Mgchanica! Design
of Process Systems
Volume2
Shell-and-Tube Heat Exchangers
Rotating Equipment
Bins, Silos, Stacks
A.Keith Escoe
Gulf Publishing Company
Book Division
Houston, London, Paris, Tokyo
llctaniul
Design
of Pmctss Svsterns
\itme
2
SldLen*Tuh
Heat Exchangers
Roadng Equipnent r
o
Bins, Silos, Stacks
Copl right @ 1986 by Gulf Publishing Company, Houston, Texas.
All righrs reserved. Printed in the United States of America. This
b@k. or parts thereof, may not be reproduced in any form without
p.rmission of the publisher.
Llbiary ol Congress Calaloging-in-Publicalion Data
Escoe. A. Keith.
\lechanical design of process systems.
l-ocludes bibliographies and indexes.
Piping and pressure vessels-v. 2. Shell-and-tube
Conr€Drs: v.
bear exchangers; rotating equipment; bins, silos, stacks.
l.
l-
Ch€mical
I- TirleTPI55.5.E83
plants
Design and construction.
1986
660.2
', 81
85-22005
O.ATant -562-9 (v 1)
6aaa (}ET2l)1-565-3 (v. 2)
lS€fl
iv
Contents
Foreword
........vii
by John J. McKetta
Preface
..........ix
Chapter 5
The Engineering Mechanics of Bins, Silos,
and Stacks
........1
Silo and Bin Design, I
Stack Design, 8
Vortex Shedding and Frequency Responsc.
Ovaling. Helical Vortex Breaker Strakes.
Bin Stiffener Design. Vcssel Supports.
Example 5-2: High-Pressure Flare Stack Design, 20
Effective Diameters. Section
Weights-Uncorroded weight. Required t
Thickness. Anchor Bolt Design. Cantilever
Vibration. Static Deflection. Dynamic
Deflection. Anchor Bolt Torque. Design
Nozzle Loadings.
Pulsation Response Spectra Induced by
Reciprocating Equipment, 62
Example 6-l: Horizontal Centrifugal Pump
Sysrem Design, 65
Suction Line Pressure Drop. K-Values.
Discharge Line Pressure Drop. The Effects of
Liquid Viscosity on Centritugal Pumps.
Summary.
Example 5-3: Stack Vortex Strake Design, 27
Example 5-4: Natural Frequency of Ovaling
Ring Formula (Michell Formula), 28
Notation,29
References, 29
Example 6-2: Positive Displacement Pump
Design,74
Suction Line Pressure Drop. K-Values. A word
About Priming.
Example 6-3: Centrifugal Compressor Selection, 79
Example 6-4: Installing a Compressor at
Elevation, 34
Selecting the Reciprocating Compressor.
......31
Pumps, 31
Centrifugal Pumps. Hydraulic Requirements of
Centrifugal Pumps. Positive Displacement
Pumps. Pressure Protection for Positive
Displacement Pumps.
Principles of Compression. Reversible
Adiabatic (lsentropic) Compression. Polytropic
Compression. Isothermal Compressron.
Dimensionless Reference Numbers. Centrifugal
Compressors. Reciprocating Compressors.
\{ulriple Staging of Reciprocating Compressors.
Cas Temperature for Reciprocating
Compressors. Axial Flow Compressors.
Specirying Compressor Flow Conditions. Mass
Flow. Actual or lnlet Volumetric Flow.
Standard Volumetric Flow. Properly Specifying
Compressor Flow Conditions.
Piping Systems for Rotating Equipment, 60
Example 5-l: Granule Bin Design for Roofing
Plant, 11
Chapter 6
Rotating Equipment
Compressors,43
Example 6-5: Naphtha Pump System Design, 86
Flow from Reservoir to Naphtha Storage Tank.
Naphtha Pump Hydraulics. The Maximum
Capacity Condition. Reevaluation of Reservoir
Line.
Notation,9T
References, 97
Chapter 7
The Mechanical Design of Shell-and-Tube Heat
Exchangers
...... 99
Appendix A
Partial Volumes and Pressure Vessel
Cafcufations
Fundamentals of Shell-and-Tube Heat
....,177
Partial Volume ofa Cylinder, 177
Partial Volume of a Hemispherical Head, 177
Partial Volumes of Spherically Dished Heads, 178
Partial Volumes of Elliptical Heads, 179
Partial Torispherical Heads, 181
Internal Pressure ASME Formulations with
Outside Dimensions, 183
Internal Pressure ASME Formulations with Inside
Dimensions, 184
Exchangers,99
Design Classifications of Heat Exchangers.
Fixed Tubesheet Shell-and-Tube Heat
Exchangers. U-Tube Shell-and-Tube Heat
Exchangers. Floating Head Shell-and-Tube Heat
Exchangers. General TEMA Exchanger
Classes-R, C, and B. Basic Components of
Shell-and-Tube Heat Exchangers. TEMA
Formulations. ASME TUbe Joint Load Criteria.
Process Evaluation of Shell-and-Tirbe
Exchangers, 115
Tube Wall Temperature and Caloric
Temperaturc. Overall Heat Transfer
Coefficient. Fouling of Inside and Ourside Tube
Surfaces. Tube Film Coefficients.
Appendix B
National Wind Design Standards
Tube Vibrations, 139
.........
187
Criteria for Determining Wind Speed, 187
Wind Speed Relationships, 188
ANSI A58.1-1982 Wind Categories, 189
Plate-Fin Heat Exchangers, 147
Example 7-1: Regenerated Gas Exchanger
Design, 148
Tube-Side Film Coefficient. Shell-Side Film
Coefficient. Shell-Side Pressure Drop.
Example 7-2: Vibration Check for Regenerated
Gas Exchanger, 153
Example 7-3: Chlorine Superheater Design, 154
Appendix G
Properties ot Pipe
Tube-Side Film Coefficient. Shell-Side Film
Coefficient. Shell-Sid€ Pressure Drop. TUbe
Metal Temperature.
.
.
.....
193
Insulation Weight Factors, 200
Weights of Piping Materials, 201
Example 7-4: Asphalt Coating Mix Heater-A
Non-Newtonian Fluid Application, 160
Tube-Side Film Coefficient. Shell-Side Film
Coefficient. Shell-Side Pressure Drop.
Appendix D
Conversion Factors
Example 7-5: Zero LMTD Exchanger, 165
Notation, 165
References, 166
Chapter 8
External Loadings on Shell Structures
....
.
Alphabetical Conversion Factors, 226
Synchronous Speeds, 233
Temperature Conversion, 234
Altitude and Atmospheric Pressures, 235
Pressure Conversion Chart, 236
169
Lifting Lug Design, 170
Example 8-1: Lifting Lug Design and Location, 170
Notation, 175
References, 176
vl
.....225
t'oreword
chanics and the engineering mechanics of piping (Volume 1).
The chapter on heat transfer in vessels and piping illustrates lucidly the interrelationship between process
and mechanical design. Every engineer working with industrial process systems will benefit from reading this
The engineer who understands the impact of process
design decisions on mechanical design details is in a position to save his client or his company a lot of money.
That is because the test of any process design is in how
cost-effectively it yields the desired product, and how
"cost" generally translates to "equipment": How much
will the process require? How long will it last? How
much energy will it consume per unit of product?
chaDter.
Although the author has made a herculean effort in
covering the mechanical design of pressure vessels, heat
exchangers, rotating equipment, and bins, silos and
stacks (Volume 2), it is true that there are omissions. It is
hoped that, as the author hints in his preface, a future
volume might be added covering multiphase flow, specific cogeneration processes, turbines, and detailed piping dynamics.
Still, at this writing these two volumes comprise an
outstanding practical reference for chemical and mechanical engineers and a detailed instructional manual
In this two-volume work on Mechanical Design of
A. K. Escoe has performed a monumental service for mechanical design engineers and
chemical process engineers alike. The information is
Process Systems,
presented in such a manner that even the neophyte engineer can grasp its full value. The author has produced an
in-depth review of the way in which process design specifications are interpreted into precise equipment designs.
Perhaps most valuable of all are the extensiv e worked examples throvghout the text, of actual designs that have
been successfully executed in the field.
The piping system is the central nervous system of a
fluid flow process, and the author has treated this with
proper respect in two excellent chapters on fluid me-
for students.
I recommend these volumes highly for each design engineer's professional library.
Joe C.
vtl
John J. McKexa, Ph.D. , PE.
of Chemical Engineering
Universitv of kxas, Austin
Waher Professor
Dedication
To the memory of my beloved parents, Aub-ri:y
tt.
Es-
coe and Odessa Davies Escoe; and to the dedicated enei-
neer, Dr. Judith Arlene Resnik, U.S. astronaut aboid
the ill-fated space shuttle Challenger (Flight 51-L).
v||l
Preface to Volume 2
of any accepted standard or code that may govern. It is
felt that this book is a valuable supplement to any standard or code used.
The book is slanted toward the practices of the ASME
vessel and piping codes and the TEMA standard for
shell-and-tube heat exchangers. The intent is not to be
heavily prejudiced toward any standard, but to discuss
the issue-engineering. If one feels that a certain stan-
This book's purpose is to show how to apply mechanical engineering concepts to process system design. Process systems are common to a wide variety of industries
including petrochemical processing, food processing and
pharmaceuticals, power generation (including cogenera-
tion), ship building, and the aerospace industry. The
book is based on years of proven, successful practice,
and almost all of the examples described are from process systems now in operation.
dard or code should be mentioned. olease remember that
lhere are olhe15 who may be using different standards
and it is impossible to discuss all of them.
While practicality is probably its key asset, this second
volume contains a unique collection of valuable information, such as a practical approach to bin and silo design
as well as practical methods of controlling wind vibrations of stacks using vortex strakes; new information on
nozzle loadings on compressors and turbines; comprehensive discussions and examples on sizing pumps and
compressors for various process applications; expanded
tube count tables for shell-andtube heat exchangers; a
practical approach to design against tube bundle vibration; and a comparative synopsis of the various national
wind codes.
Topics included in the text are considered to be those
typically encountered in engineering practice. For reasons of time and space the dynamic analyses of seismic
response spectra and an extensive discussion on pulsation response spectra in piping induced by acoustic pulsation are not discussed. However, a short discussion is
given on pulsation response spectra induced by acoustic
pulsations. Single-phase flow is much more common in
mechanical systems than two-phase flow, so because of
time and space two-phase flow is not discussed.
This book is not intended to be a substitute or a replacement of any accepted code or slandard. The reader
is strongly encouraged to consult and be knowledgeable
The reader's academic level is assumed to be a bachelor of science degree in mechanical engineering, but engineers with bachelor of science degrees in civil, chemical, electrical, or other engineering disciplines should
have little difficulty with the book, provided, of course,
that they have received adequate academic training or
expenence.
Junior or senior undergraduate engineering students
should find the book a useful introduction to the application of mechanical engineering to process systems. Professors should find the book a helpful reference (and a
source for potential exam problems), as well as a practi-
cal textbook for junior-, senior-, or graduate-level
courses in the mechanical, civil, or chemical engineering
fields. The book can also be used to supplement an introductory level textbook.
The French philosopher Voltaire once said, "Common
sense is not very common," and unfortunately, this is
somelimes the case in engineering. Common sense is often the by-product of experience, and while both are essential to sound engineering practice, neither can be
Iearned from books alone. It is one ofthis book's soals to
tx
unite these three elements of "book learning," common
sense, and experience to give the novice a better grasp
of
engineering principles and procedures, and serve as a
practical design reference for the veteran engineer.
Finally, I wish to thank Dr. John J. McKetta, professor
of chemical engineering at the University of Texas at
Austin, who had many helpful comments, suggestions,
and words of encouragement; other engineering faculty
members at the University of Texas at Austin for their
comments; Albert T. Taube, P.E., who was so kind to
offer helpful and useful comments while reviewing
Chapter 6; and John D. Guenther, P.E., for his helpfirl
critique of Chapter 7. Last, but certainly not least, I wish
to express gratitude to William J. Lowe and Timothy W.
Calk of Gulf Publishing Company whose hard work and
patience made this book possible.
A. Keith Escoe, P.E.
The Engineering Mechanics of Bins,
Silos, and Stacks
The engineering mechanics of bins and silos differ
from the mechanics of oressure vessels because solids
behave differently from liquids and gases, both in storage and in flow conditions. The mechanics of stacks are
almost identical to those of towers, but are somewhat
simpler. An engineer has more fiexibility and approaches for solving vortex shedding around stacks than
around towers, because stacks rarely have as many attached structures.
4.
Dead storage-residual build-up of solids caused by
the inability to exit bin.
Segregation-a heterogenous solid of varying specific gravity in which the lighter particles exit the bin
first, leaving behind the heavier particles.
Degradation-the chemical change of solids caused
by remaining in storge too long. Spoilage, caking,
and oxidation are some examples.
5.
6.
Solids behave differently from gases or liquids because they can transfer shear stresses without movement,
SILO AND BIN DESIGN
The mechanics of solid flow theory is a fairly complicated subject. The proper design of silos and bins is
more than meets the untrained eye, and involves every
aspect of engineering mechanics. This chapter only
" sketches" methods of approaching this complex phenomenon, and refers the interested reader to literature on
this specialty.
The field of solids handling has been augmented the
past twenty years by two researchers-Jenike and Johanson [1]. The methods presented in this chapter are
largely influenced by their work.
Bins and silos appear to be very simple devices, but
what goes on inside is not so simple. To design an efficient bin the design engineer must understand why solids
in bins do not flow (Figure 5-1):
1. Development of a rathole or stable arch that ceases
flow.
2. Erratic flow-transient arches form within the solid
resulting in variance of the bulk density such that
flow becomes unstable.
3. Fiushing-the fluidization and flushing of powders
creates erratic flow.
and because of their cohesive strength, they can retain
their shape under load. The shear stress transferred between the solid and the channel walls is a function of the
normal pressure, w. The relationship between the two is
as follows:
1t -
tdttrg
where
{' :
p:
S
-- w
(5-l)
kinematic angle of friction between the solid
and the bin wall
coefficient of friction between the bulk solid
and the bin wall
Typical values of @' are given in Table 5-1 for various
solids and bin materials. This table can be used in applications where the bulk solid properties are not known (as
is commonly the case). The value of @'is required by the
methods presented to be a constant value so that using
the table will produce a conservative design.
There are two flow conditions that can occur-mass
flow and funnel flow. Mass flow is a flow Dattern in
which all the material in the hopper or bin is ln motion
flow occurs along the bin walls. Funnel flow is a
flow pattern in which the material flows primarily in the
center resion of the bin.
and the
Mechanical Design of Process Systems
NO
NO
FLOW
FLOW
FUNNEL FLOW
:\
):^.-,r. .. 1:' ,i
:fr,f;:,,*::',.d
r'"
RATHOLE
OR
li"li:'.;:,.,i
PIPE
OEAO STORAGE
Lqilii
I
I
I
-l
t.-.
t,;
t.|..:
ARCH OR DOME
Funnel Flow Charactedstics
1. Material
segrEgates and ratholes may be formed.
2. Flow may be erratic.
3. Low headroom.
4. Powders willflush.
Figure 5-1A. Problems of flow of solids.
Table 5-1
Properties of the Materiats Used in the Stacking-Out Bins
[11
9r
Hopper
Material
Iron ore
Rec.
39 33
39 33
63 47
63 47
46 40
46 40
*
concentrate
(H2O, 1.5%)
Iron ore
(H2O, r0.0%)
Cir.*+
Rec.
Cir.
Dolomite-
Rec.
Michigan
(H2O,4.2%)
Cir.
Dolomite-
Rec.
(Moller)
(H2O,8.2Va)
Cir.
+ Rectangular opening,
4
*+ Circular openinq,
4
ft
by 2.5
diam.
ft.
55
lo
55
39
tb/tt3
23
190
23
25
190
141
tbfil2
585
T,
fi
sec
calculated,
lb/sec
1.25
5.50
5.7
16,7N
467
1.25
343
4.65
1.50
5.7
9.5
18,200
0.97
8,450
25
25
l4l
395
r.05
t0s
1.50
286
v.f
9,250
1.14
3.20
8.1
8,150
25
1A
105
100
229
263
t.t4
2.80
1.05
t .70
8.1
11.9
6,220
26
100
2r0
1.05
1.60
11.9
6,660
8,600
The Engineering Mechanics of Bins. Silos and Stacks
arch lhickness, T
Figure 5-2. Formatjon of an arch.
FR€E SIJifACE
srREss
{q)
sTiEss
(L)
sti€ss
t laLl)
CALCUIATEO S-IRESS
Mass flow characteristics
I
1. Material segregation problems are minimized
2. Fine Dowders deaerate
3. Material flows unilormly
4. Smooth steep hopper
IALL
)
Figure 5-18. Ideal flow of solids-mass flow.
Figure 5-3. Stress distributions along hopper wall [1].
The strength of the solid material is the criterion for
flow behavior in bins. Failure conditions ofthe solid oarticles can result in arching. no flow. piping (a hole
formed in the solid formation), or limited flow Figure
per wall. When the hopper angle is less than 30', the
limits of radial stresses will occur in conical hoppers, as
shown in Figure 5-4.
Even though the hopper opening is large enough to
prevent arching, mass flow piping will occur. The critical diameter at which the pipe is unstable is given by the
followine:
5-2 illustrates an arch formed by a solid in a hopper. The
failure of the arch will occur when the major compressive stress, R equals the unconfined yield strength, fc. lii)
prevent arching, the critical dimension, B, ofthe hopper
opemng must De
_flJ>
'
7(1
where
+
m:
m:
?
:
m)
D>
4\+
^l
(5-3)
(5-2)
0 for slot opening of width B
1 for circular opening of diameter B
bulk density of the solid, lb/ft3
The calculated stress and radial stresses are shown in
Figure 5-3. When the stresses induced between the solid
particles and the hopper wall are not compatible with radial stress, a flow pattern will not develop along the hop-
Figure 5-5 shows a plot ofthe piping factor, O, against
the angle of internal friction, f. The limiting relations
for arching and piping in Equations 5-2 and 5-3 are functions of the material yield strength, f". This parameter
can be determined empirically only if the consolidating
pressure ol for steady flow is known. This pressure is
denoted bv
or
:
IBQ
(54)
Mechanical Desisn of Process Svstems
z.^
E
=
-to
Figure 5-4. The criteria for
flow when 0' < 30".
o(1
where Q =
d:
o=
+
sin 6)
2sin0
mass
(s-5)
angle of hopper slope
computed stress function along the wall
Combining Equations 5-2 and 5-5 we obtain
1>
t"
(r +
where o1lf"
-)e
:
(s-6)
flow factor of solid
The critical flow factor for arching in channels
represented by
n:
:
(?J".-*,
(ff)
is
'e_
(1
+
m)Q
(s-'t)
F
o
z
Figures 5-6-5-9 show the values of ff for straightwalled converging bins with various material properties
and wall slopes. These factors are presented as straight
lines in the f" vs. o1 graph in Figure 5-10.
The consolidating pr€SSUre 01 that the flowing solid
particles exert in a vertical cylindrical channel is
ot =
D"yG
I
30
30
40
50
60
70
ANGLE OF Ii{TERNAL FRICTON IDEGREESI,Q
Figure 5-5. Piping factor, iD, versus angle of internal friction,
(5-8)
6.
The Engineering Mechanics of Bins, Silos and Stacks
EFFECIIVE AI{GLE OF Ti|cNOfl
2O3.6070
IOEGf,EESI,
E.rECrrE
6
Figure 5-6. Wall friction angle, @', versus effective angle of
friction,6.
^*GLE
OF FitcT|Ox roEci€Est,6
Figure 5-7. Wall friction angle,
friction,0.
{',
versus effective angle
d',
versus effective angle
5
6ro
EFFECTTVE AXCTE
Figure 5-8. Wall friction angle,
friction,6.
d',
versus effective angle
of
Of FFICTION,6
Figure 5-9. Wall friction angle,
friction, d.
Mechanical Design of Process Systems
of the flow of solid particles. This pressure is reduced
internally somewhat because as the solid particles de-
I
scend through the hopper, a vacuum in the void between
particles develops and produces a negative gauge pressure. As the particles approach the outlet, atmospheric
pressure is obtained.
While the wall pressure is maximum at the bin-hopper
tangent line in mass flow, it is only a fraction of a hydrostatic pressure for a liquid head equivalent to the height
ofthe solid in the bin. Thus, designing solid bins for hydrostatic loads results in overdesign of the bins. As a
guideline, the maximum hoop pressure at the bin-hopper
tangent point is about seven times that of the pressure of
the solid induced by gravity. That is,
t(,
=
lrl
E
(',I
F
CR
ot
JI
lrJ
>l
ITICAL
STREI{GTH
RoP(e$i{L
I
o
trj
.
lrl
<=
ori
l!
=
-o
()
F .I'
-t!
taE
()C
z,
--------)coNsoLroaTr G PRESSURE,
=
l6
P*:7{'y)*{H)ft
q
Figure 5-10. Critical values of or and f". Line A represents
strength properties and Line B the constant flow factor [1].
where G is a function of the effective angle of friction, 6,
and the internal angle of friction, {. This consolidating
pressure, o1, provides the strength of the material that
forms the pipe in the bin. Combining Equation 5-3 with
5-8 we have
(+)
\r./
"
where "y
H
:
:
(5- 10)
bulk density of the solid, lb/ft3
height that solid is stored in bin,
Table 5-2
Critical Hopper Dimensions tor Material With Flow
Properties Shown in Figure 5-12 [11
Critical width
ot a slot opening
o*o
.,,,:(,1)",.""=o*o
ft
lor arching, ft
(5-e)
The value of ff is plotted against 6 and { in Figure
)-l l.
Figure 5-12 shows flow properties of a typical bulk
solid, which are quite useful in problem solutions. Thble
5-2 lists critical hopper dimensions for the material with
flow properties given in Figure 5-12.
Once the problems of arching and piping are solved
and the bin is designed to handle the solid mixture, the
next step is to examine flow pressures induced by solid
particle flow. As mentioned previously, solid particles
suspended in vertical storage bins do not behave linearly,
such as liquids. To a much greater extent than liquids,
solids manifest shear forces between particles and on bin
walls. Figure 5-13 shows typical pressure distributions
for mass flow and funnel flow, and illustrates how in
mass flow the pressure is maximum at the bin-hopper
junction poilt. The geometric discontinuity causes an increase in flow pressure because of change in momentum
Type
Flat bottom or nonmass flow
Freshly
stored
Stored for
24 hr
bins
0.2
1.0
Stainless lined hopper
0*
o.4
0,*
0.6
(d, = 30", 6"= 21.t
Mild steel hopper
(0'
:3o" a' :3s")
Critical diameter of
a circular opening
for arching, ft
Flat bottom or nonmass flow
Stainless lined conical hopper
0*
2.0
0.9
Mild steel conical hopper
(0' : 15", d' : 35')
0.4* *
2.O**
0.4
bins
(0'
:
1s",0' :27")
Critical dimensions
5.6
bins
7.7
+
Dictated only by porticle size or dynamic conditions.
+* mese ralues are the same as the flat botrom bin values because the
6' = 35" is too rough to proride
of the cone when 0' : 15"
steel conical hopper when
walls
mid
flor"'along the
The Engineering Mechanics of Bins, Silos and Stacks
The internal pressure in Equation 5-10 can be inby the use of pneumatic air supplied to the bin.
In the case of bins where funnel flow exists or for small
bins with cohesive solids, supplying forced air through
ducts in the bin is desirable to prevent the formation of
arches and pipes within the solid itself. To compensate
for the additional internal pressure, Equation 5-9 be-
crease.d
60
comes
e,
z
E
P.,":77H+Pu;
t40
where
P";.:
(s-1r )
air pressure, psig
=
o
The use of pneumatic air in bins is often desirable and
o-z
in the situations where air cannot be used because of
chemical interaction with the solids in a closed svstem.
nitrogen is commonly used.
40
50
60
ANGLE OF FRICTION (OEGREES),6
Figure 5-11. Critical flow factor for piping.
Hlso
(!
6'
?
3
1oo
Figure 5.12. Typical bulk solid flow properties used to determine critical dimensions for piping and arching.
coNsoltDAT|NG
PRESSUAE,
q, Lb/Fr2
Mechanical Desisn of Process Svstems
q,
PSI +
0 Psl
bin
fu _
FUNNEL FLOW
bin haf
tu
-
F
I
Figure 5-13. (A) Pressure distribution for solid flow is maximum at cylinder-cone intersection primarily because of discontinuity
stresses; @) The relationship between mass flow and funnel flow for conical sections. The angle of kinematic friction, d', is a
function of the coefficient of friction between the solid and bin material and the compression the solid is subjected to in storage.
In stacks, lining is often used where high temperatures
STACK DESIGN
The analyses of stacks subjected to wind and seismic
response spectra are identical to those methods used for
process towers discussed in Chapter 4. The differences
in the two types of equipment are twofold: (1) stacks
have different values for logarithmic decrement and dynamic magnification factor, and (2) the solution to problems induced by vortex shedding are different. Both of
these factors are a result of stacks having simpler geometrres.
The simpler geometry of the stack works for
and
against the engineer. The positive aspect comes as a result of the methods used to break vortex shedding-vortex breakers are much easier and more practical to install
on stacks than on process towers. The negative aspect of
stacks is that they do not have connected piping and
structures to break up vortices and to damp wind-induced vibrations. Thus, we will focus our discussion on
those aspects of wind design that are peculiar to stacks,
remembering that the fundamental basis of design is the
same for stacks and towers.
Vorter Sheddlng and Frequency Response
As explained in Chapter 4, only the fundamental mode
of vibration is considered for process towers and stacks.
Consequently, the Rayleigh method is applied to obtain
the vibration characteristics of the stack.
are encountered and carbon structural steel is the stack
material. Lining must be used for temperatures in excess
of 800 " F because of the danger of carbon precipitation in
the steel. To avoid this and not use lining, one must use
hot-rolled, high-strength low-alloy steels that have good
elevated-temperature properties. Such steels are not generally pressure vessel quality and require heat treatment,
such as the Cr-Mo steels described in ASTM specifications A-387 and A-542. These low-alloy steels are of
structural quality, contain 0.75-1.257o chromium, and
are cheaper than pressure-vessel-quality alloys.
When common carbon structural steel is to be used
with lining, the effect of gunite lining must be considered
with the mass and stiffness to accurately determine the
fundamental frequency of the stack. An approximate
value of the modulus elasticity of gunite is 1.3 x 10opsi.
The effect of lining in a stack must also be considered
with the flexibility of the base. Table 5-3 is a list of conservative values of the logarithmic decrement and dynamic magnification factors for various soil conditions
for lined and unlined stacks. For explanation and use of
these values the reader is referred to Chapter 4.
Ovaling
When slender stacks, i.e., rings in which the thickness
is small in comparison to the radius, are subjected to vortex shedding caused by air currents, the elastic strain en-
The Engineering Mechanics of Bins, Silos and
ergy of the cylinder is distributed in such a manner as to
induce flexural and torsional modes of vibration. The
ring is subjected to the following modes:
1. Extensional (axial elongation and contraction about
the ring's own axis).
2. Torsional (twisting of the ring about its own axis).
3. In-plane flexural (inextensional vibrations in the
4.
plane of the ring).
Out-of-plane flexural (inextensional displacements in
the plane of the ring).
The flexural modes are generally the only modes of
practical significance since the fundamental natural frequencies of the torsional and extensional modes are
much greater than the fundamental natural frequencies
of the flexural modes. Figure 5- l4 shows these various
modes.
Stacks
9
These relationships were formulated by the great pioneers Michell and Love during the nineteenth century.
The reader is referred to Example 5-4 for further clarifi-
cation of units.
In practical stack design, because vortices form alternately on either side of the stack, the flexural frequency
(ovaling frequency) given in Equation 5-13 is taken to be
twice that of the vortex shedding frequency. The vortex
shedding frequency is given by Equation 4-101 as
-'D 0.2v
(4-l0l)
Now since f
,,
:2f,
we solve for
V
and obtain
60f,D
(s-14)
The flexural modes, in-plane and out-of-plane, are
used in determining the resonance frequency of the stack
caused by ovaling. Since out-of-plane flexural vibrations
in which
are coupled to torsional vibrations, it is the out-of-plane
frequency used ro describe the vibration of the siack;
however, the natural frequencies of the flexure modes in
and out of the plane of the ring vary only slightly for circular cross sections. The natural frequency of the ring is
critical wind velocity in which ovaling occurs.
Both the vortex shedding and flexural frequencies
should be evaluated at each elevation if ovaling rings are
to be used. Norrnally, rhe upper third of the stack is all
that is required to be investigated, based on various wind
siven
as
, -_ I I Etn2(n2 - l), lo5
" t tpAr6t+ I + /t
(s-12)
The lowest flexural mode exists when n
tion 5-12 reduces to
"
:
2 and Eoua-
4.4O9t E
(5-
f'
l3)
s:
the Strouhal number (is equal to 0.2 for a
wide range of Reynolds numbers). The value of V. is the
tunnel tests.
Now we come to the most practical aspect of stack design-how to alleviate flexural excitation. This can be
done in two ways-ovaling rings or vortex strakes.
Ovaling rings are used to increase the mass distributed
along the tower to dampen flexural vibrations. When the
flexural frequency equals twice the vortex shedding frequency, i.e., if the design wind speed range includes the
critical wind velocity, V", stiffeners are added at those
sections where f = 2f. The section modulus ofthe stiff-
eners is given by
s
-
(7
where V"
:
:
o, :
l):
j-r
H,
i, t
n=2
Figure 5-14. Stack mode shapes.
(s-15)
,"r"0 velocity (Equation 5-14), fpm
D = "rnr"u,
internal stack
!l \
n=l
x l0 )v:DrH,
investigation,
diameter at elevation under
ft
stiffening ring spacing, ft
allowable tensile stress of stack material.
DSi
Ovaling rings provide a redistribution of the mass of
the stack, resulting in localized stiffening that tends to
offset flexural frequency modes. This is particularly desirable with stacks of several diameters. However, with
stacks of constant or tapering cross section the use of
vortex strakes is becoming increasingly popular.
10
Mechanical Design of Process Systems
Helical Vortex B?eaker Strakes
a stack. The helix angle,
{,
should fall into the following
range:
For critical wind velocities less than 35 mph, dynamic
stresses should be investigated. One optimum solution
for such stresses in stacks has been found in wind tunnel
tests and in practice to be helical vortex strakes.
The application of helical vortex strakes to vertical cylindrical towers has shown remarkable results. The
strakes' function is to break up vortices such that flexural frequency modes are quickly dampened. It is significant to note that adding the strakes increases drag and
thus wind loading. These strakes are shown in Figure
)-l).
To minimize the flow-induced drag and optimize the
vortex-breaking effect, the strake height, W(ft), should
be in the following range:
D:
There are always three strakes per stack to counter the
of vortices on either side of the
stack.
Strakes can be fabricated from a flat piece of metal,
normally 3/ro-in. or 5 mm thick. Each strake is divided
up into a certain number of strips, usually five to twenty
alternate formation
segments, depending on the length of the stack. The
overall length of the individual strakes that is divided up
is determined by
(5-16)
S:[(?rD)2+L2]oj
where D = OD of stack, ft
L height of tower portion straked (V: of total stack
0.09D<w<0.10D
where
54'<d<58"
:
height),
OD of stack, ft
Figure 5-15 shows a helix generated on a cylinder by
taking a template z'D long by L high and wrapping it
around a cylinder. The length, L, of the helix is the top
l/3 of the stack. Wind tunnel tests have shown that vortex
breaking devices are most effective on the upper third of
The number
ft
"S"
is divided into individual strips that
are cut from a larger piece of plate shown in Figure 5-16.
The strips must be cut to a radius of curvatue, r, that is
determined as follows:
+8
a2a2
(5-17)
aa2
.
D-
wherea: --, lt
z
,L
0.090s W<0.1D
d=
54o
Helix angle
2rw
<C358'
r,r
:
number of revolutions around stack cylinder made by
helical strake (usually
<o
:
1)
An alternative formula, developed by Dr. Frank Morgan, and two to three percent in error of Equation 5-17,
IS
XW
(s-18)
1-)\
\rhefe A
T
L
I
|-,D
Figure 5-15. Cylindrical strake helix geometry.
S,
interior arc Iensth of helix
= _ : ------:--------:
S" exterior arc length of helix
(5-le)
The value Si is determined by using the outside diameter of the stack in Equation 5-15, and S" is obtained by
using D * 2W in place of D in the same equation. For
the most accurate results, Equation 5-16 should be used,
as it is the exact radius of curvature of a helix projected
on a cylinder [3].
The Engineering Mechanics of Bins, Silos and
Strips are laid out, as shown in Figure 5-16, with an
inner radius of curvature determined bv Eouation 5-17
and outer radius of curvature of r : r + W. it is desired
that the helix be perpendicular to the centerline of the
cylinder along the entire length of the helical strake
shown in Figure 5-15. To obtain this each metal strip is
placed in a rig shown in Figure 5-17. The rig is composed of two clamps, each 45' from the plane perpendicular to the table, or 90" offset from each othe;. O;ce the
metal strip is clamped-in, a hot torch is run up and down
the length of the metal strip hot-forming it to the shape
formed by the clamps. The strip should not be heated any
longer than necessary to hot-form.
The metal strips should be the same material as the
stack. The effectiveness ofthe system is not impaired by
a gap of 0.005D between the helical strake and cylinder.
This method leads to ease and quickness in fabricating
helical vortex strakes.
EXAMPLE 5.1: GRANULE BtN DEStcN FOR
ROOFING PLANT
Figure 5-16. Strake fabrication detail.
1t
As seen in Figure 5-13b, the minimum hopper angle
for mass flow is
0 :37.74'1"
From Figure 5-4,
6'
From Figure 5-5,
<D
:
l0
=
0, which implies that we will not
have piping forrning in the bin
6=70'
For a circular opening, m =
1
s'(l + sin 6)
^
(5-5)
zslnd
From Figure 5-6,
ff
:
1.6
ff=(l+m)Q
Q:
or
Twelve granule bins are to be designed to provide
granules for the manufacture of roofing shingles of Example 3-6. Each bin is to contain 10.02 tons of sranules.
yielding 120.24 lons rolal capacity for all twe'ive bins.
The client desires to use an existins steel frame that limits the bin to a rectangular shapJwith an off-centered
opening as shown in Figure 5-18. From this figure we
consider the first criterion in bin design-to satisfu flow
conditions such that the granules wili move.
Stacks
:
1=
:
o1 :
B
=).
=
(s-7)
0.80
7BQ
90 lb/ft3
0.667 ft
(90)(0.667)(0.80)
:
43.6, tbrtU
From Figure 5-12,
f"
:
s0 lb/fC
Figure 5-17. Clamping each strip on 45 degree offsets and hot
forming with torch obtains desired geometry.
Mechanical Design of Process Systems
12
l--j*---l
E
,.T
;l
t;;lr\l
tl
\
1 /\
I
Figure 5-18. Granule bin silo.
:
In this problem, a
12.625 ft and b = 4.00
pressure at the bottom of the plate is
Thus, the critical arching dimension is
B=
r(l
f{o
'
+ m)
Since 0.278
the bin
-'
(90X2)
:0.278
(5-2)
ft
ft < 0.667 ft = 8 in. archins will not form
sure distribution exerted on the bin walls is taken to be a
simple hydrostatic load. The bin walls are fixed on three
ends and free on the top edge. The solution for the maxi-
mum stress is given by
uno F :
orPb at x = 0, z :
a
b
0
:
t
:
4.000
12.625
*r :0.030
Vz
=
0.032
The maximum stress occurs at the bottom side at
z:0
(5-21)
:
12.625
ft:
plate thickness, in.
x=
0 and
/<.)n\
151.50 in.
For 5.4-516 Gr. 55,
o4
:
13,700 psi. Solving for t in
Equation 5-20 we have
r: /v,pu'\o'
l__-l
reaction force exerted on the plate edge normal to the
plate surface, lb/in.
load per unit area, psi
p,r
(5-20)
where Vr, V2, 01, and 02 are in Figure 5-19
P
z,ur
_ _ vrPb2
*1!o' unoF orPbatx +a.z b
=
=
=
=
'
ifu > borz:0.4bif a'( b
:
(n.6zs)ttffi :
From Figure 5-19 we obtain the following:
b
F
eo*
The
in
After flow criteria have been met, we proceed to the
structural design of the bin. The allowable stress used in
the case of bin design is the ASME allowable, since the
granule weight forms a pressure distribution, thus making the bin walls pressurized components.
For simplicity and ease in calculations, the solid pres-
: v{bt
:
P
ft.
1:l
ko.o:o)(z.ssr)
I
.\
tn'
r:,eoo
(rsr.sofin.'lo,
--lb-
|
I
:0.627 in.
The Engineering Mechanics of Bins, Silos and Stacks
The stress at mid-plane is
""
z
,
:
b
a
t2
:
,
12.625
4.O
At x = 0, z :b = 12.625 ft
4.734 psi
_ lro.orzlr+.rl+rr rs r. sor'lo ' = 0.502 in.
Selecting SA-516 Gr. 70,
.
Deflections of bin plate"
v,Pb2
0.4b, P
_ [ro.o:otr
z.
13
oat:
ae1)fl51.50),lo
I
(0.00020)(7.891) ',Jb- 1+t.oy in.,
Dlb
ln.
17,500
5
-- 0.557 in. at bottom edge
_lto.ozzx+.tt+xrsr.sor,lo' _= 0.446 in.
ar
z = 5.050 fr
D
:
flexural rigidity of plate
Et3
12(1
-
v'?)
o
16
I
Figure 5-19. Rectangular flat plate solutions.
14
D
Mechanical Design of Process Systems
(30.0
>
12(1
106x0.562)r
-
0.311
:48:
.b49.25J
in which,
w :7.4565
x
10-o in.
Bin Stilfener Design
To reduce bin plate thickness, stiffeners can be used
with thinner plate. A thinner bin plate makes fabrication
simpler because a thinner plate is easier to weld and is
cheaper.
With stiffeners, each enclosed area is analyzed as a
flat plate with three edges fixed and one edge simply
-b =
Atx = u,z
t
supported. The stress in the plate is given by the following:
(0.004x7.891)(48.0),
w_
ob
Ph2
= 't,'l:-:
and
^Ph2
: *,5o'
and F
t-
481 ,649.253
w=
1.4913
x
Itr
l0-1 in.
For a e/ro-in. plate deflections are negligible and no stiffeners are required for this plate thickness.
"
F-
QrPb at
x = 0. z = 0
-
02Pb ur
*
: tJ. z'0.4b
\5-22)
(5-23)
where V1, V2, 01, and 02 are shown in Figure 5-20
.09
.o8
.o7
.05
.o4
Figure 5-20. Rectangular flat plate solutions.
The Engineering Mechanics of Bins, Silos and Stacks
:
P:
t:
F
reaction force exerted on the plate edge normal to the
plate surface, lb/in.
load per unit area, psi
plate thickness, in.
rhI
P = 90--l f 2.625
fcl
:
:8.0 ft, a/b :
0.50. From Figure 5-20 we
obtain Vr = 0.064. Thus, from Equation 5-22 we have
_ :_
o.",
(0.064x 7.891)(96)2
_
11
r
(0140 = JJ.009.228 psi > al)owable
Consider b : 4.0 ft, a/b = 1.0. From Figure 5-20 we
have i{'' : 0.192 and from Equation 5-22,
o^, : 24,756.921 psi > allowable
:
Similarly, considering b
o-"-
:
11,475.865 psi
<
2.0 ft,
:
17,364.2?9 psi
- 3.5O)
-(rq)
4.036 psi
allowable
=
<
5-21 hold, using Figure 5-18. By iteration we obtain
: 6.458 ft, P - 4.036 psi, a/b = 0.619, Vr :0.091
o^":15,643 psi o 17,500 psi
b
and
Since the maximum stress is less than the allowable for
the top portion, no third stiffener is required.
First Stiffener Design
a = 4 ft-o in.: b
:
2 ft-8
in. a/b:#:t.roo
17,500 psi
ofb :
By a process of iteration we obtain a value
in., in which
o^,
(2.667
The top portion ofthe bin is now a plate with three sides
fixed and the top edge free. Thus, Equations 5-20 and
First Stiffener
Consider b
-
15
/'-TR
2
ft
lt
Pt
8
| |
I
I
l.
tco
fi l'
,H1
17,500 psi allowable
/r )ll
\q--7891 psi
|
Thus, we place the first stiffener 2 ft 8 in. above the bottom seam,
'Yr
= 0.383
v
ffi
UV
u,
Second Stiffener
At 2 ft 8 in. the maximum pressure exerted on the bin
wall is
rh
P - e0;
/ rf':
2.62s - 2.667\ ft ln;-l
Consider b = 4.0 ft. a/b
:
\
=
1.0 in which Vr
6.224 psi
:
0.192 from
Figure 5-19. Thus,
o-",
='o'n',)lu:?.',!'08)2
(0. 141)
:
I
STIFFENER
19.s26.e psi
>
R
:
.yrpb
:
(.383)(7.891X32.0)
:96.712lbhn.
:
w
17.500 psi
By a process of iteration we arrive at b = 3
which o-"" : 17,502 psi
ft I in. in
Third Stiffener
At the new elevation, 6.167 ft above the bottom seam,
we obtain the maximum pressure exerted on the wall.
With plate pushing uniformly on stiffener, the latter will
be analyzed as a fixed end beam with uniform loading.
96.712 lb/in
16
Mechanical Design of Process Systems
w/
w:
:
(96.712X48)
(4'92
-
M-^.
M -
^-; W=wf
24
M.*:
4,642.18 tb
181x48 0)
24
:
=
9.284.36r in.-rb
, _- (8,532.384) in.Jb (0.54) in. _ ., ".,, ,l?soo rbfinj
773.697 ft-Ib
rtun
I
For design purposes select a design stress of o
:
0.37 in.a
t/+-in. thick,
(9,284.361) inlb(.49)
in.
:
17,000 lb/in.'?
.zr
:0.39
=
P
-'yD
From data provided by the client, P = 400 lb/ft'z
tion point. Using a factor of 7 we have
0.268 in.a
at
junc-
P = 7(a00) = 2,800 lb/ft2
in.a
Therefore, 3-in. x 2-in.
x t/+-in. 4 is sufficient
Stiffener at Junction Point ot Bin
Hoop Force
x2-h. a
o
17,000 psi.
I:M"g
I of
:
Therefore, Ztlz-in. x 2-in.
With a factor of safety of 2. This would give a yield stress of
34,000 psi, which is conservative.
Select a 3-in.
x z-in. x tl4-in. 4
Select a 2rl2-in.
I
'
'ol Rs1?.3E4in.-rb
A-","". =
'266 '1921(48
I:M"q
Mc
,
@
><
tla-in.
4
is sufficient
P
:
2,800
rb/rt
(r-lq)
=
re.zt44 psi
UseP = 20 psi
For bottom plate,
a:4
ft-0 in.:
: 0'383
R : (0.383X20.0X32.0)
b:2
ft-8 in., a/b = 1.500
rr
= 245. r20 lbl in.
w,
w = (245.t20X48.0)
M.*: =-:
1.+
Second Stiffener Design
M _ ( I 1.765.760X48) :
A_.-'--
P = 6.224 psi
a:
4ft-}in.;b
:
3 tt-6
By linear interpolation, 1t
R:
pr-". =
in.;
a/b
=!:3.5
:
4
slj.520 injb
t.t+l
88.879 lb/in.
{: w = (88.879) lb/in.(4E.0) rn.
:
11.765.760 Ib
Select a 3rl2
in. x 3 in. x tla in. 4
:9.349
(0.340)(6.224) lbl\n.2(42.0) in.
w
1"t
=
,266 .192
lb
I.in :
(23,531.520X0.79)
_
1.094 in.a
17,000
I = 1.3 in.a for section
Therefore, 3rlz-in. x 3-in.
long side facing bin
x r/+-in. r is sufficient with
The Engineering Mechanics of Bins, Silos and Stacks
Bottom Portion of Bin
0. | 825(6.31 3X50.928)'
-
Bottom portion of bin will be approximated with four
tdangular plates welded together, as shown in Figure
5-18.
'-'----'''
(0.438)2
Therefore, use 716 in.
f,
for bottom plates
Bending Stress in Bottom Portion
*ll11
->l
Ptt
I
ll-tl
ll
--'l'
Y
Pr = 7.891 lb/in.2
pz
:
e0 lb/n3(16.50
ft)
:
J
[-]q144
10.313 psi
--tt t La-
t-ll
It-
At an angle ot90o-0:37.7474,
P:
10.313 sin
37
.747" = 6.313 psi
CROSS SECTION CUT AT
MIDPLANE OF TEIANGLE
By linear interpolation, B' :9.3659
o:412
o=
It;
-il
rJ
1$
-_tt
=o.rszs
0.1825Pa'z
,,
qan
,
P = 6.313 psi on triangular plate
m.l8r5x6.rl3x5o.%y
- \l
17.s00
= u.4rJ rn.
A
with
t:3/E in.,
,'" -_
0.1825(6.113)(50.928),
(0it5,-
:
21249.532
38,000
:
:
-
area of triangte
= Ia'20'lro.z*> =
\21
: 1,497 .589 in.2
= F : (6.3 13) lb/in.,(I,497.589) in.2 :
at3 : (4.244)(12)13 : 16.916 in.
M, : F(a/3) : 160,495.84 in.-lb
s?? nci
YJ'
-= ,t
'''-",4q -J-
:
38,000 psi
55.92% of minimum yield
Mc
% yield,
:
with rhe
in.
21249.532
70,000
f,
,
:
t0.40
ftj
ot A
For SA-516 Gr. 70, minimum yield
% yreld
From previous information,
= l/,JWPSl
30.36% of ultimate yield
I
thJ r/{O Otl\3
r:-=-:[,007.49Er
l,/.
Iz
9,454.279 lb
17
Mechanical Design of Process Systems
18
,^ 50.928
atJ:_=lD.y/orn.
For three horizontal plates,
3
(
160,495.84)(16.976).
o"u
(1r,007.498X
:
(r2.62s itx8.0 rt1 =
'2
17,500 psi
1!30-1f
- z,3ts.22JIb
or for three plates,
,_
'
-
(160.495.84) in.-lb (16.976r
(r 1,00?/98xr?J00)
Therefore, tlrc
in.
t_
in.
_ .,.,,,,
i"rlb/i"r - " "'-'
m.
wt :
6,945.669 lb
is sufficient.
i:\\:-j
Vessel Supports
Consider all trusses as pin connected.
Side Truss
For simplicity and to keep things conservative, let us
analyze the internal plate to determine if we need any
supports on inside of structure.
weighr of internal load
w
rblfr
t:
3/8
: (t20.24) lz'z+o v\
'on'I ,on /
:
269,337 .60 tb
End Truss
For two outside plates,
in.;
wt :
(12.625)(8.0)(0.375)(1,14)(.283)
wto'.r
:
:
1,543.482 Ib
3,086.964 lb
For two side plates,
Wtt"d
ftXt)
:
(1s 1.s0)(192)(0.s63)
wt:
:
=
6,173.9r,
tO
For each bin,
16,362.0 in.3
ro*r
2(3,086.964)
Under Bins-4 Triangular Plates
Weight of steel (Wt):
(12.625 ftx16.0
:
A
0.283 lb/in.3
(16,362.0)(0.283)
:
4,630.446 tb
/a qor \
- 4 l- '"'l A.244\tt44\
wt of
\21
each
bin
-
=
5.990.355 in.1 of metal
(5.990.355)(.283)
=
1.695.270 lb
The Engineering Mechanics of Bins. Silos and
Number of Bins
:
as continuous beams in the longitudinal and lateral direc-
:
13,562.164 lb
Empty weight of structure
:
:
=
Wt of granules
Total
wt loaded
w
-
:
wL: lzsss.+rglli [+.olrt :
so,g73.ozo ro
lt:
:
4
4.0 ft
RA
:
:
Ro :
911,210.313 lb/in.
rur Y, w . (9 .210.313r lb
E
in.
: 174,952,380.1 lb
(174952'380 1)(192)
8"
:
0.393 wt
=
RB: Ll43 wf:
303'739 771 ..
75.934.r93 lb/rt
4.0
Rc
Considering the plate in Figure 5-18,
M-
FoR EACH spAN
303,'736.7711b
Total number of internal plates
Total length
tions.
4,630.446 lb + 6,945.669 lb
+ 3,086.964 lb + 6,173.928 lb
+ 13,562.164 tb
34 ,399 .r7 | Ib
269,337 .60
:
19
The frame structure shown in Fieure 5-18 is analvzed
8
Therefore, Wtrorur
Sacks
1. 143(30,373
.676)
=
11,936.3tt
,O
= 34,117.rt b
:
0.928(30,373.676)
:
wf:
1.143(30,373.676)
:34,717.rt
0.928 wf
1.143
0.393(30,373.676)
28,186.77t tb
rO
Solr ing for reacrion\ in lateral plate
92.1 ,n.
FOR EACH SPAN WL= 30.373.676 lb
= 4 rqx x\7 r)l,n
-rh
Therefore, bin must have internal supports under botaom.
Number of vertical supports
=9=R:
=
Number of ioint suDDorts
F
tol 716 ?71
: --"'
_-:j____: :
IJ
303
33,748.530 tb
: 9
tl
20,249.118 lb
'73-6'771
9
v.* :
V-* :
0.607(30,373.676) tb
18,436.821 lb
RB
=;6 (10.373.676X2) = 37,967.0q5
Ra
= ft. =
lb
11,390.129 lb
Design each support column for 37,967.095Ib
srde saructure
=
38,000 lb
The bin structural detail is shown in Figure 5-21.
20
Mechanical Design of Process Systems
BIN JUNCTURE DEIAIL
STIFFENER DETAIL
Figuie 5-21. Bin struclural frame detail.
EXAIIPLE 5-2: HIGH.PBESSURE FLARE
STACK DESIGN
Add 12 in. for platforms and 12 in. for ladders.
A high-pressure flare stack shown in Figure 5-22 is to
be designed and construcred to the following specificatrons:
Base diameter
:
l0 ft
Height from bottom of steel base to tip of flare stack
ft
Gas pressure in stack = 2 psig
Gas temperature = 100oF
Design wind velocity = 100 mph
Maximum gas flow rate 300 MMscfd
Earthquake design
:
:
World Mercali 6-7
Effectlve Diameters
:
200
Add 4-2-in. d lines.
2-in. g dia. line
D
:
(3.375X4)
D"^"".,
:
DB :
Dc :
De
:
:
+
2.3'75
in.-Add
:
=
2(12)
42
+
37.50
:
79.50 in.
90
+
37.50
=
127.50 in.
120
+
t/z
13.50 in.
13.50
37.50
:
37.50 in.
157.50 in.
in. insulation
The Engineering Mechanics of Bins, Silos and Stack
Height
(fD
Wind Pressure
P, (rb/ftr)
w = B x De x
Wind Load
Pz
(5,270.98X110.5
26
: to6)(!f)tz6):20415
30-40
33
: ro.olffit:3):25e.88
40-74
38
: toor(lle)o
74-76.5
44
: too(l#J(44):34650
'16.5-125
44
:
0-30
125
48
:
28o.so
= t0.6tl'-'""1t48t =
\ 12 /
306.00
159-t74
r:
so\
: ro.orfifJt+t):
48
866.25
+ 2.5) +
x
(90.0
+
(13,604.25)(24.2s
+ 2.5) +
(2,862.0)
(10,404.0)(65.5
+
2.5)
+ 2.5)
:2ee.2s
,0.u,(]?Za)r*)
/r
159
Moment
lb/tt
reo.8o
51 PSF
174-200
:
51
<o.orit#)or) =
202.'73
48
Wind Load
159
PSF
Moment
s.270.98
(s,270.98)(13.0 + l5 .0) + (2, 862.00)
2,862.00
llrl
\21
44 PSF
169,052.44 ft-lb
(5,270.98)(28.0 + 34-0)
+-
(')
!
__!
86rn)
38 PSF
r0,404.00
x
(7.5
+
34.0) + (1 o,404 .0) I34.01
\)
I
622,44r. 76 ft-lb
(5,270.98)(62.0
+ 48.5) +
,rO-l
30_
_t
-l
;1.
33 PSF
(2,862.0)
26 PSr
t3,6U.25
x
(41.5
+
+ 48.s) + (10,404.0x17.0 +
(13.604.25)
48.5)
/an s\
| -'l = 1.851.388.35
\2l
fr-lb
Figure 5-22. High-pressure flare stack; unless otherwise indicated, all dimensions in feet, design wind speed
100 mph.
:
22
Mechanical Design of Process Systems
Wind Load
For Section D
(5,270.98)(113.0
+
+
34.0)
(2,862.0)
x (92.5 + 34.0) + (10,404.0X68.0 + 34.0)
+
x
.25
+
34.0)
+
x
(126.50
+
(r3 ,6O4.2s)(60.7
x
(35.25
+
10.0)
I
+
(2,862.0)
102.0
+
+ r0.0)
/,,r.0\
+
30.0)
+
(13,6M.25)(70.7
x (45.25 + 30.0) + (10,174.5)(27.0 + 30.0)
30.0)
+
:
s,
r:t,+rr.zo
0.56 t" E
y
'.E:29
:
30,000 psi
x
o.oo5
>
o.oo425
(0.56X0.005)(29.0 x 109
0.004(29.0 x 109/(30,000)l
+
90.00
o. = 20,021.918 psi
!:
d
(0.500
rt-ru
- 0.12s)
=
0.009
Section Weights-Uncorroded Weight
-
d (1 + 0.004 E/y) '
:
t"_(0.625-0.125) :0.006
wr =
'
o l25)
16,684.932 psi
Section
Allowable Shell Buckling Stress
109
o. = 30.032.877 psi
(6,142.50)
i3o'oJ
0.00425
For Section A
5 + 30.0) + (866.25)
+
-
120
d
(2,862.0)
(136.50 + 30.0) + (10,404.0X112.0 + 30.0)
(2,598.80)(s.0
x
>
For Section B
l+-lt
'\2
x
+
(0750
:
(10,174.5)
:3,672,858.86
6,142.50
!:
d
li
(2.s98.80)
+
o.oo6
For Section C
5 + 10.0) + (866.25)
x (r7.0 + t0.0) r
(5,270.98X157.0
120
(0.56)(0.006x29.0
3,228,045.06 ft-lb
+ 10.0) + (10,404.0)(
- 0 125) :
o,
:
10.0)
(0'875
"" _ tl + (0.004x29.0 x 109(30,000)]
: 20,02i.918 psi
(866.25)
\'2
*
d
- .-. - /:+.0\
+ 34) + 00.174.5)
l:-jj: I
(5,270.98X147.0
2,598.80
+
(13,604.25)(26.'75
13
A
(0.2833)
''
j:
(37.0)( 12)
'n.
',[l/€)'-litt\'l',
[\, / \2 I )
8,199.69 lb
Section B
106
psi;
wr
- (02813) { rzoo,rz,' "
[(T)'
= 45,340.61 lb
(*, )']'"'
The Engineering Mechanics of Bins, Silos and Sacks
Section
Section C
wr
(ry ro]l_.,
- (0.2833); (44.0X12)'n.n [('r),
[\, | \ 2 l)
: 42,029.09 lb
'n
(16)(42 .0)(169 ,0s2 .44)(12)
rl (42 + @D2l(1.2.0 + 41.0X30,032,877)(1.0)
8,199.69
+
r(42.0 + 41.0X30 ,o32.877)(l .0)
Section D
t.
wt = (0.2833)
in.
--ll(30.0)(r2)
:
Total
"
:
:
Mr
r(D"'?+Dr'?)@"+D)oE
r(D. + D)oE
oe
:
18.25F](120.0
+
I 1 8.25X14, 182.
:
A." -
(16)(120.OXs, 138,419.76)(12)
(1
, OK for buckling
l2o + 2(2.50):
=;
125.00
:
Wn
- l?!'e!6 58 - 76,84r.ros lb
*,- = ottl24(125.00)
24
'']!;01?,tu'
Section D
+
[
Total tension in each bolt
Thickness
16 D"
r[(120)'?
in.
Try 24-11+-rn. d anchor bolts
dec
t
1/z
Anchol Bolt Design
128,966.580 lb
Required
in. =
0.052
[(9' - (r94,)]'"
33,397 .r9 tb
wt
A
:
19X1.0)
40,000 psi
76'841 109
= |.921 in.2 <
40.0(n
l3/+
1.980 in.']
in. dia, 8-thread series
128,966.580
+ 118.25X14,182.19)(1.0)
in. + 7r in. [ , OK for buckling
r(120.0
t,
:
0.381
Check
[/av\
: t-wl
t\d/
I
^AR:No,
1
Section C
r1r20)'?
+
r(120.0 +
, = 0.245 in. -
rl
+
(24)
95,569.39
I 18.5)(16,684.932X1.0)
Ar =
t/q iI^. 'll_ , OK for buckling
Bearins pressure
+
(16)(90.0X1.8s1.388.35)(l2l
(88.75f1(90.0 + 88.7s)(20,021.918)(1.0)
53,540.300
r(90.0 + 88.75)(20,021.918)(1.0)
t, = 0.183 in. .r :/s-in. [ , OK for buckling
1.913 in.'?
48(s,
^'
Section B
(90),
(4X12X5,138,419.76)
(12s.50)
(16)(120.0X3,672,858. 86)(12)
(1 18.5F1(120.0 + I I 8.5)(16,684.932)(1.0)
1.980 in.'?
= P-- =
48Y + W
:i- 7rl:in.
nDu' j
r Drj "
r38.419.76)
:
Base
fl
psi
<
Fb
;e
t28.966.58
7r(
:
thickness, T1
t" : " (;oiltJ
128,e66.58]
(40,000)
r( 125.00)'/(7.50)
Pt :7\3.734
Tr
<
-
125.00X7.50)
1.33(900)
:
:
1,197 psi
compression
=B* C
:
Z3tqin.
I
+
thickness
Zttcin.
:
5.5o
24
Mechanical Design of Process Systems
=
Te
(5.50r
After one iteration,
Il,lr r l rarl "t
= 1.800 in.
l:j;;:;=l
I zu.uuj I
l'''
-''
:0.151
1
K:
[ :twu) o
[:1zo.r+r.roenorl''
[4(20.000)el [ 4(20.000X5.5) I
1+
(61,789.8ss)
(10x1,096.373)
After six iterations,
K:0.178
B.ownell and Young Base
d
Bolt circle
P
Base
4 :di
:
f,
f"-Eq
= n E' --
Method
125.00 in.
lo(1.096.373)
=
fc,-o,.area,
(1.0e6.373)
125.00
130.00
130.00
:
212.50\:
(7.00)
2(7
1 16.00
130.00 in.
116.s0 1t.
:
: 7.00 in.
K=
1,000;
=
I
L4
:
(1,200)
\r/2
I ^"
JI.
- ^1^-l
:
:
1,106.925 psi
[ 2(0.333x125.00) +
(5.138.419.76)
r,=-
'
[46.,rr'l,,rr.*,
I
t,26t. sto)1"'
- ,.'' "' [:rt ,o"ooo I
2.181 in. (without gussets)
lr(
""-"
h = -r
1.588; C,
= 2.316 z:0431l.
-
00l
.,"\ ll25
(128.966.58){0.r'''
12
/
559,723.403
A
z'd
=
,..,,
f,'s,
gusset spacing is
7.00
1.980 in.2 (12)
?r(
125.00)
t2
n
b
"' = 32.725 in.. | = A = 5.00 in.
O\
5.00
32.'125
From
tble
4-8, using linear interpolations,
My: -
O.467fcrt2
My=
0.467 (1,268.836)(5
-
r,- _ l(oJ{l+.6rr.oou)l =
- U.UOI ln.
:
t
6l,789.855
20.000
'00f :14'813.660 in.-lb
2.10g in.
I
t = use 2rls in base
Brownell and Young External Chair Design
Fc
t:
:
=
I
0.333
0.782
:
7.001
2(0.333X12s.00)
K = 0.333; c"=
For
t",^ ,"8)(t25.0) +
1.268.836 psi
-
Using 24 gusset
j
t0,963.73
:
with fc,".,
fc(Bc)
:
559,'723.403
7.00
-
0.061
+
128,966.58
:
6.939 in.
:
688,689 983
688,689.983
rcr6.e3e
-
(10)(0.06rI
($Q)<r.sasr
=
r 5.00
22
b
:
gusset spacing
1,096.373
For |ta-in.O bolts,
=
32.725 in.
t 15 :
e -:"
2
t.375 in.
The Engineering Mechanics of Bins, Silos and Stacks
:
:
PB
\r.
max. bolt load on upwind side
fsAB
-
2r.708.185[
4r t
=
lr/+
fw
:
1.33'yn(0.55), for wind or earthquake
21,708.185 lb
fw:
*
(t + 0.30),n Izrs.ool I
[z'(L375)J
,l
I
:
i.33(20,000X0.55)
Weld size
=
14,639.99
5 154 1)1
--- = 0.396
-.'14,630.00
3,612.549 ir..-lb
or
.' _ [{6x3612.549)lr" _,
t 15,000 I
=
:
= (10,963.73)(1.980)
in. in. f,
"^.
0.396
'2
for compression ring
= 0.198+
Va
in. minimum weld each
side
Cantilevel Vibration
'.
Calculation of Gusset f, Thickness for
Compression Rings
:
(,aJo o
. (,$n',
=
5 860 rt
Corroded Stack weisht
r,2
[ = 4qr2-r2 =].
t2
,=
:0
[ereL, ]
withk=%(1.250)=0.469
*,^
:
6nluurf(,sl
-
(91 :6,16'".ze4tb
*,"
:
<arr oezrl(r1)'
-
(r91 :36,323217
r35 in.
h:G+H I21h n. :9 + lt/+ in. i
h 12.500
r 0.135
P
2t/c in-
tb
= l2tlz in.
*,:,ounn
Bolr Load
lttt
rl(?l- (rtl]I|l:
35,o6oe6o,b
23,905.217 tb
101,457.688 lb
18,oo0rtr-Ptt- htP
I,500
18,000(5.00)t63
-
Lc
:0
(12.500),(21.708.185)
_
1,500
qt
-
q=
0.24ltS
0.40
in.
r/z-in.
f,
5.00:
13.0
= U.UtJ <
trl
0
=
(200X5.8601
LD,2= 4!4:1688=
ft
U.5
14.773
<
2r)
Therefore, vibration analysis r,?as, be performed.
- 0.025:0
=
8.00 +
r^ rlnn
L 200
(21,708. 185)k,
_
:
Wa
is OK
Skirt-to-Base Ring Weld
':
-
,: (#ft)* (";)'0u."
r:a.+ ro.76x r2)]
, _ [r+xs.
r-[
--;6 20"0)!-l t
r28.966.58
"(t20-00)
:
101,457.688 lb,
:
193.50
-
lr.O
*
ff
:
r'v))
ft
1.648( 193.501
L?
5r(ET, = o.gaOx:sJt-lItc
t.648
I
:
t: ,uB
= )'tv+ tzl
L" = 200
0.511 cps
vc :3fDrr:3(0.s11X5.860)
:
8.983 mph
seconds
26
V:o
v*
Mechanical Design of Process Systems
:
100 mph
:
(roo)
r-
(*J'"' :
k_
L..Ws
_
fu
13 1.
165(1.3)
:
193.50)1t
0
l5 mph
170.5
(0.0077X5.860)5(29.0
(
x
_
(
2
:
"f
it{zs.zts), -
\
/.
(34.71
(0.207X5. 86oX
x
x
t :6047
-'
106)0
5)2
5
(1.760) = 3.520
/ ss
cps
\-/l ,
lfl in.a :
/
77,307.326
6.047 cps
10 ft,
6o(to0l--
0.2(66)
:
2t,:2.640 <
\/ss.zs + o.zs\
<
f'" -_ 7.58(0.625X29.0 x lfff5
_
=
a)\).^<
1.320 cps
4.252
At bottom section,
in]
f,' _
7.58(0.751(2?.0
x
t06)05
60(10.01
=
5.102 cps
i,:o2t66t=1.320cos
'10
8EI
8(29.0
60(7
At 120-in. dia :
0.523 in.
P"D,(LF(12)j
-
_
7.58(0.5x29.0
'
10
,
'=: \'oo/\
34."111 ir.
-.
D.=
t.:
"
2f,:2
0.107 psf
0,,,) * (,z,|(?..,")
i+r \/ +r r o.zs
r:
:
- 0.r25) + (,$,o.uro :
," = (_..)(? *
:35.285 in.
0.2v 0.2\66,
:D=(35;=r'l/rcPS
/.f
1.0X0.00238X 1.467P(8.983,,
(,$,o.to
vortex shedding frequency
f _ 0.2(66) _ | %n
2
,
=
. t,
At 90-in. dia : 7.5 ft,
Static Deflection
^ ^
Y.-{.,o-
20.826 cps
2f"=7.54t
Therefore, the stack is free from cantilever vibration.
tt.467V
:
106)
t.457.688.)
115
:0.002 <
0-l-]06t
60(3.50F
13r.165 mph
Maximum gust velocity :
0.0077D,5E
7 58(0'3zs-iq9
l93.so)4(t2f
106)(77 ,307
.326)
=
0.164 in.
2f,:2.640
. t.rO,
Therefore, stack is free from ovaling vibration.
Dynamic Deflection
Using a magnification lactor of 30.
6
:
0.164 (30)
:
4.915 in., which is permissible
Ovaling Vibration
Natural frequency of free ring
''^
7.58r.(E)o
5
:t
AIICHOR BOLT TOFOUE
Anchor bolt torque on stack bolts is handled exactly
like tower anchor bolts as discussed in Chapter 4. Using
Equation 4-66 and considering lubricated bolts we have
T:CDFi
where the uplift load on each bolt, F, is
6oD2
At 42-in. dia : 3.50 ft,
(4-66)
-t,:
r2)
,2a1us.0ot
4(5, r38,4r9.76X
r0r,457.688
a
: tt't6t
'tztD
The Engineering Mechanics of Bins, Silos and Stacks
.\hich results in a required bolt torque of
r:
(0.
rs) (r.75)(77
ALL MATERIAL TO BE SA-285
_C
,987 .312)
= 20.471.67 in.lb = 1.706 ft-lb
Use 1,706 ft-lb torque with lubricant grease Fel-Pro C-
or equivalent.
The skirt base and anchor bolt detail for the stack is
hown in Figure 5-23.
5,A,,
Design Summary
Static wind shear at base = 22,355.110 \b
Static wind moment at base = 1,299,115.509 ft-lb
Dynamic wind shear at base = 22,844.841 lb
Dynamic wind moment at base = 1,308,916.974 ft-lb
Total deflection at top of original tower 4.418 in.
Total deflection at top of modified tower
5.898 in.
Base plate thickness:2lle-in. plate
Compression plate: 1l/4-in. plate
:
:
trL_u--l
ffi
ALL WELD SIZES
16) l:/+-in. anchor bolts
Required anchor bolt torque: 1,710 ft-lb
Total operating weight = 128,966.580 lb
,
IN
INCHES
EXAMPLE 5.3: STAGK VORTEX STRAKE
DESIGN
An exhaust stack 126 ft tall is to be Drovided with heli.'al vortex strakes. The length of the stack to be straked is
the top portion 31 ft 6 in. long. Cornpute the radius of
iurvature of the strake to be cut from flat olate. Referring to Figure 5-15 we have the following:-
D:ODofstack:7ft4in.
L:31
ft 6 in.
D
7.333
: J.DO/
.i = _ = _
L _31.5 :
2ro 2rtl)
zl-tci I
.t
a-tgg-'et. a THBEAo sERtEs BoLTS
TO STRADDLE CEI.ITERLINES
BOLTS
t{
\ou,
+b2
_
_
a2cu2
_
_
(3.66'7)2(r)2
- --;F-
:=
(5-17)
+
(5.013F
(356?X1t10.521
ft
Figure 5-23. High-pressure flare stack base support detail.
28
Mechanical Design of Process Systems
Check
BASE PLA?E
-
3/16r
Using the approximate Morgan equation we have,
Si
:
:
interior arc length
[(rDJ'? +
52:exterior arc length =
:
41.637
ft
L2]0 5
:
39.025
ft
[[?r(8.667)]'? + (31.5)'?105
STRIPS CUT FRO}I
x:9:t?'o,T:r.nt
s.
(s-1e)
BASE PLATE
41.637
r
\w
: ._________
(5-lg)
(0
667)
r - |937)(0
- 9.966 ft = 9 ft i t.594 in.
0.937
10.521 - 9.966
_
va e:,rof =
= 5.276Eo errol
ff
t
0.5ft + 0,66?ft
= 11.-2.
The final product is shown in Figure 5-24.
EXAMPLE 5.4: NATURAL FREOUENCY OF
OVALING HING FORIIULA IMICHELL
FORUULA}
To use the Michell equation (5-12) dimensional analysis must be applied to obtain Equation 5-13. The original
Michell equation is as follows:
f.
'' =
,
I
rtJrJ
- 'J].--.-(n'. +l+/)
-.
(5-12)
2"Y PAf
-r/
where p
:0.283 lb/in.3 for
A:
(t)
in.
x
steel
(1) in.
f : in.a
E : lb/in.2
I - T-; . per unit lenpth ofring.
t2
z
:
in.'
l/r for steel
386 lb.-in.
rgl
I
z7f
'i-c'
(0.283) -.l!l
E
- : 4.409r
Ir
---- Vt1
1
in.2
1(36)r(in4)
1
in.a (5.333)
(5-13)
Figure 5-24. Manufactured strake elements.
The Engineering Mechanics of Bins, Silos and
:
:
a:
B:
D:
A
cross-sectional area of stack, in.2
anchor bolt area, in.2
stack radius = D/2, ft
critical arching parameter, dimensionless
critical diameter at which piping is unstable, di-
mensionless; internal stack diameter (Equation
5-15), ft; outside diameter of stack (Equation
5-16), ft; dynamic magnification factor (Thble 5JI
E = modulus of elasticity.
psi
: material yield strength, psi
ff: critical flow factor for arching in channels, dimensionless
f, : natural frequency of a ring, Hz
f" = stack vortex shedding frequency, Hz
G : consolidation particle parameter (Equation 5-8),
dimensionless
H : height that solid is stored in bin, ft
H, : stiffening ring spacing, ft
I = moment of inertia of stack cross section, in.a
L : height of tower portion straked, ft
m : geometric parameter for arching (Equation 5-2),
dimensionless
n : flexural mode (Equation 5-12), dimensionless
P"1. = air pressure (Equation 5-11), psig
Pn** : maximum hoop pressure at bin-hopper tangent
point, psi
r : outside radius of stack (Equation 5-12), ft; nf.
S=
Low
Oamping
6D
HiBh
Greek St/mbols
:
bulk density of solid. lb/ftl
6 = logarithmic decrement, dimensionless
7
Damping
=
:
modetutelt stiff soil; aormol spreadfooting or pile sup-
port
soft soil; foundation on highlJ stressed Iriction piles
perpendicular to stack centerline (Figure 5-14),
:
d' :
dr :
ot :
or :
p
: interior arc length of helix (Equation 5-18), ft
: exterior arc length of helix (Equation 5-18), ft S. = section modulus of stiffeners (Equation 5-15), ft'
t : shell thickness of stack, in.
V = wind velocity, ft/min
V" : critical wind velocity in which ovaling occurs
(Equation 5-14), fum
w : width of strake, ft; normal pressure applied on
mode shapes relating translational displacements about the x, y and z axes, respectively
30
6 : piping factor, dimensionless
0_: ungle of hopper slope, degrees
0 : modal shape relating to rotation about an axis
Si
7.1
90 0.052 60 0.105
tural Itame support.
Average Dampin?
So
])
Average High
Damping
6D6D
Damping
2" gunite lining 0.070 45 0.100 31 0.300 10
9
4" gunite lining 0.117 27 0.r25 25 0.360
Inw Danping = rocky, very stiff soil; Iow-stressed pile suppon, or struc'
ft
bin walls by solid (Equation 5-1), psi
0.035
Unlined Stacks
Lined Stacks
dius of curvature of vortex strake (Equation 517), ft
over-all length of vortex strake (Equation 5-16),
XI
29
Table 5-3
Conservative Values for Logarithmic Decrement
and Dynamic Magnification Factor tor Various
Stacks
NOTATION
AB
Stacks
dimensionless
coefficient of friction between the bulk solid and
the bin wall (Equation 5-1), dimensionless
kinematic angle of friction between the solid and
the bin wall, degrees
consolidating pressure for steady
flow (Equation
5-4\, tbflft2
allowable tensile stress of stack material, psi
number of revolutions around stack made by a
helical strake, dimensionless
REFERENCES
1. Jenike, A. W., Johanson, J. R., and Carson, J. W,
Storage and Flow of Solids, American Institute of
Chemical Engineers, New York, New York, 1981.
2
.
Blevins , R. D . , Formulas For Natural Frequency and
Mode Shape, Van Nostrand Reinhold Company, New
York. NY. 1979
3. Thomas, G. B., Calculus and Analytic Geometry,
Addison-Wesley Publishing Co., Inc., Third Edition,
1960.
Rotating Equipment
Not all PD pumps are purely rotary or reciprocating, but
we will focus our attention on these types. PD pumps, by
Fluid movers and their use are vital to the process industries. This chapter focuses on two basic typespumps and compressors. The sizing of these units and
their interaction with the other components of a process
definition, deliver fluids at a rate proportional to the
speed of the pump action and this rate is independent of
the pressure differential across the pump. For this reason
means must be provided to limit the discharge pressure
and this will be discussed under the section of positivedisplacement pumps. Typical rotary positive-displace-
system are discussed. This chapter does not address the
detailed mechanical design of sophisticated equipment,
such as turbine blade design and gas dynamics in a turbine. That type of material is a separate field of study
and lies outside this text's objective of examining how to
select and apply rotary bquipment to process systems.
For further reading, see the bibliography at the end of
the book.
ment pumps include screw, gear, vane, cam, and lobe.
Reciprocating positive-displacement pumps include piston, plunger, and diaphragm.
Selecting the type of pump to use is a function of the
service to be handled. Sometimes, the selection is obvious; for example, if you wanted to pump molasses, you
would choose a positive-displacement pump. In the situation where neither a standard type of pump is used for
the service, nor is it obvious what type to use, a centrifu-
PUIIPS
As the primary movers of liquids, pumps come in
gal pump is always considered first. The reason for considering a centrifugal pump initially is because of its low
initial cost, economical cost of maintenance, wide range
of materials of construction, and relatively large clearances. Factors to be considered in selecting a pump are
many types and an understanding of the various kinds is
essential in successfully applying them to process systems.
Pumps are used to transfer liquids from one point to
another. They basically fall under two categories-centrifugal and positive-displacement. The centrifugal pump
gets its name from the fact that the pump's impeller im-
as follows:
1. Efficiency
parts kinetic energy to the liquid with centrifugal force
acquired by the impeller's rotation. This simple mechanism allows the centrifugal pump to be practical for high
capacity, at low to medium heads. The aspect of low to
medium heads will be discussed shortly. Typical centrifugal pumps include mixed flow, propeller, peripheral,
and turbine.
Positive-displacement (PD) pumps trap a quantity of
liquid and force it out of the cavity against the pressure
of the discharge by means of rotary or reciprocating action. Ideally, a PD pump will produce whatever head is
impressed on it by the system restrictions to the flow.
2. Net positive suction head (NPSH) required by pump
3. Operating costs
4. Shaft speed
5. Magnitude of clearances
6. Materials of construction
7. Fluid service to be handled
8. Availability and delivery time of pump
The type of pump to be used for a specified service or
duty can be selected from Figure 6-1. This figure clearly
indicates how different pumps have overlapping charac-
31
Mechanical Design of Process Systems
10
ro-
F
o
I
J
I
234
-l
5
Figure 6-1. Pump selection guide.
teristics. Depending on the relative importance of the
previously cited criteria, a certain type of pump will be
selected. Figure 6-1 will help the reader determine from
a quick glance what type(s) of pump(s) will be required.
Gentrifugal Pumps
Centrifugal pumps are the most widely used because
of their wide operating range and the reasons previously
cited. These pumps come in a vadety of types, depend-
ing on the type of impeller, casing, stuffing box, and
bearings. These components are shown in Figure 6-2.
The radial type impeller is by far the most common
centrifugal pump in the process industries. The flow is
directed by the impeller imparting motion on the fluid,
driving the fluid to the periphery of the impeller. This
allows the velocity head to be converted mostly to pressure head in the volute.
The mixed flow pump impeller consists of vanes doubly curved or screw-shaped so that the impeller moves
the fluid by both centrifugal and pushing action. The result is a discharge of axial and radial flows.
The axial flow pump impeller develops head by a lifr
ing or pushing hydrodynamic action that results in totally
axial flow on discharse.
The impeller is hydrodynamically balanced to ensure
minimal vibration. The casings can come in a variety of
designs, but are either vertically or horizontally split. A
vertical-split casing implies that the casing is bolted together along a vertical plane. Similarly, a horizontally
split casing is bolted or connected along a horizontal
plane. The advantage of the vertical split casing is that
the pump is supported along the shaft allowing for thermal movements without causing shaft misalignment.
Packing and seals on the shaft are the most common
of failure for a pump. In low-pressure applications, soft or metallic packing will suffice in a stuffing
box. In most low-pressure applications, a single seal will
usually suffice. When pressures exceed about 50 psig
and there can be no tolerance for leakage, a double seal
is utilized. These seals come in various configurationstandem. bellows. and face-to-face.
source
When process conditions get severe enough, a double
inside-outside seal, where part of the seal is outside the
stuffing box, is used. The disadvantage of this type of
seal is that not all stuffing box arrangements allow such
a configuration.
For proper cooling and lubrication the seal must be
supplied with a fluid, called a seal flush. Figure 6-3
shows such a system.
G:oup ll and lll
Standard Pumps
Group I
Standard Pump
Materials Common io all Alloys Unless otherwise Noted
Parl No.
Malerial
Parl
104
lmoeller Gasket'
107
Rear Cover Plate Gasket*
Durabla
108
Bearing Housing Adapler
Casl lron
109
Bearinq flousrno Fool
111
Gland Studs or
112
Sealcaqe'(E)
PTFE
113
Molded Rino Packinq'rE)
Kevay'il
114
Inboard 0ellector
PTFE
115
Casino Studs/Hex Nuls
118
Inboard
119
Bearina Housing
Cast lron
120
Inboard Eearinq'
Sleel
121
0utboard Bearino'
Steel
122
0ilSlinoer
Steel
123
Bearino Cover
Cast lron
124
Bearing LockNut
Steel
125
Bearin0 Lockwash€r
Steel
126
Beaino Cover Gasket
Cork
127
Bearino Shim'
129
outboard
130
Shall Couolino Kev
131
Beanno Housrng Adapler'
132
Soherical Washer lor Foot
Steel
133
Trico 0iler (nol shown)
Steel-Plaslic
134
Bearinq Housino Venled Drarn Plu0
Plastic
136
Cao Screw for Foot
Steel
138
Cap Screws
139
Machine Eolts lor Bearing Housrng
140
CaD
F
Casl lron
3M S.S./303 S.S
anqe Studs with Hex Nuts
304 S.S./316 S.S.10
TFSB
0ilSeal'
Steel
oilseal'
Screws
TFSR
Steel
0"
Binq
SBR
lor Eearinq cover
iorAdarterto
Steel
Steel
Cover
'Pafls 10rtra'y sl0ck.d by cLsrome.lor e4erqenc/
rs
'Ppd
"Trrd.name ol lnternanonal Nrrel Coooanv
(A)Nor avarable In Recessed h0eller pumps
(BlNor avr'abre In Seri Pnmno oumoe
(Cr \or rva ubre on 4x3 LS.loii 4d US I3 o' 614 US l3A rcast sleel suotntuledr
Sleel
(E) Used n Packed PonPs only
{t) Trtanrum Dumos havs GraJor rmpell€. oaskels
Cdro,r b a reo'9ercd lraoe name or un'on Carbrde Coro0 anon
lGr Allov rs B7 Sio. Duclilp lron rnd Crlbon Sleel oumos
{H) Icd€name ol E Duponl deNamoors & ComDafiy Inc
I
{01Jackeled cover oral€s are carhon sre€l
Figure 6-2. Centdfugal pump components. (Courtesy of the Duriron Company.)
Mechanical Design oI Process Syslems
A seal flush configuration. (Courtesy
Durametallic CorDoration.)
Figure 6-3.
The various types of seals are shown in Figure 6-4.
The pump manufacturer should be relied upon for the
choice of seals. Sealing technology is a subject vast
enough to encompass this book and the reader is referred
to Buchter [1] for additional sources.
Bearings, like seals, are for the most part the main responsibility of the pump manufacturer. In all situations,
the bearings should be of the outboard type (not subjected to the process fluid), unless situations prevent this
type of arrangement.
Hydraulic Bequirements of Centrifugal
Pumps
In this section the reader will find it advantageous to
refer to Chapter 1 . The most important hydraulic parameter in pump selection is the net positive suction head
(NPSH), which is the total pressure at the pump suction
point minus the vapor pressure of the liquid at the pumping temperature. NPSH is the energy that forces the liquid into the pump, and is expressed in foot-pounds of energy per pound of mass (normally referred to as feet of
head) or pounds per square inch of absolute pressure.
When values of pressure are expressed in feet of liquid,
the theoretical height to which a liquid can be lifted at
any temperatnre is the difference between the atmospheric pressure and the vapor pressure of the liquid at
that temperature. Figure 6-5 helps simplify the calculation of the NPSH.
of
the
In selecting a pump the engineer must refer to the performance curves the pump manufacturer prepares for
each model ofpump. Most performance curves are plots
of flow capacity (gpm) of water versus break horsepower or total dynamic head in feet. Such a curve is
shown in the examples that follow. As seen, the efficiency curves are plotted with various lines indicating
impeller size and the NPSH required at various points. In
reading the performance curves, it is emphasized that the
extreme right side of the curve should be avoided, because the capacity and head change abruptly. Pumps are
normally selected to operate in the area of high efficiency. The danger in selecting a pump on the extreme
left is that at low flows the pump horsepower overheats
the liquid. If low rates carmot be avoided, a by-pass may
be required to prevent vaporization and subsequent
pump damage. Thus, vaporization of the pumped liquid
can occur two ways: (1) the NPSH required is not being
met and cavitation occurs in the liquid causing vapor
bubbles that can severely damage the impeller or (2) the
pump horsepower overheats the pumped liquid, forming
vapor bubbles that can (and normally will) damage the
pump.
Excess heat resulting
in pumping a fluid can be
avoided by determining t}re minimum flow required to
allow proper heat dissipation. At low flow rates or shutoff conditions, heat is transferred to the liquid contained
in the pump casing at a rate representing the power
losses of the pump. The power loss is the difference between the brake horsepower consumed and the water
horsepower developed. The remnant energy in the pump
bearinss and that lost to convection to the outside atmo-
h
O
l-o
:.
9?
;7
3.:
E>
.9+
9@
E.)
I
q=
oii
!
36
Mechanical Design of Process Systems
Pump Hydraulic Design Calculation Sheet
Liquid
Viscosity at P.I (Pumping Temp.)
Vapor pressure at PT
Sp. gr. (7) at PT.
Flow at ambient temD.
Operating flow at PT.
Design flow at PT.
psra
gpm
gpm
gpm
_
Suction
Discharge
Source'pressure
psra
Terminal pressure
psia
Static
psi
psi
psra
Static (head)(lift)
APr discharge
Piping system
Other
Discharge press.
Suction press,
psl
(+ headx- lifi) =
- APr line loss
Suction pressure
- Vapor pressure
psra
psra
NPSH avail
NPSH avail
NPSH req'd
-
ft
ft
[,lin NPSH avail > NPSH req'd + 2
'lnilial press., e.9., ATM
or
O
-
unp at Duty condition
(gpmXTDHXr) _
ono" _
psi
psi
psia
psia
TDH
TDH
psra
leet
fl
@
Onp at Maximum Capacity
66o.," =
(3,e60Xr)
Condition
(gpm)CrDHXr)
(3,960Xri)
TDH = total dynamic head
TDH = discharge press. - suction press.
4 = pump efficiency,
PT.
=
o/o
pumping temperature
Figure 6-5, Pump hydraulic design calculation sheet.
sphere is negligible. The temperature rise per minute is
computed by the following relation:
42.2(bhp,")
W*Cp
where At :
bhp," :
W* :
Co :
(6-1)
temperature rise per minute, oF/min
6.u1" horsepower at shut-off
weight of liquid in pump, lb
specific heat of liquid in pump
which is the power required if the desired head at the required capacity could be produced with zero losses.
For water flowing through the pump, conditions become stabilized and the temperature rise is determined
by the following:
". _
(bhp
-
whp) 2,545
m
where 2,545
:
ir :
(64)
Btu equivalent of I hp-hr
mass flow rate- lb/hr-
The break horsepower of the pump is given by
..
OH"y
bhp = -,::--r
J,vou4
Another variant of Equation 6-4 that relates the tem(6-2)
=
:
flow rate, gpm
H = total head, ft
where Q
"v
q
=
=
^ ^o(;-,)
specific gravity
pump efficiency (fraction)
':
QHI
3,960
(6-5)
In Equations 64 and 6-5 the compressibility of water is
The water horsepower is given by
who
Derature rise to the total head is
(6-3)
neglected.
To prevent overheating of the pumped liquid, a bypass
piping arrangement is used to have the pump operating at
full capacity. Such an arrangement is shown in Figure
6-6.
It is always desirable to pass the bypass liquid
Rotating
through an intercooler to cool the fluid before it enters
rhe pump suction port. Under no circumstances should
the bypass line connect directly from the pump discharge
to the pump suction.
So faq we have not considered the pumping of viscous
liquids. For a liquid that has viscosity greater than about
10 cp, a viscosity correction must be made, because the
pump motor must work harder to pump the fluid.
All pump manufacturers' pump performance curves
are based on pumping water. To correct for the pumped
liquid's viscosity, Figures 6-7 and 6-8 are used to approximate the equivalent water performance. The figures, developed by the Hydrauiic Institute, are used by
entering the bottom with the viscous flow rate (gpm),
moving vertically upward to the desired viscous head
(head per stage for multistage pumps), then moving horizontally to the left or right to the viscosity line, and proceeding vertically upward to the correction-factor curves
for the head and capacity. The equivalent water-performance values are then obtained by dividing the viscousperformance values by the correction values. Thus, the
pump selection can be made on those ratings established
for water. The efficiency of the viscous liquid pumping
conditions can be calculated using the efficiency correction factor multiplied by the pump efficiency for water.
In this manner the viscous performance of the pump can
be determined using the manufacturers' performance
curves, which are always based on pumping water. This
procedure is illustrated in the examples later in this chapter.
Positive Displacement (PDl Pumps
Positive displacement (PD) pumps are usually selected
after it has been determined that a centrifugal design can-
Equipment
37
not meet the requirements. Thus, PD pumps are used
where centrifugals cannot operate-under low NPSH requirements or handling a highly viscous liquid. There
are several types of PD pumps, as previously mentioned,
and their positive attributes are that they
at relatively high efficiencies when pumping
viscous liquids.
Operate under low NPSH conditions and produce
high suction lifts.
Operate with high heads at a wide range of capacities .
Have a wide speed range, which is limited by the liq-
1. Operate
2.
3
.
4.
uid's viscosity.
inherently self-priming.
5. Are
Selecting the fype of rotary pump is primarily a function of cost and the particular requirements that are to be
met.
1.
Vane ptmps-normally have a capacity up to about
380 gpm and operate by trapping liquid within vane
differential pressures, usually at around 50 psig. The
practical limit on viscosity is approximately 100,000
SSU. Vane pumps are subject to wear and should not
be used with a liquid that has poor lubricating quali-
ties.
2- Gear pumps-normally
are used up to about 1,000
gpm and can handle liquids with viscosities up to 5
x 106 SSU. These pumps operate at approximately
1,200 rpm with liquids of 10 to 500 SSU viscosity
(see Figure 6-9). It is desirable to have internal timing gears and bearings since only one shaft sealing
area is required. A variant of a gear pump is shown in
Fieure 6-10.
INT€RCOOLEA
Figure 6-6. Excessive heat build-up is often caused by operat-
ing pumps at reduced flow rates. To prevent overheating the
pumped liquid, it is advisable to pass the liquid through an intercooler before it enters the pump suction port.
Mechanical Design of Process Systems
l
00
.90
.ao
.70
o
.60
z
.50
_40
.30
.20
."n,
B S9
.icF
CP
.\$
?p
r_':
\9,
rd
^
3cP
'6
g
1s"
Hp
Zro
o!o
-co
g
vrscoslTY-ssu
'. s
u";*t*
s
g;*1"
I
15
20
25
30
40
CAPACITY.GALLONS PER I\4INUTE
50
(At
60
bEP)
Figure 6-7. Performance correction chart for viscous liquids. (Courtesy of the Hydraulic Institute, Cleveland, Ohio.)
Rotating
Equipment
ol
fil
-l
v,
l(
o
F
()
[>l
z2l
ogl
trol
HEI
!t ol
8el
>l
FI
gl
o-l
5l
gt
<l
FI
:l
tuI
o-l
rr
lrl I
:l<l
lrl
-l
I
4
6
CAPACITY
810
IN lOO
15
GPM
Flgure 6-8, Ferformance correction chart for viscous liquids. (Courtesy of the Hydraulic Institute, Cleveland, Ohio.)
39
Mechanical Design of Process Systems
Figure 6-9. This drawing of a rotary gear pump illustrates the
positive-displacement principle. The fluid is captured in the
gear teeth and displaced to the suction port. The crescent acts
as a seal between the suction and discharge ports. An application of this type of pump is illustrated in Example 6-2.
Figure 6-10. The internal bearing gear pump is a variant of
the rotary gear pump in Figure 6-9. (Courtesy of Worthington
3.
Friction head-the pressure (psi) required to overcome frictional resistance of a piping system.
Velocity head-expressed in psi, see Chapter 1.
Tbtal suction /r/-the total pressure below atmospheric (in Hg or psi) at the pump suction port during
pump operation and equals the following:
Screw pumps-these pumps, depicted in Figure 6- 11,
are used where large flow capacities, 4,000 gpm and
3,000 psi, are required. Screw pumps can handle vis107 SSU and have bearing and
cosities up to 10
x
timing gear requirements sirnilar to gear pumps.
Screw pumps come in various designs, and one type,
shown in Figure 6-12, can handle highly viscous,
non-Newtonian fluids such as glues, molasses, tar,
asphalt, and wastewater with ease.
Positive displacement ( PD) pumps come in a vast variety and you should refer to the manufacturers' literature
to best determine the selection of the particular pump to
be used. However, PD pumps are sized very much like
centrifugal pumps, and the calculation sheet in Figure
6-5 can safely be used for sizing either type. Pump sizing
is focused upon here to illustrate the various ways in
which a pump may be specified. Figure Gl3 shows various installations for a pump. Some properties and characteristics illustrated in Figure 6- 13 are
lfi-the
vertical distance in feet (expressed in psi) between the liquid level ofthe liquid to be
pumped and the centerline of the pump suction port
when the pump is located above the liquid level of the '
liquid to be pumped.
Static suction head-the vertical distance in feet (expressed in psi) between the liquid level ofthe liquid to be
pumped and the centerline of the pump suction port
when the pump is located below the liquid level of the
liquid to be pumped.
Static suction
Pumps, Mccraw Edison ComPanY.)
1. Static suction lift plus the frictional head, or
head minus the static suction head (only if
the frictional head is greater than the static suction
2. Frictional
head).
Total suction head-the total pressure (psi) above atmospheric at the pump suction port when the pump is operating and is equal to the static suction head minus the
frictional head .
Static discharge head-expressed in psi, is the vertical
distance in feet between the centerline of the pump and
the point of liquid discharge.
Total discharge head (TOH)-the sum of the frictional
head in the discharge line (discharge frictional head) and
the static discharge head.
Tbtal static head-the difference between the static
discharge head and the static suction head or the difference between the static suction lift and the static discharge head.
Toial dynamic head-the sum of the total discharge
head and the total suction lift or the difference between
the total discharge head and the total suction head'
E -o
E.i
aa
E
i
E
35
Et=
,^.c!
'6'y
P:;
q .=
.:..
-o
'T
0)
o
!
9q)
.E
CDY)
(.)c,
,*(5
.g
E
r].1
o
3t*
;
i:
AE F.q
.?3H
;6o
b5
9E
o.; -o
:", \ d 9 o.:
i!-P I E.EE
oo
6-E9g
ao
E';e qIb
!E9
s
g
3
=
il
-oo
EE3
dz
=E
;-F
B o-
-
bX-
€
.=o
$Egq
'EE
P H:1
:..6
9?
E=
=.!ebo
;.
o
t!
-
.F
c
s
9!
b;d
9=Y"t
o I cg
.2
o
E:0i
(sYE:,il
E Xe.d"
:
r ".!
33 r_d
?E
49 &:
E06: r *
xE ;i
P:
EP
I
!
(L
=;=
6-d
PU(J
thJ
rDt
5.s,b
F>\
DDq O
x rE F ='; I
ai dE 6 crt
gl'" dd E
'i-oi
E= =;
F
d)
Mechanical Design of Process Systems
Figure 6-12. A cavity screw pump is ideal for
handling higbly viscous non-Newtonian liquids.
(Courtesy of Moyno@ Industrial Products, Fluids
Handling Division, Robbins and Meyers, Inc.)
t|'r$|lhF..Dl$hra
When using PD pumps where a suction lift is required,
remember that the theoretical height to which a liquid
can be lifted at any temperature is the difference between
atmospheric pressure and the vapor pressure of the liquid
at that temperature, when both values of pressure are expressed in feet of liquid. However, the suction lift practical for actual pumping installations is somewhat less
than the theoretical value. Figure 6-14 shows the theoretical and practical suction lifts for water. Also, remember
that the higher the installation is above sea level, the
lower the vapor pressure, and the lower the maximum
suction lift.
Application of PD pumps to practical installations is
given in the examples. The unit conversions included in
Appendix D are helpful in pump calculations.
Pressure Protection For PD Pumps
By definition, a positive-displacement pump transfers
at a rate proportional to the speed of displacing action and this rate of transfer is independent of the pressure differential across the pump. Thus, means must be
provided to limit the pressure and the pump discharge
side should the discharge piping become restricted or
blocked.
There are various methods used to prevent overpres-
fluid
sure:
1. Install a relief valve at the discharge of the pump with
the relief valve discharge being piped back to the
pump inlet in which an intercooler is placed in the
line. Such a configuration is shown in Figure 6-15. In
Figure 6-13. The principal parameters of pump selection.
(Courtesy of Viking Pump Division, Houdaille Industries,
Inc. )
such an arrangement a temperature sensor device is
placed at the pump discharge to detect excessive temperatures. The intercooler, or heat exchanger, is used
to cool the pumping fluid. Normally, temperature becomes a problem when the instantaneous discharge
and inlet flows are equal. Gear and multiplex
Rotating Equipment
(plunger, diaphragm, and piston) pumps are examples
of such pumps in which this situation occasionally de-
2.
velops.
Place a pressure switch in the discharge side of the
pump piping, interlocked to shut off the pump driver.
Since pressure switch set points are not as reliable as
relief valves, a relief valve must be added to the discharge piping and set at a pressure slightly greater
than the pressure switch to ensure adequate protection. The relief valve would be piped-up similarly to
that shown in Figure 6-15.
3. Install a torque{imiting device in the pump driver
when a relief is not practical, such as slurry service.
A torque{imiting device can come in the forms of a
shear-pin or torque limiting coupling. These devices
Figure 6-14. The theoretical and maximum recommended
lift for water at various temperatures, 'F. (Courtesy of
Viking Pump Division, Houdaille Industries, Inc.)
suction
have advantages other than protecting the system
against overpressure; they protect the pump against
foreign material or whenever the pumped fluid might
tend to solidify.
Overpressure protection
is essential in positive-dis-
placement pumps. Relief valves applied should be added
to the discharge piping itself, because built-in relief
valves on the pump that are not removable for testing are
undependable.
COMPRESSORS
The three types of compressors used in the process industries are centrifugal, reciprocating, and axial flow
compressors. Like pumps, depending on the application,
the type of compressor is roughly a function of the gas
capacity, action, and discharge pressure. Figure 6-16
shows the operating ranges of the three basic types of
compressors. As clearly shown, one type of compressor,
despite its disadvantages or advantages compared to
other types, is usually the obvious choice.
Reciprocating compressors are normally used when a
relatively low flow rate is required, but high discharge
pressures are expected. This situation is common in the
gas processing industry where high discharge pressures
are needed for process conditions. The need and use of
reciprocating compressors is unavoidable in many process system applications.
Centrifugal compressors are the most common typ€ in
hydrocarbon processing plants and are to some extent the
workhorse of chemical process compression needs.
There are four basic advantages a centrifugal compressor
has over a reciprocating compressor:
1. Lower initial capital investment. The cost advantage
is increased as the power demand is increased.
(B)
Figure 6-15, A temperature switch can be used in lieu of an
intercooler (heat exchanger) in which the switch can shut off
the pump driver when liquid temperatures become excessive
as in (A) or can be used with an intercooler in (B) to divert
flow through the exchanger. In either case, a pressure safety
valve should be used on discharge. (B) assumes the suction
temperature is constant. To prevent overheating on low flow
rate conditions, a flow switch is often used.
44
Mechanical Design of Process Systems
2. Lower
Princlples of Compresslon
3.
The general gas law that applies to all gases can be
written in several forms:
4.
operating and maintenance cost. The operating and maintenance cost of a centrifugal is approximately one-third that of a reciprocating compressor.
Compactness of size. Centrifugals occupy less space
and make much less noise.
Simplicity of piping. Reciprocating compressors can
cause severe pulsation shock response in piping systems. The cost in preventing the effects of pulsation
in piping systems can entail many hours of engineering and a healthy capital investment for either analog
or digital simulation tests. Centrifugals do not have
this problem.
Axial-flow compressorc operate at greater capacities
Axialflow compressors are governed by the same formulas
that apply to centrifugals. The axial units are more efficient than the centrifugals, but the latter have a much
wider operating range. Axials are used primarily for
and are often used in series with centrifugal units.
PV =
zmRt
(6-6)
zmRt
(6-7)
mw
:
PV:
zM.Rt
(6-8)
zRt
(6-e)
where
clean gases such as air, because they are much more susceptibie to corrosion, erosion, and deposits than centrifusals.
:
V:
z:
R:
R:
P
absolute pressure, psra
volume of gas, ft3
:
compressibility factor for real gases (z
1 for
a perfect gas)
R/mw gas constant of the particular gas
universal gas constant
1,545 ft-lbr/lb.
:
t=
m=
:
:
v:
mw
mole
-
:
'R
absolute temperature,
mass of gas, lb-
'R
: 'F + 459.7
molecular weight of gas
number of moles of gas
m/mw
specific volume of gas, ft3llb.
:
Mo
A very important gas property is the specific heat ratio, k. This property is determined from the following:
.c"c"
K=---j=
c"
where C,
Cp
cP
:
1.986
(6-10)
specific heat at constant volume, Btu/lb.-mole-
= 4.97 Btu/lb,-mole-"F for ideal monatomic gases
= specific heat at constant pressure, Btu/lb,-mole-
:
s
-
7.00 Btu/lb.-mole-"F for most diatomic gases
Reverslble Adiabatlc (lsentropic)
Compression
a
The reversible adiabatic (isentropic) compression of
o
an ideal gas is obtained when no heat is added to, or removed from, the gas during compression. The process is
reversible when no friction exists. The formulations differ for a perfect gas versus a real gas.
6
Perfect Gas
INLET FLOW,ACF
souRcE:DriroPLot{ t2l
Flgure 6-16, Approximate ranges of application for
cating, centrifugal, and axial-flow compressors
recipro-
[2].
PrV,K
:
(z
PtYtx
! : l&F
tr \Pr/
:
1)
(6-11)
(6-12)
Rotating Equipment
Real Gas (z
P1V17
t'
t'
:
*
1)
: gas flow rate in standard cubic feet per minute of
gas (60"F, 14.7 psia)
P, : absolute pressure at suction, psia
Pd: absolute pressure at discharge, psia
t. : absolute temperature at suction, oR
where Q
(6-13)
P2V2'y
lP:l "
(6-14)
\Pr/
_2"*24
:
mean comoressibilitv factor
where. for any system of units
:
:
:
-y :
t:
P
absolute pressure
V
k
volume or specific volume, v
specific heat ratio
isentropic exponent for real gases, Co/Cu
absolute temperature
z.
za
:
:
compressibility factor at suction
compressibility factor at discharge
For a gas capacity of Q
:
100 scfm, Equation 6-16
becomes
subscripts
spectively
I
and 2 denote inlet and discharge conditions, re-
[,,,-,
To determine the exponent, T, real gas properties must
k-r
kt
be used. These properties can be obtained from gas
property charts and used in the following formulation:
r
/ \'l
I-I-y =*l'*,lSll
[ \atloj
(6-15)
JCp
where J
:
mechanical equivalent of heat
:
'778 ft.-lbrl
Btu
/,el :
ll-l
d[,l p
\
rate of change of compressibility facror. z. with respect to the required temperature. t. along a constant
pressure, P. path
To determine a mean value of the isentropic exponent
for a real gas, ?, over a compression range, Equation 615 must be solved by iteration.
In Equation 6-15 if we have a perfect gas in which
4"
:
:
?
'v=k
For a compression ratio PzlPr < 2.0,
mately equal to k for most real gases.
t
[,
],
\k/t
t
(6-17)
qn
:
:
mechanical efficiency
the ratio of the actual horsepower delivered to the gas to
the brake horseDower. or
shp
bhp
:
:
(6-18)
overall adiabatic efficiency
the ratio of the isentropic horsepower, hpr, for a stage
of compression to the brak€ horsepower, or
hD"
is approxi
For isentropic compression of an ideal gas the theoretical horsepower requirement is as follows:
hp':ffi|('iJ'*-', -'l['',J'
adiabatic efficiency
the isentropic horsepower, hp1, delivered by the actual
horsepower delivered to the gas, or
hpr
4,o
JCP
I
gnp
''''
R k-1
l\P,/
In applying these formulations that deal with the isentropic compression of an ideal gas, efficiency factors
must be defined in order to apply the equations to real
world compressors. These efficiencies are as follows:
l=l =0andz:1.0
then Equation 6-15 becomes
],
h._ =6.42llPdl k _rl{r,l_
-l\520/-
(6-19)
bhp
In defining the horsepower input for a single stage of
.
compression, utilize the overall efficiencv as follows:
6'6, bhP=*=ffi[(,t-']F;'{*)
\ k /r
(6-20)
Mechanical Design of Process Systems
For bhp at 100 scfm, Equation 6-20 becomes
J
The isentropic energy transmitted to the compressed
gas in ftJb/lb- of gas represents the adiabatic head, or
t
\t
,[,,*-,
I
- 'la
\mw/ \K- r/ [\Ps/
",: llsl{IlllSlT
I
(6-2r)
The compressor driver horsepower (bhp or ghp) is related to the adiabatic head by the following:
ghp:
bhp
:
(6-22)
33,000a"
frfl,
(6-23)
33.0001""
where rir
:
mass
PlVtn
=
where
n:
(6-26)
flow rate of the gas, lb./min
The adiabatic efficiency can be defined in terms of the
polytropic efficiency by the following:
PrYro
(6-27)
the polytropic exponent,
n
+ I orn +k
Expressing Equation 6-27 in terms of temperature and
pressure we have
t' /p,\?
t' -- \P,/
The value
gas
;H"
constant
When Equation 6-26 is expressed between the initial
and final conditions we have
bhp=ffiH=-'l'H
\-o /1
:
PV'
(6-28)
ofn
depends on whether the gas is a perfect
(z: l) or a real gas (z *
1) as previously dis-
cussed.
For a perfect gas the relationship between adiabatic
and polytropic efficiencies is given by Equation 6-24.
Similarly, the polytropic exponent, n, for a perfect gas is
related to the polytropic efficiency and adiabatic exponent. k. as follows:
n-1
k-l
n
lll
(6-29)
\4el
k-1 _R
(6-30)
JCo
(6-24) sincek:
Equation 6-24 is discussed in more detail below.
For a single stage of compression, neglecting any
changes in potential and kinetic energy, the temperature
change from the inlet and discharge is given by
Af : r. - r : 6.33(2,547bhp
-
q)
(6-2s)
QCo
where q
:
total heat energy lost to the surroundings or to any
available cooling water or cooling jackets. This
value does not include thermal enersv for intercoolers or aftercoolers.
For a multistage compressor, Equations 6-20 through
6-25 must be applied separately for each stage.
Polytropic Compression
ColC"
The relationship between the polytropic efficiency and
adiabatic (isentropic) efficiency of a perfect gas is shown
in Figure 6-17. The polytropic efficiency, 4p. is usually
determined by the compressor manufacturer using either
an old design or testing a new design.
The polyropic exponent, n, for a real gas is determined from real gas properties or with using real gas
data and using the following expression:
n-
I
n [z+ t l_tl
/a'\]
_t_
JCo lqo
\at/l
Equation 6-31 is identical to Equation 6-15 except that
the isentropic exponent for a real gas, 7, is replaced by
the polytropic exponent, n, and the compressibility factor for real gases, z, is divided by the polytropic efficrency, ?p.
This type of compression occurs when a gas is reversibly compressed along a path that is defined by the followins relation:
(6-31)
Similarly to Equation 6-15, Equation 6-31 must be
solved by iteration for a mean value of the polytropic exponent, n, over a compression range.
Rotating
6A 70
72
74
ciency for a perfect gas (Z
lp
In Equation 6-31, if we have
l3l :
ouno z
\r/p
*'ffilett'le
= I fora perfect sas
then,
JCp4p , /r \
K l-l
@32)
\4pl
For most real gases below a compression ratio of approximately 2, then
n
=
1).
'' (,C,tffi
(6.33)
For ghp at 100 scfm,
n-l:j-:=
n
47
Figure 6-17. The relationship between the
polytropic efficiency and the adiabatic effi-
767880
POLYTROPIC EFFTCTENCY
Equipment
- I _k n
ll\
'K l-l
1
,no
(il t=l
:
k /t[tfl
H!-1J_j1?L
\;/\
_ (,$,,,
H,6.34,
]
The equations for polltropic head are similar to those
for adiabatic head. Equation 6-21. Thus.
\ql
The basic horsepower and head expressions for polycompression are similar to those for isothermal
compression, Equation 6-20. Thus, we have
fopic
FJ
. : (.*_)t^J
IH(l
,]
"
(6-35)
48
Mechanical Design of Process Systems
If the polytropic head is known, the compressor horsepower (ghp or bhp) can be obtained from the following:
bhp
:
ehp
:
mil
(6-36)
33,000a*
riH
bhp
t, = i&)H
\P,/
(6-38)
values):
/\
I lk-ll
.
y
v
(6-3e)
./ - -t----t
-4p\ K /
\p
: k-l
(6-40)
k
Normally, the value of ?e is estimated from data supplied by the manufacturer. For initial or preliminary values of the polytropic efficiency, 10, Figure 6-17 may be
used.
lsothelmal Gompression
This compression occurs when the temperature of the
gas being compressed remains constant during compression. For a perfect gas in which z
1.0 and (AzlAip
0 we have
:
P1V1
:
:
(6-41)
P2V2,
OI
PV
:
(6-42)
constant
The theoretical horsepower developed during a reversible isothermal compression process is
ho,:atz
" 8.1l0hl&)
\P,/
(644)
7h
where
:
Ia :
isothermal efficiency
4,
overall efficiency
: Itlln
F)
.
hp, hpr
tlfl- tl:.
(64s)
Equations 6-35 through 6-38 are used separately for
each stage of a multistage compressor. Equations 6-38
and 6-39 can be used to calculate the polytropic efficiency directly (provided t, ta, P,, P6 and k are known
wnere
_
: overall polytropic efficiency
: IpI.
The outlet and inlet temperatures for polytropic compression are related by the following expression:
!
not
achieved, because the heat of compression causes the gas
to exceed the inlet temperature.
The actual performance of a real compressor can be
evaluated by the following:
(6-37)
33,00040
where 4oo
Equation 6-43 assumes that the heat of compression is
fully removed by cooling. In practice this is
(6-43)
After applying Equation 644 and determining
the
brake horsepower (bhp) for a single stage of compression, the discharge temperature can be determined by
Equation 6-25.
Dimensionless Reference Numbels
In sizing and selecting the type of pump or compressor
to be used, a logical correlation is often desirable. The
following dimensionless parameters apply to pumps and
compressors and are the specific speed and specific di
ameter, as defined as follows:
N :
'
N(Q)o
5
(6-46)
H0.75
: specific speed, dimensionless
N = speed, rpm
Q : capacity of flow rate, ft3lsec
H : head, ft-lbrilb.
where N,
^
"":
where D.
:
D:
H:
D(H)o
25
e*
(6-47)
specific diameter, dimensionless
diameter of impeller ot rotor, ft
head, ft-lbr/lb.
Figure 6-18 shows the dimensionless parameters as
originally presented by Balje [3]. This figure is the
graphical combination of Equations 6-46 and 647. Past
experience often dictates what type of pump or compressor is to be used and in cases of uncertainty or new applications, this figure will be useful in equipment selection.
Figure 6-18 must be applied to each stage separately,
as each impeller or stage must be chosen with each separate inlet capacity or head for that stage.
Rotating Equipment
^.
10
E
G
I
4
=N
'/q/Ha1
D,= DHltalJT'
/V
O
D
= Speed, rpm
= Flow, fr3/s
= lmpeller diameter,
0.3 0.6
ft
30
1
60
Specific speed,
r00
3m 6m 1,000 3,0()()
10,000
4
Figure 6-18. The initial selection ofa single-stage compressor is made using the specific speed and specific diameter parameters
t3l.
Gentffugal Gompressors
The centrifugal compressor powered the first turbojetpowered aircraft and is still used today injet engines as a
supercharger. The main advantage
of the
centrifugal
compressor is that it produces a large pressure ratio for a
single stage of compression, and is easily manufactured.
Its advantages over the reciprocating design were cited
previously.
Most centrifugal compressors are designed so that the
gas enters the impeller axially-parallel to the rotating
shaft-as shown in Figure 6-19. The gas flow is then
changed to the radial direction and is accelerated in a peripheral direction as it moves along the impeller. As the
gas exits the impeller, it enters a stationary diffuser
where the gas velocity is reduced. This process is repeated at each stage on multistage compressors. Most of
the pressure increase in the gas occurs in the impeller
and the greatest pressure drop occurs in the diffuser. In
multistage compressors, cooling the gas between stages
is quite common and many such compressors have water-cooled separators or diaphragms.
The polytropic relations, Equations 6-26 through 640, are usually preferred for centrifugal compressor calculations. Figure 6-20 shows why with a schematic plot
of the centrifugal compression process on a temperatureentropy graph. Using the adiabatic (isentropic) process,
the actual discharge temperature is underestimated
Figure 6-t9A. Centrifugal compressor-single-stage. (Courtesy of Dresser Industries, Inc., Roots Blower Operation.)
50
Mechanical Design of Process Sysrems
Changing the speed of a centrifugal compressor involves the "affinity laws," which apply to single-stage
compressors, multistage compressors when each stage is
considered separately, and to multistage machines over a
narrow speed range representing no more thm a 15%
change in speed. These laws are stated as follows:
1. The developed head (feet) varies to the square of the
speeo.
2.
3.
The required power varies to the cube of the speed.
The capacity (cfm) varies to the speed.
Figure 6-21 shows the effect of varying centrifugal
compressor speed.
In centrifugal compressors a phenomenon known as
surge occurs when the compressor capacity is lower than
a specific flow rate. This specific flow rate is shown in
Figne 6-22 as the "surge limit." The phenomenon of
surging is manifested by cyclic vibration of gas flow,
which can even result in reversal of flow direction,
power requirement, and discharge pressure. The phenomenon normally is associated with excess noise and
1
2.
3
4
5
6
7
8.
Nozzte
9. Shaft
Cover
10. Oi Fterainer
Sub Cov€rSeclion 11 BeartngSrand
Bearing Stand Cap
l2 Coupting End Beanng
SteelShim
13 tmpelerEnd Bearino
r'rus Bed nq
4. Or'Ferar-e.
-!run Ho-s nq 5eal
t5 Sa.t
Spaci.g Fing
16 Votute
Discharge
Casing
17 Intetsection
j8. impe|er
j9. clideVane Housing
ZO. In er Nozzte
21 cuideVane
22 curoevaneLrtdop
moe er End ptdl;
23
24. Intet Wearing Fing
Figure 6-198. Cross-section of a single-stage centrifugal
of Dresser Industries, Inc., Roots
compressor. (Courtesy
Blower ODeration.)
(ideal). Since the polytropic compression process, by
definition, is the path connecting the inlet and actual discharge conditions, the polytropic formulations are preferred by compressor manufacturers. This factor becomes extremely important in sizing intercoolers, since
using the adiabatic discharge temperature would result in
undersizing the cooler. The larger the compression ratio
of the machine, the more severe the mistake ofundersizing the cooler becomes.
Gas inlet conditions can change and when they do they
affect a centrifugal compressor differently frorn a positive-displacement compressor, such as a reciprocating
machine. Table 6-1 lists the effects of changing inlet parameters on a centilugal compressor operating at a constant volumetric flow rate and a constant sDeed.
Atidd: t2t-tl
At*,-r=t2-tl
ENTROPY s
Figure 6-20. Centrifugal compression process.
Rotating Equipment
/.
:.1
9
t
.46
il
/. ,lPji: ;.J
2
t{l
I
k'
"y
{
lsr N
t\\
3A\ a\
1\
I
t;
(Vtt
I s,l t[t
)
>-Kl
J;Al
un
4
d .t
AI
*f
\\N \E.I
NN
\'lN
\'l
N
/s
A
ll
N;
\
w:,
I
I
.1
'=\\
E
E
${ \l
il
.lI\
'I
sI
aE:93Bs3B9BEig9S3P3e9
lstu Stnsslud
1N3?8ld
!3/VlodtsuoH
R
lNlltld
!
8
L
61
I
\ \
I
=
c
5T--r-t
N \ ii",-l
oU;
I
?;
3;t
\
3io-
\\
83q33P339
3Sll ]Unss!rd 1i!ltld
!3NrOd3S!08 1tt3U3C
ga.
_11
-t
;L al,l
L ,/a
=rl
l I
I
I
.J .J
:-
|t\
3\
\
t\
:9
\ \
\l \
>,
3
E33P
cY3ll I rillu ld
9833P33
t3fl0dlst0lt 1r!llttd
;-n
<E
.ti
ry'E
oa.
< Or^
=E
ltY
5l
Mechanical Design of Process Systems
52
Table 6-1
E tects ot Varying Various Inlet Parameters on a Centrilugal Compressor
Increasing
lncreasing
Increasing
Increaslng value ot
Inlet
lnlet
Molecular Weight
Polytropic n or
Pressure
of Gas
Adiabatic k
Pressure Differential
Deateases
Decreases
Decreases
Decreases
Decreases
Decreases
Constant
Decreases
Compression Ratio
Inlet Density
Discharge Pressure
Discharge Temperature
Power Required
Head Developed
Mass Flow Rate
r20
COMPRESSOR CHARACTERISTI(
I
B
I
,
I
s80
7
I
...
I
460
c0MPn€ss0F
SURGE LIM
40
I]
I
I
t
t0
0
D
0 r0 20 30 40 50 60 70 80 90
too tn
PERCENT CAPACITY
Figure 6-22, Pressure vs. capacity for a constant-speed centrifugal compressor [4].
vibration of the compressor and sometimes the compressor piping. Normal surge limits are 40% to 90% of rhe
design point, with the higher range (close to 90Vo) being
associated with multistage mach ines.
Controlling surge in centrifugal compressors is more
difficult than in centrifugal pumps, but the following factors ease the problem considerably:
1. Throttling at the discharge flange.
2. Throttling
Increases
Increases
Increases
Increases
Increases
Increases
Constant
Increases
Decreases
Decreases
Constant
Decreases
Increases
Constant
Constant
Constant
J. Using a variable speed driver, usually accomplished
CONSTIiIT SPEED
0
o.
Increases
Constant
Increases
Increases
Constant
Increases
Constant
Increases
at the inlet flange, which is usually more
efficient than throttling at the discharge flange.
by the turbine driver.
4. Bypassing or blowing
off
excess gas to avoid surge.
These steps will help in alleviating surge problems,
but if a variable rate operation is required, the compressor manufacturer should be consulted.
Antisurge devices can be incorporated into compressor systems. For nontoxic or inexpensive gases the compressor discharge can be vented to the atmosphere as
shown in Figure 6-23. For expensive or toxic gases an
automatic anti-surge system can be installed as shown in
Figure 6-24. In this type of arrangement a heat exchanger is placed in the system to remove the heat of
compression from the vented discharge gas to prevent a
loss of compressor performance caused by the temperature rise above the design value at the inlet.
Compressor manufacturers use standard cubic (scfm)
feet to speciry compressor performance, just as pump
manufacturers use water to determine pump performance. The manner in which scfm and altitude correction is handled is discussed later.
Impellers are critical in the selection of centrifugal
compressors. The three basic types of impellers for centrifugal compressors are shown in Figure 6-25. The conventional closed impeller shown in Figure 6-25 is used
for adiabatic heads up to approximately 12,000 ft-lbri
lb-. The open, radial-bladed impeller shown in Figure
6-25 develops more head with the same impeller diameter and shaft speed. The open inducer impeller can
produce heads up to 20,000 ft-lbrnb*. Whenever the
head requirement becomes too great for a single impeller, then one must think in terms of multistage compressors. Each stage of compression of a multistage compressor is treated as a single stage compressor and the
same formulations hold.
Rotating Equipment
Reciprocatlng Compressofs
cle. Figure 6-26 shows the reciprocating compressor
cycle. This cycle involves this displacement of gas,
These compressors normally are sized according to the
adiabatic expressions of Equations 6-11 through 6-25.
Normal practice in calculations for reciprocating compressors is to use the adiabatic exponent, k = Cp/C,,
then adjust the results according to the specific compressor design and configuration. The parameters that affect
the compressor horsepower, cylinder capacity, and discharge temperature are length of stroke, shaft rotation
hence the classification of a reciprocating compressor as
a positive displacement type of unit. The compressor is
speed, cooling efficiency, and fixed clearance of cylinders. All of these parameters vary for each given application, but have the same basic cylinder design and cy-
drscharge
unable to exhaust all gas from the cylinders and the residual gas remaining in the compressor at discharge conditions expands to inlet conditions. This phenomenon is
shown in Figve 6-27 .
The clearance voiume is usually set by the compressor
manufacturer and is specified to match the specified capacity with the standard size compressor unit. Power
consumption is not affected by the clearance volume or
the volumetric efficiency.
The use of "clearance pockets" is used in some compressors to vary the volumetric efficiency. These clearance pockets can be sized to affect the capacity of the
compressor, as in Figure 6-28. Power consumption at reduced flow rates is minimized by use of capacity control.
The use of a clearance pocket (additional clearance volume) reduces the volumetric efficiency of the compressor, because the re-expanding gas fills most of the cylinder, and the suction valve opens further in the stroke.
This mechanism is economical, because the energy expended in gas compression is retrieved in expansion. The
clearance pocket is separated from the cylinder by a stop
valve. Figure 6-28 shows how varying the cylinder
clearance affects the numeric value of the volumetric efficiency at constant compression ratio. The volumetric
efficiency for a reciprocating compressor is given by:
inlet
actual capacity
piston displacement
Figure 6-23. Manual surge control system for centdfugal
(6-48)
comPressor.
The parameters that affect the volumetric efficiency
are as follows:
l.
flow monitor
2.
3.
centrifugal compressor
Figure 6-24. Automatic surge control with recirculating bypass.
The ratio ofa relative clearance volume, e, which is
the ratio of clearance to theoretical displacement expressed as percent.
The compression ratio, C., of discharge to inlet pressure.
The various exponents of the polytropic curve of reexpansion. Such a curve is shown in Figure 6-29.
Here the cylinder is normally cooled by a water
jacket or surrounding air. The small volurne of gas
that remains in the clearance volume expands and
contracts with a cooling surface. Consequently, the
re-expansion curve (curve 3-4) is initially steeper
than the adiabatic curve (curve 1-2). With continuing
expansion ofthe gas, the gas temperature falls below
that of the piston and walls, and heat is transferred
from these surfaces to the gas. Thus, the exponent of
the re-expansion curve (curve 3-4) is variable. For reexpansion oflower compression ratios, Chlumsky [5]
Mechanical Design of Process Systems
OPEN BACKWARD.BLADED
IMPELLER
OPEN RADIAL-BLADED
IMPELLER
CLOSED BACKWARD.BLADED
IMPELLER
'120
BACKWARD
LEANING
B LADED
IMPELLER
e
63
RADIAL
BLADED
IMPELLER
si
100
80
60
(PARAMETER-
s
% SPEED)
(PARAMETER.
% SPEED)
40
149
120
EH
o
o"o,
-4,
?E
40 60 B0 100 120
qoRATEO INLET VOLUME
BACKWARD
LEANING
IMPELLER
AOJUSTABLE
IN LET
GU IDE
3
1?O
q
E
100
E
c'
ao
E
BLADED
IMPELLER
s
ADJUSTABLE
ol
s
l
ll
opi-l RADIAL
IN LET
GUIDE V
WIDE
VANES
UIDE
VAN ES
G
T
100
100
Vcc
g'g
.-B
d>
ro
ao
so
s9
40
20 40 60 80 100
oToFATED
INLET VOLUME
120
20 40 60 BO 100
obFATLO
l\-ET
120
VOIUMF
Figure 6-25. Basic types of impellers for centrifugal compressors. (Courtesy of Dresser Industries, Inc., Roots Blower Operauon.)
Rotating
Equipment
;
P2
= receiver pressure
P1
= inlet pressure
Compression Stages:
O = start
@ = comPression
@ = discharge
@ = expansion
O = intake
-tl
@@
Figure 6-26. Reciprocating compressor cycle.
o/o
Clearance =
Clearance volume (100)
Volume
Figute 6-27. The effect of clearance capacity.
55
Mechanical Design of Process Systems
Clearance volume
tts
l{ts
F 6.
It
rsl<\
|
rls lrlo
115
I
100
o/o
Piston DisDlacement
Figure 6-28. A clearance pocket (additional clearance volume) reduces the volumetric efficiency of the compressor because the
re-expanding gas fills most of the cylinder, and the suction valve opens further in the stroke.
|
CLEARAT{CE :C
0O5L + O.Smn,
WHENE L=STHOKE L-ETGTH
voLuME -.---------+
sourcE
:
cH urMsl(Y
l5l
Figure 6-29. A pressure-volume diagram of a compresor with clearance (zero flow resistances)
[51.
Rotating Equipment
recommends fof compression ratios of appfoximately
2; the re-expansion may be approximated as an adia-
batic process. For the volume, Va-the volume to
which the gas expands during the pressure drop from
P2 to Pr-we have the expression
., :
".
.. /pl,
(64e)
"" \p,/
For compression ratios of 4 and higher, the re-expansion cannot be considered as an adiabatic process. For
these compression ratios the polytropic exponent m
(where m denotes the difference between the re-expan-
PV'
(constant) and the compression PVn (constant).
1.25.
For diatomic gases, m
The value of the polltropic curve exponent, m, varies
sion
:
with pressure. Chlumsky [5] recommends for a com-
pression ratio of 3:4 the following values of m be used:
Substituting Equation 6-49 into the expression for
volumetric efficiency, we have
First stage
Second stage
,lt
-
v"+v"-v4
-
-----------=;--
Third stage
Fourth stage
Fifth and further
'u'(*o]'
-
stages
m:l 20
m : 1.25
m: 1.30
m = 1.35
m:k
or
These values are given at different pressure levels, as ex-
-t
-.[(,*i -
where e =
*vp:
(6-50)
.utio of the clearance volume. Vo. to
the volume swept by the piston stroke.
v"
?" =
#vp:
V^
expression for volumelric efficiency.
Equation 6-48, the ratio of gas volume
pumped to the volume swept by the piston (compressor displacement)
Figure 6-30 shows the graphical solutions of Equation
G50 for various compression ratios and exponents of the
polytropic curve of re-expansion and clearance values.
34
_L-
I9n
ist in multistage compressors with the suction of the first
stage at atmospheric pressure.
The volumetric efficiency for a perfect gas (z = 1),
not realistic, is given by
4,r:100-c(cRr/k-1)
where 4,, : theoretical volumetric efficiency
The volumeuic efficiency for a perfect gas (z
with realistic effects.
4":100-cR - c(cR'/k - l)
Cs : compression ratio : PzlPr
1@Z
80
c
Figure 6-30. Curves for determining volumetric efficiency [5].
(6-s
l)
:
1)
(6-s2)
58
Mechanical Design of Process Systems
The difference between Equation 6-52 and Equation
6-51 is that the theoretical volumetric efficiency should
be reduced by a value equal to the compression ratio to
obtain an actual value for a perfect gas. This is a factor
that has been determined from field experience.
For a real
lv:
100
gas
(z
*
22:
_ cr _ c1(cR)i" _
(6-53)
I
rnlet and discharge compressibility factors, respec-
tively
As stated previously, reciprocating compressors follow the expressions for an adiabatic process. The work
required for the adiabatic compression of a perfect gas
(z : 1) is found by the following expression:
w:
1. Operating at high speeds, they can be coupled
1) with realistic effects,
where
zt,
dency has been to increase the cylinder size using a
smaller number of cylinders. Multistage reciprocating
compressors have the following advantages:
PV (-o_JhtJ=
2.
3.
fluctuation of torque. The more cylinders, the less
the fluctuation of torque.
4. Starting multistage compressors is easier because
they have small moving masses and thus can be
driven by electric motors with less inertia torque and
lighter construction.
5. Variations of pressure and flow velocity in the intercooler or oil separator are less, thus making these
6.
-']
(6-54)
7.
6-16 or bv the followine:
:
u [ll,I- . rl'l [,, * ,l
33.ooo k-l [\Pr/
\ 2., /
(P
Vrrr44
For an ideal
where
ga's, 21
P1, Pz
:
:
parts smaller.
Machines of various capacities can be manufactured
using identical parts, making interchangeability efficrent,
The theoretical horsepower may be found by Equation
6o.
di
rectly at high shaft speeds thus utilizing cheap electric
motors.
Better balance of inertia forces.
The mass of the flywheel, which rotates at high
speeds, can be made smaller, resulting in a smaller
(6-5s)
22
inlet and discharge pressures, respectively,
Multistage compressors are better suited to automatic
operation.
Gas Temperature for Reciprocating
Compressoas
The discharge temperature of a positive displacement
compressor, a class of which the reciprocating is included, can be predicted by the following expression:
psia
Vl, V2 = ir et and discharge
gas
flow rates,
respec-
tively, acfm
In Equation 6-55, the theoretical horsepower may be
varied by the following parameters:
l
2.
3.
4.
lncreasing
Increasing
Increasing
slon rate,
Increasing
the compression ratio, Cp
the specific heat ratio, k
the inlet pressure at a constant compresthe actual inlet volume (nat standard vol-
ume).
Multiple Staging of Reciprocatang
Compressors
Multiple staging is the compression of a gas from one
pressure to another involving more than one step. Each
step acts in series with the others and entails a basic machine element. In multiple staging of reciprocating compressors, increasing the cylinder size is less expensive
than increasing the number of cylinders, thus the ten-
,r
/P'\?
t-\Pj
(6-56)
where t :
absolute temperature for any system
P = absolute pressure for any system
:
1, 2 :
k
Cp/C', adiabatic exponent
inlet and discharge conditions, respectively
Axial Flow Gompressors
In axial flow compressors, the flow enters the unit
oarallel to the axis ofthe shaft and the flow direction esientially remains unchanged from the inlet to the exit of
the unit. Airfoil blades are located on the rotor shaft,
varying in pitch and size according to the flow conditions. The gas passes through the airfoil blades in an axial direction.
Axial flow compressors are used for applications of
about 25,000 cfm upward. The formulas for centrifugal
compressors apply to axial flow machines. Axial flow
compressors can handle greater capacities, which is the
primary reason why they have replaced centrifugal com-
Rotating Equipment
pressors in aircraft gas turbine units. The characteristic
curve (head versus flow) for an axial flow compressor is
much steeper than for a centrifugal compressor and the
surge limit is a function ofdesign capacity. Contrary to a
centrifugal compressor, the required horsepower for an
axial flow compressor at constant speed and pressure decreases with increased flow Axial flow compressors are
not as common in the process industries as centrifugal or
reciprocating types of machines.
Fans and Blowers
Fans and blowers are basically compressors. They fall
under two types of compressors-centrifugal and axial
flow. If one understands the basics of centrifugal or axial
tlow compressors, fans and blowers come easy, for they
are less complicated than compressors.
Specifying Gompressor Flow Gondltlons
Specifying compressor flow conditions is a major
source of confusion in applying compressors to process
sl stems. There are three basic ways to specify compres-
:or flow conditions:
l.
flow-define the mass flow rate of the gas, Ib./
in the English system and kg/hr-m in the Sl/metric.
3. Actual, or inlet, volume flow-volumetric flow rate
of the gas at the inlet conditions, expressed as acfm or
icfm in the English system and m3/hr in the SI and
MKGFS systems.
-1. Standard volumetric flow-the volumetric flow rate
of the gas at the inlet conditions expressed in terms of
standard cubic feet of gas per minute (scfm) or millions of standard cubic feet of gas per day (MMscfd)
in the English system and m3/hr in the SI and
MKGFS systems.
Mass
Iass
Flow
The method of defining the mass flow rate of the gas
h terms of the inlet conditions of the comoressor is far ored by many and is mandatory in calculating gas propenies between stages. Mass flow rate ,?2uJt be specified
as either dry gas or wet gas. Ifthe gas, for example, conrains water vapor, this could drastically change the compressor design. One of the problems of using mass flow
is not speciffing the flow conditions as a dry gas, which
ir reality is a two-phase or multiphase flow.
Another disadvantage to using mass flow is that it does
not allow one to appreciate the physical size of the sysrcm. An intuitive feel for any system is essential to its
successful desisn.
Actual or Inlet Volumetric Flow
Actual flow rate conditions at the inlet to the compressor is denoted as acfm or icfm-acfm meaning actual cubic feet per minute and icfm meaning inlet cubic feet per
minute.
The disadvantage to specifying acfm is in the internal
components ofthe compressor, e.g., a sideJoad refriger-
ation compressor, or in a multistage compressor. In a
multistage compressor the previous stage's discharge
temperature is a function of the previous stage's compression efficiency, and mass flow rates are better for
such conditions.
Acfm is best for plotting compressor performance
curves, because the impeller is sensitive only to the actual volumetric flow and is insensitive to the gas state
conditions.
Mass flow and acfm volumetric flow should be used
because mass flow is invaluable in communicating with
tle compressor manufacturer and in dealing with internal machine flow conditions, and acftn is essential in
getting a feel for the physical size ofthe system. The use
of mass flow and acftn should counter the disadvantages
of both approaches.
In computing pressure drop through connecting piping
systems to compressors, it is imperative that acfm be
used to avoid any confusion in designing the piping systems.
Standard Volumetric FIow
Specifying gas conditions in terms of standard volumetric flow is done extensively throughout industry. The
gas flow conditions are based on standard inlet condi-
tions-pressure, molecular weight, temperature, and
compressibility-all based on "standard" conditions.
Thus, the standard specific volume is constant being that
u.,.
: "'+J'':
constanr
(6-57)
where z.,a : compressibility factor at standard conditions
R: universal gas constant, which is a function of
the molecular weight of the gas
:
P$d :
tsld
temperature at standard conditions
pressure at standard conditions
Volume flow is expressed as
Q,ta
:
mV,ro
(6-s8)
where the standard volumetric flow is directly proportional to the mass flow rate.
60
Mechanical Design of Process Systems
As with using mass flow, when using standard flow
conditions one cannot appreciate the physical size of the
system. And worse still, using scfm does not provide any
of the advantages of using either mass flow or acfm. To
specify something as "standard" one thing is essential,
that all parties agree on what is "standard." Unfortunately, this is not the case with using scfm, as the following "standards" cited by Lapina [6] indicate:
The specific volume, V, may be determined by
sas\ /
' \
v = z /rl::_:l
I::-::l
mw
/
\
where, as before, mw
scfm
(6-61)
\1,14Pl
:
molecular weight
(379.46)mh
:
(6-62)
60
Metric system
English system
1. P",a : 14.7 psia
t'ta : 60'F
2. P,u : 14.7 psia
t"a:70"F
3. Pd : 14.7 psia
t.to : 32'F
1
2.
P",a
=
where mh
101.3 k?a
: 0'C
P"a : 101.3 kPa
t,ra
and
tsa:15'C
rir
=
moles/hour
= (rfi)(mw)
(6-63)
and finally,
aclm:
qs _
= [(MMscrdx106)1 1,0
Thus, what is considered "standard," as Lapina [6]
writes, varies from industry to industry and engineer to
engineer. In the net result what is often gained is confu-
where
sion.
tion) conditions.
lie
nu)1/f*l*)|/t)
t--aOoz, t \-pJ\460
+
-'
rJ\il .""_*,
subscript, s, denotes properties at the inlet (or suc-
Equation 6-64 may be expressed as follows:
e.=acrm=*-tltjHP*.,-J
Properly Specifying Gompressor Flow
Gonditions
To properly size or select a compressor, the capacityno matter how it is given-must be converted to the inlet
conditions. To do this the following expressions are
used:
(6-6s)
where the scfm is based on a dry gas.
To convert the standard volumetric flow to mass
the following relations are used:
flow
English system:
PrVr
tflt
_
P2V2
tzzz
(6-66)
V:
P:
where
t:
z
:
volurne
absolute
pressure
absolute
Sl/metric system:
Iemperalure
compressibility
factor
rir
In Equation 6-59, if z
and
t
acfm
:
where
e_ = rirV
ri :
V
p
:
:
mass
scfm fP"o
\zd
'
ro'\
(6-61)
R.td t.ld/
1.0 for a perfect gas, and P
are at standard conditions, then
:
:
: "'
p
flow rate, lb./min
specific volume, ft3llb,,,
density, lb./fC
PIPING SYSTEilS FOR ROTATING
EQUIPMENT
(6-60.)
For rotary equipment to be functional and contribute to
the process system, it must be connected to the system
with piping. The science of connecting piping systems to
rotary equipment is a relatively new field and has drawn
Rotating Equipment
the stalwarts of academe to join with industry in solving
problems of piping and equipment.
The two problems focused upon here are nozzle loadings and pulsation response spectra distributed to the attached piping system by reciprocating machines.
Table 6-2
Typical Manufacturer Allowables lor Nozzle
Loadings tor Inline PumPs
Nozzle Loadings
In earlier years various rotating equipment manufacturers would define allowable nozzle loadings as "zero
force and zero moments." Such statements were not only
ludicrous, but showed how little confidence some rotary
equipment manufacturers had in their products. Ultimately, the pipe stress engineer was left to use his (or
her) sole judgment to determine if the piping loads were
substantial enough to damage the attached equipment.
There are several standards for handling nozzle loadings on rotating equipment, and probably the best known
are those of NEMA (National Electrical Manufacturers
-{ssociation). NEMA provides guidelines for nozzle
Ioadings for steam turbines for mechanical drive service.
Unfortunately, its guidelines are appiied to every prece
of rotating equipment by eager customers and engineering contractors. For example, what is valid for steam
turbines is not valid for inline pumps. Because steam turbines are more fragile than most types o[ rotary equipment, using the NEMA standard produces over-conservative designs for most types of rotary equipment.
The American Petroleum Institute (API) also has standards for rotating equipment: API 611-General-Purpose Steam Turbines For Refinery Service; API 612Special-Purpose Steam Turbines For Refinery Service;
,\PI 617-Centrifugal Compressors For General Refinery Services; and API 618-Reciprocating Compressors
tor General Refinery Service.
Applying API standards to nozzle loadings on rotating
equipment leads to the argument in which rotating equiprnent specialists claim that the API standards are only intended for procurement purposes, and the pipe stress engineers, having no other guidelines to follow, assert that
the API standards are what is to be used in practice.
The best criterion for judging nozzle loadings is experience with a given piece of equipment. For example, my
several years of practical experience with turbo expanders dictate they can withstand three times the nozzle
loadings allowed by NEMA (remember-only for steam
turbines!)
.{lowables for inline pumps, as above, did not exist a
tew years ago. Such pumps were regarded as piping
components, e.g., valves, and allowables were considered unnecessary. But "thinning-up" casings to reduce
naterial and costs makes such allowables possible, alrhoush controversiai at times.
PUUP
SIZB
(
in)
Fa lb
Mi=
!
Mo=
Fo
2x3x6
4000
50 00
4000
3x4x6
6000
60 00
5000
2x3xo
4000
5000
4000
3x4xB
5000
6000
5000
4x6xg
6000
7000
6000
4x6xl0
5000
7000
5000
6x8x!
0
8000
9000
8000
6x6x20
500 0
6000
5000
| 0x1 0x20
800 0
9000
6
12x12x20
r 2000
F *Miao * !{oact 1to,n",
F" Mi.o
Lo
-tb
t-1
13000
Li
000
10000
2.g
Hhere,
F
= resultant of actual force applied,lb
Mh. u.tuut bending monent on suction nozzle,ft-1b
Mou;, actual b€nding nonent on discharge noz2Ie,ft-1b
62
Mechanical Design of Process Systems
There are three basic options to solving nozzle loadings on rotating equipment.
1. A detailed finite element study of the equipment.
Destructive testing of the equipment.
2.
3.
Close interface between the rotating equipment manufacturer and the piping stress engineer.
The problem with finite element analyses is who is going
to pay for it-the client, the engineering contractor, or
the rotating equipment manufacturer? Next, can the rotating equipment manufacturer disclose proprietary information often required in finite element analyses? Destructive testing poses the same question, who will pay
for it? The third option-the pipe stress engineer conferring with the equipment manufacturer-is perhaps the
most viable of the three, because if the NEMA and API
criteria cannot be met, then the rotating equipment manufacturer can at least expect extra loadings and can design for it, if time permits. Thus, the rotary equipment
vendor working as a team with the piping stress engineer(s) can help to alleviate most nozzle loading problems.
NEMA and API standards are very safe and a piece of
equipment that meets their requirements should not have
any nozzle loading problems, such as leaks. The problem comes in modular skid construction, where the values provided by the standards are very conservative.
Manufacturers often give allowable values for their
equipment, and Table 6-2 presents some typical ones. A
generalized standard taken from several pump manufacturers' allowable standards is shown in Fieure 6-31.
Reasonable nozzle loadings for turbo expandJrs worked
out by the author and several turbo expander manufacturers are listed in Table 6-3.
Neither Thble 6-2 nor Table 6-3 should be substituted
for the manufacturer's allowables, if the vendor has his
own. However, the information can be a valuable tool.
Rules of thumb often are not only invalid but are often
based on special situations that may not be true for every
case.
One must be extra careful in piping steam turbines, be-
cause these units are usually fragile. Example 2-2 in
Chapter 2 illustrates a piping arrangement connected to a
steam turbine. If expansion joints are allowed, the configuration shown in Figure 6-32 is ideal.
PULSATION BESPONSE SPECTRA
INDUCED BY RECIPROCATING
EOUIPI'ENT
Reciprocating machinery often induces pulsation response spectra
in attached piping systems. This subject
alone is comprehensive to fill several volumes, so we
will just outline the problem here.
Mno
=\fif,,T Mfi
Mfl
MF"
=..ffi*r N/-t+Tlg
MFN = greater of Mpo & Mp", where Mso &
resultant moments applied at nozzles
MRO = resultant bending moment about
DM,
DM,{
.-.-L
FFs
=
= F"-(0") +
= F"y(d") +
+ M"y+
FDy(dD)
+
l\4"y
tr\arr
12 t\-a i,
LtAr'.-"t_ | lL,/..r,r[Fs2"
+ F!, + F!.]o5
Fno = [F2o* + FBy +
FB
FD,(dD)
= greater of
MDy
+
110.5.
)l
;
FzD.]o 5
FRs
or
l\iDy
FFD
*&*^!!'*ffi. z.o
Figure 6-31. Generalization of forces, moments, and allowable nozzle loadings.
-
MRs
are
Rotating Equipment
Table 6-3
Reasonable Turbo Expander Nozzle Loadings
Nozzle
Size (in
4
6
8
10
'|.,
t4
l6
Nozzle
Size (in
4
6
8
10
2,436
3,654
4,870
M,
3,383
4,474
5,074
6,710
6,7&
8,947
6,088
7 ,306
8,524
8,455
10,146
11,838
I 1,184
9,730
l3,513
t7 ,870
2,436
3,654
4,870
4,474
6,088
11,184
M,
g9
l too
1
974
1,948
1,948
I,948
) q))
1,624
5q1
3,896
2,436
7 )47
3,246
4,869
?OO
too
|,623
,
1,948
2,272
aa \
La \
so5
5,189
5,189
&9
r too
1,299
9',14
1,948
1,948
1
t
<o7
3,246
3,895
)
3,895
5 R4?
6,817
7 ,784
d n{q
4,871
5,683
6,486
13,421
15,658
F,
1 too
1,623
t
<o7
3,246
,) <o?
3,246
1,948
1,624
3,383
5,074
3,896
2,436
a )L1
4,869
4,059
5,843
6,817
4,87r
,784
6,486
8,455
10,146
11,838
13,513
I O))
6,7&
6,710
8,947
,306
13,42r
8,524
15,658
9,730
r7 ,810
5,189
3,895
A \A\
5,189
648
972
l,080
F,
1,080
|,659
2,699
r,620
2,488
1,620
2,429
2,699
1,620
4,U9
4,O49
4,147
6,220
10
|,296
|,620
2,160
2,699
3,318
4,147
4,049
10,367
L,944
4,976
4,859
6,748
8,098
6,748
12
2,160
2,699
? )10
2,268
3,779
3,779
5,806
9,448
50?
4,3t9
4,319
10,798
10,798
4,859
r2,147
12,t47
16,588
18,661
100
4,859
< ?oo
13,497
13,497
20,735
6,486
6,486
6,63s
7 ,464
8,294
9,964
5,669
6,479
7 ,289
8,099
8,098
9,448
12,M\
t4
16,216
16,216
24,912
12
t4
l6
|,948
1 11)
t
so{
3,895
4,545
Nozzle
Size (an
6
8
l6
l8
20
24
,
') cll5
3,240
3,892
<
1r10
7
5,683
l tlo
9,730
s ?oo
7
s lqq
8,294
14,514
Mechanical Desisn of Process Svstems
64
Table 6-3 (continued)
Compressor Discharqe
Nozzle
Size (in.)
4
6
8
l0
1''
14
16
18
F,
F,
650
|,444
i
974
2,165
2,888
3,610
,
1,300
1,624
I q4q
)
,
4
)74
sqq
? ol o
PG:
lA:
G:
HEJ:
GEJ:
111
Fz
Fs
M,
rqq
2,048
3,072
4,097
5,121
1,624
,
2,436
?
1,949
soo
3,249
3,899
{ n{l
4,548
6,486
5,198
5,838
Planar Guide
IntermediateAnchot
Guide
Hinge Expansion Joint
Gimbal Expansion Joint
Figure 6-32. An expansion joint arrangement ideal for steam
turbines where nozzle loadings must be kept low (almost always the case with steam turbines) and the use of expansion
joints is practical. (Courtesy of Pathway Bellows, Inc.)
Currently, two methods are used to predict pulsation
problems: (a) modeling the system on an analog computer and (b) simulating it on a digital computer. Basically, the piping system is modeled with support and soil
stiffness vaiues input at every pipe support as discussed
in Chapter 2. Then the system is excited with various
forcing functions that represent the reciprocating machine or machines. The piping supports are moved
6,145
,169
8,193
7
9,202
7 )49.
\
My
M'
Mp
165
3,W7
4,046
6,016
6,070
8,093
t4q
4
at)
4,060
4,872
5,684
A1L
7,5r9
10,116
6,496
'7 a'7q
9,023
t0,527
12,139
6,496
8,662
12,030
14,162
16,185
9,730
13,514
l8,
'7 1a-l
181
around, deleted, or added to decrease the amplitudes
generated by the forcing functions. This analysis can be
done on either an analog or digital computer.
There are two methods available on existing computer
software that can help head off pulsation problems.
These methods arc modal ertaction analysis and time
spectra (time history) analysis. Modal extraction is computing the natural frequency of the piping system, after
modeling the pipe support and soil stiffness values, and
comparing this frequency to that of the shaft speed of the
equipment. Time spectra analysis is a transient analysis
that basically does exactly what modal extraction does
except on a transient basis for every time interval over a
specified period of time. In other words, we compute the
system's natural frequency for every second over a period of one hour. Over the period of one hour we excite
the system with a forcing function that accurately defines
the rotating equipment.
Figure 6-33 shows a piping system excited by pulsations from a reciprocating machine. A complete investigation of the pulsation frequencies and surge capacity is
normally required, which involves the compressor bottles (surge drums), compressor suction header, and suction compressor bottle, the discharge header, and discharge compressor bottle. Two companies are engaged
separately in investigating these problems-Southern
Gas Association's compressor analog computer at Southwest Research Institute and the Structural Dynamics Research Corporation (SDRC). The compressor bottle (or
surge drum) acts as a pulsation dampener. A typical bottle is shown in Figure 6-34. The compressor bottle acts
as an acoustic filter designed for all frequencies induced
as the reciprocating engine speed varies. The compressor bottle cannot damp out all frequencies, but should
store energy generated from the various frequencies and
reduce them to produce a relatively smooth and continu-
Rotating EquiPment
Figure 6-33. Piping system excited by pulsations from a reciprocating machrne'
ous operation. Sizing the compressor bottles should be
done by a specialist who has worked in this field for several years.
In the days before analog and digital simulations, pulsation Droblems were solved (and still are) with orifice
plates. These plates were placed in the piping system and
the orifice diimeter was approximately 0.53 times the
internal diameter of the pipe. These plates' distributed
throughout the piping system, acted as pulsation dampeners. Although orifice plates produce huge pressure
drops, they are effective in many installations.
EXAMPLE 6-1: HORIZONTAL'
CENTRIFUGAL PUIIP SYSTEM DESIGN
A food processing plant is having a cooking kettle installed to process molasses into refined syrup for breakfast foods. A horizontal centrifugal pump is to be installed next to a fuel tank to supply fuel oil to a burner in
rhe cooking kettle. The fuel oil tank is to have a 50 psig
Figure 6-34. Typical pulsation bottle (or drum) configurations that act as pulsation dampeners.
nitrogen pad because the tank cannot be raised for higher
head at the pump. The cooking kettle is 200 ft downstream and 15 ft above the discharge flange of the pump.
desired to select and size the burner feed pump
shown in Figure 6-35. The discharge pressure at the
burner end is to be 40 psig.
It is
Suction Llne Pressure DloP
Fluid
:
tuel oil
TemDerature
:
90'F
Pressure = 50 psig
p 54.725 lb^lft3
:
p: 139.53 cp : (139.53)(6.72 x 10-a) :
lb./ft-sec
e : 0.0018
L:1.0ft
Suction line = 3 "dSch 40, Di : 3.068 in
Q : 150 gpm
0.094
Mechanical Design of Process Systems
cooking kettle
Figure 6-35. Hot-oil pump piping scheme for Example 6-1.
fuel tank
3" x 1tlz"
burner feed pump
(r5o)sar
lrj,
ll]]ry\
s€c/
min \7.479 gal/ \60
(7.393) in.:
I t n'in.r/)
Entrance and
l-3-in.d 90"
= 6.51I ft/sec
exit: K:1.78
std
ell
1-3-in.d gate valve
: K : 0.30
: K : 0.14
\-.. *
\1,14
l3
068li.,o.srr, rt (s4.72s)l9r
N.-=DVP-\ 12l
r
sec
lh
ft'
-
From Equation 1-4 we compute the frictional pressure
drop as follows:
nur.,
r0.094;-1\
* r.leY
'' : ILL
\D -'l- I2e,
n-sec
With NR"
ao,
:
969.1, the flow is laminar.
From Equation 1-6b we compute the friction factor
as
follows:
6L
6A
f=j_:
N*" 969.1
oo,
- fro.ooorrts.oorrtzr,,.rrl
t (3.068) I
:0.066
rsa.72sr
K.Values (Velocity Heads)
Referring to Figures 1-7 and 1-11 we have the following:
llr(6.511)? tt2
ftr
zr:z.zr
Ap1
:
L524 psr
sec2
n-111
sec'-ln
I\144'o',,l
in.2/
Rotating Equipment
o,,:[ry.0"']
Discharge Line Pressure DroP
The conditions are the same as the suction line except
for the following:
@.64D'?#Hh)
ts+.zzs1$
Line size = 2-in. Schedule 40 for which Di
For 1l/z-in. d pump discharge,
.";;;m[
:
(150)#[+r-J(#,J
2.067
^."^
-'-Apr
=
23.642
:
fr-lb.
^.
-' sec2lbr
2.982 Psi
fr
:
sec
K-Values lor 2-in. Portion
2-2-in.-std90' elbows = K = 0.40
For 2-in. S/40 discharge line,
exit:K:1.0
EK:
r4o
L-200ft
-^r,r
^ ^.
For 2-in. d S/40 pipe,
t, ., ,.oOl
06zr -. -l
th.
'il r14.343).. _ft2 I tfr:
t
[{0.044)r200.0X
[-o
rS+.225r
I
.z \raa in.,]
fr-lh
(ry) - (14.343)A(54.72rk
S€C'-lD1
=r/.lR?
A* =
(o.os+) -.1!.
n-sec
63.72 psi
:
too high-choose a 1 r/z-in.
x
3-in'
diftuser
With 3-in.d Sch 40 PiPe,
64
64
" Nr"_ 1,438.3 _^^^^
(lso)sa,
L+fu)(,**)
(7.3e3) in.2
(r-
K-Values for 11/2-in. Portion
:
:
K 0.78
Entrance
From Thble 1-7, for a 2-\t.
E*:
L
:
r".
x
lll2-in. diftuser, K
:
0.055
o.srt
=
[('-ryt tz
- l\
I
|I
@ :0.037
Nt"
sec
*--L)
K-Values for 3-in. d PiPe
2-2-in.-std 90" elbow
3.0 in., d
ft
=K=
0.54
Dr:
t.so
exit:K:1.00
1.610 in.
e3.642t L,ro.rrr,
'-
10.094;.'"'
tt-sec
hl
tt'l
=
l1!4lr
r.zzo.s
Nn"
: \l2 l
I
(6.511)
a,so.tts, l!:
sec
(0.094);lb'
I
n-sec
6A
f: -
Nn"
=
0.066
:
969.125
Mechanical Design oI Process Systems
68
^_t
^pf_[
(0.066x200.0)(12)
(3.068)
(s4.7zs)t#(6.51rF
+
g
(,* *-)
fr-lh
SeC'-lDr
Apr
:
13.309 psi
=
use 3-in.
{
S/40 pipe
New K-Values for 1r/2-in. Pipe
:
Entrance
K
From Table l-7
K 0.337
:
E*:
:
0.78
, for a 3-in.
x
fluid being handled should be Newtonian. Gels, slurries, asphalt, and other non-Newtonian
fluids should not be considered with these charts. In handling such fluids a positive-displacement pump is usually
required. (Example 6-2 is an illustration of how to handle such a liquid.)
To use Figure 6-39 we must convert the absolute viscosity io kinematic viscosity. This is done as follows:
use the charts, the
r.54]
:
w:
p
139.53 cp at 90'F
54.725 lb/ft3
io.oooozog\tu-r..
(139.53)cpl
. --"1 ;;--(32.17) -ij-i:!-.
lllz-in. diffuser,
rr-lh
\ rcp / r('
r.ttt
rDr-sec'
th
154.'725)=
L : 3.0 in.: d : 1.6i0 in.
Nn.:1,720.5;f=0.037
rt"
z
:
f12
0.0017-:sec
..^.:
ji1Ii0.,
L (1.610) '-'"rll
lQ
or
ll
lh
fr2 / rfr? I
,I
\s4.125)'+ (23.642f ::-
0.0017
fr-1h
)/1t tr " '"m
0.0000107639
Irr
V--
| '"
sec? \ 144 in.2/
sec'-lDl
:
sec
centistokes
i:
sec
v:
159
.261 centistokes
3.912 Psi
Total pressure loss in discharge linc
13.309
3.912 = 17.221 psi
Using Table l-8 we make the viscosity conversion
from centistoke to SSU as follows:
Using the pump manufacturer's curve in Figure 6-36,
we can enter data on the Hydraulic Design Calculation
Sheet in Figure 6-37 to size the pump.
0.226r-::::=v
Apr
-
-
The Effects of Laquad Viscosity on
Gentrifugal Pumps
From the previous analysis and Figure 6-36 we know
the hydraulic performance required of the pump. Before
the actual horsepower requirement for the motor and the
impeller size can be determined, the viscosity effects of
the liquid being handled must be considered. One requirement of a centrifugal pump is that the handled liquid be relatively clean of suspended particles. Obviously,
for the same size pump and motor a highly viscous liquid
will tax the unit more than would a low viscous liquid.
Thus, the viscosity is an important property that affects
the horsepower of the pump motor. To account for this,
the Hydraulic Institute has prepared charts shown in Figures 6-38 and 6-39 for determining viscosity effects. To
rq5
t
- 704.695t t : 706 SSU
t2
862.832
=
0
Now, looking at Figure 6-39 we see that for 150 gpm,
: 82 feet, and 706 SSU we obtain the following
coefficients:
TDH
Cr:056
Ce:090
x Q^*, where QNw is the water
capacity at which maximum efficiency is obtained
Cu = 0.90 for 1.0
The corrected flow rate becomes
^
Qc =
sDm"i...
:-: =
LO U.YU
150
166.61
=
167 spm
Rotating
EquiPment
O
o
@
(o
<o
{)
5lL
a
69
70
Mechanical Design of Process Systems
Pump Hydraulic Design Calculation Sheet
Liquid
fuel oil
Viscosity at PT. (Pumping Temp.)
Vapor pressure at
Sp. gr. (.y) at PT.
Flow at ambient
Operating flow at
Design flow at
139.53
0.010
PT
temp.
PI
PT.
cp
psra
o.477
150
150
150
_
Suction
Source pressure
Static head
- APr, line loss
Suction pressure
- Vapor pressure
NPSH avail
NPSH avail
Discharge
64.7
1.9
1.52
65.08
=
=
_
gpm
gpm
gpm
-
0.01
65.07
171
t
Terminal pressure
Static head
psia
psia
psia
Piping system
Other
Discharge press.
Suction press. =
-
-
ft
ft
NPSH req'd
=
psra
psi
psi
71-38
psia
'1.9
psl
17.221
psi
psl
96.201
psia
3'1.12
psra
psra
82.017
feet
APr discharge
=
TDH
=
bhp at Duty Condition
=ffi
DnpD =
= 515hP=5v+hP
bhp at Back-Pressure Condition
or'c* =
Sffi
=
*AlrffiB
=
3.7o6hp
-
4hpwithwater
Figure 6-37. Pump hydraulic design calculation sheet for Example 6-1.
centrifugal pump with a l0-hp motor and a 5-in. impeller. In selecting a centrifugal pump it is desirable for the
The total dynamic head becomes
Hc
TNH R'
= 'i-"
=;:91.
LH
U.YU
= 9l
fr
Now, referring to the manufacturer's curve in Figure
6-40, for Qc : 167 gpm and TDH : 91 ft, we determine the pump efficiency as
n:63%
The NPSH required
= 8 ft
To correct the efficiency for viscosity we have
r"
:
!C,t = (63%)(0.56) = 35.28% efficiency
The brake horsepower for pumping the liquid is
bho,,,"
QHl- = 3,960
4.
(167)19l)10.877)
(3,960X0.153)
- 9.53 ho
Referring to Thble 6-4, we see that the next larger mo-
tor size is a 10 hp rnotor, thus we select a 3
x
lllz-in.
required flow rate to fall in the middle of the pump
curve. Avoid extreme sides of the manufacturer's performance curves. Select an impeller that is at least two sizes
below the largest size available for the pump, because if
greater head is later required, e.g. , if additional piping is
added to the system, changing impellers is much cheaper
and expedient than purchasing a new pump.
In the final analysis the design engineer must not forget the potential problem of back pressure that the pump
could be exposed to under varying conditions. For example, if the discharge line contained a bypass valve that
diverted flow to either the cooking kettle or to a reservoir that collected water, the reservoir would be used if
and when the pump and piping system are cleaned with
water or a cleaning agent. In this situation the pump
would have to be sized for handling water or whatever
cleaning is to be used. When the bypass valve is shut off,
closing the discharge piping connecting the pump to the
cooking kettle, the flow conditions are changed, resulting in a lower TDH. With the same size impeller, as the
TDH lowers- the flow rate increases as the curve shifts
Rotating Equipment
300
26
150
1(n
80
60
40
30
20
15
10
8
10,000
8,000
6,000
'4,000
3,000
tO
15
20
25
30
40
50
60 70 80
90
100
CAPACITY-GALLONS PER MINUTE
Figure 6-3g. Viscosity corrections for capacities of 100 gpm or less (Courtesy of the Hydraulic Institute, Cleveland Ohio.)
72
Mechanical Design of Process Systems
i
F>
*.2
;t
?E
P,Z
E<
o6
;
Figure 6-39. Performance correction chaft for viscous liquids. (Courtesy of the Hydraulic Institute, Cleveland, Ohio.)
Rotating Equipment
Table 6-4
NEMA Frame Dimensions
___o
Ir
r--i
F- E =q-
E -->l
H-SIZE HOLE
Source: Goulds Pumps, Inc.
74
Mechanical Design of Process Systems
to the right in Figure 6-40. Since the impeller does not
change, more horsepower is required for the lower
TDH. This condition is known as the break horseoower
(bhp) required at the end of the pump curve. or maximum flow capacity condition. In our case we have a
minimum TDH of approximately 45 feet in which the
bhp becomes
'
bhp
=
{llE(s){l
0)
3.960(0.46)
:
3.706 or 4 hp with water
Thus, we see that our 10-hp motor is sufficient against
back pressure. Often, the water condition requires more
horsepower, and thus a larger motot than the process
liquid condition. The design engineer must be always
cognizant of any other fluid that the specified pump may
have to handle.
:
N*"
:
DVP
'4
{lP}n
: \tzl
(3.78r)
a
sectes.soer k
n"
(0.630)-
_lb.
'
ft-sec
193. t 16
From Equation 1-6b we compute the friction factor as
f: -:-
Nn"
=
0.332
K.Values (Velocity Headsl for Suction Line
Referring to Figures 1-7 and 1-11 we have the followtns:
En'irance andexit
K 1.0 + 0.78 1.78
:
2-4-in. plug valves
:
:
:
K:
2(18X0.017)
1-4-in.-90" standard elbow
EXAUPLE 6.2: POSITIVE DISPLACEIIENT
PUMP DESIGN
A positive-displacement pump is required to transfer a
adhesive coating mix from a storage tank to a bin in
which the mix is dropped onto a nylon sheet (see Example 3-6). The adhesive coating mix adheres the particles
together to form roofing shingles.
First, we must perform a fluid analysis of the system
shown in Figure 6-41.
ft-sec
(_ri'
)tr_ry
sec
min \7.479 gat/ \60
(t2.73)h.2H*l
:
:30(0.017):0.510
\-r :
3.781 ftlsec
2.9O2 velocirv
From Equation 1-4 we compute the frictional pressure
droo as follows:
r2)
* a.M8l
oo, [<o.zs:xgo.ox
L (3.068)
I
k
(6.5ilr
g
fr-Ih
mix
p : 95.909 lb*/fc
:400'F
Temperature
L : 11.0 ft
Pressure = 20 psig
a : 150 gpm
Suction line = 4 in. Schedule 40 + Dr = 4.026 in.
e : 0.0018
p : 938.08 cp = (938.08)(6.72 x 10-4)
:0.6:0 lb'
0.612
heads
Suctaon Line Pressure Drop
Fluid = coating
:
K
LtK
(e5.eoe)
(rso) sar
:
Apr
:
J
F-!-,-
SeC'-lD1
40.822 psi
Referring to the pump hydraulic calculation sheet,
Figure 6-42, we summarize our results. From this we
compute a total dynamic head (TDH) of 93.76 feet. Past
experience indicates that a rotary gear pump of the type
shown in Figure 6-43 is excellent for handling high viscosity liquids. The pump manufacturer has the performance curves rated in terms of kinematic viscosity in
SSU. Now converting our viscosity to SSU's we have
Ssu
:
ll(.1,]1 635) (938.08X4.635)
w/g
195.9091
l-l
\
32.2
l
=
1.459.78 SSU
L)
o
o
o
ro
q
o
r)
o
to
N
o
o
GI
o
lo
o
o
o
to
(o
o
lt
ir
o o o o o
izu(o!@sl-
a
z
E
75
Mechanical Design of Process Systems
//t
ir
Rotating Equipment
Pump Hydraulic Design Calculation Sheet
mtx
adhesive
Liquid
VG;o;itrt
PJ. (Pumping
Temp.)
938
\/.^^r
at PT
qn ^;aee,,ra
/_ I .r PT
^r
rioriat ihbient temo.
Operating flow at
08
cp
.1.537
PSla
-
not
lEn
j:X
PT.
{^n,.r PT
YI:
150
Suction
-
APr line loss
Suction pressure
-
=
4.0
psi
2.O
psi
Static tift
- aPr discharge
Piping system
Other
Discharge press.
Suction press.
psia
8.70
psra
Vapor pressure
=
NPSH avail
NPSH avail
NPSH req'd
Terminal pressure
psia
14.7
Source* pressure
Static + (headlift)
8.70
psia
6-90
ft
ft
ri na
=
-
TDH
TDH
=
=
16.70
2g.g1-
=
=
=
psia
psl
13.74
psi
psi
53.75
psia
-8.70
psia
67.58
psia
feet
2+2=4ltrcqulred
lrin NPSH avail > NPSH req'd + 2 lt
(oom)ffDHX'v)
..
bnp"c = :(38;bX4-
bhp at Duty Condition
nr"^ _
* (150X67.58X1.537) = n =
(3,960Xrr) (3,s60X10)
(gpm)CrDHXr)
3g.g4o/o
TDH = total dynamic head
TDH = discharge press. - suction press
4 = pump efficiency,
bhp at Maximum Capacity Condition
o/o
Figure 6-42. Pump hydraulic design calculation sheet for Example 6-2.
We now refer to the manufacturer's performance
curves which, in this case, are rated to the viscosity of
the service fluid. The closest curve is that shown in Figure 6-41. As a starting point, it is always desirable to
start at the middle of the curve. Extreme ends of any
pump performance curve should be avoided, as the
pump's performance varies significantly at either end of
the curve. Thus, we select a very common speed for this
type of pump-155 rpm. Now for 150 gpm and 62.45
psi TDH, we find that we need approximately an 1l-hp
motor. Solving for the pump efficiency we have
bhp = Q(rDH)"y
(6-2)
(3,960)rt
Thus, we have
(150X93.76X 1.537)
,, _
'
(3,960)(10)
:
0.496
or
49.6%
This efficiency rating is quite common with a rotary
gear pump handling a highly viscous liquid. Now, refer-
ring to Table 6-4 one can observe the classifications of
electric motors. From Figure 6-44 we see that the viscosity of our fluid, 1,460 SSU, is about mid-way between
the two curves shown. Thus. the required horsepower is
between 8 hp and l0 hp. Looking at Thble 6-4 we see that
electric motors are lUz hp and 10 hp. To meet our requirements, we select a lO-hp motor, because 7llz hp is
too small. Notice that the pump has built-in jacketed enclosures to match the piping, which is hot-oii traced, to
keep the fluid in the piping and pump liquid. These jacketed systems are discussed in Chapter 3.
In this problem we have a suction lift on the suction
side of the pump. It is important to remember that the
theoretical height to which a liquid can be lifted at any
specified temperature is the atmospheric pressure at the
installation site minus the vapor pressure of the liquid at
the specified temperature minus the friction loss in the
piping. The theoretical and maximum suction lift for water is shown for various temperatures in Figure 6-14. For
non-volatile liquids, the maximum allowable suction lift
should never exceed 15 in. Hg (7.4 psia) under ideal
conditions. For volatile liquids, the maximum allowable
Mechanical Design of Process Systems
Complete jacketing ol
casing, head and rotor
bearing sleeve for
heating or cooling
liquids.
Hich ten
Dronze
for long,
rugged
service.
on head for handling
hot liquids.
Figure 6-43. The type of gear rotary pump selected in Example 6-2. (Courtesy of Viking Pump Division, Houdaille Industries,
Inc.)
Rotating Equipment
Figure 6-44. Rotary gear pump performance curve. (Courtesy of Viking Pump Division, Houdaille Industries, Inc )
suction
lift
should never exceed 10
in. Hg. If these val-
ues are exceeded, then the suction source should be pres-
surized with a neutral gas (inert nitrogen) to offset any
pressure that may fall below the vapor pressure of the
liquid. At the liquid vapor pressure, vaporization occurs,
resulting in possible cavitation and pump damage.
A Word About Prlming
A positive-displacement pump, like the rotary gear
pump in this example. must be primed when pumping
low viscosity liquids. This is done by a vacuum device or
by using a foot valve. Also, with a low viscous liquid,
the fluid drains back to the suction when the pump is
idle. For a viscous liquid, like the one in this example,
the liquid is retained in the rotary gear clearances and
thus acts as a seal when the pump is restarted. However,
before restarting the pump, the liquid being pumped
should be introduced through the discharge side of the
pump to lubricate the rotating components.
Since the coating mix is not a clean service, a centrifugal pump is impractical because it cannot handle a nonNewtonian fluid containing suspended particles.
EXAilPLE 6-3: CENTRIFUGAL
COiIPRESSOR SELECTION
A centrifugal compressor is to be specified for a gas
plant, which is at sea level. The unit is to compress 3,000
lb./min of gas mixture at 50 psia at 60'F to 150 psia.
The gas mixture is composed of 40% ptopane,3O%
ethane, and 30% methane.
The reduced pressure, P", the reduced temperature, L,
the molecular weight, and the specific heat of the mixture is determined as shown in Table 6-5. Using the data
in the table we calculate the ratio of specific heats for the
mixture as follows:
c-.
cp. - 1.986
13.08
13.08
-
1.986
(6-10)
=
1.18
The compressibility factor for the mixture is determined from the reduced pressure and reduced tempera-
ture. Thus.
Mechanical Design of Process Systems
80
Table &5
Tabulation of Gas Mixture Properties
Mol
Gas
Propane
Ethane
Methane
o/o
P"
(psia)
t" ("R)
Pc
40
44.t0
616
666
.64
246.q
30
30
30.07
708
668
550
9.O2
212.40
343
4.81
31.47
20Q.40
16.07
17
Gas Mixture
659.20
266.40
165.00
102.90
534.30
6.86
3.68
2.54
13.08
Table 6-6 16l
Typical Centrifugal Compressor Frame Data*
Nominal
Nominal
Nominal
Nominal
Nominal lnlet Volume Flow
ffi (icfm)
Frame
(m3/h)
l,000-7,000
B
6,000- 18,000
13,000-31,000
D
E
F
*Wite
23,000-44,000
c
33
,000- 65 ,000
48,000-100,000
this table is based on
P
.D
50
a
(lt-lbl/lbm)
1,700-12,000
10,000-31,000
10,000
10,000
22,000-53,000
39,000-75,000
56,000-110,000
r0,000
82,000- 170,000
534.30
:
4.97 3
:
:
rp^ :
10,000 ft-lbfnb.
76%
|,370
150
50
(6-14)
(6-61
-
460.)
1O,339.276 icfm (or acfm at the inlet)
7,700 rpm
54
an, machinery duplicating this table woud be purely coincidenml.
t1
Using Table 6-6 from Lapina [6], we find our unit to
he a Frame B with nominal values to be as follows:
N"
914
1,120
Thus, we have
Now from Eouation 6-32 we have
n-r /r- r\
T=\-o
1"
From above,
kr
Hp"
44
factor
- ,mRt,
----"
V:
(mw)Pi
:
30
36
406
584
:
-
Y
l6
(mm)
l), we can use
Assuming that we have a perfect gas (z
Equation 6-14 to find the average discharge temperature.
Using Equation 6-6 the inlet volumetric flow is
(0.972x3,000)( l.545x60
(144)(31.47Xs0)
78
78
^'' P,
Pr
: 0.972: inlet compressibility
,,
77
77
30
(in,
l l,000
7 ,700
5,900
4,900
4,000
3,300
76
76
30
30
30
30
30
lmpeller Oiameter
Metric
English
Computing the compression ratio we have
Now from Figure 6-45, we have
zr
(%)
Speed
(rpm)
(k.Nm/kg)
survey of currently available equipment, the instance of
:0.076
60 + 460
Rotaiional
Efficiency
10,000
10,000
10,000
659.20
t
Polytropic
ltp'
:
l'18
= 0'76
Thus,
18\
l0
r0.i6l
u.18/
-
0.116
Rotating
t?
=
0116
tr(C " :
(60
+
460X3.0)
zz
:
0'93
or
t, :
590.68'R
:
v-22
=zt
130.68'F
Now, the average compressibility for the gas mixture
must be obtained. From above the inlet compressibility,
zr :
81
Using the compression ratio and pressure ratio we determine the outlet compressibility factor from the compressibility charts in Appendix E. Thus,
from which
n-I
Equipment
!
zz
_0.972 + 0.93 _ 0.95
In determining the polytropic head we use Equation 633, where
0.972
Compression ratio,
p-
rc^r,=:j:
P,
'-"
150
659.20
=
Pz=Pa
O.228
of specific heat, k, is k = 1.18 =
inlet conditions, which is an approximation. Thus,
and the average ratio
Temperature ratio,
' = (-*-) (*,{,) [[&J-"*-" -'],u
,_,
_tz_560.68 _ r
trR,2-L-534-30-'"^<
f- compressibility tactor, Z =
1.00
PV/RT
\--
---1
------J
NS
\
N \s
iK
(\
S
\
\-"%_
=
0.94
\*r-1
\l
I
Y
x
\
'1 0
-tl =
riP{
N
ilxl/-
-x
-0.85
BO
\t 'oS
= 2.00
1.60
401
-t
-'----
x
'r;{
I
-->
=
><
\
ii(
0.60
(6-33)
>i
*al
\"'r
\
\
0.92
\
0.91
0.01
0.02 0.03 0.04 0.05
0.06
reduced pressure, Pr
0.07
0.08
0.09
Figure 6-45. Compressibility curves for very
low values of reduced pressure. (Reprinted by
0.10
permission of Chemicql Engineering, McGraw-Hill Company, July 1954.)
a2
Mechanical Design of Process Systems
from which
r:
H=
Thus,
[(t't31srq'01
(8.62r) r(3.0f ,,6
-
*- ='ni?l lo' -
r]
29,913.143 ft-lbr/lb.
N:N"l '
by
II
:
maximum polytropic head per stage,
(see Figures 6-46 and 6-47)
tttm'ntl I
^ [t26.
L krzrrr I
L(
=
ft-lb/lb.
^"
r.t:
tzo.
r
lt: r .+zr I
)(0.972)(520t
| . t8
P,r
(6-69)
7
l3l
rpm
rir
H.
'
33,000
:
(3,000)(29.913)
4o
(33,000X0.76)
3,578.11 hp
Using Table 6-7 to determine the mechanical losses,
we find that
1.377
:
Il,:-"''
rqqrr lo'
| r t.ooox r)l
The required shaft power is
L. :
From Figure 6-46,
He.
(6-10)
I
\Ho. N.J
Lr
Using Table 6-5, we have
0
I u
..P \05
N = r7 TOOr
(6-68)
-q
where Ho.
3
The required rpm is
The required number of compressor stages is determined
:
N.,
'.H-
2.ite =
11,000 ft-lbfnb.
(0.02sx3s78.11)
(P.rL"*r
:
P.r
+ L.
:
:
99.453
3,578.11
12,000
11,000
10,000
6:
I
limit for miled yield
9,000
slress mpeIers
8.000
I
lNTuw
ltl
I
7,000
6.000
E
5,000
4,000
3,000
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
2.1
0
Figure 6-46. Maximum polytropic head per stage-English system [6].
L.,
ta
+
89.453 :3,667.563hp
Rotating EquiPment
trl
Eru
=32
ot
928
u=@
v krzlTt
ttl
- I'n,J,,'*Lon"N
slress impellers
Ezc
e20
o
.-
16
5rz
'i^
't.0 1.l
1.2
1.4
1.5 1.6
1.7
1.8
1.9
0
Figure 6-47. Maximum polytropic head per stage-metric system [6]'
Table 6-7 [61
as a
Losses
Approximate Mechanical
Percery
Mechanical
Losses,
Metric
(kw)
English
(hp)
3
0-2,500
0-3,000
2.5
2
2,500-5,000
5,000-7,500
3,000-6,000
6,000-10,000
10,000+
L,'n
(ohl
1.5
7,500+
nents.Thistablewitt'howewr'ensurethatmechanicollossesareconsideredandtiea
uselul valuas
for estittutinS purposes.
The discharge temperature becomes
tz
= rr(C ("
')/"
=
(520X3.0)0.r'6
:
590.68'R
tz:130.68'F
This example demonstrates how centrifugal compressors are estimated. The reader should be cautioned as
when to use inlet values for the values of k and z. The
value of k will decrease during the compressron process
and calculations for the polytropic head and discharge
temperature should be made with average values of k,
including single stage compressors. Compressor manu-
facturers use the inlet values at each stage of compression, but the inlet values for each stage wi1l be different.
In calculating the polytropic head, the inlet value of k
can be used to achieve an approximate value of the head
with some error, because the polytropic head is insensil).
tive to the value of k and thus n/(n
-
The discharge temperature is much more dependent on
the value of k. Using the inlet value of k will yield a conservative value of the discharge temperature, generally
25-50'F in extreme cases.
For a more detailed discussion of the specification and
design of centrifugal compressors, the interested reader
is referred to Lapina [6].
Mechanical Design of Process Systems
84
EXAMPLE 6-4: INSTALLING A
COMPRESSOR AT ELEVATION
8p00
A reciprocating air
compressor is to be installed in a
food processing plant, which is at an elevation of 6,562
feet. The desired capacity is 33.3 m3/min. The machine
to be used is to be refitted and is of Polish make. From an
elevation-barometric conversion chart, such as Figure
6-48, we determine that the atmospheric pressure at the
site location is 11.53 psia. The compressor is to compress the air to 7 atmospheres, or 102.87 psia.
Now,
r' /^- ^. . rP\
",1 :
v : 33.3 rmtn
l3s.314
\
m"i
2,000
t4
t3
t?
tl
Alfr o3ph.ric Pn33ur., lb./sq. in.
Figure 6-48. Atmospheric and barometric pressures at various altitudes [7].
I.175.96 cfm
Compression ratio:
For a multiple stage unit, the compression ratio is
Pr
=
11.53 psia
Pi
:
102.87 psia
C-
:
t02
I
g
l.)J
:
Cnr
= 8.92 > 6. thus requiring
Crz
LD
'', : iP.
wnere
D.
With an intercooler, you must consider the gas pressure drop across it. The minimum horsepower is developed when the ratios of compression are equal in all cylinders. The ideal case is with no intercoolins in which
Ludwig [7] suggests
Pr P2 P3
_
Pa2_
-z
p.
cD'.J
(6-71)
: --:l
Dl
^n
Pn-r
Po3_
p:
rol
P,
P"
D1
'o.-l
Thus, for two stages,
and with intercooling,
Po1
(6-73)
p.
two-stage
compresslon
Pr=Pr=&:...:
- CR3 :.-":[bJ
/P.
Pr.
n -P__,'-4- 4-'
(6-'72)
where subscripts 1,2,3, ..., n
subscript d
prime
:
:
(') :
\0.5
t_,21
LRI : LR2 : l;l
\r
(6-74)
l,r
gas conditions across a cylinder in which I represents
the first stage, 2 represents
the second stage, etc.
Thus, the compression ratio per stage is approximately
interstage discharge pressure condition, directly at
the cylinder
represents the actual pressure to the suction of the
succeeding cylinder, which
and for the
CR:(8.92)05=2.99
Pr
:
Pdr
first
stage,
11.53 psia
:
(2.99x11.53) +
rs the interstage discharge
subscript
f:
condition that is reduced bY
pressure drop over the intercooler system
final discharge pressure
from a multistage machine
5
i
=
36.94 psia
For second stage,
Por
=
(2.99r(11.53)
- i:
31.97 psia
Rotating EquiPment
:
Pr
102 87 Psia
The discharge temperature the first stage is by Equation
6-5s
ta, :
bho
'
=
l ','lu" /
\ l.u x '=.
-. 11.203,486.3721 l
(69.6)
Total horsepower
:
=
ttFJ?
for
k=
tu,
:
(85
:
287 94"F
83 763 hp
+ 83.763
182.669 or 183 hp
98.906
Equation 6-75 is based on a given compression ratio,
Cp, 6rake horsepower/ 106 ft3ld at 14.4 psia and suction
ternperature. F,s is a constant which is a factor for the
specific gravity of the gas.
1.406,
+
=
460)(2.99)0'?8e ='147.94"R
or
tnt
60
based on the discharge temperature from the intercooler.
The intercooler cools the air to 90'R which is the suction
54f
:
tr2 :
tiiR"G tvr
=
(90
+
460)(2.99)0 287
:
48r
46r
754.80'R
pressor size is to use the "horsepower per million"
iurves depicted in Figure 6-49. The "horsepower per
million" ii the bhp/MMcfd and is used to determine the
horsepower per stage by the following relation:
rr:#:b(MMcrd)F,,
(*)
=
(r.r75.e6){60x24)
:
I,421,068.508
:
(6e.6)
=
('-lr;(14_:#.
J
(
Hi+Hfl
:
ll-
/,,/'
"'l
I
30
l-
28f
26
lllllll
Ratios below 1-4 are subiect
v
manufacturer foa best dala.
ttttttl
l-
24Y
22u
lo
signiticanl etror, consult the
1.5 1.6 1.7 1.9 1.9 2.0 2.1 2.2 2.3 2.4 2.5
Ratio of comPression
Figure 6-49. Power requirements for reciprocatmg compressors. (Courtesy of Ingersoll-Rand Company.)
q:
e8.eo6 hp
/,, ..\
t.421.068.s08\j-r:)
:1,203,486.372
3o
7/.,
69.6
'
For the second stage,
MMcfd :
36
(6-75)
where F"n is determined in Figure 6-50, converting the
acfm to MMcfd we have
t
40l*l
9
i.?_
2
Ml
A reliable and quick method to approximate the com-
z
.
$
o2l
For the first stage, F.,
'14.4 psia
50|.-
Selecting the Reciprocating Gompressor
bhp
to
Gas ref(
1
294.80"F
MMcrd
(
521 intake I
temperature to the second stage. Thus
kz
l:
ical efiiciency, 95j
58fiMechan
through valv€
Gas vek
561- :3,000 f 'city | (APl equat( rfll
The discharge temperature for the second stage is
I
1f9_!Jl)
_
touo
uu /
0.60
1.5
2.0
2.5
3.0
Ratio of compr€ssion,
Figure 6-50. Horsepower correction factors for specific grav-
ity [8].
86
Mechanical Design of Process Systems
Next, the cylinders must be sized. This can only be
done after the interstage temperatures and pressure are
defined . Because of the clearance required to allow operation and permit the provision of passages, the piston
does not sweep the entire volume of the cylinder.
Thus, the actual cylinder capacity is lower than the
displacement of the cylinder. Relating this in terms
volumetric efficiency we have
o
(6-i6t
LD
where 4"
Q
Cp
:
:
:
volumetric efficiencY
capacity at inlet conditions, acfm
cylinder displacement, ft3/min, where
= I4*l
I \121
""" \ 144",)E'|"
where L =
:
A"" :
,46"
N:
A
of
(6-77)
piston stroke, in.
ar€r of head end of piston, in.2
area ofcrank end piston (,46" minus the area
the piston rod), in.2
of
Ipm
where
- .. [eU:l
I zdtzs I
C"
Cp
:
:
(6-78)
cylinder clearance
compression ratio
ratio of specific heats
colllpr€ssibility factors at the suction and discharge conditions, respectively.
k=
2., za =
For our machine we have the following design:
L = 220 mm :
in.
9.661
- 500 rpm
Dr : 500 mm :
:
For the second stage,
piston rod diameter
o,. =
piston stroke
:
:
" (";t")'
10e.563 in.2
convenient formula recommended by Neerken [8] is
n. = o.si
,2.]2t )lr uu'),roo,
.."\= lrogL:t44
: 1,512.514 ft3lmin l\t2 I
_
60 mm
:
2.362 in.
roe.563 in.?
*(.9)'
,n.,
:
105.181 in.'z
+ ro5.r8r 'l
c":l 10e.563 r44
{gjutl ,roo,
l\ t2 I
:
538.165 ft3/min
The volumetric efficiency is approximated by Equation
6-76 as
n, = o.si
-
(0.lr)[(2
ee)'i -
r]
= 0.81i :8t.iEa
This analysis is only a preliminary estimate of what
the compressor design is to be, although in this example,
data is drawn from an existing unit. The actual selection
of a compressor can only be accomplished using the
manufacturer's data on such items as piston displacement
and the volumetric efficiencies of the cylinders. The
manufacturer's data should always be used before attempting a final design. The actual unit in this example is
similar to the one shown in Figure 6-51 .
A more detailed discussion on how to specifr and design reciprocating compressors is given by Chlumsky
t5l.
N
19.685
in. =
diameter of first stage
cylinder
Dz
:
300 mm
=
11 .81
1
in.
:
diameter of second stage
cylinder
For the first stage,
:
=
65 mm
/r o <rs\t
r l'- """1
=
304.341 in.2
-
&.
:
\21
304.34r
/r
sso\'
- " \;)
=
A cosmetic manufacturer of women's lipstick contracted a chemical company to formulate a chemical that
satisfies certain specifications. The chemical process engineers determined that
piston rod diameter
A,- =
EXAMPLE 6.5: NAPHTHA PUMP SYSTEiI
DESIGN
2.559 in.
2ee. re8
in.'
a light cut of naphtha would
make an excellent base for the lipstick. The pump in this
application can also be used to supply the naphtha to a
small chemical company nearby for manufacturing paint
thinner. This second application is called the "maximum
capacity condition" and will be discussed after the pump
is sized for the first application. The pump must be sized
for both
cases.
Figure 6-51. Two-stage reciprocating compressor with a shell and tube intercooler. The first stage is achieved with the vertical
.yiinder and the seconl stagi with tiie horizontal cylinder. Pistons of the first stage are aluminum and the second stage are cast
iion. (Courtesy of Zaklady Budowy Maszyn, Aparatury im Szadkowskiego, Poland )
In the first case, a rail switcher transports the naphtha
to the chemical plant from a nearby refinery The plant
only needs to send one 50,000-gallon railroad tank -car
once every four months to meet the cosmetic manufacturer's needs. The light naphtha cut is 68"API. The task
is to design a pump and hydraulic system that will store
and transport the naphtha according to the configuration
shown in Figure 6-52.
The reservoir is large enough to consider the fluid as
having a constant head. The plant manager estimates that
the naphtha head required is 12 feet, but wants to have it
resulting in a colorless liquid. Next, the naphtha is processed through an activated charcoal filter to remove the
fuel odor. Finally, the finished process liquid is loaded
into the 50,000-gallon tank car.
In the petrochemical industry, the specific gravity of
petroleum is given in terms of hydrometer termed 'API.
The relation for API is as follows:
"4p1 =
(6-79)
^tp
7w
evaluated.
The basic process involves the naphtha passing
throush a scrubber that contains caustic soda (NaOH).
The ciustic soda removes the straw color in the naphtha,
141.5:131.5
where
:
l* :
.yo
the specific gravity of the petroleum product at
60"F
the specific gravity of water at 60"F
Mechanical Design of Process Systems
88
NLL = normal liquid level
9"
g', g',
$+-Llj
g',g',2,-O,g', 9"
5',-O"r
_L
Figure 6-52. Pump-piping scheme of light naphlha cut used 10 manufacture women's lipstick. (Example 6-5).
'API, temperature is given
of
in Figure 6-53. For our case 68oAPI, using Equation
6-79, we have
The Flow from the Reservoir to Naphtha
Storage llank
ro:141 5:
7* 199.5
in which 7o :
of liquid is
The relationship between the
o.zo9
(0.709)(62.4)lb/ft3
:
44.26lbifC at 60'F
The maximum pumping temperature is controlled at
90'F. The coldest pumping temperature is at 34'F Since
the density is higher at the lower temperature, that is the
one used for frictional pressure drop calculations. Thus,
referring to Figure 6-53
"Yp
:
0'13
45.55
Dresslon:
o
:
rr.os
o'(\)"
(6-79)
The velocity heads on the line from point @ to point @
are as follows:
and
p:
The reservoir is of such large magnitude that the head
considered constant, because the railroad
switch engine delivers the naphtha regularly to the plant.
The flow rate from the reservoir to the storage tank in
gallons per minute is determined from the following ex-
lb/ff
Values of f1 are determined from Figure 1-7.
Rotating Equipment
Entrance:K:0.78:0.78
18 fr : 18(0.017X2) : 0.612
2-4-in. plug valve: K :
Q
:
1e.65(4.026)
APr
Exit:K:1.00:1.00
sr- :
LtK 2.392
:
[rrrt*J"
177.2
12
x=
38
sec
p
3.900 psi
10.5 psi nitrogen pad
)
10.5 psi
6.60 psi
=
20.308
ft
:
ft
12.35 psi
-
:
1.223 psi
I
l. 127 psi
>
10.5 psi
The new flow rate is
(1!4|-(a.a67;x A(45.ss)k
=
lb.
2.640
-
:
:
Adding an additional 26 ft of head we have
ft
:::-
DVp
<
x + 3.90
0.0884 ft,
-.
l\Re :
ft of naphtha head = (12X0.325) psi
This pressure differential will cause the naphtha to be
forced back into the reservoir. The number of feet required to deliver the liquid to the tank will now be determined. Since we already have 12 ft in the tank, then
wm
o
4.46'1
1.223 Ot'
3.90 psi
4 lb./ft-hrl :
lb^
'a = r. r co'\ [2 lcp / z.u ft-hr
:
:
I
I
hr
ft-hr \3,600
Q
:
1e.6s(4.026)
(#r)0' :
315.317 gpm
I
sec/
f l rnin I
\oo r""/
93,088
0.0884 ft,
Using Np" to check the friction factor,
r-05:
(rgl*
(1-6a) Nr": \ul
-2r"r.[+. rt=*)
(7.e48rx
tb
=
'7
.948
sec
a
r" :
secr+s.ss1$
- - ft-hr lt*
-"*n
\:.ooo
165,633
\
sec/
2.51
(93,088)(0.17875)
f:
Applying Equation l-6a,
r.-"1
0.03198
ft
aP. = l(o.o3l9x1o5.83)
Now,
t--
,,,
4.026
t12J
l- x.l4I
| 16
I
aP,' = ILL
+H
t.t
\s
\
||
(1-4)
t(Hft
I
(4s.5s)k $.46if
##j
fr-lh
SeC"-lDf
f:
+
0.0319
2.3921
|
I
-n
'Etc
o,,: [rr1*opu"' * r.,nl
-
rrelr' ft-lb.
SeC'-lOf
AP1 :
38
ft
3.364 Or'
-
APr
8.486 psi
<
=
12.35 psi
-
3.864 psi
10.5 psi pad
Select a 6-in.
{
fi
-:-
Sch 40 pipe
:
8.486 psi
90
Mechanical Design of Process Systems
To determine the flow rate we must consider what the
system is to service. Plant operations dictate that the
loading of the tank car must not take longer than four and
one-half hours. The rail tank car capacity is 50,000 gallons. We select 4.35 hours, which yields a flow rate of
Repeating the hydraulic analysis we have
2-6-in.
e
:
{
plug valve:
1e.6s(6.065) (,
K
Entrance and exit: K
18 fr
18(0.015)
:
:
or--)"
=
:
:
Dr :
1.78
0.27
z.oso
s9.990 eat
513.107 gpm
-
\ 12,----7------
--
re | .57
0D(#(*J
-
a4
1'79 0L')
-
(0.0884)
:
[]-::Yl(a.8a)(a5.55)
N*"=''-';
f:0.01803
t
:
r
2.6401
rll
ssxs zot'?\r++/
^.^lt+s - ffiAPr:l l(0.0r803x105.83) -r, ^-.U)Urz\rz'z
APr
= re2 spm
will size a centrifugal pump
192 gpm,
,r,
lll
t*tr-oj
Ir
r
with 192 gpm capacity. For
sec
19'ut\,r.rouo,
rr ne
:
We
fr
5.700--
0.2006
hrs {+!!)
\60 min/
4.35
l6.o6sl
I
I
\-rzl
I
f+
I
:
0.032 (from Equation 1-6a)
./ r\
l.---.
tt'd'*l@
r
38 ft - APr : 12.35 psi - 0.930 psi :
11.42 psi
>
10.5
pst
So there is 0.92 psi (11.42 - 10.50) net positive pressure head of naphtha entering the storage tank.
or,-ll+.oze\
- l,o.orrt,zr.rtr, * ,.rrnlI
|
t I
I
I
't
APlo
For a 3-in. Iine,
_
-
Suction Line
:
23.313
2(32'2\
= 9.5110t'
Naphtha Pump Hydraulics
L
:100.863
\3,600/
9.939 Ot'
For 4-in. Sch 40 portion of line,
i
4.84 ftlsec
L:
1.0
,rnr,l-l\[)
\7.47e1
\601
(0.0s130)
ft
-
8.34 ft/sec
ft
3',0168),s.:0,,+s.:s,
K-Values
Entrance and exit:
1-4-in. plug valve:
4-in. x 3-in. reducer:
K : 1.75
K : 0.306
K=0.163
srLtK
=
2.219
For 3-inch Sch 40 portion of line:
K-Values
(18)(0.018) : 0.324
3-in. diffuser: K:Kr:0.055
3-in.d plug valve: K
4-in. x
:
D*-*"
|
tl".: I}-
1
2.6401
..
=
t32.449
I
\3.600/
f:0.0344
re,.'' =
APi.
=
t ol'l4t(t or
la5.5sl,t.r,'(,;)
o
3791l(o
lr /r.oos\ r| 2\32 2)
\,2/
9.175 ntt
Rotating Equipment
The total pressure drop for the suction line
AP.
=
APlo
+
APr3
:
:
AP,
,0,,0, ,r,
i1,uti,,
I 1)
|
N^".'"-';
-ttl
0.686 Psi
i
z
60.708
ft, 4-in.
rl
Sch 40
aP,, :
l(o
: 170
: 0.136
4-4-in. plug valves: K : (4X18X0.017) = 1.224
5-4-in. std 90' elbows: K = (5)(30)(0.017) : 2.550
1-4-in. swing check: K: (100)(0.017)
1-4-in. gate valve: K : (8X0.0i7)
Entrance:K=1.0:i.00
D" :
o^oto
t*. = E*'
AP1,
:
APp
=
AP1,
I
too.8b3
l(o
:
ol2'(6oi7o8)
|t 14.0261
I r?
select
+ o.oro
2(32.2)
r
: | 42'7 + 0 460 :
-
APo
1 887 psi
+x+
friction
static head (psi)
oressure
\ = i/ tiquio uupot
x
:
\preisure
'i
rpsiarJ
minimum pad pressure required, pslg
20.85
+
21.361 psi
x = Tpsig
Referring to Figure 6-55 and 6-56, we re-evaluate the
pump performance. Since the light naphtha cut has a low
viscosity
1.427 Ot'
For the 3-in. portion of the discharge line,
For 3-in. Sch 40 pipe, d1 3.068 rn.
:
K-Values
4-in. x
34r(*)
I
14.7+x+3.557:0.511 +
|
APlo
o.e43l
line tAP.rf
\arop on suction
I
where
ar,, =
+ APi.
/
=
0.032 (from Equation 1-6a)
t
*
5r(8
The total pressure drop for the discharge line
\3,600/
:
(45
0.460 Psi
ATM. pressure (psia)
s+x+s.ssr
2.6401
f
934'(i
o)
From Figure 6-54, the pump hydraulic design calculation data sheet, it is obvious that the available NPSH is
much higher than the required NPSH. This means that
the 10.5 psi pressure for the nitrogen pad is excessrve.
The minimum pad pressure required is
(0.0884)
026'1,+.
roo/
It lr.068l
I 17 I
K-Values
14
132'449
fi = 0.0344
Discharge Line
L=
e+o[3
=
Entrance:
3-in. reducer:
K
:
0.780
K:0.163
DK = o,sa3
L
:
3 ft.
bhp
:
bhe
-
QHr
(6-2)
3,96Ou
(19?)(6172)(9 73)
(3,960x0.61)
= 3.i
or a4 hp motor
The Maximum Capacity Condition
The small chemical company nearby that manufactures paint thinner needs the naphtha only about once a
year. However, when the naphtha is needed, it must be
delivere.d quickly. Consequently, delivery time is crucial
to the client.
Mechanical Design of Process Systems
Equivolents of Degrees APl, Degrees Boum6,
Specific Grovity, Weight Densily, ond
Pounds Per Gollon ot 6OF/5OF
Degrees
Values for API Scale
API
oil
Baum€
Scale
!peci6c
Values for Baum6 Scale
Liquids Lighter Than water
W€ight
Pounds
LblFt3
Gallon
D€nsity,
per
6
8
,,.
'.:
,.oooo
l8
0.9861
0.9725
0.9593
0.9465
61.50
60.65
59.83
59.03
0.9340
0.9218
0.9100
57
0.E984
56.03
20
22
'),4
'].6
28
0.8871
30
0.8762
32
0.8654
0.8550
0.8448
34
36
38
40
42
Lb
8.337
a.xll
8.108
.998
.891
7
7
.043
6.960
0.8235
0.8140
0.8046
0.7955
0.7865
0.7883
49.
50
0.7796
48.62
48.09
47.57
47 .07
46.57
6.499
6.429
0.7778
0.769X
6.359
6.292
0 .7
0.7389
0.7313
0.7238
46.08
45.61
6.160
6.097
6.034
0.7165
5.973
70
0.7022
0.6953
43.79
43.36
42.94
0.6E86
78
80
a2
84
1.1789
0.8537
0.8434
0.8333
6.646
0.7093
l.1600
.679
7.579
7.48X
7.124
0.8642
49.7?.
68
.781
0.8750
o .797
44.64
44.23
7
7
.305
6.799
45.14
1.1069
1.1240
7
6.879
5E
.994
.886
0.8861
5l .46
0.7547
0.7467
8.105
7
7
.396
0.81 55
o.7624
60.63
59.80
58.99
7
0.8251
54
l.o74l
56.70
0.E348
o.77tl
8.337
6t.49
0.909r
0.4974
7
l6
oa.s
7.587
7 .490
52.69
52.06
t
''.
1.0140
1.0284
1.0432
1.0584
58.20
.787
0.8063
7X
Gallon
Specific
Gravity
Weight
Density,
Lb/Ftx
0.7609
527
0.7447
E.Zt9
7
54.57
53.90
53.L4
5L.60
.387
.295
.205
7.117
7
7
7
.03r
5t.97
6.947
50.76
50.18
49.61
49.05
6.786
6.708
48.51
47 .97
47.45
46.94
46.44
45.95
45.4E
45.00
5.913
0.7368
0.7292
o.7216
0.7143
o.7071
5.854
5.797
0.7000
0.6931
43,66
43.22
42.40
42.34
41.98
0.6E63
7E.64
80.03
8t .47
42.96
.29
10.512
10.698
10.891
1r.091
11.297
1.3810
| .4078
86.13
67.80
89.53
91.34
|.4356
11.513
11.737
11.969
12.2rO
12,462
I1.64
14.924
r
14.46
t5.302
1.EE31
t17.44
15.699
1.9333
120.57
16.118
5.836
5.774
5.722
5.666
39.84
39.4E
39.69
39.33
38.98
5.306
5.274
5.096
1.2609
1.2832
1.3063
1.3303
77
I
5.454
5.404
95.
1.5591
97
5.506
s.ttl
3E.63
34.29
37 .96
75.99
1.7901
0.6482
5.r41
1.2185
1.2393
9.828
9.990
10.159
10.332
I . E354
5.424
5.186
1. 1983
6.016
5.955
40.80
40,42
40.05
38.79
38.45
38.12
L67r
73.52
14.22?
o.6542
39- 13
9.518
106.39
108.95
5.474
0.6275
o.6120
0.6166
0.6112
9.371
7r.20
1.7059
1.7470
41.58
0.6364
0.6306
0.6250
0.6195
0.6140
0.6087
l.t4t7
9.XX8
6.079
6.143
0.6667
0.6604
0.fl3r.
70.10
13.895
6.209
4t .72
41.33
40.95
40.57
40.20
0.6388
8.955
9.0E9
13.244
r3.583
0.66S0
90
92
94
96
98
100
66.99
67 .99
69.03
4.8L4
12.998
0.6731
0.6422
4.697
99.37
101.60
103.94
0.6796
0.6446
65.06
66.01
1.5934
1.619L
1.6667
42.12
88
8.337
8.454
8.574
l9
.2]
47..53
E6
1 0902
6.484
6.413
6.344
44.10
4t.19
62.36
63.24
64.t4
1.4646
1.4948
0.68r9
0.6754
0.6628
0.6566
0.6506
Pounds
per
Gatlon
.s
0.9333
0.9211
7
,87
54.64
1.0000
0.9859
4.9722
0.9589
0.9459
46
48
64
66
/Ft3
Pounds
pef
','
50.86
50.28
60
Weight
Density,
r.0000
l0
t7
I4
Gravity
s
s
0
2
Specific
Liquids Heavier Than Water
5. 1r9
..'
,'.
Figure 6-53. Relationship between 'API and temperature. (Courtesy of Crane Company.)
'..
Rotating Equipment
Pump Hydraulic Design Calculation Sheet
Light Naphtha
Liquid
Viscosity at PT. (Pumping Temp.)
Vapor pressure at PT.
Sp. gr (-y) at PT.
Flow at ambient temp.
Operating flow at PT.
Design flow at PT.
Cut-68'
API
_cp
'1.1
psia
20.85
0.73
gpm
't92
't92
gpm
gpm
Discharge
Suction
Source pressure
Static head
- APr, line loss
Suction pressure
-
Vapor pressure
NPSH avail
NPSH avail
25.20
Terminal pressure
Static head (litt)
APi discharge
Piping system
Other
Discharge press.
Suction press.
psra
psi
-
=
=
0.51 'l
28.248
20.85
7.398
-
1.3
NPSH req'd
-
psi
psia
psra
psia
-
ft
ft
psra
=
=
=
=
6.313
psi
1.887
20.o
44.90
psl
psl
psra
28.244
psia
psia
feet
bhp at Duty
onpo
=
Condition
bhp at Maximum Capacity Condition
Q{l(IPr)1!
(3,960Xn)
onp"" =
QSTrylI1
(3.960Xr)
Figure 6-54. Pump hydraulic design calculation sheet for Example 6-5.
Referring to the pump manufacturer's pump performance curve, Figure 6-55, we see that approximately
400 gpm is the maximum limit. Using this flow rate we
re-evaluate the pump for the maximum capacity case.
Suction Line
:
APr,,
2.200 ps
For the 3-in. portion of the suction line,
u.- :
lq)
r8.34r
\t92l
**. :
= r7.37sa
sec
:275,e35
(,rr4) 032,44s)
Referring to previous calculations on the suction side
we have the following:
u.
From Equation 1-6a,
: {gl r4.84r = io.o8jl
sec
\tvtl
1n ORI
N^. : l',"i,'l r100.863) \ +.d4 /
f:
0.03395
It
I
210.062
From Equation 1-6a we obtain
f :0.0315
or,.
:
APr
o1le1'"'r * r,nl (4s.ss)(ro.osf(1-L;
[ro
2(32.2)
rffi
I
o:'n''lt o' * o rrnl
rffi
on,. = ['o
:
9.759 Ot'
AP,:APso*APi.
AP,:2.29*a.trt
AP,
=
2.959 Ot'
l
2(32.2)
I
..1
E
.z
=if,
=
(oEn
E
\J
ii
tal
2
ab
L,' 9
-r6
G+i
\r l,
,i
.2
H
...i
^
:>,
(J I +:
EE
O.;\
=!
c.r
Ei
(\t
l!,,
\J
9?ts
E ,6
tr!J
o.E
: R
.b
lrt.:i
9X
ttc
o ooooo
o @(o\fc\l
Rotating Equipment
Pump Hydraulic Design Calculation Sheet
Light Naphtha Cut-68o API
Liquid
Viscosity al PT. (Pumping Temp-)
Vapor pressure at PT
Sp- gr. (1) at PI
Flow at ambient temp.
Operating flow at PTDosign flow at P.T.
1.1
cp
psra
20.85
0.73
't92
gpm
gpm
gpm
192
'192
Suction
Source pressure
Discharge
=
21.70
3.559
Static head
=
APr, line loss
Suction pressure =
Vapor pressure =
NPSH avail
NPSH avail
NPSH req'd
-
psia
-
0.51
24.744
psl
psi
psra
-
20.85
psia
12.3
1.3
ft
1
Terminal pressure =
Static head
aPr discharge
Piping system
-
Other
Discharge press. =
Suction press. =
psra
-
tt
bho"
=
psra
psi
1.847
psi
psi
psra
24.744
psia
psia
leet
20.'152
63.77
TDH
=
bhp at Duty Condition
'16.7
6,313
bhp at Back-Pressure Condilion
(SPmXTDH)(?)
bho"" =
(3,960X4)
(gPm)[rDH)(?)
(3,s60)(a)
Figure 6-56, Re-evaluation of pump hydraulic design calculation sheet of Example 6-5.
Discharge Line
Referring to previous calculations on the discharge
side we have the followins:
v.
sec
(lryrt (100,863)
I' l4ql
\
/
: zto,o6z
12
AP6n :
I
--"-'--'\r44l
l,or.rrxro.oo,{*}
-^^+ 6.610l
[+.ozo\
IrrI
|
)
6.143 O.'
:
APo :
lgl(8.34):
\t>Ll
2(322\
AP6o
*
AP1,
=
6.143 psi
+
1.989 psi
3.132 ntt
Referring to Figure 6-57, we reevaluate the pump for the
maximum capacity condition.
Normally, we would use a 9.5-in. impeller, as indiIn
this case, being that the application is infrequent, we
keep the 8.Gin. impeller. As the flow rate increases with
the same size impeller, the TDH decreases and the required NPSH increases. As we see on Figure 6-55, the
available NPSH of 4.589 ft is slightly exceeded at 400
cated on the pump manufacturer's curve, Figure 6-55.
For 3-in. portion,
u, =
2(32.2)
I
J
APlr:1.939
ap,. _ l(0.031sx60.708)
-l
f:0.03395
APp
^".- ..^
(,1q; 032,44e) :275,e35
Al-h = l------l--------- + U,y4Jl
f:0.0315
t.^
:
II
,or.rr,,rr.rrrr(r{)
l(0.03395X3.0) ^ ^.^l
: {g} (4.84) = ro.o8l
\t921
N* :
*""
r7.37sa
sec
Mechanical Design of Process Systems
96
Pump Hydraulic Design Calculation Sheet
Maximum Capacity Condilion Reevaluaiion
Light Naphtha
Liquid
Viscosity at PT. (Pumping Temp.)
Vapor pressure at Pl
Sp. gr- (r) at PT.
Flow at ambient temp.
Operating flow at PT.
Desion flow at
cp
0.73
pT.
Suction
Source pressure
=
4no
4uu
gpm
Terminal pressure
Psia
psl
psi
Static (lifi)
APr discharge
Piping system
Other
Discharge press.
Suction press.
- 20.85
1.45
4.589
psia
psia
-
ft
ft
NPSH req'd
16.70
=
TDH
TDH
8.132
=
=
=
=
=
bhp at Duty Condition
bhp at Maximum Capacity Condition
ono"=9##
.
.
Psia
psl
6.313
-
psia
NPSH avail
NPSH avail
gpm
gpm
Discharge
21.70
3.559
- 2.959
Static head
- APi, line loss
Suction pressure =
- Vapor pressure =
psia
20.85
20.00
51.145
psi
psl
psra
22.300
24.845
91.282
psia
psia
feet
(oom)fiDHXr)
bnp"" = =.(3GbX4.
Figure 6-57. Maximum capacity re-evaluation of pump hydraulic design calculation sheet of Example 6-5.
gpm. It is suggested that a flow rate of375 gpm be used
to avoid cavitation. From Figure 6-55 the actual TDH is
TDH
:
34
ft
The required brake horsepower rs
..
'
necting the reservoir to the storage tank, considering the
pipe to be 4-in. schedule 40, is as follows:
(375 x34.0X0.73)
(3,960X0.65)
-
J'v'
,, _
(3?r
" -'
(ciL)(=*-] tl+tl
\min/ \7.a79 eau \60 sec/
0.0884
ft?
= 9.45j a
sec
ttv
:
A 4-hp motor is sufficient for normal and maximum ca-
2.640
pacity operations.
lb'
lnr
fchr
From Equation l-6a,
Re.evaluation of Reservoit Line
f-05
Since the nitrogen pad on the naphtha storage tank was
:
-lr"c. [+ .
decreased from 10.5 psi to 7.0 psi, we must reconsider
the line size.
With 38 feet of head in the reservoir, we incurred a
pressure drop of 3.9 psi, yielding an entry pressure of
8.5 psi. In the back-pressure condition, we need a flow
rate of 375 gpm. The new presure drop in the line con-
f:0.031s
*]-tt)
196,992
Rotating
k
From Equation 1-4 we have
aP.:lLL*rrl
\d -
or, =
m
Pv'
l2e"
1+s.ss1
:
mw :
n:
N:
N, :
NPSH :
P:
Q:
R:
R:
scfm :
fiIo
olualgrl,o
p
* r.rnrl
I
1r.+s:;,#
(*q-J
fr-lh
SeC'-lDf
APr
:
5.41f Or'
38ft:12.008psi
:
:
ratio of specific heats
CplC,, dimensionless
mass, lb. and re-expansion polytropic expo-
flow rate, lb-/hr
moles of gas
m/mw
molecular weight
mass
:
polytropic exponent
speed, rpm
specific speed, dimensionless
net positive suction head, feet or psia
pressure, psi
flow rate, gpm or ft3/sec
R/mw : gas constant of a particular gas
universal gas constant : 1545 ft-lbr/lb. molestandard cubic feet per minute, ft3lmin-see
discussion under standard volumetric
With 38 feet of head in the reservoir we have an entry
pressure to the storage tank of
Entry pressure
97
nent
dl =
I (r!flr
[,o
:
:
Equipment
12.008 psi
-
5.411 psi
:
6.597 psi
Because 6.597 psi < 7.00 psi pad, we keep the 6-in.
schedule 40 pipe. The 6-in. line was evaluated for 513
gpm, so it is adequate for the 375 gpm in the 4-in. line.
The system is now completely designed for hydraulics,
using a 4-in. x 3-in. horizontal centrifugal pump.
t: temperature, "F
At : temperature differential, oF
V : volume of gas or cylinder, ft3
v = specific volume of gas, ft3/1b*
w* : weight of fluid
whp = *ur". horsepower, hp
y : constant : (k_ lyk
z : compressibility factor, dimensionless
flow
Greek Symbols
:
:
€:
p:
?
4
NOTATIOl{
acfm
bhp
=
:
e:
Co :
C. :
C" :
D:
D"
ghp
=
=
:
icfm :
J:
H
actual cubic feet per minute, ft3lmin
6.u1" horsepower, hp
clearance volume, in.3
specific heat at constant pressure, Btu/lb-mole-"F
compression ratio
specific heat at constant volume, Btu/lb.mole-'F
diametef of impeller or rotor, in.
specific diameter, dimensionless
gas horsepower : horsepower delivered to
gas, hp
head : energy per pound of mass, ft-lb/Ib.,
or better known as feet of head, ft
actual cubic feet per minute at compressor inlet, ft?/min
mechanical equivalent of heat: 778 ft-lbrl
Btu
specific gravity, dimensionless
efficiency, expressed as percent
ratio of clearance volume to the volume sweot
by the piston stroke
density, 1b./ft3
REFEREilCES
1. Buchter, H. Hugo, Industrial Sealing Technology,
John Wiley & Sons, New York, N.Y., 1979.
2. Dimoplon, William, "What Process Engineers Need
to Know About Compressors," Compressor Handbook for the Hyd,rocarbon Processing Industries,
Gulf Publishing Co., Houston, Tx., 1979.
3. Balje, O.8., 'A Study on Design Criteria and
Matching of Tirrbo-machines-Part B," Trans. ASME,
J. Eng. Power, Jan. 1962.
The Mechanical Design of Shell and
Tube Heat Exchangers
A heat exchanger in process systems allows the transfer of energy as heat from one source to another. Witlout
this essential piece of equipment most industrial processes would be impossible.
There are various types of heat exchangers, each of
which is designed to accommodate the requirements of
the specific needs at hand. Shell and tube heat exchangers are by far the most common because of their
relative simplicity and ability to handle the largest variety of fluids. Plate fin heat exchangers have become
quite popular in cryogenic gas services and have largely
replaced shell and tube exchangers in gas processing
plants. Finned-tube exchangers are used for gas-gas heat
transfer, such as in waste heat recovery units, and have
gained popularity in the past few years because of emphasis on cogeneration to satisfu energy needs.
bottom shell-side nozzle cooled to the desired temDerature. The tube bundle is supported between two iubesheets with baffle plates spaced at intervals to support
and brace the tubes. In this figure the tube-side flow enters the tube bundle on the bottom left side and exits on
the top left side with a horizontal baffle plate separating
the two tube-side flows. This type of arrangement is
called a l-2 exchanger, one shell-side pass and two tubeside passes. The various configurations of exchangers
will be discussed shortly.
Figure 7 -2 shows a reboiler in which isobutane vapor
is formed by heating liquid isobutane. This type of reboiler is called a "kettle" type reboiler because ofthe excess area above the tube bundle that is provided for vapor separation. Figure 7-3 shows another type of
reboiler where the shell and tube exchanger is mounted
vertically alongside a process tower. Here the heat energy of steam is used to separate the propane and propylene liquid into a gasJiquid two-phase mixture. This type
of arrangement is common in the gas processing industry
and, as will be discussed later, one must be very careful
in designing the support(s) for such an exchanger, because of the tubes' thermal expansion.
All shell and tube heat exchangers are exposed to internal pressures, tube-side and shell-side. Thus, in the
United States the ASME Section VIII Division I Pressure
Vessel Code governs the vessel design of such exchangers. The detailed design of shell and tube exchangers is governed by TEMA (Tubular Exchanger
Manufacturing ASsociation), whose published standard
classifies exchangers by the severity of process requirements. The three classes are Class "R," Class "C," and
Class "B" exchangers. Before discussing these classes,
we must clariry heat exchanger design types and terminology (see Figure 74).
FUNDAMEHTALS OF SHELL AND TUBE
HEAT EXCHANGERS
A shell and tube heat exchanger is a cylindrical vessel
housing a set oftubes (called the tube bundle) containing
a fluid at some temperature and immersed in another
fluid at a different temperature. The transfer of heat occurs between the fluid flowing over the tubes and the
fluid flowing inside the tubes. The fluid flow inside the
tubes is said to be "tube side" and the fluid flow external to the tube bundle is said to be "shell side."
The simplest type of shell and tube heat exchanger is
the type shown in Figure 7-1, where warm kerosene enters on the top shell side. The kerosene's flow path is
guided between the tubes by baffle plates and exits at the
99
100
Mechanical Design of Process Systems
WARM WATER OUT
KEBOSENE IN
KEROSENE OUT
(cooLED)
COOL WATER IN
Figure 7-1. An example of a fixed tubesheet heat exchanger. (Courtesy of Howell Training Company.)
ISOBUTANE VAPOF
LEAVING AT
2OOOF
orL
ENTEBTNG AT 6650F
LIOUID ISOBUTANE
LEAVING AT 2OOOF
LIOUID ISOBUTANE
ENTERING AT I95OF
Figure 7-2. This U-tube exchanger represents a kettle type reboiler. (Courtesy of Howell Training Company.)
The Mechanical Desien of Shell-and-Tube Heat
Exchangers
101
PAOPANE & PAOPYLENE
50% VAPOR - 50% L|OUTD
FRACTIONING TOWER (DE ETHENIZERI
PROPAN€ AND PROPYL€NE
50% vaPoR 50% LroulD
CONDENSATlON
Figure 7-3. Iilustration of a thermos]phon reboiler. (Courtesy of Howell
Training Company.)
PROPANE ANO PFOPYLENE
100% Ltouto
Design Classifications of Heat
Exchangers
Typical shell and tube heat exchangers and their functions are as follows:
Reboiler-transfers heat to a liquid to produce a twophase, gasJiquid mixture used in a distillation column.
Thermosiphon Reboiler-provides natural circulation of
the boiling
fluid by a static liquid head shown in Fig-
ure 7-3.
Forced Circulation Reboiler-a reboiler in which a
pump is used to force the liquid through the heat exchanger (reboiler) into the distillation column.
Condenser-a heat exchanger to condense vapors by removing heat from a gas.
Partial Condenser-only partially condenses a gas to
provide heat to another medium to satisfy a process
condition. The residual gas is recirculated through a
heater and recycled. A common application is using
excess steam to heat up a process fluid. A typical application of a partial condenser on a distillation column is to condense only enough liquid for the reflux
when the overhead product is vapor.
Final Condenser-an exchanger where all the gas is condensed and all the heat is transferred to the other medium.
Steam Generator-a device that generates steam, such as
a boiler. to provide energy for process requirements.
The most classic example is the old stearn locomotive,
which is a shell and tube exchanger "mounted on
wheels" with the steam used to Dower the locomotion.
(This unit is a fired vessel and is not covered by ASME
Section VIII Division.)
Vaporizer-an exchanger that fully or partially vaporizes
a liquid.
Chiller-an exchanger in which a process medium is
cooled by evaporating a refrigerant, or by cooling and
heating with little or no phase change.
102
Mechanical Design of Process Systems
HEAD IYPIS
'AIIONARY
I
A
Uff ' "
ANO iEA{OVA8TI COVEP
tn
F
WTh
B
G
LONGIIUOINAT
Ul(E "4" STATIONARY HEAO
3AFFIE
N
LIKE
BONNST (INIEGRAI COVER)
H
SIAIIONARY HEAO
'1T STAIIONARY
HEAD
P
OUI5IOE PACKED FTOA'ING
c
'IFAO
CHANNET INTECFAL WITH IU8E.
SHETT AND RE/nOVASIE COVTR
s
J
T
N
PUIT TIiROUGH FIOATIIIG HE^O
''UBT-
CHANNEI INIEGRAL WIIH
5HEET ANO REITOVABLE COVER
K
U
D
x
SPEC|AL
hICH
PREsSURE
CTOSUI€
Figure 7-4. Nomenclature of shell and
tube heat exchangers. (@1978 by Tlrbular Exchanger Manufacturers Associauon.)
These classifications are the major types of services
that shell and tube exchangers provide in the process industries.
Process requirements dictate the type of design to be
used. Figure 7-4 shows some of the major types of con-
struction. The standard TEMA classification of ex,
is to use the shell identification and number
with the exchanger designation type. For example, an
18- 150 BEM is an exchanger having an 18-in. shell with
150 tubes, a bonnet (integral) cover with a fixed tube-.
sheet at one end (B in Figure 7-4), a fixed tubesheet and
a stationary head at the other end (M), and a one-pass
changers
shell between both ends (E).
Fixed Tubesheet Shell and Tube Heat
Exchangers
Fixed tubesheet shell and tube heat exchansers are the
simplest of the shell and tube designs. They ionsisr of a
tube bundle attached to a tubesheet on each side of the
tube bundle. The tubesheets are welded to the shell pro,
viding an absolute seal to prevent the shell-side fluid
from leakage. Often the tubesheets extend beyond the
shell diameter and have flange bolt holes that allow the
tube heads to be bolted to the tubesheets.
In fixed tubesheet exchangers, tubes can fill the entire
shell to achieve maximum heat exchange (of course, this
The Mechanical Desisn of Shell-and-Tube Heat Exchansers
also increases shell-side fluid pressure drop) such that
tolerances between tubes are minimum. However, this
factor limits the shell-side fluid to a relatively clean service, because the exterior of the closely-packed tubes
cannot be mechanically cleaned or inspected. Another
limitation to the design is that there is no allowance for
thermal growth of the tubes , except if an external expansion joint is used, which is quite common for this type of
exchanger. Normally, single convoluted bellows are
used since the maximum temperature differential is
200"F and the cyclic loading is insignificant.
Tube-side headers, channel covers, and internals of
tubes can be cleaned quite easily and the shell side can be
cleaned only by circulating a cleaning fluid or backwash-
ing.
U.Tube Shell and Tube Heat Exchangers
U+ube shell and tube heat exchansers consist of one
tubesheet with tubes bent in a U-shipe atrached to rhe
single tubesheet. This type of exchanger is used for large
temperature differentials where there is a lot of tube
growth. This type of design allows for easy access to the
shell side of the tubes and removal of the tube bundle.
The inside of tubes must be cleaned with soecial tools
and then only when the bending radius is fairly large.
This tne of design is also very suitable for chemical
cleaning.
The maximum number of tubes per tubesheet is less
than the fixed tubesheet design beciuse of the minimum
bending radius required to form the U-shape. The Utube design is also very applicable to high-pressure servlces.
Floating Head Shell and Tube Heat
Exchangers
This type of shell and tube heat exchanger has a floating head that is designed to accommodate thermal expansion of the tubes and to provide access to the tube-side
and shell-side exchangei components. This type of design is expensive and its use should be considered against
other possible designs.
Packed Lantern Ring Exchanger (Figure 7-5a). This
construction is normally limited to design tempera-
gland tollower
floating-head
cover
(B) Outside-packed floating head exchanger
(A) Packed lanternring exchanger
flange
floating-head
cover
backing ring
shell
f
tlange
gasket
shell
cover
floating tubesheet
floating
tubesheei
floating-head cover
gasket
(C) Internal floating head
exchanger
103
(D) Pull-through lloating head exchanger
Figure 7-5. Several configurations of floating head exchangers.
'lO4
Mechanical Design of Process Systems
< 370"F and design pressures < 300 psig. This
type of design is used only for mild services, such as
steam, air, low viscous oils. In this design the shell-side
and tube-side fluids are sealed by separate packings
which, in turn, are separated by a lantern ring. The lantern ring fits between the packings that separate the shell
and tube-side fluids and normally contains weep holes
that accommodate any leakage through the packing.
Such leakage, which is passed to the outside and drops to
the foundation below, will not cause shell and tube-side
fluids to mix.
The tubesheet must be designed such that it is large
enough in diameter to encompass the packingJanternring ensemble and differential thermal expansion of the
tubes. Occasionally, a skirt is attached to a thin tubesheet
to act as a bearing surface for the packingJantern-ring
tures
ensemble.
Outside-Packed Floating Head Exchanger (Figure
7-56). Rings of packing contain the shell-side fluid,
which is compressed by a gland follower that is guided
by a tube sheet skirt. The skirt is integral to the floating
tubesheet. This removable-bundle construction allows
for differential expansion between the shell and tubes.
This design is normally limited to 600"F and 600 psig,
which is one reason why it is the most commonly used
removable-bundle type exchanger in the petroleumchemical industry, even though usage has decreased over
recent years.
Internal Floating-Head Exchanger (Figure 7-5c).
This design consists of an internal floating tubesheet
held by an internal backing ring, which is bolted to an
internal floating head cover. The internal backing ring
and internal shell cover are beyond the end of the shell
containing the tubes. To remove the tube bundle, the
shell cover, split backing ring, and internal floating head
cover must be removed. The internal floating head cover
acts as a return cover for the tube fluid with an even
number of tube-side passes. with an odd number of
tube-side passes, a nozzle must be extended from the in-
ternal floating-head cover through the outside shell
cover. Clearances between the shell and the outermost
tubes are 1rla in. for pipe shells and 17re in. for mediumsized rolled plate shells. This design is more suitable for
higher shell-side temperatures and pressures than for
pull-through bundle types of construction. This design
has been used extensively in the petroleum-chemical industry, but there has been a decline of use over the past
few years.
Pull-Through Bundle Floaiing-Head Exchanger
(Figure 7-5d). This design consists of a floating head directly bolted to an internal floating head cover. The tube
bundle can be removed without removing either internal
floating head cover or shell cover when bundle is pulled
out an opposite end of shell cover facing internal floating
head. This feature reduces down and maintenance time
during inspection and repair.
The clearance between the outside of the tubes and
shell inside must be sufficient to allow space for both the
gasket and bolting at the internal floating head cover.
This clearance is usually twice that required for the split
ring design used in the internal floating head in the previous section. This type of design is normally limited to
services where leakage of the internal gasket is tolerable.
With an odd number of tube-side passes, a nozzle must
extend from the internal floating-head cover through the
shell cover. The number of tube-side passes is simply
limited by the number of tubes. This design is generally
suited for lower temperatures and pressures than that of
the internal floatine head exchanger described earlier.
General TEIIA Exchanger Glasses-Rr Ct
and B
There are three basic categories of shell and tube heat
exchangers in TEMA-Class R, Class C, and Class B.
The difference in class is the degree of severity of service the exchanger will encounter. Descriptions of the
three classes are as follows:
Class
R
C/css
C
includes heat exchangers specified for the most
severe service in the petroleum-chemical processing industry. Safety and durability are required for exchangers designed for such rigorous conditions.
includes heat exchangers designed for the gen-
erally moderate services and requirements.
Economy and overall compactness are the two
essential features of this class.
Class B are exchangers specified for general process
service. Maximum economy and optimum
compactness are the main criteria of design.
Rubin [3] described the TEMA classes of exchangers
in terms of the various components and how they vary
from one class to another. This data is given in Table 7-1.
Ludwig [4] described various types of heat exchangers,
their applications and limitations, which include shell
and tube exchangers as well as other types. This data is
-oresented in Thble 7-2.provide
a comprehensive view of
tbles 7-1 and 7-2
and their applicaof
heat
exchangers
various
types
the
of the
on
the
components
can
now
focus
tions, so we
shell and tube design.
Table 7-1
Comparison of TEMA Classes R, C and B Exchangers [31
Para-
graph
Toplc
1.12
Definition
1.51
2.2
2.5
Corrosion allowance on
carbon steel
3.3
4.42
4.7 |
5.11
5.31
TUbe diameters
Tirbe pitch and minimum
cleaning lane
for the generally severe
requirements of
petoleum and related
processing applications.
r/s inch
for the generally
for g€neral process
moderate requirements of
comrnercial and general
process applications.
sefvrce.
3h, 1,1\+, 1tlz, and 2
R+%,
inch od
1.25 x tube od. r/+ inch
R+5/E tubes may be
lane.
located 1.2
8 inch tabulated
6 inch tabulated
tho inch
3/s, rlz, and
5/e
xtube od
r/ro inch
R*5/e
R*lane may be 3/re inch
in 12 inch and smaller
shells for s/s and 3/+
tubes.
Minimum shell diameter
Longtudinal baffle
V+
inch minimum
t/8 inch
3/s
inch
% inch in 6-15 inch
r/+
alloy,
hch CS
thickness
Minimum tie rod
diameter
Floating head cover
cross-over area
Lantern ring construction
6 inch tabulated.
Va inch alloy, r/+ inch
carbon steel
r/+ inch 6-15 inch shells.
shells
flow
1.3 times tube flow area
Same as tube
375"F maximum.
300 psi up to 24 inch
diam shell
600 psi maximum.
(same as TEMA R)
Metal jacketed or solid
metal
(a) internal floating head.
O) 300 psi and up.
Asbestos permitted for
300 psi and lower
(same as TEMA C)
150 psi for 25-42
shells
a.rea
Same as tube
flow area
irch
75 psi for 43-60 inch
6
.2
shells
Gasket materials
Metal jacketed or solid
metal for
(a) internal floating head
coYer.
(b) 300 psi and up.
(c) all hydrocarbons.
6.32
7
.131
pressures.
Peripheral gasket contact
Flatness tolerance
No tolerance specified.
No tolerance specified.
surface
specified.
Outside diameter of the
tube.
0.75 xtube od
and smaller.
(same as TEMA C)
Minimum tubesheet
thickness with expanded
tube joints
.44
Ti.rbe Hole Grooving
.51
7.7
Length of expansion
7
7
Ttrbesheet pass partition
grooves
9.3
9.32
9.33
9.1
Pipe Tbp Connections
10.1
Pressure Gauge
Connections
Thermometer
for 1 inch
z/s
TWo grooves
inch for 1% od
inch for 1tlz od
1.25 inch for 2 od
Above 300 psi design
(same as TEMA R)
Smaller of 2 inch or
pressure: above 350'F
design temp.-z grooves
Smaller of 2 x tube od or
(same as TEMA R)
tubesheet thickness
3/re inch deep grooves
Over 300 psi rAo inch
(same as TEMA C)
I
required
6000 psi coupling with
bar stock plug
required in nozdes 2 inch
&
uP.
lequired in nozdes 4 inch
deep grooves required or
other suitable means for
retaining gaskets in place
3000 psi coupling
(shall be specified by
(shal1 be specified by
purchaser)
Nozzleconstruction
no reference to flanges
same as
Minimum bolt size
3/a
t/z inch recommended,
inch
(same as TEMA R)
purchaser)
6a up.
Connections
3000 psi coupling with
bar stock plug
TEMA R
smaller bolting may be
used
(same as TEMA R)
All
nozzles larger than
one inch must be
flanged.
5/s inch
106
Mechanical Design of Process Systems
Table 7-2
Selection Guide Heat Exchanger Types l4l
Relatlre Cost
Type Deslgaatlon
Fixed Tube Sheet
SlEnlficant Feature
Both tube sheets fixed to
shell
Applications Best Sulted
Llmltatlons
Condensers; liquidJiquid;
Temperature difrerence at
extremes of about 200" F.
due to differential expansion
1.0
Jnternal qasketsofter danqer
t.2a
Bends must be carefully
1.08
gas-gas;
gasliquid; cooling
and heating, horizontal or
vertical, reboiling
Floating Head or
Tube Sheet (Removable and nonremovable bundles)
One tube shea "floats"
in shell or with shell, tube
bundle mav or mav not
be removable from shell.
but back cover can be rej
moved to expose tub€
ends.
U-Tubei U-Bundle
Only one tube sheet required. Tubes bent in Ushape. Bundle is removable.
Kettle
Tube bundle removable
High temperature differedtials, above about 200' F.
extremes; dirty fluids .equiring cleaning of inside as
well as outside of shell, hori-
zontal or vertical.
High t€mperature differentials. which migbt require
provtslon tor exDanslon ln
6xed tube units.elean service or easily cleaned coodi
tions on both tube side and
shell side. Horizontal or
vertical.
Boiling, fluid on shell side,
as U-type or
as relrrgerant, or
(r!9engagrng.
flu-id in
floating
head. Shell €nlarqed to
allow boiling and vapot
proc€ss
fluid beioe vaporized. Chilline or co6lini of tube side
Co[structlon
of leakine. Corrosivenesjoi
fluids on-shell side floatins
parts. Usually confined t-o
horizontal units-
made or mechanical damase
and danqer of ruDture ctn
result. fube side'velocities
can cause erosion of inside
of bends. Fluid should
be
free of susp€nded particles.
For horizontal installation.
Phy.sically large for other
applcatrons.
retrig;rant evapora-
tiofl on shell sideDouble Pipe
Each tube has own shell
forminq annular
for
aliy
she-il side
use
soace
fluid. ijsu-
externally finned
ba[ks for
larger applications. Especially suited for high prcs-
sures in tube above 400 psig.
tuDe.
Pipe Coil
Relatively small transfer
area service. or in
Pipe coil for submersion
rn coll-trox ol water or
with water is
simplest type of exsprayed
Services suitable for 6nned
tube, Piping-up a
0.8-1.4
large
numDer olten r€qurres cost
and space,
Condensins, or relativelv
low heat l;ads on sensiblir
transfe!.
Transfer coefiicient is low,
Condensing, relatively low
heat loads on s€nsible trans.
fer.
Transler coefiicient is low,
takes up less space than
plpe co{.
0.8-1.1
Condensing, high level heat
transter.
Transfer coefiicient is low,
if natuaal convectiol cir-
0.8-1.8
requir€.s,
space
lt
relatively
0.5.{}.7
l.arge
heat loaq rs hrgh,
changet.
Open Tube Sections
(Water cooled)
Tubes require no shell,
only end headers, usually
long, water sprays over
surface, sheds scales on
outside tubes bv exoansion and contraciion.tan
also be used in water box.
Open
'(AirTube Sections
Cooled)
Plain or finned tubes
No shell required, only
end headers similar to
'w'ater untts.
culation, but is improved
with forced air flow
across
tubes.
Plate and Frame
Composed of metal-form-
ed thin plates
separated
by gaskets. Compact, easy
to
Viscous fluids, corrosive
fluids slurries, High heat
transfer,
clean.
Not well suited for boilins
or
condensing; limit 350500'F by gaskets. Used for
Liquid-Liquid only; not
0.8-1.5
gas-gas.
Spiral
Compact, concentric Cross-flow,
condensing,
Process corrosion, suspended materials.
0.8-1.5
Chemical resistance of Clean fluids,
tubes; no tube fouling.
condensing,
Low heat transfer coefrci-
2.0-4.0
plates; no bypassing, high
turbulence.
Small-tube Teflon
heating.
ln
C.arbon Steel
The Mechanical Design of Shell-and-Tube Heat
Baslc Gomponents of Shell and Tube Heat
Exchangels
There are various components to a shell and tube heat
exchanger, but the following are the essential ones:
1.
Tubes
2. Baffles
3. Tie rods
4. Tubesheets
Tubes
There are basically two types-finned tubes and bare
tubes. Finned tubes have external fins mounted by various mechanical means. The necessity of having external
fins mounted on tubes is to provide more heat transfer
area and thus more heat influx to the tube fluid. Finned
tubes are most common where there is a gasJiquid or
gas-gas transfer of heat with the gas always being external to the tubes. Typical applications of finned tubes are
waste heat recovery exchangers, waste heat boilers, gas
turbine regenerators, and air-cooled exchangers. Examples of some finned tube designs are shown later.
Plain or bare tubes are the most common in shell and
tube design. These tubes come in two basic types-solid
wall construction and duplex construction. The duplex
design consists ofa tube within a tube in which the outer
tube is mechanically drawn over the inner tube. The
solid wall tube is what the name implies, a simple tube of
solid wall construction. Tubing is available in almost as
many materials as piping and is available in standard
gauge sizes listed in Table 7-3, along with diamerers and
section properties.
In applying the U-tube exchanger design, tubes must
be bent 180'. Thble 7-4 lists the recommended minimum
bend radii.
Baffles
Baffles serve several functions and consequently the
design of each is dependent on its purpose. Baffles can
act as:
l
2.
3.
Structural supports for the tubes.
Dampers against vibration.
Devices 1o control and direct flow Datterns of the
shell-side liquid.
Baffles as Tube Structural Supports. Like piping,
tubes behave as structural beams and consequently will
develop excessive deflection, or sag, if left unsupported.
Baffles act as the structural supports in the shell and tube
exchanger. Another structural function of baffles is to
add stiffness to the tubes so that each tube. in effect. is
Exchangers
1o7
constrained at each baffle. Thus, the hole in the baffle,
being larger by varying amounts than the outside tube diameter, acts as a limit stop for the tube. In piping mechanics (see Chapter 2) a limit stop is a restraint that limits the amount of pipe (in this case, tube) movement to
the distance between the hole diameter and the outside
diameter of the tube. In other words, the tube can translate in the lateral direction perpendicular to the tube axis
only by the amount of clearance between the tube OD
and the hole diameter. Translation is mentioned instead
of rotation because even though the tube rotates, it is insignificant. Thus, the baffle hole acts as a limit stop and
prevents lateral buckling of the tubes when they are induced to thermal expansion by temperature differentials.
In this sense the tubes are much stiffer and stronger than
they would be without the baffle supports. The consequences of strengthened tubes affect the integrity of tube
joint connections in the tubesheets and this will be discussed shortly. We see from this discussion that the baffle plates act as both structural supports and as buckiing
stabilizers.
Baftles as Tube Vibralion Dampers. Figure 7-6
shows baffles of circular rings with rods that run vertically in the first two rings and horizontally in the second
two rings, thus damping vibration much in the same way
as helical vortex strakes on stacks (Chapter 5). The rods
break up forming vortices that induce vibrations, a phenomenon discussed in Chapters 4 and 5 called vortex
shedding. The rods also reduce turbulence to below res-
onant levels of the natural frequency of the tubes and
they reduce fluid elastic vibration.
Baffles Conlrol and Direct the Flow Pattern of the
Shell-Side Fluid. There are various types of baffles that
direct and/or control the flow ofthe shell side fluid. Fieures 7-l and 7-2 are examples of baffles guiding or d'irecting the flow in the vertical direction. Fig]ure 7-7
shows baffles diverting flow in the horizontal direction.
The flow direction is a function of the orientation of the
baffles and their respective geometries and is dependent
upon process requirements. The arrangement in Figure
7-7 is said to be vertically cut and the arrangements in
Figures 7-l and 7-2 arc said to be horizontally cut.
Often, process conditions require the shell-side fluid
to flow horizontally, parallel to the longitudinal axis of
the exchanger. This arrangement, called a longitudinal
baffle, is shown in Figure 7-8. Figure 7-8a shows a twopass shell-side arrangement and Figure 7-8b shows a
four-pass shell-side arrangement. The baffles control the
flow in the sense that both the direction and flow rate are
dependent on orientation and number of passes, respectively. With the same inlet flow rate, the fluid velocity
108
Mechanical Design of Process Systems
Table 7-3
Characteristics of Tubing
Sq.
tt.
Sq. Ft.
o.D.
Y.
tt
B.W.C.
Gage
22
24
2?
yt
t8
%
%
Yl
20
22
?4
h
l8
20
v,
22
%
%
t2
%
vs
%
%
l3
l4
l5
Sq.Inch
.028
.018
.016
.0360
.0313
.049
.035
.028
.0603
.0731
.0799
.0962
.09E2
.0982
.0725
.0798
.0835
.022
.0850
_0982
.0E57
.065
.1075
.1269
.1309
.035
.028
.t452
.1309
.1309
.1546
.1309
.109
.095
.1301
.14E6
.1655
.1817
.1924
.2035
-049
.0E3
17
.05E
x
20
t/.
l0
.134
.1E25
.t20
.2043
.109
.063
.2223
.2463
.2679
.0t2
.2884
.055
.056
.049
.035
.3019
.3157
.165
.134
\2
%
%
1A
l3
l4
l5
t7
l8
20
I
.0508
_0539
.0560
.022
l6
II
lengrtl
.0655
.0655
.0655
.0555
.072
.065
l8
l9
LenAtlr
.0295
.0333
.049
.042
.035
',|
WGisht
len8th
Tube
.095
.218t
-2298
.2419
.1636
.1636
.1636
.1636
.0570
[21
Steel
Tubo
t.D.
Ssctlon
.194
.054
.045
.26
.00012
.00011
.2t4
.040
.218
.00009
.00008
,lil
.277
.00083
.00071
.0810
.0E?4
52
t.2t4
l.16E
LI46
.0195
.0159
.0t31
1.354
.0502
1.233
.0374
.0305
.00064
.0829
56
56
_l164
94
.1556
.1606
_305
.319
.00045
.083
.331
.00036
.0969
.302
.0022
.00E5
.1052
.236
.0018
.l t26
.l162
.@72
.171
.370
.402
.430
.00t4
_0056
.0012
.0046
.1066
.1139
.602
.537
.019i
.t202
.479
.425
.388
.0061
.0057
.0053
.0049
.0045
.l4I
.350
.303
.407
.435
.459
.461
.495
.509
.0042
.0037
.0033
.t636
_1453
.262
.221
_555
.0028
.1963
.1963
.1953
.1262
.1335
.884
.809
.482
.0129
.510
.0122
.1393
.1466
.1529
.748
.532
.560
.t587
.520
.1623
_1660
.4t6
.0116
.0107
.0098
.0089
.0083
.367
.t963
46
.104
.1380
.1963
.1963
.1963
.9792
.t27
.1636
.1636
.1963
.00098
,0036
.0029
.0025
.0020
.14t6
.3339
.1953
.3632
.1963
.\107
.1780
.3525
.4?AE
.4536
.4803
.2618
.1754
_2618
.2618
,2618
.51t3
.5463
.666
.592
.428
.269
.521
.541
.5E4
.606
.620
.634
.652
.680
.0076
.0163
.0170
.0155
.0145
.0131
.0118
.0105
.0091
.12t3
lt4
.\227
125
.\248
134
.1649
.167r
.1864
.1903
.1938
.1971
.I993
198
227
241
232
258
283
300
.2016
3V
.2043
340
.2068
.2089
358
377
.0344
.0326
.0309
.0285
.2229
285
319
347
.0262
-23/6
.24t0
.0238
.0221
.2267
.2299
.2340
.2433
-2455
384
416
450
471
.649
.6390
.26t8
.2361
20
.035
.6793
.2618
.2435
.496
.360
tt/t
1
t%
t%
.6221
.3272
.2330
.32t2
_2409
.890
.920
_\425
.6648
2.057
1.921
.0E90
l0
.180
.165
.134
_0847
.1355
.t20
.7574
_25t
I.59E
.982
1.010
.0741
.u86
.8012
.8365
.0666
1.a32
.4612
1.094
.3272
.3272
.3212
_3?t2
.3272
.3272
.3212
.327?
.3089
.456
Ll80
.0579
.0521
.0426
,0334
.0247
.1100
.1027
.0926
.0833
.06E2
.0534
.0395
Ll92
_3927
1.232
.3927
.3927
.3921
.3225
.3356
1.955
1.291
1.398
l.6lE
t.2E?
.3492
1258
.996
1.334
l_370
.0755
_1008
.5079
2,410
1_760
.3144
.6660
2.201
t.934
t.182
.2904
_6697
3890
.4739
.2586
.3141
.2904
.2586
.6144
4014
_4801
1.6s9
.2300
.2300
,6784
1t/t
II
lYa
t2
tYl
ty.
l3
l4
t%
t6
t)A
t\
IE
20
.083
.065
,049
.035
t\t
tw
t\t
l0
.134
\2
.i09
tk
l4
l6
z
lt
z
2
2
t2
l4
.109
.095
.0E3
_8825
_9229
.9852
'\.042
.065
t.471
.120
2.433
2.494
2-513
2.642
.t09
.095
.0E3
.5236
.5236
.5236
.2644
.?t02
1,448
1.329
.2715
Ln3
.2E36
1,033
_823
1.060
1.0E4
1.120
.629
1.t52
.2932
.3587
_4606
.1665
1.810
1.834
.103
l_186
1.155
.089
L125
.065
1.556
1.410
1.339
.260
.238
.220
.196
t.284
_174
l.?3E
.153
.140
.0t7
t.411
t.2t0
.t26
0t24
_z?t8
_049
I
1.228
1.235
1.199
.5755
.5945
E
1.263
.079
.813
I
.125
.430
.364
.332
.305
.?10
.239
.2183
_2241
l8
.l4l
.ll4
1299
1.493
1.366
1.316
.2618
.2618
.2618
.714
.158
1.352
550
.9lE
l5
.t7l
1.43i
.3009
.3098
.2t21
I
I
.0415
.0784
.0700
.0654
.0615
.0559
.0507
.0455
.0419
.0332
.0241
_2518
l3
l4
1.126
1.536
1.103
.760
.782
.610
.634
.856
.870
.902
.930
I
1.241
L163
Ll50
1.037
-132
-0244
.(]EE6
_0694
.0511
521
567
.0051)
Lt29
.109
.095
.083
.072
.065
l133
.2484
.2532
.0067
.1990
2041
.t20
t2
1.176
1.183
.19t6
l0
.0!t7
{92
.0203
.0178
.0134
.670
I
I
1.289
1.351
L46?
1.2t1
E
5q. Inch
t.D.
_066
.00068
.00055
.1259
.1296
.1333
o.D.
.0392
.0350
.0321
.0307
.0280
.0253
.0227
.0210
.0166
.1354
.1159
.0931
.3140
.3V4
.3211
.3255
.3291
555
708
749
E04
852
898
.l0E
1.279
t.167
_210
.3314
921
1.149
.191
.3366
997
1.t09
.146
.341{
1060
1.075
_106
.3836
.3880
.3974
.4018
970
1.404
1.359
.565
.4052
1037
ll82
.605
'\.273
1250
1305
1.238
I440
I537
I.153
t.2t
_470
_426
.391
I
.4097
.1136
.4196
_4250
.4291
I31l
1.0E5
.185
t707
L059
_134
.1806
,1546
_4853
.4933
1860
.t241
.50tE
.575
.476
.370
2299
1.218
1-170
1.121
1.095
3795
1.136
.709
.647
l5?6
2014
2l6l
4t2l
Ll79
.315
.304
.212
t.ll6
.293
l.\22
Ll05
.559
.500
t.090
l.0i
1.09
l
t3
l.I4
The Mechanical Design of Shell-and-Tube Heat Exchangers
109
Table 7-4
Minimum Tube Bend Radii l4l
Tube Outside Dia. (in.)
Duplex, all sizes
*Plain:5/s
I
Bend Radius (in.)
3 times Tube O.D.
Center-to-Center Oistance (in.)
6 times Tube OD
t3/te
15/s
1
2
131t6
2z/s
*For bends this sharp, the tube wall on the outer circumference of the tube ma\ thin down lt/z to 2 gauge rhicknesses. dependin| on condition and specific
tube materiaL Morc genercus ndii \9ill reduce this thinning. TEMA presents a formula for calculating the minimum wall thickness.
VAPOR IN LET
FLUID
IN
LET
FLUIO OUTLET
CONDENSATE OUTLET
Figure 7-7. Baffles can divert flow horizontally. (Courtesy of
Howell Training Company.)
Figure 7-6. Although complex, this design eliminates tube vi-
bration. To use this configuration, one must be cognizant of
pressure data [5]. (Courtesy of Heat Transfer Engineering,
Hemisphere Publishing Corporation, New York, Washington,
D.C.)
Figure 7-8. Longitudinal baffles direct flow in the axial direction. (Courtesy of Howell Training Company.)
1
10
Mechanical Design of Process Systems
flow area decreases, that is, the velocity
increases with an increase in the number of oasses.
The control of flow in exchangers is accomplished as
increases as the
well with orifice baffles. Figure 7-9 shows an annular
orifice baffle. To utilize this type of design a very clean
shell-side fluid is required, since the fluid must flow in
the annular space between the tube outside diameter and
the hole in the baffle forming the orifice. The flow at the
orifice is very turbulent and the pressure drop through an
orifice-baffle arrangement is very high. Consequently,
these baffles are not used often in industry. Also, since
the orifice baffle requires a very clean fluid, non-Newtonian fluids are completely ruled out. We will see later
in the chapter that the plate fin type of exchanger is superior to the shell and tube design for many clean services.
The reason for the shell and tube desisn to be dominant
is because of the wider variery of fliids it can handle
versus any other design.
Other baffle arrangements are possible with varying
baffle shapes and orientations. Figure 7-10 shows baffles in disc and doughnut shapes, which disperse the
flow in a radial direction. Baffles can be cut to allow for
horizontal or vertical flow in varying amounts as shown
in Figure 7-11.
Figure 7-9. Annular orifices between tube outside surface and
hole in baffle plate [6].
Tie Rods
These are structural rods that run oarallel to the exchanger tubes through the outer perimeter of the baffles.
fastened to the tubesheets such that they space and support the baffles. Tie rods, being attached to the baffle
plates, also prevent them from vibrating and damaging
the tubes. Table 7-5 lists what TEMA recommends as a
minimum number of tie rods and rod diameters for a set
of shell diameters.
Figure 7-10. Doughnut and disc type baffles [6].
Tubesheets
These are the structured plates in which the tubes are
connected at each end ofthe exchanger. Tubesheets come
in two basic types-single and double. Double
tube-
sheets consist of two tubesheets mounted together at each
end of the tubes with a clearance between the two sheets.
The reason for using two tubesheets at each end is to reduce the possibility of a leak of the tube-side fluid. Dou-
ble tubesheets are quite common with highly toxic services, where a leak cannot be tolerated.
Single tubesheets are much more common than double
tubesheets because ofprocess applications and economy.
Typical tube-tubesheet connections are shown in Figure
1
1a
Of great immediate concern in tubesheet design is the
loading induced by the tubes thermal movement, which
Table 7-5
TEMA Tie Rod Standards (in.)
Nominal
"R" Exchanger
ShellDiameter
8-15
r6-27
28-33
34-48
49-60
"c"
"R"
Exchanger
Tie Rod
Dlameter
& "8"
Exchanger
Tie Rod
irinlmum
Dlameter
of Tie Rods
3/z
3/t
4
3/a
tlz
tlz
tlz
Number
rlz
tlz
o
o
8
10
The Mechanical Design of Shell-and-Tube Heat
Exchangers
is a definite problem in fixed
% Cul Bd!.d on Diomehr
tubesheet exchangers.
TEMA gives two equations for determining the compressive stress induced on tubesheets for all three types of
exchangers-Classes R, C, and B:
Ihis Areo Cll Ool to Arlor Vopor Passog..
Siz€ of Cul Set by Combiiolions ol Heol
Troisf€r Co€llici€nt oid Pressure Drop.
: ::
when Cc < ktlr
z\Ku r
_ | ,,-,,-,1
o. = : ll - llllJ I when C" > k#r
t I
lLc I
o,
This Areo Reooead lron Soiil€ lo Allo* lor
Liquid D,oinoqa,Sire Sel to Slil Erp€cl.d Fkr
Soltb
{iidor,
Voror Possoq. Areo
where
rl Bollh Cll
or lor 0.oininq olrer lfoshout.sir. ro Suil
Flor.Ihis b l'lol Becohriended tor
Should be Rrhoved
coidensed liquid
=
oy
:
t
Tubes)
rh.n
rhr
C"
:
:
tr :
ki =
:
Mun be Horironlor,
Ihe. S€dionlind0ding
(7
is High.
tloriron16l Condenseri.
I8) tlorkonlol C!l 8!ftle
Figure 7-11. Baffle details [4].
(7-2)
[rf,:i"
minimum yield stress oftube material ofdesign
remperalure
radius of gyration of tube
0.25[d3 + (d" - 2t,)2]0 50, in.
tube wall thickness, in.
equivalent effective unsupported length of the
tube. in.
unsupported tube span, in.
Applied Process Design for Chemicol ond Petrochemicol Plonts
Flush lo
Tube Shee
Clod
Tobe Sheet
I
Ferrule,some
l/l6"to l/4'
nne
0s tnner
Tube Woll
8= l5'Avirose
Beoded or Belled
Flored
We ld ed
Dupler Tube
Beoded or Eelled
This Tube Moy olso be Inslolled
Ploin End (No Ferrule)or Flqred
With or Withoul Ferrule,
l/8"
5/16' Minimu m
I
Minimum
p-tre'' Uinirr.,Usuolly l/4"
ssq+
$\
-r)
f
lA) VeflicolCul Eoltle
Ploin
111
usn"
Typicol Grooved Detoil
Figure 7-12. Typical tubesheet-tube connections [4].
112
Mechanical Design of Process Systems
r
{o'
['o
:
4 :
oc :
Et
for unsupported tube lengths between two
tubesheets
for unsupported tube lengths between
where f" :
C:
mode constant from Thble 7-6
span length, in.
I:
E=
I =
W:
Wt :
Wq :
W6o :
a
tubesheet and a baffle
for unsupported tube lengths between two
baffles
modulus of elasticity of tube material at mean
tube metal temperature, psi
outside diameter of tubes, in.
allowable tube compressive stress, psi, for the
tubes at the outer periphery of the tube bundle
Equation 7-1 is based on Euler's columl equation and
Equation 7-2 is based on the short column formula developed by Professor J. B. Johnson during the nineteenth
century.
Other TEMA formulations are summarized in the following sections. The reader is urged to be familiar with
the TEMA standard and follow its guidelines in designing a shell and tube heat exchanger.
tube natural frequency, Hz
modulus of elasricity. psi
moment of inertia, in.a (Table 7-3)
Wr
+
Wn
+
MWr", lbs/ft
weight of empty tube (Table 7-3)
weight of fluid inside tube 0.00545
p"d"'?
M : added mass coefficient from
p : fluid density, lbs/ft3
d : diameter of tube, in
Table 7-6
subscripts:
i :
o:
inside
outside
Allowable Tube Compressive Stress-Periphery of
Bundle. The allowable tube compressive stress, psi, for
the tubes at the periphery of the bundle is given by:
TEMA Formulations
a,:ffi-28
Baffles and Support Plates
Natural Frequencies ot Straight Tubes on Multiple
Equal Spans
-r
s"=\l
- 21r -
when C.
-. I
(kur)l
2C"l
s
kf/ror
whenc >kur
/:*
3.36C
where
C"'Vsr
= l/
^
Table 7-o
Mode Constant-C
Extreme Ends Supported
No.
of
Spans
lst
I
2
3
4
Mode
31.73
31.73
3r.73
5
6
7
31.73
9
31,73
31.73
a
to
2nd Mode
126.94
[21
Extreme Ends ClamDed
,l-r+r
Fr-l-'-l*,.1
|--___l
/T-7\--lzf-R
lst
Mode
2nd Mode
49.59
49.59
37.O2
37.O2
198.34
72.36
59.56
49.59
34.99
34.32
33.67
34.99
34.32
33.67
40.52
38.40
&.52
33.O2
33.02
72.36
40,52
33.02
33.02
33.02
p1d1,
weight of fluid displaced by tube 0.00545
Extreme Ends Clamped-Supported
r-fr-fr
lst
Mode
49.59
37.O2
34.32
44.r9
37.O2
34.99
znd
Mode
160.66
63.99
49.59
42.70
39.10
37.O2
32.37
31.73
31.73
35.66
34.99
34.32
33.67
The Mechanical Desien of Shell-and-T[be Heat Exchansers
yield stress, psi, oftube material at design metal
temperature used.
radius of gyration of tube
0.25
KT:
.vu +la" -
2tJ1,
only, may be calculated as follows:
2.74C"
R2
where
fnu
R
=
:
:
U-tube natural frequency, Hz
mode constant for U-bend
bend radius, in.
spans between two tube-
Note: For other than simple support conditions the calculated
frequency may be estimated by multiplying the above
spans between a tubesheet
value for f,, by the appropriate ratio of mode constants
from Thble 7-6 using single span values.
sheets.
0,8 for unsupported
quency, assuming simple supports and for the first mode
in. (Table 7-3)
equivalent unsupported buckling length of the
tube, inches. Use the largest value considering
unsupported tube spans.
unsupported tube span, in.
0.6 for unsupported
113
and a baffle.
1.0 for unsupported spans between two baf-
fles.
Note: The value of S" shall not exceed the Code allowable
tensile stress of the tube material at desisn metal temperature used.
Effect ot Longitudinal Tube Stress
ASME Tube Joint Load Grlteria
I
The ASME Secrion VItr Division Dressure vessel
code lists formularions in evaluating tube forces exerted
on tubesheets. Referring to Figure 7-13 and Table 7-7
the formulas for the maximum tube force are as follows:
Dt2
'Er.,j
where fnp
:
tube natural frequency in stressed condition, Hz
tensile, negative
for compressive)
P = axial force, lbs (positive for
Natural Frequencies of Straight Tubes on Unequal
Multiple Spans
f" :
For
F, :
joint types a, b, c, d,
(7-3)
A,o,11f,
For joint types
F,
:
e:
f, g, h, i, j,
k:
(7-4)
A,o"11f,f"f,
where
:
maximum tube joint force, lb1
cross-sectional metal area of tube, in.2
oall : ASME maximum allowable stress. psi
f= joint reliability factor
Ft
10.83 t'z
f. (no tesg = maximum value without test given
For a tube on multiple unequal spans with the extreme
ends fixed and simply supported at the intermediate supports, ki can be obtained by solving the following characteristic determinant for an n span system.
Natural Frequencies of U-Tubes. It must be recognized that each tube is a continuous beam that has a single fundamental frequency. This frequency may be
largely governed by the lowest "stand alone" frequency
of either the longest straight span or the U-bend. It is
suggested that both be calculated and that the lower value
be used, keeping in mind the approximate and somewhat
conservative nature of the result. The straight span frequency may be determined from Thble 7-6 using the appropriate mode constant. The U-bend out-of-plane fre-
f, (teso
:
in
Table 7-'7
maximum value with test as specified in
the ASME Section
VIII Division
1
code, per section UA-002
Figre 7-14 shows how the tube joint load varies for
various tube gauges of various process conditions. Naturally, as the tube wall increases, the tube stiffens and,
consequently, the force exerted by the tube on the tubesheet joint increases. The engineer should evaluate the
tube loads with the various process conditions possible
and use the worst for determining the maximum tube
joint force, as shown in Figure 7-14. The TEMA standard gives the formulations to determine the tube ioint
lorces and the user is referred to this standard for these
expressrons.
The buckling of exchanger tubes can be a problem if
thermal expansion is not properly accounted for in de-
Mechanical Design of Process Systems
114
Table 7-7
Reliability Factors, f,
Joint
Type
Notes
Descriptions
Welded only, a> 1.4r
Welded only, tsa<L.4t
a
b
(1)(7X8)
(1X2)
(1X3)
(1X6)
(1X7X8)
Brazed, examined
Brazed, not fully examinable
Rolled, welded, a> l.4t
Rolled, two or more grooves,
and welded, a< l.4r
Rolled, single-groove, and
welded, a < 1.4r
Rolled, no grooves, and
and welded, a < 1.4r
Rolled, two or more grooves
Rolled, single groove
Rolled, no grooves
c
d
f
c
h
I
j
k
[71
l. (tesr)
f, (no test)
1.00
0.50
1.00
0.80
0.55
0.80
0.40
0.80
0.95
o.75
0.85
0.65
0.70
0.90
0.80
0.60
0.50
0.70
0.65
0.50
0.70
1.00
(1X4)(s)
(7)
(l
)(4)(s)
(7)
(l)(4)(5)
(7)
(l)(4xs)
(l)(4x5)
(l)(4)(5)
Notes:
(l) The use of f. Ceso factor requires qualification in accordance with UA-003 and UA-004.
(2) For welds where a is less than t, fi (no test) 0. Tubes with Type (b) joints where a<t may be considered as acting as stays and contributing to the
strength of the tubesheet only when the joint is tested in accordance with UA 003 and UA-o(X.
(3) A value of 1 00 for f, (test) or .80 for f, (no test) can be applied only to joints in which visual examination assures that the brazing filler metal has
penetrated the entire joint [see UB-14(a)] and the depth of penetration is not less than three times the nominal thickness of the tube wall.
(4) When the ralio of OD. to LD., using nominal tube dimensioos, is less than 1.05 or geater than l-410, qualification in accordance with UA403 and
UA-oO1 is required.
(5) The nominal pitch used in the desigo of tubesheets for roller expanded joints shall not be less than the following:
-
P=
d" + 0.165 (d" + 2r)
= nominal pitch (center-to-center distance of adjacent tube holes),
= tube o.D_, in.
I = nominal thickness of average wall tube, in.
in.
except that:
(a) nominal pitch shalt not be less than 4 + 2t unless the joint is qualified in accordance with UA-003 and UA-004; and
(b) 96% of the ligaments between tube holes throughout the thickrcss of the rnachined tubesheet shall not be less than 0.85
(P-4). Ligaments which
do not meet this requirement shall be evaluated and €orrections made as may be necessary.
(6) A value of .50 for f, (test) or .40 for f, (no t€so shall be used for joinls in which visual examination will not provide proof that the brazing filler metal
has penetrated the entire joint Isee US-14(b)1.
(7) The value of f. (no test) applies only to material combinations as provided for under Section IX. For material combinations not provided for under
Section IX, f. must be determined by test in accordance with UA-003 and LIA-0O4.
(8) For joint types involving more than one fastening method, the sequence used in the joint descriptions does not necessarily indicate the order in which
the
oDerations are Derformed.
sign. One such formulation to predict the critical buckling load is as follows:
P.,
q'' t0.5216r
- , "
,,
I L** l'
\Ns + t/
where L,u6"
:
NB :
t7-51
total length of tubei between tubesheets
number of baffles
Equation 7-5 is based on the Euler column formula. In
situations where there are several baffles, such that the
effective length, L", divided by the radius of gyration, k,
is between 30 and 120, exclusive, then the Johnson short
column equation is more accurate. For a tube to be considered as a series of short columns constrained by fixed
ends, one must be certain that the baffles constraining
the tubes allow practically no translational or rotational
movement. The stiffness of the baffle plate should be
analyzed, as small translational and rotational tube
movement allowed by the baffle plate could considerably alter the buckling characteristics of the tube. The
evaluation of a baffle plate containing several tubes can
be a somewhat detailed analysis, and it may be faster to
consider the tube as a continuous beam in determining
buckling characteristics.
For further details on the mechanical design of exchangers, the reader is referred to TEMA. We will discuss tube vibrations shortly.
The Mechanical Desien of Shell-and-Tube Heat
PBOCESS EVALUATION OF SHELL AND
TUBE EXCHAI{GERS
mechanical engineering coincide. Thus, the mechanical
engineer must be cognizant of process evaluation of heat
exchangers in order to design these units.
A thermal evaluation of shell and tube heat exchansers
concerns primarily two modes of heat transfer-conJuction and convection.
In Chapter 3 we considered heat transfer through piping and vessel components as well as jacketed systems.
As described in Chapter 3, the basic expressions used in
conveetion are as follows:
We are concerned here only with any particular heat
exchanger and determining whether it can transfer heat
energy as required. How the unit affects process conditions of the entire system is not our concern here, because we are interested only in the proper performance
of the unit. Evaluating the exchanger in relation to the
process system is the primary concern of the chemical
engineer. The thermal evaluation of the exchanger is one
area where chemical and mechanical engineering overlap; just as in Chapters 2 and 4 we saw how civil and
:
q:
q
rhcpat
(3-24)
UA(LMTD)
(3-26)
t2l
{1t
Some ecceptable weld geometriea where
t
is not less
(61
lhan
Exchansers t15
l.4t
l7l
(81
Figure 7-13. Joint types [7]. (Courtesy of ASME.)
116
Mechanical Design of Process Systems
J
;
sooo
l!
F
=
-
7t)00
U
ul
.o
*
6000
.o5 .o5 st
.oa .o9 Jo 11 12 13 .1+ .15 16
t7
TUBE WALL THICKNESS Iin|
Figure 7-14. Tube joint loads.
Equation 3-9 is a variant of Fourier's heat law of conduction in which,
q: KAAI
(7-6)
The treatment of shell and tube exchangers requires
the same basic theory for use in Chapter 3, but a different application. In these types of exchangers we are pri-
marily concerned with the heat duty or heat load required in the same general sense as the jacketed vessels
in Chapter 3. Process requirements are the criteria used
to determine the heat duty. The two basic components of
heat transfer in the shell and tube exchanger are sensible
heat and latent heat. These concepts are described mathematically with the use of Equation 3-24. Using this relation we have:
q = r;cp(ao
q
:
rimrg
(7-7)
(7-8)
The Mechanical Design of Shell-and-Ti.rbe Heat Exchangers
Equation 7-7 determines sensible heat change and
Equation 7-8 determines latent heat change and is a form
of Equation 3-13. You will recall that sensible heat is the
amount of heat energy required to either heat or cool a
given mass (solid, liquid, or gas-without a phase
change) to a measurable degree. Thus, if we have a kettle full of water and we heat the water mass at atmospheric pressure to 212'F, adding additional heat to the
kettle will not raise the temperature. Thus, the sensible
heat is the amount of heat required to raise the water
temperature to 212'F. The additional amount of heat required to convert the water to steam is called latent heat.
Sensible heat can be detected by the human senses and
thus physically measured, as with a thermometer. Latent
heat is heat energy that cannot be detected by the human
senses and is more intrinsic to the basic nrocess-the hot
steam plus the additional heat provided- to rhe kertle to
convert the water to steam.
While these terms are rudimentary, their importance is
fundamental to heat exchangers. Combining Equations
7 -'7 and 7-8 we arrive at the total heat duty of the exchanger as:
q:rirco1a9:rirtrr,
\'7
117
pass to another in a muhipass exchanger. Figure 7-15 illustrates how a different LMTD occurs for each oass.
showing that using the inlet and outlet ofrhe rubesid; and
shellside would not produce an accurate LMTD value.
Thus, the value obtained from Figure 3-10 must be multiplied by a correction factor, F, as provided in Figure 716. These correction factors were tabulated by TEMA
and are determined by the "P" and "R" parameters
shown in Figure 7-16. For a true counterflow or parallel
exchanger a correction factor is not necessary. Use of
these tables is demonstrated in the examples which follow.
It should be pointed out that the straightline exchanger
curve in Figure 7-15 is for a single-component fluid.
Most industrial applications are multicomponent mixtures. Chemical engineers do vapor-liquid equilibrium
calculations that show vapor and liquid compositions in
multicomponent mixtures to be different and changing
within the exchanger. Thus, real curves are not straight,
but often can be approximated as such in multicomponent flow. Assuming a straight line is a source of many
oesrsn errors.
-9)
The first term on the right side of Equation 7-9 represents the sensible (cooling or heating) heat and the sec-
ond right-hand term represents the latent (condensing or
boiling) heat.
In Chapter 3 we discussed the LMTD and the reader
can use Figure 3-10 to quickly determine this parameter.
The difference between that value used in Chaoter 3 and
the application here is that the LMTD will vary from one
Tube Wall Temperature and Caloric Temperature
Chapter 3 dealt with the LMTD in the computation of
heat transfer problems. One of the assumptions used in
defining the LMTD is that the overall heat transfer coefficient, U, remains constant. With multipass exchangers
this is certainly not always the case, as indicated by Figure 7-15. Even with counterflow exchangers, as the cold
fluid gets hotter, the viscosity decreases, changing the
overall U-value. In many instances, the U value will
vary more than the inside tube coefficient.
Colburn [8] addressed this problem by assuming that
the U value will change linearly with temperature and
deriving an expression for the temperature differential.
Colburn thus elected to obtain a single overall coefficient, U,, at which all heat transfer surfaces can be assumed to transfer heat at the computed LMTD. In this
way the overall U-value, U*, can be expressed as
r.
E
P
\|TTD/
Toral Heat Transler, Btu
Figure 7-15. The amount ofheat transferred varies from
to another [4].
pass
a_ ,,
IGTTD - LITD
;- uxt,l
I\ r" lcrrDl
I
(7-10)
I
/
Such a value of U* exists at a temperature, t", known as
the caloric temperature. It is this value of t" at which the
inside and outside tube film coefficients, h1 and h., respectively, are evaluated. The caloric temperature is
found by multiplying the respective hot and cold temper(tert continued on page 122)
118
Mechanical Design of Process Systems
r.0
5
F
o.s
2
(l
o -.'
:
P .TEMPERATURE EFFICIENCY
I
/tL--.....-.-,
lr-t'
l.-+<_
LMTD CORRECTION FACTOR
SHEIL
PASS
'
D
!
EVEN NUMBER OF TUBE PASSES
-.:l-J
Gl=
T,-t,
r
'2
-l/
oa
o
F
O.9
z
9^"
o 0.7
=
o.6
P
.
03
0.5
0.6
T€MPERATURE EFFICIENCY
LMTO CORRE
2
SHETL
PASSES 4 OR MUTTIPLE OF 4 TUBE PASSES
P'++
I:I
Q-tr
Figure 7'16. LMTD correction factor. (@1978 Ttrbular Exchanger Manufacturers Association.)
The Mechanical Design of Shell-and-Tlrbe Heat
Exchangers
5 o.g
F
z
I
o.e
o o.7
F
o.6
P
'
TEMPERATURE EFFICIENGY
3 SHELL
LMTD CORRECTION FACTOR
PASSES 6 OR MORE EVEN NUMBER OF TUBE PASSES
P'++
I:l
R' tr-1r
P o.s
2
o
tr
o.8
o
O.7
F
t
o.6
T-
4
SHELL
LMTD CORRECTION FACTOR
OR MULTIPLE OF 8 TUBE
PASSES 8
gHELIS
I
I
-r_
"'++
Figure 7-16. Continued.
]-J
tr- tr
PASSES
119
'120
Mechanical Design of Process Systems
t.o
E
P o.g
z
tr o.8
tr o.7
:
5
SHELL
PASSES
10 OR MORE EVEN NUMBER OF TUBE PASSES
r'#-+
.t
o.3
0.4
Tr-Tr
"=
0.5
0.6
P = TEMPERATURE EFFIoIENcY
LMTD CORRECTION FACTOR
6 SHELL PASSES T2 OR MORE EVEN NUMBER
9:-]3-J
' T,-t'
Figure 7-16. Continued.
R
=
-l--3
OF
IUBE PASSES
The Mechanical Desien of Shell-and-Tube Heat
Exchangers
P =TEMPERATURE EFFICIENCY
I
DIVIDED FLOW SHELL
PASS
o. -13--:!
'
I
T,-t,
EVEN NUMEER OF TUBE PASSES
I-I,
o.g
z
P o.t
o
F
o.7
=
o.6
P.IEMPERA
LMTD CORRECTION FACTOR
SPLIT FLOW
SHELL
e'f{
Figure 7.16. Continued.
2
''r-rE
TUBE PASSES
121
122
Mechanical Design of Process Systems
ature differentials by a caloric fraction, F". That is, the
fraction, F., is multiplied by the temperature rise of the
controlling stream and adding the resulting rise to the
lower terminal temperature of the stream. Figure 7-17
helps in determining the controlling streiim. Colburn [8]
correlated the data for the insert in the top left-hand corner of Figure 7- 17.
The fluid stream, either shell-side or tube-side, that
has the largest U-value corresponds to the controlling
heat transfer film coefficients, h1 and h., which are used
to determine U*. Basically, rhis implies that we must find
the values of U6 and U" for both separate streams, and
the stream that has the largest c value, based on Figure
7-17 is the one used to compute h. and hi in computing
U,, where Uh is the overall heat transfer coefficient at
the hot end of each respective stream and Uc is the overall heat transfer coefficient at the cold end of each respective stream. In equation form we express the caloric
temperatures as derived by Kern [9] as follows:
t* =
The hot fluid caloric temperature ls
h1"
:
ho
:
tqh:th.*F.(th,-th")
(7-1 1)
The cold fluid caloric temperature is
r.c: tc + F"(t." - r")
where tch : caloric temperature ofhot fluid, .F
th" : outlet hot fluid temperature, oF
1,, : inler hot fluid temperature. .F
t.. = caloric
t" :
tc"
F"
:
:
(7
-r2)
temperature ofcold fluid, .F
inlet cold fluid temperature, .F
outlet cold fluid temperature, "F
correction factor determined from Figure 7-16
Outside tube wall temperature for the hot
inside of the tube is
fluid on the
hi^
,
nio
f-
no
(t.h - t".)
(7-
l5)
or
t.h
h
+. ]:.
n,.
+
(r.r,
no
- l.)
(7
-16)
Thus, the pipe wall temperature can be computed
when the caloric temperature values are determined. The
temperature difference across the tube wall is customarily assumed to be negligible because the entire tube is at
the outside surface temperature. The terms in Equations
7-13 through 7-16 are as follows:
t* :
tube (outside surface) wall temperature, 'F
inside film coefficient of tube using outside surface
temperature, Btu/hr-ft2-' F
outside film coefficient of tube, using outside tube
surface temperature, Btu/hr-ft2-'F
The tube wall temperatures are to be used in computing thermal movements of the tubes and all other mechanical computations. As explained previously, these
tube wall temperatures are based on the caloric temperature values that truly reflect the mean value of the varying values of h1, ho, and U,. It is a common oversight in
exchanger design to use the arithmetic mean rather than
the caloric values. Equation 3-26 should not be used because Equation 7-10 more accurately describes the true
mean values in the exchanger.
Overall Heat Transter Coefficient
Once the hot and cold caloric temperatures are determined we can now compute the tube wall temperature,
because the caloric temperatures represent the true mean
values for the varying values of U^, hi, and h". Kern [9]
has expressed the tube wall temperatures in the follow-
ing forms:
Outside tube wall temperature with hot
fluid external
to tube is
The thermal duty of an exchanger cannot be discussed
without first defining the overall heat transfer coefficient, or "U-value." This parameter is referred to in the
previous discussion and it is noted that this value can
vary with various types of configurations. Now, after
discussing how a variable U-value is handled on multipass units using the caloric temperature, we are ready to
treat the overall coefficient in detail. The overall heat
transfer coefficient, denoted as U, is defined as follows:
hi..
t" = t.r, .n,o +
-
(t"n
nu
-
r...t
(.7
-13)
or
t" = t.r,
u=
l,TuT,tT" -r-
hi Kr, k"
h"
n,o
-
+
(Lr,
no
-
t".J
(7
-14)
where
hj
Tn
(1- 11)
-h.
-l-
-k.
= inside tube film coefficient, Btu/hr-ft2-'F
= thickress of inside tube deposits. ft
The Mechanical Desien of Shell-and-Tirbe Heat
Exchansers
123
E
ut
e
3
t4
ul
g
4
=
F
u,l
e
3
|'|-
ul
()
e
ul
tlll
.f J
.9
s'
F
o\
o
o
t\
to
tt
;l;
lJ
110 J0
rr|ivr9 'l 'd'v
:
124
Mechanical Design of Process Systems
kn
:
T" =
k* :
ho
Tro
k,o
:
:
=
thermal conductivity of foreign deposits on
inside of tube, Btu/hr_ftr_.F
tube wall thickness, ft
thermal conductivity of tube wall,
it contacts tube surface, resultinq in a coating effect. Thus, the depositing of foreign miterial adds
to the resistance of heat flow from the tube and she side
flows. Fouling can occur inside and outside of tube surfaces. The complexity of fouling and how it occurs does
not easily allow this phenomenon to be treated analytically. There are far too many variables involved for one
to accurately compute fouling factors. Thus, this phenomenon is treated in a more subjective light, using experience as a guideline. Years of experience with various
services have resulted in the use of accurate foulins facphases when
Btu/hr-ft2-"F
outside tube film coefficient, Btu/hr-ftr-.F
thickness of outside tube deDosits. ft
rhermal conductivity of deposits on outside of
tube, Btu/hr-ft2_oF
The terms in Equation 7-17 , llh, T/kf, and T*/k*, are
known as film resistance, fouling resistance (we will refer to this as fouling factors), and tube wall resistance,
respectively. These parameters represent the resistance
to heat flow through the fluid film, foreign deposits, and
the tube wall. This is shown in Fisure 7-18 where the
temperature is shown varying throGh the various resistance zones. This figure is a conceptualization of the
temperature profile, as the degree of gradient change in
temperature is a function of the flow conditions daminar
versus turbulent) and on the type and amount of foreign
deposits. To understand Equation 7-17 we will discuis
each resistance separately.
Fouling of Inside and Outside Tube Surfaces
Fouling occurs when deposits are made on the walls by
particles contained in the fluid medium or bv the fluid
itself forming a layer on the tube walls. This can occur
two ways, either by adhesive characteristics of the deposited matter or by the foreign material being bonded to
the tube surface by thermal gradients between the tube
wall and the foreign material, so that the latter chanses
tors.
Fouling factors are very important in the design of
shell and tube heat exchangers. Bare or plain tubes,
which are almost always used, generate low U-values
when compared to those generated by tubes with fin attachments. Finned tubes, especially those with fairly
high fins, experience very little fouling unless the deposIts cover an appreciable portion of the fin height. With
the normally accepted long periods between tube cleaning in plants, fouling certainly must be considered in the
calculation of the U-value. One must be aware of the
shell- and tube-side fluids and select those foulins factors thar best reflecr the op{imum fouling thar williffect
thermal duty.
The fouling factor in Equation 7-17 is T/fu. This term
is the inverse of the thermal conductance of heat throush
the foreign matter. denoted by k,/T,. Thus, the reciproial
of the thermal conductiviry of the foreign material is
known as the fouling factor. Fouling can exist on both or
one side of the tube. Typical values for fouling factors
for common services are siven in Table 7-8.
Direction
+
Att
At1 = Temperature drop through inside
Att
Atz = Te6p"tu,ur" Orop through laminar boundary tayer inside
Atr
At.
At"
-----T At,
turbulent boundary
rayer
tube
Ats = Tsrnpsr.lrra drop through fouling layer inside tube
At4 = Temperaiure drop through tube wall
Ats = Tsrnpg,.1r,a drop through outside touling layer
At6 = Temperature
drop through outside laminar boundary
rayer
Atz =
T66p"r"rrr" drop through outside turbulent boundary
taver
Figure 7-18. Temperature profile through tube wall.
n
fl
The Mechanical Design of Shell-and-Tube Heat
Table 7-8
Recommended Minimum
Fouling Resistances
Fouling
Factor
Gases and vapors
Cenrrifugal compressor exiaust
Reciprocating compressor exhaust
Reciprocating compressor refrigerant vapor
Centrifugal compressor refrigerant vapor
Oil-free and clean high-quality steam
Oil-free and clean low-qualitv steam
Oil-bearing steam
Compressed air
-
l-,iatural gasl
Liquiafs
Bay water
-
0.002s
0.0015
0.0003
0.0005
0.001
-
Acid gas
;olr€rt rapors
0.001
0.01
0.002
0.001
0.001
0.001
Fuel oils
0.0025
0.0005
0.0033
0.0033
0.0015
0.0012
0.0015
0.006
Clean organic solvents
0.001
Vegetable oils
0.004
Refrigerant liquids
Industrial heat -transfer oils
0.001
0.001
0.001
Distilled water
Hard well water
Untreated cooling tower water
Treated cooling tower water
Engine jacket water
Treated boiler feed water
Hydraulic fluid
Natural gasoline
and liquefied petroleum
Rich oil
Lean oil
gases
and Tate as fbllo$
N-,"
:
coetTicienr
\\:, :
\r. :
:
\p.
L
=
greater heat transfer between the shell-side and tube-side
fluids, resulting in higher film coefficients. For a more
detailed discussion of boundary layer theory one is referred to a basic text on heat transfer, such as the l/andbook of Heat and Mass Transfer, Volumes I and 2, N. P
Cheremisinoff, ed., Gulf Publishing Co., Houston,
Texas, 1986.
oi thernal conductivity of fluid
rn,lde rub('. lJlu hr-ft- "ts
\usselt number (see Chapter 3)
Re) nolds number
Prandd nunber (see Chapter 3)
total tube lensth. ft
lluid viscosity at bulk tenperature. Ib,,,/ft-hr
or cp
fluid viscosity at wall, lb./ft hr or cp
The viscosity at the wall, p,", should be evaluated using either Equation 7-15 or Equation 7-16.
The bulk temperature of the fluid is in practice the average of the inlet and outlet tube fluid temperatures.
For turbulent flow inside tubes wall effects can play a
role in the film coefficient value. The correlation that is
widely used is the one developed by Sieder and Thte,
which is as follows:
In the region close to the tube wall the fluid becomes
stagnant and forms a film around the tube surface-on
inside and outside surfaces. This stagnant region is
called the "boundary layer" because it forms at the
boundary of the tube wall. The size and properties of the
particular boundary layer are a function of the fluid
properties itself and whether the fluid flow is either turbulent or laminar. Turbulent fluid motion always leads to
(7-18)
inside pipe or tube diameter. ft
where
i
Tube Film Coefficients
s:
= r 86{Nn.)r' (\,.)'' (q)'" (4)'''
T
0.002
-
125
Inside Tube Coefticients. In Example 3-5 we used
correlations to determine film coefficients inside tubes.
Here, we will give a more comprehensive treatment of
film coefficients inside tubes.
In laminar flow there is more fluid stagnation around
the tubes because in the boundary layer itself the flow is
laminar, whereas in a turbulent boundary layer the sublaminar boundary layer is only a small percentage of the
total layer. Thus, fluid properties at the walls in laminar
flow must be evaluated. The laminar film coefficient is
largely dependent upon the viscosity and, thus, the temperature (which controls the viscosity) of the wall controls the value of h. The most commonly used correlation for laminar flow inside pipes is that given by Sieder
0.001
0.00
Exchangers
NN,^
"
:
for 0.7
/ \o 14
0.027(NR"ro
<
Np,
<
\N.,t' '
l4l
\4"/
(7-
le)
17,000
As for Equation 7- 18, the value of p*, should be determined using temperature values calculated using Equations 7- 15 or 7- 16.
McAdams [10] suggests that for temperature differences between the bulk fluid temperature and the pipe
wall surface temperature the following expression can be
used:
Nu, = 0.023(NnJo 8(NrJ"
(7 20)
126
where
Mechanical Design of process Systems
n = 0.4 for heating
n : 0.3 for cooling
Nr,
And the temperature differences are as follows:
At
At
At
: pipe surface temp-bulk
< lO'F for liquids
< 100"F for gases
fluid temp
Outside Tube Film Coefticients, Forced convection
around immersed bodies is a complex subject, especially
when a bundle oftubes is involved. We will only give L
rather brief discussion of how one can obtain a s;neral
magnitude of film coefficients. The -reader
should be aware that process design is not addressed.
Thus, for solving problems dealing with condensation,
order
of
nucleate boiling, and film boiling-to name a few_the
reader should consult other sources that treat Drocess de-
sign in detai[ [4.81.
For gases flowing normal to circular cylinders a simple relationship is contrived by M. Jakob [1] using an dyercge Nusselt number for the gas. An empirical version
of this expression is given by
hd,
where h
:
= C(NIJ"
('7
-2r)
hd'
-
:
Kf
Forced convection normal to tube bundles is mucl:
more complex than that of a single tube. The size of the
bundle and how the tubes are oriented (tube pitch ar_
rangements) in the bundle are of prime importance.
First. we will discuss an approach io determining the
film coefficients for bundles and then discuss the mr-erits
of arranging tubes in various geometries.
There are four basic types oT tube arrangements-tri-
angular pitch, inJine triangular pitch, inJine square
pitch-, and diamond-square pitch. These four geomelries
are shown in Figure 7-19. Tubes arranged in bundles are
more complex than a single tube becaule the flow vortices formed by the flow around the first tubes affect the
flow around the tubes farther inside the bundle. Mose
researchers agree that this transient effect is substantially
dampened after the flow passes over the first ten tubei.
Numerous research studies have been made that analyzed flow effects on tube bundles. E. D. Grimson [12]
concluded from several studies that for tube bundlei ai
least l0 tubes in depth the following expression can be
used to predict the film coefficient:
hd,
:
B(pvd"irr.r)"
-23)
average
where
pf
:
_:
h
p:
ki :
A variant of Equation 7-21 is widely used for forced
ofair normal to a cylinder is given by the fol-
B and n
do
Range ol Reynolds
Numbers
0.989
40 < NR" < 4000
0.683
0.193
0.027
4000<NRe<40,000
:
=
Reynolds number at maximum fluid
velocity,
0.91
I
V.",
film coefficient, Btu/hr-ftr-.F
air density, lb./ft3
thermal conductivity of fluid,
Btu/br-ft-'F
average
constants given in Table ?-10
tube outside diameter
(4, Triangular pitch,
NR" <4.0
NR" <40
lb-/ft-hr
Figure 7-19):
Circular Cylinders
40,000 <NR" <400,000
absolute viscosity,
The Reynolds number in Equation 7-23 is evaluated at
the maximum fluid velocity. This velocity is obtained at
the minimum flow passage between the tubes. This minimum distance is shown in Figure 7-19. Tbe minimum
distance is expressed in terms of the tube bundle geometry for each of the four configurations. as follois isee
Table 7-9
Parameters for Fluid Flow Normal to
0.40<
:
V : velocity of air, ft/hr
Nx"
convection
rowrng:
<
(7
k1
film coefficient for gas, Btu/hr-ft2-.F
dt = tube diameter, ft
ks : gas coefficient of thermal conductivity,
Btu/hr-ft-.F
C and n : parameters from Thble 7-9
4
C(PJ'/r(NRJn
d-,"
: * 2''
0.330
0.385
(b) InJine triangular pitch, dni"
0.466
(c.l
0.618
0.805
.
=W
-
d,
InJine square pitch, dmi. = W
(d) Diamond square pitch, d.;" : P cos 45'
0.707p - D
-
D
:
The Mechanical Design of Shell-and-T[be Heat
Exchangers
127
(B) Inline triangular pitch-apex facing nor-
(A) Triangular pitch-apex facing tlow
mal to flow
l
Flow
+
+
+++ 9-
(D) Oiamond squars pitch
(C) Inline square pitch
P=
Pitch
Figure 7-19. Tirbe bundle anangements.
Table 7-10
Grimson Constants for TUbe Bundles
Containing 10 or More Tube6
w/do Ratlo
Tube
wdo
Bank
Geometry
Flgure 7-19)
Inline
t.25
.348
1.50
.JO
2.00
3.00
0.600
0.900
1.000
Staggered
1.25
(see
/
.418
.290
2.0
1.5
.5E2
.586
.570
.601
Bn
B
.275
.608
.100
.7U
.250
.620
.101
.299
.357
.@2
.584
.229
.702
.632
.cgl
.))a
.581
.063
.068
.752
.74
.198
.&8
.286
.608
.213
.636
.446
.571
.401
.581
.565
.Jl6
.560
.srs
.so
.478
1.250
.505
.ssc
.519
.451
.4U
.460
.416
.562
2.000
3.000
.568
.572
.452
.482
.522
.488
.562
1.500
.556
.s68
.556
.310
.592
.356
.562
.421
t.125
.568
.580
.40
.449
.568
.570
.574
128
Mechanical Design of Process Systems
The cross-flow are for various types oftube bundles is
shown in Figure 7-20.
From the concept of continuity, where for two points
.
along a flow path, or streamline,
: V2A2
where V1 : velocity of fluid at point I, ftlsec
Al : cross-sectional area, ftz
VrAl
'A
)</
e-24)
\@
we can deduce
For staggered and iniine tube arrays,
:
With all tubes being placed at a constant pitch and Vr
Vr : fluid velocity, we have
v.,, = v'l+l
(7-2s)
\o.,"i
o,
=
o'10
- p,"" * 9!:
*]44 [o"
Pn - [
o,yl
"l
,rc
For triangular layouts,
.= B
n.
r++
[^ - -D," + o,^-dr.
..1 .^
(P - dJl
[D"
+---i
,rt'?
where, DL = OD of tube bundle
D" = lD ol shell
dr = OD of tube
Equation 7-25 represents the fluid velocity that would
be used in Equation 7-23.
For tube bundles containing less than l0 tubes, values
of the film coefficient in Equation 7-23 must be multiplied by the correction factors in Table 7-1 1.
Each tube pitch arrangement has its own advantages
and disadvantages. A listing of these facts is given in lable 7-12. Whatever the tube arrangement selected, the
tube arrangement in the tubesheet should be made verv
carefully. Clearances, which could be such items as impingement baffles, channel and head baffle lanes, must
be considered. Table 7 -13 is a compilation of various industrial standards for tube sheet layouts. Fipure 7-21
shows a typical tube sheet layout.
One of the easiest and most common methods used to
calculate shell-side film coefficients is that proposed by
Kern [9]. The Kern correlation, which is used for all fluids. is as follows:
'lu l' '
o ro lq"o)"'l,9url'
k
\p/ \t/ \pJ
h"&
B = baffte spacing
Ar = flow area-cross-llow area for one s€ction
tween two baffles
Figwe 7-20. Tube bundle cross-flow
area.
(7-26)
or
h"rD":
o.:orN""f
t,*rr"t
(")o''
Equation 7-26 is divided into two components, jH and
Np" in which
Figure 7-21. Typical tubesheet layouts.
T
:iw
The Mechanical Design of Shell-and-Tube Heat Exchangers
j":+H'(,+)
Table 7-1
where h.
-27)
film coefficient, Btu/hr-ft
"F
G,
flow rate of fluid, Iby/hr
mass
thermal conductivity of shell-side fluid, Btu/hr-
ft-"F
D. = shell-side equivalent tube diameter, in.
C, : sPecific heat of fluid, Btunb-"F
123456789
0.64 0.80 0.87 0.90 0.92 0.94 0.96 0.98 0.99
Staggered 0.68 0.75 0.83 0.89 O.92 0.95 0.97 0.98 0.99
('7
outside tube bundle
:
k:
Kays and London Constants for Tube
Bundles Containing 9 Tubes or Fewer
Number of Tubes
In-line
:
1
129
For a square pitch tube arrangement,
l(p: -
nd; )
l
i-
(7-28)
?iorn
Table 7-'12
Pros and Cons of Various Tube Arangements
Tube Pitch
Arrangement Advantage Disadvantage
Yields higher film Medium to h igh
Pitch
coefficients than pressure drop.
in-line square Cannot be used in
pitch. More tubes foulrng serrice..
can be contained in Can only have
shell becau.e of chemical cleantng.
For a 60'equilateral triangular arrangement,
D.
:
.1(0.-13o:
-
-_:
0.5rdi
ilt
(.7
in
29)
a
(a) Triangular
(b) In-line
Triangular
Pitch
compact arrange-
g rcB'
ment.
p(144)
Film coefficients
Medium to h igh
are not as high
pressure drop. Can
only have chemical
cleaning.
as
triangular pitch,
but greater than inline square pitch.
Suitable for fouling
conditions.
(c) InJine
Good for condi-
Relative low film
Square
tions requiring low
coefficients.
Pitch
pressure drop.
Ar-
for easy
access
of
Square Pitch
pitch. Easy access
for mechanical
cleaning. Good for
fouling service.
ft:
17-30
r
D, = ID of shell, in
c: clearance bgtween tubes nleasured along tube
pitch, in.
B : baffle spacing, in.
G, : mass flow rate of fluid, lb,/hr
G.:th
p : viscosity of the shell-side fluid at the caas
at the tube
wall
temperature, lb/ft-hr
tubes for mechanical cleaning. Good
for fouling service.
Better film coefficients than inline
square pitch, but
not as good as triangular or in-line
ft:
loric temperature, lb/ft hr
p* = viscosity of the shell-side fluid
rangement allows
(d) Diamond
uhere p : tube pitch. ir.
d,. = ID of shell. in
a, : flow area of tube bundle,
Relative low film
coefficients. Does
not have as lowpressure drop as
the inline
square
prtcn arrangement.
The parameter js is plotted against Nx" in Figure
l-22a. The value ofjH is determined from the figure after the Reynolds number is calculated. Then from Equation 7 -27 the film coefficient is determined.
The use of baffles is extremely important in directing
the shell-side flow, tube support, and controlling the
shell-side flow rate. As the number of baffles is increased, the flow rate increases. Likewise with an increased flow rate, the pressure drop increases substantially with an increasing number ofbaffles, with the film
coefficient increasing as well. Ludwig [4] reports that
for a constant flow rate, the velocity across the bundle is
doubled with an increase in the film coefficient of approxirnately 44%
.
(text conttuued on page 139)
130
Mechanical Design of Process Systems
Tube Count for
TEMA
Fixed
Tubesheet
Outside Packed
No. ol Passes
No. of Passes
Head
668
588
18 t2
26 24
52 48
98 84
142 t28
168 156
232 220
798 292
388 3s2
484 456
570 s48
922
902
812
808
22
10.02
0
12.N
170
212
21.25
23.25
25.00
27 .00
29.00
31.00
33.00
35.00
P
70 t6
30 28
66 60
106 96
164 148
196 r88
270 252
348 332
440 420
554 524
646 612
5.047
6.065
7 .981
13.25
15.25
17 .25
19.25
Table 7-13
in. OD Tr.rbes on 13^6-in. A pitch
TEMA
LorM
Shell
lD in.
g/a
68
283
3&
454
562
1230
868
l2t2 lt72
1590 1560
1516
TEMA
Type s
Head
No, ot Passes
l106 1092 1040
1438 1430
1496 1468
6l
104
151
178
24r
316
396
490
764
1336
Tube Count for s/s in. OD Tubes on Z8 in,
TEMA
TEMA
LorM
Fixed
Tubesheet
No. of Passes
Shell
lD in.
5.047
6.065
7 .981
l0.02
12.N
13.25
15.25
t7 .25
19.25
21.25
23.25
25.W
27.W
29.W
31.00
33.00
3s.00
P
18 t6
30 24
61
s2 48
96
94 80
151
138 132
187
176 168
241
232 224
302 292
396
384 352
482
472 456
568
554 536
792 780 752
Outside Packed
Head
No. of Passes
418
506
14 t2
26 16
48 44
82 76
124 t12
148 t32
196 184
266 252
334 312
4t6 396
492 472
704
700
22
19
31
26
1062 1030
1008
13s6 t346
13c4
55
88
130
151
206
270
JJO
946 930
660
896
1234 1220 n80
U
Inside
t9 14 t2
31 26 16
56 52 44
96 90 76
lsl 138 t28
187 184 160
258 242 224
336 326 304
421 412 392
s26 502 480
608 s98 556
868 836 804
t152 lt24 t088
t9
JI
TEMA
U-Tube
No. of Passes
1424
A pitch
TEMA
Tvoe S
Inside
Head
No, ot Passes
14 t4 t2
22 20 16
51 48 40
85 76 72
130 120 112
163 152 144
216 2r4 196
288 282 264
358 350 340
450 436 416
526 506 484
724 720 696
994 978 948
1288 1252
1220
TEMA
U
U-Tube
No. of Passes
The Mechanical Design of Shell-and-Tube Heat Exchangers
Table 7-13
Continued
Tube Count for s/s-in, OD Tubes on ZB-in.
TEMA
M
Type L or
Shell
lD in.
5.047
6.065
7 .981
r 0.02
12.00
13.25
t5.25
.25
19.25
t'7
21.25
23.25
25.00
27 .00
29.00
31.00
33.00
35.00
Fixed
Tubesheel
No. ol Passes
21 16
26 26
52 52
89 82
128 124
158 158
2r3 208
277 266
344 332
420 404
502 4't6
694 668
922 910
1181
1166
TEMA
Type P
Outside Packed
Floating Head
908
I 160
1070 l0g
52
80
r20
148
208
264
336
400
488
664
l2
16
44
68
92
r20
164
220
284
TEMA
TEMA
TYPe S
Type
l2
2l
'74
109
138
188
246
TEMA
M
316
394
432
456
.1.18 14
608
6.10
636
62.1
812
86? 8.18
8,10
Fixed
Tubesheet
Shell
lD in.
5.O4'7
6.065
7.981
10.02
12.00
13.25
15.25
t7 .25
19.25
2r.25
23.25
25.00
2'7 .00
29.00
31.00
33.00
35.00
37.00
39.00
42.00
45.00
48.00
51.00
54.00
60.00
No. ol Passes
19 14 t2
27 26 20
55 48 40
85 76 72
126 118 104
151 148 140
206 196 180
268 266 240
340 330 320
416 408 392
499 480 460
576 558 530
675 661 632
790 ',7',13 736
896 875 858
1018 1011 976
1166 I137 1098
1307 1277 1242
1464 1425 1386
1688 1669 1618
1943 l9t2 1878
2229 2189 2134
2513 2489 2432
2823 2792 2752
352'7 3477 3414
TEMA
Type P
Outside Packed
Floating Head
No. of Passes
U-Tube
No. of Passes
12 12
16 16
38 32
10 68
92 88
136 128
18,1 t'76
241 210
308 30,+
388 38,1
360
1048
U
Inside
I122 1112
Tube Count for 3/4-in. OD Tubes on 1sA6-in.
Type L or
Pitch
Floaling Head
No. of Passes
No. of Passes
13 t2
22 22
45 44
76 76
109 104
137 t28
\'77 t76
241 236
293 284
366 364
436 432
612 608
828 812
t6
!
1100
A Pitch
TEMA
Type S
lnside
Floating Head
No, of Passes
TEMA
Type
U-Tube
No, ot Passes
l0 104
64
t4t48
t9 18 12
t4 8
l8 22 18 16
38 42 40 36 32 42 40 32 30 32 24
68 14 72 60 54 73 66 60 54 56 52
98 109 106 96 86 109 106 92 86 92 80
134 130 124 112 108 140 138 124 108 114 104
r'76 114 168 156 152 187 184 168 152 83 74
230 24t 222 2t6 2r0 253 242 224 2tO 220 204
302 288 282 2@ 260 320 294 280 2@ 290 268
384 384 368 344 338 400 380 352 338 360 340
456 469 449 430 418 454 436 416 410 220 21.O
516 544 529 500 490 514 498 471 465 506 488
s96 @3 616 600
s1s 607 s87 560 558 614 580
720 744 132 '704 695 707 690 '769
663 657 720 684
760 830 804
859 83s 812 800 816 79'7
9'13 959 926 900 931 910 876 870 944 916
1118 1093 1054 l0l0 1062 1039 998 993 1076 940
1253 t224 ll84 1150 1200 lt77 tt35 |24 1218 1184
1392 1359 l3l8 1286 1341 1318 1282 t2g 1366 1324
1616 1602 1552 1482 1558 1554
1870 1833 1800 1770 1875 1834
2145 2107 2060 2025 2132 2100
2411 2395 2344 2305 2431 2392
273'7 2683 2@2 2612 2730 2684
3400 3359 3294 3220 3395 3346
U
1502 1482 1600 1552
1'736 1708 1854 1800
1998 196/. 2122 2064
2286 2250 2410 2356
2574 2536 2732 2668
3228 3196 3398 3336
131
132
Mechanical Design of Process Systems
Table 7-13
Continued
Tube Count for 3/a-in. OD Tubes on 1-in.
TEMA
TEMA
LorM
5.047
6.065
7 .981
10.02
12.00
13.25
15.25
17 .25
t9.25
21.25
23.25
25.00
27 .00
29.N
31.00
33.00
35.00
37 .00
39.00
42.00
45.00
48.00
51.00
54.00
60.00
14 14 t2
22 20 16
42 40 36
7372&
109 86 80
139 134 124
187 180 168
241 232 220
296 290 280
372 354 344
434 420 404
507 489 476
604 s94 s68
689 679 660
808 804 772
906 891 860
1030
1152
1273
1485
r72r
1026 1000
1134 1090
1259 1222
1461 \434
1693 1650
1968 l94l
2221 2187
2502 2465
3099 3069
1902
2134
2414
3010
TEMA
Outside Packed
Head
Head
No. ol Passes
10 108
10 104
64
19 18 16
19 14 l2
108
40
38 36 32 28 37 32 28 26 28 24
64
&62
6058
61 60 48 46 56 44
98
95 94 84 78 96 94 80 78 86 72
122
12L ll0 100 98 r21 ll8 104 98 106 96
t& 151 146 140 138 163 1& 144 140 148 136
212
208 196 188 160 216 214 196 158 200 184
270
258 242 232 230 276 270 260 235 254 240
330
320 316 296 298 338 338 324 3m 3r4 300
404
380 372 364 33s 396 396 376 339 388 368
482
475 466 452 430 460 440 420 4r4 452 432
582
530 526 508 49s 558 554 536 494 538 524
672
653 &2 620 610 624 605 s89 581 632 612
724 696 688 669 7s6 744 '116 669 732 708
859 848 818 805 818 797 783 771 838 808
946 922 9M 880 980 978 944 880 950 916
1106 1081 1054 996 tU1 1039 1001 996 1074 rO40
1218 1208 tr74 1r2s rt72 1164 1130 1125 1200 1164
1426 1399 1376 1306 1367 1350 1322 13M 1406 1364
1652 1620 1586
1635 1608 1536 1s04 1632 1s84
1894 1861 1820
1887 tUz 1768 1740 1870 1832
2142 2101. 2060
2143 2lA4 2019 1992 2122 2076
2417 2379 2326
2399 2366 2270 2244 2396 2340
29W 29s7 2906
2981 2940 2932 2800 2992 2936
TEMA
LorM
6.065
2l
.98r
38
61
7
10.02
12.00
13.25
).5.25
t7 .25
19.25
2r.25
23.25
25.00
27.N
29.N
31.00
97
117
158
zlo
262
J10
370
442
524
602
698
f-in.
!
Pitch
TEMA
TEMA
s
P
U
Fixed
Outside Packed
Tubesheet
No. ol Passes
lnside
Head
No. ol Passes
No. ol Passes
l2 t2
16 16
38 32
60 52
90 88
I 16 112
158 148
208 188
256 244
316 308
372 368
432 428
524 500
596 580
692 688
U-Tube
No. of Passes
22
TEMA
5.U7
U
Inside
No. ot Passes
Tube Count for g/q-in. OD Tubes on
Shell
lD in.
TEMA
s
P
Fixed
Tubesheet
No. ol Passes
Shell
lD in.
A pitch
12
16
37
t2
16
32
)/ )t)
89 82
9'7 94
t37 128
177 176
224 216
274 270
333 332
414 406
464 456
570 562
628 620
Head
98
16 16
32 12
52 24 56 52
76 56 89 82
88 80 104 104
120 lt4 r45 140
164 160 188 184
208 198 238 236
268 260 304 292
316 308 344 332
392 344 398 386
448 424 484 472
548 496 554 532
612 576 650 @8
4
12
U-Tube
No. of Passes
64
88
32
t2
24
20
'tA
<t
44 40
80 56 68 68
96 80 90 88
140 tl4 128 120
180 160 176 168
232 198 112 108
284 260 138 134
332 308 340 332
366 344 400 388
468 424 472 460
510 496 554 544
640 576 640 624
4
t2
Exchangers
The Mechanical Design of Shell-and-Tube Heat
Table 7-13
Continued
Tube Count lor s/+-in. OD Tubes on 1-in'
LorM
Fixed
Tubesheei
No. of Passes
Shell
lD in.
33.00
35.00
37.00
39.00
42.00
45.00
48.00
51.00
s4.00
60.00
782 768
894 892
1004 978
I102 1096
768
880
964
1076
1283 1285 1270
1.484 1472 1456
l70l 1691 1610
1928 1904 1888
2154 2138 2106
2683 2650 2636
s
P
Outside Packed
Head
No. of Passes
TEMA
M
Fixed
Tubesheet
No. of Passes
Shell
lD in.
5.047
6.065
7 .981
10.02
12.00
t3.25
t5.25
.25
19.25
17
21.25
23.25
25.00
27 .00
29.00
31.00
33.00
35.00
37.00
39.00
42.OO
45.00
48.00
5l .00
54.00
60.00
\2
2r
37
l0
8
18
16
28
32
61 54
97 90
113 108
156 146
208 196
256 244
314 299
379 363
448 432
522 504
603 583
688 667
788 7'70
897 873
1009
983
48
84
104
136
184
236
294
352
416
486
568
654
756
850
958
1118 1092 1066
1298 1269 1250
1500 1470 1440
1714 1681 1650
1939 1903 i868
2173 2135 2098
2692 2651 261.2
682
824
882
1062 1045 1026 972 1048 1028 996
1232 1222 1218 1140 1224 1200 1170
1424 1415 1386 1336 1421 1394 1350
1636 t634 1602 1536 1628 1598 1548
1845 1832 1818 1764 1862 1823 l7'/9
2080 2066 2044 1992 2096 20.+8 2010
2582 2566 2556 2476 2585 2552 2512
TEMA
No. ol
f in. '
668 724
160 836
8'72 940
't20
8L2
924
9'72 1048 10/10
1140 1222 1204
1336 1420 1400
rs36 1624 1604
t'164 1852 1820
1992 2084 2064
2416 2596 2564
TEMA
TYPe
S
TYPe U
Inside
Head
Passes
No. of Passes
1864 1837 1804
2098 2062 2026
26W 2560 2520
No. of Passes
Pitch
Head
t2 10 8
16 t2 8
32 28 24
52 46 40
81 74 68
9't 92 84
140 134 128
188 178 168
241 228 216
300 286 272
359 343 328
42t 404 392
489 472 456
575 556 540
660 639 624
749 728 708
849 826 804
952 928 908
1068 1041 1016
1238 t2t6 tt96
1432 1407 1378
1644 t6Il 1580
U-Tube
Head
No. ol Passes
742 732 732 668 '130 112
816 8r2 804 760 848 828
952 931 928 8'72 931 918
Type P
Outside Packed
U
lnside
Tube Count tor 3/4-in. Oo Tubes on
Type L or
TEMA
TEMA
TEMA
TEMA
n Pitch
U-Tube
No. ol Passes
108
24 20
42 36
66 64
86 80
124 116
174 164
2t8 202
272 260
334 320
390 380
468 452
550 532
626
'720 608
700
818 796
928 904
1036 1016
1220 rr92
t4t2 1384
804 788
1834
1804
2584
2544
20'72 2036
133
134
Mechanical Design of Process Systems
Table 7-13
Continued
Tube Count for
TEMA
M
Fixed
Tubesheet
Shell
lD in.
5.M7
6.065
7
.98r
10.02
12.00
t3.25
15.25
.25
19.25
17
21.25
23.25
25.00
27 .U)
29.OO
31.00
33.00
35.00
37.00
39.00
42.00
45.00
48.00
51.00
54.00
60.00
864
14 148
26 26 16
42 40 36
64 61
56
85 '76 72
ll0 106 100
147 138 128
184 175 168
227 220 212
280 265 252
316 313 294
371 370 358
434 424 408
503 489 468
576 558 534
643 634 604
738 709 6U
8M 787 772
946 928 898
1087 1069 1042
1240 1230 rl98
t397 1389 1354
1592 1561 1530
1969 1945 t90/.
OD Tubes on 11/a-in.
TEMA
Type L or
No. ol Passes
l-in.
Type
TEMA
P
outside Packed
Floating Head
No. of Passes
TEMA
M
Shell
lD in.
5.O47
6.065
7 .981
10.02
12.00
13.25
15.25
17 .25
19.25
21.25
23.25
25.00
27.W
29.00
31.00
Fixed
Tubesheet
No. ot Passes
86
12
24
37
57
70
97
r29
t62
205
238
275
330
379
436
l0
4
8
20
l6
32
53
28
48
70
90
&
84
r20
r52
1t2
193
184
228
264
220
256
315
363
300
360
422
410
142
TEMA
Type S
Inside
Floating Head
No. ot Passes
Type
U
U-Tube
No. of Passes
74400
l0 104
44
22 18 16 14 l8 t4 812
14 8
38 36 28 24 33 28 16 18 26 24
56 52 48 46 51 48 42 44 44 36
13 72 60 44 73 68 52 44 56 52
100 98 88 80 93 90 78 76 86 76
130 126 116 104 126 122 112 192 114 104
170 162 148 140 159 152 132 136 152 136
2r2 20r 188 176 202 r92 182 172 19? 176
258 2s0 232 220 249 238 21.6 2t2 232 220
296 294 276 250 29r 278 250 240 270 256
3ss 346 328 300 345 330 298 288 322 3U
416 408 392 360 400 388 356 348 378 3U
475 466 446 420 459 450 414 400 444 424
544 529 510 498 s26 514 484 4& 508 492
619 604 582 s66 596 584 548 536 s78 560
696 679 660 646 672 68 626 608 660 632
768 753 730 723 756 736 '7M 692 740 '1r2
908 891 860 840 890 878 834 808 872 836
1041 1017 990 968 1035 lm8 966 948 1010 980
1189 1182 1152 1132 1181 l162 lll8 tO92 1156 tt24
1348 133'1 1300 1280 1350 1327 1277 1254 1322 1284
l53i 1503 1462 r4r'iO 1520 r49Z 1436 1416 1496 1452
1906 1879 1842 1802 1884 1858 1800 1764 1866
Tube Count tor 1-in. OD Tubes on 11/4-in.
Type L or
A Pitch
TEMA
Type P
Outside Packed
Floating Head
No. ot Passes
54
12
2t
l)
4
l0
8
18
16
lt
52 46
61 58
89 82
113 1r2
148 138
180 r74
22r 210
261 248
308 296
359 345
418 40r
28
40
56
76
104
128
168
2N
236
286
336
388
1828
v Pitch
TEMA
TEMA
Type S
Inside
Floating Head
No. of Passes
Type
U
U-Tube
No. of Passes
00
44
108
24 i0
36 32
50 44
70 64
96 88
124 t20
156 152
200 188
232 220
282 268
330 320
382 368
{l
The Mechanical Design of Shell-and-Tube Heat Exchangers
Table 7-13
Continued
Tube Count for 1-in. OD Tubes on 11/4-in. 0 Pitch
TEMA
Type L or
Shell
lD in.
33.00
35.00
37.00
39.00
42.00
45.00
48.00
51 .00
54.00
60.00
M
Fixed
Tubesheet
No, of Passes
495
556
632
705
822
946
478 472
552 538
613 598
685
672
'799 786
922 912
1079 1061 1052
1220 t159 1176
1389 1359 1330
1714 l69t t6&
TEMA
Type P
Outside Packed
Floating Head
No. ol Passes
477
540
608
674
788
910
1037
1181
1337
1658
Tube Count
TEMA
M
Type L or
Shell
lD in.
5.O4'7
6.065
7 .981
10.02
12.00
13.25
15.25
17 .25
19.25
21.25
23.25
25.00
27.N
29.N
31.00
33.00
35.00
37.00
39.00
42.00
45.00
48.00
51 .00
54.00
60.00
Fixed
Tubesheet
No. of Passes
964
L2 l2 12
22 20 16
38 38 32
)o
)b
Jz
69 66 66
97 90 88
t29 \24 120
t64 158 148
202 l9l 184
234 234 222
272 267 264
328 317 310
378 370 370
434 428 428
496 484 484
554 553 s32
628 621 608
708 682 682
811 811 804
940 931 918
1076
1218
1370
1701
106l
l0,l0
1202 tt92
1354 1350
1699 1684
460
526
588
654
765
885
TEMA
Type S
lnside
Floating Head
No. ol Passes
&O
7s6
866
1138
1292
r@4
OD Tubes on 1tA-in.
TEMA
Type P
Outside Packed
Floating Head
No. ol Passes
U-Tube
1002
1018 1000
1160 1142
1307 1292
1626 1594
!
U
No. ol Passes
440
498
562
630
144
872
448
508
568
lor 1-in.
Type
424
484
548
620
728
852
980
1116
12@.
1576
Pitch
TEMA
Type S
lnside
Floating Head
No. ot Passes
TEMA
Type
U
U-Tube
No. ot Passes
544-544-00
1264-126444
21 16 16 12 t7 12 812
12 8
32 32 32 18 30 30 16 18 24 20
52 52 44 24 52 48 42 24 38 36
61 60 52 50 61 56 52 50 52 48
8984806485786264.7268
l 13 112 rt2
96 108 108 104 96 98 96
148 144 140 114 144 136 130 tt4 t28 124
t'18 178 t'72 156 1',73 166 154 156 166 156
216 216 208 192 217 208 194 192 200 196
258 256 256 212 252 240 230 212 240 232
302 300 296 260 296 280 2'70 260 284 276
356 353 338 314 345 336 310 314 332 332
4r4 406 392 368 402 390 366 368 290 384
476 460 460 420 461 452 432 420 442 436
542 530 518 484 520 sr4 494 484 254 248
602 596 580 550 588 572 562 548 574 560
676 649 648 625 66r &0 624 620 W 628
782 780 768 730 776 7s6 738 724 758 748
9M 894 874 850 900 882 862 844 872 868
1034 rO27 101,2 980 1029 i0l6 984 9'72 1002 988
1178 1155 1150 1125 1170 1156 tt26 1114 1146 ll40
1322 1307 1284 1262 1310 1296 t268 1256 1300 1288
1654 1640 1632 1585 t64t 1624 1598 15'76 1620 1604
135
136
Mechanical Design of Process Systems
Table 7-13
Continued
Tube Count tor 11/4-in, OD Tubes on 1sfi6-in.
TEMA
Type L or
shell
lD in.
5.047
6.065
7 .981
10.02
12.00
13.25
15.25
1',7 .25
19.25
21.25
23.25
25.00
27.W
29.W
31.00
33.00
35.00
37.00
39.00
42.00
45.00
48.00
51.00
54.00
60.00
M
Fixed
Tubesheel
No. of Passes
744
864
t9 14 12
29 26 20
423834
52 48 44
69 68 60
92 84 78
121 1l0 104
147 138 128
r74 165 156
196 196 184
237 226 224
280 269 256
3t3 313 294
357 346 332
4t6 401 386
461 453 432
511 493 478
596 579 s70
687 673 662
790 782 758
896 871 860
1008 994 968
1243 1243 l2l0
Type P
Outside Packed
Floatlng Head
No. of Passes
TyPe
LorM
Shell
lD in.
5.04',1
6.065
7 .981
10.02
12.00
t3.25
15.25
17 .25
19.25
21.25
23.25
25.00
S
TYPe U
Inside
Floating Head
U-Tube
No. ol Passes
No. ol Passes
00
00
64
14
22
32
48
64
86
tt4
138
t62
196
232
268
310
356
4M
452
534
626
720
822
930
00076414 14822 20 16
37 36 28 22
44 44 36 28
64 62 48 45
85 78 72 69
109 w2 96 86
130 130 116 1r2
163 152 r44 130
184 184 1"12 164
22r 216 208 196
262 252 242 228
302 302 280 270
345 332 318 305
392 383 3& 3s7
442 429 4r2 407
493 479 460 449
576 557 544 5r2
657 640 628 596
756 745 728 696
859 839 832 820
964 959 940 892
1199 1195 1170
1160
1116
Tube Count for 11/4-in, OD Tubes on 11fi6-in'
TEMA
A Pitch
!
t20
144
164
296
3M
388
440
522
6t2
700
800
908
1140
fvoe
rtinq Head
88
184
220
256
TEMA
No. ol Passes
52
76
132
152
Tvpe S
lnside
I Head
42
104
l'vDe P
No. ol Passes
32
60
80
TEMA
No. of Passes
16
44
Pitch
Fixed
Tubesheet
12
28
TEMA
Outside Packed
444
664
12 12
24 22
37 34
45 42
61 60
80 76
97 95
t24 124
t45 145
172 168
12
20
0000000
6640664
t2 12 lZ
21 16 16
32 32 32
38 38 32
52 52 52
70 7o 68
89 88 88
rr2 112 ll2
138 138 130
164 l@ 156
0r2
12 21
18 29
24 38
48 52
s0 70
80 85
96 108
114 136
136 154
12
12
28
34
48
66
84
108
128
rs4
4
8
16
34
44
56
70
100
128
142
U
No. of Passes
000
000
064
12 128
18 20 20
24 28 28
48 42 36
50 56 56
80 74 68
96 98 96
114 124 120
136 140 136
n
The Mechanical Design of Shell-and-Tube Heat
Exchangers
Table 7-13
Continued
Tube Count lor 'l'tlq-in. OD Tubes on l/rs-in.
TEMA
Type L or M
Shell
lD in.
27 .OO
29.00
31.00
33.00
35.00
37.00
39.00
42.00
45.00
48.00
51.00
54.00
60.00
TEMA
Fixed
Tubesheet
No. of Passes
210 202
24r 234
272 268
310 306
356 353
396 387
442 438
518 518
602 602
682 681
7'.70 760
862 860
1084 1070
202
230
268
302
338
384
434
502
588
676
756
8s6
1054
!
lnside
Floating Head
U-Tube
No. of Passes
No, of Passes
No. of Passes
1042 t034 1026 1008
5.047
6.065
7 .981
10.02
12.00
13.25
t5.25
t7 .25
r9.25
2t .25
23.25
25.O0
27 .O0
29.00
31.00
33.00
35.00
37.00
39.00
42.O0
45.00
48.00
51.00
54.00
60.00
544
664
13 108
24 20 16
37 32 28
45 40 40
60
56
'79 56
76 '16
97 94 94
t24 tt6 ll2
148 t42 t36
174 166 160
209 202 t92
238 232 232
275 264 264
314 307 300
359 345 334
401 387 380
442 427 424
522 506 500
603 583 572
682 669 660
1"t"t '762 756
875 857 850
1088 1080
1058
<
,
TEMA
Type P
Outside Packed
Floating Head
Type S
lnside
Floating Head
No. of Passes
,l
,tl
12 108
2t 18 16
32 28 28
3',7 34 32
52 52 48
70 70 64
90 90 84
tt2 108 104
140 138 128
162 162 156
191 188 184
442 ,130 416
26t 249 244
300 286 280
34t 330 320
384 372 360
428 412 404
497 484 4'72
5',75 562 552
660 648
640
743 '728 716
843 822 812
1049 1029 t0t6
U
Pitch
TEMA
No. ot Passes
Type
184 180 158 r12 176 176
2t7 212 204 198 200 196
252 248 234 236 232 232
289 2',76 270 264 272 268
329 316 310 304 312 296
312 368 354 340 348 348
420 .102 402 392 396 392
485 116 468 464 472 456
565 55J 5+6 544 552 536
653 616 628 ',705
620 '7t2
628 620
738 126 ?20
708
837 820 811 80.+ 808 804
1036 l0lE i0r2 1008 l0t2 992
Tube Count tor 1tlc-in. OD Tubes on 1el16-in.
Shell
lD in.
TEMA
Type P
Outside Packed
Floating Head
193 184 184 172
224 224 216 198
258 256 256 236
296 296 282 264
336 332 332 304
378 3'70 370 358
428 426 414 408
492 492 4U 464
570 566 556 544
658 648
648 620
742 '729 722 7t2
838 823 810 804
TEMA
Type L or M
Fixed
Tubesheet
No, of Passes
Pitch
TEMA
Type S
TEMA
Type
U
U-Tube
No. ol Passes
00
00
44
12
20
26
40
56
74
96
t2
20
24
36
52
68
88
120 ttz
142 136
170 164
200 192
228 220
268 256
306 296
346 336
390 380
456 448
542 528
618 604
708 692
802 '784
l0l0
984
'137
-o9.
9.
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.
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o
o
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P
6
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E
The Mechanical Design of Shell-and-Tube Heat
iGlD.(NB +
1)
(5.22X10)roD"7
r
where (p/p,,). G,, D., D.
NB
Polh ot Fluid
A. Shell side fluid baffling showing segmental cut baffles.
^l
t.
Fluid Flo13 Poroll.lhTubrs os,t Po3r.3
/From one Bolll.d A..o io N.rr.
eorrrr
"wintoi' or "co'l
03 %cu!,{hkh
O O J Eac$ed
sotlrs Ooid
O
B. Segmental baffles showing window are for fluid flow.
oootoo
ooolooo
ooooo
ooooo
ooooo
ooooo
)OOOooO
oo
Iilol.:Ar0o Avo,l0bla tor Cror! Flor
i:l:1if.' 4,i! *,
C. Cross
orhe'
L3ed Cort,r,!rr r .' peler*ce I . oth.t
a,,olq!-e.rt ro ooh . E3se"',- ||e so-.
flow area for iube layouts.
Figurc 7-228. Various baffle *indou schemes
[,1].
Baffles neveq except for unusual designs such as orifice baffles, extend a full 360" around the shell. The baffle plate is cut such that the shell-side fluid can flow
around its edge. The open area between the baffle edge
and the shell wall is known as a baffle "window." Baffle
windows are commonly referred to in terms of percentages of the entire circular shell area. Figure 7-22b illustrates various baffle window schemes.
Shell-Side Pressure Drop. There are several methods
to calculate the frictional pressure drop across tube bundles, and the reader is referred to Ludwig [4] or Kern [9]
who give comprehensive discussions of the various techniques. The method we
will
(7 31)
:
:
are previously defined
number of bafiles
= specific gravity of
:
shell-sidc
fluid
combined friction factor deter
mined from Figure 7 23
is
{%XSherl 10.).
Ner Fror Ateo ol Wiido* is
Full Windor A/.0 Diius Ar.o
Boftr.s @0,'d@
139
Kern [9], where the expression for the shell-side pressure drop is given as follows:
Sallle Pilch or Stoci.q
;9 ]
Exchangers
use is the one developed bv
TUBE VIBRATIONS
Chapters I and -1 described how fluids moving around
objects can produce r ibrations. The same thing happens
in shell and tube heat exchangers, but it creates a different problenr. Chapters I and ,1 were primarily concerned
with Yorte\ sheddrng. This chapter covers vortex shedding and sereral olher t\pes of vibration phenomena.
Also. the problen is difterent from rhat in Chapter 4 because the boundarr conditions of the system have
chansed. Chapter I used a cantile\er beam to show how
a til\\ er or srack is restrained several different ways at
the ends."
There have been nrany research studies made in the
field of tube vibrations. Probably the most numerous
stem lrom the nuclear industry. The problem is complex
and no one method proposed is a full and complete anal-
ysis of tube vibrations. Consequently, research is still
being done to better understand the causes and prevention of tube vibrations. Here we will outline the causes
of the phenomena and present some quanlitative approaches to the problems.
Presented first is a simple and quick approach to pre,
dict tube vibrations caused by shell-side flow. This approach was originally developed by John T. Thorngren
[14] in 1970 and is called the "maximum velocity
method." We will present a modified version of the
method proposed by Thorngren to encompass a wider
range of applications and to specifically define all the
variables in the equations. This method addresses the
tube vibration caused by vortex shedding when the shellside fluid alters direction at the baffle plate and strikes
the tubes. The arrows in Figure 7-l show how flow di,
rection of a fluid turns at the baffle plate and strikes the
tubes midwal between rhe bafile plates. Thi5 causes rhe
tubes to deflect and the hole in the baffle plale acts as a
fulcrum for the tubes to deflect against. Two types of
problems can result a fatiguing of the tubes at the baf:
fle hole and eventual tube rupture, or the tubes colliding
For low-Finned Tubes
f" (sq. ft)/(sq. in.)
'
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zl x Sooo
-o9= eElDF;
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Ess_ii3;S
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t -:
a*:L:L+:
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<t
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ro
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tl.E
oti
ii,
The Mechanical Desien of Shell and-Tube Heat
with each other resulting in abrasion and rupture. This
phenomenon can be offset somewhat by anticipating
shell-side velocities. The velocity of the shell-side fluid
can be kept reasonable if the entry and exit nozzles are
properly sized.
To determine the force exerted on the tubes by the
fluid vortices we refer to Equation 4-80, the von Karman
eauation as follows:
E_
Co pY212
(4-80)
2g"
In the case of tubes the characteristic area, f2, can be
replaced by the outside tube diameter, d. (ft), and the
value for the force becomes:
CFpV2do
:
force per unit length of
tubes
(4-80a)
Chapler 2 introduced the concept of the Strouhal number as the numeric constant between the resonant frequency of vortex shedding, f,, and the cylinder diameter,
d., divided by the free stream velocity, V This is written
AS:
f.d"
()-31)
Exchanqers
141
7 -24, we notice
how the drag coefficient varies over a wide range of
Reynolds numbers. For viscous liquids moving at low
velocities, it is very possible for the Reynolds number to
be low, making the drag coefficient high. Thus, we keep
Cp as a variable in Equation 4-80.
In Figure 2-32 we see that at NR" > 3.5 x 106 the
vortex street is again developed. At this Reynolds number the fluid flow velocity would be too high to consider
wind design as discussed in Chapters 2 and 4. Also,
those two chapters were only concerned with a single
cylinder, whereas here we are studying the effects of
vortices on an array oftubes. At values of Nn" ) 3.5
x 106 for tube arrays we would be more concerned with
flow-induced vibration. which is discussed in the next
section. Also. Reynolds numbers in this range rarely, if
ever, occur in heat erchangers.
In an arral oftubes the maximum velocity ofthe shellside fluid occurs at the minimum cross section between
the tubes. Thus. V increases such that as the tubes get
closer together the ralue of Nq. approache\ 3.0 x 105
and the rorter street is broken up as previously described. Thus. the effect of vottex shedding in tube arrays is onl1 si-enificant for tubes spaced such that the
Relnolds number falls within the appropriate range. The
effects of tubes being spaced closer are discussed later in
this chapter.
viscous liquids. Now, observing Figtre
For considering vorteK shedding, Equation 4-80 represents the maximum force exerted on the tubes. To ana-
As observed in Figure 2-32 the vortices break up when
Nq" approaches 3.0 x 105. Referring to Figures 4-21
and 4-29 we see that the force or drag coefficient is constant in this range. However, in Chapter 4 rve are dealing
with air as the flow medium. In our application here we
are dealing with a wide range of fluids-gases to heavy,
lyze the tubes, one must consider them as continuous
beams supported by baffle plates. The baffle plates act
like beam supports as the fluid exerts a force in the tubes
forcing them against the baffles. The general equations
for the shear force and deflections of a continuous beam
take the following general forms:
FiE)re 7-24. Drag coefficients versus
Reynolds number for long circular
cylinders in crossflow.
'to
'142
Mechanical Design of Process Systems
F. : aFrL
^
bFI L4
EI
(7
-32)
(7
-33)
The values for a and b are dependent upon the boundary conditions of the continuous beam. Typical values
are presented in Figure 7-25 and are fairly comprehensive for most shell and tube exchangers. For cases not
covered in Figure 7-25, the specific values must be
solved for using the analysis for a continuous beam.
As the shell fluid exerts pressure on the tube, the tube
deflects at mid-span forcing the tube at the baffle against
the baffle hole. The stresses induced in the tube are a resuit of localized forces at the tube-baffle contact points.
At these points the tube behaves similarly to a horizontal
vessel such that only a portion of the tube wall offers effective resistance against collapse. Thus, Equation 4-2
predicts the amount of tube wall that effectively resists
the baffle wall reaction, and is written as
a:11{\12+ :olI
(4-2)
180
Continuous Beams
dmar
br"r
I
l .200
2
3
0.550
0.0059
0.0099
0.0069
0.0094
0.0097
0.0065
1.100
1.223
4
0.572
1.143
5
6
4
[.r.
(0,130 r
fton A] =
t.005r
,rrlsl
A
€ comtruous
! il.r. (0.tt , tioE
^
.'
a
r.&
o.raa I
rroi
A
o. D)
-
0,0rl
!r.
(0,415 r
koh
E,
5
o.m!a
!r./al
BEAM-FoUR Eeual spaNs-LoAD FtRsr aND THrRo spANs
o) a 0,00n &,4/El
a
6.
rr.r.
tl.r.
(t az
rlr.n
A) E 0.6tt
{,r/al
coNTlNuous BEAM-FoUR EeuAL spANs--{LL spaNs LoAoEo
r
^
.L
(Gaa I lr.h A .na a)
Figure 7-25. Boundary conditions of continuous beams
u5l.
-
O.Ol5
d./s
The Mechanical Design of Shell-and-Ttbe Heat
where d
=
A=
angle of contact
where
sisting tube wall area
:
that neither the tube nor baffle hole will deform to reduce stfesses, which is the worst condition. For determining contact stresses between the two bodies, Timoshenko [16] has shown that for the case in Figure 7-26
the diameter of the circle of contact is
:
149
constant that represents the amount of effective re-
radians
Thorngren [14] proposed that about 40% of the tube
metal is effective in resisting wall membrane stresses. In
Equation 4-2 this would make the value of 0
144' ,
greatef than most saddle-shell connections for horizontal
vessels . To take the problem furtter we consider the tube
wall as a ring shown in Figwe 716. The assumption is
d
:
q
Exchangers
1.76E(qi_e")g4" l"'
[ 2EEB(d, + dJl
Now combining Equations 7 -32 and 7-35 we have the
followins:
:
" I--Lil--qe-)||--t')'
\aF,L/ \4 + dB / \0.798/
r-v! l-u$
where c =
z,
= hisson
ratio for the tube material, dimension-
less
/B
= hisson
ratio for the baffle plate material, di-
mensionless
E=
Ea
From Equation 7-34 one can deduce that the tub€-bafalLalyzed as point loadings. For
such loadings as shown in Figure 7-26 the contact force
representing the shear of the tube against the baffle plate
:
modulus of elasticity for tube material, psi
nodrlus of elasticity for baffle plate material,
pst
fle interface should be
*. (#,.J"L,,*',J'
c = constant, in./lbr
cr
:
constatrt, dimensionless
To arrive at the modified damage numtrr
damage we solve for F1 in Equation 7-32:
Q-3s)
(7-37)
EB
Q-34)
ts
(7-36)
F,:
-
for baffle
F"
o'al-
Evaluating the relationship for shear in Equation 7-32 we
have
F.
=
aaFrl-
Now dividing this relation into Equation 4-80 we obtain
Cpd,p\Palc _
1.0
2g"F.
Letting the baffle damage number be represented by
Nss, a dimensionless parameter, we have:
*,
^"" -
Cpd.pV2alcv
--fdE-
where Nss
(
Q-38)
1.0
If NBE > 1.0, then tube damage at the baffle is very
probable and a tlicker tube should be selected and the
analysis repeated.
The analysis of determining the dimensionless parameter, NsD, which governs tube damage induced by excessive displacements in tube movements, is similar to that
for the baffle damage parameter. Solving for F1 in Equation 7-33 we determine F1 as follows:
Figule 7-26. Fluid foroe causing tube to impinge on
plate.
baffle F"" : E
bL4
144
Mechanical Design of Process Systems
Dividing this expression into Equation 4-80 we have
Ded,pV'?bLa
_
2g.6E,I
1.0
We define N6p as
rrcD -
CDd,pv2bL4
2g.6E
where NcD
<
(7
I
-39)
1.0
>
1.0, then thicker tubes should
Once again, if NcD
be selected and the analysis repeated.
Equation 7-39 is similar to that obtained by Thorngren
[14] and Coit [17]. The dimensionless parameters, Nss
and N6o, in Equations 7-38 and 7-39 should be regarded
as mere rules of thumb. Even though they are dimensionless, they do not have the same firm basis as do dimensionless parameters used in fluid mechanics and
transport phenomena.
One can approximate the tube behavior by using the
principles in Chapter 2, Example 2-6. Using the baffles
as supports and spacing them (either equally or unequally), one can simulate the tube displacements. However, since we are not dealing with a single tube, vortex
shedding around tube bundles can presently only be accounted for in design by being conservative.
Flow-induced vibration of exchanger tubes is another
mode different and distinct from vortex shedding. In
vortex shedding a component of the flow, the vortex, is
the contributing cause to the tube vibration. In flow-induced vibration, forces are exerted on the tubes that are
caused by flow field interactions around the tubes. Fluid
that flows normal to the tubes is forced into a smaller
area between the tubes resulting in a Venturi effect
known as "jetting" or "jet switching." This phenomenon
is shown in Figure 7-27 where a control volume of fluid
is shown being compressed between two tubes. The result of this 'letting" effect is the fluid exiting the narrow
area between the tubes diverges into a diffused mass that
whips or whirls around remaining tubes. This "whirling" effect is another mode of vibration.
Vibration induced by turbulence is the most common
mode. This phenomenon is commonly confused with the
other modes because the term turbulence is viewed synonymously with fluid flow and vibration resulting from
such flow. However, vortex shedding, jetting, and
whirling are different from turbulence because even
though they exist in turbulent flow, they can all be final
causes of failure and each must be controlled. Turbulence can be best viewed as a pressure field around a
tube shown in Figure 7-28. Herc we see a pressure dis-
FigUJe 7-27. Jet switching in tube arrays.
F-+
6= futr)
p = p_(t)
where t= iime
(r\
Figure 7-28. The magnitude of the direction of the fluid striking the cylinder can be thought of mathematically as a forcing
function, F-, mapping a pressure distribution around the cylinder over region R.
'wi
The Mechanical Design of Shell-and-Tube Heat Exchangers
tribution around a cylinder in much the same way as an
aircraft airfoil. This pressure field, or distribution, varies all through the flow regime and is also a function of
time. As this pressure distribution fluctuates and
changes, the tube is subject to vibration as the fluctuation frequency approaches that of the natural frequency
of the tube. It is this fluctuation frequency that is referred to as the turbulence response spectra. As the pressure distribution changes over random time intervals, vibration is generated.
We will describe briefly the methods to analyze these
modes of vibration. The subject is exhaustive and is far
from being a perfected science. One could spend many
volumes the size of this one and not adequately cover the
subject. For this reason the reader is referred to Blevins
[18] for more details.
As previously stated, turbulent flow induces continuously varying pressure distributions all around the tube
surface(s). The efficiency as to how the pressure forces
excite the tubes in each mode (first, second, third, etc.)
of vibration is termed 'Joint efficiency," denoted by
J;(<,r). This parameter represents the model efficiency of
the pressure forces at a given frequency c,.r, where col is
the natural frequency ofthejth mode. Figure 7-29 shows
the joint acceptance of a single tube plotted against cull
V. (U in Figure 7-29), where L is the tube length between spans and V is the fluid velocity. The ratio of the
t
5
:
3
0.01
fluid velocity to the turbulence frequency,
as the correlation length ard is given by
145
r,r, is known
(7-4o)
> I, then the varying pressure forces that act
If L. >
along the tube oscillate in phase. Also, ifthe value of L"
is much smaller than the length of the tube, such that
coL
_ >> I
then the joint acceptance is independent of the mode
shape and is proportional to the value of LclL.
The mean response of the tube is the average tube displacement induced by the mean flow over the specified
time interval. The greatest percentage of the response
exists in the fundamental mode. For a tube that spans
several baffle supports the following expression is used
for the mean response:
6-, = 0 036cv'd, (*)(*)
where C
=9.7x10
p=
'(*.)""'" ('.J
(7
-4r)
1(sec)05/(ft)r5
density of fiuid external to tubes, slugs/ft3
slue
32.2 lb.)
:
(1
/''i V""-;''\
,,, ,,,
Figure 7-29. -Th€ joint acceptance of a simply suppofted tube subjected to turbulent flow. (From FlowJnduced Vibration by R.
Blevins @ 1977 by Van Nostrand Reinhold Company, Inc. Reprinted by permission.)
146
Mechanical Design of Process Systems
V : fluid velocity of fluid external
:
dr :
L:
Lr :
fN :
m
mass density of
to tubes, ft/sec
fluid external to tubes, slug/ft
tube OD, ft
tube length between baffles, ft
total length of tube between tubesheets, ft
fundamental natural frequency of tube portion
between baffles, Hz
sum of structural damping and the fluid dynamic
damping
distance along tube, ft
I :
x:
d" :
4Rs
:
4(hydraulic radius)
:
4 (flow area between tubes)
wetted perimetel
- ;] ".
tubes on an equilateral
triangular pitch of P
_
-;
+0,
[/r\
t\-dJ
- f] -
ro.,"0",
on a square pitch ot P
t2
o*": E-Cp1*-y
6.*
:
:
2.586.-, (for
x
: L/2)
F i,l2 -L
,lZ r0
(7
4=
=
(7
-46)
/\
."^ _ pv'0, 6"" 16,l
2e,
where
K,
:
\d,/
2T-
tn
D
T
/nVfor :r ) l 5
\T/ D'
Kr: l:l
(7-43)
5
- ;;;
6L-
dti
-4s)
(P\'",
\T/
r<
D
1.5
drag coefficient of tube surfaces
The value for the natural frequency at the tube in
:
mr :
(7
\o,/
K, = C'(D/T)
Equation 7-41 takes on several forms. The easiest to use
is the formulation developed by Blevins [18]:
where E,
zE"
(7-42)
Equation 7-42 represents the maximum tube deflection to be incurred. The factor 2.58 represents the ampl!
tude of the highest one percent of cycles.
"7(
rN
pv':d, -. 16,l
ru' : -N" l=l
-
Using Figure 7-29 the value of thejoint acceptance for
the appropriate mode and the first mode are obtained.
The ratio of the joint acceptance of the mode being considered to that of the first mode is multiplied by the value
of 6.*, obtained from Equation 7 41. The relationship in
Equation 7-41 is based on the theory of tube turbulence
developed by Wambsganss and Chen [9], which yields
the followins maximum stress value:
where Ce
port end conditions, and tubes that have equal spans and
unequal spans. These expressions were presented earlier
in this chapter and in Thble 7-6. Equation 7-44 is simplest to use because it requires less input. However,
when the information is available and time permits, the
expressions recommended by TEMA should be used.
The phenomena of "jetting" and "whirling" are not as
well founded as vortex shedding and turbulence. This
does not say that vortex shedding and turbulence are solidly based, but relatively speaking, they are compared to
the other vibration modes, such as jetting and whirling.
From Figure 7-28 one can predict that when the tubes
are inclined to the fluid flow, the results are force components about the x and y axes. Equation 4-80 illustrates
how one can determine the force induced per unit length
of a circular cylinder. In the case of whirling and jetting
the term CD is a variable. This term is called the force
coefficient and is used in Equation 4-80 to evolve the following expressions:
-44)
modulus of elasticity of tube metal, psi
mass density of tube metal. slugs/ftl
tube OD, in
tube ID, in.
TEMA gives a listing of expressions for the natural
frequencies of the tubes based on several types of sup-
-(,n)'.,(,n)'
where D and T are parameters defined in Figure 7-30 and Fig-
ure 7-31.
Values for K, have been plotted against the parameter
T/D. These values are shown in Figures 7-30 and 7-31 to
represent the whirling parameter 2(2?r)0 5/(C"Kr)0 '?5. Experiments indicate that the lower the whirling parameter
the greater the probability that whirling (and jetting) will
occur.
To determine
if the tube deflections are within a safe
range one must estimate the components F, and F* at
their maximum values using Equation 4-80. From the
tube spacing determine the force coefficients K, and C*
from Equation 7-46. Then solve for 6, and 6" and determine if those deflections are acceptable. After determin-
The Mechanical Design of Shell-and-Tube Heat Exchangers
ing that the deflections are in a safe range, use Figures
7 -30 and7 -31 to determine the whirling parameter. If the
parameter is on the low side, then the tube spacing
should be increased to raise the whirling parameter. Unfortunately, at the current state of technology, there are
no critical values to decide whether the whirling parameter is critical. One manner in which to avoid nroblems
with whirling is to use Table 7-14 in derermining the
maximum shell-side fluid velocity flow. This table and
the previous discussion will eliminate any problems with
jetting or whirling. If the velocities cannot be controlled,
because of someone else's design or a client's requests,
then this procedure can give one an idea of whether
whirling can be anticipated. The main focus is to keep
the tubes spaced such that the maximum velocity will be
reasonable. It has been confirmed bv exneriment that the
critical velocity for whirling increises'rapidly wirh the
minimum spacing between the tubes and that inline tube
arrangements have lower critical velocities than staggered tube arrangements (refer to Figure 7-19 for the
various illustrations of arrangements).
PLATE.FIN HEAT EXCHANGERS
These units use have been on the increase the past sev-
eral years because of an increasing number of liquified
gas and cryogenic plants. The plate fin heat exchanger is
1
147
more efficient than the shell and tube exchanser because
the comparable shell and tube exchanger req-uired to re-
fin would be eight times the volume and
twenty-four times the weight of the plate fin if constructed of aluminum. The reason for this is that if the
plate-fin is made of brazed aluminum, the aluminum
place a plate
conducts heat better than most materials and can be used
down to absolute zero (-460'F). Since the ductility of
carbon steel is lost at -20"F, one must revert to expensive nickel alloys or stainless steels in the shell and tube
design. Thus, for cold services, the plate-fin offers some
advantages.
It is here that the advantages of the brazed plate-fin exchanger end. For the plare-fin to be applied, a very clean
service is required. Even in clean services, these units
can accommodate certain thermal shock and fatisue. It is
quite possible after continued and repeated therrial loading in excess of differential temperatures of 50'F that internal components can fail. In addition, because these
units are aluminum. external nozzle loadings induced by
the piping can cause pipe stress problems. One must be
extremel! careful ho\\' much loading is induced to the
nozzles. because even if failures do not occur, leaks are
common if overloading exisrs. Thus, if the service is not
clean. a shell and tube design must be used.
In gas processing and cryogenic services, the plate-fin
exchanger suffices because in these applications the ser-
--loF
\JT
rl-L
o
Oo
./
./
,-7
-rlA
---_
-
i,
. -2 . 5,onr-3ro'2 '
xY
-lDt'3
(0,1,3
Figure 7-30. Whirling parameter of a tube row
expressed as a function of transverse spacing.
(From Flow-lnduced Vibration by R. Blevins
@1977 by Van Nostrand Reinhold Company,
Inc. Reprinted by permission.)
148
Mechanical Design of Process Systems
!M!!
"F
A
o
o
o
.-1'h
>;
-/l
,r1
o
--r.
h
-- u+
I
o
Figure 7-31. Whirling parameter for tube ar-
rays. (From Flow-lnduced Vibration by R.
Blevins Oi977 by Van Nostrand Reinhold
Company, Inc. Reprinted by permission.)
With newly developed techniques in vacuum brazing,
stronger bonds have been achieved that reduce failures
of internal components subjected to thermal shock and
Table 7-14
Maximum Recommended Shell-Side Velocities
All liquids in 10 fusec
Gases and Vapors-in fl/sec
Pressure
(psi)
18 30 50 100 150 200
2'7 -tn.(vac) 250 185 160 110 100 90
15-in.(vac) 130 100 85 65 60 52
0
100 80 70 50 45 40
50
65 55 45 35 30 25
100
200
500
1000
fatigue.
Molecular Weight
55 45 35 25 20 18
50 40 30 23 19 t7
40 30 20
20 15
400
77
45
35
20
16
vices are relatively clean. However, it must be noted that
shell and tube exchangers are more popular because of
their flexibility ofuse. Certainly with moderate to heavy
viscous fluids, the shell and tube exchanger is the only
design to use.
Figtre 7 -32 shows a plate-fin exchanger with rectangular boxes containing an assortment of plates and fins
resembling honeycomb structures. Fluids flow in tubu-
lar channels formed by fin attachments between plates
(Figure 7-33). The plates that separate the two services
vary from approximately 0.006 in. to 0.023 in. in thickness, depending on the pressure of the service. This design is commercially available at a temperature and pressure of approximately
-
452"F at 1,400 psig.
The aluminum flanges used on these units are designed per ASME Section VIII Division I and, quite
commonly, are identical to ANSI 816.5 flanges.
For further discussion on the thermal analysis and design of plate-fin units, the reader is referred to Kays and
London [20].
EXAMPLE 7.1: REGENERATED GAS
EXCHANGER DESIGN
A gas-gas shell and tube heat exchanger is to be designed. The exchanger is to be used to exchange heat between a hydrocarbon process gas and a gas used for regeneration. The unit is to be designed per specification
sheet in Figure 7 -34. The exchanger is shown in Figure
7-35.
The process gas is to be cooled from 965'F to 705'F.
The regeneration gas is to be heated from 200"F to
661'F in a parallel configuration. Thus,
975'F
200'F
GTTD:775"F
750'F
tiITD
:
625"F
125'F
.M
The Mechanical Design of Shell-and-Tube Heat Exchangers
LMTD:
'7'75
-
125
149
:356"F
h (E,l
u25/
now,
q
:
riCo(LMTD)
The shell-side mass flow rate : 22,050 lb,/hr for the shellside gas, Co : 1. 10 Btu/lb.-'F. The required heat duty of the
unit is
q = 122.050r
'
q
:
l!hr rr. ror j'l=
1:so.r"r
lb",-'F
--
Rfr
8.634.780
I
nt
The available tube area in the exchanger is determined
follows: From Table 7-3, we determine that for a l1/+in. tube the square feet of external surface per foot of
tube is 0.3272 ft:. Thus.
as
Figure 7-32. The plate-fin exchanger. (Courtesy of Albraze
International, Inc.)
Available area
=
(0.3171)
'ft
T (ZS:),u0., (tr) ,,
=
1.38E.95
it:
ng Sh€el
Bar
Turning Distributor Fin
Figure 7-33. Tubular channels in plate surfaces result in excellent heat transfer in plate-fin heat exchangers. (Courtesy ofAlbraze
International. Inc.)
150
Mechadcal Design of Process Systems
I
HEAT EXCHANGER SPECIFICATION SHEET
2
5
5
7
a
9
lo
ll
t2
l3
l5
l6
t7
t8
t9
20
2l
22
23
?1
27
2E
?9
30
3l
33
34
35
36
38
39
40
41
42
43
1t6
47
4E
19
T"b"-T,rb".h".t
J.i.t
50
Bundle
Entranc€
Bundtc Erir
52
53
57
5a
59
6l
Figure 7'34. Heat exchanger specification sheet. (O1978 Tubular Exchanger Manufacturers Association.)
The Mechanical Design of Shell-and-T[be Heat Exchangers
151
For the tube-side gas, 1%-in.-11 gauge tubes
sa-tua-600
:
k:
osME)
0.7, obtained ftom Process data
Np"
P
0.03 Btu/hr-ftL'F
0.01 Cp : 0.024 lb/ft-hr
=
Tirbe-side mass
r.gu;riil{
flow rate = 41,884 lb./hr
For each tube,
.
----
41:qq4 9./hr
283 tubes
:
148
rb-ihr
: O.1524lbJft3 '
4 =: l'25 in"
1'010 in';
di
Ar : 0.8012 in''?
P
:
48.48 ff/sec
From Table 7-14 this velocity is reasonable
sa-ra8-6lrt
(^snE)
Flgure 7-35. Vertical gas-gas exchanger.
Shell-side nozzles C and
makes the flow area
l. = a'(16)'z=
D are
16
in. in diametel which
_:
Nr" :
Nr"
2ol.o6 in.2 : t.396 ftz
(48.4D
a
93,278
>
(1.oro) in.
ffi
,o
tou
*
10,000 and Equation 7-19 applies
0.027(93,278)0.8(0.7)t/3(1.0)
:
226.78
h..1.
Shell-side mass density
v:
22,050
:
p.
rr. / rr,. \
+
nr l=.:;r-l
Ijbtt, secl
j::--l:i:-
:
0.09 lb./ft3
Nr" ::+:1
From which,
:
48.75 ff:/sec
------o.os !!r n.396) ft,
ftr
From Table 7-14 we observe that this is a reasonable
velocity.
ftrbe.Slde Film Coellicient
Btu
: ro
-- hr-ft2-"F
-- lt
For turbulent flow inside tubes we use Equation 7-19,
the Sieder-Thte correlation,
Shell-Side Fllm Goefficlent
Nu"
N.,"
=
0.027(NrJ03(Np.)18 (rJrJ''4
:
?
= o.:o (Ps,
)"'rN*,',,
(;)"
Q-26)
152
Mechanical Design of Process Systems
For 60"-4 arrangement, p
:
1.75 rn.
1.r.
^"" _
-
-
8[0.43P'z
0.52'd"'z/4]
-- -
c=
B
:
0.119
:
L75
-
1.25
:
_I
0.50 in.
80.83
-.
- -^.
I
-
ln.
n
8 baffles
:
=
(1.75xt44)
in
j\
hr-ftr-"F
1.lso;"n
1,384.91 ft':
From previous calculation,
- l. t9 rt'
-ft'
Available area
:
1,388.95 ft'z
In most applications the available area should not be
n
:
p
0.09 lb-/fC average for tem0.05 lbm/ft-hr
:
Shell.Side Pressu:e Drop
Ap-
lh
<n '"m
12.348.00-15
hr-ft2
D.G, {0.119) fr (12.J48.00) lb./hr-ttz
^, _ 4 __.
0.05 lb./ft-hr
NR":29,388.24
Ns
D.
G,
=
:
:
ure 7-22,
8 baffles
t)
(7_Jt)
:
:
3.333
40 in.
shell ID
12,348.00 lb./hr-ft2
=
For Np"
29,388.24,
f = 0.0022
ft
from Figure 7-23.
f
f,=::=0.00t8
t.1.
:
'y :
D"
100
/
rr.re,r"t
f C.rD,(l_.,t8__t
(5.22X10)!oD"1d
For plain and bare tubes,
The exchanger has baffles with 25 % cut, thus from Fig-
=
:
.
+nr
10% greater than the required area, such material is not
wasted.
c"" - .=^.+ =
1.79 11'
Np.
8,634,780
1tz.st,)
as
ff
"l/'\l--- hr-ft2-'F
a,,
2
For the shell-side gas, p
peratures specified, and
:
I
+ 23.40
Btu
:
(7-301
(40) in. (0.50) in. (22.50)
rt
+ 0.001
Area required :
D.(cXB) . ,
a\=-ll" p(t44)
^rn
0.001
22.50 rn.
Computing the flow area of tube bundle
n"
+
distance between baffles
B:
:
Btu
hr-ft2-o F
IT _
ft
tube clearance
._
jn
tnnll
l^',',"=l t0.8tr/\tt
\u. r lvl
For gases used in this application the fouling factors are
0.001 shell-side and 0.001 tube-side. Solving for the
overall heat transfer coefficient,
or
:
1100)
(7-2e)
"dr,
8[0.43(1.75)7 - 0.5rr1.25r']l41 _,/1rr^' _
r(l .25)
D"
=
\o
t+
[aJ
0.119
specific gravity of shell-side gas
r
0.8 from process data
d
:
r.0:
/
\o t+
tl]
= 0.9
Exchangers
The Mechanical Design of Shell-and-Tube Heat
(0.0018)(12,348.00f (3.333X8
aP" =
AP.
+
From Equation 7-35 we compute the shear force induced
on the tube at the baffle hole,
1)
(5.22X10)ro(0. l 19)(0.9X1.0)
=
0.0015 psi
7-34
<
<
10 psi allowed on data sheet, Figure
I ^" \ /R:l#kltto-.tnr]
V
t=''
qEB + --l --f",&:
"=
EXAIIPLE 7.2: VIBRATION CIIECK FOF
c_
2(1.00
span between baffles
=
Shell-side gas density
4
:
:
=
22.50 in.
16.015
1.25 in.
ds
:
=
=
*
in.
1/o+
<olito.ri
Fr.
:
1.200 lbr/ft
F.
:
eaF,
1.156, where t/e+ in. is the baffle hole clearance (s€e
Figure 7-34)
A,'
: + [o," - o,"* + D'= d'te - al nz
t44t
P
I
^,
Ar
210.0
in., D,o : 37.125, P
=#[oo
:
- rr.,r,
=
G":
18,522.0
(5.145)
(1. 1ox1.2oo)
rtBE ^,
-
-
117.236
A
sec
b
:
0.0069
o
SeC"
F
+ (zig*")
-
=
6.471
CpdlpV2ale
(7-38)
------;----zE"r
'
r.2s)]
lh
.:"'
!-:
lDf
J-(l6.0lt
- SeC-
+n
ft'-sec
,
(2.0s1) ft,
5
n'-sec
0.0e
:
:5.14s
-;l
tt'-hr
1.10 and
aFrL
2(32.,
l|1
:
-
Nse
2.051 ft2
*,0-', (oryJ
16.015 lbf/ft
1.75
.tf#6.?s
1trpsi
10_E
p orr.rrur$ (9
z1tzz1 !":
tDf
L = q:
From Figure 7-20 we compute the shell-side gas velocity
bgtween tubes.
:
x
ft=
in.
D.
27.0
crPP4
Fr:
18,052 psi at shell-side conditions
1.25
=
lbr/ft
Frorn Figure 7-25, a
0.09 lb-/ft3
*
=
'. [.' ?]il''"l,o
From ASME Section VIII Div. I (see Chapter 4) for the
tube rnaterial at design temperature,
o"n,
= 4.941 x
7-l is to be checked for
possible vibration problems. To accomplish this we compute the damage numbers of equations 7-38 and 7-39.
B = tube
-
Es
(7-35)
0.?33)
27xlop
REGENERATED GAS EXCHANGER
The exchanger in Example
153
5
betwe€n tubes
NeB
:
rr.rr
(lJoJ
ft6.471)
1.00
Cedp\Pbla
,.."
", _ _EJE;_
(7-39)
154
^
Mechanical Design of Process Systems
bF, L4
For the tube-side,
E,I/\
(o.oo6ex t.2o)
6
:
N.o
l]i
I (22.50)a
\Lz ln.i
106)::] (0.06881 in
f(
x l0-5
9.520
rt
th-
\
(27
ry
M,:1.448f:o.o+sf
fr
0.036 r4.94r
6..,
:
7.553
in.
\ 12 |
:
0,.. :
x l0 7 ft
1.000
H (;9" [.J",r [.)
o.o36cV2d,
(7
-4r)
(1-44)
d,
=
1.25
dt
:
1.084
'"
- 8(rrjo4:
9.063
x
10-6 in.
in. =
in.
0. 104
:
EXAMPLE 7.3: CHLORINE SUPERHEATER
DESIGN
A plant wishes to use hot oil to heat chlorine sas. The
exchanger unit. a chlorine superheater. is to be i TEMA
18-150 AEL. The chlorine gas is to be heated from 77oF
to 158'F and the hot oil is cooled from 250.F ro 176.F.
The exchanger is to be rated and analyzed for tubetubesheet loading. The exchanger specification is shown
in Figure 7-36. The thermal duty is 600,000 Btu/hr. The
exchanger is a parallel flowing unit.
ft
0.090 ft
., ,0"" lb.
" "*- *l
ttt.zsF in.2 +
(1.084)2 in.2
/ r ,rug \ /rzza in.r\
1:z-z ruJ \--
ft-/
LMTD =
For shell-side fluid,
crrD -
(with
a
lbJ|
LTTD
\tttol
_
173
'n
-
t8
:68.496.F
irz:\
\-tr /
parallel exchanger no correction is needed for LMTD)
Tube-Side Film Goefficient
For chlorine gas,
frr \ 32.2
250'F
77"F
:
. /crro\
'"
1.710 Hz
,'^
/,^,..^\
r:!,llils
in.
176'F out
in.
158'F out
173'F LTTD: l8"F
Shell-side (hot oil)
Tube-side (chlorine gas)
GTTD
(27 x. ro6)-,-]k
o.oe
:
With this magnitude of tube displacement and Nss and
Nsp being in the safe zone, we conclude that the exchanger will not have vibration problems.
With NBE and NcD not exceeding 1.0, we do not expect
vibration trouble. To be certain we compute the maximum tube deflections as follows:
p
' =
ol
x t0-)(t,r.rru,2 lit,ltl F
\ 12 / \0.04s/
- fr I 9.520 x l0-5
lb.
rt2
/rr <n\n
tItT.236f " , (0.00691 l':::l fi.
sec'
f" =
:
:
",
Nco
d-,
4
:
rb-/fc
o.oo3:15
ft'
q
:
rirCog-Uf O;
Co:0. l16 Btu/lb.-'Fi p:
|.667
The Mechanical Desisn of Shell-and-Tube Heat
H
Exchansers
EAT EXCHANGER SPECIFICATION SHEET
I
2
3
Add.€ss
Plaht Locarion
Prcposal No.
Dale
Rev.
5
6
7
a
9
Siz.
(Horlvert)
TypG
Surf/Unii (Gross/Eff.)
In
Pa.allet
Series
So rl
PERFORMANCE OF ONE UNI'I
ShcllSid€
Ffuid Ouantitv.
Total
Tube Side
Ur:T otL
to
ll
Connected
Surr/Sh.ll (Gross/Eft.)
So Ft: Shells/ Unit
Lb/Hr
EEDfuflE
GA-
72
Liquid
14
t5
l6
t7 T€mper.tur.
l8 soecific
(lnlo!l)
,
cravitv
lC
l9 Viscosity, Liquid
20
2l
22
23
21
25
26
27
2E
29
30
3l
32
33
31
^IEg
I ^fiO
Cp
Molecular W6isht, Vapor
Molecular Weighl Noncondensable
o.+zao
Specitic Heat
Btu/Lb "F
Thermal Conducalvity Btu Ftltlt Sq Fr ' F
Latent Heat
Btu,/Lb @ "F
Inlet Pressure
O.11to
Psia
Ftls
Pressur€ Drop, Allow. Calc.
Foulins Resisranc. (Min.)
Psi
(D O O.OOO
Heat Exchansed
Bru/Hr: MTD (Correcr€d\ b ,t,5
Transler Rate. Service
CONSTRUCTION OF ONE SHELL
sletch (Bundle,Noz:le Orientation)
Shell Side
D€siRn,/T€st Pressur. Psir
15U
DesiEn
TemD€rature
35
No. Passes Der Shell
36
Corrosion
Allowance
t
'F
/,79
ln,
ln
37
3a
39
7{6
'F
Sizo &
Out
Ralins
op I
rube No.,5O
4l Tsbe Type
1to
4Z
Shell
13
11
45
46
47
4a
49
Channel or Bonnet
Tubesh€ct-Stationary
FloatinE Head Cover
Bafites.cross
In.;rhk
(Min/^vs)
In.r r€nsrh r5Ff': Ft; Pitch
Material
If{
In.
+30 a.50€-so
€>a5
Tubesheet.Floating
lmpins€menr Protectio!
b
Supports-Tube
Bypass Seal Arransem€nt
TvDe
4h
% cut (Diam/area) 1 .j/4"spacine:
U-Bend
cuc
tnlet
In
Type
Tube-Tubesheet Joint
50
5l
Bundle Exit
Gaskers-Shell Side
Code Reo0irem€nts
Weight/sherl
TEMA Class
55
57
59
50
5l
Figure 7-36. Chlorine superheater heat exchanger specification sheet.
Lb
155
156
Mechanical Design of Process Systems
P
nr
700,000
ft:
Btl,
9.116 _
t*
88.0ee.783'u.(
hr \3600
^
5nr
88,099.733
(68.496).F
-r
rDm-
:
(.42o
)
sec/
lh
ftr
For each of the 150-l-in.-14 BWG tubes,
14,680
:
25.'796 ft/sec
Llg{'o)
sec\12 / ',
(1.667r
'
The smallest shell-side nozzle is the 3-in. outlet, where
!!r
Ar
ftr \ lhr"''l/
{:ooo
'frhr
(5.0
'
=
0.027(298,860.527)0E(0.835)r/3(1.01
(re)'
'', 0.7 <
(610.464r(5.0
N",:\!i =h,
lqi,t\n
l
-+nr-n'- -f
Shell.Slde Film Goefficient
p
fiCP(LMTD)
:
lh
Np,
:
<
17,000
^ _
619.a64
D"
:
8[0.43 p')
0.5rd!4]
8(0.43)(1.2sf - 0.5 r(l.0)z l 4l
r(1.0)
0.711 or De : 0.059 ft
c: |.25 - 1.00 : 0.25 in.
B : 30 in. for 6 baffles
D, : 18.00 in. : shell ID
D.cB
I-" = _-
(
18.00)(0.25 X30)
p(144)
\1.2s)(t44)
: t-t.11 ll.
as
.a^
iI (3.600):::
lh
sec
hr : 31.987.20
^ : ______=-_:=_______j::
-G.
.+
(J. /) rt'
hr-tt'
(6.664)
k=
-
Tdo
^rn
0.426 Btu/lb,-"F;
62 46 -;T:
Btu
hr-ft- "F
t l0-,) Bt'
hr-ft-'F
\12
:
Btu
For 60" A arrangement,
NN"
cp
=
lb^
ft-hrro.426rlb.-'F = t4.075
0.077
Btu
x l0 3)
'hr-ft-"F
'
Very reasonable
u = 2.544ltt^tft-hr
,0.116r
'
ft-hr
lb^-'F
_____
=Aal(
tN.,l,'
ft2
v : _-- !g :2.092:! 0.051 ftr
sec
Np,
0.027(NrJo
:
in.'?:0.051
fr3
Btu
:
q
7.393
12.5+4t
N*"
h, = 41.866
:
r'l'.: &,
u".:l.Cp,k=5.0x
to-r-gu
^' k
hr-fc'F
=_
0.10? ft3/sec
Reasonable
:298,860.527
lb'
:
ftr
-
lb'
(0.036)
-r'
l9r
E9
62.46=
Nq. = j:l; I = 0.0148 Cp = 0.036 lb./[t-hr
ro.036r
6.664
ft3
I
Nn. =
!r
sec
th
v = -........- 2( J9c =
(0.0037941ft
50)tubes
r2s.7e6t
6.664
sec
:!
| .667
:
i-frl
14.680
d+ (68.4e6).F
0.077 Btu/hr-ft-'F
lh
The Mechanical Design of Shell-and-T\rbe Heat Exchangers
Nn"
: DG _
(o'059)ft(31'987.
P
z.su
,0#
lb^
'v
=
741.842
ft-hr
r,.12
I
h- -
ratio of OD to ID of tube
1.199
h' 73'629 ot.+os Blu
: Ar
=
l.l99 - --"-'br-ftL'F
\0.14
U" =Jx!11-trr:l
"' Pl
D.'
:
Ar =
1-JJ
in=
1.001
d=1.0
Aa
The exchanger has baffles with 45 % cut, so from Figure
=
\p",
(l2xo.o77)
Btu
tt t tt ;$:F
o.o5964.025)r/36)
Since both gases are relatively clean, the fouling factors
for both sides are 0.0001.
-
h=
196.720
t* =
161.436"F
6r.M
+ 107.480
Maximum allovable tube joint load
1
-
99.680)
= L"*"
1..* = A,ouf,
For SB-l6l-2fi) at 162"F,
* o.oor + o.ooo8 * 43.866
,1 ..
37.779
(196.720
61.,109
r -, :
o"n:
10,000 psi
g
=
(0.239)in.1lo,m)
tn.'
(1.0)
2,3e0.00 lbr
U=19
700,0m#
Area required
:
=
521.875 ftz
(re.582h;h(68.4e6)
Available area
=
(0.2618X150X15)
:
589.050 ff3
This implies a 12.87 lo excess, which is acceptable.
The tube wall tenperature is used in a method developed by Miller [21], which is a more exact approach
than most and consequerdy results in a more economical
design.
P,
:
shell-side pressure
At = tw -
:
D"
ID =
18
in.
=
1.5
ft
ft,gSZ.Z0,l\.
nr-n'
shell
=
, . ..
18.0
ID =
-
f
i=
0.w225
D" = 0.059 ft
70'F
Ds
0.0
-
:
91.436'F
CA
18.0 in.
(looxg'o)
PR
-= og - qfp- <te"zooltt.ol -o.ettool = 0.0558 in.
Use ta'a
=
34rc-in.
For the shell,
f"=
:
70oF
CA = corrosion allowance = 0 for pure helium (inert)(erosion is negligitle)
'st'ctt
C"
-
:
+ l)
o)'D.rd
6 baffles
shell
161.436"F
ambient air temperaturo
Plessure Drop
f"G.,D"(N"
\ :
D, :
=
100 psi
:
D. :
At
^'' = iSzrl
ta; ta
:
aPs =
=
F.+
=
=
0.1875 in.
27.546
x lffpsi
(0.w2zs)(3r,987.20f(1.5x6
at 161.436'F
+ l)
(s.22X10)ro(0.059)(1.00lx1.0)
0.008 psi which is acceptable
158
Mechanical Design of process Systems
Tube Metal Temperature
:
:
ar :
:
n:
na, :
where E1,
modulus of elasticity of tubesheet metal
tubesheet thickness
1.1875 in.
cross-sectional area of tube (see Table 7-3)
:
T
For parallel flow,
Atn:259-77:173.F
At: tla - 158 :
At": 18 =o,no
Atn 113
lS.F
600,000
rt
I Ol2
/rtr'vr-
4
B=
:6.794
(s 10.510x173)
6oo'o00
' = (s 10.510)(18)
ltl
^'-l_ luh
A
=
-u"l _
6.794 U[ ,-i-5i%
From Figure 7-1"1, F"
:
65.2e41
176
L":
t"i
+
+
(0.28X250
F"(t""
-
O.28
(7-11)
-
176)
:
tljOt :
Pri
:
= 99.6t0",
C
:
254.469 in.2
-t2)
I'
Ler
= !4a,
E,B-
dt
=
- 70"F :
Ul8.J75P .{l8.r2s),J
-
Let APn
=
(13.79q
t21.546
86.394 in.2
:
168.075 in.2
:
:
100 psi
^y
106X35.850)
106X7.1668)
-)
sosr
equivalent pressure difference. psi
D
rri
in./in.-'F at 161.436"F
tube-side (channel-side) pressure
At = 161.436'F
total cross-sectional
Area or tube holes
^
For the shell material,
10-o
-
(A-C)
tl :--
coefficient of thermal expansion, in./in.-.F
o, : 6.090 x
shell cross-secrional area
86.394 in.z
-o3r = I
t*=t"i,-,n,o!.+ tt.n-r".t
n.
:
:
.1668 in.2
r96.jZO.F
(7
711
254.469 in.2
expressed as
t"i)
t-=77 + (0.28X158 -
ct
=
The ratio of the inside shell bore area to the net tubesheet area minus the tubes is the net area that resists the
tube and shell reaction forces and moments. This ratio is
referred to as the ligament or deflexion efficiency and is
l=u6eo
Lr,=tr,o*F.(tr-tm)
t"i -
7
-
6s )q^
(Di"
{
:
For cold end,
g-
:
4
c-
:
number of tubes
150
(ls0)(0.239)
35,850 in.2
rr lR Or2
A = ':A
For hot end,
Ul:
0.239 in.2
n
ar
:
100
-
100
-
(100)(35 850)
168.075
-21.3298 psi
Computing the differential thermal expansion
:
Ac
Aa=e,A,-o,A.
4*:
91.436.F
(7.010
x
10 6X91.436)
-
(6.090
x t0 9(91.436)
:0.000084
0.834
PE
:
the effective pressure differential induced by the equivalent pressure difference, APs, and thermal expansion,
Aq
P,:P+(ao)
qna'
A_C
(7
47)
fl
The Mechanical Desien of Shell-and-Tube Heat Exchansers
Pe:
:
(13
-2r.32e8 + (0.000084)
7e?l
159
lq6)(3s 85)
168.075
226.263 psr
Assume ihe normal tube projection beyond the tub€sheet to be
r/a
in.,
L
:
(13X12)
-
2(1.1875)
-
2(0.125):
Defining the dimensionless parameter, tr,
\
|
:
1.08
as
t025
-
:rr-l
l--[Lr -DTdA -
153.375 in.
(748)
D.
L,J
a
1.08
"I
(13.799
x
i09(3s.8s0)
(153.37sX1. 12sf(27.s46 x 109(168.075)
4
6
A
'10.25
I
(18.125)
1ot2
\
Figure 7-37. Tube stress factor
14
Ir
16
versus
\.
\:2.696
:
4r-*r :
q,(.-r
-415.968 psi for
| :
f+
:
-0.046
-415.968 psi is well below the maximum allowable
stress, which means that the tubesheet is of sufficient thickness.
One could repeat the process if it was desired to use a
thinner tubeshe€t. Had o.1-o*1 exceeded the maximum
lowable stress for the.tubesheet material, then a greater
tubesheet thickness would have to be selected and theprocess repeated.
al-
From Figures '7 -37 , 7 -38,
fI
:
1.55;
lz:3.12l,
l: :
7 -39
,
and 7 40:
-0.046; f+ = 1.970
The maximum radial stress in the tubesheet is expressed
.'-.,,ffi11,9'
f-"
I00){2s4.469X2.sOs8)
:
I (rg.rz5\t
(168.07s) I \ 1.125 i
4[(2.50s8X1.ss)
o.1."";
as
(7-4e)
4(Vfr + fr)
l,o,o.,,
-- -{
1oo
q
-1,418.659 compression
for the tubesheet material
+
<
3.12]
16,?00 psi allowable
2
4
6
a
lo12
14',r6
X
Figure 7-38. Tube stress factor 12 versus tr.
|a
160
Mechanical Design of Process Systems
The maximum stress in the tubes is the sreater of the follow-
ins:
",
:u-[^,.na,
(n,
APt*
- A_C
(7-50)
({ + lr)
I
or
[
-\- -:t'e
(A-crl]l
",{t"
_clAP,_
=A nu,[
(* + |.4)
o.2
q
o.o
(7
-sr)
I
-o2
;.lr"-l-,,,,n
-ot
-0.6
(100x254.469X2.50s8)
ro^ -,lrr^
168.075
t-" -'
-oa
-1.O
(2.5058
+
1.970)
T
Figure 7-39. TUbe stress factor f3 versus
\.
o,1^
1:
-92.62 psi for Equation 7-51
EXAMPLE 7-4: ASPHALT COATII{G lllx
HEATER-A NON.IIEWTONIAN FLUID
APPLICATION
A roofing manufacturer needs a shell and tube heat exchanger to heat an asphalt coating mix from 425'F to
500'F to improve flow characteristics. The fluid to heat
the asphalt coating mix is a leading manufacturet's hot
oil heat transfer fluid. The asphalt coating mix is to be
tube-side and the hot oil is to be shell-side. Determine
the size of unit required with the design to be counterflow. The process is described in Example 3-6. The exchanger heat duty is to be 1,000,000 Btu/hr. See Figure
7-41 for complete exchanger specifications. First we
compute the LMTD for a counterflow exchanger,
Shell-side (hot oil)
650"F in
550'F out
500'F out
425'F rt
150'F LTTD:
125"F
TLrbe-side
(asphalt coating mix)
GTTD:
2
4
6
8
rO12
I
14
16
Figure 7-40. Tube stress factor f4 versus
18
\.
- qrp
. lcrrDl
'"\rt-/
LMrD: crrP
_ l5o_- l?5 : r.7.t2"F
,
11501
'\*/
The Mechanical Design of Shell-and-Tube Heat
Exchangers
161
HEAT EXCHANGER SPECIFICATION SHEET
I
Job
No.
2
Addr€ss
Plant Location
Proposal No.
Date
Rev.
5
6
Siz.
7
Surf/Unit (Gross/E f.)
(Horlv€rt)
Type
9
HOT otr-
to
t1 Ffuid OuantitY, Total
t2
t3
Liquld
t1
2l
Lb/Hr
Tsmpe.ature (lnlout)
t8 sDecific cravirv @
l9 Viscosity, Llquid
20
gtu/Lb "F
Btu Ft Hr Sq Ft ' F
Btu/Lb @ 'F
26
Ftls
Pressure Drop,
2a
Foulins Resisranc€ (Min.)
Heat Exchanaed
r-".r".
n"r",
4z€
q3*
7
l-lz,
d.<2b
a.7b
a.7>
Ft
0.52b
q4?
D:47
t
I
IO
Psi
b
t0
tO
atu/Hri MIO (Correcied)
"F
S"-i."
so
32
DeEisn/TestPressurc
Psis
l<D r 221
rt " r
Sketch (Bundle/No:?le Orientation)
CONSTRUCTION OF ONE SHELL
Shell Side
3l
EO
/ 226
O.sasn Temperature
35
No. Passes D€r Shcll
36
Corrosion
3a
39
40
Si2G &
Ratins
Allowanc€
ln.
Out
op 74
tp
274l
luge !o. 5gt
Tubc Type
42
sh€l
11
Channel or Eonnet
Tubesheel-StationarY
Flo.lina Head Cover
16
47
4a
49
So
Psia
Allow.,/Calc.
27
41
a
h.4)
Cp
Specitic Heat
Thermal conductivity
24 Latent tleaa
25 Inlet Pressurc
31
Se.i€s
ASHJNLTCd'NN6FNIf,
Molccula. Weipht. Vaoo.
Molccula. Weisht, Noncondensable
23
30
5=
//.60
t.60
656cp
22
29
Parall€l
PERFORMANCE OF ONE UNIT
ShellSide
a
77
Connected In
Su.r/Shell (G.oss/Efi .)
Sq Ft: Shells/Unit
Baftles-Lorg
Supports-Tube
Bypass Seal ArranAem€nt
In.:rhk (Min/^ve
lIl 8ly6
In.; Len$h
20
Fr;
Pitch
I.A
In. <-
30
fgl+119 9 !!
Material
op
In. lshen
cover
0nt€s.) (Rernov.)
I Channel Cover
Tubesheet-FloatinE
lmoineement P.otection
o/o Cur (Dia6lA.ezt
Seal Typ€
U'Bend
Spacina:
c/c
Inlet
In
Type
Tub€-Tubesh.et Jolnt
50
5l pvt-lnlet Nozzl€
Gaskets"shelr
53
side
Bundle
Entranc€
Bundle Exit
Tube side
-FloatinE Head
codc Requirements
TEMA Class
55
59
50
61
Figure 7-41. Asphalt heater heat exchanger specification sheet. l@1978 Tubular Exchanger Manufacturers Association.)
162
Mechanical Design of Process Systems
In a counterflow exchanger we must correct the
LMTD. Using Figure 7-16 we have for a one-shell-pass,
two-tube-Dass.
P=
500
6s0
-
425
-
=
425
0.333; R
:
(0.93X137.12)
650
500
:0.93.
From Figure 7-16, F
LMTD becomes
LMTD
:
:
127
-
550
425
Thus, the corrected
For asphalt coating mix at 450'F we have the following properties:
q
:
:
:
0.368 Btu/lb.-'F;
2,251.20 tb^/ft-hr
fiCo (LMTD)
=
1,ooo,ooo
rO
16Rr
---'''lh
-i:L
r
-oF
p
:
89.2321b.ift3; p
:
933
"O
1,000,000 Btu/hr
9!!
hr
l--t?
:
2l,309.196 lb^/hr
{t)\oF'
'---'
/\ thf
21.309.196 "' l ' '"
hr \3600 sec/
^ ^,, _tt3
i u.uob
th I
Nn"
l-4x13*xal3
1-xa
I
lh
co,'tt'"m
sec
where
x
We will try 594-3lq-in. tubes-14 BWG. Checking the
tube wall thickness for internal pressure, 150 psig
PD)
- 0.6P
o"11E
:
E:
P:
ID :
where o1
t-,"
"- =
t""r4
:
maximum allowable stress for tube material, psi
tube weld joint efficiency
l.g
internal pressure, psig
tube ID, in.
150)(0.584)
(17.s00x1.0)
-
:0.005
0.6( 150)
0.083 in.
Flow velocity through each tube is
v
i:
- =j!L
(0.0019)ft'z(594)tubes
-0.066
=
fi3
0.059 frlsec
ratio of the fluid particle yield stress to the shear
Lab tests reveal that
fluid particles at the tube wall
x : 0.5
(0.5r
.I 4 (U.))
.^
- - -. + -:-------"
n=
1l (u.)f
:=
- =:;
=
and
1
:
3.9 for which
O.378
Now,
:
(
:
stress in the
It,
t-,":
(1-7 )
When working with non-Newtonian fluids, rheological
data are necessary. The reader is encouraged to refer to
Govier [22], but will often find that rheological data are
not available in literature. In this situation a samole of
the fluid must be sent to a testing lab. Do not attempt to
approximate a non-Newtonian fluid with Newtonian
equations and assumptions-the results can be a catastrophe. At the current state-of-the-art there are no simple
answers for such complicated subjects such as non-Newtonian fluids.
Samples of our fluid were sent to a testing lab to have
the properties evaluated. Some of these properties have
already been given. The fluid is determined by the lab to
be a Bingham fluid, in which the shear stress and velocity gradient ofthe fluid particles are linearly related. For
a Bingham plastic, n in Equation 1-7 is
I
^
DiV2 - ip
:
.522"F
Tube.Side Film Coefficient
Cp
To obtain the tube-side film coefficient we must obtain
the Reynolds number. The asphalt base coating mix is a
non-Newtonian fluid (see Chapter 1), so Equation 1-6 is
not valid. So, to compute the Reynolds numbet we must
use Eouation 1-7.
(0.584)0 r78(0.059)?-"
N.'* =
€r
-1 (89.232)
sec
8.0
th
+n"
:
0.092
in.
The film coefficient is determined from Figure 7-42,
which is the Metzner-Reed-Reynolds number (Equation
1-7) versus friction factot f. From this figure we obtain
f
:
180
Now, we must compute the pressure drop through each
tube to determine if a 3/+ in. 14 BWG tube is adequate.
-
The Mechanical Design of Shell-and-Tube Heat
Exchangers
163
with a viscosity of almost 1,000 cp. The Prandtl number
for our fluid is
(2251.20\
f
N".:
Np,
o
=
lb' ,0.368' Btu
ft-hr
lb--"F
Btu
(o.lo)
' - hr-ft-"F
8284.416
For laminar flow, the Sieder-Tate correlation is
lt-
c
N", =
.9
.9
u-
N",
hrD
k
Meizner Reed Reynolds Number' Re"*
:
T:
r.86
,
eo
kl''
ffi]"',t.,
[,o.or,,rrro.o,u,
= 2.r85
Rr,r
(- j6) ){{l ll
Figurc 7-42. Friction factors for flow of non-Newtonian fluids [22].
[6*.16.,;[n)]''
"L_,|
hr-ft-'F
10.5841
\
'-''
12 /
-^
Btu
hr-ft2-'F
For our velocity heads we use the entrance and exit loses
Shell-Side Film Coef ticient
and get
:
!f
O.ZS
+
1.00
:
1.78 (see Figure l-1
l)
q
Using Equation 1-4 we compute the pressure drop over
2O-ftJong tube as
* r* )qr
' : ILL
\d - lze,
:
p!g(zo{l?I'* *
(t -4)
:
r.zr
]
(8e.82)k(o.o5eFg(,-iI--J
2(32.2)
=
2.47gpsi
:
:
0.526 Btu/lb--'F;
62.213 tb^/tt'
0.076 Btu/hr-ft-'F;
: Acceptable
_/-\
l'tu
I
p:
p
:
t
Looking at this pressure drop one realizes that a flow
velocity of 0.059 ft/sec is not so slow for a bulky fluid
0.30 cp
I
tb.-'F
It-lD;T
sec'-rDl
(O.997)(O.a)
:
0.720
nr
hr \J.600 sec/ , ...
Rf
{0.526) "'- 1127.522\'F
t.000.000
m
aP,
rirCp(LMTD)
For the hot oil at 600"F the following properties exist:
a
Ce
op,
ae,
:
4.141
62.213
th
:!
sec:
th
+tt'
^.-
^
U.UD/
ftt
-Sec
lb-
lb.ift-hr
164
Mechanical Design of Process Systems
The smallest nozzle shell-side is a 3-in. nozzle, making
the maximum shell-side velocit)
0.067
Fouling factors are as follows:
i:fr3
sec
' - boslF
:
Btu
h-" = 155.959
hr-fta'F
Asphalt coating mix
1.305 ftlsec
-
Hot oil
Very reasonable
:
:
0.01
0.004
1
(0.720) lb'
,,.,
rrpr _
-
Btu
ro.526r
ft-hr
lh -oF
ACp
k
_ rl + 0.004 + 0.01 +
155.959
Btu
(o.o76t
'
'hr-ft-'F
"
-"
4.695
Elr,r
hr-ft2-'F
Fora60'Aarrangement,
n
810.43
p']- 0.5rdl/41 810.4311.00) -
-
r4
D" = 0.127 or De :
0.5rrl.0r/41
?t
"(0
D.(c)B
(27.00X0.25X
15.0) ^ -^^
144p (1.00)(144)
. 4.t41jl t3,600r l
^msechr
U<=-:
as
=
0.703
21.201 .920
*, _ D.G, _
1\Rc---
fl
th
p
5
nr-It"
lh
'
jH:
\o
'
Available area
=
323.918
Tlr,r
- i27.s22f
nr-rt'- -|:]
-'.-
:
1,830.308
:
(0.1963)
F
ft'?
iIt
(zo)
rt 694)
:
2,332.94^ tt
extra margin is needed, so25% to 30% excess area is not
unreasonable. For more heat exchange it would be better
to consider a surge tank with interior and exterior heating elements, since we are at t}te limits of the shell and
tube design and, with a more viscous fluid, a surge tank
of the type in Examples 3-3 and 3-4 is more practical.
ft-hr
12 for baffles
with 15% cut
Shell-Side Pressure Drop
tGiD,{NB + l)
^. _ (slt(t0t6.1d
rq
From laboratory tests it was determined thar plp* =
2.0.
Ns
=
16 baffles
D. = shell ID
(
nr
Twenty-seven percent of the excess area can be eliminated by reducing the number of tubes. This would increase the flow rate in each tube and thus the pressure
,
:'*L
n" = lo4rNr,f ':[aJ
(4.284)
!!
drop, which already is at 2.5 psi. For non-Newtonian
fluids, properties can vary from sample to sample and
(0.011) fr (2t,201.9201
/
"
nr-n'
From Figure'1-21
:
0.011 ft
c: 1.00 - 0.75 = 0.25 in.
B : 15.0 in. for 16 equally spaced baffles over 20 ft
D. = 27.00 : shell ID
"
Area required
1,000,000
Btu- ft
l2)(0.076)
hr-ftr-'F
(4.983)'/r(2.0)o
(0.011) ft
:
27 in.
:
2.25 ft
G, = 21,201.92 lb./hr-ft2
r4
Nr" = 324 and from Figure 7-24, f =
O.0O75
The Mechanical Design of Shell-and-Tube Heat
f o nn75
F_'-"'"--nnn<t<
'
t.2
:
dT(t)
d:
specific gravity
/
a, and if the ratio of dT(t)/dt to
_l
dt
:
0.997
-:
L{r, = ln l2oo
\o t+
-
t\
\80/
dl(r) / ao \/-r\
1.0: (E
dr
(0.0062s)(2 r,20 l. 9D, Q.2s) (r7 )
(s.22)(10)'0(0.01 1)(0.997)(1.0)
:
165
T(t):(200-0-(140-60)
1.2
D" = 0.011 ft
"y
:
L(t) : 0 when t
dl(t)/dt exists, then
:
For plain and bare tubes,
Exchangers
\200
-
ri \80i
-1
200-t
I'Hospital's rule states that
0.188 psi, which is acceptable
EXAMPLE 7.5: ZERO LMTD EXCHANGER
A candy manufacturer wishes to cool hot molasses to
140"F for the food processing of various confectionaries. The molasses is coming from a heating-blend kettle
at 200'F. Spring water is to be used and it never varies
( + t/+'F) from 60'F. The water is to be heated to 120'F,
and held at that temperature to heat honey. Determine
the LMTD. The exchanser is a counterflow desien.
Tube-side
Shell-side
at:
200'F in
120'F out
80'F
140"F out
60'F in
At
=
,. T(t.) .. dT(r)/dt
1.'t L(t) i-= d dl(r)/dr
or, witha : 120'R
r1
|
-1
liml
r.al _I l=
I
|
troo
lim
t-uu
- tl
Therefore,
LMTD
:
to-Ro
.lnt/so\
- t)
80"F
80'F
With this value of LMTD, the exchanger can be designed, using the correction factor in the case of a counterflow unit.
80'F
Now using Equation 3-23 we have
LMTD:
(200
o
NOTATION
A
:
tube surface area, ft2
At : cross-sectional area of tube, in.2
a = constant for a continuous beam shear, dimen-
o
I
\80/
This problem is somewhat similar to that of Example
3-4 in its formulation. We must define the LMTD as the
ratio of two functions T(t) and L(t) for which
b:
c=
c:
C
:
sionless
constant for a continuous beam deflection
tube clearance, in.
constant, in.2/lb1 (Equation 7-37)
10 a(sec)05/(ft)'5 (Equaconstant
:9.7 x
tion 741)
1141P
:
T(t)
Lt)
: (200-0-(140-60)
.ln l-l1200 \80/
rl
As temperature t approaches a certain value such that
T(t) and L(t) become zero being divided by zero. The derivatives of T(t) and L(t) exist when t approaches this
value of t, so we can apply I'Hospital's rule that if T(t)
g" = 12fE t or)o 5 (Equation
7-2)
: drag or force coefficient for a body immersed
in a fluid, dimensionless
Cp : specific heat at constant pressure, Btu/lbn'-'F
D:4 x hydraulic radius. in.
D : tube diameter, in.
D : parameter (Equation 7-27)
ds = diameter of baffle hole, in.
di : inside tube diameter. in.
Cp
166
Mechanical Design of Process Systems
: outside tube diameter, in.
:
4 outside tube diameter, ft
Ea : modulus of elasticity of baffle material, psi
4 : modulus of elasticity of tube material, psi
F" : correction factor, dimensionless (Figure 7-16)
F". : critical buckling strength for tubes, lb.
Fr : force induced by fluid flowing around immersed body, lbg
F, : shear force against tube at baffle, lbr
used in determining tubejoint force,
; I constants
lbs (Equations 7-3 and 7-4)
i' I
f" 1 fundamental natural frequency of tube, Hz
gc : gravitational constant : 32.2 lb.-ftilbr-sec,
: parameter (Figures 7-30 and 7-31)
Tn : thickness of inside tube deposits, ft
Tro : thickness of outside tube deposits, ft
T* : tube wall thickness, ft
t"" = caloric temperature of cold fluid, 'F
t"1 : caloric temperature of hot fluid, "F
Li = inlet cold fluid temperature, oF
t"" : caloric temperature of cold fluid, 'F
thi : inlet hot fluid temperature, 'F
th. : outlet hot fluid temperature, oF
t = tube wali thickness, in.
t* : outside tube wall temperature, 'F
ar = temperature differential (tr - tz), .F
U : overall heat transfer coefficient for exchanger, Btu/hr-ft2-'F
U, : the value of the overall heat transfer coefficient at the caloric temperature. Btu/hr-ft2-.F
V : flow velocity, ft/sec
T
do
GTTD = greatest temperature difference between the
shell and tube side fluids, 'F
h = film coefficient, Btu/hr-ft -'F
hi = film coefficient inside tube, Btu/hr-fl:,-'F
h" : film coefficient outside tube, Btu/hr-ft -'F
hi, : outside film coefficient of tube, using outside
I:
:
k:
k:
k* :
Ir
tube surfaces temperature, Btu/hr-ftl'F
moment of inertia, in a
moment of inertia of tube cross section, in.a
structural constant, dimensionless (Equation
7-2)
equivalent effective unsupported length of the
tube, in.
coefficient
of thermal conductivity of tube
wall, Btu/hr-ft-'F
kr = thermal conductivity of fluid, Btu
kn : thermal conductivity of foreign deposits inside of tube, Btu/hr-fi-'F
kso : thermal conductivity ofdeposits on outside of
tube, Btu/hr-ft-'F
L = tube length or span length of tube, ft
LMTD : logarithmic mean temperature difference, "F
LTTD : lesser temperature difference between shell
and tube-side fluids, 'F
/ : typical dimension of body immersed in fluid,
n
rir = mass flow rate, lb-/sec
mt : mass density of tube metal, slugs/ft3
NB = number of baffles
Nna : baffle damage number, dimensionless
Nco = critical damage number, dimensionless (Equation 7-39)
Np, : Nusselt number, dimensionless
:
:
P:
p:
q:
Np.
Nr"
r=
Prandd number, dimensionless
Reynolds number, dimensionless
axial force, lbl
tube pitch, in.
rate of heat transfer, Btu/hr
radius of gyration of tube, in. (Equation 7-2)
Greek Terms
:
6:
p:
ct
factor of effective tube resistant area, dimensionless
deflection or displacements, in.
dynamic viscosity of the fluid inside tube, lb./fthr
p* = dynamic viscosity of fluid at tube wall, lb-/ft-hr
uB : Poisson ratio for baffle material
ut : Foisson ratio for tube material
or : frequency of a given mode, Hz
p = density, lb*/ft3
d"1 = allowable stress for tube, psi
o" : allowable tube compressive stress, psi, for the
tubes at the outer periphery of tube bundle (Equations 7-1 and 7-2)
o, : minimum yield stress of tube material at design
temperatue, psi
:
f sum of structural damping and the fluid damping,
dimensionless
REFERENCES
l.
Heat Exchangers, Howeli Training Company,
2.
Houston. Texas. 1975.
Snndnrds of the Tubular Exchanger Manufacturers
Association (TEMA), 6th Edition, Thrrytown, New
York, 1978.
F. L. . "What's the Difference Between
TEMA Exchanger Classes," Hydrocarbon Processing, 59, June p. 92, 1980.
Ludwig, E . E., Applied Process Design for Chemical and Petrochemical Plants, Volume 3. Second
3. Rubin.
4.
The Mechanical Design of Shell-and-Thbe Heat Exchangers
Edition, Gulf Publishing Company, Houston,
Texas. 1983.
5. Small, W. M. and R. K. Young, "The Rodbaffle
Heat Exchanger," Heat Trans. Eng., I, ro. 2, Oct. Dec. (1979), p. 21.
6. Skrotzki, B. G. A., "Heat Exchangers,"
Power,
June, 1954.
7. ASME Boiler and Pressure ry'essel Code. Section
VItr Division 1, American Society of Mechanical
8.
9.
Engineers, New York.
Colburn, A. P., Ind. Eng. Ch.em.,35, pp.873-877,
1933.
Kern, Donald Q., Process Heat Tlansfer, McGrawHill Book Company, New York, 1950.
10. McAdams, W. H., Heat hansmission, Third Edition, McGraw-Hill Book Company, New York,
ll.
1954.
Jakob, M. Heat Transfer, Yol. l, John Wiley &
Sons, New York, 1959.
12. Grimson, E. D., "Correlation and Utilization of
New Data on Flow Resistance and Heat Transfer for
Crossflow Over Tirbe Banks i 'Tiansaaions of the
ASME," Yol.59, pp. 583-584, 1937.
13. Engineering Data Book, Wolverine Division of
UOP, Inc., A Signal Company, 1959.
14. Thorngren, John T., "Predict Exchanger Tube
Damage,' Hydrocarbon Processing, I*l,l. 49, rc. 4,
p. 129, r97o.
167
15. American Institute of Steel Constrtclion, Mantal of
Steel Construaion, Eighth Edition, AISC, Chicago,
trlinois, 1980.
16. Timoshenko, S., and J. N. Goodier, Theory ofElastr:ciry, Second Edition, Engineering Societies Monograph, McGraw-Hill Book Company, 1951.
17. Coit, R. L., C. C. Reak, and A. Iohmeier, "Design and Manufacturc of Large Surface Condensers-Problems and Solutions," American Fower
Conference,
April
1965.
18. Blevins, R. D., Flow-htduced Wration, Van Nostrand Rheinhold Company, New York, 1977.
19. lbmbsganss, M. W., and S. S. Chen, "Tbntative
Design Guide for Calculating the Vibration Response of Flexible Cylindrical Elements in Axial
Floq" Argonne National Labomtory Report ANL-
ETD.7l-{r/, l9r.
20. Kays, William M. and A. L. Lofron, Compaa
Heat Exchangers, Third Edition, McGraw-Hill
Book Company, New York, 1984.
21. Miller, K. A. G., 'The Design of Tirbe Plates in
Heal Exchangers," Proceedings of thz Institwion of
Mechanical Engineers, \bl. lB, pp.215-231.
22. Ctovier, G. W. and K. Azrz, Thc Flow of Complex
Minures in Pipes, Robert E. Krieger Publishing
Company, New York, 1977.
23. Metzner, A. B. and J. C. Reed, AICLE Joumal, I,
p.434, 1955.
External Loadings on Shell Structures
where
In a book about the mechanical design of process sysit is impossible to ignore the phenomenon of external loadings on shell structures. Such loadings occur
when piping is flanged to pressure vessels and the vessel
nozzle is exposed to loads induced by the piping, and
when vessels are erected and the force of gravity induces
loads at the lifting lugs.
We have already discussed external loadings in the design of piping supports in Chapter 2. Vessels require a
simiJ.ar analysis, but the phenomenon is different because in a vessel the loadings are more localized. particularly in a large vessel. In the case of external loadings
on vessel nozzles one must consider primary stresses induced by internal pressure and secondarv stresses induced by the external loadings. In the design of the lifting lugs only secondary stresses need to be considered,
since vessels being lifted almost never have internal
diameter of the branch
diameter of the header
Also. \\'RC 197 and WRC 107 do not consider the
case of erternal ioading combined with internal pressure. Current studies are being made to accomplish this
task.
Stress induced by internal pressure at the nozzle-shell
intersection are extremely complex, so an analytical solution is impractical. Discontinuity stresses at the nozzleshell juncture are caused by the change in geometry from
the nozzle shell into the vessel shell. Consequently, a
stress concentration factor, ko, must be applied when using the following expression for internal pressure stress:
"n
pressure.
The two "standards" that are most widely accepted for
external loadings on pressure vessel nozzles are the
WRC (Welding Research Council) Bulletin 107 [1] and
the WRC 297 l2l. The latrer is an expanded version with
more curves to cover more cases, but it is only for cylindrical shells. Neither WRC 107 nor WRC 297 are considered standards per se. Therefore, one must take the
results of the methods outlined here and add the primary
stress, which is the internal pressure stress.
The reader is cautioned that the WRC 297 Bulletin is
under evaluation at the time of this writing. Shell theory
was used to develop the WRC 297 , and the results are
being compared to finite element studies currently being
made. The reader is especially cautioned to use the Bulletin when the ratio of the dianeter of the branch to the
diameter of the header is between 0.5 and 1.0. exoressed
P(ID)k"
(8-1)
2t
where
P
ID
I
kP
:
:
=
:
internal pressure, psi
inside diameter of shell, in.
shell thickness, in.
internal pressure stress concentration factor,
dimensionless
Values of
\
are far too exhaustive to be listed here, but
are available in a work by Forman [3].
For many years reinforcing pads have been used for
external loadings and it has been accepted practice to assume that such pads remove discontinuity stresses at the
nozzle-shell juncture. While this is true, one must realize that the reinforcement decreases the flexibility of the
nozzle-shell attachment. As shown in Figure S-la, the
nozzle with the reinforcement will have maxirnum membrane stresses occurring at the nozzle-shell juncture (assuming the circumferential bending stresses are negligible compared with the membrane stresses). As Figure
8-1b shows that as the reinforcement thickness increases,
mathematically as
0.5 < db/DH <
=
:
db
DH
tems
1.0
169
170
Mechanical Design of Process Systems
c
r tiryrcJtl
F----'1
M-'x'i€m5'mm'n'|ll
ll
I
r,
--------|B
w>
1.6s(arf.
r5
ll
HI
__-____1---r
I
I
l
|
I
--'_;J
II
tN_
i
R-r
Figure 8-1. simple schematic of maximum combined stress disribution, as supported by field tests and finite element studies.
the maximum stress shifts towards the edge of the pad,
and as the ratio of the reinforcement pad to the shell
thickness approaches a "critical value," the maximum
stress induced by external loading occurs at the reinforcement edge-shell juncture point, shown in Figure 8lc. Considering this it would intuitively appear that a tapered pad would ideally be the best in application,
especially for thick pads (pad thickness relative to shell
thickness), as shown in Figure 8-1d. The disadvantage of
such a pad would be the increased difficulty and expense
to fabricate such a pad. Analytical, finite element studies, and field experience bear the previous facts out. The
width of a pad, from the nozzle edge to the pad edge'
should not exceed 1.65VRT. Beyond this range a pad has
been shown to be ineffective.
Pads can be even dangerous on thin-walled shells. In
many instances, adding a t/z-in. pad to a nozzle on a thin-
walled pipe, such as Schedule 55 (0.083 in. on a 4-in.
pipe), is prohibitive. Such a pad could very easily transier the maximum loading to the pad edge as shown in
Figure 8-1c, resulting in crack propagation or even ruptuie. Caution should be taken in working with thinwalled shells, where the flexibility of the shell is often
sufficient to decrease induced stresses from external
loadings.
LIFTING LUG DESIGN
The design of lifting lugs can become an arduous task
one is not familiar with the erection of equipment.
Lifting lugs must be designed to withstand the stresses
inducad from all the loading conditions; allow lifting and
if
setting the equipment in one operation without readjusting oi re-rigging the crane or other equipment' and proteit equipment and personnel. The lugs must not interfere with vessel components, such as platforms, ladders,
or piping.
advantage to lifting lug design is that only secondary stresses must be considered-primary stress, such as
internal pressure stress, can be ignored. We can assum€
that the vessels are not lifted while they are pressurized.
Thi
Consequently, the AISC Manual of Steel Constructi.on
(unlike
[4] can be used in which the factor of safety is 2: I
ASME's 4:l).
The vessel is to be considered as a simply supported
horizontal beam. All non-shell components, head, ladders, etc. are considered as concentrated loads. The total
erection weight is the sum of the concentrated loads and
the distributed loads of the shell weight and internals.
Various types of lifting lugs are shown in Figure 8-2.
Lifting and'election procedures are shown in Figure 8-3
Techniques for designing the lugs are given in the following examples.
EXAMPLE 8-1: LIFTING LUG DESIGN At{D
LOCATION
and tube heat exchanger is to be
onto
an offshore structure' The exa
dock
lifted from
lbs, which is the total erection
158,750
weighs
changer
to
locate and design the lifting
is
objective
weight. The
chocker length and
minimum
the
lugs, and determine
angle.
chocker
maximum
A 96-in. ID shell
Mechadcal Design of Process Systems
172
t
1T
A
norizontal
It
+
lili
.l
J\
U
+
"1" or
"W" beam
Figure 8-3. Lifting lug and erecting procedure (moments induced by lift load at choker angle d can be avoided with a
spreader bar or with the lug design in Figure 8-28.
c
spreader bar rig avoids
€xcessive bending
moments on lilling lugs
First, we construct a free body diagram, as shown in
Figure 8-4. Each lifting lug is located such that the point
of lift is located on a hypothetical vertical line that passes
close to or through the centroid of the ellipsoidal head,
shown in Figure 8-5. Summing moments to zero and
solving for the reactions we have
GDt. : 0 :
-Rnt46.542)
+
Rr
and
Rr.
:
:
(2,283)(40.7
(2,094)(46.7
+
(346x44.000)
A = 16.50in.,B
E
:
6.50 in.
Hole diameter
Lug width
:
:
Wr
:
=
:
(4.50
+
:
4.50in., D
:
0.125)
mmlmum
3a
:
3(4.50)
wL
_
13.50
=
1.688
88
75,888.874 lb
For lug supporting the fulI vessel weighing 158,750
lb, referring to Table 8-1 we write
a
6.50in., C
:
:
4in.,
4.625 in.
13.50
in.
:
minimum
Lug Thickness, t1
s) + (346)(2.542)
5) + (1s1,587)(23.27 r)
75,698' 126 lb
:
tL :
Larger of
w _
1.6ao,
in. r/ use 1.75 in.
158,750
(1.6X4.625X38,000)
= 0.565 in.
174
Mechanical Design of Process Systems
For lug material SA-516-GR 7O, o,
Table 8-1
Anchor Shackles
: *
- (".
" | (?.,)['
n
tl
H:
R":
where,
ll
/\
D'
,\
-)
*({*
\2
50.0 + 1.75
n
tl
|l
"["-(
H:
1"b
lvt
Pin Dia.
D
(in.) (in.) (in.) (in.) (in.)
rh trys rlz shd tllrc
,1,
tl"
t1o
,t"
1
1tl4
lrl^
71rc
5/s
3/c
r'lrc
lrl,
2rltu ltlrc
ZIz lh
ls
llrc
rlz
5/a
3lc
1ls
Yt^ 171rc |
33lq 111/to 1Vs
4r1o tt3lrc ltlc
43h Ztlta 13/e
rr-r" stlo 2tls lvz
-/"
lrlz
1t/"
2
53lq 2tlq
27lt
1
7rl" 3tlc
3?'1"
zrh
qu"
tou
it, -9V^
i1o tluz 4lz
lslt
15
3t/z
15Vz
4118
5t/z
Safe Lilting
Load-|9!
|
4.00
Lslrc
le/rc
|1ha
4,500
6,400
8,700
2tla
23lg
25lL
3
1I
=
I'
:
greater of RR or R; for horizonal
vessel
reaction at lug when lifting at skirt
and lug end
5(19.690) in. (75,888.874) lb
ll.
(38,000)
t13 50)2 in'
+
ln.'
:
1.079 in. < 1.75 in.
Lug thickness is sufficient
'4OO
___J3_5W
351rc
35la
16'500
Minimum Weld Size
2!,59q
u,w
33,600
R[0.47
44,800
56,000
67
'2w
81,ooo
6tlz
100,800
63/q
125,000
t
where
o,*
:
lTtlz
6tlz
4tlz
7)lz
200,000
181/z
6tt/rc
43/q
73lc
224,N0
313,600
448,000
0.45(h/w)]
ra
:
allowable shear stress in weld
weld minimum yield
(7s888.874)
stress/
in tension
I ot . o.ot rr2jry\l
\ir.roo1
[o
(0.30)(70,000)(13.50)(0.707)
r79,200
41lt
+
re(wr)(0.707)
50,000
6tlq
5tlz
where R
R
2,200
2,900
23lq 6
6t/+
3
33/q
r, ) *.
or w'
1,675
lrlrc
16l lz
21
+ n JO
-
19.690 in.
.79-91'100
r3/rc
451rc
2
211+ 5
5Vq
2tlz
13
3tl+
50-00
6. 50
Check lug thickness
ft+l
,l*
- ")']"
insulation thickness
shell outside radius, in.
(b) round Pin
lttn
Itl,
;f
;'
lug height, in.
t:?
f-et
r
q*
,1"
38,000 psi
Lug Height (assume 2 in. fireProofing)
(a) screw Pin
THWP,
=
r* =
0.426 in. minimum
Actual weld size
:
t*u
:
0 3q*
External Loadings on Shell
:
r*a
Larger
and twr
where
f t,
ot ,, -_
I
t, =
=
:
Ds:
du:
H:
Kp:
L.:
A,B,C,D,E
vessel thickness, in.
1.75
in.
>
tv, so that
-
0.0625
=
175
NOTATIOil
,t,u in.
>h
In this case, tL
t*"
t/ro in.
Structures
1.688
constants (Figure 8-6)
header diameter, in.
branch diameter, in.
8-l)
internal pressure stress concentration
constant (Thble
factor, dimensionless
minimum chocker length,
ft
Ml= moment resolved about the left
Mr:
For each side of weld
end
(Figure 84), ft-lb
moment resolved about the right end
(Figure 8-4), ft-lb
t-,:l'688:0.844
--2
since
t*" > > t*, A
a/+-in. weld is sufficient
Choker Angle (0)
o
:
arctan
[----tlt' I
-,
l3w(H.A.;ll
U: "r*rI
(38,000x13.50)(1.75F
3(1,58750.00) (rn.uno
*
r6.s0 +
4t0)
0:4.905"
R"
I.:
12 sin d
, :
t"
:
minimum choker lensth
50.00
12
rin (4.90t
A = 16t/z in., B =
61/z
in., C = 4!z in., D = 4 in.. E = 6t/z in.
= '+6'/rl n
Because of height restrictions, the lug had to be lowered from 19.690 in. to 11.00 in. Thus, we now have the
following:
I
l3.soxl.7sy I
lrrtst.zso.ooy {rt.oo * ro.so * 4ll
zll
"
.:qrt.grt-l
(38.ooox
\
t
0
:
6.327'
and
LC:
12 sin (6.327)
=
37.807
ft
Figure
&6. Detail of choker
and shackle.
176
Mechanical Design of Process Systems
P
RL
R"
RR
t
t1
t*
wL
:
:
:
:
constant (Thble 8-1)
reaction at left side (Pigure 8-4), ft-lb
shell outside radius, in.
reaction at right side (Figure 8-4), ft-lb
= shell thickness, in.
= lug thickness, in.
:
:
weld size, in.
lug width, in.
Greek Symbols
o,*
:
:
0=
7A
minimum weld yield stress in tension,
psl
allowable shear stress in weld, psi
chocker angle, degrees
REFERENCES
t.
Welding Research Council, Welding Research Council Bulletin WRC 107 bcal Stresses in Spherical and
Cylindical Shells Due to External Inadings, Match,
New York, 1979.
z. Welding Research Cotncil, Welding Research Coun'
cil Bulletin WRC 297, Incal Stresses in Cylindical
Due to External Inadings on Noales-Supplement to
WC Bulktin No. 107, New York, August, 1984.
J. Forman. B. Fred. Incal Stresses in Pressure Vessels,
Second Edition, Pressure Vessel Handbook Publishing, Inc. Tirlsa, OK., 1979.
A
American Institute of Steel Construction, Manual of
Steel Constructior, Eighth Edition, AISC, Chicago,
Illinois,
1980.
178
Mechanical Design of Process Systems
Example-Spherically Dished Horizontal
(a)
Head
A spherically dished head with a I l4-in. { OD is spun
from 1-in. plate. Determine the partial volume of 10 in.
of liquid. From vessel head manufacturer's catalog we
determine the following:
IDD
R:'2
e:
L:
Figure A-2. Partial volume of vertical hemispherical
(B) Partial volume of horizonral hemispherical head.
:
p
16.786 in. (Figure A-5),
l14
o\
" - -)/t.'"'=
159.43"
108
-
:
:
108 in.
56.0in.
2.78
16.786
:
91.21 in.
head.
-_T---T
-+l
itv ln'
tl
tf
I
PARTIAL VOLUMES OF SPHERICALLY
DISHED HEADS
--
J___
--.-{,>--
_
Horizontal Head
The partial volume of a horizontal head (Figure A-3) is
(A-3)
Figure A-3. Partial volume of spherically dished horizontal
neaos.
Vertical Head
The partial volume of a vertical head (Figure A-4) is
.,
v=' nv(3x2 + -vr)
6
atl
P"l
x
v----i\:-7lTv
(A-4)
-v----T
-<--E--------i-:--rllDD
ot
I
..
.v)
y: nv2(3o
3
(A-5)
Figure A-4. Partial volume
heads.
of
spherically dished vertical
Appendix
Yr
A:
Pressure ry'essel Formulations
179
= 6.786"
Flgure 4"5.
_
V
:
--i86at -
lV(r08,
.,-
v?ro8r
-
5-dF
IJ
(9t.2r)(562
38,893.21 in.3
-
6.7862)
=
168.37 gal
t\
Itr
t\
t\
ti
Example- Spherically Dlshed Vertical
ll
Head
;;=*--:-__T,
For the same head above, determine the partial volume
-_-
of a head of liquid of 9 in.
x
:
u
-
55.456 in.
zr(9)[3(55 416)'?
+ 9'z]
in.t =
= A.874
"'
6
64.4 gal
End View of Horizontal Head
PARTIAL VOLUIIES OF ELLIPTICAL HEADS
Figure A-6. Partial volume of horizontal elliptical head.
The exact partial volume of a horizontal elliptical head
(Figure A-6) is as follows:
..
(IDD)q
(A-6)
Venical Elliptical Heads
Volume of top portion @ of Figure A-7 is
-a
Y'
'" 2 l"l' - 3(rDDFl
v,.' = 'Ri'
(A-7)
I
Volume of bottom portion
.
,
2r(IDD)R,2 rRl
I
O
- "-----: lw
2(
is
u3
I
3(rDDll
(A-8)
Figure
47,
Partial volume of vertical ellipticat head.
180
Mechanical Design of Process Systems
Horizontal Head Example
A
Find the partial volume of a 2: I (R;/IDD = 2) elliptical head that is 108-in. OD. The level of the liquid is 35
in., and the head is spun from l-in. plate.
vertical head
IOR - ?rl O\
IDD -- '"-______:rr:',
= 26.50 in.
KR
From Equation ,4-6 and Figure A-8 we have the followlng:
IDD
-x
y = (IDDI a vm7 --tl'6R,
a=
138.80" =2.42
v _ ( 19.0)(2.42t !463r- *
6(53)
V
:
17,512.94
B
{Iqy-rr
horizontal head
in.r:75.81
gal
Vertical Head Example
For some head above, determine the partial volume for
a vertical head with 19 in. ofliquid. Using Equation A-8
we have the following:
c
., _ 2a'(IDD)R1'?
vertical knuckle region
o
v _ 2?r(26.s0x53.01 _ 1(5i.0)
6
V=
Y :76,641.06 in.3 :
77,951.81 in.3
n
2 [,o
t--"
_
trq.or, ]
3(26.s0),.j
13i0.75 in.3
331.78 gal
H=IDD-KR
D
horizontal knuckle region
Figure A-9. Partial volumes of torispherical heads: (A) vertical, (B) horizontal, (C) vertical knuckle region, (D) horizontal
Figure A-8.
knuckle resion.
Appendix
A:
Pressure Vessel Formulations
PARTIAL VOLUIIES OF
TORISPHERICAL HEADS
For Figures A-9 and A-10,
:
Vo :
Vk
KR =
volume
volume
radius
knuckle
dish
knuckle
Figure A-1o.
:
IDD :
y
p=
height of liquid
inside depth of dish
inside dish radius
For vertical heads (Figure A-9c) the knuckle-cylinder
Dartial volume is
v*: ?rtJ
+ 4ry2 +
(A-e)
r,2;
The partial volume ofthe dish region of a vertical head is
?ry(3x2 + y2)
.,vD_-6-
(A-
l0)
The total partial volume in a verticil head is
nH
Ty(3x2 + y2l
,. +. -----6-------:,,
vu : -6- (ro' + 4rM' + ri')
(A-ll)
whereY=IDD-KR
Horlzontal Torlspherical Heads
Partial Volume of Dish @ (Figure A-11)
VO:
o
./(p, -y-il.t
V(pt-7F_L(Ri,. yi,)
=
JZ
|
,o_,r.,
Volume of Knuck-Cylinder Region @ (Figure A-12)
uo =
"[#
+
Ri-
KR) +
(R,- KRr]
end view of dish
volume
Flgure A-11, Sketch for example partial volume calculation
of horizontal torisoherical head.
(A-13)
The total partial volume for a horizontal torispherical
head is as follows:
V1
: V6+ V6
-
.
.vG,
- R-iT
L(Rr2
"lry + Ri- KR) + (& - KR),]
wherel: p _ IDD
-
yi2)
(A-14)
Flgure A-12.
182
Mechanical Design of Process Systems
Horlzontal Head Exampte
A
102-in. S OD flanged and dished (torispherical)
)
head made to ASME specifications (KR
0.60p and
KR > 3th, tr, = head thickness) is spun from l-in. plate.
The head is horizontal and the liquid level is 35-in. determine the partial volume.
From the vessel head manufacturer's catalog and Figure A-12 we determine the following:
:
p
R,
96 in., KR
ltut
= :z
:
6.125 in.,
IDD
= 50in.. L = 96.0
-
:
The head is vertical and the liquid level is 18-in. Determine the partial volume.
From the vessel head manufacturer's catalog we determine the following:
p
:
R,
l?R trl 5l
= '-" - 2=-"'-' = 67.50 in.;
x
:
17.562 in.
17.562
=
132 in.,
67
.50
KR
:
IDD
3 in.,
- (3f -
H2lo 5
=
:
20.283 in.
66.446 in.
78.438 in.
For knuckle-cylinder region,
From Equation A-14 we have
vr
:
Q.532)
_
(78.438X50'
- ls)
|
+
ro:
,4%t_ 1s+ _\@6r:50it
(5o.oo
-
6.12s)
Vr = 34.093.44 in.r =
r-
67.50;
11
J?r'
+ (s0.00 - 6.l25fl
'J
h
Yv
147.59 ga.
:
138-in. d OD F&D (flanged and dished) head nor
made to ASME specifications is spun from I l/z-in. plate.
120.283
-
Ri
=
r.= 67.50 +,-@.50
(3.0
*
KR:67.50
=
ob.u;
+
15.0)l
r(I'1 .283)[3(64.500)'?
:
-
3.00:64.50
2.283 in.
:
146,893.558 in.3
+
(17.283)2]
6
vv:31,247.726 in.3 +
Vv
-
+() 19,4\
+ 4(66.0), + (64.5011
= " -;-"-'l(67.501
b
Vertical Head Example
A
=
in.
r
/,'' <1r, 14(6.125)
[
Ri
:
115,645.832 in.3
635.903 gal
I
Appendix A: Pressure Vessel Formulations
INTERNAL PRESSURE ASME FORMULATIONS
WITH OUTSIDE DIMENSIOI{S
Cylindrical Shelt
Longitudinal Joint
.PR
-
oE + O.4P
oEt
-
R
0.4t
Circumterential Joint
r=
PRo
2oE + '1.4P
2oEt
- 1.4r
^
Ro
2:1 Ellipsoidal Head
^
r=2oEPDo
+ 1.8P
2oEt
- 1.8t
Do
Sphere and Hemispherical Head
-
'-2rE+0,8P
2oEt
- 0.8r
R.
ASME Flanged and Dished Head
when UR = 164s
s
0'885P1
r =0.885L
= oE + 0.8P
When
PLM
t= 2oE+P(M-0.2)
UB <
-
0.8t
16ry3
2oEt
^ ML-(M-0.2)
Section
PDo
r=
- 2 cos o(oE
+ 0.4P)
^
2SEt cos d
Do
-
0.8t cos o
183
184
Mechanical Design of Process Systems
INTERNAL PRESSURE ASME FORMULATIONS
WITH INSIDE DIilENSIONS
Cylindrical Shell
Longitudinal Joint
PRi
'-rE-O.6P
Ri + 0.6t
Circumferential Joinl
t=
PRi
^
2oE + O.4P
1-\
i-r-----T;-',-il
/l\
2oEt
Ri
-
0.4t
2i'l Ellipsoidal Head
2oEl
^
Oi
+ 0.2t
Sphere and Hemispherical Head
{,;ft
\<=]li
-
}<T-t"._
2oEt
R + 0.21
ASME Flanged and Dished Head
when UR = 1 6?3
P=0.885LoEt+ 0.1t
oc-v.tr
I
Ft
When UR
pt
FOR VALUES OF
M
<
164s
tu
2^tr1
SEE SUPPLEMENT
-./L-
#+\
\-__=-2,
F--- q--l
LM + 0.2t
\
Conical Section
PDr
2 cos d(oE
F.-t
p
-
0.6P)
2oEt cos
=Di + l.2l coso d
Appendix
A:
Pressure Vessel Formulations
185
Supptement for ASME Formulations
't. For a cvlindrical shell, when the wall thickness exceeds one
half the inside radius or P > 0.385dE, the tormulas in ASME
Code AoDendix l-2 shall be used.
For hemisoherical heads without a straight llange, the efficiencv ot the head-to-shell ioint is to be ussd it il is less than
lhe efficioncy ot the seams in the head.
For elliDsoidal heads, whsre ths mtio ot the maior axis is
other than 2:1. retsr to ASME Code Appendix 1'4{c).
4. To use the fomulalions lor a conical seclion in the table, the
halt apex anqle, d, shall not exceed 30o. ll d > 30o' then a
soeci;l analysis is required per ASME Code Appendix
1-5(e).
5. Foian
when
ASME flangsd and dished haad (torispherical head)
used:
Ur< 164r the tollowing values ot M shall be
Values ot Factor M
Ul
1.00
1.00
M
Ur
7.00
M
1.41
'
1.25
1.03
7.50
1.44
'1.10
1.13
8.00
8.50
9.@
9.s0
1.46
1.48
1.50
1.52
The maximum allowed ratio:
M=
'('.
1
2.25
1.75
1.08
2.00
'1.06
1.50
L-r
=
2.50
2.75
3.00
.15
10.0
1.54
1.17
10.5
1.56
1.18
'| 1.0
1.58
1
D When L/r >
162/3
3.25
1.20
11.5
1.60
3.50
4.00
1.22
1.25
12.O
r3.0
1.62
't.65
4.50
1.28
14.0
1.69
5.00
1.31
15.0
1.72
5.50
1.34
16.0
1.75
6.00
6.50
1.36
1.39
16?s
1.77
(non-ASME Code construction), the values ot M may be calculated by
Appendix B
National Wnd Design Standards
A standard is a collection of current practices, past experiences, and research knowledge. Standards that are
developed by consensus groups (e.g., ASTM, ANSD,
trade associations (e.9., AISC, ACI), or government
groups (e.g., HUD, CPSC) carry more authority than
other standards because they reflect wider ranges of materials.
The ANSI A58.1-1982 is a collection of information
that is considered to be the state-of-the-art in the desien
of buildings and other structures. Local and region-al
building codes adopt portions of the ANSI srandard for
their own use. These local and regional codes are developed to represent the needs and interests of their respective areas and are written in legal language to be incorporated into state and local laws. Because these building
codes are regional or local in scope, they often do not
include everything in the ANSI standard, which is national in perspective. For this reason, one must be certain that a local code written for one area is applicable to
the site being considered.
The ANSI standard does not have as much authoritv as
the ASME vessel codes. and, unfortunarely. does not
have a referral committee or group to officially interpret
the document. Therefore, one must rnake decisions
based on past experience and accepted methods of design. The ANSI standard (Paragraph 6.6, p. 16) states
that in determining the value for the gust response factor
a rational analysis can be used. A note below the paragraph states that one such procedure for determining the
gust response factor is in the standard's appendix. The
note at the top ofthe appendix (p. 52) states clearly that it
is not a part of the ANSI 458.1 miminum design standard. What all this implies is that one may follow the
guide of the ANSI standard's appendix or use another rational analysis, which includes another wind standard.
Thus, one care use another standard for design purposes.
147
One of the most widely accepted international standards
is the Australian Standard 1170, Part 2-1983, SAA
Loading Code Part 2-Wind Forces.
The Australian Standard I 170 is more applicable to the
process industries because in it are shape factors for
geometries that are more common in that industry, e.g.,
circular shapes. However, before applying the shape factors of the Australian standard to the ANSI or any other
national standard, one must be very careful to correctly
convert the factors. This is because the codes have different basis upon which these factors are determined,
and a direct application of other parameters is not possi
ble. This is discussed later after we discuss the basis for
the various standards.
CRITERIA FOR DETERMINING WIND
SPEED
Wind is caused by differential heating of air masses by
the sun. These masses of air at approximately one mile
above the ground circulate air around their centers of
pressure. At this altitude, the velocity and direction of
the wind is almost entirely determined by macro-scale
forces caused by large scale weather systems. Below this
gradient height, the wind is modified by surface roughness, which reduces its velocity and changes its direction
and turbulence. A secondary criterion, except for extreme wind conditions, is the temperature gradient,
which affects the vertical mobility of turbulent eddies
and therefore influences the surface velocitv and the eradient height. Therefore. the exact nutur" of the suriace
wind at any point depends, first, on the general weather
situation, which determines the gradient wind and the
temperature gradient, and, second, on the surrounding
topography and ground roughness which, together with
188
Mechanical Design of process Systems
the temperature gradient, modify the gradient wind to
the surface wind.
Wind motion is lurrher complicated by rhe rorarion o[
_
the earth. which induces additional forces that cause the
alr movrng across the earth's surface to be subiected to a
force at righr angles ro the wind velocity vecior. These
additional forces are known as Coriolis iorces.
Each country has adopted its own standard for measur_
ing wind velocity. The U.S. National Weather Service
and U.S. codes use the fastest-mile wind speed, which is
defined as the arrerage speed ofone mile ofair passing an
anemometer. Thus, a fastest-mite wind speed of 120 mph
means that a "mile" of wind passed the anemometer dur_
ing a 30-second period. Other nations, namely Australia
and Great Britain. use the two-second gust speed. This is
based on the worst 2-second mean as measured bv a cuo
anemometer. The mean gust speeds are recorded over a
period of time such that a mean recurrence interval is de_
termined. The mean recurrence interval is the reciprocal
of the probability of exceeding a wind speed of a'given
magnltude at a particular location in one year. The risk.
or probability. R. thar the design wind speed will be
equaled or surpassed at least once in the life ofthe tower
is given by the expression
R:l-(l-P,)"
where P"
:
n:
annual probability of exceedance (reciprocal
of the mean recurrence interval)
life of the tower or stack
The risk that a given wind speed of specified magni_
tude will be equaled or exceeded increaies with the Deriod of time that the tower is exposed to the wind. Values
of risk of exceeding design wind speed for a designated
annual probability and a given design life ofthe structure
are shown in Table B-1.
_ For example. if rhe design wind speed for a tower is
based on an annual probability of 0.02 (mean recurrence
interval of 50 years) and the projected tower life is 25
years, there is a 0.40 probability that the design wind
Table B-1
Probability of Exceeding Wind Design Speed
0.
l0
0.05
0.01
0.00s
r
5
0.100
0.0s0
0.010
0.005
0.410
0.226
0.049
0.025
l0
15 25
speed will be exceeded during the life of the structure.
The United States and Australian wind codes use rhe 50_
year recurrence interval.
The instrument for measuring the wind in the United
States, Great Britain, and Australia is the cup-generator
anemometer shown in Figure B-1. This device is oper_
ated by rhe wind striking rhe cups, which drive a small
permanent alternator. The indicator, which incorporates
a rectifier, is simply a volrmeter calibrated in miles oer
hour. [n most recent cup-generator models the generator
output is used to activate a pen-chart recorder w-hich oro_
vides a record of continuous wind speed.
WIND SPEED RELATIOIISHIPS
As stated previously, another method can be substi_
tuted for the appendix in ANSI A59.1. What this means
is that another code could be used instead of the appen_
dix. To do this one must be careful to utilize the correct
conversion factors between standards. To accomplish
this we refer to Figure B-2. For a 100-mph fastest mile
wind speed in ANSI A58. I we wish ro determine the
equivalent fastest mile wind speed for a 2-second gust
using either the Australian or British code. From Fis-ure
B-2 we read from the ordinate 1.54 for 2 sec. Knoiins
that one mile of wind moving ar 100 mph will pass thi
anemometer in 36 sec, we read 36 sec on the curve and
arrive at V,/V366
1.30. Thus, the equivalent fastest
:
Pr = 1-(1 - PJ"
PA
Figure B-1. Cup generator anemometer
mile wind speed is
I 54t
: tffil
(100y rnp6 = 118.4 mph
"
I
50
100
0.651 0.794 0.928 0.995 0.999
0.401 0.537 0.723 0.923 0.994
0.096 0.140 0.222 0.395 o.634
0.049 0.072 0.rr8 0.222 o.394
for a 2-sec gust. For I l0 mph, the values becomes
V:
(l.l8x1l0) mph =
129.8mph
n
Appendix B: National Wind Design Standards
189
110
Figure B-2. Ratio of probable maximum wind speed averaged orer t seconds to hourlr mean speed.
Thus, the
gust code
1.
if
l8 factor would
have to be used in the 2-sec
that code were to be substituted for Appen-
dix A of ANSI A58.1-1982.
Similarly, the Canadian code we must convert to ob
tain an equivalent fastest mile wind speed from the mean
hourly. The mean hourly implies that the rvind moves an
:verage of 100 mph across the anemometer in a period of
1.600 sec. Reading Figure B-2 we have V,/V,,o, : 1.9.
Thus
!! :
1.3
o.ros
rvhich yields an equivalent velocity of 76.9 mph. With
the Canadian code one must use 0.769 in use of shape
constants and the various other parameters when using
rvith ANSI A58.1. A comparison of the major wind
codes is given in Thbles B-2, B-3, B-4, and B-5.
A-A verl restricted category in which the
rvind speed is drasticalll reduced. Most petrochemical
and power facilities do not fall within this category.
The wind force is reduced because the structure is considered to be among many tall structures. One example would be a ten-story building in downtown Manhattan, New York, where the taller buildings would
block the stronger air currents.
Category B-A classification that encompasses some tall
structures, but not enough to block the majority of
wind gusts. An example of this category would be a
tower in the midst of a large petrochemical facility
where there were other towers that would block some
of the wind force. A forest surrounding a tower is another example.
Category C-The most common classification for petrochemical applications. This category is open terrain
where the tower would receive full impact from the
wind with minimum ground resistance to the wind. An
example of this category would be an open field or an
Categorl
alrport.
ANS|
A5A.r-r982 W|ND
Category D-A classificarion for wind moving over water. A beachhead, in which there is flat beach up to a
CATEGORTES
In the ANSI A58.1-1982 there are four wind categocategories are described as
follows:
ries-A, B, C, and D. The
row of buildings would be rn Category D. Miami
beach, from the ocean front up to the facade of hotels,
is a good example. Behind the hotel fronts would be
Category C. Another example of this classification
would be a tall vertical vessel on an offshore structure.
190
Mechanical Design of Process Systems
Table B-2
Maior U.S. and Foreign Building Codes and Standards Used in Wind Design
Code or Standard
Australian Standard I170,
Part 2-Wind Forces
British Code of Basic
Data for Design of Buildinss
(cP3)
Wind Loading Handbook
(commentary on CP3)
National Building Code
of Canada (NRCC No. 17303)
The Supplement to the
National Buildins Code of
Canada (NRCC 17724)
ANSI A58.1- 1982
Uniform Building Code
Edition
1983
Address
Standards Association
of Australia
t972
80 Arthur Street/North Sydnev.
British Standards
Institution
1974
Building Research
1980
Establishment
National Research
Council of Canada
National Research
Council of Canada
1980
t982
1982
1982
Canada
Ottawa, Ontario
KIA
OR6
Canada
1430 Broadway
Southern Building Code
Congress International
Building Officials and
1984
London, WlA 285, England
Building Research Station
Carston, Watford, WD2 7JR, England
National Research Council of
New York, New York 10018
1983 rev.
Basic Building Code
2 Park Street
Standards Institute
International Conference
with
N.S.W. Australia
British Standards Institution
American National
of Building Officials
Standard Building Code
Standards House
Code Administrators
International, Inc.
5360 South Workman
Mill
Road
Whittier, California 9060 I
900 Montclair Road
Birmingham, Alabama 35213
17926 South Halsted Street
Homewood, Illinois 60430
Table B-3
Reference Wind Speed
Beletence
Averaging time
Equivalent reference
wind speed to fastest
mile 100 mph
Australian
British
1
2-3
second
gust speed
I18.4
1
2-second
gust speed
1
18.4
Canadian
I
Mean hourly
76.9
United States
1
Fastest mile
100
Appendix B: National Wind Design Standards
191
Table B-4
Parameters Used in the Maior National Standards
Parametel
Australian
1983)
(sAA,
Brltlsh
(BSr, re72)
Canadian
(NRCC, 1980)
Unlted States
(ANS|, 1982)
Wind Speed
4
3
Yes
None
Yes
Yes
Terrain roughness
Local terrain
Height variation
Ref. speed
Wind Pressure
Pressue coefficients
Yes
Yes
None
Yes
2-sec gusts
z-sec gusts
Mean hourly
Fastest mile
tbles in
Tables, includes
figures
Figures and
Tables, figures
and notes
Gust speed
Reduction for
large area
Dynamic consideration
Gust speed
None
Gust effect factor
Gust effect factor
Gust response factor
Area averaging
Dynamic
consideration
not included
Dynamic
consideration
Dynamic consideration
for h/b
appendix includes
figures
tables in
commentaries
Gusts
Magnitude
Spatial correlation
Gust frequency
>
5
for h/b > 4
in. or for
for h/b
>
5
h>400ft
Analysis procedure
This standard is consid- Overall a very good
ered by many the best
code, its weakest part
for us€ in the process
is the lack of dynamic
industries. Figures and
tables are easy to read.
The standard actually
provides the user with
equatrons to curves.
The analysis procedure
is straight-forward.
consideration.
An excellent wind Although the appendix
standard. The
analysis procedure
is straight-forward
and the docu-
is technically not considered a part of the
standard, it contains
figures difhcult to read,
ments-code and
namely Figure 6. For
supplement conmany structures the
tain tables and fig- data extend beyond the
ures easy to read, limis of the curves in
Figures 6 and 7. In the
method in the appendix,
one must assume an initial natural frequency,
resulting in an iterative
process. This method is
extremely difficult in
designing petrochemical
towers without the use
of a computer.
192
Mechanical Design of Process Systems
Table B-5
Limitations of Codes and Standards
Code or Standard
Australian Standard
I170, Part 2 1983
National Buildinq
Code of Canada (NRCC, r980)
British CP3
United States
ANSI A58.I
Uniform Building
Code
Basic Building
Code (BOCA, 1984)
Standard Building
Code, 1982 (SBCCI,
t982)
statement ot Limitation
"Minimum Design Loads
Location
Title
on Structures"
"...EssentiallyaSer
Guide to the
Use of the Code
of Minimum Regulations . . ."
". . . Does Nor Apply to
Buildings. . . Thdt'Are of
Unusual Shape or Location
Section
I
(Scope)
For Which Special Invesrisations
May Be Necessary . . ." -
"Minimum Design Loads . . ."
"Specific Guidelines Are Giyen
For. . . Wind Tunnel Investisations
... ForBuildinss.. . Havin--s
Irregular Shapei. . ."
"The purpose . . . is to provide
Section 102
"The Basic Minimum Wind Speeds
Section 912.1
TitIE
Paragraph 6.1
minimumstandards.._"
Are Shown in Figure 912.1 . . ."
"The Purpose of This Code is to
Provide Minimum Requirements
..
"The Building Official May Require
-
Evidence to Support the Desisn
Pressures Used-in rhe Designof Structures Not Includedln
This Section."
Preface
.',
Article 1205.2(a)
194
Mechanical Design of process Systcms
PROPERTIES OF PIPE *
The tollowinq lormulds C're used
lhown in the toble:
in ihe computotior ol the volues
i weight ol pipe per toor (pounds)
weighl ol wcter !'€r toor (pour&)
squdr€ leet outside iurloce per toot
Bqucre leet ilside surloce p€r toot
inside qrea (squqre inch*)
olea of Inetdl (squcte hches)
momert ol inertid (inch6s.)
i tbo fsrridc steels rlay
b€ qbout S% les., @d tbo dultesitic stoh.
l6ss ste€ls dbout 2/o qred'ler th@ the values lhown in this tqbl€
which dre bdsed o! weights lor carbon steol.
10.6802(D-r)
0.3{05d
:
=
r schedul€ Du.Ebers
0.2618D
0.2618d
Stotdord weigbt pipe ond schedule 40 dle the sqme in dll sires
througb lo-inch; Irom l2,iach through 24-iach, stondqrd weight pipe
hcB a wdll thicble$ oI %-inch.
0.78sd
0.78s{Dr-d)
0.049r(Dr-d.)
Ertro Btlong eeight pipe (r|td sch€dule gO q!6 the sdme in sll siz6!
lhrough 8-inchr trom 8-irch thlough Z4-irch, ert ci sttoag weight
A^n;
sectio! boduluB (inchest)
rodius oI glrotion (illches)
=
0.0982(D.-d.)
=
o.zs
pipe hds c wdll rhjcLdess ot %-irch.
D
l ozlp-
Double enrd stloEg weight pip€ bas no cor*ponding scbedule
nu.Eb6r.
A, = dreo of Estcrl (Equa.e nocles)
d = inside dida€ter (iach€6)
D = outsids didnete! (bchos)
R, = lodiu! ol gFotior (irches)
t : pip€ wdU thicloess (inchss)
DoEinol
piF rize
%
0.405
%
0.540
thick-
b
40
80
;;
%
0.840
std
std
l0s
0.049
40s
0.068
0.0740
0.0568
0.095
l0s
0.065
0.410
0.1320
40s
80s
0.088
0.364
0.1041
0.119
0.302
0.0716
ss
0.065
0.710
l0s
0.(E5
0.396
0.2933
40
t;
{0s
0.091
0.54S
0.493
80
xs
80s
0.t26
0.423
0.1405
0.065
0.710
o.6't4
0.622
0.546
40
80
;;
XS
40
80
;;
xs
0.466
o.2s2
0.u99
0.065
0.920
0.655
0.2011
l0s
0.083
0.884
0.6t4
10s
80s
0.1l3
0.I54
0.2t8
0-s21
o.?42
0.614
0.434
0.533
0.432
o.2521
0.333
0.435
0.570
0.718
1.185
1.103
1.097
0.945
0.864
0.719
0.083
40s
80s
0.109
0.147
0.187
;;;
xs
0.308
l0s
40s
80s
t60
xxs
r%
{0
;;
J.660
80
xs
0.t{0
r.380
xxs
r%
l0s
0.0r395
0.1716
0.01197
0.00586
0.00730
0.00862
0.0285
0.01737
0.02160
0.02554
0.2150
0.2159
0.2090
0.0120
0.0285
0,01431
0.0341
0.0407
0.0478
o.0527
0.0577
o.2750
0.2692
0.2613
0.2505
o.2102
0.2409
0.2314
0.2157
0.1943
0.1607
37
0.344
0.344
0.344
0.310
0.2872
o.2716
0.2s20
0.2134
0.1570
0.06s
t.?70
2.461
0.t09
1.682
0.37s
0.613
0.197
0.497
0.1271
0.1215
0.1146
0.00378
o,275
0,273
o.275
0.275
o.275
o.275
1.534
0.00437
0,00525
0.01230
0.0660
1.107
0.00088
0,00106
0.01032
0.671
1.057
in
0.00331
0.1765
0.1628
0.1433
0.63r
gYrd-
0-00600
0.538
1.160
I
UorL
0.00I22
0.I859
0.896
0.8b
lus,
0.002?9
0.220
0.220
o.220
0.220
0.220
0.220
0.250
0.382
r.496
r.283
0.0321
lodiu!
0.0572
0.04s1
0.0310
0.1295
0.1r06
0.
lb
a6clioE
Erodu.
0.330
0.425
0.535
o.t77
0.t77
0.t220
|'roEeDt
ol
inertio.
0.3ts
o.t427
0.3{{
0.3{{
designctioD
0,0246
0.0157
0.t77
0,434
0.434
0.434
0.434
0.134
0.434
1.27a
0.186
0.245
0.538
0,423
0.568
0.739
0.326
U.53I
0.669
40s
0.0s04
0.070s
0.0563
lbf
0.1859
r.839
1.530
lt
0.0794
0.341
t.442
per
0.220
1,076
0.109
It
il|3id€
0.141
0.2818
0.065
Bq
0.I4t
0.s22
1.049
0.957
0.815
wdl ihicla€ss
ANSI835.19 stainless sloel piF,e scbedule du.Dclors
0.1073
0.0955
0.599
0.133
0.1?9
0.250
0.358
55
,::
0.1479
0.r06
0.2553
0.113
0.4s4
0.639
0.836
r0s
160
1.900
0.065
0.109
0.2961
0.r06
0.106
0.1582
0.1246
0.1670
0.2173
0r9{
l0s
836.10 steel pipe rtoEinql
"q.tt..
ouardo
0.141
0.1583
0.1974
0.2503
0.320
0.383
0.504
xxs
40
80
0.19t0
b: ANSI
lr'6ight
weight ol
wcler
,
| auddc.€! sur{dc6, Fr It, p€r lt,
|I
|
0.0970
0.12s0
0.1s74
0.3ss9
0,357
0.304
0.2340
0.1706
160
I
0.0364
0.0548
o.0720
0.0925
836.10 steel pipe schedule Dumb€rg
e
|3cr'l|r" I pertr
0.307
0.269
0.215
xxs
.1.3r5
cleq, ldred,
. I
_
3q.In.
in-
160
1.050
inside
didm- io"ia. |l -.tot
in.
xs
80
%
o.675
wcll
Bchedul€
oulside
diclmeter,
ll|"
o: ANSI
0.t011
0.0827
0.0609
0.17t
0.rs47
0.851
0.1316
0.0ttl0
1.0€8
0.10I3
0.02010
r,301
0.0710
0.0216
0.022\3
0-t2125
0,684
0.857
o.2aa2
0.02451
0.2661
0.02970
0.0370
0,0448
0.0527
0.0579
't.7t4
l.l3t
t.414
1.937
2.441
0.2301
0.1875
0.1284
0.0541
0.858
0.478
1.404
0.{09
0.1t04
0.2810
0.0760
0.ll5l
0.443
0.42A
0.407
0.387
0.361
1.679
0.374
0.311
0.I056
2.811
0.2281
3.659
0.t221
o.1252
0.1405
0.1329
0.1605
0.1900
0.2137
0.1038
0.1605
0.1948
0.2418
0.2839
0.1250
0.1934
o.2346
0.2913
0.312
1.r07
o.797
1.805
0-7al
0.361
2.273
2.997
0.648
0.2t92
0.349
0.343
0.334
2,t72
0.401
0.l9sl
0.0467
0.0566
0.0706
0,0853
0.1004
0.0500
0,0757
0.0874
0.378
0.1594
0.1628
0.1547
0.335
0.304
0.2346
5.2t4
0.458
0.2732
0.341
0.41I
0.469
t.274
1.067
0.I580
0,{40
2.085
0,962
0.2469
0.1663
0.2599
0.32r
0.30{
0.42t
0.564
0.550
0.540
0.524
0.506
0.472
0.649
0.63{
tCt,kne\) ,'f ITT Ctinkll.
Appendix C: Properties of
PiPe
195
PROPERTIES OF PIPE (Continued)
noEitrol
prpe
qumber'
outside
diomelet
ia.
thick-
srd
xi
40s
8os
xxs
2
2tl
0.154
0.218
0.343
0,436
0.s62
0.687
2.875
80
";;
xs
40s
80s
160
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1;
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80
3.500
160
10s
3h
40
80
i;xs
80
4'JU)
xs
5.563
D-622
0.541
1.411
0.822
0.622
0.822
0.622
0,622
0.508
0.442
0.393
0.328
0.262
5.O22
1,280
0.868
0.731
7.444
9.029
0.971
1.163
0.979
0.76S
I.312
1.I01
t0.882
0.533
0.311
L.442
1.2140
1.5130
t2110
0.753
0.?s3
0.753
0.753
0.753
0.753
0.753
0.?s3
0.709
0.6s0
0.646
0.608
0.556
0.464
0.3s9
0.334
2.499
2.361
2,016
1.837
1.535
0.710
0.988
0.4s4
1.530
1.064
1.925
1.339
13.70
15.860
1.067
l.ss8
t1-729
0.554
2.872
3.0890
3.2250
0.873
0.s53
0.803
3.03
4.33
7.58
3.78
1.301
3.6r
LazZ
1.154
10.25
tl-32
2314
18.58
1.801
1.431
2-226
2.476
3.43
1.136
0.687
0.602
0.537
o.171
3.02
3.90
5,03
5.39
t.724
0.75S
3.20
2.864
7.O73
0.916
0.916
0.916
0.916
0.916
0.916
0.916
0.916
1.021
t.o47
1.004
1.463
1.047
0.984
3.41
4.91
2.680
3.68
a,721
1.047
t.o41
0.92S
0.881
12.51
1.047
0.7t6
22.850
3.8S
2.S30
3.92
6.40
2.1s0
2.556
3.199
3.641
0.083
0.120
3.334
3.260
3.068
2.900
2.626
2.300
2.050
8.73
8.35
7.39
0.89r
r.s00
2,5,13
0.r20
0.188
0,237
0.337
o.437
0.500
160
0.62S
)o(s
r.075
o,z6s2
o,420
0,561
s.2t2
0.674
0.800
0.925
4os
80s
0.499
1.276
t20
xs
0.3rs
1.582
1.455
t.275
0.109
0.134
0.258
0.375
0.500
80
r.715
2.638
3.653
1.826
0.531
;; ;;;
0-622
0,622
0.472
2.184
0.226
0.318
0.636
r0s
0.787
0.7s0
0.875
1.000
3.834
3,760
3.548
3.364
2.72A
4.334
4.260
4.L24
4.026
3,826
3.626
3.S00
3.138
3.152
2.900
2.650
5.34S
5.29S
5.(X7
1.813
4.563
4.313
4.063
3.813
3.553
6.6r
5,12
4.15
3.299
11.10
9.89
8.89
5,845
r.704
1.2?4
2.224
3,02
1.2L
5.4t
6.317
1.178
14.7S
11.25
13.357
t2.73
It.50
2.547
3.17
4,41
r0.33
s.521
s.28
7.80
6.602
5.513
0.817
0.802
o.741
0.755
o.129
0.703
0.6710
0.6410
0.t23
1.525
40s
80s
:o,s
t,229
1.001
0.58I
1.60d
t.771
0.I20
r60
r.251
0.508
0.598
0.6470
0.6670
8.6?8
2.945
4.03
4.663
10s
120
1.774
0.{12
0.588
0.565
4.19
4.24
3.55
0.2I6
40s
s0s
l.5m
0.326
0.39r
0.I57
1.039
0.083
;; ;;
1.689
I.939
0.623
0.50s
0.310
0.246
o.724
0.300
0.437
0.600
0.725
0.850
IGS
o.176
tio|1.
inJ
in..
7.7tO
2.635
2.469
2.323
2.L25
80s
xrs
0.{97
lus,
lb
0.483
0.568
0.6140
0.6340
2.r09
0.083
1,qn
2.551
rodiue
gYrc-
o.4tz
1.885
0.083
0.120
0.203
0.274
0.3?5
0.552
0.675
0.800
40s
xi;
2.247
rnodu-
6.40€
I.{29
80s
lt.
a6ctioE
ol wsler oI
p€r It,
in€diq,
1.859
r.406
0.950
0.567
0.283
{0s
per
w€isht
0.882
0.765
0.608
1.I00
xs
suatcce, EurIqce,
pe.Il
po. ft
rrreight
3.631
1.338
;; ;;
It
itrlide
2.7t8
0.400
3.96
3.65
3.36
2.953
2.210
rq
0.3s3
0.350
0.288
o.223
0.281
2-245
2.157
2.081
lt
outsido
o,42r
r.058
0.850
0.600
eq
0.497
0.497
0.497
0.497
0.497
0.799
1.767
0.109
;;
rD.
2,036
0.06s
l0s
rq.
1.500
5'S
xxs
3q. in.
1.6r0
0.650
160
metol
0.200
los
80
iriide
0.I45
0.52S
.:
2.375
diqa-
in.
160
L90{)
inrid€
!646.
b
q
40
80
1%
wcll
rchedule
rir.
6.283
6.62
8.10
9.294
12.385
2.175
3.531
5.793
7.661
I0.01
zt-447
24.0s'l
9.r!
t.178
l.ll5
1.178
1.082
1.178
r.054
10.79
1.178
1.002
14.98
1.178
0.94S
r.178
0.916
0.900
0.825
0.759
0.694
r8.96
21.360
1,178
1.178
10.384
1.r78
t.178
8.560
0.792
o.111
r.041
1.208
t.t96
1.094
1.0,17
6.50r0
3.7t50
1.0140
6.8530
3.9160
0.9810
5.01
4.81
4.28
1.960
2.756
4,19
6.28
s,8d80
0,980
1.38s
L.312
5.800
5.51
4.98
4.48
4.160
1.378
2.394
3.14
4.9240
1,337
1.307
1.2100
2.811
t.249
1.562
3.96
5.8500
L.762
2.6000
3.21
4.27
1.549
123
11.65
t2.17tO
4-O2
13.27
21.54
31,613
35.318
3.38
2.864
15.29
2.391
t7.?130
1.399
1.386
6.35
7.77
9.73
6.95
8.43
l{.62
16.66t0
1.868
1.456
2,285
4.30
t.456
1.4s6
r.321
18.19
6.ll
1.456
1.260
20-74
t.89
I6.35
1.456
1.t95
27.O4
14.6r
7.95
9.70
1.456
1.129
32.96
t2.97
I1.34
1.455
r.064
38.5S
7.(x)
6.33
s.62
rt.4l3
12.880
l.{s6
0.998
0.933
43.8t0
{.951
36.6450
17.7s1
4.232
39.lll0
1.156
2.I4S0
2.2430
0.988
0.975
0,947
0.924
0.894
0.844
0.8140
0.7860
1.103
22.44
22.02
20.01
1t.328
0.68t
0.549
0.5200
0.4980
15.17
20.68
25.74
30.0
5.6760
5.90
6,79
7.4050
7.8720
2.494
3.03
5.15
7.13
9.25
10.80
1.5250
t,510
t.177
1.445
1.1250
t.116
1.37{
1.3380
r.3060
1.920
1.878
1.839
1.799
1.760
I2.10
13.1750
11.0610
1.6860
1.5s20
196
Mechanical Design of Process Systems
PROPERTIES OF PIPE (Continued)
pipe Biz€
schedule
in.
wall
inside
thick-
diom-
l0s
0.109
6.407
32.2
0.134
6.357
0.219
6.187
3t.7
30.r00
5.761
28.89
26.07
40
sia
40s
0.280
80
xs
80s
0.432
tItetol
sq. in.
rn.
b
6
inside
3q.
rL
aq
lt
outside
sq ft
inBide
surrcc
pe! It
per
lt
weighl
per It,
lbf
5.37
r3.98
ll.8s
3.58
1.664
9.29
t3.74
14.40
4.4I0
4.35
t.734
t.734
1.620
22.6600
6.8400
1.588
15.020
18.97
r3.100
5.58
12.51
28.\4
8.s0
8.40
I.734
1.508
28.57
It.29
t2.2s
2.I95
L440
36.39
I0.30
40.5
49.6
14.98
2.153
1.358
5S.0
66.3
r7.8I
2.r04
20.03
72.r190
21.7720
2.060
2.0200
76.5970
23.t240
1.s850
5.50r
23-77
10.70
5.189
4.897
18.83
15.64
1.734
1.734
1.734
L000
L t25
4.62S
16.792
t7.662
t.734
r.211
45.30
s3.16
60.076
4.37S
Is.02s
19.429
t-734
1.t45
66.0S4
0.109
4.407
9,91
8.329
2.180
r3,40
0.219
8.187
2.258
2.258
2.258
2.258
2.258
2.25A
2.258
2.25A
2.2A1
0.I48
2.916
3.94
2.150
19.640
2.t27
2.1t3
22.36
24.70
28.55
r.282
8.17
7.284
24.07
23.59
22.500
22.48
8
20
0.250
8.125
s4.s
52.630
51.8
8.625
30
0.27',|
8.07r
51.2
0.322
7.991
0.406
50.0
47.9
10.48
0.s00
7.813
7.625
45.7
t2.78
100
0.593
7.439
t20
0.718
7.18S
I
l{0
t7.44
2.25a
2.258
1.882
0.8I2
7.001
43.5
40.6
38.5
19.93
8.625
2.2s8
L833
160
0.906
6.813
2t.9?
2-2s8
1.784
74.69
15.80
1.000
6.625
6.375
23.942
26.494
2.258
2.258
t.?34
81.437
90.1r4
14.945
r.669
2.744
2.728
2.70
r8.70
24.63
2.683
28.04
a;;
80
XS
4;;
80s
l0s
;;
30
5.800
6.58
8.40
14.96
2.089
2.045
1.996
L948
22.t8
18.84
t21.4
28.t4
2.847
17.60
140.6
32.6
2.807
r6.69
1s3.8
35.7
2.117
38.5
2.7 4A
4r.0140
2.7I90
2.68I0
13.838
10.250
9.25
0.307
r0.r38
2.815
2.815
2.81s
2.654
34.24
10.020
82.s
80.7
78.9
2.623
40.48
)0.750
80
100
120
2.938
50.87
60.63
0.250
xs
2.962
2.953
2.S09
0.219
60
I3.39
t4.6S
r6.81
2.578
36.9
36,2
35.8
35.0
l0
63.4
24.52
2.815
l.9l
ll.s000
r05.7
2.815
10.07
3.00
2.9700
sr.3200
19.80
5.49
7.24
l
8.2I
20.58
4.52
0.365
0.500
0.593
3.0r
35.4
88.8
85.3
;,;
6.13
20,79
86.3
2.815
26.4S
21.69
r0.420
r0-312
83.52
2.304
2.295
2.2700
2.245
35.64
43,39
t0.482
0.134
0.t 65
40
40s
80s
34.454
3L903
luB,
r.677
0.562
40
60
inertia,
tb
1.734
0.7I8
I0s
per It,
rddius
gyration,
in.
1.734
160
0.864
oI
2.231
2.733
t20
xxs
w€ighl
37.4
177.t320
r90.62I0
44.2020
63.7
76.9
I1.85
14.30
3.75
3.74
100.46
r8.69
3.72
I13.7
21.I6
3.7r
137.S
160.8
25.57
29.90
3.69
34.1
9.750
s.564
'14.7
16.
t0
2.815
2.5S3
54.74
32.3
7t.8
2t2.0
39.4
3.53
t8.92
2.815
244-9
9.314
68.I
45.6
3.60
22.63
2.815
248.2
0.843
53.2
9.064
64.5
3,56
26.24
2.815
0.87S
27.t4
2.815
2.36
L000
t.125
28.0
27.6
324
9.000
64.33
76.93
89.20
92.28
31.1
0.718
2.504
2.438
2.373
8.7S0
60.1
30.6
2.815
2.:91
104.13
26.1
368
8.500
2.815
2.225
37.3r
2.815
2.16
t26.42
428.t'I
1.500
7.750
47.r5
3.52
3.50
3.47
3.43
3.39
43.57
2.8I5
2.03
148.19
24.6
23.2
20.5
399
8.250
56.7
s3.45
34.0
1.2s0
60.3
62.04
58.4
74.3
79.66
478.59
89.04
3.31
0.156
12.438
rzt-4
t22.2
12.390
r20.6
19.20
7.11
3.24
52.2
I40.S
0.2s0
!2.250
u7.9
22.t3
3.34
3.21
3.34
3.17
43-77
19.1
191.9
248.S
30.1
12.0S0
ll4_8
5r.l
0.330
9.84
r2.88
20.99
24.20
33.38
52.7
0.180
3.34
3.34
0.375
12.000
I
3.14
49.S6
4S.0
279-3
11.938
llt.9
3.34
0.406
14.58
1s.74
0.500
u.750
3.34
3.08
0.562
I1.626
106.2
2t-s2
3.04
362
401
11.376
r0t.6
56.7
62.8
0.687
26.04
3.34
3.34
48.5
47.0
46.0
47.1
19.24
53.53
65.42
73.16
300
108.{
4.45
4.44
4.42
4.39
4.38
4.37
4.33
2.978
88.51
44.0
0.7s0
0.843
0.87s
1r.250
99.40
.28.27
3.34
2,94
96.2
43.1
475
510.7
11.064
96.t
41.6
562
t20
3.34
2.897
2.88
07.20
t0.9
4I.l
578,5
1.000
10.750
l{0
36.9
3.34
2.8t4
10.500
4l.l
3.34
642
70r
1.250
10.250
45.16
150
r.3t2
35.8
755.5
10.126
3.34
3.34
2.749
2.68
25.49
39.68
53.6
39.3
r,125
95.00
90.8
86.6
82.50
80.5
31,5
32.64
3.34
I1.000
2.651
4D.27
34.9
781
140
I60
l0s
;i
30
40
t2
;;
12.750
80
I00
;;;
4;;
.-.
80s
t3.l
41.1
3.34
3?.S
333.46
39.0
43.8
?
4.5
80.1
90.7
4.31
4.27
4.25
4.22
4-21
I09.9
4-t7
4.I3
118.5
122.8
4.09
4.01
100.7
3
'1'
Appendix C: Properties of
Pipe
197
PROPERTIES OF PIPE (Continued)
aoniaal
pipo riz.
rchedule
outtide
woll
iDsid€
thicL-
diqn-
inside
metal
h.
sq. it!.
11646,
iD.
b
Frlt
13.688
147.20
6,78
3.67
3.58
145.80
13.580
141.80
3.67
3.67
3.57
0.2r0
0.219
r3.562
144.50
8.16
9.10
9.48
to
0.2s0
t3.s00
143.I
10.80
;;
0.281
13.438
141.80
l2.tt
140.5
139.20
t3.42
;;
40
0.312
0.344
0.375
0.437
;;
80
100
13.312
13.250
13.126
137.9
14,76
16.05
I35.3
18.62
19.94
0.469
13.082
1s4.00
0.500
0.ss3
0.625
0.750
0.937
13,000
t32-7
12.8I4
129.0
24.94
12.750
t27.7
t22.7
26,26
12.500
woisht
trrr fL
tb
trlo|ne|''t
ol
modu-
i|'ertiq,
luB,
tioD.
iD..
in.t
i!-
aectiorr rcdiu6
9Yra-
3.55
23.0
27.1
30.9
32.2
3.67
3.53
36,71
62.1
3.67
3.52
4t.2
6I.5
285-2
40.7
3.50
45.68
60.9
3.48
3.4J
3.44
s0.2
s1.57
63.37
67.8
50.3
3r4
34{.3
14.9
49.2
58.7
s8.0
429
456.8
55.3
1-79
72.09
57.5
484
69.1
84.91
55.9
562
80.3
s8s
81.1
4.18
4.14
4.73
4.69
4.63
1.58
4,53
4.18
3.67
3.57
3.42
3.67
31.2
weight
3.67
3.67
12,t28
3.40
3.35
3.34
3.27
3.17
r62.6
63.1
62.8
130.73
150.67
30.9
225.1
t2.2
4.47
36.S
4.86
4.85
59.7
89.28
106,13
2t8,2
4.90
4.88
1.87
194.6
53.2
s0.0
47.5
45.0
27.8
53.3
61.2
687
94.2
825
117.8
tr21
132.8
146.8
159.5
4.84
4.8s
4.82
1.80
1.093
1.2s0
It.8l4
109,6
44.3
I1.500
103.9
50,1
3.67
180
1.406
lI.l88
98.3
55.6
3.6'r
IS.670
I92.90
8.21
i;
0.16s
0.188
0.250
15.624
r5.500
191.70
188.7
9.3{
t2.3?
1.19
4.19
0.312
1s.376
185.7
15.38
0.37S
1s.250
182.6
15.000
14.688
t76.7
4.19
3,93
60
0.500
0.656
18.4I
24.35
4.IS
4.I9
4.10
4.09
4.06
4.03
3.99
4.19
80
0.843
14.314
160.9
40.1
4.19
100
1.03r
13.938
1s2.6
48.5
{.19
120
1.218
1.437
13.564
144.5
13.126
t35.3
65,7
4.19
4.19
3.85
3.75
3.65
3.55
3.44
1.593
12.814
129.0
72.1
4.I9
5S
0.r65
17,670
4.71
4.63
106.2
368
40.8
6.31
l0s
0.188
t7.624
I7.500
245.20
243.90
4.',1L
4.61
36
105.7
4t7
46.4
5.30
41-39
59.03
104.3
5{9
61.0
6.28
102.8
75.S
6.25
70.59
t01.2
678
807
89.6
8.23
82.06
93.15
r04.75
99,9
93r
103.4
6,21
98.{
1053
117.0
6.19
97.0
rt72
130.2
120
140
20
30
40
l0s
;;
xs
t40
t60
;;
30
;;
80
169.4
t7,34
4.71
0.375
17.250
233.7
20.76
4.71
230.4
227.0
223.7
24.11
4.71
4.58
4.55
4.52
4.48
21.49
4.71
{.45
30.8
4.71
4.71
4-42
4.32
4.22
0.437
17.126
0.500
17.00
0.562
16.876
0,750
0.937
16.500
213.8
204.2
40.6
s0,2
1.7r
16.126
193.3
61.2
4.7
r
182.6
4-71
4.7
|
4.7
!
3.89
3.78
140
1.562
r60
1.781
14.438
163.7
71.8
80.7
90.7
0.188
I9.634
302.40
I1.70
0.218
19.564
300.60
0.250
0.375
r9.500
r9.250
30
40
0.500
0.s93
t9.000
18.814
60
0.812
I8.376
18.2s0
80
0.875
1.031
100
1.281
17.438
298.6
291.0
283.5
278.0
265,2
261.6
252.7
238.8
1.375
s;
2.929
237,r
r5.688
r5.250
r4.876
l0
ts
240.5
r.r56
20
4.
3.01
u.376
r00
I20
l0s
3.09
9.24
r0.52
13.9{
0.2s0
0.312
20
20
20,000
rurlqce,
lt
ingide
per lL
rurldce,
lbt
per lL
13,624
l{
18,000
sq
0.188
t1.000
t8
3q.
It
outside
0.1s6
l0s
16.0U)
iD-
sq
17.938
173.8
23.t2
30.6
36.2
48.9
52.6
61.4
s.21
5.24
s.24
s.24
5.24
t10,22
I89.12
42.8
I0l7
28
32
83.5
25?
8S.0
292
42.05
81.8
80.s
384
52.36
62.58
42.71
10r.50
79.1
36.5
48.0
473
562
59.2
?32
9t.s
?0.3
136.45
73.4
89.7
ll57
114,6
164.83
66.1
1365
170.6
58.5
I?60
220.0
1894
236.1
933
192.29
223.81
245.11
138.17
92.7
t70.75
88.S
1834
4.ll
207.96
2180
3.9S
244.14
274.23
83.7
79.2
75,3
203.8
242.2
2499
z'17.6
2',150
308.5I
7
r.0
3020
306
335
168.3
40
131.0
574
5.12
46
r30.2
663
5.ll
s2.19
78.60
129.5
126,0
1I
104.I3
5.24
4.97
4.93
5.24
5.24
5.24
5.24
5,{8
5.43
194.5
5.14
s.60
5.59
5.37
5.21
5.17
5.12
6.10
6.01
s.97
5.90
5.84
5.77
7S?
7S-7
7.00
6.99
6.98
l4
lll.4
6.94
t22.8
t457
6.90
r22.91
120.4
1704
145.7
170.4
4.8r
I66.40
115.0
6.79
178.73
Ir3.4
2257
2409
225.?
4.78
4.70
4,57
208.87
256.10
109.4
2772
240.9
277.2
103.{
3320
332
5.0{
57.4
198
Mechanical Design of Process Svstems
PROPERTIES OF PIPE (Continued)
nominol
pip6 rire
wcll
schedule
b
20
20.ooo
in.
iD.
16.500
16.064
227.0
213.8
202.7
2r,624
367.3
t.968
s.24
5.24
s.24
4.45
4.32
296.37
341.10
4.21
379.01
17.18
0.37s
2t.250
354.7
25.48
0.500
0.625
346.4
339.2
33.77
5.76
322.1
41.97
50.07
58.07
5.?6
0.875
21.000
20.750
20.s00
20.250
80
l.t2s
I9.750
306.4
13,7A
5.76
r00
1.37s
19.2s0
291.0
276.1
8S.09
5.76
104.02
5.76
30
xs
0.750
;;
18.7S0
330.r
?.70
l0l0
91.8
87
153.7
1490
lls
135.4
7.69
7.65
150.2
1953
t77.5
7.61
t43
146.6
2t8-2
1?0
143.t
2400
2829
3245
434
18.65
5.76
5.76
5.99
s.96
5.92
5.89
6.17
5.83
5.78
140.80
156.03
t76-2
3140
26t.4
174.3
172.4
3420
285.2
37I0
309
r88.9
I152
96.0
216
238.11
168.6
4256
4650
s670
354.7
t73
8,07
6850
571
7830
8530
9460
719
788
7.95
7.47
7.79
7.10
41.{
6.28
6.28
6.28
398
45.9
50.3
54.8
436.1
16.29
388.6
63.54
70.0
6.2S
I42.1
6.28
150
19.314
293
159.4
6.28
0.2s0
2S.s00
t0
0.3I2
25.376
0.37s
510.7
505.8
500.7
490.9
0.625
24.500
0.875
24.250
24.000
23.7s0
20
std
20
30
xs
6.54
6.48
2S6.36
158.3
367.40
429,39
149.3
141.4
483.13
541.94
t34.S
t27.0
388
8.18
8.15
22t.4
1646
126.6
s.l0
88
2t9.2
r59.7
9.08
I03
217,1
2076
2479
3259
4013
4744
2t2-8
190.6
9.06
250.7
308.7
9.02
8.98
8.93
s.89
8,85
8.80
6.41
202
6.81
235
452.4
6.8I
6.35
6.28
267
20s.6
204-4
200.2
r96.1
443.0
87,91
6.81
6.22
299
ts2.t
594.0
71
92
2s1.3
2098
2601
149.8
185.8
9.81
2S5.0
22t-A
9.77
520.8
94.98
252.6
248.0
243.4
238.9
234.4
230.0
225.6
3l0s
530.9
21.80
z',t.t4
32.54
43.20
53.75
64-21
74.s6
84.82
1.20
0.875
r.000
1.r25
27.500
27.376
27.250
27.000
26.750
26.500
28.250
26.000
2s.750
0.375
0.500
0.625
t0s
6.81
6.81
r55.8
8.22
8.41
6.81
0.750
l0
6.68
6.64
55
8.29
a.z7
8.25
49.82
0.3r2
xs
6.81
186.24
1316
59.49
69.07
78.54
0.250
30
6.8r
t7t.I?
188.0
471-4
461.9
1.000
std
19.8S
25.18
30.19
40.06
5.48
5.33
s.20
5.06
63.41
481.1
1.t25
l0
8.35
8.31
7.07
16I.9
126.3
0.750
8.10
212.5
231-0
310
26.000
109.6
7.t5
1943
326
0.500
t07.2
2550
2840
1s.876
20
45t
7.31
7.23
183.8
1.812
25.250
2s.000
24.750
119.6
7.39
180.1
178.1
2.062
2.343
srd
351
403
4?58
5432
6054
s4.62
406
87.2
108.1
t26.2
125.49
4
344
303
7.47
6,09
21.83
36.S
365
40i29
7.52
295.0
366.3
432.6
493.8
550.3
602.4
6.O2
425
140
L2l8
1.53t
132.8
237 -2
6.r5
t20
80
5.04
4.91
I97
2Sl
6.28
6.25
6.28
6.28
6.28
5.28
6.28
6.28
6-28
100
5.56
5.50
5.43
5.37
5,30
5,17
4.78
415
382
6.41
157.4
23.500
23.250
23.000
22.816
22.750
22.626
22.500
2s.564
22.250
22.064
21.s64
20.938
20.376
0.968
459
't.71
0.250
0.8?5
6.56
6.48
80.4
l0
;;
422
885
132.68
0.218
376
1s8.2
118,55
402
4220
4590
5l
26t.6
0.750
98.3
92.6
87.9
14.92
247.4
0.687
tb
69.7
17.750
io
9yra.
lion,
in.
Eroduinerlid, lus,
756
r8.250
0.62s
rqdiur
oI
r59.t
r.875
0.562
per lt,
lnoEent rection
44
2.t25
0.375
n eight
12.88
140
160
0.500
tbt
perlt
363.1
;;;
lt
lt
per
2r.500
20
sq
lreight
in8ide
gurlqce, surlcce, per Il,
0.250
30
30
30.000
lll.s
lt
oubide
21.564
XS
2A
87.2
Bq
0.188
0.218
20
28.000
I00.3
17.000
120
28
aq rr'"
1.750
160
metdl
sq in.
1.500
l0
24.000
inside
140
I0s
22
inaide
dicm-
r20
5S
22.004
lhick-
588.6
583.2
572.6
562.0
s51.5
541.2
0.250
29.s00
683.4
23.37
0.3I2
29.376
477.8
29.19
0.375
0.500
29.250
29.000
28.750
672.O
34.90
660.5
46.34
649.2
57.68
0.62S
7.t7
'1.33
7.33
7.G)
7.33
7.85
7.85
7.85
7.8s
7.8s
lll
?.13
7.07
7.00
t17
6.34
2tg
6.87
183
253
288
6.74
323
7.72
7.69
7.66
7.59
7.53
79
99
119
158
!96
296.3
293.7
291.2
286.2
281.3
364.9
5458
419.S
6149
473.0
6813
524.1
4085
5038
5964
6855
714D
8590
9.79
23 1.8
359.8
426.0
490.3
6t3.6
9.68
9.61
9.60
s.55
9.51
t72.3
2t3.4
10.52
3201
3823
254.8
10.18
s033
6213
335.5
I0.43
4t4.2
10.39
258S
10.50
n-.
Appendix C: Properties of
Pipe
199
PROPERTIES OF PIPE (Continued)
nominol
schedule
pipe size
oulside
wcll
thick-
inside
dicm-
irBide
sq. in,
didmeteL
metal
Bq.
in,
sq It
sq It
outside
inside
weighl
pe! ft,
lbt
weight
per It
!(rdiug
ol
ilrerlio.
lb
lus,
gvrqiion,
per It
per rl
7.46
234
276.6
271.8
137
|
491.4
10.34
272
84S4
566.2
10.30
310
2E',t.O
9591
639.4
10.26
347
242.2
10653
t0.2
t0.22
in.3
0.750
0.875
28.500
637.9
68.92
30
28.250
620.7
80.06
7.85
7.85
30.000
I.000
28.000
615.7
9t.Il
7.85
7.39
7.33
l.l2s
27.',750
6D4.7
r02.05
7.85
'1.26
0.250
31.500
'179.2
24.93
8.38
8.2S
85
337.8
11.22
3I.02
8.38
8.21
106
335.2
3l4 t
38gl
196.3
773.2
243.2
11.20
766.9
37.25
8.38
t27
332.5
4656
291.0
11.18
7
54.7
49.48
8.38
B.l8
8.l l
168
321.2
383.8
u.l4
473.6
I1.09
40
l0
0.312
std
0.375
xs
0.500
31.250
31.000
7
32
30
0.625
30.750
7
42.5
61.59
8.38
8.05
209
321.9
6140
7578
32.000
40
0.688
s0.624
736.6
67.68
8.38
8.02
230
319.0
8298
518.6
11.07
0.750
30.500
730.5
73.63
8.38
7.98
250
316.7
8990
561.9
I1.05
0.87s
30.250
8.38
8.38
7.92
7.85
10372
648.2
lr.0l
30.000
85.52
s7.38
291
1.000
718.3
706.8
33t
306.4
I
I680
l0.ss
l25
29.?50
694.7
8.38
7.',19
371
301.3
I3023
730.0
814.0
0.250
0.312
33.500
881.2
26.50
8.90
8.1',|
90
382.0
3173
22t.9
33.376
33.250
874.9
32.99
8.90
8.7 4
1r2
379.3
4680
2',t5.3
IL33
I t.9I
867.8
39.61
8.90
8.70
sssT
329.2
11.89
33.000
s5s.3
52.82
8.S0
8.64
t79
370.8
7385
434.4
r 1.s5
841.9
65.53
72.00
8.90
8.57
365.0
I1.80
3M.l
587.8
I
78.34
LS0
8.54
8.51
9124
9992
535.7
8.90
223
245
266
359.5
1082s
637.0
11.76
20
L
t0
st;
20
34
34.A00
XS
0.62s
40
0.688
32.7s0
32.624
0.750
32.500
0.875
32.250
829.3
816.4
91.01
8.90
8.44
310
3S4.1
12501
735.4
tt.12
1.000
32.000
804.2
I03.67
8.90
8.38
353
348.6
l4l t4
830.2
t.125
3t.750
791.3
lI5.I3
8.90
8.31
395
343.2
15719
924.7
I1.67
I1.63
0.250
35.500
s89.7
28.11
L42
9.29
96
429.1
4491
24S.5
t2.84
0.312
35.376
982.S
9.42
9.26
lIs
426.1
12.62
3s.2s0
s75.8
L42
9.23
143
423.1
5565
6654
309.1
0.37s
310.2
12.59
0.500
35.000
962.1
34.95
42.D\
55.76
9.42
9.16
190
417.l
8785
488.1
12.55
30
0.625
34.750
948.3
69.50
9.42
9.10
236
4lt.t
10872
504.0
12.51
40
0.750
34.500
934.7
83.0I
9.42
9.03
242
405.3
12898
7I6.5
12.46
0.875
920.5
96.s0
9.42
399.{
I4903
82',t.9
907.9
109.96
9.42
8.97
8.90
324
I.000
34.250
34.000
374
393.6
I6S5I
936.2
t2.42
I2.38
1.125
33.750
a94.2
123.19
9.42
8.89
419
387.9
18763
t042.4
12.34
0.250
0.375
41.500
1352.6
32.82
tt2
586.4
r28
339.3
14.?3
1336.3
4S.08
10.80
t320.2
65.18
t0.99
10.73
s79.3
s't2.3
I0627
I4037
t4.7r
0.s00
I67
222
506.r
XS
668-4
t4.67
1304.r
81.28
10.67
276
565,4
1288.2
1256.6
97.23
r0.99
I0.99
330
558.4
427.3
985.2
14.62
14.59
128.81
10.99
10.60
10.47
17373
20689
1.000
41.250
41.000
40.7s0
40.500
40.000
10.99
10.99
10.86
std
438
544.8
210a0
39.500
39.000
t225.3
160.03
t0.99
10.34
1194.5
190.85
10.99
10.21
s44
649
531.2
517.9
33233
39181
r2s9.5
rs82.5
14.50
1.250
1.500
1865.7
14.33
20
36.000
10.92
30
l0
36
0.375
0.500
109.0
2i
42
30
42.000
40
XS
0.62S
0.750
835.S
7
I.78
14.41
200
Mechanical Design of Process Systems
INSWATION WEIGHT FACTORS
To determine the rveight per foot of any piping
insulation, use the pipe size and nominal insulation
thickness to find the insulation l.eight factor F in the
chart shorvn belorv. Then multiply fl by the density
of the insulation in pounds per cubic foot.
Nominal Insulation Thickness
Nominal
Pipe Size
2rt"
1%"
I
1%
1%
10
12
.051
.066
.080
2
214
3
.09r
.r9
.10
.17
.24
.21
.24
.!7
.31
,41
.30
.39
.34
.38
.45
t2
.50
.46
.44
.66
.59
.68
l4
.70
.78
.88
.90
1.0r
16
18
.6{
.87
l.t2
20
24
.70
.83
.96
1.13
1.44
.58
.56
.58
.64
.80
.93
.70
.68
.78
.83
.81
.s7
.88
.97
.71
.83
1.17
1.07
1.34
1.24
1.37
1.49
.96
1.10
1.04
1.20
1.34
1.13
1.36
1.54
t.12
1.1I
5t4"
.59
.63
.o.t
.34
.43
.30
.38
.36
.34
4%"
.40
.39
.48
.47
.31
.29
.29
.21
4
10
3%"
.23
ll
l4
3%
6
8
Example. For 4" pipe rvith 4" nominal thickness
insulation, f : .77. Il the insulation density is
12 pounds per cubic foot, then the insulation rveight
is .77 X 12 : 9.24lb/lr.
1.99
1.52
1.74
r.s9
1.57
1.81
2.01
2.07
2.29
2.40
2.80
3.16
1,64
1.92
1.50
t.7s
1.77
2.10
2.09
2.44
2.24
2.34
2.58
2.82
2.50
2.62
2.88
3.14
3.06
3.54
3.40
3.92
LOAD CARRYING CAPACITIES OF THREADED HOT ROLLED STEEL ROD
CONFORMING TO ASTM A-36
Nominal Rod
Diameter, in.
Root Area of
Thread, sq. in.
Max, Safe Load,
lbs. at Rod
Temp. of 650'F
%
.068
lz
V+
%
.126 .202 .302 .419
610 1130 1810
1
.1ya,
ry4
.693
.889
1y4
1.293
2
1.144 2.300
2l+
2
3.023
3.719
2y4
4.619
3
3r/t
3
5.621 6.124 ?.918
27t0 3770 4960 6230 8000 11630 15?00 20700 21200 33500 41580 50580
71280
3
v
Appendix C: Properties of
1tt
WEIGHTS OF PIPING MATERIALS
Pipe
2O1
prpo r.Brs, o.D.
{?
t-2
{.J-r'
z
?
z
B
{\
{;\
f,.-l
,4L,
E=:r
L+!
!-r__--,
{--J--r
\.lJ
Temperature Range "F
FiberSodium
s$
z
i
sr_r_u$
NJM
{N:IS
4
z
/.4
F
4l
z
/>
Soldface
tvoe is weieht in
pounds. Lighifice type b6neath
weight,
is weight fa.ctor Ior
insulation.
Insulation thicknesses
and
\.reichts are based on averase
conditions and do not constiiuie
a recommendation for specific
thicknesses of mrterials. Insuhtion iveights are based on 85/,
magnesia and hvdrous cdcium
silicate at 11 lbs/cubic foot. The
listed thicknesses and rveights of
combination covednq are the
sums of the inner laj'er of diatom{Lcecus earth at 21 lbs/cubic
fooi end the outea layer at
,N.
11
lbs/cubic foot.
Insulation rveights inciude al,]O\llnces
lol wIIe, cemen!, can-
vas, bands and paint, but not
sbecial
surface 6nishes.
-
To find the weight of covering
on flanges, valves or fittings,
multiply the \r'eight fuctor by the
@
+€
nCI
tsO
* 16 h cu. ft. den-.ity.
SJrr
weight per foot of covering used
on straight pipe.
Valve \reights are approxi-
m:Lte. When possible, obtain
veights from the nranufacturer.
Cast iron valve Neights are for
flinged end valvesi steei weights
for rvelding end valves.
All ftanged fitting, flrnged
valve and flcnge $eights include
the oroDortional Ncieht oI bolts
or siulli to make up all joints.
202
Mechanical Design of Process Systems
lYn"
z
F
PIPE r.660" o.D.
WEIGHTS OF PIPING MATERIALS
w'
4\
z
di
F
t_L_,
Tempcrature Renge
Fiber-
'F
Nom. Thick.,In.
Sodium
Nr$
is \eight in
t)pe benexth
is weight factor for
Boldface
.ty"pe
pounos. Lrghflace
weight.
Insulation thicknesses and
weights arc based on averaqe
mnditiors and do Dot constituie
ts-ts$
{l.-.-tis
z
F
,41
/A
#
,N
z
Jrtd
-J
a
recommendation
tr
@
IrtJ
@
FsO
specific
combination coverinq are ihe
sums of ihe inner layer of dia-
2l lbs/cubic
foot and the outer laycr at
tomaceous earth &t
1l lbs/cubic foot.
Insulation weiqhts include al-
lowances for
wiri,
cement, can-
vas, bands and paint, but not
special surface
@
for
of materials- Insulation lveights are based on.85/p
magnesra ano nl drous c3lclum
silicate at 11 lbs/cubic foot. The
listed thicknesses and neights of
thicknesses
fi
nishes.
To find the weieht of coverine
on flanges, vatvds or fittings]
multiply the weight factor by the
\aeight per foot of covering used
on straight pipe.
Valve rveiqhts are loproxi-dbtain
mate. When
possible,
lreights from the manuf&cturer.
Cast iron valve weiqhts arc for
flanged.end valves; stiel weights
lor weldrng eno valves.
All flanged fitting, flanged
valve and flange weights include
the proportionrl weight of bolts
or studs to makc up all joints,
* 16 lb cu. ft, density.
]
Appendix C: Properties of
.IVEIGHTS OF PIPING X{ATERIALS
Schedule No.
{,1
t2
nuj
>f\
i
t />
LLP
tij
e
i
-1/
40
80
Wall De,<igna.tion
std.
NS
lhickness-In.
Pipe-Lbs/Ft
lVatcr-Lbs/Ft
.145
.200
.281
.400
2.72
3.63
4.86
6.41
.88
.77
.61
.41
.8
1.1
1.4
I.E
.6
.3
.7
.3
L.R. 90" Elbow
S.R. 90' Elbow
L.R. 45" Elbow
Tee
4,
.E
1
.2
.2
2.5
3.L
3.7
.6
.6
.6
5.4
Latera.l
1.3
.6
q--- 1_
-0
dti
Reducer
,2
c"p
.7
.2
.9
.2
.2
.5
.7
.7
.3
.3
.3
Temper&ture Range
Nlaqnesia
'F
\om. Thick., In.
t00-199 200,29e 300,3c0 .100-.199 ;00-it)9 000-0119 ;00-;,1,1 s00-sf)1r 1t00-!r!9 11000-1099
1
I
\)t
.84
.84
1.35
2
2
214
!:
Caliium
Siili.crp
Lbs,/Ft
{
Combina-
\om. Thick.,In.
2tt
Lbs/Ft,
1.t0
z
Fiber-
Nom. Thick., In.
Sodium
LbslFt
PressLrre
,MS
A rtr
za|
lg
tsrj_ri}
{rrTs
..4
a
/:)
Z
tt!4\
-
?41
|
/A
3,\
1.07
Ratiig
250
SIip-On
1.5
7
1.5
\eck
S.R. 90" nlbow
lltn
FrO
* 16
h
G:rt{!
I)tessure Seal
Borrrret-(-irte
Pressurc Seal
Ilonnet Giobe
cu. ft. density-
r.85
3.50
3.5
1.5
10
3.7
I
7
5
4.52
4.s2
4.52
21 ;
2)1
3
3
3
1.20
1.20
5.62
5.62
5.62
2\l
2%
3
3
4.76
4-16
3.50
6.16
000
900
r500
9
l9
l9
1.5
9
1.5
1.:)
1.5
I
\2
l2
l9
l9
34
1.5
1.5
1.5
1.5
1.5
*eights
9
1.5
9
t9
19
31
r
9
10
l0
1.5
1.5
1.5
t2
23
26
3.8
3.9
l9
t7
20
5.6
19
1.5
rveight
is
insulation.
tl pc bene&th
rveight iactor lor
Insul&tion thickncsses rnd
based on :rverage
and do not constitutc
conditions^te
rocommcnd&tion
for
spocilic
of m"rtorial-q. Insulation Neishts :rre bstxl on 85f6
mrgnesia ud hrrlrous lrrlcium
3l
l
46
!-.. , ,,,,1,i
^ f^^r
Tl-
listcd lhiclinesses orxl \\'cights of
combinltion covering rte the
sums of the inner l.rver of dirtomaceous
errth at 21 lbs .ubic
foot anrl the outcr hl cr at
39
23
30
70
5.8
6
70
1.2
.l.il
125
40
45
.t.2
t70
4.2
30
35
40
I
4.1
.1.1
6.8
tlpe is weight in
pounds. Lightfi.ce
thicknesses
4
ll
2500
1.5
t.5
9
Roldf.rcc
400
8
1.5
3.5
Flanged tsonnet,
GLrlrc or Angle
Irlanged Bonnet
1.8s
3.47
300
Ilanged lJonnet
Clheck
++I
1.5
L.R. 90' Elbow
Tee
2
3
blecl
i j;0
L5
Lap Joini
Rlind
1.01
1ta
Casl lron
125
45'Elbow
j=<l
s k3J
1.07
1%
1100-L:00
tl i
2.52
1
ps'
Screled or
\Yelrling
erce
xxs
.2
.6
l/2"
r.eoo'o.D.
203
160
_5
.2
Pipe
5
42
1.9
l0
t.2
11 ltls/cubic foot.
Insuhtion \\'ci,ahts inrluclc cllouanr:rs for \\'iro, ccmcnt. ernvlt'\, brnds llnd l)rint, but not
st'ccirlsrrrf,,rc ti n rs)'cs.
Tu lin,l tlLe \, iHl,t .f,1,v, ring
on flugcs, vrlvos or fittings,
rveight f.|rtor l)y thc
rvcight lrcr fooi of covcrir)g uscd
or) strLright pipe.
\'.rlvt} \ 0iJahts lrre appro\i-
multiplt thc
mcte. \\'hcn lrossiblc, obtrin
rveights f|om the munuf:rcturer.
(iust iron vrlvc \!eights:Lro for
lhnged cnrl vxlves: stecl $eighls
for \eldins end vrlves.
,\ll firLneed fittins,
flrnjaed
vrlvc ond 1|Lngc *cights includc
iho I)r'otxJrtional \!1'ighi, of bolts
or studs to make ur) !.lL joints.
ioints.
2O4
Mechanical Design of Process Systems
2" ptpn z',s,, o.D-
wErcHTS oF pIprNG MATERTALS
Schedule No.
A
40
80
Wall Designation
std.
XS
Thickness-In.
Pipc-Lbs/tr 1,
.154
.218
.343
.436
5.02
7.41
9.03
I4'ater-Lbs/Ft
1.46
L.R. 90" Elbow
q
t!-/
S.R. 90' Elborv
F
!w t/>
L.R. 45' Elbow
zf.
A^
'HJ
.5
.5
1
1.3
.2
Tee
.6
.6
Lateral
5
1.4
7.8
\i/
crp
Nom.
2.9
.5
.3
r.1
1.6
1.8
.6
.6
1.6
1.9
1.2
t,2
,+
.+
1.4
1.2
.3
.5
Temperaiure Range "F
z
I
1.5
.2
Reducer
xxs
1.2E
.E
!_l--__,
160
Thick.,In.
Megnesia
Calcium
Lbs/Ft
silicate
100-199 200-299 300-399 400-499 500-5s9 600-699 700-7c9 800-899 900-9s9
I
I
L%
1.01
1.01
t.7l
2.53
2.53
Nom, Thick., In.
* uomDlnx; tion
Lbs/Fb
z
Fiber-
Nom. Thick.,In.
Sodium
Silicate
Lbs/Fb
Pre-ssure
psl
sffi
O
Z
,h
d-ir
SIip-On
'|1'elding Neck
6N_l-M
Lap Joint
ryi:-s
Blirrd
,-{l
t?.4
E II' Y
ll_______.rl
ru
",1.{l
3m
+<f
rc
I
I
1%
1%
1.26
1.26
1.26
2.20
2.20
Cast Iron
or
trLrlS
2t4xJ
i rlt
E,N
e
/9S
z
Scre* ed
Rating
I
L.R. 90' Elbow
45"
lllbow
2%
3
3
3
3.48
3.48
4.42
4,42
4.42
2%
2%
3
3
3%
4.28
4-2E
5,93
5.93
7.80
2
2
4.57
3
3
5.99
5.99
150
300
400
600
900
1500
2500
9
6
9
ll
ll
32
32
4E
10
13
t3
3l
3l
{E
type is weieht in
weigii. is yreight factor for
Boldface
pounds. Ligh[flce type bineath
lnsul&llon.
1.5
9
12
4E
1.5
6
10
4-8
l0
3l
t2
3l
1.5
19
35
3.8
3.8
3.8
3.8
1E
27
22
4.r
3l
4.1
4.1
14
l6
3.4
3.4
23
37
83
4,2
Gat€
6.9
7.1
Flanged Bonnet
Globe or Angle
30
7
64
Flanged Bonnet
Check
26
7
5t
190
4
4.5
5
40
3.8
for
specific
combination coverins
arl
the
sums of the inner Iajer of diatomaceous eerth st 21 lbs/cubic
l1
los/cuorc loo!.
on
EO
45
4
recommendation
thicknesses of materials. I-nsulation weights are based on.85/,
magnes,a anct nydrous c&lctum
silicate st 11 lbs/cubic foot. The
listed thicknesses and weiqhts of
129
40
30
a
Insulation weishts include allowances for wird, cement, canvas, b&nds and paint, but not
3.9
41
3.8
49
fnsulotion thicknesses and
weights a,re based on average
COnOrtlons ancl do not constitute
foot and the outet layer at
73
6
I'langed Bonnei
235
4.5
60
300
4.2
5.8
Pressure SeaI
150
Pressure Seal
165
3
Bonnet-Clobe
4.57
3%
Steel
1'ee
Bonnet-Cste
214
250
16
S.R. 90' Elbow
1000-1099 1r00-1200
2%
special surface finishes.
To find the weisht of coverins
flanqes. valvds or fittincs]
weisht factor by tle
wergnt.per too! ol coverrng usecl
on srrargn! prpe.
V&lve weishts are aooroxi-dbtain
muhipltth!
mete. When possible,
weights from the rnanuf&cturer.
C&st ircn valve weiqhts are lor
flanged,end valves; sGel weights
IOr Welolng eno valves.
All
flanged fitting,
flanged
valve and flange weighls include
the proportional weight of bolts
or 6tuds too make up
uD all
s.ll joints.
ioints.
16
lt
cu.
ft.
density.
'
nr
Appendix C: Properties of
WEIGHTS OF PIPING MATERIALS
2.875'o.D.
Pipe
2/2"
2o5
Ywn
A
(.!-f
z
w
F
fl\
F-:l
z
F---i
-2t"
J
' /-\
!-L-t
(--r..}
\.u
Temperature Range
z
I
)
z
'F
Magnesb,
Calcium
Combina-
tion
FiberSodium
,ffi
9+
i ${lit$
N-ls$
N
()
z
I
/A)
,4"1
,N
z
g!4
l-{
.t
@
+€
flt' )
|<IJ
* 16 lb cu. ft. density.
type is seight in
\r'eight is weight factor for
Boldface
pounds. Lightfece type beneai,h
insulation.
Insulation thicknesses and
weights are besed on everage
conditions and do not constitute
a
recommendatioD for specific
thicknesses of materials- Insulation weights are based on 85/6
magnesia and hydrous cclcium
silicate at l1 lbs/cubic foot. The
listed thicknesses and rveights of
combination covering lrre the
sums of the inner laver of diatomaceous earth at 2i lbs,'cubic
foot and the outer l:r|cr at
lbs/cubic foot.
Insulation weights include allowances for wirc, cemcnt, canvrs, bends rnd print, but, not
special surftce linishes.
To find the rveight of covering
on flnnges, valves or fittings,
multipiy the \reight factor by the
weight per foot of covering used
on straiqht DiDe.
11
Valve *eiftrts are approximate- When possible, obtain
weights fronr the manufrcturer.
Oast iron valve weiehts ere for
flanged end valves; stiel weights
for *elding end valves.
AII flanged fitting, flenged
valve and Iiange \\eights include
the proportionel iveight of bolts
or studs to rnake up all joints.
206
3
Mechanical Design of Process Systems
tt
"tpr
B.boo" o.D.
WEIGIITS OF I'IPING NIATERIALS
rt?
8
z
F
F
z
B
uf
/\
{_0
{l}
L:-I
-{\
fl-\
ri\
{----fr
\iJ
l
z
cnrpentLurc Rcngc "F
Magnesia
Calcium
Nom. Thick., In.
F
z
(--oDlbi
tron
r-
FiberSodium
weight
${rn$
Insulation ihicknesses and
weights are based on average
Njs
a
/A
-11
z
is weight in
ffi
qN
z
Boldface type
,N
/9N
49!S
pounds. Lightface type beneath
is weight Jactot Jor
insuLation.
conditions and do not constitute
recommendation for specific
of materials. Insulation $eights are based on 85/p
magnesia and hydrous calcium
silicate at ll lbs/cubic foot. The
listed thicknesses and weights of
thicknesses
cornbinetion covering are the
sums of the inner layer of diaiomrceous eerth at 21 lbs/cubic
foot and the outer la] e. at
11 lbslcubic foot.
Insul{rtion Ncights include al-
for \\'irc, cenrent, canvas,.bands- and prlitrt, but not
lorvarrces
suf tace hnrshes,
speclsL
-
t<t
@
0
J{
a
Fs3
To iind the ueight of covering
on flanges, vs,lves or fittings,
multinl\' the weishtfactor bY Lhe
weighi irer foot 6f covering'used
on straight pipe.
Yalve weiehts are aDDroxi-dbtain
mete. Wben-
possible,
weights from the ma,nufacturer.
Cs.st iron valve weights are for
flanged end valves; steel weights
for rveldinq end valves.
All
flanged
fitting,
flanged
valve and llanee weiqhts include
the Drooortion;l weriht of bolts
or siudi to meke u[ all joints.
* 16 lb cu. ft. deDsity.
fl
Appendix C: Properties of
WEIGHTS OF PIPING MATERIALS
4.ooo"
o.D.
Pipe
3/2"
202
ewy
{f
(.-!-f
z
/'h
t4J
F
tij
z
&>",
f,l-\
ri\
Temperature Range'F
z
Celcium
F
Combina-
z
\om. Thick.,In.
tion
FiberSodium
Boldface
z
J
in
ffir$
4(|l_M
\Yeights are based on average
conditions and do not constitute
lr, rccommendxtion for specific
thicknesses of materitls. Insuletion \Yeights are b.r,sed on 85%
magnesir and h\'drous calcium
silic&te at 11]bs./cubic foot. The
listcd thicknesses and leights ol
combin.rtion covelir)g lLIe thc
sums of the inner hler of diltomrceous earth lt 2l Ibs,/cubic
Nls
TNN
/
z
F
,11
-4
N
/>
1
1-<J
'
type is \leight
poun,ls. Lightfece tl pe beneath
neiglt is Beight
insulation.
fscLor lor
Insulation thicknesses
and
foot end thc outer l:ryer at
ll
lbsrcubic foot.
Insulation weighis include allorv:rnces for \rire, cemcnt, .r,nvas, b0nds and l)l!inl, but not
spccitl surfrlce linishes.
To find the $eiglrt. of covering
on llrnges, volves or 6iiings,
multit)l]'the weieht frctor bv tho
@
ff1
weight per foot of covcring uscd
on straight pipe.
+<J
flangcd cnd valves: steel ueights
for *eltlirrg end valves.
rc
16
lt
cu. fr. density.
Vrlve weights irrc appro\i-
matc. \!'hen possiblc, obtrin
neights from the mxnufs(iturer.
Cut iron valve s'eights are lor
lll
flarrged 6tting, fir.ngerl
valve lnd flrnge seiglrts include
thc proportional rveight of bolts
of studs to make up all joints.
208
Mechanical Design of Process Sl stems
4" ptpn 4.boo' o.D.
WEIGHTS OF PIPING MATERIALS
\\'stcr-Lhs/l t
/a)
tu
z
k
o
&?
h
1: ,t
{l\
tr;:I
tr:JI
/\
\JJ
'li,mtx'nrluro
z
trlagnesia
Calcium
ComLirur-
I
rngo
"I
\om. 'l'hick., In.
Nom. T)rick.,In.
iioIl
IiberSodium
NrS
z {Nj+ln}
N_ts
rx:w
,.'Nl
7
/
F
,41
,l)
Boldface type is weight in
pounds. Lightface tvpe bene&th
rveight
is \reight fsctor Jor
insulation.
Insulation thicknesses lnd
weights are based on average
conditions and do not conslitutc
a recommendation for specific
thicknesses of mgterials. Insulation weights are based on 8596
magnesia and hydrous calcium
silicate &t 11 lbs/cubic foot. The
Iisted thicknesses and \reigllts of
combinstion covering are the
sums of the inner layer of diatomaceous earth at 21 lbs/cubic
foot and the outer ieter'at
N
z
/\
1
ll
Ibs/cubic fooi,
Insulation weights includc allowances fo wire, cement, canvas, bands and paint, but not
speciel
surlace 6nishes.
-
To find the weighl of cover;ng
F<3
3
@
fi\
+<l
F<U
on flanges, velves or fittings,
multiply the weight frcior by the
seight per foot of covcring uscLl
on str{righi pipe.
Vrlve weights are approrimate. When possible, obtoin
$eights from thc mxnufacturer.
Cast iron valve Ncights are for
flanged end valves i steel $eights
for rveldinq end valves.
All
flanged
fitting,
flrnged
valve and flangc wcights includc
the proporbionxl \\eiglrt of bolts
or studs to mrke up all joinbs.
I
16
li
cu.
ft.
density.
Appendix C: Properties of
WEIGIITS OF PIPING MATERIALS
Schedule No.
ul
,a g.I/
zf\
F ! li
E4\
o
f'+
3 4/4-
40
80
Wall Designation
std.
XS
Thickness-In.
Pipe- Lbs/ Ft,
.258
t4.52
Water-Lbs/Ft
8.66
14.7
1.3
21
L.R.,90" Elbow
9.8
13.7
.8
S.R. C0" Elbow
L.R. 45' Elborv
.8
7.3
.5
20.78
7
120
160
.500
.62'r
27.M
32.96
38.55
7.09
6. J3
5.62
.89
r
0.2
15.6
.5
.5
t7 .7
.5
43
26
39
1.2
1.2
1.2
Laterel
3l
50
2.5
LJ---.D
Reducer
6
.4
E.3
.1
\tJ
cop
.7
.7
t4.2
.4
{---J--r
Nom. Thick.,In.
Z Sodium
Silicate
9
F-
Lbs/Ft
B tion
Lbs/Ft
Nom. Thick.,
85%
!Iagnesia
Calcium
Lbs/Ft
,ffi
O -'r-
Screu ed
or
'|r,\'elLling
2.92
2.92
I
I
2.34
2.34
i50
20
32
l8
1.5
1.5
+<i
ft.
3
3tl
3ti
4
4
7.01
9.30
I1.8
I1.8
14.9
14.9
2%
2%
3
3
4
4
9.31
9.31
14.31
14.37
t.5
l
58
94
80
5
73
1.5
100
1.5
162
1.5
259
1.5
rvcight
713
103
162
293
\reights.rre brsed on rverage
49
1.5
7l
32
1.5
98
168
1.5
50
39
1.5
1.5
l3
t23
t
78
205
4.3
1.lr
172
1.5
268
435
4.8
5.2
104
1.5
pounds. Lightf.rce type benerth
is
rveight factor ior
insulrtion.
Insuiation thicknesses
and
condirions and do not constitute
rocommendrtion for specihc
of materials. lnsuhtion wcights rre brsed on t5%
mrgnc-.ia antl hydrous crlcium
rot. The
silicatc at 11lbs,/cubic foot.
righrs oi
listed thickncsses 3nd rreighls
3
thicknesses
combination covering lrre lhe
dieof the inner later of dirtomrceous errih rt 2I lbs cubic
-cums
3.3
3.8
3.8
90
t45
ll9
t72
179
304
6.5
0.4
6.4
6.8
7
138
264
150
3r0
7.9
4.3
4.9
455
5.5
Flanged Bonnet
Globe or Angle
138
)47
ls5
2t5
515
Flanged Bonnet
Check
llE
210
110
7.6
E
4.3
8
is $eight in
1.5
5
1.5
I.5
Boldf&ce type
l
98
density.
2ra
2|rc/..)
66
{ilobc
10.4
1500
E3
Bonnet
10.4
s00
51
Pressure Seal
E.41
600
t2a
Pressure Scal
8.41
400
9l
Bonnet-Cate
6.90
300
1.5
Cet,e
- FdJ
JiLII
;hJ
4
Stecl
250
105
Flanged Bonnct
4
3.76
2.34
1.5
Tee
1-{
11,.i
68
45" Elbow
Y
1,t;
Casi,
L.R. 90' Elbow
Et\
3rl
4.08
|
1100,1200
3r/t,
2%
2ra
2
S.R. 90" Elbo*
,an
16 lb cu.
1.86
37
/,$
.7
22
Blind
rc
1%
Ncck
El:::lr$F
E II'
1
125
Lap Joini
/a
1l
.7
00-199 200-20s 300-399 400+s9 500-599 000-699 700,;9c 800-Ec3 900-999 1000-1009
18
3,\
'
Rctiltg
N-l,Ns
0
F
|
z
Pressure
psr
Slip-On
i sli19
ll
In.
Nom. Thick.,In.
5" pge
1.3
t9.E
Fiber-
O.D.
209
xxs
Tee
Tcmpereture ll.enge "F
5.56:J"
Pipe
rl er
foot end the outer irl
t23
5.2
165
5
1E5
665
615
6
1340
7
on llenges, !lll\'fs or littings,
rnc
)r DJ
bl th.
muitiplt thc \reight fsctor
350
350
3.1
soecial surfxco linishes.
co\,enng
1o hnd tlrc $Lrglrt ol coverlne
950
6
5
Di
Dt
415
4
5
ll
lbs/cubic foot.
.lurie rlInsulation \\0ighis inclurie
lorvances for \\'ire, cement, crnnoi
vns, bends xnd p.rint, hut not
350
130
560
6
1150
7
520
3.8
865
4.5
280
4
450
4.5
lng used
rveight per foot o[ covering
on,str.riqht t,ifo.
x||ro\l\'!ive \\'.rqh is rrc approximrtc. \\-hen possiblc, oblarn
weiglrts fronr the mllnufrcLurerC.rst iron vrlve rvcishis l|re fol
\reights
fluged end vrlves;steel \reightl
for $cLdirrq end vlrlvcs.
flanged
,\ ll fianee(l fittiDs, flanged
include
vol\c .rn.l ILrngc wprgl,tsr includ€
bolts
tl,c t,rol,ortionxl \eight of bolt!
ll joints
up all
ioints.
or siuds to make up
2'10
Mechanical Design of Process Systems
6" pr""
6.625, o.D.
WEIGHTS OF PIPING X{TTERIALS
\\'eter-Ils/Irt
z
'.
z
F
u/
AX
w
{T\
LilI
t---1
\JJ
Tempcraturc Ilange "F
z
Magnesia
Calcium
t
z
Combinst)on
Fiber*
Sodium
Boldface
sq-,$
z
#r|&
N-S
dISrsS
z
-Xl
t#
rA
kL
,N
z
/>
lt' '{
l-dl
.|
@
ru
1-<i
rc
type is weight in
tleight iactor for
trpe
benea,th
oounds. Liehtiace
'
iveight.
is
Insulation thichnesses and
weights are based on average
conditions and do not constitute
a
recommendation
for
specific
thicknesses of materials. Insulation weights are based on 85%
masnesia and hvd.ous calcium
siliate at 11 lbs/cubic foot. The
listed thicknesses and weights of
combinstion covering &re the
sums of the inner layer of diatomaceous es,rth at 21 lbs/cubic
foot and the outer layer at
l1 lbs/cubic foot.
Insulation $eights include aIIowrnces for \aire, cement, can-
vas, bands and paint, but not
special surface finishes.
To find the weight of covering
flanges, valves or fiLtings,
multiplt; the weight fxctor bl the
rveight per foot of covering used
on straight pipe.
on
Valve ueights xre sppro\imete. When possible, obtrin
weights from ihe mrnuf&cturerClst iron valve ueights are for
flenged end valvcs; steel weights
for rveidinq end valves.
All
flanged
litting,
flanged
valvc 3nd nlnge Ncrgnts Incluoe
tLe DrotJortional $cieht of bolts
ot stud" to mrke up all joints.
* 16 lb cu. ft. density.
,qR
Appendix C: Properties of
WEIGHTS oF PIPING
MATERIALS
8.625.
Pipe
o.D. 8''
211
"T"e
t'-
2
i.
z
B
r_!j
w
{t}
E:I
,4\"
A
F--l-r
\tJ
Temperature Range
'F
Magnesia
2 Calcium
F
-
z
Combina,-
tron
Nom. Thick.,In.
FiberSodium
ffi$
2
F
a
7
Neight.
is veight
Jactor lor
Insulation thicknesscs cnd
\reights are based on average
$\
a
is
conditions and do not constitute
A
recommendation for specific
of materiols. Insulation rveights are based on 85%
magnesio and hJ'drous calcium
silicate at 11lbs/cubic foot. The
Iisted thicknesses aod $'eights of
combinetion covering are the
/A
foot and the outer la]'er at
A
egilq
thicknesses
sums of the inner layer of diatomaceous earth at 21 lbs/cubic
11 lbs/cubic foot.
Insulation rveights include al,lowances
lor wDe, cemenl, c&nvas, bands and paint, but noi
soecial surface finishes. '
d
-
j.43
t4r\
+<i
FsO
|
tlpe js Neiaht in
ffi
d <,fs$
z
Boldfnce
pounds. Lighilirce tvpe bineeth
16 lb cu.
ft. density.
To find the weight of covering
on flanges, valves or frttings,
multiply the weight f&ctor by the
Neight.per folt of covering used
on slrarghl prpe.
Yalve rveights are approximcte. lYhen possible, obtcin
lleights from thc manufrcturer.
Cast ilon valve weiehts are for
flanged end valves; sGel \\'eights
Ior seldinq end valvcs.
AII
flcneed fitting, flanged
valvc and llangc rveights include
tlrc nroDortioDrl \eiqht of bolts
or stu,li to make ut all joints.
212
Mechanical Design of Process Systems
10"
z
(,
z
prpn
lo.zbo, o.D.
IVDIGIITS OF PIPING tr{ATDRIALS
Ih
fl\
L:J
.4'4^
L:!-l_,
\]J
lrmpcr:rturc lirnge'F
z
Magnesia
Calaium
F
P
z
Combina-
\om. Thick., ln.
iion
FiberSodium
(,
ffi$
qFl
rr$
N-|s
ryrTqJr
Ai
z
Boldfece
/AJ
!.
,-11
z
,N
/>
tHt'{
lN'
@
ff1
+<i
f<o
t{pe is l\'eight in
pounds. Lightface t1'pe benerth
*eight is rveight foctor ior
insulation.
Insulation thicknesscs
\Yelding Neck
and
rveights are based on average
conditions and do not constit,ute
a recommcndetion for specific
thicknesscs of materials. Insulation weights are based on 85/o
magnesie and hl drous crlcium
silicate at 1l lbs/cubic foot. The
listed thicknesses and weights of
combination covering are the
sums of the inner layer of diatomaceous earth at 2I lbs/cubic
foot and ihe outer lsyer at
11
ibs/cubic foot.
Insr-rlation Neights include allowances for vire, cemeni, can-
vas, bands and !B.int, but not
spacirl surfrce 6nishes.
To find the weight of covering
on ffanges, valves or fittings,
multiplt' the $eight frctor b! tLe
lieight t'er foot of covering used
on streight pipe.
\'rlve \rcights ere approri-
matc. \Yhen possiblc, ol)irirr
ciglrts from thc nrnnufrcturcr.
(lxst iron vrlYc \\'ciglrts arc for
lllngcrl cnd vrlrcs: stcoi teights
fol lcldilg cnd vrlves.
rr
-\)l
fl.rngcd fitting,
flnngcd
!'rlvc :!nd l]3nge \\'eights include
tlru prolroriioDxl scislrt of l)olts
or studs to mrkc up:rlL joints.
*
16 lb cu.
ft. derxity.
Appendix C: Propenies oi
rz.lso'o.D.
WEIGHTS OF PIPING MATERIAI,S
Schedulc
)io.
|
20
{,)
IJJ
f4
(_!-f
.
2n^
F flIT
Eji1
o -: -t
i3tr-/>"
t-
d_l\
.330
43.8
49.7
L.R. 90' Elbow
S.R. 90" Elbow
L.R.
.406
.500
49.6
53.5
65.4
49.0
48.5
47 .O
.375
100
120
12"
.687
.843
1.000
EE.5
t07 .2
r25.5
44.0
4
r.6
39.3
.562
46.0
l-J!
139.7
t58
t51
3
3
80
2
104
2
60
7E
181
167
360
3
1.o
Calcium
silicate
,s| Combina;z iron
FiberSodium
,ffi
;+
z
5.4
33
44
30
3E
,|
Reducer
9,1
'|
E9
1.5
900-999 1000-1099 1100-1:to
100-199 200-299 300-399 400-49S 500-5s9 600-699 700-799 800-E99
Nom. Thick., In.
1)4
114
2
2t/4
3
3
3rlt
4
4
4%
Lbs/Ft
6.04
6.04
8.13
10.5
t2.7
12,1
15.r
17.9
17.9
20.4
20.4
3
3%
4
4
414
1)i
17.7
21.9
26.7
26.7
31.1
3l, r
2\/r,
216
4
4
5
c
14.20
14.20
24.&
4.64
32.&
32.40
Nom. Thick.,In.
Lbs/Ft
Nom. Thick.,In.
Pressure Rating
psr
Screwed or
Slip-On
Cast
250
71
r37
1.5
1.5
a4
a lAl
S.R. 90' Elbow
/..4
L.R. 90' Elbow
A,N
I
/}!
45' Elbow
z@
600
900
1500
| 72 |
| 1.5 |
88 I
1.5 I
164
1.5
261
3EE
820
1611
434
1.5
843
1.5
1919
1.5
433
902
1573
1.5
163
1.5
212
164
ta7
286
1.5
1.5
1.5
475
t474
261
1.5
453
345
509
669
El5
5.2
5
5.2
485
624
6.2
6.2
6.2
6.2
235
383
2E2
6E4
6.2
4.7
1124
4.8
5r3
754
7.4
943
1361
r92E
8.3
a.7
s.3
1420
5.5
215s
7
2770
7.2
4650
8
1410
7.2
2600
8
3370
8
1975
2560
45r5
6
7
7.8
1015
5
Fhnqed Bonnet
Globi or Angle
808
1200
7t0
1410
9.4
9.5
5
Flanged Bounet
674
ll60
560
Checlc
9..1
9.5
densrty.
6.2
4.5
635
4
Bonnet-Globe
I.D
469
8.5
Pressure SeaI
t.5
1775
159E
720
705
l.c
92E
414
1298
Bonnet-Gate
5.8
2500
1.5
4.3
4.3
6E7
Pressure SeeI
1.5
209
7.8
Flanged Bonnet
Gate
r.o
lllE
r.5 | 1.5
265
5
Tee
fi.
400
r44
341
177
403
IP '{
300
72 |
96
|
150
1.5 |
Lap Joint
Blind
l1/r,
1r/1,
ffi
125
Welding Neck
{N
* 16 lb cu,
1rt
t%
Lbs/Ft
'$$js
E
l
273
1E0
Lateral
#rils
,
;
2.5
2.5
cap
z
9
3
119
r32
Temperature Range "F
Pwr:
1{0
45" Elbow
Tee
213
XS
sid.
Wall Designation
Thickness-In. | .250
33.3E
Pipe-Lbs/Ft
5l .10
Wsier-Lbs/Ft
80
60
40
30
PiPe
214
Mechanical Design of Process System:
14" ,trr.
14'o.D.
WEIGHTS OF PIPING ]IATERIALS
{.f
z
|.
z
t
/)
fl\
fJJ
t
-t
c---r---l
\L"J
Tcmpcrature Range
z
Alagnesia
Calcium
'F
Nom.
Thick.,In.
Nom.
Thick.,In.
F
t Conlbination
z
1
l\'pc is Ncight in
*eight is lYcight lactor for
Boldlace
ffi
pounds. Lightface tl pc l)eneath
S{r-rM
$eights are based on lverage
insulation.
N]s
{N
z
/.4
--ll
/,4
z
,N
i>
Insulation thicknesses
and
conditions and do not constitutc
a recommendation for spccific
thicknesses of rnaterials. Insulation $eights are ba-sed on E5%
magnesia and hvdrous cak.ium
silicate at 11lbs/cubic fool. The
listed thicknesses and lreights of
combination covering Lire the
sums of the inner l&\'er of diatomaceous
e:irlh at 21 lbs/'cubic
la] er at
foot and the outer
11 lbs/cubic foot.
.{l
Insulation \reights include alfor lvire, cement, canvas, bands and ptint, but not
ru
To find the leight of covering
on flanges, valves or fittings,
multiplt the weight fcclor b]'the
MeiAht pcr foot of covering used
on strnight pipe.
0,
@
0
+<i
FSO
lorvances
special
su
ace finishes.
Valve s eights are spnro\imate. When possible, obtain
weights from the mrnufscturer.
Csst ilon velve Neights are for
flanged end valves: steel weights
for rveldine end valves.
All
flaneed fitting,
flanged
valve cnd flonge $eights include
the nroDortiorrrl \\'cigl,t of holts
or sludi to mrkc up all joints,
* 16 lb cu. ft. density
il
-
Appendix C: Prop€rties of
WEIGHTS OF PIPING MATERIALS
re"
o.o.
Pipe
16t'
215
plpu
tl
A.
vz
z
;
lJj
i\
w
{T\
1-5:I
J,1
E=_:ir
t
fl\
\iJ
.+r
Temperature Ra.nge
z
'F
l 100-1200
I\Iagnesia
Calcium
F
Combina-
z
tion
!'ih.rSodium
z
Boldfxce tvDe
stjjs
Insulrtiod thicknesses and
weiqhts are bascd on averase
conditions and do not constituie
& recommend&tiol for spccific
thicknesses of materials- Irrsuhtion weights ere bosed on 85%
magnesir and hydaous cnlcium
silicate &t ll lbs/cubic foot. The
listed thicknesses &nd \yeights oi
A
combiortion covering are the
sums oI the inner layer oI diatomaceous earth at 2l lbs/cubic
.A
1
Lighifirc tt pe benesth
is rveight factor for
insulation.
$$l.M
z
rveielrt in
teight
qr\ssF
z
is
S$
pounds.
foot and the outer layer at
rr rDs/cuDLc ioot.
A
Instrlati<.rn weights irclude al,low&nces
Io! $alrc, cement, ca!!
4!B
vas, bands and pcint, but
Dot,
specilll surlace fi nishes.
To find the weight of coverbg
on flanges, v&Ives or fittings,
@
t
i[I
multiply the weight frctor by the
r eight per foot of covering used
on str&ight pipe.
Flenged Bonnet
@
t4
* 16 lb cu. ft. density.
Valve Neights are approximatc. When possible, obtrin
weights from the m.nuf&ciurer.
Cllst iron v.rlvc \reights:rre for
flanged end valves: steel $eigh6
Ior rvelding end valves.
All
flcnged fitting,
flanged
vclve and flangc wcights include
the prot)ortionul Neighi of lrclr,s
or studs to make up 3ll ioinis.
216
Mechanical Design of Process Sy:,rems
18" plpr 18" o.D.
WEIGI{TS OF PIPING MATERIALS
LLl
z
F
z
E
f^
('4r
fl\
H'
UL,
c.=-=I
IA
\JJ
'fcnpcnturc ll
z
Magnesia
Calcium
tCombin.r.-
Dgc
'I,'
Il,s / Iit
\om. Thir,k., In.
tion
Fiber-
\om. Thitk., In.
Sodium
ffi
z
ffi
Nl$
si)\r'|\s
Z
F
/'a
IA
rA
,N
z
/$
4444
is lcicht in
t5 pe b-enerth
reiglrt. is \cjght fschor for
Boltlface tvne
pounds. Lig)rifrce
Instrlation thicknesses
aod
rvciglrts flrc l,rsr:d on r,vcrrge
conditions ltnrl do not (oustituta
a r-ccommcndrtion for specific
thicknesscs of matcricls. Insulation \reights ore bascd on 85/o
magncsia and h-Ydrous calcium
silicrte at 11 lbs/cubic foot. The
listcd thickncsses and rveights of
combination coveljng are the
sums oI the inncl hver of diatomaceous eorth at 21 lbs/cubic
foot and the outet laver at
11 lbs/cubic foot.
Insulation s'cights include alIolanr:cs for \rirc, cemcnt, conves, b:rnds and print, but not
spccial sur'Iace finishcs.
To find ihc \lcight of covering
on flanges, valvcs oa fittings,
multit)l]'the xe;ght factor by the
a
@
iln
+<t
rc
\eight pcr foot of covering
used
on stroight pipe,
Vrlvc \rriqhts rre aptrroxi-dt,tain
mate. \l'hen possil,le,
lscights from the m$nufacturer.
Cast iron valve \yciqhts are for
flanged end velves; st-eel \\eights
Ior welding end valves.
All
flanged
fitting,
flanged
valve and flange scights include
thc proDortionrl \\ci(lrt of bolts
or si,udi to meke up all joints.
* 16 lb cu. ft. deDsity.
::
Appendix C: Propen:*
1VEIGIITS OF ]'IPING }I.\TDRI,\LS
20,,o.D
l-
21
20"
e-,rz
l{t)
Pip€'-Lbs./I,t
\\'at.r
3;9
Lbs/ I,t
Ll
9
'17
&Jj
z
F
i:
z
Ih
\-.1-_t
{l\ -'t
r'-:
F4
,!^
!*J----!
'Icmpcraturc Renge "F
z
300-3c3 100+cc i00-;9u 1000-6e0
I{agnesia
o Calcium
2a.l
F
Combina-
z
4l.:
tion
43.r
Fiber-
{-1-
1
\om. Thick.,In.
Sodium
1-1.03
Pressure
ffi
z
psr
Rnting
sm$
N+s
gr(\i.x$
z
F
(,
z
g
J
/A
/41
/,+
A\
/>
€4!4
@
fln
l'langed tsonnet
Globe or Anglc
J-<f
rc
* 16 lb cu. ft. deDsity,
(last.Ir('n
|
ll25 l2s
is r..r: : .:
rir)f I :..,:
\l{ttglrL. ls \\etglll Iri-: : :::
Illsulrtion thi|krrts... ::
vc;ghts uc brsc(l 0r ,,. :. ::corrditiols urrtl iIr rror ,,.:.-:.:::r! rccommrr{lxti(,n a,)r .-- l
tlti< kncsscs of mritli,.l: I: --.-tiorr rveiehts rLn' 1,,,.t i :. :i I
nNgncsil rLnd lrr,ir ru.
-:-sili(rtc lri 11 lLs r ui,:. :
- .
listc(l tLi( knciscs ,t:. i , :: , ::conrl)in$tion co\'!f:r:: .. ::
sums of t))r inncr -.:.,: : ,tolnxceous rtLrtlr :,i l: .: i - :
fooL oniL tl)c a';:.: - . : -:
ll Ibs r:ulric fooi
IusulLtion r, r::.:. ::
-loNrurccs ior r|ir,.
vrLs, blnrls:i'l:,1 :.:.:
- : :
sp( ( lrLL :Llr 1t1.. :.: :, . .
Roldfrrce tYpe
poun(ls. Lighthcc
\lrgllt l)ff iL_'r: .: ' I : _. onstfrLigi,:r: f.
\_rtlvc Li,:::.:. .:. ..
nlrtr'. \\ '.1:
\fi{)its ir,r:r :].- r..
, (,Lst ir,:r'. ....
: -- .- :.fl:LrLgcrl i r:
i
iot $r:Lli:-ir::- .. : ..
.\ll :l:,r..r. : : :: : _'
:
vrh-c rrri i ::.,::r': r. ::r -.
tlrc prorl:l:,:.1- .:: : ::
or studi i1r ::r:i:
.:
; ,.- .:
218
Mechanical Design of Process Systems
24"
prpr.
24" o.D.
\T UIGI I1'S OF
I'IPI\G
}IATEITIALS
\Y.ltcr-Lbs/It
ui
Z
F
z
e
f><
w
{T\
trJ-t
-/A
J]\
t___-l____-!
Icnrpcrlturc llongc 'F
Magnesia
z Calciun
F
p Combinction
z
FiberSodium
ffi
z qN
trs
Njs
EN,fr\l
z
::
d
,N
z
/D
Boldfsce troe is weicht in
pounds. Liehifl.ce tvDe b;neath
-
rreight'iactor for
Insulation thicknesses and
$'eights are based on averaqe
ireight.
is
conditions and do not, constitule
a
recommendation lor specific
of materials. lnsuhtion ucights are bused on.85/e
m3gnesla ano nyorous cstclum
silicate at ll lbs/cubic foot. The
listed thicknesses and lr'eiqhts of
combinotion covering arl the
sums of the inner layer of diatomaceous earth at 2l lbs/cubic
thicknesses
foot and the outer lsyer at
ll
lbs,/cubic foot.
tt, .rl
IH
l=<[J
@
e
++J
rc
* 16 lb cu. ft. density.
{:
I}zAppendix C: Properties of
WEI(IHTS OF PIPING MATERIALS
z
F
F
a
za"
o.o
Pipe
26t'
219
prps
Llj
/\
Iit
{1\
E--I
t J'\
z
-:I
!-I_'
\"J
Temperature Range
'F
Ilagnesia
z Calcium
brUcate
o
F
3 combina3 tion
3;m::;FiberSodium
Boldface type is weight in
pounds. LiEhtface type beneath weight is weight factor
ffi
z
for insulation.
Insulation thicknesses and
weights are based on average
conditions and do not constitute a recommendation for
specifrc thicknesses of mat€rials. Iosulation weishts ate
based on 85% magndsia and
hvdrous calcium silicate at 11
l6s/cubic foot.The listed thicknesses and weights of combination covering are the sums
of the inner layer of diatomaceous earth at 21 lbs/cubic
s.{-n$
N-is
fFq.s
|
z
F
,41
AI
foot and the outer layer at
/r+
11 lbs/cubic foot.
Insulation weights include
,N
allowances
&"f
n'
!l
u:-Ji
ing on flanges,
t<t
rc
ft.
v-alves
or fit-
covetlngused on siralghl plpe.
Valve weights are approxi-
mate. When possible, obtain
weights from manufacturer,
Cast ilon valYe weights are
for flansed end valve€i steel
weishts Ior weldineend valves.
A'il flane€d fitting, flanged
+<i
16 Ib cu.
cement,
tings, multiply ihe weight factor by the weight per.foot of
@
fi)
*
fo! wire.
canvas, bands and iaint, but
not special surface ffnishes.
To-find the weiqht of cover-
valve and flange weiRhts in-
clude the propo-rtionaf weight
of bolts or studs to make up
deDsitt'.
all joints.
220
Mechanical Design of Process Syslems
28"
prpn
28- o.D.
WEIGHTS OF PIPING MATERIALS
W
/4
{.J-f
F
Ih
t-+J
{1}
trJ:I
B
\IJ
Tempelature Range "F
nlagnesia
Calcium
Combina-
tion
FiberSodium
ffi$
ffi
ds]-s
iN
z
F
F
z
,-a
A
tr' .{
B---Jl
t=<3
@
0
+<i
rc
* 16 lb cu. ft. derBity.
Boldface type is weight in
pounds. Lightface type beneath weight is weight factor
for insulation.
Insulation thicknesses and
weights are based on average
conditions and do not co[stitute a recommendation for
sDecific thicknesses
of
mate-
rials. Insulation weights are
based on 857, magnesia and
lrydrous cjrlciuJn silicat€.at 11
lDs/cuorc root. I ne lrsteo [nlcknesses and weights of combination covering are the sums
of the inner laver of diatomaceous earth ai 21 lbs/cubic
foot and the outer layer at
11 lbs/cubic foot,
Insulation weights in€lude
for wire, cement,
allowances
canvas, bands and paint, but
not special surface finishes,
To find the weight of cover-
ing on flanges, valves or ffttings, multiply the weight factor by the weight per foot of
covering usedon straight pipe.
Valve weights are approxi-
mat€. When possible, obtain
\reights from manufacturer.
Cast iron valve weights are
steel
weishts forweldinsend valves.
A-ll flanged fftting, flanged
for flanged end vslves;
valve and flahge weights in-
clude the proportional weight
of bolts or studs to make up
all joints.
Appendix C: Properties of
WEIGHTS
0I' PIPIN(} MATERIALS
Bo"
o.D.
Pipe
30"
221
prpe
u-f
Ih
fl\
E-I
F
z
4',q
E::l
'
L--r-----U
\L/
Temperature Range
'F
Ilagnesia
Oalcium
t
tlon
Fiber
SodiLtm
ffi
z
E
lr-'$
Nls
CI-]-\}
Boldface type is weight in
pounds. Lightface type beneath weight is weight factor
for insulation.
Insulation thicknesses and
weights ale based on average
conditions and do not constitute a recommendation for
specilic thicknesses of mate-
rials. Insulation weights
are
based on 859t magnesia and
hydrous caicium silicate at 1l
lbs/cubic foot. The listed thicknesses and weights
of
combi_
nation covering are the sums
of the inner layer of diatomaceous earth at 21 lbs/cubic
foot and the outer layer at
11 lbs/cubic foot.
Insulation rveights include
allorvances for wire, cement,
canvas, banCs and paint, but
not sDecial surface finishes.
To_lind the u'eight of covering on flanges, valves or fit-
z
tinss. multiDl\.the weieht factoibl the rieight per-foot of
covering used on straight piPe.
Valve weights are approxF
G
@
CD+
* 16 lb cu. ft. density.
rrt
mate. When possible, obtxin
weiqhts from manufacturer.
Cist iron valve weights are
for ffanged end valves; steei
weights lor weldingend valves.
All flanged fitting, flanged
valve and flange weights include the proportional weight
of bolts or studs to make up
all joints.
222
Mechanical Design of Process Systems
32"
prcn sz, o.D.
WEIGHTS OF PIPING MATERIALS
tu?
tg
z
f\
l_p
{T\
7
!
LJJ-
4',4
{-r-,
lr-f-r
\L/
Temperature Range .F
Magnesia
Calcium
z Silicate
{ uomDlna5 llon
FiberSodium
Boldface type is weight in
pounds. Lightface type beneath weight is weight factor
,@$
3*
for insulation,
Insulation thicknesses and
3
tute a
euls
weights are based on average
conditions and do not consti-
fsls
speciflc thicknesses
!J:!i.\\!
,-11
z
F
tr
z
/A
.A
A
of materials. Insulation weights are
based on 857. magnesia and
hydrous calcium silicat€ at 11
lbs/cubic foot.The listed thicknesses and weights of eombination covering are the sums
of the inner laye! of diatomaceous earth at 21 lbs/cubic
foot and the outer layer at
11 lbs/cubic foot.
Insulation weiEhts include
t"{3
allowances for w-ire. cement.
eanvas, bands and paint, but
not special surface finishes.
To find the weieht of covering on flanges, valves or fittings, multiply the weight factot by the weight per foot of
m
weights from- manufacturer.
Cast iron valve weiehts are
for flanged end vatves; steel
t€
valve and flange weights include the orooortional weieht
4!4
@
lt
lecommendation for
+<i
* 16 lb cu. ft. density.
covering used,on straight pipe.
v alve wergn!s are approxlmate. When Dossible. obtain
\
eights f or .!rrelding end valves.
All flanged fitting, flanged
of bolts oi
all joints.
stluds to make-up
\
Appendix C: Properties of
WEIGHTS OF PIPING MATERIALS
s4"
o.D.
Pipe
223
34" *trc
G
/.^
u-/
b
/-i\
z
F
I
z
rT
F
2,1
c_=_=r
-r
"t\
{---t-r
\IJ
Temperature Range "F
2
Magnesia
Calcium
{ tion
z
FiberSodium
ffi
z
{
ffi
Njis
N
z
3
a"
z
-l)
/A
AI
//
N
/>
@
m
+<i
rc
* 16 lb cu. ft. density.
r-
for insulation.
Insulation thicknesses and
weishts are based on average
conditions and do not constitute a recommendation for
sDecific thicknesses of mate_
rials. Insulation weights arq
based on 857, magnesis altd
hvdrous calcium silicat€ at
11
l5s/cubic f oot. The listed thicknesses and weights of combi-
+.{
3
Boldface type is weight in
pounds. Lightface tYPe beireath weight is weight factor
nation covering ale the sums
of the inner layer of diatoma-
at 21 lbs/cubic
foot and the outer layel at
ceous earth
11 lbs/cubic foot.
Insulation weights include
for v/ire, cetnent,
allowances
canvas, bands and paint, but
not special surface frnishes'
To find the weisht of coverine on ffanees, v-aives or fittinles. multi6lv the weiqht fac-
tor"bi the iveight per-foot of
coverrng usecl on slralghl plpe.
Valve weights are approxi-
mat€. When possible, obtain
weights from manufacturer.
Cast ilon valve weights are
for flanged end valves; steel
weiehts forweldinsendvalves.
A'il flanged fitting, flanged
valve and flange weights include the proportional weight
of bolts or studs to make up
all joints.
224
Mechanical Design of Process Systems
36" "t"u s6" o.D.
z
F
EI
3
WEIGHTS OF PIPING MATERIALS
W
uj
f\
w
{T\
t=l
_/A
F--i
A
\iJ
Temperature Range'F
I\{agnesia
Ctllcitm,
Nom. Thick., In.
Fiber-
Nom. Thick,, In.
Sodirm
ffi
z
6{fliN$
N-S
{raT,s
,tA
z
F
4t
/A
z
/t\
l|' tl
p6l
.lk{
l-<J
lli'l
+q]
@
* 16 ]b cu. ft. derNity.
Boldface type is weight in
pounds. Lightface type beneath weight is weight faetor
for insulation.
Insuiation thicknesses
and
['eights are based on averag:e
conditiods and do not consti-
recommendation lor
specific thicknesses of mate-
tute a
rials. Insulation weights
aae
based on 85% magnesia and
hydrous calcium silicate at
11
lbs/cubic foot. The listed thicknesses and weights of combi-
nation covering are the sums
of the inner layer of diatoma-
at 21 lbs/cubic
foot and the outer layer at
ceous earth
11 lbs/cubic foot.
Insulation weights include
allowances
for urife,
cement,
canvas, bands and paint, but
not sDecial surface finishes.
To-find the weight of cover-
ins on flanees. valves or fittirigs, multiply the weig-ht factor by the welgrr! per lool or
covering used on straight pipe.
Valve weights are approxi-
mate. When possible, obtain
weiahts from manufacturet.
Cast iron valve weights are
for flanqed end valves; steel
weichts iorweldineend valves,
A-ll flanged fitting, flanged
valve and flange weights include the proportional weight
of bolts or studs to make up
all joints.
D
Appendix D
Conversion Factors
225
226
Mechanical Design of Process Systems
Alphabetical Conversion Factors
TO CONVERT
INTO
MULTIPLY BY
A
Abcoulomb
Statcoulombs
Sq. chain (Gunters)
sq feet
acres
acres
actes
acres
acre-feet
acre-feet
cm
cm
in.
In.
meler
meter
ampere-hours
arnpere-hours
ampere-turns
ampere-turns/cm
ampere-turn5/cm
ampere-tutns/cm
ampere-turn5/in.
ampere-turns/in.
ampere-turns/ In.
ampere-turns/meter
ampere-turns/meter
ampere-turns/meter
Angstrom
An8stron
un
un
it
it
Angstrom unit
amps/sq
amps/sq
amps/sq
amps/sq
amps/sq
amps/sq
Btu/min
Btu/sq ftlmin
.4047
10-:
3.259 x
cm
meter
cm
In.
coulombs
faradays
gilberts
1Cl'
6.452
10.
0.1550
6.452 x 10-.
3,600.0
0.03731
2.540
r00.0
amp-turns/cm
amp-turns/meter
grlberts/cm
39.37
0.4950
amp-turns/ in.
0.0254
3937 x 10-'
Acre (US)
.0247
ft of water (at 4'C)
1x 10-ro
1x 10-.
|
I19.60
o.o247 |
100.0
1.495 x 101
.007348
76.0
33.90
29.92
1.0333
In. of mercury (at 0"C)
kgs/sq cn
kgs/sq meter
l0,332.
pounds/sq jn.
t4.70
tons/sq ft
1.058
B
Barrels (U.S., dry)
Barrels (U.S., dry)
Barrels (U.S., liquid)
barrels (oil)
oars
bars
cu. tnches
quarts (dry)
8al tons
gallons (oil)
bars
arrnospnetes
dynes/sq cm
kgs/sq meter
bars
bals
Baryl
Eolt (US Cloth)
pounoS/sq In.
Dyne/sq. cm.
Meters
BTU
Liter-Atmosphere
8tu
ergs
Btu
Btu
Bttr
Btu
t'(U
Btu
graln-caloneS
horsepoweahrs
ioules
kjlogram,calories
8tu
Btu/hr
foot-lbs
krlografi-meters
kilowatt-hrs
foot,pounds/sec
horsepower
kilowatts
waIls
watts/sq in.
Cubic Cm,
cu
ft
0.0700
3.929 x
0.2931
12.96
0.02356
0.01757
l0 '
t7.57
o.r22r
1.818 x 10'
1.2445
cu In.
2,150.4
cu meters
o.03524
laters
pecks
pints (dry)
quarts (dry)
4.0
64.0
32.0
105.0
31.5
42.0
0.9869
105
!..020 x lcr.
2,089.
14.50
1.000
10.409
1.0550 x 10'o
778.3
252.0
3.931 x l0-l
1,054.8
0.2520
107.5
2.928 x
o.2t62
c
Candle/sq. inch
centares {centiares)
Lamberts
sq meters
Fahrenheit
glams
Ounce fluid (US)
centiliters
0.01257
ncn
Meter
l\4 icron or (i.,lu)
Kilometers
Ton/sq. inch
cms of mercury
toot-lbs/sec
B.T.U. {mean)
Lambeats
centiglams
Centiliter
Centiliter
Centiliter
0.3937
0.01
Astronomical LJnit
Atnospheres
norsepower-hrs
watts
Calories, gram (mean)
Candle/sq. cm
Centigrade
t.257
amp/turn5/cm
sq. yards
acres
sq meters
gram-cal/sec
MULTIPLY BY
I0 I
amp{urns/in.
amp{urns/neter
gilberts/cm
I
Bucket (Br. dry)
bushels
bushels
bushels
bushe,s
bushels
bushels
bushels
tNt0
1,550.0
|.257
gilberts/cm
/hr
Btu/man
43,560.0
neler
Btu
8tu/min
1.562 x
4,840.
In.
Btu /hr
Btu/hr
Btu/min
I x 1Cl'
4,O47.
Ares
ares
atmospneres
atmospheres
atmospneres
atmospheres
atmospneres
atmospheres
atmospheres
10
43,560.0
sq mete6
sq mrles
sq yards
cu feet
gaflons
amperes/sq
amperes/sq
amperes/sq
amperes/sq
amperes/sq
arnperes/sq
10ro
160
Rods
Square links (Gunters)
Hectare or
sq. hectometer
Acre
2.998 x
TO CONVERT
10-'
centimeters
centimeters
Cubic inch
m
meters
es
mallimete6
m ils
yards
centrmeters
centimeter-dynes
cm-grams
centimeter-dynes
meter-xgs
po!nd.feet
centimeter-dynes
centimeter-grams
cm-dynes
centimeter-grams
rneter-kgs
poundJeet
centimeter-grams
centimeters of mercury atmospheres
centimeters of mercury feet of water
centimeters of mercury kgs/sq meter
centirneters of mercury pounds/sq tt
centimeters of rnercury pounds/sq in.
centimeters/s?c
feet / min
centameters/sec
centameters/sec
feet/sec
kilometers/hr
centimeters/sec
centimeters/sec
centlmeters/sec
centimeters/sec
centimeters/sec/sec
centimeters/sec/sec
xnotS
l0-'
lO-.
1,094 x 10-I
1.020 x 10-!
1.020 x 10-l
7.376 x 10-r
980.7
10-5
7.233 x 10-5
0.01316
0.4461
136.0
27.85
0.1934
1.1969
0.03281
0.036
0.1943
mete6/min
miles/ hr
miles / rn in
centarneters/s€c/sec
feet/sec/sec
kms/hr/sec
meters/sec/sec
centimeters/sec/sec
miles/hrlsec
Chain
Chain
Chains (surveyors'
or Gunter's)
Inches
meters
Cords
Cord feet
Coulomb
coutomos
.6103
0.01
3-281 x
0.3937
10- 5
0.01
6.214 x
10.0
centimeters
centimeters
centimeters
Circumference
0.01
liters
feet
kilometers
circular mils
1.0
(C'x9/5)+32
2.705
inches
10
3.142
.4870
drams
centrmeters
cent,meters
circular mils
circular Inils
3.9685 x
o.02237
3.728 x l0-r
0.03281
0.036
0.01
o.02237
792.00
20.12
yards
sq clns
sq mils
Radians
sq Incnes
22.O0
cord feet
cu. teet
8
Statcoulombs
faradays
5.057
r 10-.
0.7854
6.283
7.854 x
10-'
l6
2.998 x 10'
1.036 x 10-'
I
Appendix D: Conversion Factors
227
(Continued). Alphabetical Conversion Factors
TO CONVERT
coulombs/sq cm
coulombs/sq cm
coulombs/sq in.
cou,ombs/sq in,
coulombs/sq meter
coulombs/sq meter
cubic centimeterc
cubic centirneters
cubic centimeters
cubic centimete6
cubic centimeters
cubic centimeters
cubic centimeters
cubic centimeters
cubic feet
cubic feet
cubic feet
cubic
cubic
cubic
cubic
cubic
cubic
feet
feet
feet
feet
teet
feet
cubic feet/min
cubic teet/min
cubic teet/min
cubic teet/min
cubic feet/sec
cubic teet/sec
cubic
cubic
cubic
cubic
cubic
cubic
cubic
ctibic
cubic
cubic
cubic
inches
inches
inches
inches
inches
inches
inches
inches
inches
meters
rneters
cub,c meters
cubic meters
cubic meters
cubac mete6
cubic meters
cubic meters
cuDrc meters
cubic yards
cubic yards
cubrc yards
cubic yards
cubic yards
cubic yards
cuorc yards
cubic yards
cubrc yards/min
cubic yards/fiin
cubic yards/min
I
INTO
coulombs/sq in,
coulombs/sq meter
coulombs/sq cm
64.52
10.
coulornbs/sq meter
coulombs/sq cm
coulombs/sq in.
cu feet
cu inches
cu mete6
cu yards
Sallons (U. S. liq.)
1,550.
l0-.
6.452 x t0-l
3.531 x 10-'
0.06102
10-.
liters
pints (U.S. liq.)
quarts (U.S. liq.)
bushels (dry)
cu cms
cu inches
cu meters
cu yards
gallons (tJ.S. iiq.)
liters
pints (U.S.liq.)
quarts (U.S. liq.)
cu cms/sec
gailons/sec
liters/sec
pounds of water/min
million gals/day
gallons/ min
cu cms
cu feet
cu meters
cu yards
ga
onS
liters
mil-feet
pints (U.S. liq.)
quarts (U.S. liq.)
bushels (dry)
cu cms
cu feet
cu tnches
cu yards
gallons (U.S. liq.)
liters
pints (U.S. liq.)
quarts (U.S. liq.)
cu cms
cu feet
cu rncnes
cu meters
gallons {U.S. liq.)
liters
pints {U.S.
quarts (u.s.'iq.)
liq.)
cubic ftlsec
Sallons/sec
liters/sec
ULTIPLY 8Y
1.308 x
10-'
2.542 x
0.001
2.113 x
1.057 x
l0-!
lO-'
10-!
0.8035
-
2A32O.O
Gram
days
decrgrams
seconds
grams
deciliters
tlers
oecrmelers
degrees (angle)
degrees (angle)
degrees {angle)
meters
quadrants
radrans
seconds
oramS
oramS
otams
Dyne/cm
oyne/sq. cm.
Dyne/sq. cm.
Dyne/sq. cm.
t,72A.O
o.02832
0.03704
7.4a0s2
dynes
dynes
dynes
dynes
dynes
dynes
2432
59.84
472.0
0.t247
0.4720
IN?O
MULTIPLY 8Y
fadians/sec
0.01745
revolutaons/min
0.1667
2.778 x
revolltions/sec
gtams
r0.0
liters
10.0
10.0
meters
10
ounces (avoidupois)
0.r371429
ounces (troy)
0.125
cubic cm.
3.6967
1.7714
Srams
grains
ounces
27.3437
0.0625
Erglsq. millimeter
Atmospheres
Inch of Mercury at 0'C
Inch of Water at 4'C
grams
.01
9.869 x 10-'
2.953 x l0-'
4.015 x 10-'
1.020 x 10 I
10-'
JOUTeS/Cm
joules/meter (newtons)
kilograms
poundals
pounds
oynes/sq cm
bars
EII
Etl
Cm.
1
'
101.020 x 10 6
7.233 r 10-5
2.248 x 10-'
10-6
62.43
0.646317
448.831
5.787 x 10-.
1.639 x 10-'
2.143 x 10-5
4.329 x l0-3
0.01639
1.061x
105
0.03463
0.01732
106
5C.lt
61,023.0
1.308
264.2
1,000.0
Em, Pica
Ern, Pica
2,1r3.0
1,057.
7.646 x IO'
27.O
Dyne
ergs
ergs
Btu
dyne-centimeters
foot'pounds
erSs
ergs
ergs
ergs
Srarn-calo es
erg5/sec
cm/sec
t2.74
l0-1.
kilowatFhrs
O.277ax
watt-houts
Btu/min
farads
Faraday/sec
faradays
faradays
Fathom
Iathoms
microfarads
Ampere {absolute}
ampere-hours
coulombs
feet
leet
centimeters
teet
feet
leet
feet ol water
feet of water
leet of water
l0-rr
1.0
Joules
Kg-carofles
Kg-melers
Sram-cm5
ft-lbs/sec
feet
feet
1.000
9.480 x
7.367 x 10-l
0.2389 x 10
1.020 x 10 !
3.7250 x 10-r'
102.389 x l0 -rl
1,020 x 10-'
kg-calories/min
kilowatts
202.0
764.6
1,615,9
807.9
0.45
3.367
0.01111
0.01745
3,600.0
-
ft-lbs/min
0.7646
0.1
0.1
0.1
.4233
Crn.
ergs/sec
46,656.0
1.650 x
86,400.0
114.30
45
Inches
Inch
*glsec
ergs
ergs
ergs
0
Dalton
CONVERI
degrees/sec
degrees/sec
degrees/sec
oeKa8rams
dekaliters
dekamete6
Drams (apothecaries'
or troy)
Drams (apothecarieS'
or troy)
Drams (U,S.,
fluid or apoth.)
TO
l{eter
feet
krlometers
meters
rniles (naut.)
miles (stat.)
millimeters
'
'
I0
t3
0.2778 x 10 -ro
5,688 x 10-,
4.427 x lO-'
7.3756 x 10-l
1.341 x l0-ro
1.433 x l0-'
10-,0
10
9.6500 x
26.4O
lcr
l0
9.649 x
1.828804
6.0
30.48
3.048 x 10
'
0.3048
1.645 x l0-.
1.894 x 10 .
304.8
lg
mr ls
1.2 x
armospnere5
an. of mercury
Kgs/sq cm
0.02950
0.8826
0.03048
228
Mechanical Design of Process Systems
(Continued). Alphabetical Conversion Factors
TO CONVERT
teet of water
feet of water
feet of water
teet/m in
feet/ min
INTO
kgs/sq meter
pounds/sq ft
Pounds/sq in.
feet/ min
feet/ min
cms/sec
teet/sec
kms/hr
meters/min
feet/min
miles/hr
feet/sec
feet/sec
feet/sec
feet/sec
feet/sec
feet/sec
teet/sec/sec
feet/sec/sec
feet/sec/sec
feet/sec/sec
feet/ 100 feet
crns/sec
Foot
-
candle
kms/hr
knots
meters/min
miles/hr
males/
rn
in
cms/ sec/sec
kms/hr/sec
meters/sec/sec
miles/ hrlsec
per cenl graoe
Lumen/sq. meter
MULTIPLY BY
304.8
62.43
0.4335
grains (troy)
grains (troy)
Srains (troy)
giains (troy)
Srains/U.S. gal
grains/U,S. 8al
0.5080
0.01667
0.01829
0.3048
0.01136
30.48
1.097
0.5921
18.29
0.6818
0.01136
30.48
1.097
0.3048
0.6818
10.764
1.286 x 10-3
1.356 x 10'
0.3238
5.050 x l0-'
1.356
3.24 x 1.0 .
foo!pounds
Btu
foot-pounds
loot.pounds
foot-pounds
foot-pounds
foot-pounds
foot-pounds
ergs
foo!pounds
foot-pounds/min
foot-pounds/min
loot-pounds/mjn
loot-pounds/m,n
foot-pounds/min
toot-pounds/sec
foot-pounds/sec
foot-pounds/sec
toot-pounds/sec
foot-pounds/sec
kilowatt-hrs
3.766 x
Btu/min
1.286 x
foot-pounds/sec
hotsepowel
kg-calories/min
kilowatts
0.01667
3.030 x 10 -5
3.24 x lO-.
2.260 x l0-5
Btu/hr
Btu/min
o.o77 17
grarl1-calofles
np-nrs
JOules
kg'calories
kg-meters
horsepower
Furlongs
kg-calories/min
kilowatts
miles (u.S.)
turlongs
rooS
furlonBs
feet
Sallons
garrons
galrons
Sallons
gallons
gallons
gallons (liq. Br. lmP,)
gallons (U.S.)
gallons of watef
gallons/min
gallons/min
gallons/min
gausses
Sausses
Sausses
gausses
gilberts
gilberts/cm
gilberts/cm
gilberts/cm
cills (British)
gills
cu cms
cu feet
cu Inches
cu meters
cu yards
liters
gallons (U.S. liq.)
eallons (lmp.)
pounds of water
cu ftlsec
liters/sec
cu ft/hr
lanes/sq in.
weDers/sq cm
webers/sq in.
webers/sq meter
ampere-turns
amp-turns/cm
amp-turns/in
amp-turns/meter
cubic cm.
liters
Sills
pints (liq.)
Grade
Radian
drarns (avoirdupois)
Grains
0.r383
parts/rnillion
l0-'
l0-3
l0-'
1.818 x
0.01945
1.356 x 10-'
grams/cm
Slams/cu cm
gr-arns/cu cm
Srams/cu cm
grams/ liter
grams/ liter
10-t
0.04167
17.118
142.56
14.286
980.7
joules/cm
joules/meter (newtons)
kilograms
milligrams
ounces {avdp)
ouhces (troy)
pounoals
pounds
pounds/inch
pounds/cu ft
pounds/cu in
pounds/mil-toot
grains/gal
pounds/ gal
grams/liter
grams/liter
parts/nillion
grams/sq cm
pounds/sq
gram-calones
gram-calories
Sram-catones
Stam-catofles
Sram-calories
gram-calones
gram-caloraes/sec
gram-centimeters
gram-centimeters
gram-centrmeters
gram'centametels
6tu
grafi-centimeters
2.0833 x
parts/million
oynes
Slarns
grams
grams
grams
grams
g,ams
1.0
0.06480
pounds/million gal
Srams
Srams
Srams
Srams
MULTIPLY 8Y
grains (avdp)
grams
ounces (avdp)
pennyweight (troy)
grains/lmp.8al
Sralns
1.0
INTO
TO CONVERT
pounds/cu
ft
ft
foot-pounds
horsepowet-hrs
kilowatt-hrs
watt-hr9
Btu/hr
Btu
ergs
joules
kg-cal
xg-meters
15.43
9.807 x lo-t
9.807 x 10-!
0.001
1,000.
0.03527
0.03215
0.07093
2.205 x l0-'
5.600 x l0-r
0.03613
3.405 x l0-t
58.417
8.345
o.062427
1,000.0
2.0481
3-9683 x 10-t
4.1868 x l0'
3.0880
1.5596 x l0-.
1.1630 x l0-.
1.1630 x 10-3
14.286
9,297 x lO-.
980.7
9.807 x l0-5
2,343 x 10-3
10
o.125
-'
40.0
660.0
Hand
nectares
nectares
neclograms
3,785.0
23i.0
3.785 x 10-'
4.951 x 10-t
3.785
1.20095
o.83267
8.3453
2.22a x
l'-t
0.06308
8.0208
6.452
l0-l
6.452 x
10-,
10-.
0.7958
0.7958
2.02r
79.58
142.O7
0.1183
0.25
.01571
0.03557143
10.15
Cm.
acres
sq feet
grams
hectoliters
liters
hectometers
hectowatts
henries
Hogsheads (British)
Hogsheads (U.S.)
Hogsheads (U.S.)
meters
watts
millihenries
cubac
ft.
hoasepower
Btu/min
foot-lbs/min
foot-lbs/sec
horsepower
kg.calories/min
kilowatts
ho15epower
horsepower
horsepower (boiler)
horsepo',ver (boiler)
horsepower-hrs
horsepower-hrs
horsepower-hrs
horsepower-hts
norsepower-nrs
1.076 x
100.0
100.0
100.0
100.0
1,000.0
10.114
horsepowet
(550 ft lb/sec)
horsepower (metric)
(542.5 ft lb/sec)
watts
Btu/hr
kilowatts
Btu
ergs
footl bs
gram.calol|es
JOU
leS
103
8.42184
cubic ft.
gallons (U.S.)
holsepower
horsepower
horsepower (met.ic)
(542.5 ft lb/sec)
horsepower
(550it lb/sec)
2.471
42.44
33,000.
550.0
0.9863
1.014
10.68
0.7 457
7
45.7
33.479
9.803
2,547.
2.6845 x 10u
1.98 x l0'
641,190.
2.684 r l0'
Appendix D: Conversion Factors
229
(Continued), Alphabetical Conversion Factors
TO COI{VERT
tt{To
ho.sepower-hrs
horsepower-hrs
horsepower-hrs
nours
houls
HundredweiShts
Hundredweights
Hundredweights
Hundredweights
Hundredweights
Hundredweights
kg.calories
l(g-meters
ilIULTIPLY BY
641.1
kilowatt-hrs
qays
2.7X7 x
lU
o.7457
4.167 x
5.952 x
10-r
t12
(long) pounds
(long) tons (long)
(short) ounces (avoirdupois)
(shortl pounos
(short) tons (metric)
(short) tons (long)
l0-r
0.0s
t600
100
0.0453592
o.0446429
I
inches
inches
inches
inches
Inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
centimeters
meIels
miles
millimeters
mils
mercury
mercury
mercury
mercury
mercury
of mercury
of
of
of
of
ot
of water (at
of watet (at
of water (at
of water (at
of water (at
of water (at
International
4'C)
yaros
atmospheres
feet of water
kgs/sq cm
kgs/sq meter
2.540
2.540x 10-t
1.578 x 10-5
25.40
1,000.0
2.77a x rO-'
0.03342
pounds/sq tt
pounds/sq an.
atmospheres
4'C) inches of mercury
4'C) kgs/sq cm
4'C) ounces/sq in.
4'C) pounds/sq ft
4'C) pounds/sq in.
Ampere Ampere(absolute)
InternationalVolt
Inte.nationalvolt
lniernational volt
JOUIeS
joules
joules
ioules
joules
joules
joules/cm
ioules/cm
joules/cm
.loules/cm
ioules/cm
volts(absolut€)
Joules(absolute)
Joules
Btu
ergs
footpounds
kg-calories
kg-meters
watlhrs
grams
dynes
joules/meter(newtons)
poundals
pounds
0.03453
345.3
70.73
5.204
0.03613
.9998
1.0003
l-593 x 10-''
9.654 x l0'
10-'
107
l0-'
lO-'
1.020 x 10.
10'
100.0
723.3
22,44
K
kilograms
kilograms
kilograms
kilograms
kilograms
kilograms
kilograms
kilograms
kilograms/cu meter
kilograms/cu meter
kilograms/cu fieter
kilograms/cu meter
kilograms/meter
Kilogram/sq. cm.
kilograrns/sq cm
kilograms/sq crn
cm
cm
cm
rneter
meter
meter
meter
meter
kalograms/sq meter
inches of mercury
kilograrns/sq
kilograms/sq
kilograms/sq
kilograms/sq
kilograms/sq
kilograms/sq
kilograms/sq
kilograms/sq
kilograms/sq mm
kilogram-calories
kilogram-calories
kilogram-calories
kilogram-caloraes
kilogram.caloaies
kilogram-calories
kilogram-calories
kilogram meter9
kilogram meters
kilogram meters
kilogram meters
kilogram meters
kilogram meters
kiloliters
0.07355
2.540 x l0-1
0.5781
0.7376
2.389 x
0.1020
2.77Ax
INTO
HULTIPLY BY
24.
pounds/sq lt
pounos/sq In.
2,O44.
14.22
9.678 x 10-'
98.07 x l0-.
3.281 x l0-:
2.896 x 10-l
0.2044
1.422 x
10.
atmospheres
oars
teet ot water
inches ot mercury
pounds/sq ft
pounds/sq in.
kgs/sq meter
l0-'
Btu
foot-pounds
hp-h.s
3,088.
1.560 x 10-1
4,186.
426.9
4.186
1.153 x l0-3
9.294 x 10-r
9.804 x 10'
joules
kg-meters
kilojoules
kilowatt-hrs
Btu
foo!pounds
9.804
2.342 x lO''
2.723 \ 1O-'
1,000.0
1,000.0
10,
3,281.
3.937 x lO
1,000.0
JOUIeS
kg-calories
kilowatt-hrs
kilolines
o.4912
2.458 x 10-!
9.480 x
TO CONVERT
dynes
980,665.
grams
1,000.0
joules/cm
0.09807
joules/meter(newtons) 9.807
poundals
70.93
pounds
2205
9,842 x 10-'
tons (lond
tons (short)
1.102 x 10-r
grams/cu cm
0.001
pounds/cu tt
0.06243
pounds/cu in,
3,613 x 10-5
pounds/mil-foot 3.405 x 10-'o
pounds/ft
0,6720
980,665
oynes
0.9678
atmospheres
feet of water
32.81
kilometers
kilometers
kilometers
liters
centimetels
{eet
inches
kilometers
meterS
kilometers
miles
millimeters
kilometers
kilometers
kilometers/hr
kilometers/hr
kilometers/hr
kilometers/hr
kilometers/hr
kilometers/hr
kilometers/hrlsec
kilometers/hrlsec
kilometers/hrlsec
kilometers/hrlsec
kilowatts
kilowatts
kilowatts
kilowatts
kilowatts
kilowatts
kilowatt-hrs
kilowatt-hrs
kilowatt-hrs
kilowatt-hrs
kiiowatt-hrs
kilowatt-hrs
kilowatt-hrs
kilowatt-hrs
kilowatt-hrs
0.6214
lCl'
1,094.
27.74
54.68
yards
cms/sec
feet/min
teet/sec
0.9113
knots
meters/nin
miles/hr
0.6214
27.74
cms/sec/sec
ft /sec/sec
meters/sec/sec
0.9113
0.2774
miles/hrlsec
Btu/min
0.6214
foot-lbs/min
foot-lbs/sec
4.426
737.6
norsepower
kg-calories/min
Btu
foot-lbs
1.341
14.34
1,000.0
3,413.
3.600 x 10r'
2.655 x 10.
859,850.
gram-calories
horsepower-hrc
joules
xg.carofles
k8-meters
knots
knots
l(nots
knots
1,341
3.6 x lcl.
5bu.5
3.671 x 10'
pounds ot water
evaporated from and
at212'F.
kilowatt-hrs
\W
3.53
pounds ot water raised
frcm62" to 212" F.
feet/hr
kilometers/hr
nautical miles/hr
statute miles/hr
22.75
6,080.
1.8532
1.0
1.151
230
Mechanical Design of Process Systems
(Continued). Alphebetical Conversion Factors
TO CONVERT
knols
knots
INTO
yards/hr
feet/5ec
MULTIPLY BY
2,027.
1.589
L
leaSue
Light year
Light Year
lines/sq cm
lines/sq in.
lines/sq in.
lines/sq in.
lines/sq in.
links (engineer's)
links {surveyor's)
liters
liters
liters
liters
liters
liters
liters
liters
liters
liters/min
liters/min
lumens/sq ft
Lumen
Lumen
Lumen/sq. ft.
tux
miles (approx.)
Miles
Kilometers
9.46091 x 10"
gausses
Sausses
0.1550
5.U
5.9 x 10rr
1.0
weDers/sq cm
w€bers/sq in.
webers/5q meter
inches
inches
bushels (U.S. dry)
cu cm
cu feet
cu tnches
cu mete6
cu yards
eallons (u.S. liq.)
pints (U.S. liq.)
quads (U.S.liq.)
cu ft/sec
gars/sec
foot-candles
Spherical candle power
Watt
Lumen/sq. meter
foot-candles
1.550 x
l0-l
l0-'
1.550 x 10-r
t2.o
0.02838
1,000.0
0.03531
61.02
0.001
1.308 x 10-r
0.2642
2.r13
1.057
5.886 x l0-'
4.403 x 10-'
1.0
.07958
.001496
10.75
0.0929
tl
maxwells
kilolines
0.001
megohms
megohms
fieters
centimeters
meters
metets
meters
metels
meters
meters
meters
metets
leet
meters/m,n
cms/sec
meters/man
feet/min
39.37
0.001
5.396 ! 10-1
6.214 x 10-'
1,000.0
1.094
1.179
1.567
3.281
meters/mrn
meters/min
metels/min
meters/min
meters/sec
teet /sec
0.05458
kms/hr
0.06
knots
0.03238
0.03728
mete6/sec
feet/sec
meters/sec
meters/sec
mere6/sec
metels/sec
meters/sec/sec
meters/sec/sec
kilomete15/hr
5,O
kilometers/min
0.06
miles/hr
miles/min
0.03728
mete6/sec/sec
mete6/sec/sec
meterkilograms
meteFkilograms
meteFkilograms
microfarad
micrcgrams
micrchms
anches
kilometers
miles (naut.)
miles (stat.)
millimeters
yards
miles/hr
feet/
m
in
1Cl.
10u
10.
100.0
3.281
kms/hrlsec
rniles/hrlsec
cm-dynes
cm-grams
pound-feet
farads
glams
megohIns
9.807 x
liters
Microns
miles (naut.)
miles (naut.)
miles (naut.)
miles (naut.)
miles (naut.)
miles (statute)
miles (statute)
miles (statute)
miles (statute)
miles (statute)
miles (statute)
miles (statute)
mererc
19
I x 10-'
feet
kilometers
6,04O.27
meters
miles (statute)
yards
centametels
1,853.
1.1516
2,027.
1.509 )(
5,280.
6.336 x
feet
inches
kilometers
meterc
miles (naut.)
yards
cms/sec
leet/man
mil-feet
cu inches
milliers
kiloSrams
meters
feet/sec
kms/ht
meters/min
miles/min
sec/sec
feet / sec /sec
/
kms/hr/sec
10
r.609
1,509.
0.8684
1,760.
M.70
8&
t,467
26.42
0.1667
44.70
L.467
1.509
meters/sec/sec
cms/sec
teet/sec
kms/min
knots/min
0.4470
2,642.
88.
miles/hr
60.0
9.425 x
1,000.
g|a Ins
grams
parts/million
millihenrie5
henries
milliliters
liters
centimetels
feet
inches
kilometers
meters
millimete6
miles
millimeters
millimelers
million gals/day
mils
mrls
yards
cu ftlsec
0.8584
0.001
1.0
0.001
0.001
0.1
3.281 x
10-.
10-'
1.094 x
l0-'
1.54723
anches
mils
mils
kilorneters
yaros
2.77Ax
cu ft/min
cubic cm.
cubac cm.
oeSrees
quadrants
radians
seconds
kilograms
kilometers
kilowatts
10-t
0.001
6.214 x
mils
centimeters
feet
10-'
I x lo-t
0.01543235
2.540 x
8.333 x
0.001
2.540 x
myriagrams
myriameters
myriawatts
1Cl'
o.o26a2
0.8684
knots
cms
1..'J5
1.609
kms/min
milliSrams/litet
millimeters
millimeters
millimeters
millimeters
millimeters
IT.IULTIPLY BY
10-.
10-.
miles/hr
rniles/h.
miles/hr
miles/hr
miles/hr
miles/hr
miles/hr
miles/h.
miles/hr/sec
miles/hrlsec
miles/hrlsec
miles/hr/sec
miles/min
miles/min
miles/min
miles/min
miles/min
miner's incheg
Minims (British)
Minims (U.S., flu;d)
minutes (angles)
minutes (angles)
minutes (angles)
minutes (angles)
r00.0
ft/sec /sec
ohms
micrcliters
mils
195.8
3.281
INTO
microhms
Millimicrons
Milligrams
milligrams
10-l
webels
maxwells
microhms
ohms
megaltnes
TO COI{VERT
t.5
10-t
10-!
10-'
lO-'
0.059192
0.0516r2
0.01667
1.852 x 10-'
2.909 x l0-.
60.0
10.0
10.0
10.0
lCr'
l0-.
N
10-.
decibels
10-rl
Dynes
8.686
1x105
Appendix D: Conversion Factors
231
(Continued). Alphabetical Conversion Factors
TO CONVERT
INTO
MULTIPLY BY
0
OHlvl (lnternational)
ohms
ohms
ounces
ounces
ounces
0unces
ounces
ounces
ounces
ounces (fluid)
ounces (fluid)
ounces (troy)
ounces (troy)
ounces (koyJ
ounces (troyj
Ounce/sq. Inch
ounces/sq In,
OHIV (absolute)
megohms
mtcrohms
drams
grains
grams
pounds
ounces (troy)
tons (long)
tons (metric)
cu rnches
liters
grains
grams
ounces (avdp.)
pennyweights (troy)
pounds (troy)
Dynes/sq. crn.
pounds/sq rn.
1.0005
10 .
1@
16,0
437.5
2a349527
0.0625
0.9115
2.790 x 10-5
2.835 x 10-5
1.805
o.02957
480.0
31.103481
1.09714
20.0
0.08333
4309
0.0625
P
parts/mil!ron
lViles
Kilometers
grains/U.S. gal
grains/lmp. gal
parts/mjllion
pounds/million gal
Pecks (British)
Pecks (British)
Pecks (U.S.)
Pecks (U.S.)
Pecks (U.S.)
Pecks (U.S.)
pennyweights {troy)
pennyweights {troy)
pennyweights (troy)
pennyweights (troy)
pints (dry)
pints 0iq.)
pints (liq.)
pints (lrq.)
pints (liq.)
pints (l'q.)
pints (liq.)
pints (liq.)
pints (riq.)
Planck's quantum
cubic inches
Iters
Parsec
Parsec
parts/ftillion
Poase
Pounds (avoirdupois)
poundats
pounoars
pounoars
pounoats
poundats
pounoars
pounds
pounds
pounds
pounds
pounds
pounds
pounds
pounds
pounds
pounds
pounds
p0unds
pounds (troy)
pounds (troy)
bushels
cubic inches
liters
quarts (dry)
grarns
ounces (troy)
grams
po!nds (troy)
cu lncnes
l9 x 10rl
3.084 x 10r3
0.0584
0.07016
8.345
554.6
9.091901
0.25
n.'
Erg
-
second
Gram /cm, sec,
/
ft
tt
in.
R^"n.i</(^ if,
pounds/sq inpounds/ sq In.
pounds/sq in.
pounds/sq
8.809582
8
24.O
lo(/<n mptar
n.ic,cn in
^^
atmospheres
fact
w.tEr
^f
inches of merclry
kgs'sq meter
pounds/ sq ft
MULTIPLY BY
13.1657
t2.0
240.0
o.a22457
3.6735 x 10 '
3.7324 x 10-l
4.1143 x 10-'
0.01602
27.68
0.1198
2.670 x 10-'
1.356 x 10'
r3,825.
0.1383
0.01602
t6.o2
5.787 x
5.456 x
27.64
2.768 x
1,724.
9.425 x
1.488
10-'
10 '
10
L0-'
178.6
2.306 x 1Cr'
4.125 x lO
0.01602
0.01414
'
4.882
6.944 x t0-l
0.06804
2.307
2.036
703.1
144.0
0.05
4.1667 x
0.01671
24.87
4.732 x l0
6.189 x 10-'
0.125
o.4732
0.5
6.624 x 1O 1'
'
1.00
14.5833
oynes
13,826.
14.10
Srams
joures/cm
1.383 x
joules/rneter (newtons)
0.1383
kilograms
0.01410
pounds
0.03108
drams
44,4423 r.
dynes
grarns
7,000.
grams
453.5924
joules/cm
0.04448
joules/meter (newtons)
4.448
0.4536
kilograms
16.0
ounces
14.5833
ounces (troy)
pounoals
pounds (troy)
t.21528
0.0005
tons (short)
l0
5,760.
373.24177
o
10-l
33.60
ounces (troy)
grarns
grams
'n,lc
^^"nd<r<^
473.2
cu feet
cu lncnes
cu meters
cu yards
gallons
Irters
quarts (liq.)
INTO
CONVERT
pounds (troy)
ounces (avdp.)
pounds (troy)
ounces (troy)
pounds (troy)
pennyweights (troy)
pounds (troy)
pounds {avdp.)
pounds (troy)
tons {long)
pounds (troy)
tons (metf ic)
pounds (troy)
tons (short)
pounds of water
cu feet
pounds of water
cu inches
pounds of water
gallons
pounds of water/min cu {t/sec
poundjeet
cm-clynes
pound-feet
cm-grams
poundjeet
meter-kgs
pounds/cu ft
grams/cu cm
pounds/cu {t
kgs/cu meter
pounds/cu tt
pounds /cu in.
pounds/cu ft
pounds/mrlJoot
pounds/cu in.
grns /c! cm
pounds/cu in.
kgs /c! meter
pounds/cLr in.
pounds/cu ft
pounds/cu in.
pounds/mri foot
pounds/ft
kgs'meter
pounds/ in.
grns/ cm
pounds/mil-foot gmslcu cm
pounds/sq ft
atmospheres
pounds/sq ft
feet of water
pounds/sq ft
inches of mercury
(n
TO
quadrants (angie)
quadrants (angle)
quadrants (angle)
oegrees
rad ra ns
q!adrants (angJe)
quarts (dryj
1.571
seconds
cu tncnes
cu cms
cu teet
cu inches
cu meters
cu yalds
gallons
3.24 x
quarts lliq.)
quarts (liq.)
quarts (liq.)
quarts (liq.l
quarts (liq.)
quarts (liq.)
quarts (1,q.)
90.0
5,400.0
minutes
liters
1O5
67.20
946.4
0.03342
57 .7
5
9.464 x
1.238 x
0.25
l0-.
10-l
0.9463
1
R
ians
radians
radrans
radians
rad
W
radians/sec
radians/sec
radians/sec
radians/sec /sec
€dians/sec /sec
raorans/ sec/sec
revolutions
revoru!ons
tevotutons
revolutions/min
revolutions/min
revolutions/min
rninutes
quaorants
seconds
degrees/sec
revolr.rtions/min
revolutrons/sec
revs/min /min
revs/nrn/5ec
revs/sec /sec
quadrants
radrans
oegrees/sec
fadians/sec
revs/ sec
57.30
3,438.
2.063 x 10r
57.30
9.549
0.1592
573.0
9.549
0.1592
360.0
4.0
6.243
6.0
0.1047
0.01667
232
Mechanical Design of Process Systems
(Continued). Alphabetical Conversion Factors
TO CONVERT
revolutions/min/min
revolutions/min/min
INTO
radians/sec/sec
revolutions/min/min
revs/sec/sec
revolutions/sec
revolutions/sec
revolutions/sec
revo,utions/sec/sec
revolutions/sec /sec
revolutions/sec/sec
oegrees/sec
Rod
Chaan (Gunters)
xoo
Meters
radians/sec
MUI.TIPLY BY
1.745 x 10-r
0.01667
2.778 x 10-.
360.0
6.283
50.0
radians/sec /sec
revs/min/min
revs/man/sec
3,600.0
60.0
.25
5.029
INTO
TO COI{VERT
square
squate
square
square
square
square
square
square
square
mrls
!nrl5
yards
yards
yards
yards
yards
yards
yards
sq
cns
gra,ns
minutes
quaoranls
radians
Kilogram
tempemture
("c) +273
Pounds
20
2,778\ lO .
0.01667
3.087 x 10-6
4.848 x l0-l
14.59
32.17
Steradians
circular lnils
sq feet
sq rnches
sq miles
sq millimeters
sq yards
acres
circular mils
sq cms
sq inches
1.973 x 10'
1.076 x l0-3
0.1550
0.0001
3.861 x 10-'r
r00.0
1.196 x 10-.
2.296 x 10-,
1.833 x l0o
929.O
144.0
0.09290
square Inches
square
square
square
square
square
square
square
square
square
square
square
square
square
square
square
square
square
square
square
square
square
square
square
square
square
square
square
Inches
Inches
Inches
inches
k'lometers
kilofleters
kilometers
kilorneters
kilometers
kilometers
kalometers
meters
meters
melers
meters
meters
meters
meters
miles
miles
miles
mrles
millimeters
millimeters
millimeters
millimeters
rn ils
sq mrles
sq millimeters
sq yaros
circu lar mils
sq cms
sq teet
sq millimeters
sq mils
sq yards
acreS
sq cm5
sq ft
0.8361
3.228 x 1O-,
8.361 x l0'
sq males
sq millimeters
3.587 x l0-r
9.290 x lCr
0.1111
1,273 x 106
6.452
6.944 x
l0-3
tons
tons
tons
tons
tons
tons
tons
tons
tons
tons
tons
tons
tons
tons
tons
tons
tons
(long)
(long)
{long)
(metric)
(metric)
(short)
(short)
(short)
(short)
(short)
(short)
(short)
(short)/sq ft
(short)/sq ft
of water/24 hrs
of water/24 hrs
of water/24 hrs
cns
sq feet
sq miles
sq feet
sq xms
sq meters
sq yards
circular mils
sq cms
sq feet
sq inches
circular mils
3.861 x
1,973.
0.01
1.076 x 10-r
1.550 x 10-!
1.273
5/9
foot-lbs/min
3.4129
0.05688
107.
44.27
0.7374
watts
kg-calories/min
kilowatts
1.341 x l0-1
1.360 x 10-!
0.0t 433
0.001
Watts (Abs.)
Watts (Abs.)
watt'hours
B.T,U. (mean)/man.
0.056884
joules/sec.
Btu
3.413
3.60 x 10'o
walls
watts
1.196
640.0
27.88 x 10.
2.590
2.590 x 10d
3.098 x 106
1.0
.003336
toot'lbs/sec
106
10-'
('F)
.39370
Volt/cm.
Statvolts
eags/sec
1Cp
1.8
kilog€ms
1,016.
pounds
2,240.
tons (short)
1,120
kilograms
1,000.
pounds
2,205.
kilograms
907.1848
ounces
32,000.
ounces (troy)
29,166.65
pounds
2,000.
pounds (troy)
2,430.56
tons (long)
0.89287
tons (metric)
0.9078
kgs/sq meter
9,765.
pounds/sq in.
2,000,
pounds of water/hr
83.333
gallons/min
0.16643
cu ltlhr
1.3349
Btu/hr
Btu/min
1,550.
sq millimeters
sq yards
actes
1.0
w
watts
lO-.
('C)
v
Volt/ inch
Volt (absolute)
10.
7.716 x 10-.
247.1
10x
10.76 x 106
1.550 x 10'
0.3861
1.196 x
2.471 x
10.
10.76
absolute temperature
temperature ('F)
temperature
('c) + r7.78
temperalure
absolute temperature
("F) +460
temperature ("F)-32 temperature ('C)
106
sq mrles
sq yards
sq
9.0
,296.
T
s
square feet
't
sq inches
sq meters
feet
Scruples
seconds {angle)
seconds (angle)
seconds (angle)
seconds (angle)
Slug
Slug
Sphere
square centimeters
square cent|melerS
square centimeters
square centrmeters
square cen!melers
square centimeters
square centimeters
6.452 x 10-6
10-6
2.066 x 10-.
8,361.
sq Inches
acres
sq cms
Rods (Surveyors' meas.) yards
rods
MULTIPLY BY
horsepower
horsepower (metric)
watt-hours
watt-hours
erSs
watt'hours
gram-caloneS
horsepolver-hrs
kilogram-calories
watt-hours
watt-hours
watt-hou.5
watt-hours
Watt (lnternational)
foofpounds
I
2,656.
859.85
1.341 x
0.8605
kalogram-meters
kilowatt-hrs
Watt (absolute)
0.001
1.0002
1Cp
kilolines
10,
l0-1
-----Appendix D: Conversion
Factors
Synchronous Speeds
syncnronou3
sPc.o
Frcqusncy
r
120
- T;;Ei;;FIEQUEiICY
60.ycle
50
.y.lc
3600
3000
r800
t
6
8
50 Gycl.
12
171.1
142.9
500
11
|
63.6
136.4
1200
1000
a6
|
56.5
130.4
900
750
375
18
l50
r25
600
300
111
t20
500
250
t38.5
124.6
214.3
133.3
||t.l
375
187.5
128.6
t
l0
l2
600
II
5r
t6
150
t8
400
4.3
|
500
56
166.7
5.a
o7.l
t21.1
103.5
360
300
t50
60
120
100
327 .2
272.7
136.4
62
rr6.t
96.8
2l
300
250
61
2.5
93.7
26
276.9
230.8
lt5.a
66
t0t.
28
257 .1
211.3
t
07. t
58
r
30
210
200
100
32
225
187.5
93.7
72
31
2n.8
175.5
88.2
71
97 .3
8r.l
36
200
166.7
83.3
76
91.7
78 -9
38
t89.5
157 -9
78,9
92.3
76.9
10
r80
150
75
?0
75
Courtely Ingersoll-Rand Co.
80
I
90.9
05.9
88.2
102 -9
85.7
t00
83.3
2Sg
234
Mechanical Design of Process Systems
Temperature Conversion
NOTA Thc G.nter .oluh'l of nu|'b.t! in boldfo.. .efeB to the teDperotur. in desreei, either Cenrig.odc or Fohrenh.ir, whidr it ir d.!ir.d to conv.rt inlo lh.
olh.rtol.. lf.o.v.rtins kom fohr€nhcil lo Ccntis.ode degr€e!. the equivolent tempe.oiure will bc found in lh.lefi col'r6n, whileil convc.li.s lron d.s.c€i
Ccnrigrodc to
d.gr..r fobr.nhi.t,
thc oniy€r
Cenlisrod.
-20.6
-16.7
-t6.1
- .l
-159.1
-151
-136
-4t8
-2oO
328
-100
-361
-316
-tlo
-tto
-292
-271
-256
-t50
-lao
-r30
-238
-220
-202
-120
-181
-t66
-18.3
-15.6
-50
-67 .0
-58 .0
a5
-49.0
-/2.9
-,40.0
-!l
-40
-35
-31.1
-3t .7
-28 .9
26.1
t7 .2
.8
u
5r.8
-8 .9
-8 .3
l4
l5
220
225
t2a
I
l0
163.4
165.2
I
t6
230
235
240
116
155
461
167 .O
I
l8
7.45
173
25
27
80.6
2.4
8? .,{
a9
3l
81.2
86.0
82.8
32
89.6
7a
75
76
7a
,9
!o
152
168.8
170.6
l2l
t72.1
127
129
121
171.2
't76.O
27 .2
27 .S
8l
177 .8
a2
t79.6
28.3
28.9
29 .1
30.0
30.6
83
3t.l
ll3
l8l
132
135
138
t{
3f
98.6
3l
100.,{
39
40
102.2
104 .0
8.9
/t8
118.,(
-4.0
9.1
105.8
to7 .6
109.1
.7
32.2
32.8
33.3
33.9
31.1
35.0
31
35.6
36.7
114.8
37 .2
| 16.6
536
545
554
E5
185 .0
86
186.8
l,a9
154
|
88.6
t60
|
90 .,4
t66
300
310
320
330
t71
3:10
626
611
a,
E8
s72
590
608
89
90
192.2
194.0
177
350
662
9l
|
95.8
182
t88
360
370
680
.6
99.4
r93
3t0
,16
201 .2
t99
731
203.0
204.8
201
390
a0o
210
216
at0
420
206,6
208.4
21o.2
212 .0
221
r30
805
L0
aso
150
170
{r0
ago
500
gza
812
92
93
9a
95
95
9A
99
197
r
227
40 .6
t05
221
238
43.3
0
213
219
a9
50
120.2
,(6.l
||5
122.O
5l
t20
t25
218
251
t23.9
18.9
5t .7
257
260
| et-r'r
Degreca KeMn,'K:'C + 273.2
518
290
495
.,a
230
239
=
500
509
lt6
100
cent,'.=|et + ,ot -ro
280
2t5
ta2
191
143
9f
113.0
250
233
260
255
270
215
137
I83.2
!4
95.0
-22.0
Desr€e'
26.1
26.7
8.3
10.0
l0 .6
23.9
21.1
25.0
25.6
l]1.2
(ony€rling Ceotigrcdc or foh.enhcil
i.lo thc othcr 3cal.r.
119
77 .O
14
15
a6
17
formulor ol lh. .isht hoy oho bc ured
215
25
6.7
.4.0
ttt
t02
t04
t07
-3 .9
12
-t0
212
-1.1
5-6
6.1
-t3.0
110
100.0
23
24
10.0
392
,a0r
,3
{3
383
200
371
210
22.8
96.8
195
t5.4
205
d8.0
69.8
71.6
73.1
75.2
36
t90
I
317
356
93.9
20
93.2
85.0
82.8
l15
117.2
t
338
96.1
72
9t.,(
!65
t70
t75
ta0
329
13.6
73.9
76.7
79.1
s2.2
.6
154.4
| 56.2
158.0
159.8
161 .5
fl
34
35
38.2
l{0.0
l4r.8
t20
50.8
2t .7
22.2
LI
71.1
I55
t50
3ll
34.6
| 36.4
150
t
2t.r
0.6
65.6
68.3
55
57
62.6
61.1
66.2
0.0
32.8
r
l8 .9
t7
t8
t9
30
293
2e1
149.0
59
70
1.7
l,l5
55
20.6
2l
.0
266
8.3
60 .8
6.7
-6.1
r3l
t30
t35
ta0
90.6
93.3
t5
/tt
-31.0
l,
|
5.0
-25
-20
-ll
18.2
50.0
5l
3.9
4.1
-50
9
52
53
61
20.0
-t 03.0
-65.0
-75,0
t6.7
6l
59.0
-75
-55
16. r
I9..{
-t l2 .0
-53 .9
-51 .l
|
5t
57 .2
-90
91.0
59
60
l5 .6
t0
t3
1.7
2.2
-ro
16.4
60.0
62.8
|
t2.a
I
12r.2
57
14.1
15.0
lt.6
5t.t
13.3
t3.9
al.0
125.6
127.1
52
53
5a
55
55
39 .2
-10.6
-10.0
-148.0
-t 30.0
-r0
11.7
12.2
3
7
-t2.8
-t2.2
-382
-I00
.l
32.0
1
-13.t
-r3.3
-230
-220
-210
-ll0
23 -O
35.6
37.1
5
C.ntlgrod.
Centigrode
I2.8
2
-15.0
-14.1
-116
-f10
-t34
-129
-123
-I8
-l 12
-107
-tot
-96
-90
-8{
-79
-73.3
-67 -S
-62.2
-r50
-5
I
-rao
-r90
Fohrenhcil
0
-tsf
-56.7
fo'rnd in the column on thc right.
C.ntigrodc
-273.17 -a59.f
-268
-r50
-262
-aao
-{30
-257
-25t
-420
-216
-aro
-,100
-210
-231
-390
-3r0
-229
-370
-223
-2t8
-360
-350
-212
-3{0
-207
-330
-20t
-310
-t96
-190
-3ro
-300
-t81
-290
-179
-2t0
-173
-2f3
-f69
-168 -rro
-260
-t62
-250
-157
-59.r
$ll b.
Dcqree' Fohr.,
'F = !
9
fc + .ot -.0
c +32
Degrccr Rcrftlne, ol :oF+459.7
69S
v0
748
860
678
896
914
932
3*.
Aooendix D: Conversion Factors
Altitude and Atmospheric Pressures
Kelrq
Hs Ab3.
-1526
-1373
-5000
,{500
,{000
77
75
73
21
35.58
35.00
H9 Abr.
PSIA
.7
17.15
.229
.209
903
t7.t9
889.0
23
s{.12
87t.3
16.t0
.188
-3500
-3000
t068
71
22
859.5
16.62
.t69
-915
70
2l
33.84
33.27
8,(5.l
t
6.34
.r19
2500
-763
68
20
-610
830.6
816 .4
16.06
15.78
l8
3t .58
802.1
-305
65
61
63
32.70
32.11
.129
-2000
-1500
-1000
17
3l .02
757
6l
t6
30.17
773.9
59
29 .92
760.O
29.38
716.3
28 .46
733
28.33
719.6
706.6
-1220
15S
0
0
500
1000
t53
I500
.158
2000
6t0
?500
763
3000
915
l8
3500
1068
17
t000
1220
1373
t4
55
,4500
12
ll
50
0.95
6000
7000
1.1
l83l
1.3
2136
2111
2716
3,(
3050
23
20,000
1.9
2.4
3.8
25,000
30,000
1.7
5.7
7628
t0,000
t5,000
1.7
7.6
8.5
9.5
40,000
15,000
50,000
55,000
10.1
60p00
ll.,4
20.000
80,000
90,ooo
t00,000
t3.3
t5.2
120,000
160,000
180,000
22.8
26.6
30.4
31.2
200p00
37 .9
t,(0,000
't7.1
r8.9
1 5
| t,(
't2 | 21
6
30 t-31
-18 | -41
9153
-66
-70
-70
-70
-70
12,201
13.730
r5,255
t6/81
27.159
30,5t 0
36,612
67,t22
,(00,000
75.9
94.8
t22,010
-11
-86 I
I
500,000
600,000
It4
900,000
132
244,080
tp0o,ooo
189
305,100
1.200,000
1,400,000
1,600,000
228
266
l,8oo,ooo
312
379
2,000,000
30.{
.926
.909
t2.69
.492
.876
2t .90
632_5
609.3
555.7
561.6
5,t3.3
12.23
.78
.s60
23.99
23.10
.3,6
.91
l0
l0 .50
.797
.767
.738
10.t0
.710
.583
319.5
282.1
8.29
6.76
s.16
8.903
226.1
a
.37
.307
.060
5.558
't79 .3
3
.17
.211
.192
2r .39
20.58
16.89
13.76
1l.l?
l,{l
a7.5
68.9
2.135
1.325
ls.273-1
5.200-r
-42
2.523-t
9.955-.
.406
13.2
8.36
3
I
t.113 .
.737-t
6
.3-l
Courtdy Ins.Boll-Rrd Co-
.162
.45
51
16.97-l
3 .26-l
3.5r 3-.
3
.0738
.0158
.0285
.o179
2t.0
r
'3
| .05
.651
358-I
5.917-7
r.18-!
6.11
?
2.53-r
8.92-r
.67
L19-1'
x
| .1-l
1.605
3.56-.
t.6r
1
I .50-6
.06-l
I
366,t 20
127,110
188,160
2.O-'
L2_10
s.08-r
2.08-l
3.8-ro
9.65-'
519,1S0
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1
6r0,200
9
2.31-e
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.30-'
.57-'
.381
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.7
I
.828
2.15
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t.33
51_2
33
Dor6 ,'.m NASA Sr.ndcrd Arh6ph.r.ll9a2l.
ond b.'.m.r.r or. opp'orirot. ,o( n.soriy. clri|ld.a
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1.375
3.111
2.712
3.290
12.16
129 .O
5.9 .
--
.960
12.93
5.1-t
I
3.66
.956
.978
.913
| .281
5.816
t2z I -88
.0333
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13.t7
-7
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-135 | -93
r4.696
t,(.13
t,(.16
t3.91
13.1r
2.716-'
66
90
.071
.052
68t .2
668.6
656.3
611.1
-2
-3 | -r9
61,020
73,221
79,326
85,128
91,530
56.9
28t
t9t
5t,918
at.7
53.t
a L -16
12711
,(8,815
45.5
49.3
280,000
300,000
-62 | -52
-57 | 59
5t | -16
-26 I 48
2A,AOa
t5.23
I4.96
|
693.9
7
57
57
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18,306
21,357
2,{0,000
l
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6102
220,000
260,000
6
3
1o,679
35,000
8
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5000
8000
9000
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26.87
26.33
25.81
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235
236
Mechanical Design of Process Systems
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Index
American Society of Mechanical Engineers.
mass flow in, 1, 3-4, 6, 8, 11
piping,3
angle of internal friction, 3-4, 6-7
angle of friction, effective, 6*7
critical flow factor for, 7
See
ASME.
API, degrees for hydrometer,
conversions, tables of, 92
defined,8T-88
ASME Section VIII Division I
joint reliability factor, l13-l14
joint types for tubesheets. I l5
maximum tube joint force, ll3, 157
tube joint load criteria, 113
vessel code, 99, 101
Axial flow compressors
aircraft, for, 59
airfoil blades for
pitch, 58
size,58
applications of, 44, 58-59
characteristic curve for, 59
operating range of, 49
surge
piping factor, 304
pneumatic gases in, 7
pressure vessels, differences
stresses
13- 14
wall friction angle, 4-5
Blowers and fans, 59
Bulk solid properties
bins, in, 1, 6
bulk density, 3, 6
Beams, boundary conditions for, continuous beams,
142
Bins
arching (rathole, l-2, 6)
critical dimension for, 3, 12
critical flow factor for, 4
critical hooper dimensions, 6
dead storage, 1-2
critical dimensions of, 3
pressure of, consolidating, 4, 6-7
stresses,
hooper wall, on, 3
solids, in, 3
typical values oi 7
yield strength, solid material,
1
flow, erratic, I
flushing of, 1
funnel flow in, 1, 6, 8
hoop pressure in, rnaximum, 6
hooper angle,
in,
truss design, 18-20
limit of, 59
degradation flow condition, 1
design of, reasons for inefficiency,
from,
1
segregation, 1
shear stress, 1
solid flow, pressure distribution for, 8
steady flow, consolidating pressure for, 3
structural design,
conical portions, rectangular, 17
frame detail, 20
stiffener design, 14-16
hoop force, 16
Centrifu gal compressors
actual, or inlet, flow rate, 80
advantages of, 43-44
affinity laws, 50
3
237
3
Mechanical Design of Process Systems
anti-surge devices for, 52
diagram of, 53
applications of, 49
compressibility curves for, 81
compressibility factor, significance of, 83
compression process, diagram of, 50
compression ratio of, 50, 80-81
discharge temperature
average,80
dependence on ratio of specific heats, 83
frame data, typical, 80
gas, cyclic vibration of, 50-51
noise induced by, 50-51
gas inlet conditions, 50
impeller, 49
types of, 52, 52
inlet parameters, effect of varying. 52
intercoolers, sizing of, 50
mechanical losses of, 82
percentage of power required, 83
mixtures
compressibility factors for, 79-81
specific heats for, 79
nncratinc 'arlo" 44
performance curves, typical, 51
polytropic head, 81
maximum per stage, 82-83
significance of, 83
polytropic relations for, 46-50
pressure versus capacity for
constant speed compressor, 52
rpm, required, 82
selection of, 79-83
shaft power, required,
expression for, 82
single stage, 49-50
specific heat ratio
significance of, 83
stages, required number of, 82
standard cubic feet, use of, 52
surge,50
control of, 52
surge limits, 50, 52
temperature, discharge, 49-50
temperature ratio for, 81
volumetric flow, expression for, 80
Centrifugal pumps
advantages of, 31
API hydrometer,
conversion factors, table of, 92
defined, ST-88
bearings, 34
outboard type, 34
brake horsepower, 34, 36, 70, 9l
required,96
shut-off, at, 36
by-pass for, 34, 36
casrngs,
horizontally split, 32
vertically split, 32
advantages of, 32
components of, 33
efficiency of, 70
head, total, 36
heat dissipation in, 34, 36
intercooler for, 37
Hydraulic Institute, 68, 71-72
hydraulic requirements of, 34, 36-37
impeller,
axial flow pump, for, 32
mixed flow pump, for, 32
vanes of, 32
radial type, 32
volute of, 32
net positive suction head (NPSH)
definition of, 34
pressure pads for, 91
Newtonian fluids, 68
non-Newtonian fluids, 68, 79
packtng, 32
performance curves for, 34
typical, 69, 75, 95
pressure drop
discharge line, for, 67 -68, 9l, 95-96
friction factor for, 66-67 , 89-91, 93, 95-96
suction line for, 65-66, 90-91,93,95,97
viscosity, effects of, 68, 70-72
seals,32
double seals
criteria for use, 32
types of, 35
seal flush, 34
single seals
types of, 35
versus double seals, 32
selection of, 70
total dynamic head, application of, 70, 74
types of, 31, 34-35
vaporization of pumped liquid, causes of, 34
viscous liquids, pumping of, 37
correction-factor curves, 37, 38-39
criteria for, 37
equivalent water-performance of, 37
water horsepower, 34, 36
defined, 36
Compression, ideal gas
compressibility factor
discharge, at, 45
Heat transfer, convection of, air normal to cylindeq 126
mean, 45
suction, at, 45
isentropic (reversible adiabatic), 46-49
adiabatic efficiencY, 46
energy, isentroPic, 46
polytropic efficiencY, 46
principles of, ff 44-48
real gas. compressibility factor. 44
Compressors
acfm,59-60
advantages of, 59-60
conversion to, standard volumetric
flow, 60
actual volumetric flow. See acfm'
flow conditions, sPecifYing, 59
actual, or inlet flow, 59
mass
flow,
59
flow, 59-60
flow, conversion to standard volumetric flow,
standard volumetric
mass
60
principles of comPression, 44-48
scfm, 59-60
specifing flow conditions, 59
acfm, exPression for, 60
actual, or inlet flow, 59
mass flow, 59
specific volume, exPression for, 60
standard volumetric f1ow, 59-60
standard volumetric
flow
compressibilitY factor, 59
conversion to actual or mass flow, 60
disadvantages
of, 60
specific volume, exPression for, 59
'ttandard" condition, defined, 59-60
comparisons of various forms, 60
volume flow, equation for, 59
types of, 43
volume flow, exPression for, 59
External loading on shell structures
applications of , l7Q-17 5
"critical value," 170
shell thickness, 170
Hydraulic Institute, 37
Hydraulics
API hydrometer
conversion factors, table of, 92
defined,8T-88
Internal pressure, stress concentration factor, 169
lsentropic comPression
brake horsepower, 48
discharge temperatue, 48
head, adiabatic, 46
heat, mechanical equivalent of, 45
horsepower, ratio of isentroPic, 45
horsepower input for single stage, 45
ideal eas, 45
adia--batic efficiencY, 45
horsepower, isentropic, 45
mechanical efficiencY, 45
overall adiabatic efficiencY, 45
multistage,46
perfect gas, formulations for, 44
real gas,
formulations for, 45
isentropic exPonent for, 45-46
relations, basic versus polytropic compression, 47
reversible,48
Jenike and Johanson method, 1-8
Lifting lug design, 170-175
choker angle for, 175
standard designs for, 171
L'Hospital's rule, 165
Ingarithmic mean temperature difference. See LMTD.
LMTD,
application of, 148-149, 154, 160, 162' t65
correction factot F, 117 -l2l
multipass exchangers, variance in, 117
variance in shell and tube heat exchangers, 117
zero LMTD exchanger, 165
Multi-stage reciprocating compressors, 58
Flow of solids, problems of, 1-3
Non-Newtonian fluids, 162
Nozzle reinforcing pads
disadvantage of pads, 170
Gas
pad width, maximum, 170
Nusselt number, 125-126, 156
Fans and blowers, 59
compressibility tactor, 44
general gas law, 44
specific heat ratio for, 44
universal gas constant, 44, 59
Gear pumps, 37, 40
Petroleum fractions
API hydrometer for, 87-88
Plate-fin heat exchangers
advantages
of,
147
24O
Mechanical Design of Process Systems
applications of, 99
disadvantages
of,
147
illustrated, 149
Kays and London coefficients, 148
thermal shock and fatigue, 148
of, 147- 148
vacuum brazing of, 148
Polytropic compression
uses
efficiency
overall polytropic, 48
polytropic vs. isentropic, 46-47
gas horsepower, 47
head, adiabatic, 47
horsepower, compressor (polytropic head), 48
perfect gas, for, 47
polytropic exponent, 46
polytropic head (compressor horsepower), 48
real gas, for, 47
relations, basic versus isothermal compression, 47
Positive-displacement pumps
applications of, 31
brake horsepower, 77
definition of, 31
efficiency of, 77
pump selection, use in, 77
gear pumps, 37 , 40, 78
heat dissipation in, 43
intercooler, 43
temperature switch, 43
net positive suction head. See Pumps.
performance curves for rotary gear pumps, 79
pressure drop
suction line, 74
velocity heads, 74
pressure protection for, 42-43
priming of, 79
reciprocating pumps
diaphragm pumps, 3l
piston pumps, 31
nlrrnocr nrrmnc 1l
rotary pumps
cam pumps, 31
gear pumps, 31
lobe pumps, 31
screw pumps,31
types of, 37
vane pumps, 31
screw pumps, 40-41
vane pumps, 37
Prandtl number, 125,152, 156, 164
Pulsation response spectra
compression bottles, 64, 65
typical,65
methods of predicting, 64
orifice plates, application of, 65
piping system excited by, 65
pulsation bottles. See Compressor bottles.
pulsation dampener. See Compressor bottles.
reciprocating equipment, induced by, 62, &-65
Southwest Research Institute, 64
Structural Dynamics Research Corporation,
(scRc),
64
surge drums. See Compressor bottles.
Pumps
API degrees, defined, 87-88
calculation sheet for, 36, 70, 77
flow capacities of, 34
head, friction, 40
static discharge, 40
static suction, 40
total discharge, 40
total dynamic, 34, 40
total static, 40
total suction, 40
Hydraulic Institute, 68, 7 | -72
inline, nozzle loadings for, 61
lift
static suction, 40, 42
for water
maximum recommended, 43, 77
theoretical, 43, 77
total suction, 40, 42
motors, NEMA frame dimensions, 73
NPSH
definition of, 34
pressure pads for, 91
priming of, 79
pump Hydraulic Design,
calculation sheet, 36, 70,77, 93,95-96
pump selection guide, 32
of, 3l
of, 31
types
uses
velocity heads,
effect on pumps, 40
Reciprocating compressors
adiabatic compression, work required for, 58
adiabatic exponent, 53
adiabatic expressions for, 44-46, 53
adiabatic process, 57
applications of, 43, 84-86
clearance capacity, effect of, 55
clearance pockets, 43
stop valve, 53
volumetric efficiency, effects on, 56
compressibility factors
discharge, 58
inlet, 58
fr
lnder
compressor horsepower, factors affecting, 53
compression ratio, 58, 84
compressor bottles. See Pulsation response spectra.
cylinders, size of, 86
cylinder displacement, 86
diatomic gases, 57
discharge temperature, 85
efficiency, volumetric, 86
Neerken equation for, 86
gas temperature, exPression for, 58
horsepower, theoretical, 58
parameters affecting, 58
horsepower per million curves, 85
correction factors for, 85
intercoolers for, 84
multiple staging of, 58
advantages of, 58
compression ratio for, 84
cylinder size, 58
cylinders, number of,
flywheei, effect on, 58
torque, effect on, 58
operating range, 44
piston rod diameter, 86
polytropic exponent, 57
Chlumsky recommendations for, 57
pressure-volume diagram, 56
ratios of clearance volume to volume swept by
piston,57
reciprocating compressor cycle, 53, 55
58
re-expansion process, 57
schematic of, 87
volumetric efficiency
curves for determining, 57
expression for, 53, 57
for a perfect gas, 57
parameters that affect, 53, 57
theoretical,53
Regenerated gas exchanger
design of, 148- 153
vibration check, 153- 154
Reinforcing pads (external loadings)
pad width, maximum, 170
disadvantage of pads, 170
Reynolds number, 9, 66-67, 7 4, 89 -91, 93, 95 -96,
t25-127, 140, 141, l5l-152, 156-157,
1U
non-Newtonian fluid, Metzner-Reed, 162-163
versus drag coefficients for long circular cylinders,
r42
Rotating equipment
APr 611,61
APr 612, 61
API 617, 61
API 618, 61
API criteria, 61-62
NEMA. See Nozzle Loadings.
nozzle loadings on, 61-62
allowable, defined, 61-62
NEMA,61_62
applications for, 61
options to, basic, 62
steam turbines, ideal expansion joint, 64
turbo-expanders, reasonable values for, 63
typical for in-line pumPs, 61
piping systems for, 60-65
pulsation bottles. Se? Pulsation response spectra.
steam turbines, piping
to, 62
surge drums. 'gee Pulsation response spectra
Rotary pumps, types of, 37
Screw pumps, 40-41
Shell-and-tube heat exchangers
advantages of, 99
ASME Section VIII Division I Code, 99, 101
ASME tube joint load criteria, 1 13- 1 15
joint reliability factor. I l3-l14
maximum tube joint force, 113
tube joint load, 113
baffle cuts, 111
baffle details, 111
baffle lanes, channel and head, 128
baffle plates, 99
baffle windows, 139
various schemes, 139
baffles
annular orifices, 110
doughnut and disc tYPes, 110
flow direction, used for, 107
horizontally cut, 107, 109
longitudinal, 109
structural supports, as, 107
verticaliy cut, 107
vibration dampers, as, 107
baffle windows, Ill
basic components of, 107 -112
caloric temperature, 117 , 122-123, 158
Kern relationships for, I22
caloric versus arithmetic rnean, 122
chlorine superheater design, 154- 160
chiller, 101
condenser, 101
deflexion or ligament efficiency, 158
design classifications of, 101
final condenser, 101
fixed tubesheet, 102-1O4
fixed tubesheet design, 100
floating heat exchangers
211
242
Mechanical Design of Process Systems
internal floating head design, 103-104
advantages of, 104
outside-packed floating head design, 103-104
operating range, 104
packed latern ring design, 103-1M
operating range, 1M
pull-through bundle design, 103- 104
limitations of, 104
types
of,
regenerated gas exchanger design, 148-153
sensible heat, 116- 117
shell-side, defined, 99
shell-side equivalent,
tube diameter, 129, 152, 156, 164
shell-side pressure drop, \39, 152-153,157,
164-165
103- 104
forced circulation reboiler,
101
fouling resistances, recommended minimum, 125
friction factors for, shell-side surfaces, 140
heat transfer
bulk temperature of fluid, 125
continuity equation, 128
convection, basic expressions for, 115
factor jH, 129,138, 152, 157
film coefficients, shell-side, 128
Kern correlation, 128
fouling factors, 124
bare tubes versus finned tubes, 124
definition of, 124
versus thermal conductance, 124
fouling resistance, 124
Fourier's law of heat conduction, 116
Grimson equation, for film coefficient, 126
inside film coefficient, 122, 151
laminar, 125
turbuient, 125
laminar boundary layer. 125
modes
reboiler, 99, l0l
kettle type, 99
of,
115
McAdams correlation, 125
film coefficient, lZZ, 126, 1,29
overall heat transfer coefficient, 152
caloric, 117, 122, 152, 157, 158
parameter jH, 129, 138
effective diameters for, 129
versus Reynolds number, 138
shell-side film coefficient, 151-152, 156,
163-t64
tube-side film coefficient, 151, i54-156
tube wall resistance, 124
turbulent boundary layer, 125
impingement baffles, i28
latent heat, I 16- 117
ligament or deflexion efficiency, 158
outside
LMTD
correction factor R 117- 121
multipass exchangers, variance in, 117
variance of, 117
overall heat transfer coefficient, 122
caloric, 117, 122, 152
partial condenser, 101
process evaluation of, 115-140
expression for, 139, 152
shell-side mass density, 151
shell-side mass flow rate, G,, 139, 152-154, 156,
I O-l
Sieder-Thte correlation,
laminar flow, for, 125, 162
turbulent flow, for, 125
steam generator, 101
TEMA
class B exchanger, 99, lO4
class C exchanger, 99, 104
class R exchanger, 99, 104
comparisons of types, 105
mode constants for tubes, 112
natural frequencies of straight tubes, I 12- I l3
natural frequencies of U-tubes, 113
nomenclature
of,
102
TEMA specification sheet, 150, i55
tubes, stress, allowable compressive, l12
tubesheets, compressive stress induced OD,
lll
thermosyphon reboiler,
101
tie rods
TEMA recommendations for, 110
uses
of,
110
tube arrangements, pros and cons
tube bundle, 99, 126, 128
flow area of,
of,
152
Keys and London constants foq 129
tube bundle cross-flow arca, 128
staggered
inline, for,
128
triangular layouts, for, 128
tube count tables, 130- 137
tube geometry
angtlar pitch, 126-127
diamond-square pitch, 126 - 127
inJine square pitch, 126-127
inJine triangular pitch, 126-127
tubes
bare, 107
bend radii, minimum, 109
boundary layer, 125
laminar, 125
turbulent, 125
buckling of
129
{
2rl:t
Euler columl formula, 114
exchanger tubes, 113
Johnson short column equation, 1i4
finned, 107
foreign deposits, 124
inside film coefficient, 122
outside film coefficient, 122
pitch, nominal, 114
stress factors for, 159- 160
tabulated properties of, 108
tubesheets, 99
double tubesheets, 110
uses
of,
110
maximum radial stresses in, 159
single tubesheets, 110
tubesheet-tube connections, typical, I 1 1
tubesheet layouts
staggered in{ine, for, 128
triangular layouts, for, 128
typical, 128
tube-side defined, 99
tube-side mass flow rate, 151, 162
tube vibrations. See Tube vibrations.
tube wall temperature, 117,122, 124
U-tube exchangers
kettle type reboiler, 100
tubesheet
vaporizer,
fot
103
101
vapor-liquid equilibrium calculations, I 17
vertical gas-gas exchanger, 151
Silos. See Bins.
Specific diameter, 48
versus specific speed, 49
Specific speed, 48
versus specific diameter, 49
Stack design
anchor bolt torque, 26-27
base support detail for, 27
carbon precipitation in,
8
buckling stress
allowable, 22
deflection, dynamic, 26
deflection, static, 26
excitation, flexural, 9
flexural frequency, 9
lining of, 8
effect of, 8
gunite,8
modulus of elasticity of, 8
Michell and Love equation, 9, 28
ovaling,8-9
flexural modes of, 9
in-plane, 9
out-of-plane,9
modes of, 9
ovaling frequency. See Flexural frequencl ovaling rings, 9, 26
natural frequency of, 9, 26
reasons for, 9
section modulus of, required, 9
pressure vessels, vertical differences bef$'een. 8
seismic response spectra, 8
vibration, cantilev er, 25 -26
vortex shedding frequency, 9, 26
vortex strakes, 9-11, 27 -28
clearances for, 11
critical wind velocities for, 10
fabrication detail of, 11
fabrication, method of, 11
helix angle of, 10
length of, 10
Morgan equation, 10, 28
radius of curvature of, l0
strake height, 10
range for, 10
wind design
anchor bolt design for, 23
bearing pressure for, 23
base plate, Brownell and Young method, 24
chair design, Brownell and Young method, 24-25
compression rings, gusset plate thickness,
required,25
effective diameters for, 20
weld, skirt-to-base ring, 25
wind load, 2l-22
wind moment, 21-22
wind pressure, 21
wind response spectra, 8
Steam turbines
piping of, 62
Strouhal number, 9
Suction lift,
IOr WAIe\
+5, I I
TEMA
class B exchanger, 99, 104
class C exchanger, 99, 104
class R exchanger, 99, 104
heat exchanger specification sheet, 150-161
mode constants for tubes, 112
natural frequencies of,
straight tubes, 112- 113
U-tubes, 113
nomenclature for shell-and+ube heat exchangers.
102
standard, TEMA, 99, 104
TEMA types, composition of, 105
tie rods,
244
Mechanical Design of Process Systems
recommendations
uses
of,
for,
1
10
110
tube joint load formulations, 113
tubes,
minimum bend radii, 109
stress, allowable compressive, I 12
tubesheets,
compressive stress induced on, 111
Tube vibration
baffle damage,
modified damage number, 143, 153
baffle plate, illustrated, 143
displacements, inducing excessive, 143-144,
t53-154
drag coefficients versus Reynolds number, 142
flow-induced vibration, 144
fluid vortices, force exerted on tubes, l4i
jetting, or jet switching, 144
compared to turbulence, 146
cornpared to vortex shedding, 146
shear force on tube, l4l, 143, 153
shell-side fluid, velocity of, 141
maximum recommended, 148
Thorngren, John T., maximum velocity method, 139
tubes
boundary conditions of continuous beams, 142
circle of contact, diameter of, 143
colliding of, 139
deflection oI, 141, 154
effective tube wall, 141
fatiguing of, 139
fluid force causing baffle impingement, 143
force coefficient, 146
fundamental natural frequency of, 146
natural frequency of, (Blevins formulation), 146,
154
shear of against baffles, 143
turbulence
deflection, root-mean-square, 145
joint efficiency,
145
pressure distribution for, 144- 145
response spectra, 145
Wambsganss and Chen relation, 146
Venturi effect, 144
von Karman equation, 141
vortex shedding, 139, 144
compared to turbulence, 146
compared to whirling, 146
resonant frequency of, 141
vortex street, limits of, 141
vortices, breaking-up of, 141
whirling, 144
compared to turbulence, 146
compared to vortex shedding, 146
critical velocity, cxiteria of, 147
whirling parameter, for tube arrays, 148
Tubular Exchanger Manufacturing Association.
TEMA.
Vane pumps, 37
Velocity heads (K-values), 66-68,
See
7 4, 88-89, 90-9
Vibration
ovaling. Se€ Stack design.
Rayleigh method for, 8. Also see Volume l.
Viscosity
absolute viscosity, 68
conversion to kinematic, 68
centrifugal pumps, effect on, 68, 70-72
converting centipose to SSU units, 74
kinematic,68
Vortex shedding, 8-9, 139, l4l,144, 146
Welding Research Council. See WRC.
WRC 107 Standard, 169
WRC 297 Standard, 169
1