure 1 ~2
Laminor Flclw
Actual photograph of colored Alamenfs being
carried along undisturbed by a !.treom of
water.
Flow in Critical Zone, 8otw •• n
Laminar and Transition Zones.
At the critical velocity, the filaments begin to
break up, indicating flow is becoming
turbulent.
A simple experiment (illustrated above) will readily
show there are two entirely different types of flow
in pipe. The experiment consists of injecting small
streams of a colored fluid into a liquid flowing in
a glass pipe and obsel-ving the behavior of these
colored streams at different sections downstream
from their points of injection.
If the discharge or average velocity is small, the
streaks of colored fluid flow in straight lines, as
shown in Figure 1··1. As the flow rate is gradually
increased, these streaks will continue to flow in
straight lines until a velocity is reached when the
streaks will waver and suddenly break into diffused
patterns, as shown in Figure 1-2. The velocity at
which this occurs is called the "critical velocity".
At velocities higher than "critical"' , the filaments
are dispersed at random throughout the main body of
the fluid, as shown in Figure 1-3.
i
I
,
i
,1
1
I
"
The type of flow which exists at velocities lower
than "critical"' is known as laminar flow and, sometimes, as viscous or streamline flow. Flow of this
nature is characterized by the gliding of concentric
cylindrical layers past one another in orderly fashion. Velocity of the fluid is at its maximum at the
pipe axis and decreases sharply to zero at the walL
At velocities greater than "critical", the flow is turbulent. In turbulent flow, there is an .irregular
random motion of fluid particies in directions transverse to the direction of the main flow. The \'elocity
distribution in turbulent flow is more uniform
across the pipe diameter than in laminar flow. Even
though a turbulent motion exists throughout the
greater portion of the pipe diameter, there is always
a thin layer of fluid at the pipe wall .... known as
the "boundary layer" or "laminar sub-layer"
which is moving in laminar flow.
Mean velocity of flow: The term "velocity", unless
otherwise stated, refers to the mean, or average,
velocity at a given cross section, as determined by
the continuity eq~;ation for steady state Row:
v =3..
A
=~
Ap
,=
wV
A
Eq Clation J.. '
(For nomenclature, sec page preceding Chapter i)
"Reasonable" veiocities for use in design work are
given on pages 3-6 and 3-16.
.....,
..... ,--"
.~./
-~ '\~-
.
,--..;
;-'< -:. ....:... . -
Figur. 1.3
Turbulent Flow
This illustrotion shows the turbulence in th"
stream completely dispersing the, colored
filaments
0
short distance downstream fro",
the point of injection.
Reynolds number: The work of Osborne Reynolds
has shown that the nature of Row in pipe .... that
is, whether it is laminar or turbulent .... depends
on the pipe diameter. the density and viscosity of
the flowing fluid, and the velocity of flow. The
numerical value of a dimensionless combination of
these four variables, known as the Reynolds number, may be considered to be the ratio of the dynamic
forces of mass flow to the shear stress due to Viscosity. Reynolds number is:
Re
=
Dvp
Equation 1.. 2
(other forms of this equation; page 3-2.)
For engineering purposes, flow in pipes is usually
considered to be laminar if the Reynolds number is
less than 2000, and turbulent if the Reynolds number
is greater than 4000. Between these two values lies
the "critical zone" where the flow .... being laminar,
turbulent, or in the process of change, depending
upon many possible varying conditions . . . . is
unpredictable. Careful experimentation has shown
that the lammar zone may be made to terminate at
a Reynolds number as low as 1200 or extended as
high ~s 40.000, but these conditions are not expected
to be realized in ordinary practice.
Hydraulic radius: Occasionally a conduit of non·
circular cross section is encountered. In calculating
the Reynolds number for this condition, the equivalent diameter (four times the hydraulic radius) is sub·
stituted for the circular diameter. Use friction
factors given on pages A-24 and A-25.
RH = cross sectional flow area
wctted perimeter
This applies to any ordinary conduit (circular conduit not flowing full, oval, square or rectangular)
but not to extremely narrow shapes such as annular
or elongated openings, where width is small relatlvc
to length. In such cases, the hydraulic radius IS
approximately equal to one-half the width of the
passage.
To determine quantity of flow in following forll1ui,L
q
/hLD
= o.o.n 8d'\j-jL
the value of d' is based upon an equivalent ,li.Hl1<·:"
of actual flow area and 4RI/ is substitute,! lor I)
-:t:I
CRANE
:::a
General Energy Equation
Bernoulli's Theorem
:::3
.:=:1
.=-
The Bernoulli theorem is a means of expressing the
application of the law of conservation of energy to
the flow of fluids in a conduit. The total energy at
any particular point, above some arbitrary horizontal
:3
-:::8
- - - - l l -,-
Energy Gfade Line
hL
r~
:::J
-=3
2g
--11--1-
~
~
.:::1
:::::2'
•.:::3
datum plane, is equal to the sum of the elevation
head, the pressure head, and the velocity head,
as follows:
Z
+
144
P
P
+~
=H
2g
If friction losses are neglected and no energy is added
to, or taken from, a piping system (i.e., pumps or
turbines), the total head, H, in the above equation
will be a constant for any point in the fluid. However, in actual practice, losses or energy increases
or decreases are encountered and must be included
in the Bernoulli equation. Thus, an energy balance
may be written for two points in a fluid, as shown in
the example in Figure 1-4.
Note the pipe friction loss from point 1 to point 2
is hL foot pounds per pound of flowing fluid; this is
sometimes referred to as the head loss in feet of fluid.
The equation may be written as foHows:
z,
.::::1
:::I
'·5
CHAPTER 1 - THEORY OF FLOW IN PIPE
Arbitrary Horizontal Datum Place
Equation ' ..3
ZI
Figure 1 ~4
Energy Balance for
TWI)
Points
~n
.
a Fluid
+
144 P ,
PI
+ 2i
=
2 g
Zz
+ I 44P,
+ 2~g + hL
P,
All practical formulas for the flow of fluids are derived from Bernoulli's theorem, with modifications
to account for losses due to friction .
By permission. from Fll1id Mechanics'> by
R. A. Dodge and M.). Thompson. Copyright
1937; McGraw-Hili Book Company, Inc.
::::I
;:::]I
Measurement of Pressure
-=:I
Any Pressure Above Atmospheric
Figure 1-5 graphically illustrates the relationship
between gauge and absolute pressures. Perfect
vacuum cannot exist on the surface of the earth, but
it nevertheless makes a convenient datum for the
measurement of pressure.
-::;3
::::3
-:.::I
::::»
:E
v
E
At Atmospheric Pressure Level-Variable
~------~~--~~~~~~~~~~~~----"OJ
+
,.
~
::::::I
""II
e
tl
.::.:3
-~
~
E
aro
>
Any Pressure Below Atmospheric
~
ct
~
~
::::a
~
"'"
Absolute Zero of Pressure-Perfect Vacuum
figure 1 ~5
Relationship B,atween
Gauge and Absolul'e Pressures
I~
I
Barometric pressure is the level of the atmospheric
pressure above perfect vacuum.
"Standard" atmospheric pressure is 14.696 pounds
per square inch, or 760 millimeters of mercury.
Gauge pressure is measured above atmospheric pressure, while absolute pressure always refers to perfect
vacuum as a base.
Vacuum, usually expressed in inches of mercury, is
the depression of pressure below the atmospheric
level. Reference to vacuum conditions is often
made by expressing the absolute pressure in inches
of mercury; also millimeters of mercury and microns
of mercury.
*Ail sl/perlor ligures used as reference morle, reler to 'he Bibliography; see page C-f.
CRANE
1 ·5
CHAPTER I - THEORY OF FLOW IN PIPE
--
General Energy Equation
Bernoulli's Theorem
.~.
The Bernoulli theorem is a means of expressing the
application of the law of conservation of energy to
the flow of fluids in a conduit. The total energy at
any particular point, above some arbitrary horizontal
~
.---il-'"=~--
- - - - - ---11 -,-
EC~Line
HYdraulic Graoe L·
Ine
hL
----~~-+,
1."'2
2g
-_!f.--J-
>;~
..~
+
144
P
P
+~ =
;zg
H
If friction losses are neglected and no energy is added
to, or taken from, a piping system (Le., pumps or
turbines), the total head, H, in the above equation
will be a constant for any point in the fluid. However, in actual practice, losses or energy increases
or decreases are encountered and must be included
in the Bernoulli equation. Thus, an energy balance
may be written for two points in a fluid, as shown in
the example in Figure 1-4.
Arbitrary Horizontal Datum Plane
4
Equation 1-3
Z,
Figure 1 ..4
Energy Balance for Two Points in a Fluid
-
Z
Note the pipe friction loss from point to point 2
is hL foot pounds per pound of flowing fluid; this is
sometimes referred to as the head loss in feet of fluid.
The equation may be written as follows:
z,
By permission, from Fluid Nfecnanics 1* by
R. A. Dodge and M. J. Thompson. Copyright
1937; McGraw-Hili B:)()k Company, Inc .
.-
datum plane, is equal to the sum of the elevation
head, the pressure head, and the velocity head,
as follows:
+ 144P,
+ .EL
= z. + 144P. + vi + hL
P,
2 g
p.
2 g
All practical formulas for the flow of fluids are derived from Bernoulli's theorem, with modifications
to account for losses due to friction.
~easurement of Pressure
Any Pressure Above Atmospheric
~
.,.g
_______ §r-__~At~Aft~mo~s~Dh~e~ric~P~r~es~su~r~e~Le~ve~I-~va~r~iab~le~____~
~
co
+
~
~
~
~
'"II
E
B-
~
Any Pressure Below Atmospheric
Figure 1-5 graphically illustrates the relationship
between gauge and absolute pressures. Perfect
vacuum cannot exist on the surface of the earth, but
it nevertheless makes a convenient datum for the
measurement of pressure .
Barometric pressure is the level of the atmospheric
pressure above perfect vacuum.
"Standard'· atmospheric pressure is 14.696 pounds
per square inch, or 760 millimeters of mercury.
Gauge pressure is measured above atmospheric pressure, while absolute pressure always refers to perfect
vacuum as a base.
Absolute Zero of Pressure-Perfed Vacuum
Figure 11-5
Relationship Berween
Gauge and Absolute Pressures
Vacuum, usually expressed in inches of mercury, is
the depression of pressure below the atmospheric
level. Reference to vacuum conditions is often
made by expressing the absolute pressure in inches
of mercury; also millimeters of mercury and microns
of mercury.
,
I
- I
"'All supElrior figu,'es used as reference maries refer'o the Bibliography; see page C.J.
II
~~
C~H~A~PT~E~R~l T~H~E~O~RY~O~F~Fl~O~W~IN~P~IP~E
__________________________
___
________________________
~C~R~A~N~E
Darcy's Formula
General Equation for Flow of Fluids
Flow in pipe is always accompanied by friction of
fluid particles rubbing against one another, and consequently, by loss of energy available for work; in
other words, there must be a pressure drop in the
direction of flow. If ordinary Bourdon tube pressure
gauges were connected to a pipe containing a flowing
fluid, as shown in Figure 1-6, gauge PI
L
would indicate a
higher static pressure
Figure 1 .. 6
than gauge p •.
The general equlltion for pressure drop, known as
, Darcy's formula and expressed in feet of fluid, is
hL = fLv 2 /D 2g. This equation may be written to
express pressure drop in pounds per square inch, by
substitution of proper units, as follows:
pf L ;~.
l::.P = - - - 144 D 2g
Equation 1-4
has lower limits based on laminar Rowand upper
limits based on turbulent flow conditions.
.
At Reynolds numbers above approximately 4000,
flow conditions again become more stable and definite
friction factors can be established. This is imPortant because it enables the engineer to determine
the flow characteristics of any fluid Rowing in a
pipe, providing the viscosity and weight density at
flowing conditions are known. For this reason, Equation 1-4 is recommended in preference to some of
the commonly known empirical equations for the
flow of water, oil, and other liquids, as well as for
the flow of compl'essible fluids when restrictions
previously mentioned are observed.
If the flow is laminar (R, < 2000), the friction factor may be determined from the equation:
f =
(For other forms of this equation, see page 3-2.)
The Darcy equation is valid for laminar or turbulent
flow of any liquid in a pipe. However, when extreme
velocities occurring in a pipe cause the downstream
pressure to fall to the vapor pressure of the liquid,
cavitation occurs and calculated flow rates will be
inaccurate. With suitable restrictions, the Darcy
equation may be used when gases and vapors (compressible fluids) are being handled. These restrictions are defined on page 1-7.
Equation 1-4 gives the loss in pressure due to friction
and applies to pipe of constant diameter carrying
fluids of reasonably constant weight density in
straight pipe, whether horizontal, vertical, or sloping.
For inclined pipe, vertical pipe, or pipe of varying
diameter, the change in pressure due to changes in
elevation, velocity, and weight density of the fluid
must be made in accordance with Bernoulli's theorem
(page 1-5). For an example using this theorem, see
page 4-8.
,
'1
Friction factor: The Darcy formula can be ration'ally derived by dimensional analysis, with the exception of the friction factor, f, which must be determined experimentally. The friction factor for laminar flow conditions (R, < 2000) is a function of
Reynolds number only; whereas, for turbulent flow
CR, > 4000), it is also a function of the character of
the pipe wall.
64
R,
=
64 Il,
D vp
=
64 Il
d vp
124
If this quantity is substituted into Equation 1-4,
the pressure drop in pounds per square inch is:
.
IlLv
l::.P = 0.000668 ( j ' l
Equation 1-5
which is Poiseuille's law for laminar flow.
When the flow is turbulent (R, > 4000), the friction
factor depends not only upon the Reynolds number
but also upon the relative roughness, E/D .... the
roughness of the pipe walls (E), as compared to the
diameter of the pipe (D). For very smooth pipes
such as drawn brass tubing and glass, the friction
factor decreases more rapidly with increasing Reynolds number than for pipe with comparatively
rough walls.
Sinc€' the character of the internal surface of commercial pipe is practicai!y independent of the diameter, the roughness of the walls has a greater effect
on the friction factor in the small sizes. Consequently, pipe of smail diameter will approach the
very rough condition and, in general, will have
higher friction factors than large pipe of the same
material.
The most useful and widely accepted data of friction
factors for use with the Darcy formula have been presented by L. F. Moody" and are reproduced on pages
A-23 to A-25. Professor Moody improved upon the
well-established Pigott and Kemler", 26 friction factor
diagram, incorporating more recent investigations
and developments of many outstanding scientists.
A region known as the "critical zone" occurs between
Reynolds number of approximately 2000 and 4000.
In this region, the flow may be either laminar or turbulent depending upon several factors; these include
changes in section or direction of flow and obstruc-. The friction factor, j, is plotted on page A-24 on
tions, such as valves, in the upstream piping. The the basis of relative roughness obtained from the
friction factor in this region is indeterminate and chart on page A-23 and the Reynolds number. The
CRANE
~~
:::::;
::3
=:)
,:::,)
-;:)
~
.~
~
CHAPTER I - THEORY OF flOW IN PIPE
Darcy's Formula
General Equation for Flow of Fluids value of f is determined by horizonta I projection from
the intersection of the d D curve under consideration with the calculated Reynolds number to the left
hand vertical scale of the chart on page A-23. Since
most calculations involve commercial steel or
wrought iron pipe, the chart on page A-25 is furnished
for a more direct solution. I t should be kept in mind
that these figures apply to clean new pipe.
continued
causes a 10o/c increase in pressure drop; a 59c reduction of diameter increases pressure drop 23 S~. In
many services. the interior of pipe becomes encrusted
with scale. dirt, tubercules or other foreign matter;
thus, it is often prudent to make allowance for expected diameter changes.
Authorities' point out that roughness may be expected to increase with use (due to corrosion or
Effect of age and use on pipe friction: Friction incrustation) at a rate determined by the pipe
loss in pipe is sensitive to changes in diameter and material and nature of the fluid. Ippen'B, in discussroughness of pipe. For a given rate of flow and a ing the effect of aging, cites a 4-inch galvanized
fixed friction factor, the pressur.e drop per foot of. steel pipe which had its roughness doubled and its
pipe varies inversely with the fifth po\\-er of the friction factor increased 20'70 after three years of
diameter. Therefore, a 2% reduction of diameter moderate use.
Principles of
Compressible Flow in Pipe
.~
':)
-:)
-::)
,~:j
An accurate determination of the pressure drop of a
compressible fluid flowing through a pipe reqUires a
knowledge of the relationship between pressure and
specific volume; this is not easily determined in
each particular problem. The usual extremes considered are adiabatic flow (p'V:~ = constant) and isothermal flow (p'Va = constant). Adiabatic flow is
usually assumed in short, perfectly insulated pipe.
This would be consistent since no heat is transferred
to or from the pipe, except for the fact that the
minute amount of heat generated by friction is
.added to the flow.
Isothermal flow or flow at constant temperature is
often assumed, partly for convenience but more often
because it is closer to fact in piping practice. The
most outstanding case of isothermal flow occurs in
natural gas pipe lines. Dodge and Thompson! show
that gas flow in insulated pipe is closely approximated
by isothermal flow for reasonably high pressures.
Since the relationship bet\\'een pressure and volume
may follow some other relationship (p'V: = constant) called polytropic flow, specific information in
each individual case is almost a::1 impossibility.
The density of gases and vapors changes considerably
with changes in pressure; therefore, if the pressure
drop between PI and p, in Figure 1-6 is great, the
density and velocity will change appreciably.
When dealing with compressible fluids, such as air,
steam, etc., the following restrictions should be
observed in applying the Darcy formula:
1. If the calculated pressure drop (PI - P,) is less
than about 10% of the inlet pressure PI, reasonable accuracy will be obtained if the specific
volume used in the formula is based upon either
the upstream or downstream conditions, whichever are known.
2. If the calculated pressure drop (PI - P,) is
greater than about 10%, but less than about 40%
of inlet pressure PI, the Darcy equation may be
used with reasonable accuracy by using a specific
volume based upon the average of upstream and
dO\\'nstream conditions: otherwise, the method
given on page l-q may be used.
3. For greater pressure drops, such as are often
encountered in long pipe lines. the methods given
on the next two pages should be used. '
(cont;nued on the next page)
1-8
CRANE
CHAPTER I - THEORY OF flOW IN PIPE
Principles of Compressible Flow in Pipe
(continued)
Complete isothermal equation: The flow of gases
in long pipe lines closely approximates isothermal conditions. The pressure drop in such lines is often
large relative to the inlet pressure, and solution
of this problem falls outside the limitations of
the Darcy equation. An accurate determination of
the flow characteristics falling within this category
can be made by using the complete isothermal
equation:
Equation J·6
] [(P;)' ;;; (P~)']
The formula is developed on the basis of these
assumptions:
I. Isothermal flow.
2. No mechanical work is done on or by the system.
3. Steady flow or discharge unchanged with time.
4. Tne gas obeys the perfect gas laws.
5. The velocity may be represented by the average
velocity at a c.ross section.
6. l1t1e friction fa.ctor is constant along the pipe.
7. The pipe line is straight and horizontal between
end points.
Simplified Compressible Flow-Gas Pipe Line
Formula: In the practice of gas pipe line engineering, another assumption is added to the foregoing:
8.
w2 =
[
hfl.
Equation 1-1
Pi
This is equivalent to the complete isothermal equation if the pipe line is long and also for shorter lines
if the ratio of pressure drop to initial pressure is
small.
Since gas flow problems are usualiy expressed in
terms of cubic feet per hour at standard conditions,
it is convenient to rewrite Equation 1-7 as follows:
,
,
q' h =
1 14.2
~
i[(p't)' - (P")']
d.'
. f l.m T S,
Equafion J-7a
Other commonly used formulas for compressible flow in long pipe lines:
Weymouth formula":
I _
q• -
d,.m
8
2
.0
"
Equation
'[(PII)' - (PI,),] 520
S. l...
T
q'.
,'O,
The flow efficiency factor E is defined as an experience factor and is usually assumed to be 0.92 or
92% for average operating conditions. Suggested
values for E for other operating conditions are given
on page 3-3.
Comparison of formulas for compressible flow
in pipe lines: Equations 1-7, 1-8, and 1-9 are derived from the same basic formula, but differ in the
selection of data used for the determination of the
friction factors.
Friction factors in accordance with the t-..loodv" diagram are normally used with the Simplified Compressible Flow formula (Equation 1-7). However, if
the same friction factors employed in the IVeymouth
or Panhandle formulas are used in the Simplified
formula, identical answers will be obtained.
f =
Then, the formula for discharge in a horizontal pipe
may be written:
DN] [(P')'
- (P')']
1
2
Equation
(P\l' - (PI,),] 0.5394
= ,6.8 E ,p."" [
l.rn-
The Weymouth friction factor" is defined as:
Acceleration can be neglected because the pipe
line is long.
144 g
Panhandle formula' for natural gas pipe lines 6
to 2-!-inch diameter, Reynolds numbers 5 x 10' to
14 x 10', and S, = 0.6:
l-a
0.03 2
d1 /'
This is identical to the Moody friction factor in the
fully turbulent flow range for 20-inch 1.D. pipe only.
Weymouth friction factors are greater than Moody
factors for sizes less than 20-inch, and smaller for
sizes larger than 20-inch.
The Panhandle friction factor' is defined as:
f=
d
0.1225
----s
(q
h
)0.,451
9
In the flowTange to which the Panhandle formula is
limited, this results in friction factors that are lower
than those obtained from either the Moody data
or the Weymouth friction formula. As a result, flow
rates obtained bv solution of the Panhandle formula
are usuaily great~r than those obtained by employing
either the Simplified Compressible Flow formula with
Moody friction factors, or the Weymouth formula.
An example of the variation in flow rates which may
be obtained for a specific condition by employing
these formulas is given on page 4-11 ..
CRANE
1-9
CHAPTER 1 - THEORY OF flOW IN PIPE
Principles of Compressible Flow ill Pipe
(continued)
·.~
.•::;:::::J
~
.,:t
.=t
.=3
~
::=J
::J
.::::J
.:=J
=:.1
==»
.=.::t
.::::)
::::!)
:::::::::»
:::"J
~
.:=2
.-.
-,
Limiting flow of gases and vapors: The feature
not evident in the preceding formulas (Equations 1-4
and 1-6 to 1-9 inclusive) is that the weight rate of
flow (e.g., Ibs/sec) of a compressible fluid in a pipe,
with a given upstream pressure, will approach a certain maximum rate which it cannot exceed, no matter how much the dowmtream pressure is further
reduced.
The maximum velocity of a compressible fluid in pipe
is limited by the velocity of propagation of a pressure wave which travels at the speed of sound in
the fluid. Since pressure falls off and velocity increases as fluid proceeds downstream in pipe of uniform cross section, the mc:ximum velocity occurs in
the downstream end of the pipe. If the pressure drop
is sufficiently high, the exit velocity will reach
the velocity of sound. Further decrease in the outlet pressure will not be fdt upstream because the
pressure wave can only travel at sonic velocity, and
the "signal" will never translate upstream. The
"surplus" pressure drop obtained by lowering the
outlet pressure after the maximum discharge has
already been reached takes place beyond the end of
the pipe. This pressure is lost in shock waves and
turbulence of the jetting fluid.
The maximum possible velDcity in the pipe is sonic
velocity, which is expressed as:
Equation r-1 0
v, = .,JkgRT
=
.,Jkgl44P'V
The value of k, the ratio of specific heats at constant pressure to constant volume, is 1.4 for most
diatomic gases; see pages A-8 and A-9 for values of
k for gases and steam respectively. This velocity
will occur at the outlet end or in a constricted area,
when the pressure drop is sufficiently high. The
pressure, temperature, and ;;pecific volume are those
occurring at the point in question. When compressible fluids discharge from the end of a reasonably
short pipe of uniform cross section into an area of
larger cross section, the flow is usually considered to
be adiabatic. This assumption is supported by experimental data on pipe having lengths of 220 and
130 pipe diameters discharging air to atmosphere.
Investigation of the complete theoretical analysis of
adiabatic flow!' has led to a basis for establishing
correction factors, which may be applied to the
Darcy equiltion for this condition of flow. Since
these correction factors compensate for the changes
in fluid properties due to expansion of the fluid, they
are identified as Y net expansion factors; see page
A-22.
The Darcy formula, including the Y factor, is:
Equation l .. JJ
(Resistance coefficient K is defined on page 2·8)
It should be noted that the value of K in this equation is the total resistance coefficient of the pipe line,
including entrance and exit losses when they exist,
and losses due to valves and fittings.
The pressure drop, i'c,p. in the ratio i'c,P/P', which
is used for the determination of Y from the charts on
page A-22, is the measured difference between the
inlet pressure and the pressure in the area of larger
cross section. In a system discharging compressible
fluids to atmosphere, this i'c,P is equal to the inlet
gauge pressure, or the difference between absolute'
inlet pressure and atmospheric pressure. This value
of i'c,P is also used in Equation I -11, whenever the
Y factor falls within the limits defined by the resistance factor K curves in the charts on page A-n.
When the ratio of i'c,P/ P' 1, using i'c,P as defined
above, falls beyond the limits of the K curves in the
charts, sonic velocity occurs at the point of discharge
Of at some restriction within the pipe, and the limiting values for Y and i'c,P, as determined from the
tabulations to the right of the charts on page A-22,
must be used in Equation 1-1 I.
-1
Application of Equation 1-11 and the determination
of values for K, Y, and i'c,P in the formula is demonstrated in examples on pages 4-13 and 4-14.
The charts on page A-22 are based upon the general
gas laws for perfect gases and, at sonic velocity
conditions at the outlet end, will yield accurate
results for all gases which approximately follow
the perfect gas laws. Steam and vapors deviate from
the perfect gas laws, and application of the Y factor
obtained from the charts to these flows, will therefore yield flow rates slightly greater (up to about
5%) than those calculated on the basis of sonic
velocity at the outlet. However, greater accuracy
will be obtained if the charts are used to establish
the downstream pressure when sonic velocity occurs,
and the fluid properties at this pressure condition
are used in the sonic velocity and continuity equations (Equations 3 -8 and 3-2 respectively) to determine the flow rate. An example of this type of
{Jow problem is presented on page 4-13.
This condition of flow is comparable to the flow
through nozzles and venturi tubes, covered on page
2-15, and the solutions of such problems are similar.
.
,
1 • 10
CHAPTER 1 - THEORY OF FlOW IN PIPE
CRANE
Steam
General Discussion
Substances exist in anyone of three phases ....
solid, liquid, or gas. \Vhen outside conditions are
varied, they may change from one phase to another.
Water under normal atmospheric conditions exists
in the form of a liquid. When a body of water is
heated by means of some external medium, the temperature 'of the water rises and soon small bubbles,
which break and form continuously, are noted on the
surface. Th:s phenomenon is described as "boiling".
I,
!i
The amount of heat necessary to cause the temperature of the water to rise is expressed in British Thermal Units (Btu), where, I Btu is the quantity of heat
required to raise the temperature of one pound of
water from 60 to 61 F. The amount of heat necessary to raise the temperature of a pound of water
from 32 F (freezing point) to 212 F (boiling point)
is ISO.I Btu. When the pressure does not exceed 50
pounds per square inch absolute, it is usually permissible to assurr.e that each temperature increase
of 1 F represents a heat content increase of one Btu
per pound, regardless of the temperature of the
water.
II
I
~
~:
~
Assuming the generally accepted reference plane for
zero heat content at 32 F, one pound of water at
212 F contains ISO.17 Btu. This quantity of heat is
called heat of the liquid or sensible heat. In order to
~
!
~.
1
1
!
1 -
1
!
change the liquid into a \'apor at atmospheric pressure (14.7 psia), 970.3 Btu must be added to each
pound of \\'ater after the temperature of 212 F is
reached. During this transition period. the temperature remains constant. The added quantity of
heat is called the latent heat of erapuralioll. Consequently, the total heat of the \'apor, formed when
water boils at atmospheric pressure, is the sum of
the two quantities .... ISO. I Btu and 970.3 Btu, or,
1150.5 Btu per pound.
If water is heated in a closed vessel not completely
filled, the pressure will rise after steam begins to form
accompanied by an increase in temperature.
Saturated steam is steam in contact with liquid
water from which it was generated, at a temperature which is the boiling point of the water and the
condensing point of the steam. It may be either
"dry" or "wet", depending on the generating can·
ditions. "Dry" saturated steam is steam free from
mechanically mixed water particles. "Wet" saturated steam, on the other hand, contains \\'ater
Darticles in suspension. Saturated steam at any
pressure has a definite temperature.
Superheated steam is steam at any given pressure
which is heated to a temperature higher than the
temperature of saturated steam at that pressure.
2·1
rr-3
C=:J
-=3
tr-:3
~~~
//"'~"-------~
//
Flow of Fluids
(Through Valves and Fittings)
'~---------
.d
~
8:::J
~
a:::)
~
-=::J
~~-~
.::::')
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i
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e=:,)
a::::)
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~
The preceding chapter has been devoted to the
theory and formulas used in the study of fluid flow in
pipes. Since industrial installations usually contain a considerable number of valves and fittings, a
knowledge of their resistance to the flow of fluids
is necessary to determine the flow characteristics of
a complete piping system.
Many texts on hydraulics contain no information on
the resistance of valves and fittings to flow, while
others present only a limited discussion of the subject. In realization of the need for more complete
detailed information on the resistance of valves and
fittings to flow, Crane Co. has conducted extensive
tests in their Engineering Laboratories and has also
sponsored investigations in other laboratories. These
tests have been supplemented by a thorough study of
all published data on this subject. Appendix A
contains data from these many separate tests and the
findings have been combined to furnish a basis for
calculating the pressure drop through valves and
fittings.
Representative resistances to flow of various types
of piping components are given on pages A-26. A-27,
and A-30. For conversion of "equivalent length in
pipe diameters", as obtained from page A-27 or A-30,
to "equivalent length in feet of pipe" for any size of
valve or fitting, see page A-31. The chart on page
A-31 also illustrates the correlation of equivalent
length, resistance coefficient K, and pipe size. A
chart is presented on page A-32 which may be used to
readily determine the C" flow coefficient of any valve
for which the resistance coeffIcient is known or can
be determined from page A-30 and page A-31.
I!'.~
.~
A discussion of the eqUivalent length and resistance
coefficient K, as well as the flow coefficient Cv methods of calculating pressure drop through valves and
fittings is presented on pages 2-8 and 2-9.
CHAPTER 2
2-2
CHAPTER 2 - FLOW OF flUIDS THROUGH VALVES AND FITTINGS
CRANE
Types of Valves and Fittings
Used in Pipe Systems
Valves: Although the great variety of valve designs
precludes any t'lorough classification, most of the
designs may be considered as modifications of the
two basic types:
I. the gate type
2. the globe type
If valves were classified according to the resistance
which they offer to flow, the gate type valves would
be put in the low resistance class and the globe
type valves in the high resistance class. The classifIcation is not all-inclusive, however, because a
large number of modified valve types fall between the
two extremes. :lome of the most commonly used
valve designs are illustrated on pages A-28 and A-29.
Fittings: Fittings may be classified as branching,
reducing, eXf'anding, or deflect ing. Such litt in.!.;,
as tees, crosses, side outlet elbows, etc., may be
called branching fittings.
Reducing or expanding fittings are those which
change the area of the fluid passageway. In this
class are reducers and bushings. Deflecting fittings
..... bends, elbo\\'s, return bends, etc ... , . are those
which change the direction of flow.
Some fittings, of course, may be combinations of any
of the foregoing general ~lassifications. In addition, there are types such as couplings and unions
which offer no appreciable resistance to flow and,
therefore, need not be considered here.
Pressure Drop Chargeable
To Valves and Fittings
When a fluid is flowing steadily in a long straight
pipe of uniform diameter, the flow pattern, as indicated by the velocity distribution across the pipe
diameter, will assume a certain characteristic form.
Any impediment in the pipe which changes the direction of the whole stream, or even part of it, will
alter the characteristic flow pattern and create turbulence, causing an energy loss greater than that
normally accomp;mying flow in straight pipe. Because valves and fir:tings in a pipe line disturb the flow
pattern, they produce an additional pressure drop.
The loss of pressure produced by a val ve (or fitting)
consists of:
I. The pressure drop within the valve itself.
2. The pressure drop in the upstream piping in
excess of that which would normally occur if
there were no valve in the line. This effect
is small.
3. The pressure drop in the downstream piping in
excess of tha'~ which would normally occur if
there were no valve in the line. This effect
may be comparatively large.
From the experimental point of view it is difficult to
measure the three il:ems separately. Their combined
effect is thc desired quantity, howe vcr, and this can
be accurateiy measured by well known methods.
4---------C--------~
Figure 2-1 shows two sections of a pipe line of the
same diameter and length. The upper section contains a globe valve. If the pressure drops, D.P. and
D.P" were measured between the points indicated.
it would be found that D.P, is greater than D.P,.
Actually, the loss chargeable to a valve of length "d"
is D.P. minus the loss in a section of pipe of length
"a + b". The losses, expressed in terms of equi\'a
lent length in pipe diameters, of various val\'es and
fittings as given on page A-30, include the loss due
to the iength of the valve or fitting.
i
•. t::J
CRANE
2-3
CHAPTER 2 - flOW QF flUIDS THROUGH VALVES AND FITIINGS
Crane Flow Tests
..~
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b
~I
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i
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,
,~
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Crane Engineering Laboratories have facilities for conducting water, steam, and air flow
tests for many sizes and types of valves and
fittings. Although a detailed discussion of all the
various tests performed is
beyond the scope of this
paper, a brief description
of some of the apparatus
will be of interest.
-'-~,~"'"C"'''-'
The test piping shown in Figure 2-3 is unique
in that 6-inch gate. globe. and angle valves or
90 degree ells and tees can be tested with
either water or steam. The vertical leg of the
angle test section permits testing of angle lift
check and stop check valves.
r
}
F
Figure 2-2
Saturated steam at 150 psi is available at flow rates
up to 100,000 pounds pe~ rour. The steam is throttled to the desired pressure and its state is determined at the meter as well as upstream and downstream from the test specimen.
For tests on water, a steam turbine driven pump supplies water at rates up to 1200 gallons per minute
through the test piping.
:r ::::.1
Static pressure differential is measured by means of
a manometer connected to piezometer rings upstream
and downstream from test position 1 in the angle test
section, or test position 2 in the straight test section. The downstream piezometer for the angle
test section serves as the upstream piezometer for
angle valve
f;
r
;;"
r:
E
Results of some of the flow tests conducted in the
Crane Engineering Laboratories are plotted in Figures 2-4 to 2-7 shown on the two pages following.
-II>
iiti' ..g
~-)
Exhaust to
Atmosphele
~
\
Water Header
(Meteled Supply flam
tumine dliven pump)
!i'
)
.~
~
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Figura 2-3
Test piping apparatus for measuring
the pressure drop thrQugh valves and
nnlngs on sfoam or water lines.
Elbow Can Be Rotated to ________" "
Admit Water Of Steam
"
I
,
i
Flow test piping
for 12-inch cast steel
the straight test section. Measured pressure drop
for the pipe alone between piezometer stations is
subtracted from the pressure drop through the valve
plus pipe to ascertain the pressure drop chargeable
to the valve alone.
~
~~
.;;.
2-4
CRANE
CHAPTER 2 - flOW OF flUIDS THROUGH VALVES AND FITTINGS
Crane Water Flow Tests
1~ r:~:=ll::::~:rI:;"=l1::If==l::;:=l=;:::::7.I'MIrL~-:;~
8~4-~~4-+-~ji+--r-r+-r+--~/~//'~~~
I ; I
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IIII VIJLJ,
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IJIL /1/1111
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IXII V;{riv/
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I '"
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'II
I
1/ II II I 1/
I
I I
V VI
2
I
II
I
V
fhVl
1 (;)
2
4
3
20
5678910
2
3
Water Velocity, in Feet per Second
Figure 2 ...4
Figure 2 .. 5
Woter Flow Tests
Fluid
FigurE'
No.
Curve
No.
Size,
Inches
I
2
Figure 2-4
Water
I
figure 2··5
I
Curves 1 to 18
Valve Tl:'pe*
%
2
4
6
3
4
S
6
7
8
9
10
11
12
13
14
15
16
17
18
678910
Water Velocity, in Feet per Second
ISO-Pound Cast Iron Y-Pattern Globe Valve,
Flat Seat
111.
2
2%
3
Ill.
I
2
2%
3
ISO-Pound Brass Angle Valve with Composition Disc,
Flat Seat
I
I
ISO-Pound Brass Conventional Globe Valve
With Composition Disc-Flat Seat
%
II.
3,4
11,4
II
2
6
2oo-Pound Brass Swing Check Valve
!
US-Pound Iron Body Swing Check Valve
*Exccpt for check valves at lower velocities where curves (l4 to 17) bend, all valves were .tested with disc fully lifted.
CRANE
-
Crane Steam Flow Tests
LO
,
9
8
7
6
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4
i /,
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=
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4
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4
6 7 8 S 10
20
.0I 3
30
Fluid
No.
CUrvl~
19
.:':::,
29
.L
V /
"',
"-
'"
30
~
1.......
31
L
il .L
I
45678910
30
20
Figure 2-7
Size,
Inches
No.
t-2sl
Steam Velocity, ifl Thousands of Feet per Minute
Stearn Flow Tesfs
Figure
..
1/ V
1/1/
Figurn 2 .. 6
.. :=)
1
Vv
Steam Velocity, in·ThoLisands of Feet per Minute
::::)
~
1L':::::::'
V 1/
V
V
l.'f-L~V- LI~~,L.-"-i--:'::--'---::
L ' 27
I.
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.03
-;:::)
k'
L
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.L
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If
.05
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I il II.
~
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2!
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-5
gl
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2-5
CHAPTER 2 - flOW OF FLUIDS THROUGH VALVES AND FITTINGS
:::::)
20
.~
21
2
6
6
21
6
Curves 19 to 31
Valve' or Fitting Type
I'
loo-Pound
300-Pound
lOO-Pound
[ lOO-Pound
Brass Conventional Globe Valve ............. Plug
Steel Conventional Globe Valve ............. Plug
Steel Angle Valve ........................... Plug
Steel Angle Valve ......................... Ball to
Type Seat
Type Seat
Type Seat
Cone Seat
Figure 2-6
::::.)
~
-~
23
Saturated
Steam
24
25
50 psi
gauge
26
::::::)
Figure 2-7
I
I
6
G
G
I)
27
2
18
(;
29
30
31
I)
6
6
GOO-Pound
GOO-Pound
GOO-Pound
600-Pound
Steel
Steel
Steel
Steel
Angle Stop-Check Valve
Y-Pattern Globe Stop-Check Valve
Angle Valve
Y-Pattern Globe Valve
90° Short Radius Elbow for Use with Schedule 40 Pipe
250-Pound Cast Iron Flanged Conventional 90° Elbow
GOO-Pound Steel Gate Valve
125-Pound Cast Iron Gate Valve
ISO-Pound Steel Gate Valve
'Except for check valves at lower velocities where curves (23 and 24) bend, all valves were tested with disc fully lifted.
2-6
CHAPTER 2 - flOW OF flUIDS THROUGH VALVES AND FITTINGS
CRANE
Figure 2.8
Flow test piping
for 2 V:z -inch corl
steel ongle valve.
Figure 2 ...9
Steam capacity feft
of a V:z-inch bra"
relief yalve.
J
I
1j
j
i
Figure 2-10
Flow fest piping
lor
2-inch fabricaled steel
y-pattern globe valve.
CRANE
CHAPTER 2 -- flOW OF flUIDS THROUGH VALVES AND FlTIlNGS
2-7
Relatiionship of Pressure Drop to Velocity of Flow
...•»
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.=:)
Many experiments have shown that the head loss due
to valves and fittings is proportional to a constant
power of the velocity. When pressure drop or head
loss is plotted against velocity on logarithmic coordinates, the resulting curve is therefore a straight
line. In the turbulent flow range, the value of the
exponent of v has been fm;nd to vary from about
1.8 to 2.1 for different designs of valves and fittings.
However, for all practical purposes, it can be assumed that the pressure drop or head loss due to
the flow of fluids in the turbulent range through
valves and fittings varies as the square of the
velocity .
This relationship of pressure drop to velocity of
flow is valid for check valves, only if there is sufficient flow to hold the disc in a wide open position .
The point of deviation of the test curves from a
straight line, as illustrated in Figures 2-5 and 2-6,
defines the flow conditions necessary to support a
check valve disc in the wide open position.
Most of the difficulties encountered with check
valves, both lift and swing types, have been found to
be due to oversizing which results in noisy operation
and premature wear of the moving parts. Referring
again to Figure 2-6, it will be noted :hat the pressure
drop, at the point where the two curves representing
check valves deviate from a straight line, is about
1Yz to 2 pounds per square inch. This value will vary
somewhat for different valve designs depending upon
the relative weight and size of the disc; however,
it has been found to be a good "rule of thumb" to
size check valves so that the pressure drop in the
fully open position is about 2 psi in lift checks and
about Yz psi in swing checks. This rule applies
only to check valves designed on the basis of established fundamental considerations which assure a
full disc lift at low flow rates. On some poorly
designed lift check valves, tests have shown that the
disc will not lift fully even at extremely high flow
rates. In many cases, application of this rule will
result in check valves smaller in size than the pipe
line; however, the actual pressure drop will be little,
if any, higher than that of a full size valve which is
used in other than a wide open position.
The losses due to sudden contraction and enlargement which will occur in such an installation with
bushings or reducing flanges can be readily calculated
from the data given on page A-26. if tapered reducers are used, the loss due to gradual contraction at
the inlet to the smaller size valve is partially compensated for by the corresponding gradual enlargement on the outlet side, so that the added pressure
drop due to these effects is minor.
In-line ball check valves
of the design shown in
Figure 2-11 should be installed in a horizontal position wherever possible. In
this position, the flow required to move the disc
to the fully open position
is very low and the valves
Figure 2.11
can be full size to match
In· line ball check valve
the pipe line; this will
in horizontal position
result in low pressure drop
at all flow rates. If it is necessary to install this
type of valve in a vertical line, due to piping arrangement or for other reasons, it should be sized so that
the flow rate will be sufficient to cause a pressure
drop of about 2Yz psi across the valve. This will
provide full disc lift and prevent noisy operation and
premature wear of parts.
==»
:::::'»
::::3
:::::::)
-:::::)
~
,'
-
Figure 2-12
Both woter and steam fests ore conducted on this set-up.
2-8
CRANE
CHAPTER 2 - FLOW OF FLUIDS THROUGH VALVES AND FITTINGS
Resistance Coefficient K, Equivalent length L/D,
And Flow Coefficient Cv
The numerous types of valves and fittings and the
great variety of service conditions make it virtually
impossible to obtain test data on every size and
type of valve and fitting used today. For this
reason, it is desirable to find a means for utilizing
the limited test data which are available. Several
methods of accomplishing this have been devised;
the most commonly used are the "equivalent length",
.. resistance coefficient", and' 'flow coefficient".
Velocity in a pipe is obtained at the expense of static
head, and decrease in static head due to velocity is:
h = v'
-,
2g
which is defined as the "velocity head". Flow
through a valve or fitting in a pipe line also causes a
reduction in stati.C head which may be expressed in
terms of velocity head. The resistance coefficient
K in the equation
hL = K -2gv' ,
Equation 2-2
therefore, is defined as the number of velocity heads
lost due to the valve or fitting. Also, the same
head loss in straight pipe is expressed by the Darcy
equation
hL=(ii;)~
Equation 2 ..3
I t follows that,
K =
(it)
Equation 2-4
The ratio LID is the equivalent length in pipe diameters of straight pipe which will cause the same
pressure drop as the valve under the same flow
conditions.
The resistance coefficient K would
theoretically be a
constant for all sizes
of a given design
or line of valves and
fittings if all sizes
were geometrically
similar. However,
geometric simiiarity
is seldom, if ever,
achieved because
Figure 2-13
the design of valves
Geometrical dis.similarity between 2 and and fittings is dic12-inch standard cast iror:, flanged elbows
tated by manufacturing economies, standards. structural strength, and
other considerations. An example of geometric dis12-IHCH SIZE
1/6 SCALE (>'
similarity is shown in Figure 2-13 where a 12-inch
standard elbow has been drawn to 1/6 scale of a 2-inch
standard elbow. so that their port diameters are identical. The flow paths through the two fittings drawn
to these scales would also have to be identical to
have geometric similarity; in addition. the relative
roughness of the surfaces would have to be similar.
Figure 2-14 on the opposite page is based on the
analysis of extensive test data from various sources.
The K coefficients for a number of lines of valves
and fittings have been plotted against size. It will
be noted that the slopes of the K curves show a
definite tendency to follow the same slope as the
I(LID) curve for straight pipe. It is probably coincidence that the effect of geometric dissimilarity
between different sizes of the same line of valves or
fittings upon the resistance coefficient K is similar to
that of relative roughness, or size of pipe, upon
friction factor.
Based on the evidence presented in Figure 2-14, it can
be said that the resistance coefficient K, for a given
line of valves or fittings, tends to vary with size
as does the friction factor I for straight pipe, and
that the equivalent length LID tends toward a constant for the various sizes of a given line of valves
or fittings.
In the flow range of complete turbulence as defined
by the Friction Factor Charts, pages A-24 and A-25,
the K coefficient for a given size and the LID value
are, of course, constant. In the transition zone,
where I for pipe increases with decreasing Reynolds
numbers, it is assumed that the value of LID is constant and that K varies in the same manner as the
friction factor. Limited tests have shown that this
is not an exact relationship and that it may vary for
different types of valves and fittings: however, since
the tendency is in this direction, it is believed to
provide more accurate solutions than would the
assumption that K is constant for all Reynolds
numbers.
It has been found convenient in some branches of the
valve industry, particularly in connection with control valves, to express the valve capacity and the
valve flow characteristics in terms of the flow coefficient Cy . The Cy coefficient of a valve is defined
as the flow of water at 60 F, in gallons per minute, at
a pressure drop of one pound per square inch across
the valve.
By the substitution of appropriate equivalent units
in the Darcy equation, it can be shown that,
C _
y
-
~
29·9cl' _
It -
29·9cl'
-vI<
Equallo. 2-5
CRANE
2·9
CHAPTER 2 - fLOW OF fLUIDS THROUGH VALVES AND FITTINGS
Resistance Coefficient f{, Equivalent length l./D,
And Flow Coefficient Cy - continued
'
.. ~
.:=J~
.~.
;;::)
';:dI
::::::)
--
K - Resistance Coefficient
Figure 2-14, Variation of Resistance Coefficient K (=f L{D) with Size
Product Tested
Symbol
o
0-
9
-0
6
-0-
9
-¢cf
Q.
)::(
Authority
Schedule 40 Pipe, 30 Diameters Long (K = 30 f) .... : . . Moody AS.M.E. Trans., Nov.-1944'
125-Pound Iron Body Wedge Gate Valves .............. Univ. of Wise. Exp. Sta. Bull., Vol. 9, No. I, 1922"
600-Pound Steel Wedge Gate Valves ................... Crane Tests
90 Degree Pipe Bends, RID = 2 ....................... Pigott AS.M.E. Trans., 1950'
90 Degree Pipe Bends, R/D = 3 ....................... Pigott AS.M.E. Trans., 1950'
90 Degree Pipe Bends, R/D = 1 ....................... Pigott A.S.ME. Trans., 1950'
600-Pound Steel Wedge Gate Valves, Seat Reduced .... Crane Tests
JOO-Pound Steel Venturi Ball-Cage Gate Valves ....... Crane-Armour Tests
125-Pound Iron Body Y-Pattern Globe Valves ......... Crane-Armour Tests
125-Pound Brass Angle V a1 yes, Composition Disc ...... Crane Tests
125-Pound Bras!: Globe Valves, Composition Disc .... .. Crane Tests
(toflfinued from the preceding page)
Also, the quantity in gallons per minute of any
liquid having a viscosity close to that of water at
60 F that will flow through the valve can be determined from:
Equation 2-6
and the pressure drop can be computed from the
same formula arranged as follows:
/::,.p=P
62-4
(Q)'
C
-
v
Equatjon 2-6
Since Equations 2-2, 2-3, and 2-6 are simply other
forms of the Darcy equation, the limitations regarding their use for compressible flow (explained in
Chapter I, Page 1-7) apply. Other convenient forms
of Equations 2-2, 2-3, and 2-6 in terms of commonly
used units are presented on page 3-4.
2 - 10
- - - - -CHAPTER 2 -
CRANE
flOW OF flUIDS THROUGH VALVES AND fITTINGS
Relath)t1Ship of Equivalent length 1./D and Resistance Coefficient K
To Inside Diameter of Connecting Pipe
Tests have shown that the pressure drop due to a
given va!\'e or titting does not change when the
product is installed with pipe of the same nominal
size but of differem thickness, Small variations in
entrance and exit losses caused by mating the valve
ends to \'ariable pipe thicknesses, within reasonable
limits, are insignitlcant. Since the pressure drop is a
function of the square of the velocity, and velocity is
a function of the square of the internal diameter, it
follows that the equivalent length of a given valve
or fItting, expressed in terms of the pipe to which
it is connected, varies as the fourth power of the internal diameter (If the pipe, For example, if the
equivalent length of a ! i-inch valve is determined
by test to be 100 pipe diameters of Schedule 80 pipe,
its equi\'alent length will be 169 diameters of Schedule 40 pipe, since the ratio of the inside diameters
of the twO pipes to the fourth power is 1.69, This
ratio, of course, varies with the different sizes and
thicknesses of pipes.
In vie\\' of this condition, the Crane Engineering
Laboratories have established the practice of making
all flow tests with pipe having internal diameters
normally used with the particular valve or fitting.
For this purpose, pipe normally used with the various
pressure classes of valves and fittings has been arbitrarily established in accordance with the table shown
at the top of page A-30.
Computation of pressure drop using equivalent
length data established on the ba;;is of this tai'k
should be made USing pipe dimensions specified on
pages B-IO to B-19; for installation conditions not in
agreement with the table. the eLJui"aknt length In
pipe diameters. should be multiplied by the ratIo of
diameters to the fourth power.
L) a D
( L) • (d
(D
,db
-
-
-
a
)'
Equatiolt 2..7
Subscript "a" dcfmes the eLJuivalcnt lengths
\\'ith reference to the internal diameter of the plpC
in which the \'alve \\'i11 be installed.
Subscript "b" defines the known equi\'alent fengths
and internal diameters of the pipe for which
these equivalent lengths were established.
This procedure of obtaining equl\'alent length data
with respect to pipe of various internal diameters
corrects a signifIcant variable that has often been
neglected in translating tcst data and makes pos~ible a more accurate prediction of the 110w characteristics of untested valves and fittings by comparison
of detail dimensions and shapes with tested items.
Resistance coefficient K can be calculated for the
pipe in \\'hich the valve will be installed byemploying the formula Ka = fa
(~ ) .. or expressed in termS of .
resistance coefficients, the
formula may be written: Ka= K.
(X) (~:)'
Valves with Gradually Increased Ports
Various types of valves are often made with reduced
seats and have uniformly tapered ports, Straightthrough \'alves such as gate, ball, plug, and conduit
types when so designed are sometimes referred to as
venturi or reduced seat valves, The added resistance
in these valves, due to the tapered sections from port
size to seat size to port size, exceeds that of the
straight-through port" valve with correction for flow
resistance based on Equation 2-7, for included venturi
angles of 20 degrees or less with seat to port ratio of
diameters less than 0.8, Equation 2-7 yields reasonably accurate results for included venturi angles of 7
degrees or less and \\'ith a ratio of seat to port diameters greater than 0.8,
In globe and angle type valves where the loss through
the seat section is high with respeer to the loss through
the venturi ends, Equation 2-7 may be used with
reasonable accuracy for included venturi angles up to
20 degrees and for seat to port ratios of diameters
greater than 0.7.
Effect of End Connections
Before the advent of full port straight-through ball,
plug, and conduit type \'alves, the losses due to end
connections \\'ere inSignificant with respect to the
over-all loss through the valve, This is still true for
higher resistance val Yes, Where the flo\\' resistance of
a valve in pipe diameters is equal to its end-to-end
dimension, small additional losses should be computed
since they may add Significantly to the over-all valve's
loss, I n screwed end val ves, the losses due to sudden
enlargements and contractions (page A-26) may be a
signifIcant part of the total loss, especially in the
small er sizes.
CRANE
2 - 11
CHAPTER 2 - FLOW OF flUIDS THROUGH VALVES AND FITTINGS
Laminar Flow Conditions
One of the problems in flow of fluids confronting
engineers from time to time . for which there is very
meager information, is the resistance of valves and
fittings under laminar flow conditions. Flow through
straight pipe is adequately c~vered by the basic flow
equation,
L v'
hL = I D zg'
:::::::3
.==:)
::::)
..
.:=
.-.
.::=.:)
':::::)
.~
..=:::)
=:)
:::::II
':: :II
=1
::::)
~I
Subscript "s" refers to the equivalent length in
pipe diameters under laminar flow conditions
where the Reynolds number is less than 1000.
which is identical to Poiseuille's law for laminar
Row when the equation for I in this flow range,
I = 64/R" is included in the formula.
Subscript ..t'. refers to the equivalent length in
pipe diameters determined from tests in the turbulent flow range. Representative values of
equivalent length are given in the table on page
A-30.
For solution of these problems, we have developed
on the basis of data presented in "Principles of
Chemical Engineering" by Walker, Lewis, McAdams
and Gilliland", the empirical relationship between
equivalent length in the laminar flo\\' region (for
R, < 1000) to that in the turbulent region. namely:
The minimum equivalent length is the length in pipe
diameters of the centerline of the actual flow path
through the valve or fitting. \Vhile laboratory test
data supporting this method is meager, reports of
field experience indicate that the results obtained
agree closely with observed conditions.
Basis for Design of Charts
for Determining Equivalent Length,
Resistance Coefficient, and Flow Coefficient
The table on page A-30 lists average equivalent
length data expressed in pipe diameters abstracted
from all available tests. It is not practical to
identify all valve and fitting types with the many
variations in design which may affect the flow charactenstlCS. The data given for globe and angle
valves represent actual tests on the variation of
designs indicated. By using the data given in this
table along with the principles presented from page
2-8 to this point as a basis, reasonable equivalent
length values can be estimated for any valve or
fitting upon consideration of design features, such
as, the relative area of sea.t or restricted sections
to pipe diameter and the shape of the flow passage.
The chart on page A-3! provides a convenient means
of translating equivalent length in pipe diameters
as given in the table on page A-30, to equivalent
length in feet of pipe for any given size of valve
or fitting. Also, the resistar:.ce coefficient K for fully
turbulent flow range can be readily determined from
this chart for any size, if the resistance coefficient or
equivalent length for any other size of the same item
has been established, eit~er by experiment or
estimate.
The chart on page A-32 givi:s a graphical solution of
Equation 2-5 and permits a readv determination of
Cy if K is known. An example i-i1ustrating the use
of this chart is given on page 4-2.
Limitations of charts: As explained on page 2-8
and at the top of this page, the value of L;D for a
given type of valve or fitting is considered to be
constant for flow conditions resulting in Reynolds
numbers of 1000 or greater. Equivalent lengths
either in pipe diameters or feet of pipe, <;is determined
from pages A-30 or A-3J, are therefore legitimate for
all flow conditions except in the laminar flow range
where the Reynolds number is less than 1000. For
Reynolds numbers .Jess than 1000, values of L/ D
must be determined in accordance with Equation 2-8 .
[t should be pointed out that the equivalent length
data given on pages A-30 and A-31 are based upon
clean commercial steel pipe.
On the other hand, values of K, as determined from
pages A-31 and A-32, are legitimate only for flow
conditions resulting in Reynolds numbers falling in
the completely turbulent flow range, as defined by
the friction factor on pages A-24 and A-25. At lower
flow rates, values of K vary in approximately the
same manner as does tlo;, value of friction factor with
Reynolds number. At the lower flow rates, the value
of K as determined from pages A-31 and A-32 should
be multiplied by the raja:
I
f
(at calculated Rcynoks number)
(in range of complete turbulence, where f is constant)
----------------
When K has been corre~t.ed for flow in the transition
or laminar flow range, Cv can be obtained directly
from page A-32 by employing the corrected K factor.
However, if the Cv factor is furnished for the completely turbulent flow range, as defined by the
friction factor charts on pages A-24 and A-25, it
must be corrected by multiplying it by the ratio,
If
(in range of complct~ turbulence. where f is constant)
'\J I (at calculated Rc\'nG'~ls number)
since Cv varies inverse1:; with the square root of the
friction factor.
2" 12
CHAPTER 2 - flOW OF FlUIDS THROUGH VALVES AND FITTINGS
CRANE
Resistance of Bends
Figure 2-15
5Qcondory Flow In Bands
Secondary flow: The nature of the flow of liquids
in bends has been thoroughly investigated and many
interesting facts have been discovered. For example,
when a fluid passes around a bend in either viscous
or turbulent flow, there is established in the bend
a condition known as ··secondary flow'·. This is
rotating motion, at right angles to the pipe axis,
which is superimposed upon the main motion in the
direction of the axis. The frictional resistance of the
pipe walls and the action of centrifugal force combine to produce this rotation. Figure 2-15 illustrates this phenomenon.
Resistance of bends to flow: The resistance or
head loss in a bend is conventionally assumed to consist of .... (I) the loss due to curvature .... (2) the
excess loss in the downstream tangent .... and (3)
the loss due to length, thus:
h, = h.
+ h, + hL
Equation 2-9
where:
h,
h.
I!
I
total loss, in feet of fluid
excess loss in downstream tangent, in feet
of fluid
loss due to curvature, in feet of fluid
loss in bend due to length, in feet of fluid
if:
h.
Equation 2-JO
then:
h,
= h.
+
h"
The chart on page A-27 shows the resistance of 90
degree bends in terms of equivalent length of straight
pipe. These curves .... also based on the work of
Beij .... are believed to represent a\·erage conditions for the flow of fluids in 90 degree bends.
Tests have shown that the loss due to continuous·
bends greater than 90 degrees. such as in pipe coils,
is less than the summation of the losses in the 90
degree bends contained in the coil, considered separately. This is reasonable. since the loss h p in Equation 2-9 occurs only once in such a bend. Reasonably accurate results for pipe coils and expansion
loops consisting of continuous bends can be obtained
by the use of the chart on page A-27 .... if the number of 90 degree bends contained in the coil minus
one, multiplied by the resistance due to length plus
one-half of the bend resistance, is added to the
total resistance of a 90 degree bend.
For example, a pipe coil consisting of four complete
turns .... sixteen 90 degree bends .... and having
a relative radius of five pipe diameters, would have a
total equivalent length, in pipe diameters, of:
15 (8
However, the quantity h. can be expressed as a function of velocity head in the formula:
v'
h. = K.2g
The relationship between K, and rid (relative
radius*) is not well defined, as can be observed by
reference to Figure 2-16 (taken from the work of
Beij2I). The curves in this chart indicate that K.
has a minimum value when rid is between 3 and 5.
Equation 2-J J
+ 4) + 16 =
196
I t will be noted that this assumes h p = he in Equation 2-9; this relationship has not been established
by tests but is believed to represent the most accurate estimate that can be made until further
experimental data are available.
where:
K.
v
g
the bend coefficient
velocity through pipe, feet per second
32.2 feet per second per second
Resistance of miter bends: The equivalent length
of miter bends, based on the work of H. Kirchbach',
is also shown on page A-27.
"The relative radius of a bend is the ·ratio of the radius of the bend axis to
the intemal diameter of the pipe. Both dimensions must be in the same units ..
CRANE
CHAPTER 2 - FLOW OF flUIDS THROUGH VALVES AND FITTINGS
Resistance of Bends -
continued
.6r----,----,-----r----,----.-----r----.--~---r----,----.----~
I
/V -
A
~
.b
~3
°O~--~2----~4-----6~--~8----~1~O----~12~--~14~--~1~6----~18~--~2~O--~22
Relative Radius, rjd
Figure ~!-16, Bend Coefficients Found by Various Investigators (BeW')
From "Pressu.re Losses for Fluid Flow in 90° Pipe Bends" by K. H. Ber;.
Courtesy of Journal' of Research of National Bureau of Standards.
t=:)
Investigator
c:=:;,
Diameter
Balch ... , ....................... 3-inch ............... .
. Davis ........................... 2-inch ............... .
Brightmore ..................... 3-inch ............... .
Brightmore ..................... 4-inch ............... .
Hofmann ................. 1.7-inch (rough pipe) ........ .
Hofmann ............... , 1.7-inch (smooth pipe) ....... .
VogeL ...................... 6, 8, and lO-inch .......... .
Beij ............................ 4-inch ............... .
t=:t
Symbol
•o
II
o
it..
6.
T
+
Other Resistances to Flow
c,:-
~I
In addition to the resistance due to valves and fittings already discussed, losses due to sudden enlargement and sudden contraction are encountered whenever fittings such as reducing or increasing flanges,
bushings, etc., are used. Also, when a fluid enters or
leaves an open end pipe, entrance and exit losses
occur. As in the case of VE:lves and fittings, these
losses can be expressed by the formula:
hL
= K!!...
2g
Unlike most other fittings. there is no length involved
in losses due to these conditions; thus, relative roughness is not a factor in these resistances, and geometric
similarity does exist. The resistance due to sudden
enlargement and sudden contraction, as well as entrance and exit losses expressed in terms of velocity
head or K factor, are therefore independent of pipe
size. Resistance coefficient K for such conditions
are given on page A-26.
EqUivalent lengths corresponding to these resistance
coefficients for any size can be readily determined
from the chart on page A-31. For example, the equivalent lengths of sharp edged entrances (K = 0.5) to
2 and 6-inch pipes can be read from the nomograph
on page A-3J as 26 diameters of 2-inch pipe and 33
diameters of 6-inch pipe, respectively.
2 -14
CHAPTER: 2 - FLOW OF flUIDS THROUGH VALVES AND FITIINGS
CRANE
Flow Through Nozzles and Orifices
The discharge of fluids through nozzles and orifices has been subject to
continued investigation and, as a result, well-established data are still
being supplemented. A portion of the subject is co\'ered on these
faCing pages but more complete references will be found in the Bibliography" " lO, or from the data supplied by meter manufacturers.
The rate of flow of any fluid through an orifice or
nozzle, neglecting the velocity of approach, may be
expressed by:
Equation 2-J2
Velocity of approach may have considerable effect on
the quantity discharged through a nozzle or orifice.
The factor correcting for velocity of approach,
ing a low viscosity, i.e., water, gasoline. etc., the
Reynolds number need not be calculated since it
will fall in the range of the values on page A-20,
where the flow coefficient C is a constant.
Flow of gases and vapors: The flow of compressible fluids through nozzles and orifices can be expressed by the same equation used for liquids except
the net expansion factor Y must be included.
Equa/;on 2-15
may be incorporated in Equation 2-12 as follows:
q
CdA
= -;====;
~I-(~:y
.,-'V
2g hL
Equation 2.13
The expansion factor Y is a function of:
I. The specific heat ratio, k.
2. The ratio of orifice ot throat diameter to inlet
diameter.
3. Ratio of downstream to upstr.eam absolute
pressures.
The quantity
is defined as the flow coefficient C. Values of C
for nozzles and orifices are shown on page A-20. Use
of the flow coefficient C eliminates the necessity for
calculating the velocity of approach, and Equation
2-13 may now be written:
Orifices and nozzles are normally used in piping systems as metering devices and are installed with
flange taps or pipe taps in accordance with ASME
specifications. The values of hL and D.P in Equation
2-14 are the measured differential static head or
pressure across flange taps when values of Care
taken from page A-20. The flow coefficient C is
plotted for Reynolds numbers based on the internal
diameter of the upstream pipe.
Flow of liquids: For nozzles and orifIces discharging incompressible fluids to atmosphere, C values
may be taken from page A-20 if hL or !';P in Equation 2- I 4 is taken as the upstream head or gauge
pressure. f'or most conditions of flow of fluids hav-
This factor"lO has been experimentally determined
on the basis of air, which has a specific heat ratio of
1.4, and steam having specific heat ratios of approximately 1.3. The data is plotted on page A-21 and
values of other specific heat ratios have been included
to extend the use of the data. Values of k for some
of the common vapors and gases are given on pages
A-8 and A-9. The specific heat ratio, k, may vary
slightly for different pressures and temperatures,
but for most practical problems the values given
will provide reasonably accurate results.
Equation 2-15 may be used for orifices discharging
com;xessible fluids to atmosphere by using:
I. Flow coefficient C given on page A-20 in the
Reynolds number range where C is a constant
for the given diameter ratio.
2. Expansion factor Y per page A-21.
3 . Differential pressure !,;P, equal to the inlet
gauge pressure.
This also applies to nozzles discharging compressible
fluids to atmosphere only if the absolute inlet pressure is less than the absolute atmospheric pressure
divided by the critical pressure ratio r,; this is
discussed on the next page. When the absolute inlet
pressure is greater than this amount, flow through
nozzles should be calculated as outlined on the
following page.
CRANE
--c:='lll
":;::3
.~
:.:=:11
~.
.~
.::::J
=::3
2 -15
CHAPTER 2 - flOW OF flUiDS THROUGH VALVES AND FITIINGS
Flow Through Nozzles and Orifices Maximum flow of compressible fluids in a nozzle: A smoothly convergent nozzle has the property
of being able to deliver a compressible fluid up to the
velocity of sound in its minimum cross section or
throat, providing the available pressure drop is
sufficiently high. Sonic velocity is the maximum
velocity that may be attained in the throat of a
nozzle (supersonic vel.ocity is attained in a gradually
, divergent section fo.llowin,c; the convergent nozzle,
when sonic velocity exists In the throat),
continued
Equation 2-15 may be used for discharge of compressible fluids through a nozzle to atmosphere, or
to a downstream pressure lower than indicated by
the critical pressure ratio r" by using vaiues of:
Y .. , . minimum per page A-21
C .. , , page A-20
;::,p , , , . P', (l - r,); T, per page A-21
p , .. , weight density at upstream condition
The critical pressure ratio is the largest ratio of
downstream pressure to upstream pressure capable
of producing sonic velOCity. Values of critical pressure ratio r" which depend upon the ratio of nozzle
diameter to upstream diameter as well as the specific
heat ratio k, are given on page A-21 .
Flow through short tubes: Since complete experimental data for the discharge of fluids to atmosphere through short tubes (LID is less than, or equal
to, 2.5 pipe diameters)' are not available, it is suggested that reasonably accurate approximations may
be obtained by using Equations 2-14 and 2-15, with
values of C somewhere between those for orifices
and nozzles, depending upon entrance conditions.
Flow through nozzles and venturi meters is limited
by critical pressure ratio, aCId minimum values of Y
to be used in Equation 2-15 for this condition, are
indicated on page A-21 by the termination of the
curves ar p'.IP', = f,.
If the entrance is weil rounded, C values would tend
to approach those for nozzles, whereas short tubes
with square entrance would have characteristics
similar to those for square edged orifices.
::=::J
=:t
-:::::'J
:::::)
::::::)
Dischar!3e of Fluids Through Valves, Fittings, and Pipe
Liquid flow: To determine the flow of liquid through
pipe, the Darcy formula is used. Equation 1-4 (page
1-6) has been converted to more convenient terms in
Chapter 3 and has been rewritten as Equation 3-14.
The form of Equation 3-14 which is most applicable
to liquid flow is written in terms of flow rate in
gallons per minute.
h _
=.t
=:a
::::=)
=l
.'=:)
~'~
:::)
L
-
0. 002 59
d'
Loss of head in terms of resistance coefficient K has
been selected sin(;e entrance and exit losses are
usually given in terms of velocity head loss, K (see
page A-26). Solving for Q, the equation can be
rewritten,
Q
' .
i'"il;
19· 6 5d"'J K
KQ2
Q
Equation :2.76
Equation 2-16 can be employed for valves, fittings,
and pipe where K would be the sum of all the resistances in the piping system, including entrance and
exit losses when they exist. Examples of problems
of this type are shown on page 4-12 .
Compressible flow: When a compressible fluid flows
from a piping system into an area of larger cross section than that of the pipe, as in the case of discharge
to atmosphere, a modified form of the Darcy formula,
Equation I-II developed on page 1-9, is used.
The determination of values of K, Y, and 6.P in this
equation is described on page 1-9 and is illustrated
in the examples on pages 4-13 and 4-14,
,
.~
-1110
~"
3·1
formulas ~ond Nomographs
For Flow Through
.-.~.
....
,!!l
Valves, F:ittings, and Pipe
CHAPTER 3
~i
~
:t::::D
Only basic formulas needed for the presentation of
I:he theory of fluid flow through valves, fittings, and
pipe were presented in the first two chapters of this
paper. In the summary of formulas given in this
chapter, the basic formulas are rewritten in terms of
units which are most commonly used in this country.
This summary provides the user with an equation
which will enable him to arrive at a solution to his
problem with a minimum conversion of units.
Nomographs presented in this chapter are graphical
solutions of the flow formulas applying to pipe. Valve
and fitting flow problems may also be solved by means
of these nomographs by determining their equivalent
length in terms of feet of straight pipe.
Due to the wide variety of terms and the variation in
the physical properties of liquids and gases, it was
necessary to divide the nomographs into two parts:
the first part (pages 3-6 to }-15) pertains to liquid flow,
and the second part (pages }-16 to }-25), pertains to
(;ompressible flow.
All nomographs for the solution of pressure drop problems are based upon Darcy's formula, since it is a
general formula which is applicable to all fluids and
Clan be applied to all types of pipe through the use of
the Moody Friction Factor Diagram. Darcy's formula also provides a means of solving problems of flow
through valves and fittings on the basis of equivalent
length or resistance coefficient. Nomographs proVide
simple, rapid, practical, and reasonably accurate solutions to flow formulas and the decimal point is accurately located.
~
~
!
<:~::j.
I
Accuracy of a nomograph is limited by the available
page space, length of scales, number of units provided
on each scale, and the angle at which the connecting
liine crosses the scale. Whenever the solution of a
problem falls beyond the range of a nomograph, the
slide rule or arithmetical solution of the formula must
be employed.
3-2
CRANE
CHAPTER 3 - FORMULAS AND NOMOGRAPHS fOR flOW THROUGH VALVES, FITTINGS, AND PIPE
Summary of Formulas
To eliminate needLess duplication, formulas ha\'e
been written in terns of either srecific \olume '\
or \\'elf:!ht density p. but not in terms of both. since
one is the reciprocal of the other.
I
P =
~
\.
These equations may be substituted in any of the
formulas shown in this rarer whene\'er necessary.
,
Z +
I
P + ...:=....
144
p
I
CD Mean velocity of flow in pipe:
(Continuity Equolionj
V
\
!
]
I
-rrz
0.286
0.001
l'
1
I
=A
=
lI'V
=
18n
q'.T
4. P'd'-
T
V
A
V
0. 086 5
2·40 -a-
q'.T
3. 06
fL \\",V'
d'
fLpl"
fLp'v"
d-
6.P
0.001 294 ~d
6.P
43·;
6.P
0.000 1 0 ; 8 - - r = 0.000001 16-~
6.P
0.000 000 007 26
6.P
0.000 000 01959
jLpq'
--cJ.5
=
0.000 000
J 59
fLpQ'
0.000 11b ~
jL \PV
fLpR'
IL T(q'.)'S,
d'P'
jUq'.)'S;
d'p
----;;F
For simplified compressible fluid
formvJa, see page 3-22.
'X'V
d'
---;;J.2
G Reynold. number
of flow in pip,!:
CD Head loss and pressure drop
with laminar flow in straight pipe:
Equation 3-3
R, =
i
jLB'
-r
q'.S,
0.233
P'Ql
q'.S,
0.003 8 9
\YlV
qm
fUr
~~
0.0311
Equation 3 . . 2
q
B
Equol;olt 3-5 '
0.01;24
1
t'
Darcy', formula:
H
2g
1
1
Pressure loss due to tlow is t he same In a ,jorlng,
\'ertical, or horizontal rir£. Ilo\\C\'el', the ,lif·
ference in pressure due to the ,1I((crence In head
must be considered in rressure ,irop calculations:
see rage I';:
Equation 3 ... 1
• Bernoulli's Iheo,<!m:
-!
• Head lOiS and pressure drop
in straight pipe:
For laminar flo\\' conditions (R- < lOcal. the friction
factor is a direct mathematical function of the
Reynolds number only, and can he exrressed h~
the formula:/ = b4R,. Substituting this \'alueof
r i.1 the Darcy formula, it can be rewritten:
Equation 3-6
R, =
1
I
~
R, =
j
04 82 ~d;-
6·31 dJl'
R,
Dr
dl'
-.~
-~,
"
12v
I
4 I 9 000
-!cr
i
!,
o
Viscosity equh,alents:
v
=
I"
,
P
Bp
q'.S,
\X'
R,
I
1
22
774 0
35·4 dp,
dl'
00393
0. 02 75
-
IlU3
-.~,-
d P
V
3lbOv~
p,LQ
hr.
W'V
394
vd
Equation 3-4
ilL!'
6.P
0.000 668
6.P
0.000 273
6.P
--;]2
dOP
0.00 .. 9 0
J1.L \\"
d' p'
CRANE
-
-<
Summary of Formulas •
9 Limitations of Darcy formlu!a
Non_compressible fh,w; liquids:
The Darcy formula may be used without restriction
for the flow of water. oil, and other liquids in pipe.
However, when extreme \-elclCities occurring in pipe
cause the downstream pressure to fail to the vapor
pressure of the liquid, cavitation occurs and calculated flow rates are inaccurate.
CompreuibJe flow; gellse!: end vapors:
When pressure drop is less than 10'/C of PI. use p or
V based on either inlet or outlet conditions.
When pressure drop is greater than 10% of p, but
less than 40% of P" use the average of p or \7based on inlet and outlet conditions, or use Equation 3-20_
When pressure drop is greater than 40% of P" use
the rational or empirical formulas given on this
page for compressible flow, or use Equation 3-20
(for theory, see page I-g)_
9 Isothermal flow of gas
=
0.371
JV
=
Empirical formulas for the flow
of water, steam, and gas
Although the rational method (using Darcy's formula) for solving flow problems has been recommended in this paper, some engineers prefer to use
empirical formulas.
Hazen and Williams
formultl far flow of water:
-
Q = 0.442 d'.6' C
F";)
,
_
q. -
n 14-2
140 for new steel pipe
130 for new cast iron pipe
c
! 10
for riveted pipe
Equation 3-10
Spifzglass formula for low pressure gas:
(pressure less than one pound gouge)
Equation 3-ll
I(~ d'
')
V,/L,
(P,,)2 P,~ (P'2)')
The maximum possible velocity of a compressible
fluid in a pipe is equi,-alent to the speed of sound
in the fluid; this is expressed as:
v,
,I k g 144P'
V,
68_1 -.j k P' V
Equation 3-8
V
3 "'6
+
-j-
+ 0.03
d)
Flowing temperature is 60 F.
• Maximum (sonic) velocifY of
compressible fluids in pip.!
"jkgRT
JS. L
l:.h d'
Equation 3-7 a
- (P' ,)2) 5
'If'( (P',)2
f Lm T So
d
v,
355 0
(I
J( ~,4/;) (P',)2;, (P'2)2)
'\l
C
Babcock formula
for steam flow:
q'. =
- . L
P',
V, D + log,
0.1072
(P, -L P2)O-"
where:
c
Weymouth formula
for high pressure gas:
q
w
Eqllof;on 3-9
d'
• Simplifled compressible fl,)w
for long pipe lines
w
continued
Equation 3-1
in pipe lines
W
3·3
CHAPTER 3 - fORMULAS AND NOMOGRAPHS fOR flOW THROUGH VALVES, FITTINGS, AND PIPE
,_8
h
-
2
-"_667
.0 U-
Equation 3-12
,(P,,)2S.-Lm(P' 2)') (52T0)
\j
Panhandle formula' for natural gas
pipe lines 6 to 24-inch diameter
and R, = (5 x 10') to (14 x 10'):
q' h
= 36.8E
U"'·6'82 (
(P',)'
Equation 3-13
Zm (P' 2)2 Y_5'94
where: gas temperature = 60 F
0.6
flow efficiency
1.00 (100%) for brand new pipe without
any bends, elbows, valves. and change
of pipe diameter or elevation
E
0-95 for \'cry good operating conditions
E
0-92 for 8\'erage operating conditions
E
0.85 for unusually unfavorable
operating conditions
S,
E
E
3-4
continued
Summary of Formulcs •
CRANE
CHAPTER 3 - FORMULAS AND NOMOGRAPHS FOR flOW THROUGH VALVES. FITTINGS. AND PIPE
Head 1055 and pressure drop
through valves and flttings
.. Head loss and pressure drop with laminar
flow (R,< 2000) through valves; Darcy's formult!
Head loss through vah'es and fittings is generally
given in terms of resistance coefficient K which
indicates static head loss through a vah'e in terms
of "\'elocity head", or, equivalent length in pipe
diameters Lj D that will cause the same head loss
as the valve.
From Darcy's formula, head loss through a pipe is:
hL
v'
-2g
= f -L
D
Equation 3·5
and head loss through a valve is:
hL =
K v'
therefore:
K
L\ I'd'pQ
( D)
(DL) d'p
I'q
hL
1-470
hL
0.0004 08
j.l::..
D
=
fJ,P
0.000 0557
(L)
l5 dI'V
tJ.P
0.0000228
(L)
I5 d3
tJ.P
0.000 015 93
(L)
1'8
D (j3
tJ.P
0.000 002 84
(L)
I'WV
D ------cJ3
Equarion 3.15
To eliminate needless duplication of formulas, the
following are all given in terms of K. Whenever
necessary, substitute (f LID) for (K).
522 Kq'
--d-'--
KQ'
= 0.002 59 (II
0.001 270~
0.010 21
Kpv' =
0.000 1078
fJ,P
3·62
tJ.P
0.000 008 82 ~
(L)
I'~
D d'
pQ
.. Equivalent length correction for
laminar flow with R, < 1000
Equation 3-18
1000
0.000 0403
tJ.P
Kpq'
=
R,
KB'
-F =
Equation 3·14
(fJ) dp
JJ'I}
0.008 02
( DL) ~
I' \VV'
Equation 3.14
2g
Equotion 3·11
0003 28
0.000 000 0300
Kp V'
KpQ'
0.000 017 99 ~
See pages 2-1 I and A-30. Minimum (LID), ,;, length of
center line of actual ftow path through valve or fitting.
Subscript s refers to equivalent length with R, < 1000.
Subscript t refers to equivalent length with R, > 1000.
.. Discharge of fluid through valves,
fittings, and pipe; Darcy's formula
KpB'
Equation 3-:"
tJ.P
= 0.000 000280
KW'V
d'
tJ.P
0.000000000 60 5
tJ.P =
0.000000001 633
q
K(q'h)' T S.
d' P'
Q
K (q'.)' S;
d' p
W
For compressible flow with hL or .6P greater than approximately 10% of inlet absolute pressure, the denominator
should be multiplied by',". For values of Y, see page A-21 .
•
Pressure drop aMid flow of liquids, with viscosity
similar to waler al 60 F, using flow coefficient
tJ.P
Q
Cv
K
=
(Q
Cv
Y1)2.4
p
Cv ~ tJ.P
Q
6:. 4 =
~ tJ.P ~62-4)
Equation 3-1'
0.043 8pd'
W =
Cv
/tJ.P
-Y-p-
29.9 d'
29.9 d'
oJ jLjD
oJK
157.6Pd'~ ~
,
q.
40700
,
Yd' ~ tJ.P
PI
-S.
K
I 6P P'.
678 Yd' ~ KTI S. =
,
qm
q'
W
L
K
D
T =j
891
d'
(Cv )'
L
74.3
d'
j (Cv )'
/ 6P PII
Yd' \ KTIS,
Equation 3-20
24700 - -
11.30
/6PP'1
Yd' \j KTI S,
0·525
Yd' '\jK'V;
891 d'
(Cv )'
!Jt
Compressible flow:
q.
7.9 0
~
=
~
Yd'
I 6P PI
Yd'
ItJ. ?PI
412
Tv -y--pc-
= 6.87
Tv \ j - r
W=
18 91
16P
Yd' '\j KV
Values of Yare shown on page A-21. For K, Y. and
.6P determination, sec examples on pages 4-13 and 4-14.
I
.~
C R A.N E
3-5
CHAPTER J - fORMULAS AND NOMOGRAPHS FOR flOW THROUGH VALVES, FITTINGS, AND PIPE
----~--------------
.==t
Summary of Formulas -
!
•
Flow through nozzles Clnd orifices
(h L and [o.P measured acrass flange taps)
Liquid:
q
•
concluded
Specific gravity of liquids
Any liquid:
Equation 3-21
s
AC ..; 2g hL
=
p
p
Equo,ion 3·25
any liquid at 60 F,
)
( unless otherwise specified
(water at 60 F)
q
Equation 3-26
S (60 F/60 F)
Q
w
W'
=
140
130 + Deg Baume
S (60 F/60 F) =
1891 d'oC.,f[o.Pp
Values of C are shown on page A-20
Cornprnsible
Equa/ion 3-27
Liquids lighter than water:
0.0438d"oC"~:;Z = 0·P5d'oC;/[o.Pp
157.6d"oCYhLf~
131.5 +DegAPl
Equation 3-28
liquids heavier than water:
ffuid~:
145
S (60 F /60 F) =
Deg Baume
145
CD Speciflc gravity of gases
q'm
S,
R (air)
53· 3
---=
R (gas)
R (gas)
S.
M (gas)
M (air)
~.
q'
Equation 3·29
q'
• P'V.
w
p
w
R
M (gas)
29
General gas laws for perfect gases
w. RT
w.
V.
Equation 3·30
p'
144 P'
Efr
RT
Equation 3-37
1544
AT
Equation 3-33
Values of C are shown on page A-20
Values of Yare shown on page A-21
n. M RT
P'V.
=
n. 1544T
w.
= M
1544
T
Eq:.raticn 3·34
• Equivalents of head lots
and pressure drop
144 [o.P
p
p
=
w.
p'M
V. = 1544 T
P'M
10.72 T
2.70
P'S,
T
where:
[0.1'"
number of mols of a gas
•
• Changes in equivalent le'ngth
LID required 10 compensate
for different pipe I. D.
Equation 3·24
(see page A-3D)
Subscript a refers to pipe in which valve will be installed.
Subscript b refers to pipe for ,I,'hich the equival~nt length
L/ D was established.
Hydraulic radius'
cross sectional flow area
wetted perimeter
Equivalent diameter relationship:
D = 4RH
d = 48R H
'See page 1-4 for limitations.
Equation 3-35
3-6
CHAPTER 3-FORMUlAS AND NOMOGRAPHS FOR FLOW THROUGH VAlves, FITTINGS, AND PIPE
CRANE
Velocity of Liquids in Pipe
The mean velocity of any flowing liquid can be calculated
from the following formula, or, from the nomograph on the
opposite page. The nomograph is a graphical solution
of the formula.
,
l
(For values of d', see pages B-16 to B-18)
The pressure drop per 100 feet and the velocity in Schedule 40 pipe, for water at 60 F, have been calculated for
commonly used flow rates for pipe sizes of Ys to 24-inch;
these values are tabulated on page B-14.
1
w
d
p
Qq
v
Example 1
Example 2
Given: No. J Fuel Oil at 60 F flows through a 2inch Schedule 40 pipe at the rate of 45,000 pounds
per hour.
Given: Maximum flow rate of a liquid will be )00
gallons per minute with maximum velocity limited
to 12 feet per second through Schedule 40 pipe.
Find: The rate of flow in gallons per minute and
the mean velocity in the pipe.
Find: The smallest suitable pipe size and the
velocity through the pipe.
Solution:
Solution:
1
Connect
I
2.
3·
.............. page A-7
p
1.
I
W= 45 000
= 100
IQ
L--
I
Read
I P = 56 .02 I Q = 100
I 2' Sched 40 V = 10
I
Read
Connect
1.
Q
I
Q =3 00
Boiler Feed ....................... 8
Pump Suction and Drain Lines .... 4
General Service .................. 4
City.. . . . . . . . . . . . . . . . . . . . . . . . . ..
= 12
I 372' Sched 40
Reasonable Velocities
For the Flow of Water through Pipe
Service Condition
V
d = 3.2
3 1/ 2' Schedule 40 pipe suitable
2.
3·
300
Reasonable Velocity
to 15
to 7
to 10
to 7
feet
feet
feet
feet
per
per
per
per
second
second
second
second
I v = 10
CRANE
3·7
CHAPTER 3·- FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, FITIINGS, AND PIPE
Velocity of Liquids in Pipe
(continued)
d
Q
tv
10000
::::::I~
3IlOO
=~
:::::II
q
40000
30000
GOoo
4000
3000
:::3'
;:::::::11
l
:=::11
1000
1\4
:::='II
L5
100
:;
:.:
c
~'600
'"
~
'"
~
:::J
,,400
'"
"-
~3J0
~
100
0;
'"
"-
~
c
'iii'" 200
~
:::3
0;
a,
~
=c
==t
~
c
=c
~
:::JI
i
v
Q
4"::::.':31
~
~
<!J
~
~
u
c
~
c
='"
>-
~.
'"
c
",'
~
2"-
~
~
or
:.::::1
-
~
"~
~
~
~
==t
20
~
'"I
or
0- 40
I
.08 ""
.06
;:,..
10
.04
.~
.03
~
.02
2
80
60
4J
II
Zl
IS
10
8
6
4
3
2
~
='"
~
c
'"
'"
~
~
:;;
C.
.4
.3
.2
c.
"-
"-
'"
'"
:;
c
."
~
'"
>
.,
'"
2.S =
~
.=
c
,;
=
't5
~
2\2
c
0;
Q;
1
.8
.6
.::
",.
3
c.
"-
~
3.5
'"E
co
0;
~
~
N
5
c
E
.•01
.008
'::=JJ
~
.003
.8
.S
r:<J
'~I
.8
.6
.S
.3
F,
'"
~
.0
~
(.)
:;;
"~
=c
=
Q
"-
.=
,::
8
.1
10
10
12
14
18
Zl
20
.002
0
c
'"
0
:::;
=
I
'"
'"
I
Q,
16
.004
"-
~
c
'":;l
6
...~
3
~
D
~
~
~
z'"
~
~
='"
'"
'"
0;
I
2
9
<~
!
112
::=1'
=::::J
!,
P
24
25
~.
I
I
1
I
•
~"~"J,\::';::\ ::-;;"'!',i·7t~Y::'"i.:t".
- ' - -.. ~ •• ,.~ .... -"~"
,-.,.:<:;.",,~ltWI'_J,.("""'-<';'''''':-'
_ _-""..._ _ _ _ ~I.-~ •. ,
",<._"","",,,",,,,,.,,-,",,~",
~"-'="""
,--""",
-~"~"'"~---'''-''""--~---
__
"''''.'''''''''-<''''
"",,"~_"'<J."""""''''''''''''''_~
____ ' ___ '__
'_'f'
~~
Co)
Reynolds number may be calculated from the formula
below, or, from the nomograph on the opposite page.
The nomograph is a graphical solution of the formula.
R, =
22 700
~:
50.6
-~
co
!
= 6.31
(For values of d. see p"gcs B-16 to B-18)
.."
...
The friction factor for clean steel and wrought iron pipe
can be obtained from the chart in the center of the nomograph. Friction factors for other types of pipe can be
determined by using the calculated Reynolds number
and referring to pages A-23 and A-24.
I'
q.Q
!i>
-.
o-.
'"..
"Y1
0
~
...
m
n
....
:J
I
Il
..,..,
...
"'"
-
('I)
o -<
d
":J
\\7
0'
2...
Q..
p
(") '"
ti"
Q
:J
VI
J
-po
z
c
3
0'"
to
('I)..
C1i
Example 1
..... .a
<
c:
<; -.
Given: Water at 200 F flows through 4-inch Schedule
40 steel pipe at a rate of 415 gallons per minute.
Given: Fuel Oil No. 3 at 60 F flows through 2-inch
Schedule 40 steel pipe at a rate of 100 gallons per minute.
Find: The /low rate in pounds per hour, the Reynolds
number, and the friction factor.
Find: The flow rate in pounds per hour, the Reynolds
number, and the friction factor.
CO
Solution:
Solution:
o...
p
60. 107
2.
}.t
0.3 0
4·
Q = 41 5
W = 200 000
Index
5·
6.
R, =
1 000
I
1.
p
. page A-3
2.
}.t
I
Cooo'"
J.
.. page A-6
=
60. 10 7
}.t
000
I ~or~~tally
Ij
0, - 4.03
56 .02
.... page A-7
........... page A-3
9·4
= 0.017
I
Connect
3·
Q = 100
4·
W = 45 000
).
Index
6.
...
o
R, =
I
4
Read
IW
I 2" Schcd 40 I
I = 9·4 I R,
I
p
= 5602
}.t
600
I tohorizontally
I
d = 2.07
f
Q..
c: .."
o::r ~
-
R.;"~
I W' = 200 000
I 4" Schcd 40 I Index
I = 0·30 IR, = 1 000 000
p
o
Cl'"
:J r...
_.
Example 2
r.
......
<;
~
c
e;~
>
6
Z
g
g
~
~
'"
0
'"
~
0
::::
...
:r
0
C
Q
:r
<
~
<
m
!"
~
::;
~
Z
:J
~
"0
>
Z
"0
('I)
"
:!
~
m
= 45000
Index
= 14600
n
0.03
>
".
=
Z
m
(
b n n 0 UII UII
'I
r;
II II
UUtl U0 II UUnun n tl u uu u uHH
'I
W
10 000
8000
6000
Internal Pipe
Diameter, Inches
Index
_74
.21
1111r--
Re
800
600
3/8~.5
ID
Co
'"<=
"C
;;;
~
0
Co
a..
';;
.,.,
"-
'"<=
"C
.0
'"
~
OJ>
'-'
~
0
=
f-
o
"- .1
';;
., .08 ;;; .06 --
'" .04
I
~.
0
"-
';;
2
'"
~
'"
o
<=
.,>-
~
f--
.8
.9
1.0
..
P
-
;:;.
:::-.
0
1/2
-\1 \"
A\·,
.01
.02
~
<=
'-'
~"
-
2
Co
a:
.,
';;
.,
ro
V>
0
0;;
n;
'"<=
~
...ca..
0
a..
-
,<=
50
.::';;;
.,<=
0
<=
~
I
';;;
z
7
~
'<
(D
C
::J
!I)
CI)
0
:J
D..
0
c:
-
to
'"
::J"
I
...
Q.
~
0
::J
3!
.01
.008
"
CI)
12
14
.006
.004
.003
~
c
);
::J
,.'"
0
0
D..
z
Z
en
0
Z
Q
C
3:
0
~
.."
3
0>
(D
0
0-
...
,..
-.
0
..c
c:
-.
:l:
~
'"
~
5
~
~
:l:
'"
0
c
Q
:l:
D..
-n
,.<
0
.'"
~
<
m
~
~
Z
Q
,.z
!"
c
:!!
.."
m
18
20
300
.002
500-::1
600
.. -."... ~--.."",>"......,..,"""".,..."""'-..."..,.,".--.• '~--..•-",.. ~~-.-",-.•-.-.---.,...,~,.
Co)
•
24
-0
..,"",~.,.,--"""!"",~,,
..• ~
(D
- ..,VI
:.E
....
0
bQ
<=
E
.2
::I
:::';
::I
'C
n;
.,EO
n
0
Co
E
N
Factor for Clean
Steel and Vlrought I ron Pipe
;0
'"
.,
-
u
;;;
';;
f . Friction
~
Co
a::
0
(")
.c
2.5 ':-
=...
.O~
...
c
.:. 211
::tI
0
2.c:
~
"C
,-.04
I
c;
n
-..
a>
;;
,- "'t\.
.03
"f"
=~
.,<=
'\'\\
a>
'"
0
,
-...
65
.,
-.
-n
0
1.5
-
,
I~...
"1"1
::J
I
3/4
'--
.4
=-
.
f= c:::::,f-
2
.6
_
-<!
f-"
10
6
4
~
"" L
.!
"" .03
.02
_\
~
"C
',-1
-~
.0(,
'" 100 :--"0
~ 60
~ 40 -.
~ 200
<= 10
., 60
~
40 -z
20
::
~
z
m
~~~P'~-i-=-= il$
200
400 ;;
0
300 ::
:3
ID
'":Ii-
.7
1 0110
V)
W
.6
2000
<=
H-~~,.
n
d
J.l
4000
3000
"C
'iia
.. ...
-.'"
~""--"'''''.'''''''''''"'.-"''''-.."
,
~,".,
- .....,··,~.....--...~ ........ ___ ~""~_,,~""··_"'-"" ..C"'""'~'~A~.~,~
~_,,_,'"-'-',".(~""'_k'"".'_'_~""",' •.-. -<"~"'"'-'~~~.""'~."~·'-"'';''''''''''''''''_.''''''''''''-.C''''''-'''''''''''''''~_~'''''--''''''''''",b_,~ ..• ,,,,;,,,,,,.., .... ,~~_,,~ ... ~ ..... ,~ __
.........."".~~....-'.,.,_.,,-"'W._,.... ,~ ......,.,..~,.., ..........~, .,,~.'"~''''''''' ,
Co>
The pressure drop of flowing liquids can be
calculated from the Darcy formula that follows, or, from the nomograph on the opposite
page. The nomograph is a graphical solution
of the formula.
6. P 100
6.P100
0. 12 9";
f pv'
-d
4350
fpq~
de,
f W'
fpQ'
0.0216 ~-
0.000 336 ~
(For values of d and d', see pages 8-16 to 8-18)
q
12
Q
I
P
c.P,O<l
d
-
o
Example 1
Given: Water at 200 F flows through 4-inch Schedule 40
new steel pipe at a rate of 200,000 pounds per hour.
Find: The pressure drop per 100 feet of pipe.
Solution:
1;
p
60.1 0 7
· ............... , .. ,page A-6
2.
P,
0.)0
· ................... page A-3
J.
f
0.017
· ...... , .. Example I, page 3-8
4·
Q
415
5·
...
"til
III
· ...... , .. Exarnple I. page 3,8
- - - , _.._ - - Connect
Read
-T::-~-I-~--60.I07
6.
Index
7·
Index 2
I
I
Q = 4I 5
1
4" Sched 4~
Index
Index
6.P 1oo
I
2
3.6
=
.....
..
_.
w
III
I
c:
(5
III
c
C
'">
0
"tl
!<
;:
z
0
z
::J
0
V-
,.,0
-.
a...
r-.
::lI
'"'"
n"
c:
3:
0
.
".
..
..CD
Example 2
Given: No. 3 Fuel Oil at 60 F flows through a 2-inch
Schedule 40 pipe at a velocity of 10 feet per second.
When flow rate is given in pounds per hour (W), use the
following equation to convert to gallons per minute (Q),
or use the nomograph on the preceding page.
W
Q = 8,02;;
For Reynolds number less than 2000, flow is considered
laminar and the nomograph on page )-1) should be used.
The pressure drop per 100 feet and the vc!ocity in
Schedule 40 pipe, for water at 60 F, have been calculated
for commonly use,J flow rates for pipc sizes of Ys to
24-inch; these values are tafJulated on page B-14.
Find:· The pressure drop per 100 feet of pipe.
P
2.
Q
J.
f
4·
).
6.
-I
...C-
c:
c:
iD
Solution:
1.
0
-::J
56 .02
100
0.0)0
-
· ..... , ..... , .. , .... page A-7
<:onneet
1
f
1
0.030
Q = 100
Index 2
1
2" Sched 40
E
0
:Ii
· ....... , . Example 2. page 3-H
56.02
Index I
p =
."
· . ,Example I. Step 3; page 3-6
R~Il~
'I
I ;;-(l:~
--Index-
i 6.P:- o---: --:--10
1
.-- - - - - - - - - - - ----- - - -
..
:l!
I
m
I
2
~
n
:IV
:to
Z
m
n H
nIt
• ~If w.
ft • ~'1
D
U····
t n n n " rt ft U· nftJt-R--n-----u'---11ft ff~ U
rt n
r
~ U ~ v.
u U
• ~ u• u w U
lU'
n
n"
tt~1
U
\
!
q
n
Q
:>:I
~r"
Index 2
Z
30
20
»
p
r"
10000
--a 000
d
6000
.06
.OB.1
·"1
---00
J
---\ 2000
,+''
.05
S
w
800
~
600
w
.04
Q.
20
16
9
u..
'"
200
-:;
2f)
2
~
60
If)
I
'"
~
'"
b
e
~
roc
c
e'"
",.
:;;;
c
B"
""
'"
~
"'"
I
'-
~
"
~
.03
Q.
.8
.7
.6
.5
.04~ 2O~
.01
.=
50
'"
E
'"
3/8
1"
.01t 4 .;:
,,' _ '"
.ooa
.006
3_
0."-
r
-=
u
w
m
0
...0
3:
c::
);
....
~
"
0-
<n
'U
:;;
Q.
::lI
~
.....
~
c
"o
..... ..ac
"0 a..
"-
~
w
'"
""
:=:
Le-
::I
,....
tD
:::I
c
.e::
:;;
Q.
III
:;
~
~
'"
a.
k
I:
II
,
>
z
0
z
0
3:
0
C>
f
,f
I
L
~
>
"::I:
V>
0
'"
0
~
-0
:c
m
m
'"
~
!
."
C>
t
0
i:
:E
C>
0:
<
>
<
~
z
'>z"
:!!
"
m
t
!
I
i·
f
t.
1.
t
~,~
ao
100
0
i~
I.
e
c
0
40
50
60
I
IT
-
8
!I
'"0c:
::I
((
<J
V>
f
...
..,
-I
C
w
~
l
~
m
0
Q.
e
e
I
~40
I~'"
0
.4
118
en
en
C
c
"0
0-
~
100
80
'-.
C>~
-:;
w:: .2
0
:;;
Q.
u..
0
=u"
a::
5
:;:;
u
u
7 .::
6 .,;
~ .4
~•• 3
c
.02
="
-'=
u
B .=
400
300
.03 ~
;;
55 ~
1O~
,
....fI)
.::
12
12
10
.."
-I
f-
Index 1
m
/:"[>10.
i
['
!
.004 -=!.• 003
1
I
'"
Co)
I
1 0' "':<''-.1
•• _.~_.~ .".'.
..-".",..,~'"
.• "a~~""_>r;:JI"-,...,.J<,~'"""...."..._.-.'_"',',"'_' :,.',,....,~ •• , •
,,"w,._~~.,*~
.• ,_.~ •.. ~~.~~, -~.,.'''''~.".~'.."_,,.,~¥ .. _.' __ ~,,_''''''~~,,~~
!
~.
i
/ 3-12 /
CRANE
CHAPTER 3-fORMUlAS AND NOMOGRAPHS fOR flOW THROUGH VALVES, FITTINGS, AND PIPE
~~-------~----------------------~~~~~--~~~
Pressure Drop in liquid lines for Laminar Flow
Pressure drop can be calculated from the formula below,
or, from the nomograph on the opposite page, only when
the flow is laminar. The nomograph is a graphical
solution of the formula_
Flow is considered to be laminar at Reynolds number of
2000 or less; therefore, before using the formula or nomograph, determine the Reynolds number from the formula on page 3-2 or the nomograph on page 3-9.
_
6.PIOO -
)LV
0.0668 d 2
_
-
)Lq
12.25 d'
~
_
)LQ
- 0.02,3
d'
(For values of d' and d" see pages 8-16 to 8-18)
Q
q
d
Example 1
Example 2
Given: SAE )0 Lube Oil at 60 F flows through a
6-inch Schedule 40 steel pipe at a rate of 500 gallons per minute.
Given: SAE 10 Lube Oil at 60 F flows in a 3-inch
Schedule 40 pipe at a velocity of 5 feet per second.
Find: The pressure drop per 100 feet of pipe.
Solution:
Solution:
1.
P
56.02
2.
)L
45 0
..... . page A-3
J.
R,
55 0
.. ' . page 3-9
4·
Since R,< 2000, the flow is laminar and the
nomograph on the opposite page may be
used.
r=
5·
6.
!
I
Ii
I
Find: The flow rate in gallons per minute and the
pressure drop per 100 feet of pipe.
)L
=
......... page A-7
Index
0
Q
p
2.
Q
J.
)L
4·
R,
5·
54. 6 4
115
=
500
6' Sched 40
... page 3-7
.... page A-3
1100
............ page 3-9
Since R, < 2000, the flow is laminar and the
nomograph on the opposite page may be
used.
Connect
Index
I 6.P100 =
............. page A-7
95
Read
Connect
45
l.
6.
4.5
7·
p.
=
95
Index
Q
Read
=
1 15
3' Sched 40
I
Index
! 6.P100 =
3.41
~ ...
CRANE
CHAPTER 3 - ~ORMULAS AND NOMOGRAPHS FO~ flOW THROUGH VALVES, FITTINGS. AND PIPE
,;::::3
Pressure Drop in Liquid lines for laminar Flow
~~
(continued)
{ 3·13
q
Index
4
d
3
2
L:::.P,oo
1.5
1.0
.8
.6
.5
.4
.3
5
.2 .
4
.15
3ll
3
'""'
c.
'"
'"
'"
c.
'"
0-
'"
0
u
"'
::-
.,
~
::::::3
·0
"'
«
~
::::=3
::t
:=:t
",'
<.>
:?:
::=:D
::::=1_
"'
='"
'"'
-=
. '"
';;
'"
'"E
0'"
0;
'"
~
.10
~
'"
=
2
-=
.08
~
u
,;
.,
I =
.r:
'"
u
3/4 '"
';;
~
N
'"
1/2 -'"
~
3/8 z;;
u
'";;;
c.
~
.03
-='"
u
~
~
c..:>
.02
0
'"
",'
"~
.,
m
a:
.oJ
'"'"
.OOB
'"c'";;;
~
c.
'"
-c
c
~
0
0-
'"
.,
~
u..
=
~
-=
;;;
';;
e
U-
~
'"
'"
~
c.
c.
0
~
~
"''"
~
I
1/4
g
r:t;
<J
==:B
2
.002
1.5
~.
~.
0
0-
=::::t
:::::3
-c
c
-:;;
.04 u..
Il1 c.
0III =
~
u
~
.06
.05
'"
:;
.r:
-=~
1.0
.B
.7
.6
.5
.
1
.0015
.5.4
3. j:.. .0006
2!·000S
• _ .0004
.4
.IS}
.=
.3
.1- J
.2
001
.0008
.0003
"',
;-:'
3 -14
CRANE
CHAPT€R 3 - fORMULAS AND NOMOGRAPHS fOR FLOW THROUGH VALVES, fITTINGS, AND PIPE
Flow of Liquids Through Nozzles and Orifices
Example 2
The flow of liquids through nozzles and
orifices can be determined from the following formula, or, from the nomograph
on the opposite page. The nomograph is
a graphical solution of the formula.
q
'2 e ....
d" e '\jp
if':,p
= 0.043 8 do
Y}
II. = 0.)25 '0
Q
}-Icad loss or pressure drop is
measured across the flange taps.
CqQ
Cil'cn,' The flow of water, at 60 F through a 6-inch
Schedule 40 pipe. is to be restricted to 225 gpm by
means of a square edged orillce, across which there
will be a differential heaJ of 4 feet of water.
Find: The size of the orifice opening.
Solution:
I.
P
62·371
... . page :\..:6
2.
J.L
1.1
. . rage :\-3
J. Re
105000
(1.05 X 10')
.. page J-C)
4· Assume a ratio of do/d" say 0.50
5· d,
6.06;
rage B·16
6. do
0.50 d,
(0.;0 X 6.065)
).033
7.
e 0.624
' ,page A·20
I
do p
Read
Connect
8.
9·
Index
I
I Q
Index
do
= 22;
=
3"
An orifice diameter of 3 inches will be
satisfactorv, since this is reasonably close
to the assumed value used in Step 6~
1 I.
If the value of do determined from the nomograph is smaller than the assumed value
used in Step 6, repeat Steps 6 to 10 inclusive, using
reduced assumed values for do until it is in reasonable agreement with the value determined in Step 9.
10.
Example 1
Example 3
Given' A differential pressure of 2.5 psi is measured across the flange taps of a 2.000-inch LO.
nozzle assembled in a 3-inch Schedule 80 steel pipe
carrying water at 60 F.
Given,' A differential pressure of 0.; psi is meas·
ured across flange taps of a I.ooo-inch 1.0. square
edged orince assembled in I !:l'-inch Schedule 80
steel pipe carrying S:'\E 30 lubricating oil at 60 F.
Find: The flow rate in cubic feet per second.
Solution:
............. page 1\-7
I.
56 .02
P
. I !,~' Sched 80 pipe; rage 8-16
2.
d,
1.27 8
1.278) = 0.7 8 3
3· do/d, = (1.000
....
susrect fiow is laminar since
0
J.L
45
4·
Find. The flow rate in gallons per minute.
Solution:
I.
2.
3·
4·
,,
1
l
j
I
I
~
5·
6.
7·
8,
2.900
.... 3" Sched 80 pipe; page B-17
= (2.000 -7- 2.900) = 0.69
1 .07
.. turbulent flow assumed; page A-20
......... page 1\-6
onnect
I
Read
= 62,371
g
= 1.07
I, do = 2.000
I
I
I
hL = 5. 8
5
I
p
Ie
Index
Q = 200
Calculate R" based on I.O. of pipe (2.900").
. ... page 1\-3
1.1
Jl
9·
R,
10.
200000
". page 3-9
I I.
e 1.07 correct for R, = 200 000; page 1\-20
12.
When the e factor assumed in Step 3 is not
in agreement with page A-20, for the Reynolds number hased on the calculated flow, the
factor must be adjusteJ until reasonable agreement
is reached by repeating Steps 3 to 11 inclusive.
5·
e
\'iscosity is high; rage A-3
, ... assumed; page A·20
1.05
Connect
6.
f':,P = 0·5
hL = 1.3 I,
7·
Index
8.
9.
10.
1 I.
!
I
p
e
=
56 .02
I
I
= 1. 0 5 I
do = 1.0 I,
i
Read
hL =
I.)
Index
q
I
!i
,
= 0.052'
Calculate R, based on 1.0. of pipe (1.278") .
R, = 115
......... '" . page 3-9
= 1.0')
.correct for R, = 110; page A-20
e
When the e factor assumed in Step 5 is not
in agreement with page A-20, for the Reyn·
olds number based on the calculated flow, it must
be adjusted until reasonable agreement is reachd
by repeating Steps 5 to 11 inclusive.
12.
CRANE
3-15
C:HAPTER 3 - fORMULAS AND NOMOGRAPHS FOR HOW THROUGH VALVES, fITTINGS, AND PIPE
-------
Flow of liquids Through Nozzles and Orifices
(continued)
do
hL
b.P
C
Index
q
p
24
Q
alOO
LIl
lOOO
800
600
400
300
200
10
~
~
""
u
'"
~
.=
N
N
:=ro
~
=
'";;;
~
200 .....
150 -;;
'"
~
"C
0=
~
0
100
c
80 .,;
c...
~
~
Cl
e.>
~
'"
:::"'
Ii
$
"'
60 -'
"C
ro
50 e.>
40
:c
"'"
'"
0
0
Z
'";;;
'"ro
0=
'"u
-~
-
0
.E
::;;
~
u
~
10
8
U
~
~
'-'
~
'"
0
"-
~
0
""
I-
.ero
1.0
.8
.6
""
.4
0
I
.3
.:..,
20
<J
15
.2
10
6
.1
.08
.06
4
.04
.03
3
.02
Co)
""
.01
.008
.006
.5
.4
~
'"ro
~
0
""u
.=
~
.0
.004
.003
.002
.001
~
~
ro
u
~
~
=
'"
-;;
~
,;
.=
.....
;;:;
0
=
a;
.....
~
0=
~
'-'
-,
8
.6
~
0
"-
~i
a;
.....
~
.;
--
'0
0
.....
u
.0
~
'-'
u
0
-;;
.e
~
'"
~
~
0
"~
~
E
ro
?:;-
Cl
==
,;
.=
.....
ro
E
~
~
-;;
.ero
""
0>
Cl
~
CD
~
0
~
'"
Q,
><.,.."."k-'",-'·""'>'.' "
...
0.
The mean velocity of compressible fluids in pipe can be
computed by means of the following formula, or, by using
the nomograph on the opposite page. The nomograph
is a graphical solution of the formula.
V = 3. 0 6.'!1 V
a'
j
1.:06
n'I~Ul
W
(For values of d', see pages 8-16, to 8-18)
i
I
I
1
'1
1
I
I
I
1
Example 1
Given: Steam at 600 pounds per square inch gauge
and 850 F is to flow through a Schedule 80 pipe at a
rate of 30,000 pounds per hour with the velocity limited
to 8,000 feet per minute.
Find: The suitable pipe size and the velocity through
the pipe.
Solulion:
Connect
l
I.
I
2.
,j
1
I
J.
4·
5·
6.
,
-~
II
1
4
Read
F
vertically to
600
psig
horizontally to
=
I.2Z
850
V
Index
---_
..
W
V
4" Schedule
___Index
0_._.
psig
600
V
=
=
=
8000
80
pipe is suitable.
I. 22
Index
30000
d
=
14" Sched 80 pipe 1V =
:1:
,....m
(.>
I
<
,.0
-
,.'"z
!2..
0
!:!.
Example 2
'<
Given: Air at 400 pounds per square inch gauge and 60 F
flows through a I Y2-inch Schedule 40 pipe at the rate of
144,000 cubic feet per hour at standard conditions
(14.7 psia and 60 F).
Find: The flow rate in pounds per hour and the velocity
in feet per minute.
I.
W
2.
P
11 000, using So
2.16
......... page 8-2
1.0
.............
. .... page A-IO
Re~d
Connect
J.
4·
0
n
0
3
...
...!a.
"0
CD
0-
Solution:
3.7
7600
,.n...
u
d' p
p
=
2.16
,--_In_d_cx
W
I
=
11000
Y2" Sched
40
CI>
"lI'I
c
c..
In
Index.
::J
V = 6 000
-ij'
.."
CI>
3::
c:
;;:
0
z
0
3::
0
",.,....
x
'"
,.0
0
~
...,.:x~
0
c
:x
"
,.<
:;:
m
yo
~
~
z
",.
yo
.___._______
Condition
of
Steam
__. ___~..~lSonable V~.~~it~~s for."!0w._oL~!eam Throu{jh Pip_e_____._____...__ ...
Pressure
Service
Reasonable Velocity
({')
P,ig
(V)
==~=~~<:<:t-J:-~-~':~~~~t-(~-~
Heating (short lines)
I 4000 t;;""6-00()--I
25 and up
I p~;:h,;;;.-;;-;;~.;iP;:,;cnt, pro~~~pi~~-~;,---r--6.. 0()0 to 10000
Boiler and turbine leads, etc.
---[--7000t; 20 000-"Superheated
200 and UD
T
.~-------~-~--.
Saturated
z0
...
:;;
"'
o to 25
n
'"»
z
m
a ~ nI( D nU U II
U II U U U U U II U II U U U II U U U U U U U U~' \
t
w
o
d
v
Specific Volume of Steam
'">
.8
.9
Index
p
=r=~;;- .03
Z
",/
m
LO
~~
~~~ct~~~~
I-~-r--=---.,.-''''-~-;;o~
---~~-------~
~\\-I'"U?,e:
-1"-r~
=:p~o: \16u~os-~~_ - - - - - ~
==-,..
____ '___._- _
____
--,7""'~~
~
----{ --'::::::~"'j;9f-" - 1---"' _ _
_-=~
~
__
~
.05
0__ ____- . _==
•10
8
200
-----7·~r ,;.--f<'=----:.o~~ -- ... --=-- -~-'" ~6
.,.-::~
:;;:=--= ~ 5 - - - 2
- v---:
.....-",C
__
~r-,?,cl_k:::::::- ~
---
--
-c.
t==I='
' F/C::::;;-C
~~ ;;::. -;;:.~ -.:::7'. = _-=;H ~ ~
-=-~ --\----r~~g;· --~--=-- . . - .-:--- --- - ~
"~-;:~t:-"L~~()"'~--~------- -"~---
p..-=-
_ _ ____ ___
t"'_ _
C-:.:.>'t ",_
==t=:::-t - -::;:7'~f;9.. °
=± ---. -t··· -v-- 1~
u
~
i -.4
'-'
"--
0"
u
~
--=-
~~?:
--'(1--/ .~. ~5:;=--
r===!=- ----\/-
~
--
-'"
~·t-=
=-~
'0
0
LL
t=
-;.,..0 l--""?'t=:"sQ;:~~
I--~ - 2· -.5
=----;;; - - -fLO ~o=~
---"'r-=
:;; =- •6
=-:
=:9~09-~--- L5~
=------=:----. - - - ~-:..,...-- - ,o::;?,-" - :.,.;-___ =f.-=- E u>
150
3 :;;-:::-.3 ,;;
~='4.v~;::tc"~~ ;'~T';;c~ :-~~~~~
~~-~:~J-- ~ , , ; 0 0 . - - . - - "
-
_ -.S
~
:;;
'"c
-c
~
0
"-
==
1 ;;; -~~1.0 1::'
';;;
.,c
'0
::=:-,8:; _
- ~~~- ~~o
_
__ 1 /
.!:."
.,
=;::::0-
c ~
./
.5 v ,-2
___
I
Q,
7Lj-7.0::C'~'
----\;;
0=--
f=,:t~~"!: ~~;t =::- .. ;L=-~~~= ::=
~:::;:z::':--::'::: 1=--=-- ~=
i==
F~
I---T/- --r--:.L--
---
i--
--1----
.3
4
.215
400
t -
500
600
700
aDO
V
~
c
:s
60
40
~ 30
Q;
.,
LL
0
20
10
6
100 :;;
0"
80
'"
-c
c
60
50
40
'"
'"'" 2~
-c
~
c
.6
15
.=!
",I.e.
'03
.=! .2
':;
.,
>
I
.e.,
20
.e
'"
.1
'"
"'"
900
1000
II 00
~.
3
3.5
..
r::::
'"
I
10
~
i±
1200 .10 --10
""-=:====
;.g:::t-:=
----=EJcc=
.- - :::;;'
--.
=--a".
-f--'
-*"'..=1=
1"-: ---"''-
8
9
¢p~
it'vJ...I- ~k ~I-­
~i-- k:- t-::[., !;; I-c-f- --I~~
20
ok
.X
"<
-
j...-
"::I0
::-.
::I
C
flI
~
[
t!f:
n
0
3
...
-.
C'"
"C
i
(!)
til
til
~
i
(!)
.."
}
,"
!:.
a..
J
til
::J
_.
."
"C
(!)
~
::;
::!
z
Cl
,.
!"
Z
0
~
:;;
m
.
1--
1--1-
_+=(::::
Schedule Number
!
i:
I
I
t
t
}
I:
25
30 'i> 'b0 <2> '<2"~b ~~
•Ii
[
p
0
~
If
Ii~;
,-\-::
?o" p-F-
~-
~F'"
2
Temperature, in Degrees Fahrenheit
1-
k-p.-I-e::
15 -t--".f-'1I--+-r-.':l-~_
1.5
-
I
~
0
A~
f--
6 ,--
Cl
EO
.,
<
1-=;]:'1= - =.=
__ _
c
'"
'"
~;--=;,:~
E
'0
E
m
. I=:~"l-_-_
~",j
_
0"
'"'"
=
f-
!-
2.5
=
-i=
c
.,- 4.5i -EE
c : 3.:t;Z;
EI_ _L2i'
-o-
'"
c
-0
1
£, .4
u
.=
"-
~
~
c
':;
0
0
=
f-
~
0
"-
..,
=
----_.
/
300
0
:<:
".
:!l
1.6 . .
--- \'1>"\
.1.e
l
I.B =t=--~--. .i~\le ~
- -,,~=
2
- F--~-;::::
t=~~·t\~_
5
-==f::,'-+-f--+-=:1---S
2)0
;;
.e
Cl
:;;;
,6i:= ,..,
b:+:~~-~t=:~~{~:/~7!:::;~~~':P'~;::' -1--=___.4_1~~ -2.5
__
n
x
--- ~--~-=---=
=+:::-=t-·=::'-'0S-1,
.OS
__
lU
~
:::<~=-
1.4I-'~~~~
.06
15
f!
,\;~
1.2
~120
I
w
'I
t
I'
¥
!
!
I
'·· .. "-..,...."...., ..~""':"'-"""'''~-''-''r .. -'''~..,...'"''''''''' .. _.,.,....''·_~' .
-_ _ _ _ _ _ _
. ,...... ~;:L:::..!-~::>I7.;;:';'l:"':!2/:.w.w'm'1..c:;:u:~"'_""_.~.:J,;;;_.:
"-'.l':m'.$~Tt-"t4~-.:.;Wt"i.~{I'l'it1."~~$'.mcV$"""ITW'~~:f:l~''fJ,":,'··
··::::,:',;r.7:_..,,::>·;:;-,~g,[
<"..;~~.~.
____~o:
.•
._<_".~" .~ ,,,,_,""£--~'., '"~"" "'.~''''''''"'''~'.,,,u
__ I-., .. ,.~.->. '" __ ""."-' """~.:...:.,~ __ ..... ,-"'~'";~...."'.... _, "',"H."'""""'''''''''----'''''''' ,"""~_~_ ....... ~., __ .................,......... ..,_~_,~-_o........ __ '"' ...........~.....__ •.__..... _ _ . _....__ "...._·_·~......-.----- -.-~. ~---"
j
j
w
D:I
I!
I
t
The Reynolds number may be determined from the formula below or from the nomograph on the opposite page.
The nomograph is a graphical solution of the formula.
w
p.
d
The friction factor ior ciean steel and wrought iron pipe
can be obtained from the chart in the center of the nomograph. Friction factors for other types of pipe can be
determined by using the calculated Reynolds number
and referring to pages A-2 3 and A-24.
;
,I
W
R,
0.4 82
6.31 dp.
'l
2.
jJ.
f
...
0
0
tll
l~ead
Connect
I
),
1
69000, using So = 0.75 .... page B-2
0.011 .... ".""" .... ,." .. ,.pageA-5
------
~
4,
$.
W
0
0-
n
dp.
Find: The flow rate in pounds per hour, the Reynolds
number, and the friction factor.
.~
0
--..
q'. So
Given: Natural gas at 250 psig and 60 F, with a specific
gravity of 0.75, flows through an 8-inch Schedule 40
clean steel pipe at a rate of 1,200,000 cubic feet per hour
at standard conditions (scfh).
=
'<
-
=
69000
Index
p.
0,011
18" Schcd 40 pipe
-R ,= 5000000 I horizontal!
to: 8" I.D.y
0
VI
Given: Steam at 600 psig and 850 F flows through a
4-inch Schedule 80 steel pipe at a rate of 30,000 pounds
per hour.
Find: The Reynolds number and the friction factor.
Solution:
1.
d
2.
jJ.
0
0.14
Note: Flowing pressure of gases has a negligible effect
upon viscosity, Reynolds number, and friction factor.
tll
(!)
Q
::I
...
3,826
0.029
.. ", .. ,."""
., .. ,.", ,.
,page
..
C
::r
Read---I
1 .____Index
I
FZ'
7000il0
If = 10.017
=
• . . ' _ . . . __ "
..
-
CO
.. page A-2
Connect
L
0
B-17
m
'"
CO
:s
III
Z
C
3
IT
...
....
0
::I
:9-
"D
(!)
0
'"c
'"
;;:
'">
Z
"z
0
0Cl
'"
>
:x:
ro
."
0
'"
0
'"
()
0
..
3
0.."0
~
IR, = 5 000 000
=
>
."
- -..
::J
Example 2
Indcx
If
::c
1"1
Example 1
Solution:
1. W
:;.c
"Tl
Q
r.
"TI
(For v,>lues of d. see pages B-16 to 8-18)
1
..._.
o·
::J
tll
<It
~
0
:;:
...
'"
0'"c
Cl
:c
III
-.
IT
<
>
(!)
!"
"TI
0
~
<
m
~
~
z
Cl
!"
>
z
0
~
."
m
n
~
~
Z
m
I
nn
,!
~ D V Uli--il--U U HUH H
w
l'
II H II· U ·
I+~*n
Index
I~Z
d
J.I.
.3..,
j
m
.44
I
'1
Internal Pipe Diameter
in Inches
.6
.7
_____- - - 3 6
____
_ - - - - - 24
.R
.9
1.0
~_______ l~
:=::=-:::
~_____
:;
e
Re
Co
V>
-0
10000
8000 1=1
6000
4000
3000 __
2000
<=
=>
e
"-
"0
I,
V>
-0
I
__
<=
N
V>
=>
0
.c
'::J
.::
BOO1_
600
400
300
i"
200
,=>
0
'<I'
u..
"0
'"
'"
\'
-'"
:\-1-_
:z
"
100 .80
60
_
40
30
20
'"o
-0
<=
>,
'"'"
~
- -l
V2-H
•.
~\\
i~t:~_~kd=
1-- - .
_.---
~\'
10
8
6
4
3
2
'6~-
.5
.4
"0
6
'"
N
V>
'"<=
I
-1
.c
ro 5
<=
E
~
0
z
10
12
14
15--1-16
.'
0
Z
L~
1-
.02
f -
.3·
_
-Ll
.03
~
--1.04
20 ::I- '"
.045~
30
0
1'1
:J
::I
VI
:i"
CD
0
c
CD
----'
_~_.,
CD
0
-
CD
n
0
Q
::J
3
0.."
....
:E
...
0
c:
to
-...
:r
0
:J
."
-.
"C
CD
III
;;:
'"»
z
0
Z
0
3:
0
Q
..
>
'"
:I:
'"
~
0
'"
5
~
1:
...
:I:
'"0c
Q
:I:
!!!.
<
>
CD
!"
IT
."
0
~
~
~
~
z
Q
.V>
»
z
0
.."'
~
-
40J
-0
.,.,.. "",~'...,~,"?~~""'-i"_~~""''''''''',-''''
........."'...~".
IT
0
3:
'"c:
I~
.05
Friction Factor for Clean
Steel and Wrought Iron Pipe
:J
0
0..
en
.&
-0
V>
<=
-...
'"u
0
.".
Cl
Q;
H
- J.--H
.01
...............
-4
'"
LJ
"I.
3V,
'"
'"
E
CD
"<
CD
.8
"""...,...-.,-'.,.,....".""""'.""~".~.,.,..,."""-"'-.,-
~§l
I'
E
'"
-3/4
--r4
-3
;;ra
'"
""5
"-
0
..."
- ... .,
- -...
2V, .;
-
~
w
I
:I:
n c:
3
CD
<=
"'-
I~ -H
1
I,
-
c::
n
:::!'.
0
:J
."
-..
u
<=
=:
"»
0
IV, .c
::;
",'
=~
~r==J=j~~~\~~ -
f:.
e
4
\
2:'" I 000
f-
1.5
"TI
on
I~
.: 2
:t=l
~
ril
_
'"'"
3/4
_,
.c
u
4 =1=1
=+=I
3
2
IV, :::~
(IlHf
j
10
III~;
::t:
Q;
12
..-.
-1/2
_ _ _ .-."., _,
",,.~,~.u~~,
......
,~,'
,."<...--"'",.....'t"'"!'~"" .........,..,...,,...... _
....,.....,..........,... _ _ _~- •. n·¥,."",«?""' .. ·,
,
'~
I
!
t,,,
,_~"""~""'''-'''''''''''''''''''''''~~_A''''~'''''''''"'''''''''H"""""",,;,,,,,,,,>.,,,,,'_r~ ~ .• ~" ~"d,"'~~~""'~'~;';'_""'-"''';_'''''~''_"'--'''-', .... ,,__ ,<, ,,-,.-. "" ..""l/,,_,
",l>
.'",'",b.~;".L.",,,,,".'w._
.
~"""""""-'. ~~
_'_M'~.~._~_ "~-
j
)
I
~
I
~
1
Co>
,
I-)
The pressure drop of flowing compressible fluids can be
calculated from the Darcy formula below, or, from the
nomograph on the opposite page. The nomograph is a
graphical solution of the formula.
/::"P IOO
0.00033 61
/::"P 'OO
W'V
d'
0.000 001 959
f
o
f drIp
W'
0.0003)6
p
V
I,
/:>.r iOO
w
n
::l:
>
...
(q' .)' S,'
•.
~
m
-
'"..,
...
"'tJ
..
(For values of d', sec pages 13-16 to 13-18)
i!
I,
I
I
W
=
0.0764
$
lI
,I
1
1
I
~
1
I
1
c:
...
II>
...0
0
q'. S,
~
c
>=
V>
>
z
0
Z
0
"0
~
::I
>
'"
0
Cl
Air: For pressure drop, in pounds per square inch per
100 feet of Schedule 40 pipe, for air at 100 psig and 60
F, see page B-15.
1
I
II>
When the flow rate is given in cubic feet per hour at
standard conditions (q'.) , use the following equation or
the nomograph on page B-2 to convert to pounds per
hour (W).
I
~
0
Example 1
n
0
3
Example 2
Given: Natural gas at 250 psig and 60 F flows through
an 8-inch Schedule 40 pipe at a rate of 1,200,000 standard
cubic feet per hour; its specific gravity is 0.75.
Given: Steam at 600 psig and 850 F flows through a 4inch Schedule 80 steel pipe at' a rate of 30,000 pounds
per hour.
Find: The flow rate in pounds per hour and the pressure drop per 100 feet of pipe.
Find: The pressure drop per
Solution:
Solution:
/,
d
2.
J.
4·
100
feet of pipe.
/,
........ page 13-17
3.826
J1.
0. 02 9
. page A-2
f
0.017
. page 3-19
V
J. 22
.. page 3-17 or A-17
5·
W
=
30 ~-fd-~6
6.
Index
7·
Index ~_ _
2
1
f =
I_V
0,017
1,22
!!!.
69000
.. using S,
= 0.75; page 13-2
2,
J1.
0.011
. , pai:e A-5
J.
f
0.014
" .page 3-1'1
4·
P
1. 0 3
.. paile A-IO
"
~
0
:E
~
::l:
0"
'TI
<
>
~
W
~
0
0II>
0
C
..
::I
II>
c:
Cl
::l:
:;:m
.'"
~
~
z
Cl
.'"
>
Z
0
---,
Index
2
Index
1
---/::"P 'OO
II>
::l:
'"
...~
m
Read
Connect
....
"0
...
7.5
Connect
5,
W
=
69 00018-;;
6,
Index
2
7,
Index
_1_ _
1
Rend
S~ 40 pi~
i
Index
2
f =
1
Index
I
0,014
I_~_~~_J /::"P 'OO = 0.68
..,n
>
Z
m
.~;::J
3 -21
CHAPTER 3 - fORMULAS AND NOMOGRAPHS fOR HOW THROUGH VALVES, fITIINGS, AND PIPE
CRANE
~
Pressure Drop in Compressible Flow Lines
{continued)
~
;::.;
JOOH Jad spunod 0001 U! 'MOlj
g gg
__
gg g g
eo~a.noo:::t"M
80
000 0
...-fooc.oL..n~('Y)
gC'oJ
0
N
)0
8jBIl-"11
0
_oo(,O'"'"'~~
_~~I.C?~C'"t':?
('oJ
~
C'!
!'I!!IIr1dd!l,1 II! II!!!!!!!!!!!!"'!,! I,I[!,! I I!!!,i!!!!illtddddd,t! i! :'tj,I!!1!I!!!!!,1r1d.!r!' I! jll!t!!!!!!!!!!!
JOpe:l UO!P!J:l- J
Ln~
........
,:,!
~
I!!
I
!
!
~
N
(Y:J
...,,~~
.-
~
<::::>
![!!!!)!!!
I",!
~
,I! i
!
I
I
!
(op alnpa4JS - ad!d pJBpURlSJ S84JUI U! 'Jaj8WB!O IBU!WON
qo ('oJ
0
N
(,Oq-N
_
__
0_
00
(,0
U"'>
I
1
I
!
I
r'IIFIfI I ! ( i i j i l l j i l ' (
I
~
I
!!
J
~
~oor-(,O
""::I'"
i
~
C"')~
)
~
C'J
~
"'$.
............
N
I!
J!
I
~
_
!
[
to:)
.....
~
~
~
_:-;!:
s_"
I
I
-f
I
I
Ililililii\iitljilii\QQ'lllil!ilii(liil\
1.0.......
-~oql':~
cry.........
u:
~
sa4JUI U! 'ad!d )0 Jajawe!o leUJajul--1'
ijJUI aJRnbs Jad sPunod U! 'jaa.::l 00 I Jad dOJO aJnssaJd -- oo'cl'i7
L.t1
!!
N
C"')
U"'>
Ln(,Or-OOC':l 0
_ _
.......
,I"!I!,!!!!,,!!!!!!!!!!!!I!!
J
0
0 0
N
"<:t'0
U"'>
~
I f l , I , ! , ! ! ,i"!!!!!ld!I!!I!!!!!!!!!!
.....
><
~----------------.----------------------------------------------------------------
.=
~
~
~
~
g
I'I'I!'I I!i 1!"II'I"j!!!
I
I
r
1
J
ct.
~
q
~
q
punod Jad laa.:l J!qn3 U! 'P!nl:l ZU!MOI:l
)0
~
c-....
I!
I
~CJ")CX)
!
!
I
r- <D
\,.l'")
...,..
('")
awnlol\ 3!)p ad S-,1
5
50;':'>':; r-.:"=!
LO
!! I
I'" ,I,!!! 1III'I!!!!]!
/'!!
,
I'!';' I j
r I'I!!
I I j I I II r i l l I I I I
I
1111111l
I 1, j ....~1111
I
!
""""!.
t
!
~
~
~
U?
I
t
~ ":CC!~~
!
,-;
!
,:\,
C"-I
'¢
,1",1
(I
r
I!
("I")
N
("I")
I
! ' - " I ! ! ! ! ',"
j
oo::t-
I
\,.l'")
3 -22
CRANE
CHAPTER 3- FORMULAS AND NOMOGRAPHS FOR flOW THROUGH VALVES. FITTINGS. AND PIPE
Simplified Flow Formula for Compressible Fluids
Pressure Drop, Rate of Flow, and Pipe Size
The simplified flow formula for compressible fluids is
aCCllrate for fullv turbulent flow; in addition. its use
provides a good ~pproximation in calculations involving
compressible flt;.id now through wrought iron or commercial steel pipe for most normal flow conditions.
Values of C,
II"
If velocities are low. friction factors assumed in the
simplified formula may be too low; in such cases, the
formula and nomograph shown on pages 3-20 and 3-21
may be used to provide greater accuracy.
(\
2500
2000
1500
The Darcy formula can be written in the following form:
W·2(O.OO~/36f)v
=
(W'210-9)(336~00f)v
lOoo
900
BOO
c. =
700
EOO
The simplified t90w formula can then be written:
500
-- = C,C,
CJ C211
f':"P 1oo
400
P
:;
f':"P IOO P
f':"P lOo P
C2
C1
C1 = discharge factor from chart at right.
=
C2
size factor, from table on next page.
The limitations of the Darcy formula for compressible
flow, as outl.ined on page 3-3, apply also to the Simplified
flow formula.
0
DJ
::t:
Q;
2SO
c-
'"
'0
100'
§
0
a..
'0
ISO C
'0
'"
'0
'"'"'"
'"
.c
'"
'"'"
100 -,;;
90 >
80
70
0
f-
.=,,0
li:
Example 1
'0
ill
ro'"
50
Given: Steam at H5 psig and 500 F flows through 8-inch
Schedule 40 pipe at a rate of 240,000 pounds per hour.
a::
Find: The pressure drop per 100 feet of pipe.
:=
Solution:
01
40
3l
57
0.14 6
1.45
.page 3-17 cr A-16
57 x 0.146 x 1.45 = 12
2S
20
15
Example 2
LO
Given: Pressure drop is 5 psi with 100 psig air at 90 F
flowing through I()O feet of 4-inch Schedule 40 pipe.
.9
Find: The flow rate in standard cubic feet per minute.
Solution:
f':"P 1oo = 5.0
5.17
P
0.564
....... pageA-1O
C1
(5.0 x 0.564) + 5.17 = 0.545
10
.8
C2
W
q'm
q'm
2)000
W +- (4-58 Sf!)
................ pageB-2
000 + (4.58 x 1.0) = 5000scfm
2)
For
C~
va/vel cnd on example on "determining pipe size"~
see the opposite page.
CHAPTE~
CRANE
3·23
3 - FORMULAS AND NOMOGRAPHS FOR flOW THROUGH VALVES, FITTINGS, AND PIPE
Simplified Flow Formula for Compressible Fluids
Pressure Drop, Rate of Flow, and Pipe Size -
continued
Values of C,
~ominal j Schedule
Pipe Size I Number
Inches
I
40 s
80 x
Value
of C,
40 s
I
'
160
. ,II
319000.
71S 000.
Ii
." xx
405
80x
160
... xx
1
40.
80x
160
." xx
40.
80 x
160
.. xx
IV:!
40.
80x
160
... xx
2
40.
80 x
160
.. xx
2 V:!
SO x
.. xx
4
II
i; 950.
Ij 640.
I
1.59
2.04
2.69
3.59
4.93
G
40.
80x
120
160
... xx
0.610
0.798
1.015
1.376
1.861
20
30
40 s
60
80x
0.133
0.135
0.146
0.163
0.185
8
100
120
140
160
10
20
30
40.
60 x
169.
236.
488.
899.
100
120
140
160
0.0661
0.0753
0.0905
0.1052
20
30
' .. s
40
0.0157
0.0168
0.0175
0.0180
0.0195
_.. x
0.007 00
0.00804
0.00926
0.01099
0.012 44
80
100
120
140
160
18
I
II
0.00247
0.00256
0.00266
0.00276
0.00287
0.00298
10
20
.. s
30
.. x
40
60
80
100
120
140
160
0.00335
0.00376
0.00435
0.00504
0.00573
0.00669
10
0.00141
0.00150
0.00161
0.00169
0.00191
20
30x
40
60
14
i
0.0206
0.023 I
0.0267
(}.031 0
0.0350
0.0423
0.00949
0.00996
0.01046
0,01099
O.Oll 55
0.01244
0.01416
0.01657
0.01898
0.021 S
0.0252
.' xx
40.
80 x
10.0
13.2
10
20
30.
40
" .x
60
5.17
6.75
8.94 I
I1.S0 I,
IS.59
80
100
120
140
160
II
80
100
120
140
160
\'
80
100
120
140
160
2S.7
48.3
96.6
40.
80 x
120
160
. xx
0.00463
0.00421
0.00504
0.00549
0.00612
lOs
12
21.4
10
20
30.
40x
60
16
0.0397
0.042 1
0.0447
0.051 4
0.0569
SO
I
627.
904.
1656.
4630.
40 s
80x
160
Value
of C,
0.211
0.252
0.289
0.317
0.333
... :xx
I. 40S.
66.7
91.8
146.3
3S0.0
Schedule
Number
II,
!I
2110.
"490.
B640.
I Pipe Size I
I Inches !
I
40.
80 x
120
160
... xx
"
21 200.
3& 900.
100100.
62? 000.
22500.
114100.
I
5
!I
Ii Nominal i
Value
of C,
60
40.
160
3
93500.
186100.
4300000.
11180000.
Inches
II
1590 000.
4290000.
I,
405
SO x
Ii
II
I 2~ i~,g ggg: II
40 s
80 x
SOx
:1 Nomina1 I Schedule
Pipe Size i Number
24
1'1
0.00217
0.00251
0.00287
0.00335
0.00385
10
20.
30
40
60
0.000534
0.000565
0.000597
0.000614
0.000651
0.000741
80
100
120
140
160
0.000835
0.000972
0.001 119
0.001274
0.001478
., x
I
III
I
I
,:1
I
Note
The letters s, x, and xx in the columns of Schedule Numbers indicate
Standard, Extra Strong, and Double
Extra Strong pipe respectively.
.~----~------~------~----------------------
Example 3
-
Chen: /I.n 85 psig saturated
steam line with 20,000 pounds
per hour flow is permitted a
maximum pressure drop of 10
psi per 100 feet of pipe.
Find: The smallest size of
Schedule 40 pipe suitable.
Solution:
6.P"o
C,
10
v=
= 0·4
C, =
=
4.4
10';-
,.pagc3-17or,\-13
(0.4
X
4·5)
=
5.56
Reference to the table of C2 values above shows that the 4-inch size is
the smallest Schedule 40 pipe having a C, value less than 5.56.
The actual pressure drop per 100 feet of 4-inch Schedule 40 pipe is:
6.P100
=
0.4 x 5·17 x
4·4
=
9.3
3 _ 24
----
CRANE
CHAPTER 3 - FORMULAS AND NOMOGRAPHS FOR HOW THROUGH VALVES, FITTINGS, AND PIPE
Flow of Compressible Fluids
Through Nozzles and Orifices
6P
The flow of compressible fluids through nozzles and
orifices can be determined from the following formula, or, by using the nomograph on the next page.
The nomograph is a graphical solution of the
formula.
W
=
./I:;.p
0.525 Y d'o C.y I:;.p PI = 0.525 Y cPo C",,! =-
W
=
1891 Yd'OC-,jUPPI = 1891 YcPoC
~
(Pressure drop
i~:
V,
measured across the flange taps)
Example 2
Given: A differential pressure of 3 psi is measured
across the flange taps of a 0.75o-inch I.D. square
edged orifice assembled in I-inch Schedule ~o
wrought iron pipe, in which, dry ammonia (NH3)
gas is flowing at 40 psig pressure and 50 F.
Example 1
Given: A differential pressure of I 1. 5 pSI IS measured across the flange taps of a I.ooo-inch I.D.
nozzle assembled in a z-inch Schedule 40 steel pipe,
in which, dry carbon dioxide (C0 2 ) gas is flowing
at 100 psig pressure and 200 F.
Find: The flow rate in pounds per second and in
cubic feet per minute at standard conditions (scfm).
Find: The flow rate in cubic feet per hour at stand-
Solution:
I.
R
S,
3. k
2.
I.
2.
3·
35. I }
.'
1. 5 16 ........,' ... for CO, gas; page A-8
1.28
-.
.
4· P't = P + 14·7 = 100 + 14·7 = 114·7
5· I:;.P/P't = 11.5 + 114.7 = 0.1003
6. dl = 2.067 ....... . Z' Sched 40 pipe; page B-I6
7· do/d. = I.CO + 2.067 = 0.484
8. Y
0·93
........................ page A-21
I .003 .. turbulent flow assumed; page A-ZO
9· C
10.
T
460 + t = 460 + 200 = 660
12.
13·
14·
.... _ ................... page A-IO
0·71
II.
m
I
I
Connect
I:;.P = 11.5
PI
0·71 I
Read
Index
·---+----------~--------I
1C
Index J:
15·
16. q'h
do
1.000 I
Y
0·93
I
Index 3
W = 5000
I
44 000 scfh .................. page B-Z
0.018
.................. page A-5
860000 or 8.6 x 10' ........ page 3-21
C
1.003 I,S correct for
19·
R, = 8.6 X 10' ... page A-20
20.
When the C factor assumed in Step 9 is not
in agreement with page A-20, for the Reynolds number based on the calculated flow, it must
be adjusted until reasonable agreement is reached
by repeating Steps 9 through 19.
17·
I"
18.
R,
k
for NH, gas; page A-7
1. 2 9
to
determine the Y factor.
4· P', = P + 14-7 = 40 + 14·7 = 54·7
5· I:;.P /P\ = 3·0 + 54·7 = 0.0549
6. d , = 1.049 ........ 1' Schcd 40 pipe; page B-I6
7. do/d. = 0.750 + 1.0~9 = 0.716
8. Y
0.98
........................ page A-21
0·702 .. turbulent flow assumed; page A-ZO
9. C
10.
T
460 + t = 460 + 50 = 510
I I.
PI
12.
13·
Index I
Index 1. _ _-;--,.C___I_.00
__3+I--::-In
_d_e_x__
2 __
I
R = 90.8 }
S. = 0.5 8 7 ...........
Steps 3 through 7 are used
Steps 3 through 7 are used to determine the Y factor.
j
w
I~P '-..
'V
Solution:
,
\\"'
VI
ard conditions (scfh).
!
do
........................ page A-IO
0.17
Connect
I
Read
I:;.P = 3. 0 I PI = 0.17
Index 1
IC = 0·702
I
Index I
I
Index
14·
Index· 2
15·
Index 3
16.
I
Index 3
Ido
I
1
I
2
= 0·75 I Index 3
Y = 0.9 8 I W =.0.145
Y = 0.9 8
IW = 520
1·7- q'm
18.
I"
19·
R,
0.010 ....................... page A-S
310000 or 3.10 x 10'
...... pageJ-ZI
20.
C
0.702 is correct for
R, = 3.10 X 10'
.. page A-ZO
21.
When the C factor assumed in Step 9 is not
in agreement with page A-20. for the Reynolds number based on the calculated flow, it must
be adjusted until reasonable agreement is reached
by repeating Steps 9 through 20.
CRANE
--------
3·25
CHAPTER :1- FORMULAS AND HOMOGRAPHS FOR flOW THROUGH VALVES, FITIINGS, AND PIPE
;;:::1
Flow of Compressible Fluids
;::::t
Through Nozzles and Orifices
(continued)
-
" -it
6.P
do
1, TV
I,
600
3)00
500
<DOD
400
.~~
~.
I
~
,
-400
=:::::'j
ZOO
200
400
300
100
150
<DO
100
100
80
60
=
80 .::
Q
3
'"
'"
40
3)
~
=
'":u
'-5
"-
40
~
<D
o·
"
"
"-
10
8
6
0
~
Q:
4
3
ZO ce
~
15
~
~
"-
10
2
~
~
~
,":::=)
1.5
'"
1.0
.8
•6
.4
I
~
<J
'::=8
;::p
5
1.0
X
'"
".::'"
~
'"
;;;
"
0::
"-
'"
"C
=3
=
~
.8
"
"<=>
<=>
1.5
::=.l
:::::)
X
"C
'=:&
~
",.
'"
"-
1.0
=3
-
.9
10
8
6
:;
"
"Q
.8
=
~
;;;
~
'-'
'"
"'~
"
"
"-
2
~
~
.2
"
"-
=
~
1.0
.8
.6
=
.;;;
"
=
"'~
.4
.3
.2
~
'"
'"'";;;
u
"-
"'"=
"
"~
=
,;
"
"-
~
~
'"I
'"I
~
'"
=
,::
.6
.25
I
::..
~
=
'"
><
Cl
UJ
.55
:;;
..
""
'"
t
'"'"
2:
"
N
.1
-;;
::
:u"'"-
-;;
~
=l
1.0
<D
t "i
6
::::::3
Y
u
~
30
80
60
40
30
~
~
-:::=II
300
3J0
60
50
P
lOOO
800
600
1000
800
600
~
=;::J~
V
1,
w
Q.
N
=
~
N
x
"'"
.::
'"'"
-="
~
!,
0
.g
=
'"
"
"'"
u
'"
.2
"I
u
I
.1
j
.09
!j
.08
I
.07
!
l,
!
"
j
.0625
t~
:.:=:JI
A -1
~
::::)
:=;)
Physical
=.)
and Flovv Characteristics of
::=:3~
::=i~
Properties of Fluids
Valves, fittings, and Pipe
!
APPENDIX A
:=:i~
i
ii
::::j.
I
>:=:1.
I
:::3
::=:I.
.==1t
:=D
:=:I~
~
==t
The physical properties of many commonly used
fluids are required for the solution of flow problems.
These properties, compiled from many varied reference sources, are presented in this appendix. The
convenience of a condensed presentation of these
data will be readily apparent.
I
~
I
t
Most texts on the subject of fluid mechanics cover in
detail the flow through pipe, but the flow characteristics of valves and fittings are given little, if any,
attention, probably because the information has
not been available. A means of estimating the resistance coefficients for valves, deviating in minor
detail from the standard forms for which the coefficients are known, is presented in Chapter 2 .
~
.
:::::::n
i
~
I
The Y net expansion factors for discharge of compressible fluids from piping systems, which are presented
here for the first time, provide means for a greatly
simplified solution of a heretofore complex problem.
:b~
~
!
II
I
I
i
A _2
APPENOIX ,,- PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
CRANE
. 0 f Steam 14
V·ISCOSlty
.050
1\\
\\
.048
.046
.044
.040
I
!
:::;
~
.042
,
« \
:
I
Q
.036
l-
a
~
~
I,
~
Vl
Ie
,
';1
......
~
<::
.034
Cll
>.
(/l
~
-- I - - 1 - -
%
V
- ~~ %
1/
0 ~ 7~
ll~~~ % ~
\1-"'' ' '
",,,,,,,/
~
'I
"./"
'V /"
(/l
=
«
.026
./
V'o\)\)~
'>.\)\)
.~ ~
?f/
/' V'
/
/~~~ I
L/
//%V~/ I
.024
.022
/
~v
I
I
0 0/'1~
I
.020
I
,
I
I~
.018
;;
V'
I
I
V
.016
.014
.,V
/
\ ~",(J
I
~ .028
I
:t
V
V
V
,. /
I
~
.030
....
----
----
L,.
.-: .032
:>
'"
1860 ...........
.......
c:
u
on
2600
-2200-
10..
VI
U
a
'--
1
«
(/l
0.
"-
=>'"
l
Cl.>
'-.....""1
"
~
PSIG
319
1.5
-3000
1-,\
«
I
i
\
'"
UJ
.038
I
I
...
\
~RESSURE
'-
)
I
I
l/
200
I
300
400
500
600
700
800
I
900
1000
1100
1200
t - Temperature, in Degrees Fahrenheit
Example: Viscosity of 600 psig,
8;0 F steam is 0.02Q centipoise.
Adapted from:
Philip ). Potter Steam Pou'er Planls,
Copyright 1949, The Ronald Press C'..ompany.
CRANE
<:i
APPENDIX A - PHYSICAL PROPERTIES Of flUIDS AND flOW CHARACTERISTICS OF VALVES, fITiiNGS, AND PIPE
•
Viscosity of Wafer and
Liquid Petroleum Products8 ,12,23
400 0
300Ill..
~
200
18
17
1\
~
\1\1 I
1\1\
16 \
1
\
100
80
60
,
,
Cl.
c:
40
30
;:;.
20
12
I
I
o
<f)
10
8
6
::t
10
9 r,i
2
b
:6,
:=3,
6
1.0
I
5. Gasoline
I \
i\
6. Water
\
I
\
i
4
I
\1 \
\:\
7
r. . . . .
~
li
b
\
\
I"'-.,"'\. 1-
"1\
~~\!
N...,I'
1
.........
\
I ~
i'
J.
\
\
\
1\\ \
~ I
'
,
r-t- r--r-I
T-
~2
NN
1
.08
.0 6 ,..-1. ,
20
11. 35.6 Oeg. API Crude
I
r--:
"'-.,
I,
I
17. SAE 30 lube (100 V.I.)
\
18. fuel 5 (Max.) or
Fuel 6 (M;n.)
'
1
1\
I'
~
'\.1
-1
_L
\J
:\ !
,\l--
-
-
1\
I
l"\. 1'\
I
~ J
30 40
60 80 100
200 300 400
t - Temperature, in Degrees Fahrenheit
20. Bunker C Fuel (Max..) and
21. Asphelt
1\
f"\.-
1')"-.......,
19. SAE 70 lube (100 V.I.l
M.e. Residuum
i,\ '\\ ' \ \\1\
'\. ~!
~I~ \, I
15. fuel 5 (M;n.)
16. SAE 10 lube (100 V.I.)
11
\
14. fuel 3 (Mex.)
,
\ \\\\\
l'\.
~
I
13. Solt Creek Crude
,
1\ \ l\\11 \
f0'\,
'\'
12. 32.6 Oeg. API Crude
I
-....
I.
i
~
1\
\' \\ \ '\
~ ~',
~
8. Distillate
10. 40 Oeg. API Crude
\
II
\
\
~
,-:::::::
7. Kerosene
9. 48 Oeg. API Crude
I
,\ \
r----i ' 1"t'-l,I ~~~J,
t - t-
1
I
I
1
\
'(
'\
,,\
I'
i'
3L
.2
1
,
D'
,
1
I
i\
\ 1\
_\ \
I
I::::
.4
.3
I
,
1\
~
\
4. NQtu~a' Gasoline
I
5
8
.6
.04
.03
lD
,-
\
~
8t--
4
3
\
I \
" \
15~
r\ 1\\ 1\ \ \
I~
14 b- I"
1 ~l \' \
I
"'-., "b, ~ ~}.
\ \\ \\
~ ~\
,
u
I
\
~
\
11 1-.......
Vl
>
\
-.......,
_Ll
-.1 1
\ \
1\[\ \ \
~
13
2. Propene (C,H s)
,
1\
\
I 1\
\1 \
I
20 0
c:
I. Ethene (C ,H,)
,
....\
I
i
'"
'-'
1\
\
_l
400
300
~
\
,
6010-
o
\
l~
\
1\
1000
800
'"Vl
21
I 119 I II
Ill..
- I;
A-3
\
\
600 800 1000
Example: The viscosity of ,,'ater at
125 F is 0.)2 centipoise (Cur\"c No. b).
Data extracted in part
by' permission from the
Oil and Cas Journal.
A-4
APPENDIX fti,- PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES. FITTINGS. AND PIPE
~-'----
CRANE
Viscosity of Various Liquids S,8. II
10
6.0
1,\ \
4.0
\\ \
3.0
18\~
11
2.0
16~
~
ZJ
r--
'\
i
II
-
Ii
~5/
12
7
~S=
'\.
"-
~
c:
'" .5
C,)
c:
..:::- .4
'"
.3
'"
>
0
u
I
::t.
.2
r\
\.\ \
,
l\.
1\ 1\'"-,
~ ~\' "",
'\.
""-
6
.8 ,.~
.7
'"0
l'..
0.
.6
Q.)
\\,
~ ~\
i
1.0
.9
1\ i(
1\ \
5.0
'\.
...., ~.
'\.
~
r\""'"
'\.
-.\.
"" .....
\.
I'-...
I'\.. "
"'-""
'''''~
I~
--1\
~\
~~
~ p:::::::
.06
\.
11
\
"-
a
'"
I"-......
"-
"-
-----
"-
"i
I~
\\
.04
-.............
I'..
\
.05
.03
-40
'"
~
"" ~
r:::::- I-"'
-~
0.1
.09
.08
.07
.........
............
"-
.......
..........
.............
'"
'"
~,'"
;~ " ~""
&
"
.........
.....
""- .....
\
40
80
160
240
120
200
t - Temperature, in Degrees Fahrenheit .
280
320
360
1. Carbon Dioxide •• CC~2
2. Ammonia ••• " •••• NH::;.
3. Methyl Chloride •• CH;>Ci
4.
5.
6.
7.
8.
Sulphur Dioxide •. SOI~
Freon 12 ...•
F-12
Freon 114 ....•.. F-114
Freon 11 ..•....• F-l 1
Freon 113 ....... f·113
0
•••
9. Ethyl Akohol
10. Isopropyl Alcohol
11.
12.
1 3.
14.
15.
20% Sulphuric Acid ••.••• 20% H t S0 4
Dowtherm E
16.
17.
j 8.
19.
10%
20%
10%
20%
Sodium Chloride Brine ••. 10%
Sodium Chloride Brine ••• 20%
Calcium Chloride Brine .. 1 0%
Colcivm Chloride Brine •• 20%
Noel
Noel
Coel:
CaCt:
Dowtherm A
20% Sodium Hydroxide .. 20% NoOH
Example: The viscosity of am-
Mercury
monia at
40
F is
0.14
centipoise.
eRA N E
APPEND I)(
-'-'-:.-.-----
A-PrYSICAl PROPERTIES OF FLUIDS AND flOW CHARACTERISTICS OF VAlVES< FlnINGS< AND PIPE
Viscosity of Gases and Vc;pors
Viscosity of Various Gases
.
The curves for hydrocarbon vapors and
natural gases in the chart at the upper
right are taken from \lax\\·cll 15 ; the
cun·es for all other gases (except heli um 27)
in the chart are based uJXln Sutherlamfs
formula. as follows:
/1-
= /1-0
where:
=t
/1-
<:=1t
/1-0
::=3_
==l.
==:I.
.:=9
-
:=1~
::=1.
+C
T = absolute temperature, in de- .
grees Rankine (460 + deg. F)
for which viscosity is desired.
To = absolute temperature, in degrees Rankine, for which viscosity is known .
C
=
Sutherland's constant.
Note: The variation of viscosity with
pressure is small for most gases. For
gases given on this page, the correction
of viscosity for pressure is less than 10
per cent for pressures up to 500 pounds
per square inch.
~
.==11
==:S~
Fluid
0,
Air
:=:I,
,03
N,
Approxi:mate
Values of ~4C"
i
6
I
0,
/
/
/ /
Helium
/
/
Air
N, '
/ //.CO,
/ /
/:/!/V0 SO,
/i//VY~
I
.03 2
/
8
i
II
I
To
viscosity, in ce:1tipoise at
temperature To.
!
i
I
viscosity, in centipoise at
temperature T.
=
I
:
.04 0
(0<555 7:0 + C;) (~)3:,
0.555 7
=D
I
!
V/V/Y~
Y/V'XY,,{ J---I
t
VA'hc<;Y/' i/r
::;.
.;;; ,02 4
8
:;;:
~
:::I..
.02
Y
~ Vh [t' V i ;.-.! /1'a~;
V ,.¥1/10-1
;,,/.;/
i
/ V~ VV
~/
1/
I
o~
.01 6'.#'
~
VV
~/~/,
~
/iv'~/)ffi
I
,
I
I
i
,I
/ ~j//.~ i ! ).---V
.
,
/7 ~~ ~
~,
.01 2
~.
i
~~ IVV, ! II ~ I
.00
i~'
8~
o
1-- H,
i !
100 200 300 400 500
GOO 700 800 900 1000
t - Temperature, in Degrees Fahrenheit
Viscosity of Refrigerant Vaporsll
(saturated and sup·arhealed vapors)
127
120
III
CO,
CO
SO,
41b
NH,
H,
370
72
240
JIB
Upper chart example: The viscosity
of sulphur dioxide gas (SO,) ,at 200 lis o.olb centipoise.
Lower chart example: The viscosity
of carbon dioxide gas (CO,) at about 80
l- is 0.015 centipoise.
t - Temperature, in Degrees Fahrenheit
A-5
A-6
APPENDIX A-PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES. FITTINGS. AND PIPE
CRANE
Physical Properties of Water
Saturation
Pressure
Specific
Volunlc
Weight
Density
P'
\'
P
Pounds per
Square Inch
Absolute
Cubic Feet
Per Pound
Pounds per
Cubic Foot
Pounds
Per Gallon
32
40
50
60
0.08859
0.12163
0.17796
0.25611
0.016022
0.016019
0.016023
0.016033
62.414
62.426
62.410
62.371
8.3436
8.3451
8.3430
8.3378
70
80
90
100
0.36292
0,50683
0.69813
0.94924
0.016050
0,016072
0.016099
0.016130
62.305
62.220
62.116
61.996
8.3290
8.3176
8.3037
8.2877
1.2750
L6927
2.2230
2,8892
0.016165
0.016204
0.016247
0.016293
61.862
61.7132
61.550
61.376
8.2698
8.2498
8.2280
8.2048
3.7184
4.7414
5.9926
7.5JlO
9.340
0.016343
0.016395
0.016451
0.016510
0.016572
61.188
60.994
60.787
60.569
60.343
8.1797
. 8.1537
8.1260
8.0969
8.0667
11.526
14.123
14.696
17.186
0.016637
0.016705
0.016719
0.016775
60.107
59.862
59.812
59.613
8.0351
8.0024
7.9957
7.9690
24.968
35.427
49.200
67.005
0.016926
0.017089
0.017264
0.01745
59.081
58.517
57.924
57.307
7.8979
7.8226
7.7433
7.6608
134.604
247.259
422.55
680.86
0.01799
0.01864
0.01943
0.02043
55.586
53.648
51.467
48.948
7.4308
7.1717
6.8801
6.5433
0.02176
0.02364
0.02674
0.03662
45.956
42.301
37.397
27.307
6.1434
5.6548
4.9993
3.6505
Temperature 11
"f\~ater
Degrees
Fahrenheit
--
110
120
130
140
150
160
170
180
190
200
210
212
220
240
260
280
300
350
400
450
500
550
600
650
700
I
I
I
I
I
I
I'I
IiIi
II
I'
I
Ii
II
II
1\
i
II
Ii
I'
II
IIII
I
1045.43
1543.2
2208.4
3094.3
I,
\Veight
1
1I
I
I
1
j
j
Specific gravity of water at
60
F
= 1,00
Weight per gallon is based on 7.48052 gal!ons per cubic foot.
;
All data on volume and pressure are abstracted from ASME Steam
Tables (1967), with permiSSion of publisher, The American Society of
Mechanical Engineers, 345 East 47th Street, New York, N.Y. 10017.
, .,
\
J
CRANE
APPENDIX A-I'HYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTiCS OF VALVES, FITTINGS, AND PIPE
Specific Gravity-Temperature Relationship for Petroleum OilS
A·7
l2
(Reproduced by permission from the Oil and Cas Journal)
ro
o
o
±
~I
lI '
i
=::.:3
0.2 !;--'----,~--L-:':_:_--'.-~-L--:L:-L---::L--L.._:l~-L___::!_:_--'.-~---.JL-_:l:_:-.l.--~
o
300
400
500
600
700
800
900
1000
C1Ha=Propane
C.H]o=·Butane
~
t - Temperature, in Degrees Fahrenheit
C:Hs=Ethone
iC 4 H1 (l=lsobutane
;C;;.H 12 =Jsopentone
To find the weight density of a petroleum oil at its flowing temperature
when the specific gravity at 60 F/60 F is known, multiply the specific
gravity of the oil at flowing temperature (see chart above) by 62.4, the
density of water at 60 F.
Example: The specific gravity
of an oil at 60 F is 0,85 The
specific gravity at 100 F = 0,83,
Weight IDensity and Specific Gravity* of Various Liquids
Liquid
Temp ./ Weight Specific :
Density Gravity I
IpS
~cc
Deg. t Ll';,
Fahr. I Cu. for.
Temp.' Weight Specific
Density Gravity
I
I
Des·
Fahr.
S
p
Lbs.
Cu.
fer
"t.
I
Mercury
849]4 I ...
20
:\mmonia, Saturated! 10
.,.
I\1ercufV
40
848m
.
B,'nccnc
' 32
.,. I Mercury
846,32
13,570
60
I
I 1v1c rcury
Brme, 10'; Ca CI
32
.
I ...
I (3Tr~ 844,62
,
B~ iric, 10'; :--:a CI
32
I ...
l\/fcrcury
100 I 842.93 I .
I 1014 ! !\lilk
[It:nkns c: Furl \ lax
I'D
... II t ! . ..
l . . nt . . pn D:-..ulphIJc
J2
~O_·~")
Oltw 0,1
59
,7,3
0,919
1),,, !111M
,,0
52,99! 0,850
Pentane
59
38,9
0.624
l-.:~~~:rf!\-1dX---- - ~(f--5W)2~Q8
S,,\E 1O"L-uLbe-'!~---:--"7bOC;-+--;5~4-;,6-;4--';--"0;-;.8"7;;bFuel 5 \Im,
bO
,,0_~3
O,9(m
SAE )0 Lube!
60
5b,02
0,898
Fuel 5 \Ia,
l'(l
61,92
0,993
SAE70 Lubct.
60
57,12
0.916
Fuell' \Iin,
bO , 61,<12
0,993
Salt Creck Crude
60
525b
0,84J
) 2,,," A P I Crude --i--76"7C
Ca'<)line
60
4b);J
0751
0 -i---;5"'3""]"'7;--CC-CO"",8"'6'c2=Casoline, Natural
60
42 A2
0,6S0
35,6" API Crude
60
52,81
0.847
Kerosene
60
50)!5
0,815
40" API Crude
60
5145
0.825
M, C Residuum
60
58),2
0,935
48" API Crude
60
49.16
0]88
:\Ct."tone
,-
,
.
Liquid
I 60
494
I 40,9
I 5b,1
I
! 6B.05
I 67.24
b3.25
0]92
I
I
I
I
I
I
-
..
..
..
'Liquid at 60 F referred
to water at bO F·
tMilk has a weight density of 64,2 to 64,6,
t 100
Viscosity Index,
Values in the table at
the left were taken
from Smithsonian
Physical Tables,
Mark's' Engi~eers'
Handbook, and "Nelson's Petroleum Refinery Engineering.
A -8
MPENDIX A-PHYSICAL PROPERTIES OF FLUIDS AND HOW CHARACTERISTICS OF VALVES. FITTINGS. AND PIPE
eRA N E
~~------------------------------------------------------------
Physical Properties of Gases l !
= specific heat at constant pressure
c, = specific heat at constant volume
Cp
Name
of
Gas.
·
l
,CheITlical Approx. , Weight
Formula Moleeu-II Density,
or
Pounds
Symbol Weight 1
per
I Cubic
lIar
I
Acetylene
Air
Ammonia
Argon
Carbon Dioxide
Carbon MonoxidE'
Ethylene
Helium
Hydrochloric Acid I
I
,i
Hydrogen
Methane
Methyl Chloride
Nitrogen
Nitric Oxide
Nitrous Oxide
Oxygen
Sulphur Dioxide
Specific 1 lndiSpecific
Gravity I vidual I
Heat
Rela- I Gas
Per Pound
tive
Constant!
at Room
To Air
Temperature
--,--;-,
R
cp
j Cf)
1
III
M
A
HCI
H,
CH,
CH,CI
I
26.0
29.0
17.0
40.0
44.0
28.0
28.0
4.0
36.5
2.0
16.0
50.5
28.0
30.0
44.0
32.0
64.0
NH,
C~~.
He
FO:t>
I
C,H,
CO 2
I
I
II
I
l
N,
NO
N,O
0,
SO,
.06754
.07528
I' .04420
I .1037
I
I
Heat Capacity
Per Cubic Foot
at Atmospheric
Pressure
and 68 F
.350 I .2737 i
.897
59.4 I'
1.000
.1725
53.3
.241
.587
90.8
.523
.4064
38.7
.124
.0743 I
1.377
1. 516
.1599
35.1 I .205
.1721
.965
55.2 I .243
I'
.3292
.967
55.1
.40
.138
1.25
.754
386.
.191
.1365
1. 256 I 42.4
3.42
.0695 1 767.
2.435
.593
.4692
.553
96.4
.24
.2006
1.738 1 30.6
55.2 I .247
.966
.1761 i
I
.231
1.034
.1648
51.5
.221
.1759
1.518
I'
35.1
.1549
1.103
48.3
.217
.154
24.1
.1230 ,
I 2.208
II,
I
I
k
equal
to
cplc,
-I
Cp
I'
.07269
.0728
.01039
.09460
.005234
.04163
.1309
.07274
.07788
.1143
.08305
.1663
I
--1--------,-1
I
.1142
I
I
C"
.0185
.0236
.0130
.0181
.0179
.0231
.0077
.0129
.0234
.0183
.0177
.0125
.0291
.0240
.0130 I .0078
.0181
.0129
.0179
.0127
.0247
.0195
.0314 I .0263
.0179
.0128
.0180
.0128
.0253
.0201
.0180
.0129
.0256
.0204
I
1.28
1.40
1.29
1.67
1.28
1.41
1.22
1.66
1.40
1.40
1.26
1.20
1.40
1.40
1.26
1.40
1.25
*\\'eight density values are at atmospheric pressure and 68 F.
For yalues at 60 F, multiply by 1.0154.
Volumetric Composition and
Specific Gravity of Gaseous Fuels 13
,
Chemical Composition
Percent by Volume
I
Ii •
HYdrO-I Carbon
Paraffin
gen
Mon- Hydrocarbons
Type of Gas
I oxide I MethI
r
Natural Gas, Pittsburgh
Producer Gas from Bituminous Coal I 14.0
Blast Furnace Gas
1.0
Blue Water Gas from Coke
47.3
Carbureted Water Gas
40.5
Coal Gas (Cont. Vertical Retorts)
54.5
I
II
Coke-Oven Gas
Refinery Oil Gas (Vapor Phase)
Oil Gas, Pacific Coast
il
46.5
13.1
48.&
ane
27.0
27.5
37.0
34.0
10.9
6.3
1.2
12.7
83.4
3.0
1.3
10.2
24.2
32.1
23.3
26.3
I
Ethane
I
IlluITlinants
EthYl-II Benzene
ene
I Oxy-
I,
gen
I
I
I
15.8
0.6
21.7
6.1
1.5
3.5
39.6
2.7
2.8
1.3
0.5
1.1
!
Specific
Gravity
Relative
Nitro- Carbon to Air
gen
DioxS.
ide
0.7
0.5
0.2
0.8
1.0
0.3
0.8
50.9
60.0
8.3
2.9
4.4
8.1
3.6
Data on this page reproduced by permission from Mechanical En[!,ineers' Handbook
by L. S. Marks. Copyright. May. 1954; McGraw-Hili Book Company. Inc.
4:5
11.5 II
5.4
3.0
3.0 II
2.2
0.1
4.7 II
0.61
0.86
1.02
0.57
0.63
0.42
0.44
0.89
0.47
A-9
APeENDly. A-PHYSICAl PROPERTIES Of flUIDS AND flOW CHARACTERISTICS OF VALVES, FITIINGS. AND PIPE
CRANE
Steam -
Values of
k
Ratio of Specific Heat at Constant Pressure
to Specific Heat at Constant Volume
k = epIc.
1.34
~
1.3 2
""'-
"-
§
1.30
c
8.
x
L.LJ
.0..
__
£H",!e",o,J
- !o-_"i"'_
......r-
g .
c
a:>
(/)
I
~o~~
~o~
I
IOOO~
~o~
""'" 1.26
I"-
;-;::. ~
I
500 F
-
__
I
..
-r-::t,_~
-r-I·h
__~
-~OO-L..ro
400 F
---
12 8
!>;os>
300 F
J...l40...ru;.,
....
-
--
~-
.-
--
I---
-......
~
~--
---~-
--
---
~-
~-
::
~
~
~
~/
- - ~
~ ~Rl/'
- --- ........... \~\\
.//
.J~
I'
~-
1.2 4
'""
\~
t
1.22
I
2
5
10
20
50
100
200
500
pi _ Absolute Pressure, Pounds per Square Incil
For sma'] changes in pressure (or volume) along an isentropic,
pv k = constant
j
::::II
::::=3
::::::'1
. ==:1
.==8
Reprinted from "Thermodynamic Properties of Ste2.m"
by J. H. Keenan and F. G. Keyes, 1936 edition, by
permission of the publishers, John Wiley &1 Sons, Inc.
~
A - 10
CRANE
APf'<!'<PIX A - PHYSICAL PROPERTIES OF FLUIDS AND flOW CHARACTERISTiCS OF VALVES, FITIINGS, AND PIPE
'-'--'-=----
Weight Density and Specific Volume
Of Gases and Vapors
The chart on page A-I
144
p
=
P'
~
=
where:
I
is based on the formula:
MP'
2.70
10.72
T
P" =
14.7
.11 It "..;
P' S.
T
p
p
p
I
+P
Problem: What is the density of dry CH, if the temperature is
gauge pressure is 1.5 pounds per square inch?
100
F and the
Solution: Refer to the table on page A-8 for molecular weight, specific gravity,
or individual gas constant, Connect 96.4 of the R scale with 100 on the temperature scale, t, ana' mark the intersection \vith the index scale. Connect this
point with 15 on the pressure scale, P. Read the answer; 0.08 pounds per cubic
foot, on the weigh: density scale p.
Weight Density of Air
Temp,
Air
\Veight Density of Air. in Pounds per Cubic Foot
For Gauge Pressures Indicated
(Based on an atmospheric pressure of 14.696 and a molecular weight of 28.(7)
II
DegF.
o
5
psi
psi
i 10
I
psi
20
'1
psi
30
psi
't
I
40
psi
Ii
50
PSI
60
psi
70
psi
80
90
psi
psi
i
100
psi
110
120
130
pSI
psi
psi
.140
psi
150
psi
30" II ,0811 I', ,10871.1363 .1915 .247 1 ,30~ I ,3~7
.412
.467
.522
.578
.633
.688
.743
.798
.853
.909
40
11.0795 " .1065 .133,5 .1876 .242
.29, 1.3,0
.404
.458
,512
.566 I .620
.674
.782
.836
.890
50
I' .0782
.1048 1 .>314. .1846 .238
.291 .. 344
.397
.451
.504
.557
.610
.663
.770
,823
,876
60
.0764" .1024 .1284 .1804 .232 1,.284 i .336
.388
.440
.492
.544
.596
.752
.804
.856
1
70
,1.0750 i .1005 .. 1260 .1770 .228
.279 I .330
.381
.432
.483
.534
.585
.738
.789
.S40
-""8"'0~I! 0736 I .09861"--;,C;;2~36~':".1~7~3~7+1-'."'22::-C4;'--;lcc.C;;27"'4~'.:;;3"'247-.-'-:.3i:7c;.4-'---'.-;4~24;-':-'-.'-'47"'47-'---'C.50:;2-;4-'c-~~.--'~c--'7;;:.-"-.:;.7"'2:O-4-+-"':."'77"'4~---'C.8"'2~4
90
1.0722' .0968 .1.214 .17051.220.! .269
.318
.367
.416
.465
.515
.711
.760
.809
100 I .07091.0951 .un .1675 .216 ,.264
.312
.361
0409
.457
.505
.698
.747
.795
lIO
I'j ,069: .0934 I... n:1 .1645 .212 '.259
.307
.354
.402
.449 . . 497
,686
.734
.781
..
i,
1
~1~20~~I.~0~68~'~~.0~9~18~c'2.~'I~~~I~.,~1~61~7rl-.~2~08?-~I~.2~5=.5-+~.3~0~2~...:.~34;8:~~.3~9~5~~.44~I~!_...:.~48~8~:~~_~~~~~~-,...:.~67i4~~.7~2~1-+-~.768
130
Ii .0673 1 .0902 .H31 .1590! .205 .251 I .296 .342 .388 .434 .480
.663
.709
.755
1401.06621.0887 .11U .1563'1.201
.246 1.291
.337
.382
.427
Ail
.652
.697
.742
150
I, .0651
.0873 .n094 .1537 .1981 i .242
.287
.331
.375
.420
.464
.641
.686
'.730
'I
I'
I'
175
200
225
250
275
300
350
400
450
500
550
600
30 0
40
50
60
70
~g
1'[.06261.0834 .H151
!. 0602 .0807,. IOn
.0580' .0777 i .0974
1.0559 .0750' .0940
II' .0540, .07241 .()'JiOS
,.0523, .0700 ',.0078
if .0490, .0657 i .0824
1,.0462! .O?I~: .O:,§6
I, .0436 1.0080 i .(),,33
1.0414 'I .0555 : .()695
1'.0393 .0527' .Ol>f>l
ii.0375! .05021 .06.3!l
I'
i i 175
1 200
1'1'
1
I 225
.1477 i .1903 i .233
.275
.318
.361 i ,403
.446
.616
.659
.701
.1421 i .1831 1 .224 ,. 265;'--;"':'c;.30",6o--'---'C'3",4",7-'..-,,3.:,.8:,c8;-,-'...:.-;4",29.-+--,-::~_~~---'C'50:;5:0'2-,'..::.~59;c3;.--;---'C.6C;3.4;;'~"::'767~5
.13691.1764 i .216
.255
.295
.334
.374
.413
.492
.531
.571
.610
.650
.1321 .17021.208
.246
.284
.322
,361
.399
.'44~95 ".513
.551
.589
.627
.1276 .1644 i .201
.238
.275
.311
.348
.385
".495
.532
.569
,606
.1234, .15901.1945 .230
.266
.301
.337
.372
.443
.479, .515
.550
.586
.lI58 1 .1491 .182:-o5c+":.;:2~16:c--~.2c4,~9-+..:.~28;:c3~''':':.;:3~16~.....:.:.3",4",9-+-~:.::o-'--'-'4~16
.449' .483
.516
.550
.1090 1.14051 .1719' .203
.235
.266
.298
.329'
.392
0423
.455
.486
.51S
.1030 !.1327 : .1624 ', .1921 .222
.252
.281
.311
.370
ADO i .430
.459
.489
.0977 .1258 ' .1540 ! .1821 .210
.238
.267
.295
.323
.351
.379
,407
.436
.464
.0928 .1196,1 .1464 i .1731 .1999 .227
.253
.280
.307
.334
.360
.387
.414
.441
.0885 i .1140 i .1395' .1649 .1904 .216
.241
.267
.292
.318
.343
.369
.394
,420
250
I'
300
i
400
500
600
700
2.78
2.74
2.68
3.32
3.27
3.20
3.86
3.80
3.72
4.40
4.33
4.24
,2.63
3.14
3.65
4.16
1
800, 900
1000
psi'
psi
l~I~I~
~
~I~I~
~
~
~
1. 047 1.185 i l. 3Z3~"'1C'."'46"0"'1c-,1'-.-7"'36;-7-1'2.-'2"'9--+co
2"'.8"4'--:''''3C'.3"'9--''''3'''.'OC94~~4-.4'"9C-:-'''5~.0;;-;5~"'5'-.760OC-
1.026 1.161,1.1.% 1.431',1.70212.24
11.00911.142 '11.V5 1.408: 1.674 2.21
i .986 i 1.116 1.2:-*6 1.376' 1.636 2.16
ii
.968,11.09511.213
li:m: J:g~~ l::i~
1.350 i 1.605
r
2.12
U6f i i:~~; IU~ I ~:~~
tg~ n~
4.95, 5.49
4.87
5.40
4.76
I
4.67
!:g~ ::~~
100
Ii .916: 1.036 ! 1.157 1.2781,1.51912.00 12.48 2.97 3.45 3.93 4.42
lID .1: .900: 1.0181 LU7 1.255,1.492 1.967 2.44
2.92
3.39
3.86
4.34
120
".884 I 1.001 ! 1.1.;;:17;.-'-01'0'2'73i-4-c1~1:..4o-:6",7-:-;1c:..",93,"3,-1c:2""-o4;:-0c-:-2~'c;:8~6-"_~3.:;.3:;;3--+..:3c:.,,,80~_40'c;2",6-i-7-7'
130
.869 I .984' Li.lI>8 1.213 \1.442 1 1.900 1 2.36
2.82
3.27
3.73
4.19
140
.855'.967 1..05'j 1.193 11.41811.868 1 2.32
2.77
3.22
3.67
4.12
150
.8411 .951! l,.1l!(,2 1.'17311.395,1.83812.28
2.72
3.17
3.61
4.05
175
.807, ,9!411.ll'.l1l 1.127 1.340 i 1.765 I 2.19
2.62
3.04
3.47
3.89
200
.777 I .879 I .982 1.08411.289 I 1.698 (2.11
2.52
2.93
3.34
3.75
225
.7491 .847: .'146 1.044 i 1.242 , 1.636 i 2.03
2.43
2.82
3.21, 3.61 i 4.00
250
.722
.817 ', ""13,' 1.08811.198 1.5791' 1.959 2.34
2.72
3.10' 3.48
3.86
275
.698
.790
.!!lSi
.973 i 1.157 11.525 1.893 2.26
2.63
3.00 i 3.36
3.73 i
.675
.764
.852
.941 '11.11911.475.1.830 2.19
2.54
2.9013.25
3.61 i
300
1
1 ..",.m~OO","~:..8~8~3~1c:.''OC05~0~1~1~.~3~84~1_",I.~7~1~7772~'0i:5~~2:..3",8o--'~2.~7~2-+-c;.3~'0i:5~~J~.39 ,
~3",50__~_.~63~3~1~.,7~16~_
400
.596' .6751 .;;'53
.8321 .98911.30311.618 1.932 2.25 i 2.56
2.87
3.19450
.5631 .6381 .712
.786
.93411.232,1.529 1.826 2.12 '2.42
2.72
3.01
500
.534
.~£~ i .675
.745
.886 1.16711.449 1.73J 2.01
2.29
2.58
2.86
550
.508 1 " n I ,M1
.708, .84211.110 1.377 1.645 1.912 i 2.18
2.45
2.72
600
.484 i .547 i .611
.675 i .802 I 1.057 1.312 1.567 1.822, 2.08 1 2.33
2.59
I
i
I
I
Air Density Table
The table at the left is calculated for the perfect gas
la\\' shown at the top of the
page. Correction for supercompressibility, the deviation from the perfect gas
law, \\'Quld be less than
three percent and has not
been applied.
The weight density of gases
other than air can be determined from this table by
multiplying the density
listed for air by the specific
gravity of the gas relative
to air, as listed in the tables
on page A-8,
APPENDIX A - PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES. FITTINGS. AND ~
CRANE
A-ll
Weight Density and Specific Volume
Of Gases and Vapors R
continued
8g
0.35
V
0.4
p
60
Index
50
40
30
0.5
15,----1-
20
0.6
~
0
0
"0
c::
=>
LL.
u
0.7
.0
=>
Q:;
Q:;
Q;
u
Cl.
Cl.
D
~
=='"
OJ
=>
u
'"
-
~
c::
0.8
0
V>
- C-'>'"
0
0.9
.....
~
-
=>
:.0
a..
u
I
=>
c
~
C-'>
<1>
'"I
'"
:0:
~
Cl..
0
I-
100
U
2::l
'"
0
.0
'"
""I
a.
.6
.7
=>
C-'>
'"
=u
E
:':
=>
""=
""Q:;
"'-
'"
"0
SO
V>
u
'"
I
120
Q:;
>
0;,
CQ
c.
E
0;>-
Cl
c.
140
E
=>
'"
u
'"
:0;
ro
c
.?5
c'"
<..)
1.0
::E
I
Z;>
>
<1>
00
160
U
0
c::-
'-'
180
u.
'"
c::
OJ
t
200
OJ
"0
:;;
T
0
a..
co
=>
0
a..
<C
I
c
60
I;;;. &..
",-
100
.8
.9
:0;
V>
'"
i''".L
1
I
0..
150
2
50,---
3
€Ol---=I
for application of cho,."
701--~r
-
explanation
on
the
Fe:'!er to
prece#.~ng
the
poge.
Molecular weight, specific gravity,. r:mo individual
78 -
constants for various gases are give;; on page
A~8.
CRANE
APpENDIX A - PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
A-12
Properties of Saturated Steam and Saturated Water*
Vacuunl
Inches
of Hg
Absolute Pressure
Lbs. per --I-i~Ches
of Hg
Sq. In.
pi
Temperature
t
Degrees F.
I
I
I
I
Heat of
the
Liquid
Specific Volume
Latent Heat Total Heat
of
of Steam
Evaporation
V
Water
Btu/lb.
Btu/lb.
Steam
Cu. ft. per Ih.
Btu/lb.
Cu.
{t.
per lb.
I
0.0087
0.02
29.90
32.018
0.0003
1075.5
1075.5
0.016022
3302.4
0.10
0.20
29.72
35.023
3.026
1073.8
1076.8
0.016020
2945.5
0.15
(1.31
29.61
45.453
13.498
1067.9
1081.4
0.016020
2004.7
0.20
0041
29.51
53.160
21.217
1053.5
1084.7
0.016025
1526.3
0.25
0.51
29.41
59.323
27.382
1060.1
1087.4
0.016032
1235.5
0.30
0.61
29.31
64.484
32.541
1057.1
1089.7
0.016040
1039.7
0.35
(i.7l
29.21
68.939
36.992
1054.6
1091.6
0.016048
898.6
0.40
0.81
29.11
72.869
40.917
1052.4
1093.3
0.016056
792.1
0.45
0'.92
29.00
76.387
44.430
1050.5
1094.9
0.016063
708.8
0.50
1.02
28.90
79.586
47.623
1048.6
1096.3
0.016071
641.5
0.60
1.22
28.70
85.218
53.245
1045.5
1098.7
Ii
0.016085
540.1
0.70
1.43
28.49
90.09
58.10
1042.7
1100.8
0.016099
466.94
0.80
1.63
28.29
94.38
62.39
1040.3
1102.6
0.016112
411.69
0.90
1.83
28.09
98.24
66.24
1038.1
1104.3
0.016124
368.43
-~I~.O~--+-~2".~04T-~~27~.i88~-f~IOil~.7~4~-r-~6~9~.7~3-+--~10~3i6~.I--r'I~lo05i.~8-i-Aor.0·'16~1~36~-r~3~33'.7.60~1.2
'U.44
27.48
107.91
75.90
1032.6
1108.5
0.016158
280.96
1.4
2.85
27.07
113.26
81.23
1029.5
1110.7
0.016178
243.02
1.6
3.26
26.66
117.98
85.95
1026.8
1112.7
0.016196
214.33
__~1~.8~___,
3.~.6~6__+-~2~6~.2~6__~_~1~272.~2;2__-+~9~0~.1~8~~__~1~02~4~.3~-+~11~174~.5~-r~0~.Oi1~6~2~13~~~1~9~1.~8~5__
2.0
I'
4.07
25.85
126.07
i 94.03
1022.1
1116.2
0.016230
173.76
2.2
4.48
25.44
129.61
97.57
1020.1
1117.6
0.016245
158.87
2.4
I
4.89
25.03
132.88
100.84
1018.2
1119.0
0.016260
146.40
2.6
5.29
24.63
135.93
103.88
1016.4
1120.3
0.016274
135.80
1O;c;1",4__
_---;2"'.800-___L--Z.."o7-=-0-+--,;2-o;-4."'2-=-2--+---:o1-,-38;-:.-';-78i;--+-0-;1O"'6:".7"'3---t--7
.7.--+_1~lco;2-o;-1.-;"5_-+---;0,-;.0~176",18;-;;7:----t---.1726;;-,"",67.-_
3.0
!
6.11
23.81
141.47
109.42
1013.2
1122.6
0.016300
118.73
3.5
,
7.13
22.79
147.56
115.51
1009.6
1125.1
0.016331
102.74
4.0
8.14
21.78
152.96
120.92
1006.4
1127.3
0.016358
90.64
4.5
I,
9,16
20.76
157.82
125.77
1003.5
Il29.3
0.016384
83.03
____~5.~0__--~---=-10~.,~1~8--+-~1~9~.7~4~-+--=-16~2~.~24~--+'-713~0~.~20~-+__~10~0~0~.9~-+-71~13~1~.1i;-~~0-,;-.0~1-=-64-=-0;-;;7:--_~__~7~3~.5~3~2__
5.5
11.20
18.72
166.29
'I 134.26
998.5
1132.7
0.016430
67.249
6.0
12..22
17.70
1170_05
138.03
996.2
1134.2
0.016451
61.984
6.5
13,,23
16.69
173.56
141.54
994.1
1135.6
0.016472
57.506
7.0
14,,25
15.67
170.84
144.83
992.1
1136.9
0.016491
53.650
7.5
15.27
14.65
,179.93
147.93
990.2
1138.2
i 0.016510
50.294
8.0
16,29
13_63
182.86
150.87
988.5
1139.3
0.016527
47.345
1140.4
0.016545
44.733
8.5
17.31
12.61
185.63
153.65
986.8
9.0
18.32
11.60
188.27
156.30
985.1
1141.4
0.016561
42.402
9.5
19.34
10.58
190.80
158.84
983.6
1142.4
0.016577
40.310
10.0
20.36
9.56
193.21
I
161.26
982.1
1143.3
0.016592
38.420
11.0
22.40
7.52
197.75
165.82
979.3
1145.1
0.016622
35.142
12.0
24.43
5.49
201.96
170.05
976.6
1146.7
0.016650
32.394
13.0
26.47
3.45
205.88
174.00
974.2
1148.2
0.016676
30.057
14.0
I · 38.50
1.42
209.56
177.71
971.9
1149.6
J 0.016702
28.043
11
I
I
II
I
I
Pressure
Lbs. per Sq. In.
Absolute
Gage
pi
I
p
I
0.0
I
Temperature
t
Degrees F.
I
Heat of
the.
Liquid
Btu/lb.
I
I
I
Latent Heat Total Heat
of
of Steam
Evaporation
Btu/lb.
Specific Volume
V
ho
Water
Btu/lb.
Cu. ft. per lb.
1150.5
212.00
180.17
970.3
0.016719
213.03
181.21
969.7
J150.9
0.016726
216.32
184.52
!l52.l
967.6
0.016749
I
2..3
219.44
187.66
965.6
J153.2
0.016771
3.3
222.41
190.66
1154.3
963.7
0.016793
4.3
225.24
193.52
1155.3
0.016814
961.8
5.3
227.96
196.27 I
960.1
1156.3
0.016834
I 0.016854
230.57
958.4
1157.3
6.:l
198.90
I
233.07
201.44
7.3
956.7
1158.1
0.016873
8.:l
235.49
203.88
955.1
1159.0
0.016891
9.3
237.82
206.24
953.6
1159.8
0.016909
10.;;
240.07
208.52
952.1
1160.6
0.016927
ILl
242.25
210.7
950.6
1161.4
0.016944
12.J
244.36
212.9
949.2
1162.1
0.016961
13.a
246.41
214.9
1162.8
947.9
0.016977
I
I,Ll
248.40
217.0
946.5
1163.5
0.016993
i
I
15.:>
250.34
218.9
945.2
1164.1
0.0170G9
,
16.~.
252.22
220.8
943.9
1164.8
0.017024
17.,1
254.05
222.7
942.7
1165.4
0.017039
18.3
255.84
941.5
1166.0
0.017054
, 224.5
!,
19.:>
257.58
226.3
940.3
1166.6
0.017069
I
I
- , Steam fables (1967), With perm,:O:Slon of the pubH~hcr, --Ihe American
*/\bstracted from AS\1E
Society of Mechanical Engineers, 345 East 47th Street. New York. New York 10017.
14.696
15.0
16.0
17.0
18.0
19.0
20.0
21.0
22.0
23.0
24.0
25.0
26.0
27.0
28.0
29.0
30.0
31.0
32.0
33.0
34.0
0.3
1..3
I
Steam
Cu. ft. per lb.
I
I
I
I
,
I
I
I
I
I
I
I
I
I
26.799
26.290
24.750
23.385
22.168
21.074
20:087
19.190
18.373
17.624
16.936
16.301
15.7138
15.1684
14.6607
14.1869
13.7436
13.3280
12.9376
12.5700
12.2234
{confinued
on
the next page)
(;
C=f:I~
e::r=i
~i
9~~
=::bt
:::::::::s
::=:9
~
=:$
A-13
APPENDIX A - PI-YSICAl PROPERTIES Of flUIDS AND flOW CHARACTERISTICS OF VAItfft£S, FITTINGS. AND PIPE
CRANE
Properties of Saturated Steam and Saturated Wafer-continued
Temperature
Pressure
Lbs. per Sq. In.
Gage
Absolute
P'
35.0
36.0
37.0
38.0
39.0
40.0
41.0
42.0
43.0
44.0
45.0
46.0
47.0
48.0
49.0
50.0
51.0
52.0
53.0
54.0
55.0
56.0
57.0
58.0
59.0
60.0
61.0
62.0
63.0
64.0
65.0
66.0
67.0
68.0
69.0
70.0
71.0
72.0
73.0
74.0
75.0
76.0
77.0
78.0
79.0
80.0
81.0
82.v
83.0
84.0
85.0
86.0
87.0
88.0
89.0
90.0
91.0
92.0
9.3.0
94.0
%.0
96.0
97.0
98.0
99.0
100.0
101.0
102.0
103.0
104.0
105.0
106.0
107.0
108.0
109.0
I
P
t
I
Degrees F.
20.3
21.3
22.3
259.29
260.95
262.58
264.17
265.72
267.25
268.74
".,+
23.3
24.3
25.3
26.3
II
I,
28.3
29.3
30.3
31.3
32.3 ~
33.3
34.3
I
35.3
36.3
37.3
38.3
39.3
40.3
41.3
I
I
43.3
44.3
'U
45.3
46.3
47.3
48.3
49.3
50.3
51.3
52.3
53.3
54.3
55.3
56.3
57.3
58.3
59.3
60.3
61.3
62.3
63.3
64.3
I
m."
271.65
273.06
274.44
275.80
277.14
278.45
279.74
281.02
282.27
283.50
284.71
285.90
287.08
288.24
+'' ."
290.50
291.62
292.71
293.79
294.86
295.91
296.95
297.98
298.99
299.99
300.99
301.96
302.93
;303.89
304.83
,105.77
,106.69
,107.61
;;08.51
;;;09.41
310.29
311.17
312.04
312.90
313.75
314.60
315.43
316.26
317.08
3.17.89
3.18.69
3:!9.49
65.3
66.3
67.3
68.3
69.3
70.3
71.3
72.3
73.3
74.3
75.3
76.3
77.3
78.3
79.3
80.3
81.3
82.3
83.3
84.3
85.3
86.3
87.3
88.3
89.3
90.3
91.3
92.3
93.3
94.3
I
I
I
3:!D.28
I
321.06
321.84
322.61
323.37
324.13
314.88
325.63
32&.36
327.10
327.82
328.54
329.26
329.97
330.67
331.37
33,'.06
332.75
333.44
334.!l
I
I
Btu/lb.
228.0
229.7
231.4
233.0
234.6
236.1
237.7
239.2
240.6
242.1
243.5
244.9
246.2
247.6
248.9
250.2
251.5
252.8
254.0
255.2
256.4
257.6
258.8
259.9
26 I.!
262.2
263.3
264.4
265.5
266.6
267.6
268.7
269.7
270.7
271.7
272.7
273.7
274.7
275.7
276.6
277.6
278.5
279.4
280.3
281.3
282.1
283.0
283.9
284.8
285.7
286.5
287.4
288.2
289.0
289.9
290.7
291.5
292.3
293,1
293.9
294.7
295.5
296.3
297.0
297.8
298.5
299.3
300.0
300.8
301.5
302.2
303.0
303.7
304.4
305.1
Total Heat
of Steam
Latent Heat
of
Evaporation
Heat of
the
Liquid
I
I
I
I
I
I
Specific Volume
h.
i
Btu/lb.
Btu/lb.
~
939.1
938.0
936.9
935.8
934.7
933.6
932.6
931.5
930.5
929.5
928.6
927.6
926.6
925.7
924.8
923.9
923.0
922.1
921.2
920.4
919.5
918.7
917.8
917.0
916.2
915.4
914.6
913.8
913.0
912.3
911.5
910.8
910.0
909.3
908.5
907.8
907.1
906.4
905.7
905.0
904.3
903.6
902.9
902.3
901.6
900.9
900.3
899.6
899.0
898.3
897.7
897.0
896.4
895.8
895.2
894.6
893.9
893.3
892.7
892.1
891.5
891.0
890.4
889.8
889.2
888.6
888.1
887.5
886.9
886.4
885.8
885.2
884.7
884.1
883.6
1167.1
1167.7
1168.2
1168.8
1169.3
1169.8
1170.2
1170.7
I!71.1
1171.6
1172.0
!l72.5
1172.9
1173.3
1173.7
1174.1
1174.5
1174.9
1175.2
1175.6
1175.9
1176.3
1176.6
1177.0
1177.3
1177.6
1177.9
1178.2
1178.6
1178.9
1179.1
1179.4
1179.7
1180.0
1180.3
1180.6
1180.8
118 I.!
1181.4
1181.6
1181.9
1182.1
1182.4
1182.6
1182.8
1183.1
1183.3
1183.5
1183.8
1184.0
1184.2
1I84.4
!l84.6
1184.8
1185.0
1185.3
lI85.5
!l85.7
l!85.9
1186.0
1186.2
1186.4
1186.6
1186.8
1187.0
1187.2
1187.3
1187.5
1187.7
1187.9
!lS8.0
1188.2
1188.4
1188.5
1188.7
I
II
I
I
V
~
I
I
Water
Cu. ft. per lb.
,
I
I
i
I!
I
i
r,
,\j
I
,!
Ir
r
I,
I
I
O.Oi7083
0.017097
0.017111
0.017124
0.017138
0.017151
0.017164
0.017177
0.017189
0.017202
0.017214
0.017226
0.017238
0.017250
0.017262
0.017274
0.017285
0.017296
0.017307
0.017319
0.017329
0.017340
0.017351
0.017362
0.017372
0.017383
0.017393
0.017403
0.017413
0.017423
0.017433
0.017443
0.017453
0.017463
0.017472
0.017482
0.017491
0.017501
0.017510
0.017519
0.017529
().017538
0.017547
0.017556
0.017565
;).017573
(1.017582
0.017591
i).017600
v.017608
(}.017617
fI.017625
0.017634
i).017642
').017651
0.017659
0.017667
/).017675
0.017684
(;.017692
0.017700
0.017708
0.017716
0.017724
0.017732
(>.017740
0.01775
0.01776
0.01776
0.01777
0.'1l778
0.D1779
0.01779
0.01780
0.01781
I
I
I
I
I
I
.
Steam
Cu. ft. per lb.
11.8959
11.5860
11.2923
11.0136
10.7487
10.4965
10.2563
10.0272
9.8083
9.5991
9.3988
9.2070
9.0231
8.8465
8.6770
8.5140
8.3571
8.2061
8.0606
7.9203
7.7850
7.6543
7.5280
7.4059
7.2879
7.1736
7.0630
6.9558
6.8519
6.7511
6.6533
6.5584
6.4662
6.3767
6.2896
6.2050
6.1226
6.0425
5.9645
5.8885
5.8144
5.7423
5.6720
5.6034
5.5364
5.4711
5.4074
5.3451
5.2843
5.2249
5.1669
5.1101
5.0546
5.0004
4.947"
4.8953
4.8445
4.7947
4.7459
4.6982
4.6514
4.6055
4.5606
4.5166
4.4734
4.4310
4.3895
4.3487
4.3087
4.2695
4.2309
4.1931
4.1560
4.!l95
4.0837
II
I
,
i
I
II
~
A
.. 14
APPENDIX
C-'-.'--'-_
__
_
CRANE
A - PHYSICAL PROPERYIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
Prop'2 iies of Saturated Steam and Saturated Water-continued
Y
-------'-
Pressure
Lbs. per Sq. In. ___
1
AbSOpl,utc
I
I
Gap!;c
95.3
96.3
97.3
98.~
i
I
I
i
I
99.c,
100'
.0
101.3
102.3
103.3
104.3
105:3
106.3
107.3
108.3
109.3
110.3
111.3
112.3
113.3
114.3
I
,I
I
i
I
I
I
I
i
!
iI
!
I
I
I
115.3
116.3
117.3
118.3
119.3
120..3
121.3
122.3
122,.3
124,.3
12S.3
126.3
-,
128.3.
129.3
130.3
131.3
132.3
13,1.3
13'1.3
13S.3
137.3
139.3
141.3
14,1.3
145.3
147.3
149.3
151.3
15:1.3
15';.3
15;i.3
159.3
161.3
16:;.3
16;;.3
167.3
169.3
171.3
~U
,i
II
,
I
!
i
Tcmpcrature
I
Ii
--I
==c~=;:==*.===i..
110.0
111.0
112.0
113.0
114.0
11-~. 0
116.0
117.0
118.0
119.0
120.0
121.0
122.0
123.0
124.0
125.0
126.0
127.0
128.0
129.0
130.0
131.0
132.0
133.0
134.0
135.0
136.0
137.0
138.0
139.0
140.0
141.0
14'-. 0
143.0
144.0
145.0
146.0
147.0
148.0
149.0
150.0
152.0
154.0
156.0
158.0
160.0
162.0
164.0
166.0
168.0
170.0
172.0
174.0
176.0
178.0
180.0
182.0
184.0
186.0
188.0
190.0
192.0
194.0
196.0
198.0
200.0
205.0
210.0
215.0
220.0
225.0
230.0
235.0
240.0
245.0
I
17".3
177.3
179.3
181.3
18:3.3
183.3
190.3
19.1.3
200.3
20:;.3
210.3
215.3
220.3
nu
130.3
I
:
!
Degrees F.
334.79
335.46
336.12
I 336.78
337.43
33808
I
I 338.73
339.37
340.01
340.64
341.27
341.89
342.51
343.13
343.74
344.35
I
I
344.95
345.55
346.15
I 346.74
347.33
347.92
l 348.50
349.08
II 349.65
350.23
350.79
351.36
351.92
, 352.48
353.04
353.59
3~4 14
354.69
355.23
355.77
356.31
356.84
357.38
357.91
358.43
359.48
360.51
361.53
362.55
363.55
364.54
365.53
366.50
367.47
368.42
369.37
. 370.31
371.24
372.16
373.08
373.98
374.88
375.77
376.65
377.53
378.40
379.26
II 380.12
380.96
381.80
383.88
385.91
387.91
389.88
391.80
393.70
395.56
397.39
399.19
I
_~~~!b_
I
I
i
I
I
I,
I
I
Heat of
the
Liquid
I
I
I
I
I
I
,
II
!
. I
Ii
I
I
I
I
305.8
306.5
307.2
307.9
308.6
3093
309.9
310.6
311.3
311.9
312.6
313.2
313.9
314.5
315.2
315.8
316.4
317.1
317.7
318.3
319.0
319.6
320.2
320.8
321.4
322.0
322.6
323.2
323.8
324.4
325.0
325.5
.>26 1
326.7
327.3
327.8
328.4
329.0
329.5
330.1
330.6
331.8
332.8
333.9
335.0
336.1
337.1
338.2
339.2
340.2
341.2
342.2
343.2
344.2
345.2
346.2
347.2
348.1
349.1
350.0
350.9
351.9
352.8
353.7
354.6
355.5
357.7
359.9
362.1
364.2
366.2
368.3
370.3
372.3
374.2
. Latent Heat Total Heat
o f ; of Steam
Evaporation!
h
I
g
I
I
I
I
!
!
,I
I
i
I
,
I
I
I
I
I
I
L
I
I
Btu/lb.
Btui!!'.
883.1
882.5
882.0
881.4
880.9
8804
879.9
879.3
878.8
878.3
877.8
877.3
876.8
876.3
875.8
875.3
874.8
874.3
873.8
873.3
872.8
872.3
871.8
871.3
870.8
870.4
869.9
869.4
868.9
868.5
868.0
867.5
8671
866.6
866.2
865.7
865.2
864.8
864.3
863.9
863.4
862.5
861.6
860.8
859.9
859.0
858.2
857.3
856.5
855.6
854.8
853.9
853.1
852.3
851.5
850.7
849.9
849.1
848.3
847.5
846.7
845.9
845.1
844.4
843.6
842.8
840.9
839.1
837.2
835.4
833.6
831.8
830.1
828.4
826.6
1188.9
1189.0
il89.2
1189.3
1189.5
;; .
11'96
1189.8
1189.9
1190.1
1190.2
1190.4
1190.5
1190.7
1190.8
1190.9
1191.1
1191.2
1191.3
1191.5
1191.6
1191.7
1191.9
1192.0
1192.1
1192.2
1192.4
1192.5
1192.6
1192.7
1192.8
1193.0
1193.1
11932
1193.3
1193.4
,
!
I
I
!
1
I
I,
i
II
II
1193.5
I
I
I
I
I
I
,
1193.6
1193.8
1193.9
1194.0
1194.1
1194.3
1194.5
1194.7
1194.9
1195.1
1195.3
1195.5
1195.7
1195.8
1196.0
1196.2
1196.4
1196.5
1196.7
1196.9
1197.0
1197.2
1197.3
1197.5
1197.6
1197.8
1197.9
1198.1
1198.2
1198.3
1198.7
1199.0
1199.3
1199.6
1199.9
1200.1
1200.4
1200.6
1200.9
Specific Volume
v-
Water
Cu~~per I~.
I
-0"])1782 Tl4-:-048.f-0.01782
4.0138
0.01783
3.9798
0.01784
3.9464
0.01785
3.<)136
001-838813
I ~
0.01786
3.8495
0.01787
3.8183
0.01787
3.7875
I
0.01788
3.7573
0.01789
3.7275
0.01790
3.6983
0.01790
3.6695
0.01791
3.6411
0.01792
3.6132
0.01792
3.5857
0.01793
3.5586
0.01794
3.5320
0.01794
3.5057
0.01795
3.4799
0.01796
3.4544
0.01797
3.4293
0.01797
3.4046
3.3802
0.01798
3.3562
0.01799
0.01799
3.3325
0.01800
3.3091
0.01801
3.2861
0.01801
3.2634
0.01802
3.2411
0.01803
3.2190
0.01803
3.1972
001804
0.01805
3.1546
0.01805
3.1337
0.01806
3.1130
3.0927
0.01806
3.0726
0.01807
0.01808
3.0528
0.01808
3.0332
0.01809
3.0139
2.9760
0.01810
2.9391
0.01812
2.9031
0.01813
2.8679
0.01814
0.01815
2.8336
0.01817
2.8001
0.01818
2.7674
0.01819
2.7355
0.01820
2.7043
0.01821
2.6738
0.01823
2.6440
0.01824
2.6149
0.01825
2.5864
0.01826
2.5585
0.01827
2.5312
0.01828
2.5045
0.01830
2.4783
2.4527
0.01831
0.01832
2.4276
2.4030
0.01833
0.01834
2.3790
0.01835
2.3554
2.3322
0.01836
0.01838
2.3095
2_28728
0.01839
2.23349
0.01841
I
0.01844
2.18217
0.01847
2.13315
2.08629
0.01850
0.01852
2.01143
1.9984&
0.01855
1.95725
0.01857
1.91769
0.01860
1.87970
0.01863
I
I
I
I
I
I
I
I
I
I
I
ii
I
I
I
I
t
I
I
I
Steam---
I ~~~~~
A-IS
APPENDIX A - PHYSICAL PROPERTIES OF FLUlDS AND flOW CHARACTERISTICS Of VAlVES~ FlnINGS, AND PIPE
CRANE
Properties of Saturated Steam and Saturated Water-concluded
,
I
P'
I
'9=.~.
,~lji
'--"J-1lilI
.. .,jilt
250.0
255.0
260.0
265.0
270.0
275.0
280.0
285.0
290.0
295.0
300.0
320.0
340.0
360.0
380.0
JOO.O -
~
~
":=:t.
~
420.0
440.0
460.0
480.0
500.0
520.0
540.0
560.0
580.0
600.0
620.0
&40.0
&60.0
680.0
700.0
720.0
740.0
760.0
780.0
800.0
820.0
840.0
8&0.0
880.0
900.0
920.0
940.0
960.0
980.0
1000.0
1050.0
1100.0
1I50.0
1200.0
1250.0
1300.0
1350.0
1400.0
1450.0
1500.0
1600.0
1700.0
1800.0
1900.0
2000.0
2100.0
2200.0
2300.0
2400.0
2500.0
2&00.0
2700.0
2800.0
2900.0
3000.0
3100.0
3200.0
3208.2
I
I
I
I
I
I,
,
I
I
I
I
.I
I
I
I
,,
Heat of
the
Liquid
Temperature
Pressure
Lbs. per Sq. In.
Gage
Absolute
t
p
II
I
Btu/lb.
Btu/lb.
Degrees F.
400.97
235.3
402.72
240.3
404.44
245.3
406.13
250.3
255.3
407.80
260.3
409.45
265.3
411.07
412.67
270.3
414.25
275.3
280.3
415.81
417.35
285.3
423.31
305.3
428.99
325.3
434.41
345.3
365.3
439.61
444.60
385.3
I 449.40
405.3
425.3
454.03
458.50
445.3
465.3
462.82·
467.01
485.3
505.3
471.07
525.3
475.01
545.3
478.84
482.57
565.3
486.20
585.3
489.74
605.3
&25.3
493.19
496.57
645.3
665.3
499.8&
685.3
503.08
705.3
506.23
725.3
509.32
745.3
512.34
765.3
515.30
785.3
518.21
805.3
521.06
;;23.86
825.3
;;26.60
845.3
;;29.30
.865.3
885.3
S31.95
905.3
534.56
925.3
ii37.13
945.3
539.&5
965.3
542.14
E;44.58
985.3
0,50.53
1035.3
1085.3
556.28
1135.3
I 561.82
1185.3
I 567.19
1235.3 n n . 3 8
1285.3
577.42
1335.3
582.32
1385.3
587.07
1435.3
591.70
1485.3
596.20
1585.3
&04.87
1685.3
613.13
1785.3
621.02
1885.3
628.56
1985.3
635.80
2085.3
642.76
2185.3
649.45
2285.3
&55.89
2385.3
6b2.1I
2485.3
668.11
2585.3
&i'3.91
2685.3
679.53
2785.3
684.96
2885.3
690.22
2985.3
M5.33
3085.3
700.28
3185.3
705.08
3193.5
705.47
. Latent Heat
of
Evaporation
II
I
I
I
II
i
I
I
:
I
II
I
I,,
I
376.1
378.0
379.9
381.7
383.6
385.4
387.1
388.9
390.6
392.3
394.0
400.5
406.8
412.8
418.6
424.2
429.6
434.8
439'.8
444.7
449.5
454.2
458.7
463.1
467.5
471.7
475.8
479.9
483.9
487.8
491.6
495.4
499.1
502.7
50&.3
509.8
513.3
516.7
520.1
523.4
526.7
530.0
533.2
536.3
539.5
542.6
550.1
557.5
564.8
571.9
578.8
585.6
592.2
598.8
605.3
611.7
624.2
636.5
&48.5
660.4
672.1
683.8
695.5
707.2
719.0
731.7
744.5
757.3
770.7
785.1
801.8
824.0
875.5
906.0
I
;
I
1
I
I
I
I
I
825.0
823.3
821.6
820.0
818.3
816.7
815.1
813.6
812.0
810.4
808.9
802.9
797.0
791.3
785.8
_ 780.4
775.2
770.0
765.0
760.0
755.1
750.4
745.7
741.0
736.5
732.0
727.5
723.1
718.8
714.5
710.2
706.0
701.9
697.7
693.&
689.6
685.5
681.5
677.6
673.6
669.7
665.8
661.9
658.0
654.2
650.4
640.9
631.5
622.2
613.0
603.8
594.6
585.6
567.5
567.6
558.4
540.3
522.2
503.8
485.2.
4&6.2
446.7
426.7
406.0
384.8
361.6
337.6
312.3
285.1
V
ho
1201.1
1201.3
1201.5
1201.7
1201.9
1202.1
1202.3
1202.4
1202.6
1202.7
1202.9
1203.4
. 1203.8
1204.1
1204.4
- _.t204.6_
1204.7'
1204.8
1204.8
1204.8
1204.7
1204.5
1204.4
1204.2
1203.9
1203.7
1203.4
1203.0
1202.7
1202.3
1201.8
1201.4
1200.9
1200.4
1199.9
1199.4
1198.8
1198.2
1197.7
1197.0
1196.4
1195.7
1195.1
1194.4
1193.7
1192.9
1191.0
1189.1
1187.0
1184.8
1182.6
1180.2
1177.8
1175.3
1172.9
fi70.1
1164.5
1158.6
1152.3
1145.6
1138.3
1I30.5
1122.2
1113.2
1103.7
,
1093.3
1082.0
1069.7
1055.8
Ou. ft. per lb.
Cu. ft. per lb.
0.01865
0.01868
0.01870
0.01873
{l.01875
0.01878
0.01880
0.01882
0.01885
0.01887
0.01889
lJ.01899
0.01908
0.01917
0.01925
.0.01934
11.01942
0.01950
0.01959
0.01967
0.01975
0.01982
0.01990
.0.01998
0.02006
0.02013
0.02021
0.02028
0.02036
0.02043
0.02050
0.02058
0.02065
0.02072
0.02080
0.02087
0.02094
0.02101
0.02109
0.02116
0.02123
0.02130
0.02137
0.02145
(j.02152
0.02159
0.02177
il.02195
0.01214
0.02232
0.02250
0.02269
0.02288
0.02307
l)'O2327
0.0234&
0.02387
0.02428
0.02472
0.02517
0.02565
0.02615
0.02669
0.02727
0.02790
0.02859
0.02938
0.03029
0.03134
;).03262
-6-.03428
0.03681
0.04472
-'.05078
1.84317
1.80802
1.77418
1.74157
1.71013
1.67978
1.65049
1.62218
1.59482
1.56835
1.5427-<
1.44801
1.36405
1.28910
1.22177
1.1&095
1.10573
1.05535
1.00921
0.96677
0.92762
0.89137
0.85771
0.82637
0.79712
0.76975
0.74408
0.71 995
0.69724
0.67581
0.6555&
0.63639
0.61822
0.60097
0.58457
0.5&896
0.55408
0.53988
0.52631
0.51333
0.50091
0.48901
0.47759
0.46662
0.45609
0.4459&
0.42224
0.40058
0.38073
0.36245
0.34556
0.32991
0.31536
0.30178
0.28909
0.27719
0.25545
0.23607
0.21861
0.20278
0.18831
0.17501
0.16272
0.15133
0.14076
0.13068
0.1211 0
0.11194
0.10.l05
0.09420
0.08500
0.07452
0.05663
0.05078
I
~---
I
I
1020.3
993.3
931.6
906.0
Steam
Water
Btu/lb.
'Itt"'"
218.4
1&9.3
5&.1
0.0
Specific Volume
Total Heat
of Steam
I
I
A - 16
APPEN:0IX A - PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES, fITTINGS, AND PIPE
CRANE
Properties of Superheated Steam*
v = specific volume, cubic feet per pound
h, = total heot of steam, Btu per pound
Pressure
Lbs. per
Sq. In.
SflI,tt-.
Abs.
Gage
P'
P
3500
213.«13
5.31 227.%
I
30.0
15.3
250.34
267.25
40.0
25.3
50.0 i
35.31 281.02
60.0
45.3
292.71
80.0
65.3
312.04
90.0
75.3
;)20.28
100.0
85.3
327.82
120.0
125.3
35J:.04
145.3
180.0
165.3
363.55
373.08
185.3
381.80
205.3
389 . 88
225.31397.39
25.428 I 28.457 i! 31.466, 34.465 I
" 40.447! 43.435
37.458!
1239.2 1286.9' 1334.9 1383.5 1432.911483.2 1534.3
46.420
1586.3
52.388
1693.1
58.352
1803,3
V
15.859
1213.6
245,3
404.44
265.3
411.07
300.0
320.0
I
285.3
417,35
423.:11
325.3
428.99
I
I
345.3
434.41
28.943
1534.0
30.936
1586.1
34.918
1692.9
38.896
1803.2
18.699
20.199
21.697
23.194
26.183
29.168
9.424
1209.9
10.0621 11.306
1234.9 I 1284.1
12.529
1332.9
13.741
1382.0
14.947116.150
1431.7 1482.2
17.350
1533.4
18.549
1585.6
20.942
1692.5
23.332
1802.9
V
7.815
1208.0
8.354
1233.5
9.400
1283.2
10.425
1332.3
11.438
1381.5
12.446
1431.3
I 13.450
1481.8
14.452
1533.2
15.452
1585.3
17.448
1692.4
19.441
1802.8
V
6.664
1206.0
7.133
1232.0
8.039
1282.2
8.922
1331.6
9.793 10.659
1381.0 I 1430.9
11.522
1481.5
12.382
1532.9
13.240
1585.1
14.952
1692.2
16.661
1802.6
V
5.801
1204.0
6.218
1230.5
7.018
1281.3
7.794 I 8.560 1 9.319
1330.9 1380.5 1430.5
10.075
1481.1
10.829
1532.6
11.581
1584.9
13.081
1692.0
14.577
1802.5
17
5.128
1202.0
5.505
1228,9
8.277
6.2231 6.917 1 7.600
1280.3 1330.211380.0 I 1430.1
8.950
1480.8
9.621
1532.3
10.290
1584.6
11.625
1691.8
12.956
1802.4
h,
V
4.590
1199.9
4.935
1227.4
5.588
1279.3
6.216
1329.6
7.443
1429.7
8.050
1480.4
8.655
1532.0
9.258
1584.4
10.460
1691.6
11.659
1802.2
V
3.7815
1195.6
4.0786
1224.1
4.6341
1277.1
5.163715.6813 6.1928
1328.2 1378.4! 1428.8
6.7006
1479.8
7.2060
1531.4
7.7096
1583.9
8.7130
1691.3
9.7130
1802.0
4.411914.858815.2995
1326.8 1377.4 1428.0
5.7364
1479.1
6.1709
1530.8
6.6036
1583.4
7.4652
1690.9
8.3233
1801.7
h,
hg
V
i
I 1432.1 1 1482.5 1533.7 1585.8 1692.7 1803.0
1
I
3.4661 3.9526
1220.811275.3
1
6.833
I 1379.5
h,
...
3.0060
1217.4
3.441313.8480
1273,3 1325.4
4.2420 I 4.6295
1376.411427.2
5.0132
1478.4
5.3945
1530.3
5.7741
1582.9
6.5293
1690.5
7.2811
1801.4
V
...
...
2.6474
1213.8
3.0433
1271.2
3.4093
1324.0
3.7621 4.1084
1375.311426.3
4.4508
1477.7
4.7907
1529.7
5.1289
1582.4
5.8014
1690.2
6.4704
1801.2
V
2.3598
1210.1
2.i247
3.0583
1322.6
3.3783
1374.3
I 1425.5
3.6915
4.0008
1477.0
4.3077
1529.1
4.6128
1581.9
5.2191
1689.8
5.8219
1800.9
V
2.1240
1206.3
2.4638
1266.9
2.7710 3.06421 3.3504
1321.2. 1373.211424.7
3.6327
1476.3
3.9125
1528.5
4.1905
1581.4
4.7426
1689.4
5.2913
1800.6
1.926812.246212.531612.80241 3.0661
1202.11 1264.6 I 1319.7. 1372.1 11423.8
3.3259
1475.6
3.5831
1527.9
3.8385
1580.9
4.3456
1689.1
4.8492
1800.4
12.061912.3289! 2.58081 2.8256
1262.4 1318.2 1371.1 i 1423.0
3.0663
1474.9
3.3044
1527.3
3.5408
1580.4
4.0097
1688.7
4.4750
1800.1
V
V
..
V
...
V
V
V
V
h,
360.0
26.949
1482.8
V
hg
...
I
I
I
I 1.90371 2.1551
I
ii
1316.8
2.3909
1370.0
2.6194
1422.1
2.8437
1474.2
3.0655
1526.8
3.2855
1579.9
3.7217 4.1543
1688.4' 1799.8
1.7665
1257.7
2.0044
1315.2
2.2263 2.4407
1368.91 142 1.3
2.6509
1473.6
2.8585
1526.2
3.0643
1579.4
3.4721
1688.0
3.8764
1799.6
1.6462
1255.2
1.8725
1313.7
2.08231 2.2843
1367.8 1420.5
2.4821
1472.9
2.6774
1525.6
2.8708
1578.9
3.2538
1687.6
3.6332
1799.3
..
1.5399 1.7561
1252.8 1 1312.2
1.9552 1 2.1463
1366.7 I 1419.6
2.3333
1472.2
2.5175
1525.0
2.7000
1578.4
3.0611
1687.3
3.4186
1799.0
...
1.445411.6525
1250.3 11310.6
1.8421 12.0237
1365.61 1418 .7
2.2009
1471.5
2.3755
1542.4
2.5482
1577.9
2.8898
1686.9
3.2279
1798.8
I
!
V
h,
1269.0
1260.0
hg
340.0
24.952
1432.5
15.685. 17.195
1333.61 1382.5
h,
305.3
22.951
1383.0
12.624 14.165
1236.41 1285.0
h,
I
20.945
1334.2
18.929
1286.0
11.838
121 1.7
h,
280.0
16.892
1237.8
I
V
hg
hg
260.0
,
i
'Abstracted from ASME Steam -rables (1967) with permission of the publisher. the
American Society 01 Mechanical Engineers. 345 East 47th Street, "ow York. ~. Y. 10017.
1
!
1500'
23.900
1215.4
h,
240.0
1300'
V
hg
h,
220.0
I
77.807
1803.4
hg
200.0
I
,
69.858
1693.2
h.
160.0
--: 1000' 1 11 00'
61.905
1586.5
hg
140.0
900'
800'
37.985l41.986. 45.978 49.964 53.946157~9Z6
1287.3 I 1335.211383.811433.211483.4: 1534.5
hg
105.31 34l'..27
700'
33.963
1239.9
h,
55.31 302 . 93
600'
31. 939
1216.2
\'
h,
70.0
500,1
I
h,
20.0
400'
t
0.3
15.0
Total Temperature-Degrees Fahrenheit (t)
Ten'>p.
(continued oil
'he ~.l{' pog.)
CRANE
A.17
APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS Of VALVES, flnINGS. AND PIPE
Plroperties of Superheated Steam -
continued
v = specific volume, cubic feet per pound
hg = total heat of steam, Btu per pound
Pressure
Lbs. per
1
I
Sat.
Temp.
Total Temperature-Degrees Fahrenheit (t)
Sq. In.
AbS'1 Gage
P'
380.0
P
365.3
500'
t
~
439.61
h,
400.0
385.3
444.60
405.3
449.40
425.3
454.03
460.0
445.3
458.50
.,
::
465.3
1.2148 1 1.4007
1242.4 1305.8
485.3
505.3
540.0
525.3
1.424211.57031 1.7117
1360.0 1414.41 1468.0
V
1.0409 i 1.2115 1.3615
1234.1 1300.8 1 1358.8
V
475.01
hg
i
560.0
545.3
478.84
-
'v'
h,
'~
==-3
1
'~.
i
~~
580.0
565.3
482.57
V
h.
600.0
585.3
486.20
V
h.
650.0
635.3
494.89
-
II
h.
700.0
750.0
685.3
735.3
503.08
510.84
800.0
785.3
518.21
850.0
835.3
525.24
==t#
:::=t
:::::a
900.0
885.3
531.95
935.3
538.39
1000.0
985.3
544.58
=-
1050.0
1035.3
550.53
1085.3
556.28
1135.3
561.82
2.4998 2.6384
1741.2 , 1797.7
Ii 2.5230
2.12261 2.2569
1629.9 1685.1
2.3903
1740.9
2.0330
1629.5
2.1619
1684.7
2.2900
1740.6
2.4173
1797.2
1797.4
1.4508
1465.1
1.570411.6880
1519.111573.4
1.8042
1628;2
1.9193
1683.6
2.0336
1739.7
2.1471
1796.4
1.0217
1293.9
1.155211. 2787
1354.2 1410.0
1.3972
1464.4
1. 5129 11.6266
1518.6 I 1572.9
1.7388
1627.8
1.8500
1683.3
1.9603
1739.4
2.0699
1796.1
0 ..9824
1.1125
1353.0
1.3473
1463.7
1.4593
1518.0
i
1409.2
1512.4
1.6780
1627.4
1.7855
1682.9
1.8921
1739.1
1.9980
1795.9
I 1.2324
1
,1
1.5693
I
I
0.9456
1290.3
1.0726
1351.8
1.1892
1408.3
1.3008
1463.0
1.4093
1517.4
1.511iO
1571.9
1.6211
1627.0
1.7252
1682.6
1.8284
1738.8
1.9309
1795.6
0.7173
1207.6
0.8634
1285.7
0.9835
1348.7
1.0929
1406.0
1.1969
1461.2
1.2979
1515.9
1.3%<);
1570.7
1.4944
1625.9
1.5909
1681.6
1.6864
1738.0
1.7813
1794.9
0.7928
1281.0
0.9072
1345.6
1.0102
1403.7
1.1078
1459.4
1.2023
1514.4
1.2948
1569.4
1.3858
1624.8
1.4757
1680.7
1.5647
1737.2
1.6530
1794.3
0.7313
1276.1
0.8409
1342.5
0.9386
1401.5
1.0306
1457.6
1.1195
1512.9
1.2063
1568.2
1.2916
1623.8
1.3759
1679.8
1.4592
1736.4
1.5419
1793.6
I 1271.1
, 0.6774
0.7828
1339.3
0.8759
1399.1
0.9631
1455.8
1.0470
1511.4
1.1289
1566.9
1.2093
1622.7
1.2885
1678.9
1.3669
1735.7
1.4446
1792.9
0.6296
1265.9
0.7315
1336.0
0.8205
1396.8
0.9034
1454.0
0.9830
1510.0
1.0606
1565.7
U366
1&21.6
1.2115
1678.0
1.2855
1734.9
1.3588
1792.3
0.5869
1260.6
0.6858
1332.7
0.7713
1394.4
0.8504
1452.2
0.9262
1508.5
0.9998
1';64.4
1.0720
1620.6
1.1430
1677.1
1.2131
1734.1
1.2825
1791.6
0.54851 0.6449
1255.1 1329.3
0.7272
1392.0
0.8030
1450.3
0.8753
1507.0
0.9455
1563.2
1.0142
1619.5
1.0817
1676.2
1.1484
1733.3
1.2143
1791.0
I 0.5137 0'.6080 0.6875
1249.3 1325.911389.6
0.7603
1448.5
0.8295
1505.4
0.8966
1561.9
0.9622
1618.4
1.0266 1.0901
1675.3 . 1732.5
1.1529
1790.3
1.0973
1789.6
...
...
V
1
...
\
...
i
0.4821 0.5745
1243.411322.4
0.6515
1387.2
0.7216
1446.6
0.7881
1503.9
0.8524
1560.7
0.9151 0.9767 1.0373
1617.41 1674 .4 ; 1731.8
0.4531 0.5440
1237.3 ,1318.8
0.6188
1384.7
0.6865
1444.7
0.7505
1502.4
0.8121
1559.4
fJ.8723 i 0.9313 : 0.9894
1616.3 1673.5 1731.0
1.0468
1789.0
0.4263
1230.9
0.5889
1382.2
0.6544
1442.8
0.7161
1500.9
0.7754
1558.1
U.8332 f 0.8899
,615.21 1672.6
0.9456
1730.2
1.0007
1788.3
I
\
V
2.7647
1798.0
0.7944
1215.9
V
h.
2.6196
1741.6
1.3284
1410.9
I 1292.1
h.
1I50.0
2.4739
1685.8
2.2302
1796.7
0.8287
1219.1
hg
1100.0
2.7515! 2.9037
1741.9 1798.2
2.1125
1740.0
0.8653
1222.2
..
\
2.5987
1686.2
I
1.87461 1.9940
1628.7 1684.0
1.2010
1355.3
hg
'=::J
2.897313.0572
1742.2 1798.5
1. 6323 11.7542
1519.7 1573.9
1.0640
1295.7
\'
hg
1686.5
1.5085
1465.9
0.9045
1225.3
..
V-
1.85041 1.9872
1521.5 1 1575.4
1
1.7716 i 1.9030
1520.91, 1574.9
I 1500'
I
I 2.7366 '
I
1400'
1.3819
1411.8
1.2504
1356.5
h.
950.0
I
2.3200
1796.9
1.1094
1297.4
...
hg
0
2.1977
1740.3
.; 0.9466
1228.3
h.
:=:$
1300
I
9507 2.0746
1.
1 1684.4
1629.1
1.4397
1412.7
V
-
,
1.69921 1.8256
1520.3 1 1574.4
1.3037
1357.7
h.
\I
I
1.5708
1466.6
1.1584
1299.1
hg
~
1.5023 1.6384
1413.6 I 1467.3
0.9919
1231.2
f
1200'
1.936312.0790 1 2. 2203 1 2.3605
1522.1 1575.'1 1630.4. 1685.5
1.2691
1302.5
i 1362.31
i,
1.7918
1468.7
1.9759
1.0939
1236.9
h.
1100"
1.8795
1469.4
2.0825
1470.8
V
V
471.07
I
2.2484,1 2~'!.U4iI 2.5750 1
1523.811017.4: 1631.6,
j
I
2.1339 2.2901 i 2,4450 I
1523.3 i 1576.9 J 1631.21
1
j
2.0304 i 2.1795) 2.32731
1522.711570.411630.8
1.3319
1304.2
V
1000'
i
,1.1517
hg
520.0
900 0
800'
,
V
-
467.01
I
I
I 1470.1
h. ' 1239 .7
hg
500.0
0
1.567611.72581
1416.21
,
1
1.492611.6445 1
1361.1 I 1415.31
V
462.82
700
1.9139!
1417.91
1
.
.
1
1.4763, 1.649911.8151 I
1307.411363.4 I 1417.0
-
hg
480.0
I
1.559811.7410
1309.011364.5
1.2841
1245.1
ng
440.0
1.3606
1247.7
0
V
hg
420.0
600
...
. ..
0.5162
1315.2
i
I
A -18
APPENDIX A- PHYSICAL PROPERTIES OF FLUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
Properties of Superheated Steam -
T' = speciflc volume, cubic feet
CRANE
concluded
per pound
h, = totcil heat of steam, Btu per pound
p","""
So<
Lbs. per ~ Temp,
Total Temperature-Degrees Fahrenheit (t)
Sq. In.
Abs.
P'
,
I Gage
650'
P
t
1200.0
1185.3
567.19
1300.0
1285.3
577.42
1
1400.0
I 1385.3
I
1500.0 11485.3
1600.0
.
1700.0
I
587.07
1585.3
604.87
1685.3
61:1.13
1785.3
621.02
\'
2000.0
1885.3
1985.3
628.56
636.80
2085.3
642.76
2185.3
649.45
2300.0
2285.3
655.89
2400.0
2385.3
662.11
2500.0
2485.3
668.11
2600.0
2585.3
673.91
2700.0
I2685.3
679.53
2800.0
2785.3
684 . 96
2900.0
2885.3
690 ..22
2985.3
695.33
3100.0
3085.3
700.28
3185.3
705.08
3400.0
1
I
I!
3285.3
3385.3
...
.
.
I 1200' I 1300'
1400'
1500'
0.7974
1614.2
0.8519
1671.6
0.9055
1729.4
0.9584
1787.6
i?
h,
0.4052
1261.9
0.4451
1303.9
0.4804
1340.8
0.5129
1374.6
0.57291 0.6287
1437.1
.
, 1496.3
0.6822
1554.3
0.7341
1612.0
0.7847
1669.8
0.8345
1727.9
0.8836
1786,3
V
0.3667 0.4059
1251.411296.1
400 0.4712
0.4
1334.5 1 1369.3
0.528210.5809
1433.2 1493.2
0.6311
1551.8
0.6798
1609.9
0.7272
1668.0
0.7737
1726.3
0.8195
1785,0
0.3328
1240.2
I 0.3717
0.4894
1429.2
0.5394
1490.1
0.5869
1549.2
0.6327
1607.7
0.6773
1666.2
0.7210
1724.8
0.7639
1783.7
n,
0.3026
1228.3
0.3415
1279.4
0.4049 1 0.4350
1328.0 1364.0
1
0.37411 0.4032
1321.4 1358.5
0.4555
1425.2
0.5031
1486.9
0.5482
1546.6
0.5915 0.6336
1605.6 1664.3
0.6748
1723.2
0.7153
1782.3
V
0.2754
1215 ..1
0.3147
1270.5
0.3468
1314.5
0.3751
1352.9
0.4255
1421.2
0.4711
1483.8
0.5140
1544.0
0.5552
1603.4
0.5951
1662.5
0.6341
1721.7
0.6724
1781.0
0.2505
1201.2
0.2906
1261.1
0.3213
1307.4
0.3500
1347.2
0.3988
1417.1
0.4426
1480.6
0.4836 0.5229
1541.4 1601.2
0.5609
1660.7
0.5980
1720.1
0.6343
1779,7
0.2274
1185.7
0.2687
1251.3
0.3004 0.32751 0.3749
1300.21 1341.4 . 1412.9
0.4171
1477.4
0.4565
1538.8
0.4940
1599.1
0.5303
1658.8
0.5656
1718.6
0.6002
1778.4
0.2056 0.2488
1168.31 1240 . 9
0.1847 0.2304
1148.5 . 1229.8
0.2805
1292.6
0.3072
1335.4
0.3534
1408.7
0.39421 0.4320 0,4680
1474.1 1536.2', 1596.9
0.5027
1657.0
0.5365 0.5695
1717.0 1777.1
0.2624
1284.9
0.2888
1329.3
0.3339
1404.4
0.3734
1470.9
0.4099
1533.6
0.4445
1594.7
0.4778
1655.2
0.5101
1715.4
0.5418
1775.7
0.16361 0.2134
1123.9 1218.0
0.2458
1276.8
0.2720
1323.1
0.3161
1400.0
0.3545
1467.6
0.3897
1530.9
0.4231
1592.5
0.4551
1653.3
0.4862
1713.9
0.5165
1774.4
·.
0.1975
1205.3
0.2305
1268.4
0.2566
1316.7
0.2999
1395.7
0.3372
1464.2
0.3714
1528.3
0.4035
1590.3
0.4344
1651.5
0.4643
1712.3
0.4935
1773.1
...
·.
0.1824
1191.6
0.2164 0.2424
1259.71 1310.1
0.2850
1391.2
0.3214
1460.9
0.3545
1525.6
0.3856
1588.1
0.4155
1649.6
0.4443
1710.8
0.4724
1771,8
n,
·.
·.
0.1681
1176.7
0.20321 0.2293
1250.6 1303.4
0.2712
1386.7
0.3068
0.3390
I 0.3692
0.3980
0.4259
0.4529
V
...
0.1544
1160.2
0.1909
1241.1
0.2171 . 0.2585/ 0.2933 ,0.3247
1296.5 ' 1382.1 , 1454.1 11520.2
0.3540
1583.7
0.3819 10.4088
1646.0 1707.7
0.4350
1769,1
0.1411
1142.0
0.1794
1231.I
0.2058
1289.5
0.2468
1377.5
0.2809 0.3114 0.3399
1450.711517.511581.5
0.3670
1644.1
0.3931
1706.1
0.4184
1767.8
·.
·.
0.1278
1121.2
0.1685
1220.6
0.1952
1282.2
0.2358
1372.8
0.26931 0.2991
1447.2 1514.8
0.3268
1579.3
0.3532
IM2.2
0.3785
1704.5
0.4030
1766.5
·.
...
0.1l38
1095.3
0.1581
1209.6
0.1853
1274.7
0.2256
1368.0
0.2585
1443.7
1512.1
0.3147
1577.0
0.3403
1640.4
0.3649
1703.0
0.3887
1765.2
V
...
...
0.09821 0.1483
1060.5 1197.9
0.2161
1363.2
0.2484
1440.2
0.2770
1509.4
0.3033
1574.8
0.3282
1638.5
0.3522
1701.4
0.3753
1763.8
V
.. .
...
·.
· .
I
0.1759
1267.0
0.1389
1185.4
0.1671
1259.1
0.2071 1 0.2390 0.2670
1358.4. 1436.71 1506.6
0.2927
1572.6
0.3170
1636.7
0.3403
1699.8
0.3628
1762.5
·.
.. .
...
I 0.1300
1172.3
0.1588
1250.9
0.198710.2301
1353.4 1433.1
0.2827 0.3065
1570.3 1 1634.8
0.3291
1698.3
0.3510
1761.2
h,
...
· ..
..
1 0.1213 0.1510
1
11158.2/1242.5
0.1908
1348.4
0.2218 0.248810.2734
1429.511501.011568.1
0.2:f.6
162.9
0.3187
1696.7
0.3400
1759.9
V
...
."
..
1 0.1129 0.1435
11143.21 1233.7
0.1834
1343.4
0.21401 0.2405
1425.911498.3
0.2872
1631.1
0.3088
1695.1
0.3296
1758.5
V
n,
i/
Ii
V
n,
V
V
V
h,
V
nJ
V
h,
V
..
..
h,
V
V
h,
V
h,
hg
V
h.
3300.0
1100'
0.6250 1 0.68451 0.7418
1440,911499.4 ! 1556.9
h.
3200.0
I
0.5615
1379.7
h,
3000.0
1000'
0.5273
1346.9
h,
2200.0
900'
0,4905
1311.5
ii,
2100.0
I
0.4497
1271.8
h,
1900.0
800'
n,
h,
1800.0
I
1
ii,
596.20
750'
700'
V ,
h.
...
1287.9
i,
I
I
1
I 1457.5 1522.9 1585.9 1647.8 1709.2 1770.4
I 0.2877
I
I
0.2576
1503.8
0.2646
1565.8
CRANE
A-19
APPENDIX II - PHY,ICAL PROPERTIES OF FLUIDS AND FLOW CHARACnRISTICS OF VALVES. FITTINGS. AND PIPE
Properties of Superheated Steam and Compressed Water*
v = specific volume, cubic feel per pound
h.= 10101 heal of sleam, Btu per pound
Absolute
Total Temperature-Degrees Fahrenheit (t)
Pressure
=L=~~S.=.l=p;=.r=l==*=2=0=O'=io=40=0~o~I==5=0=O'=*=60=0='~1=7=OO='=4=80=0='=-,\=9=0°='=4,=l=O=OO='=*I=l1=O=O'=*,1=1=200'
1
1
i7
3500
h.
3600
0.0164
176.0
0.2'195
1693.6
0.3198
1757.2
0.2908
1692.0
0.3106
1755.9
0.0183 0.0198, 0.0225
379.3 Ii 487.6
608.1
3800
"\ 0.0164
h. 176.7
0.018.11 0.0198
379.51' 487.7
0.0224 0.029410.1169
607.5, 768.4 1195.5
0.157410.1868
1322.411411.2
0.21161 0.2340 10.2549 0.2746
1487.01 1556.8 1623.611688.9
0.2936
1753.2
4000
V 0.0164
h. 177.2
0.0182
379.8
0.1752
1403.6
0.19941 0.2210 1 0.2411
1481.311552.2 1619.8
0.2601
1685.7
0.2783
1750.6
0.2470
1682.&
0.2645
1748.0
V
0.0164
177.6
0.0302 I 0.12%
775.11 1215.3
0.0198
487.7
1
0.01821 0.0197
487.8
380.1
0.02231 0.0287
606.91 763.0
0.1052
1174.3
0.1463
1311.6
0.0222
606.4
0.0282
758.6
0.0945
1151.6
0.1362
1300.4
0.1647
1396.0
0.1883 'I 0.2093
1475.5 1547.6
0.2287
1616.1
0.2174 0.2351 0.2519
1612.311679.411745.3
'I
•
4400
V
0.0164
h. 178.1
0.0182
380.4
0.0197
487.9
0.0222
605.9
0.0278
754.8
0.0846
1127.3
0.1270 0.1552
1289.011388.3
0.17821 0.1986
1469.7 1543.0
4600
V
0.0164
h, 178.5
0.0182
380.7
0.0197
487.9
0.0221
605.5
0.0274, 0.0751
751.511100.0
0.11861 0.1465
1277.2 1380.5
0.1691 0.1889
1453.'l! 1538.4
0.2071 0.2242
160R.5!1670.3
0.2404
1742.7
\" 0.0164
179.0
0.0182
380.9
0.0196
488.0
0.0220
605.0
0.0271 I 0.0665
748.6' 1071.2
0.1109
1255.2
0.1385
1372.6
0.1&061 0.1800
1458.0 i 1533.8
0.1977 0.2142
1604.711673.1
0.2299
1740.0
V
0.0181
381.5
0.01%
488.2
0.0219
604.3
0.0265
743.7
0.1244
1356.6
0.14581 0.1642
1446.21 1524.5
0.1810
1597.2
0.1966
0.2114
5600
\' 0.0163 0.0181
h. 180.8 382.1
0.0195
488.4
0.0217
603.6
0.0260 10.0447
739.6
975.0
0.0856
1214.8
0.1l241 0.1331! 0.1508
1340.21 1434.3! 1515.2
0.16671 0.1815
1589.6 1660.5
0.1954
1729.5
6000
V
0.0180
382.7
0.0195
488.6
0.0216
602.9
0.0256 1 0.0397
736.1' 945.1
0.0757
1188.8
0.1020
1323.6
0.1544 1 0.1684
1505.91 1582.0! 1654.2
0.1817
1724.2
V 0.0163
182.9
0.0180
383.4
0.0194
488.9
0.0215
602.3
0.0252
732.4
0.0358
919.5
0.0655
1156.3
0.0909
1302.7
O.llM
1407.3
1494.2
0.1411
1572.5
0.1544
1646.4
0.1669
1717.6
V
0.0163
184.0
0.0180
384.2
0.0193
489.3
0.0213
601.7
0.0248
729.3
0.0334
901.8
0.05731 0.0816
1124.9 1281.7
O.lOM
1392.2
0.1160
1482.6
0.1298
1563.1
0.1424
1638.6
0.1542
1711.1
0.0163
185.2
0.0179
384.9
0.0193
489.6
0.0212
601.3
0.0245
726.6
0.0318
889.0
0.0512
1097.7
0.0737
1261.0
0.0918, 0.1068
1377.1':1 1471.0
0.1200
1553.7
0.13211 0.1433
1630.8 1704.6
0.0162
186.3
0.0179
385.7
0.0192
490.0
0.0211
600.9
0.0242
724.3
0.0306
879.1
0.0465
1074.3
0.0671
1241.0
0.0845! 0.0989
1361.2:1 1459.6
0.1115
1544.5
0.1230
1623.1
0.1338
1698.1
0.0162
h. 188.6
0.0178
3·87.3
0.0191
490.9
0.0209
600.3
0.0237
720.4
0.0288
864.7
0.0402
1037.6
0.0568
1204.1
0.07241 0.0858
1333'()i! 1437.1
0.0975
1526.3
0.1081
1607.9
0.1l79
1685.3
\' 0.0161 0.0177 0.0189 0.0207 0.0233 0.0276 0.0362 0.0495
J
O.0633~,: 0.0757
0.0865
1508.6
0.0963
1593.1
0.1054
1672.8
0.0776
1491.5
0.0868
1578.7
0.0952
1660.6
4800
h.
5200
h.
0.0164
179.9
0.0163
h. 181.7
-
6500
h.
7000
h.
V
7500
h.
V
8000
h,
10000
h,
0.0531 0.0973
1016.9· 1240.4
1
!
i
I
.
!
I 1666.8 1734.7
o.l2n . 0.1391
1422.3
j 0.1266
i!
V
9000
190.9
388.9
491.8
600.0
717.5
854.5
11000
0.0161
h. 193.2
0.0176
390.5
0.0188
492.8
0.0205
599.9
0.0229
715.1
0.0267
846.9
12000
Ii 0.0161 0.0176 0.0187 0.0203 0.0226 0.0260 0.0,317 0.0405 0.0508': 0.0610 0.0704 0.0790 0.086'1
V
h,
13000
14000
1
0.0335
992.1
0.0562:1 0.0676
1280.2:i 1394.4
0.0443
1146.3
::
713.3
841.0
977.8
1124.5
1258.0
1374.7
1475.1
1564.9
1648.8
V 10.0160 0 . 0175 0.0186 0.0201
195.5
392.1
493.9
0.0376
1106 .7
0.0466! 0.0558
In8.5 i, 1356.5
0.0645
1459.4
0.0725
1551.6
0.0799
1637.4
0.0354
1092.3
0.0432
1221 ...
0.0515
1340.2
0.05%
1444.4
0.0670
1538.8
0.07-10
1626.5
393.8
495.0
600.1
0.0213
711.9
0.0253
836.3
0.0.,02
197.8
"\ 0.0160
h. 200.1
0.0174
395.5
0.0185
496.2
0.0200
600.5
0.0220
710.8
0.0248
832.6
0.0291
958.0
966.81
,i
\' 0.0159 0.0174 0.0184 0.0198 0.0218 0.OH4 0.0282 0.0337 0.0405:'. 0.0479 1 0.0552 0.0624 0.0690
h,
15500
1305.3 Ii 1415.3
599.9
h.
15000
1011. 3 1 1172 . 6
]
1
-
0.176410.206610.232610.256310.2784
1338.21 1422.21 1495.51 1563.61 1629.2
I
I
!
I
0.16971 0.1996 1 0.22521 0.2485 0.2702
1333.011418.6 1492.6: 1561.31 1627.3
V 0.0164
176.3
h.
~=::::.
,
0.0225-10.030710.1364
608.4 i 779.4 1224.6
1400' 115000
.- - -
h.
4200
·.::f3
0.018310.0199
379.11 487.6
I 1300'
202,4
397.2
497.4
600.9
710.0
829.5
-;;c 0.0159 0.0173
h. 203.& 398.1
0.0184
498.1
0.0198
601.2
0.0217
709.7
0.0242
828.2
950.9
1080.6
1206.8: 1326.0
1430.3
1526.4
1615.9
0.02781 0.0329
947.81 1075.7
0.0393 i {).0464
1200.J 1319.6
0.0534
1423.6
0.0603
1520.4
0.0668
1610.8
i
*Abstracted from :\?~'1E Stl"am Tubles (lc}{)7) with pcrmj~.:-i()n of [he puhlbhcr. The
American Society 01 ~lcchanicai Engineers, 3-15 East 47th Street. :\ew York, :\. Y. 10017
A.20
API'ENDIX A - PHYSICAL PROPERTIES OF flUIDS ANO flOW CHARACTERISTICS OF VALVES, FITTINGS, ANO PIPE
Flow Coefficient C for Nozzles
CRANE
7
('
1.1
Data from Regelnfuet die Durch-
8
I I] 'III
" Ii
1.1 6 '
4'f i! Illi'
,I
,
1.1
flussmessung mit genormten Due-
sen und Blenden. VDI-Verlag G.
m.b H., Berlin, SN\V, 7, 1937.
Published as Technical Memorandum 952 by the NACA.
1.1 1
:
':
I,
I
I I
i
!
!! I'!
I ",
1.08,
1.0 6
,
-~
0.9
rnrr
iii
0.l+!,
I
f
I
f
II
'I
' " I :
' " --'""
,
VI.)':'i
:;?Vf......-: .
' I
I
0.94 4
.7
.72 s
..
.60
.SO
.40
fY~V.n
Illrvl
810'
,77
.S
\;,.~~
: III
0.9
,80
.70
,
"
I
Fiow
i Irr
Ii
J{f'
f
').11',.
1.02 "
l-i--i+-'
, ,
1.0 0"
ExalTlple: The flow coefficient C for a diameter
ratio do/d , of 0.60 at a
Reynolds number of 20,000
(2 X t04) equals 1.01.
f
,
,I
J ;,
i
.1 "i i"'1
''
1.04
I,'
i
'
"
I -,
"
'I
1.10'
I
, ! Ii!
11
1
I
.30
' '0-0.2
i
1
II
46810'
R, - Reynolds Number based on d l
Flow Coefficient C for Square Edged Orifices
7 17
•
C
1.3
l. 2
t
1.
I
I
1.0
I
I
I
I
I",Itt
I
0,
I
0,'
v
1
---
L
r,
f
I
I
,
"""" \\
'"
t-~ ::::
'-...,
I I
-..;.
-
11Wl/
*=1#]1
8 10
,
i-
-
,
--~
F=::
3OI'V
-
6
,t--
1"-...
1
,
I!I~ ~ I i~:;:::;:,r....L:
~ ~ \':: W
"
T r-:---...
.
i
,
\
\
I I
v.---t"
i
I
,/
/'
n- :50i--\Y~
!L~~
,4~ f\\\ -
0.,
i
"~vr
:.65!
1111 i
IIIIII/i
I' I, i'rl
o. 7 . " I ' ,
o. :'
0.6
iI
%;80
'=751~
t-
I
I
: 0",2)
4tJ
60 80 102
4
6
8 10 3
R,. - Reynolds Number based on d 1 -
c
=
;==~C~d=F'
~ 1 - (~)'
Lower chart data from Regeln
ruer die Durchflussmessung mit
-gt?normtem Duesen und Blenden.
Flow
---:r
VDI-Verlag G mb.H.. Berlin,
SNW, 7, 1937, Published as
Technical Memorandum 952 by
the NACA.
4
6 810'
2
4 6 810'
11, - Reynolds Number based on d,
.30
().().2
.s
APPENDIX A- PHYSICAL PROPERTIES OF flUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
CRANE
Net Expansion Factor, Y
For Compressible Flow through
Nozzles and Orifices 9,10
c:
o
.. E--L-=-::t~~~-2~~"""":","+-~~~':::""H-+-+-i--I
Vl
~ ;'F--i--::-C7"b-...4~...o.,:~-r--+--...;'>,~-+-~~""':~l-1:";"..l-'
x
UJ
:i:-r-
:......
,=~ .•
!
,
;
.55 b--r----j--+--+--+--+--+---l---";....-->-ii-l-+~
i
I
j
!
~~-r--__j---~.---t--+-~-~-+-~~+-~~
.-
Data extracted from, Fluid
l\1eters, Their Theory and
Application, Fourth EJition, 1937, and Orifice
Meters wilh Supercritical
Flow by R. G Cunningham,
with permission of the publisher, The American Society of Mechanical Engineers, 345 East 47th Street,
New York, N,Y. 10017.
."I---ir---+-+-+--t---+--+---l--.f-----l-+~_+_W
.<eE:--t---j--+--+-+--+--+---l--l----I--I-i*..l-1
i
: ! II
,
::: -a
!
"
\,
,I,
!;
r '!
J
~
to
!
I
,.
l.2~!'!
I
,
J
!
I ,
!
, I
1,
'
!
!
,';'-)
,.~
!li,!,!!,·,,!.!tI'
)'!
l ,!
I ) .
,t
!
,
!
:.C
1'
'.,
!
t,
••
II
II
[,
lin
I
LO
Pressure Ratio -
Critical Pressure Ratio, rc
For Compressible Flow through
Nozzles and Venturi Tubes 9
a..
""
a..
........
.58
.75
~"
.56
I
I
u
1.35
k=cp,c v
I
A·22
APPENDIX A-PHYSICAL PROPERTIES OF FLUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
CRANE
Net Expansion Factor Y for Compressible Flow
Through Pipe to a Larger Flow Area
k
rk
1.0
0.95
~"rrr"xlm"tch'
= 1.3
1.3 for CO,. SO,. 11,0. II,S. ~i Is. ~,O, 0,. CIl,. C,II,. anJ C,II,I
~ '-.. '-..
'\
0.90
I
I
I
.~ ~i
~
~~~ ~~
l~ ~ ~ ~ ~
I
~~
I~ ~,~ ~~
~~ t--...
1,\
~ ~ ~ 8::
I ~ ~I
~ ~~
."
""- ~ "R: '~8~
"\ ~ i'\. ~j ""~ ~t'o f:o~'01'1'0. I
K
~
0.85
0.80
y
.
0.75
I
I
0.70
'\
0.65
I
t'
~
0.1
'" ~
"'~~ '0_f 11',\ "1-0 {$. "'0
f-
\.'
"0
<9
-00
..':..0
t f'":"'01"0 '0
" '"
I~~I
l'
1'F",Y'
0.2
0.4
0.3
0.5
t::,p
0.6
O
y
1.2
1.5
2.0
.525
.550
.593
.612
.631
.635
3
4
6
.642
.678
.722
.658
.670
.685
8
10
15
.750
.773
.807
.698
.705
.718
20
.831
.877
.920
.718
.718
.718
"'\,1'
I
o
f f-,\_\.\_,\._T"l_
_\\_~
"f\,
I
0.60
0.55
Limiting Factors
For Sonic Velocity
k = 1.3
40
100
I
0.7
0.3
0.9
1.0
p'1
k
r:k ~approximatcly
= 1.4
J.4 for Air. H,. 0" "'" CO. NO. and HCl)
Limiting Factors
For Sonic Velocity
k = 1.4
0.95
K
I~~I
Y
0.80
1.2
1.5
2.0
.552
.57&
.&12
.588
.&0&
.&22
0.75
3
&
.&&2
.. 697
.737
.&39
.649
.&71
8
10
15
.7&2
.784
.818
.&85
20
.839 .710
.8831.710
.92& .710
0.90
0.85
Y
4
0.70
0.65
,f
,f
;
I
j
0.60
0.55
40
100
0
0.1
0.2
0.3
0.4
0.5
t::,p
I
P'I
0.8
0.9
1.0
.&95
.702
.
APPENDIX A - F'H'rS1CA1. PROiftERTIES Of HUlDS AND flOW CHARACTERISTICS Of
CRANE
VAtVES~
fmINGS. AND PIPE
A-23
Relative Roughness of Pipe Materials and Friction Fadors
18
For Complete Turbulence
=::::::t
:::::3
~
'::=:t
Pipe Diameter, in Feet - D
.0045'E~.J~~I~'3t2~~I}§j.~4i~.~5t·~~1~.~8~'1~~§t'§2§~,3~S4~5~~~11~~~r'~§O'~~'~~EO~2L5
'
'07
1
.
I
03"' I
•
"'
1
I
'..:=t,
'
-,:
:
! "
I i '
!
1
h'
I
\
I':
'.1
I
I
I Ii·
I i i i
I
,
II!
06
"'I i i
I
i
1
i
.021---+'~'+!-Hr--+-i(-+~~'+++--+-l'-!~-+-'-H-++-, f-t--t-t-H---i--..t-+--!-.05
~...
I
I i,\~
i '- I i I
,I
1"'-
I
"~,1 '" " I
i
~
iN I
I'l,I
II
-.04
035
t::I
=::I
::=:I
==-
==~
-
:::=2
~
~
:::::2
=:D
:::::»
01
.~­
... ~~
::::::s
"==.".=."~
Pipe Diameter, in Inches - d
~
"~
,~
-'~
i ),J{,I (.'\tr;lc{CJ ironl Fflt-lltm
I ';.{~I'.~ .!t)f PIPr: F!tlll' bv L F
\~, ""'I•.h. \l, nh pt:rml~~10n 'of the
f'uhll··-t-k:'. The .\I1'.crtcan Soci.t't \
01 ~ 1r,;"h;:~mci.l1 Engineer--:.
2'J \) e>( N,h l-!rcct. :\cw York.
Problem: Determine absolute and relatiye roughness. and friction factor, for fully turbulent flow in Io-inch cast iron pipe (I.D. = 10.16").
Solution: Absolute roughness (.) = 0.0008; . . . . . Relative roughness
(E. D) = 0.001 . . . . . Friction factor at fully turbulent flo\\" (j) = O.OlgO.
lU Uu-u U U U II U U U U U U U U U U Uun .n II. IJ..
I U U ij U UU
I
VALUES OF
0.4
0.2
0.1
0.6 0,8 I
'07Tf.li
06 I
1
I
t
) •'1.:
,
'.'
" ;, .1,
Ir:! !~\.
,04 i"
1
..
i
I
40
60 80 100
200
400
600 800
\.~()
f·'··~"
',.
.03! . i •. ~ ~ , .
II
T'Or'm'llhEE1'E'r
rtllRT'BTUllCNctlII
.i.'
i '{ .
'i
i' I I
i' f I
I
i
",.J
~~~
~
\,f'..l"}. ~
~;"
,,,,.r
'
'\':
t
r . t.
I
. "J:,
I) ,.'
(/)'211
.02
I 11111
J
I
"1
I
.' .. ..
I
:1
]
I1
·
n
I
I.
I I I II+++-t+!-H
Pipe
.'
inches
.
~1/8
.t==',;.f~
H-ffiH+l::
,t
'1 'I', ',:
rt-.
. ~;'<;;~''j.li
,:~" "'"
"",~ •..,
TT
" ,'\. I. -""
.. ~0. 'i<!.tH '
.
c.
,.~
J"I
1
"
'I~~-rl
' ' ' ••. , ' ' .
1
;....
"," \:.1') , "
,'1.'';<'1..)
c.
II Ilt41 +-1
F~j;;__~1
-1----
=1.....'...-.....,
. H
_. -
.....
...
-
'
l' """".
'1
~~ ~.
..
1M
2 3 4 5C
B10 4
f.
2 3 4 56
810 5
2 3 4 56
./
810 6
2 3 4 56
810 7
.
::1,=,a
.t;;;;l~.=::t:,
~~
o
2 3 4 56 8
0
o
2
4
0 0
Scnutllliu Numlier
1+
,.
~
~
m
z
0
)(
,.
I
.. '"
-n.. ...
Q.
~
-<
III
n
~
0'"
I~
1
6
Q
14
'"
.~
c
~
3
3(I)
~
,.z
0
V>
...D.
0
0
~
0
:0:
n
til
iii
(I)
Q
,.
,.n'"
:r
~
m
'"'a
::I
n
V>
:e
0
0..
g
~
;:
ffi
-
G'I
1"
::I
z
."
'tJ
CD
:;;
::r"
::;-
108
'"m::;
fl
::I
10
0
3Z
,.
-. ..
ihP
He - Reynolds Number
i',
6
8
-
",'
... +-
'-1--
f-..
103
3/4
+-\:.....;..,p.-,,=:;13 Ii
..ct:~~:~~
j~1Iff--l·1
I··t.·j·!.·.I··j· ... ,·[·..[·-11.···1... I·I-~~···'<I~t':'~~~r:: . '"
~~.·"r·~:·.I·.;~
........ .
; tID tilt lnli iliittllfll j
=>1J ~~J~r·::
.
1/2
BE::t:~~~ 2~i
Ii
,
~-;t
m
m
H4f- I" t I fl
. _ _C" I·
~t~t't~.l. .:•.:,""f'"~ _- ..' -..
_-- -i' I
.
t
0
iD
I ~r-N.
i-
."
Q
0
.,
"1""'"
..
'+
::I
Sjl~,
l 1U11 I I UUnll11l I!
.'.,
. ,,,
I'
--'--
-O·
I I I H-l
~·H.jl
".,~
-_...
::r
1\'
r I t I t+l4-1
Nominal
-\1'
. . - ".
-'T"
»
t
~,I...
+
I
~~tt ' ..... I ,;...
,I..l-l-W
_, ..
I
i~~Ht-I
i··
!
INN
:'
ttl·]
1\
. - I ~~, '. I-r---U
' i 1"',
I
,
>
~~f:::~t! +,,'-1--11
I
;to
TIJJ1JLIEIJf Zo'NE
tfh~t~:~rrft?::f~
·'I.~r 1~"
~ i: ~.' ! ft
.! . " i l l
Friction
Faclor ~
n
"'~\~~~~~
'l,~
z
I
'1 I i
....
1
....
.I
i i
.. r
T•. ·,' I "ll
i-
rr'f]' i
I
"~iIV':!<~. >. . ~.'.....
"t
"'},'
!,
20
TR~N~~I~.N 1.' ~"'1
I
~:;l',
•
8 10
~'l!Pl'!'!Ill
+..
1 I'
T ;
rtl ,~. I
,05 I i t \ tN.·
f
6
1 '
~MIN:r.
,
FOR WATER AT 60' F (VELOCITY IN FT,/SEC, X OIAMETER IN INCHES)
(I'd)
}i'e
For other lormJ 01 the Re equation, see page 3·2.
0
m
i»
Problem: Determine the friction factor for 12-inch Schedule 40 pipe at a flow haVing a Reynolds number of 300,000.
Solution:
The friction factor (f) equals 0.016,
»
I..:)
UI
..
~~~k,:.'·
M,."'''.,~.'''"'
~._,~~N'I~.~'!i.Iif .......~,,~........... ~.-,~ ... ·~·-,~,----- ... -
..
,~,'_.~~.'!'''".,,'':''
......
:",-'',,.,~T·
...
.... --.~ ....- - . - - -........
~,''~,.t'
.... ,_"'"." ....,....,.... ....
"..,."~,.,..-'""-"I'''I"I~*~_~.
---> ....~~--.,.- .. -..-,-~-~.~-."---------......~~-,~-~,,",,"--
__
~~_·
_ _ _ _ _ • _ _ __
" '-'~..,"""'..._"' •. c,,""_,~,.'...,.,.-
A-26
APPEN[)IX A-PHYSICAL PROPERTIES Of flUIDS AND flOW CHARACTERISTICS OF VALVES, flnINGS, AND PIPE
CRANE
Resistance in Pipe
Resistance Due to Sudden Enlargements and Contractions 20
--
LO
0,9
0,8
~
I
'"
y
~
0.7
~
<=
-
'u
0.6
'r--u
CD
u 0.5
---
' ii;
0
<=
.l3
'" 0.4
'"
CD
0:::
I
/'
V
f=
'[ ~~212J
1-
-- -- / - - -.-V
1\
.............
"
---- -- -7'K
0.3
II
-~
~
SUDDEN CONTRACTION
0.2
f
dl
~
0.1
Y'
0
t'
0.1
I
1\
~~
0.3
0.4
0.5
0.6 0.7
""-
0.8
6.065
---.
=
II.Q38
0,5 1
Note: The values for the resistance
coefficient, K, are based on velocity
in the small pipe. To det.erinineK
values in terms of the greater diameter, multiply the chart values by
(ddd,)'.
~
I
0.5 1
Sudden contraction: The resistance coefficient 1<. for a sudden contraction from 12-inch Schedule 40
pipe to 6-inch Schedule 40 pipe is 0.33,
based on the 6-inch pipe size.
d,
-d,
~
0.2
6.06 5
11·q38
SUDDEN ENLARGEMENT
1"'-
<l>
d~
l
''\
Sudden enlargement: The resistance coefficient K'for a sudden enlargement from 6-inch Schedule 40
pipe to 12cinch Schedule 40 pipe is
0.55, based on the 6-inch pipe size.
r--.....
0.9 1.0
dIld2
Resistance Due to Pipe Entrance and Exit
-
L
I
I
-~
r
Inward
Projecting Pipe
Sharp
Edged
K = 0.23
Slightly
Rounded
Entrance
Entrance
Entrance
K'= 0.78
----r
---L
K
=
1.0
Projecting
Pipe
EJtit
Jr
=
---r -r
L
0.50
-.J
-,
-~
IC = 1.0
Sharp
Edged
Exit
-
~
I
K = 1.0
Rounded
exit
L
K
=
0.04
Well
Rounded
Entrance
Problem: Determine the total resistance coefficient for a pipe one
diameter long having a sharp edged
entrance and a sharp edged exit.
Solution: The resistance of pipe
one diameter long is small and tal1 be
neglected (K = I L/ D).
From the diagrams, note:
Resistance for a sharp edged entrance
Resistance for a sharp edged exit
Then,
the total resistance, K, for the pipe.
= 0·5
= 1.0'
1.5
A-30
CRANE
APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND FlOW CHARACTERISTICS OF VALVES. fITTINGS. AND PIPE
Schedule (Thickness) of Steel Pipe Used in Obtaining Resistance
O:F Valves and Fittings of Various Pressure Classes by Test*
Valve or Fitting
ANSI Pressure Classification
Steam Rating
ICold Rating!
l50-Pound and L0::JJer 500
300-Pound to 600-Pound
1440
900-Pound
2160
1500-Pound
3600
2500-Pound
Yz to 6'
8' and larger
psig I
psig
psig
psig
I
i
I 3600
6000 psig
psig
Schedule No.
of Pipe
Thickness
Schedule 40
Schedule 80
Schedule 120
Schedule 160'---_ _
xx (Double Extra Strong)
Schedule 160
*These schedule numbers have been arbitrarily selected only for the purpose of
identifying the various pressure classes
of valves and fittings with specific
pipe dimensions for the interpretation
of flow test data; they should not be
construed as a recommendation for
installation purposes.
R,epresentative Equivalent Length! in Pipe Diameters (L/D)
Of Various Valves and Fittings
Equivalent Length
In Pipe Diameters
Description of Product
I
(LID)
With no obstruction in flat. be\'c!, or plug type seat
Fully open
340
\\'ith wing or pin guided disc
Fully open
450
---------~~~~~~~~~-~~---~-----~~~--------­
(No obstruction in flat, bevel. or plug type seat)
Y-Pattern
- With stem 60 degrees from run of pipe line
Fully open
175
- With stem 45 degrees from run of pipe line
Fully open
145
\\'ith no obstruction in flat, bc\·cl, or plug type scat
Fully open
145
Angle Valv.",
With wing or pin guided disc .
Fully open
200
Fully open
13
Vl edge, Disc,
Threc-quarters open
35
Double Disc,
Qne-hal f open
;d§Q.
or Plug Disc
Gate
One-quarter open
900
Valves
Fully open
17
Thrcc-quarters
open
50
Pulp Stock
One-half open
260
One-quartcr open
1200
,
Fully open
Conduit Pipe Lme bate, Ball, and Plug Valves
3"
Stem Perpendicular to Run
Globe
Valves
~
Conventional Swing
O.5t . . Fully open
O.5t .. _Fully ope,n
Clearway Swing
2.0t ... Fully open
Globe Lift or Stop; SteIll Perpendicular to Run or Y -Pattern
Angle Lift or Stop
2.0t ... Fully open
2.5 vertical and 0.25 hori=ontalt .. Fully open
In-Line Ball
With
poppet
lift-type
disc
0.3t . . Fully open
Foot Vatves with Strainer
With leather-hinged disc
OAt. _. Fully open
Butterfly Valves (8-ineh and larger)
Fully open
Straight-Through
1
j
,
i
f
I
f
~
II
j
I
Cocks
Three-Way
I Rectangular
plug port area equal to 100r~ of pipe area
I Rectangular plug port area equal to
J35
50
Same as Globe
Same as Angle
150
420
75
40
Fully open
18
Flow straight through
Flow through branch
44
80S; of pipe area (fully open)
140
Standard Elbow
30
Standard Elbow
16
Long Ra.:d.:i.cuc-s_E
__lc-bo'-'-_
w _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _--:-_---,_--"k==--__
Street Elbow
50
Street Elbow
26
II~Sq~u_a_re_c~o~r.n__e_r~E_l_bo_W~~-~-~-~--------------_________+-_______5.:7______
Standard Tee
With flow through run
20
1~~~~--~--~I~~~·i--t--h~fl-o-w-t--h-r--Ou~g~h~b-ra=n~c-h--__________________________~-------60~----Close Pattern Return Bend
50
- - - 1 9 0 Degree Pipe Bends
See Page A-27
Miter Bends
See Page A-27
Pipe
Sudden Enlargements and Contractions
See Page A-26
i
Entrance and Exit Losses
See Page A~26
-----'-"Exact equivalent length is
t!\.,tinimum calculated pressure
tFor limitations. see page
equal to the length between
drop (psi) acro<;;s valve to provide
2-1 I. For effect of end
flange faces or wclding ends.
sufficient flow to lift dISC fuBy.
connections, see page 2-10.
90
45
90
, 90
Fittings l, 45
1
Degree
Degree
Degree
Degree
Degree
I
For resistance :rador "K", equivalent length in Feet of pipe, end equivalent Row coefficient .. e ..... , see pages A-31 and A-32.
eRA N E
A·31
APPEND'IX A -I'HYSICAl PROPEHIES OF FlUIDS AND FlOW CHARACTERISTICS OF YAl YES, FITTINGS, AND PIPE
~~.::.-~=---'--
L and LID and Resistance Coefficient K
*ECIUivcJlent Lengths
d
L
LID
,
j
S(
I
40
!
30
20
~
..'!l
'"
'"
Q.
E
<'0
0:
Cl
0
-
'"
0:
/
Q)
Q.
'"
/
l.L.
e
.:
/
"
"
<I)
""
'"u
.t=
.E
<:
w-
/
N
C;;
.t=
c;,
e
'"
-'
c:
0
<:
/
..'!l
CO
:>
/
'"
/
<'0
.:::/ . /
/
0-
L.U
/
I
/
"-
...;:"
"
/
.--
/
w-
Q.
5 0:
'5
..'!l
0-
~
0
<U
E
..'!l
"'"
'"
0;
/
<U
.<::
<.>
'"
L.U
....,I
"
.E
6 .£
..... ~
/'
~O-
/
~
,-
..'!l
,- .--
"'.-....
10
9
8
7 .t='"
'"u
6'"
3
,
<:
'E
"<:l
0
2:
./
'"
-0
'iii
.E
2
/ , - ./
/,//
./
--- ---
---
1.0
0,9
0.8
0.7
.2
0.6
0.5
SCHEOUL.E 40 PIPE S(ZE:. INCHES
Problem: Find the cqui"alent length in pipe
Jldn1Cft.'rs and ket of Sch('duJc 40 pipe. and
thl' rc.:"'I~tancc factor" for J, 5, and 12-inch
fully-opened gate \·a"·cs.
·For limita,ions. see page
~!-11.
Solution
Valve Size
I'_L~:~I~1~:J-R~~Tto
Equi\'alcnt length. pipe di;Hncters
: IJ I IJ
Equi\'alcnt length. fcct of Schcd. ~U pipe! 1.1 I 5. 5
Resist. factor K, based on Schoo. 40 pipe; 0,30 I O.2()'
I (J /I PagC::\-JOi I J II Dotted lines
I 0.17
on chart,