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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
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Design
Pmctss
Svsterns
2
Heat Exchangers
o
Equipnent
r
Bins,
Silos,
Stacks
right @
1986
by Gulf Publishing
Company,
Houston, Texas.
righrs
reserved.
Printed in the United
States
of America.
This
or
parts
thereof,
may not
be reproduced
in
any
form without
the
publisher.
ol
Congress Calaloging-in-Publicalion
Data
A. Keith.
design of
process
systems.
bibliographies
and indexes.
v. l.
Piping
and
pressure
vessels-v. 2. Shell-and-tube
exchangers;
rotating equipment;
bins, silos, stacks.
Ch€mical
plants
Design and construction.
1986 660.2
',
81
O.ATant
-562-9
(v
1)
(}ET2l)1-565-3
(v.
2)
85-22005
iv
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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.
Example
5-l: Granule
Bin
Design
for Roofing
Plant, 11
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
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
Chapter
6
Rotating
Equipment ......31
Pumps, 31
Centrifugal
Pumps.
Hydraulic
Requirements
of
Centrifugal Pumps. Positive Displacement
Pumps.
Pressure Protection
for
Positive
Displacement Pumps.
Compressors,43
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
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.
Example
6-2: Positive Displacement Pump
Design,74
Suction
Line
Pressure
Drop.
K-Values.
A
word
About
Priming.
Example
6-3: Centrifugal
Compressor Selection,
Example 6-4: Installing a Compressor
at
Elevation,
34
Selecting the Reciprocating Compressor.
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
79
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Chapter
7
The Mechanical
Design
of Shell-and-Tube Heat
Exchangers
......
99
Fundamentals
of
Shell-and-Tube
Heat
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.
Tube Vibrations,
139
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
Tube-Side
Film
Coefficient.
Shell-Side
Film
Coefficient.
Shell-Sid€ Pressure
Drop. TUbe
Metal
Temperature.
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.
Example 7-5:
Zero
LMTD
Exchanger,
165
Notation,
165
References, 166
Chapter
8
External Loadings
on
Shell Structures
.... 169
Lifting Lug Design,
170
Example
8-1:
Lifting
Lug Design
and Location, 170
Notation,
175
References,
176
Appendix
A
Partial
Volumes
and Pressure
Vessel
Cafcufations
....,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
Appendix B
National Wind Design Standards
.........
187
Criteria for
Determining
Wind
Speed,
187
Wind
Speed
Relationships,
188
ANSI
A58.1-1982 Wind
Categories,
189
Appendix G
Properties
ot
Pipe
. . .....
193
Insulation Weight Factors,
200
Weights
of
Piping
Materials,
201
Appendix
D
Conversion
Factors
.
.....225
Alphabetical
Conversion
Factors, 226
Synchronous
Speeds, 233
Temperature
Conversion, 234
Altitude
and Atmospheric Pressures,
235
Pressure
Conversion
Chart,
236
vl
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The engineer
who
understands
the impact
of
process
design decisions
on mechanical design details
is in a
po-
sition 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?
In
this two-volume
work
on Mechanical
Design
of
Process
Systems, A. K.
Escoe has
performed
a monu-
mental
service
for
mechanical design engineers
and
chemical
process
engineers
alike.
The
information is
presented
in
such a
manner that even the
neophyte
engi-
neer can
grasp its
full
value.
The author
has
produced
an
in-depth review of the way
in which
process
design spec-
ifications
are
interpreted into
precise
equipment designs.
Perhaps most
valuable of all
are the extensiv
e worked ex-
amples 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-
t'oreword
chanics and
the
engineering
mechanics
of
piping
(Vol-
ume
1).
The chapter
on heat transfer
in
vessels and
piping
il-
lustrates
lucidly
the
interrelationship between
process
and
mechanical design. Every engineer
working with
in-
dustrial
process
systems
will
benefit from
reading this
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, spe-
cific
cogeneration processes,
turbines,
and detailed
pip-
ing
dynamics.
Still, at this
writing
these
two
volumes
comprise
an
outstanding
practical
reference
for
chemical and
me-
chanical engineers
and a detailed instructional manual
for
students.
I recommend these volumes
highly
for each design
en-
gineer's professional
library.
John
J.
McKexa, Ph.D.
,
PE.
Joe C.
Waher Professor
of
Chemical
Engineering
Universitv of kxas,
Austin
vtl
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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
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This book's
purpose
is
to show how to apply mechani-
cal
engineering concepts
to
process
system
design. Pro-
cess 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
pro-
cess
systems
now
in
operation.
While
practicality
is
probably
its key
asset,
this
second
volume
contains a unique collection of valuable informa-
tion,
such as a
practical
approach to bin and silo
design
as
well
as
practical
methods
of
controlling wind vibra-
tions of stacks using vortex
strakes; new
information
on
nozzle loadings
on
compressors and turbines; compre-
hensive
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 vibra-
tion;
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
rea-
sons
of
time and space the
dynamic analyses of seismic
response spectra
and an extensive discussion
on
pulsa-
tion
response
spectra in
piping
induced by acoustic
pul-
sation
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 re-
placement
of
any
accepted code or slandard. The reader
is
strongly encouraged
to consult and
be knowledgeable
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 stan-
dard 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-
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.
The
reader's academic
level is
assumed
to
be a bache-
lor of
science
degree in mechanical engineering, but
en-
gineers
with bachelor of science
degrees in
civil,
chemi-
cal,
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 applica-
tion
of
mechanical
engineering to
process
systems. Pro-
fessors
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 intro-
ductory 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 of-
ten the by-product of experience, and while both
are
es-
sential to sound
engineering
practice,
neither
can
be
Iearned from books alone. It is one
ofthis book's
soals
to
tx
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The
engineering mechanics
of
bins
and silos
differ
from the
mechanics of
oressure
vessels
because solids
behave
differently from liquids and
gases,
both in stor-
age 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
ap-
proaches
for solving vortex
shedding around stacks
than
around
towers,
because
stacks rarely have as many at-
tached structures.
SILO AND
BIN
DESIGN
The mechanics of
solid flow theory is a fairly compli-
cated
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
phe-
nomenon,
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 Johan-
son
[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
effi-
cient 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.
The Engineering
Mechanics of
Bins,
Silos,
and
Stacks
4.
Dead
storage-residual build-up
of
solids
caused
by
the
inability
to exit bin.
5. Segregation-a
heterogenous
solid
of
varying spe-
cific
gravity
in which
the
lighter
particles
exit the
bin
first,
leaving
behind the heavier
particles.
6. Degradation-the
chemical change of solids caused
by remaining in storge
too long.
Spoilage,
caking,
and oxidation are
some examples.
Solids
behave
differently
from
gases
or
liquids
be-
cause they can transfer shear stresses without movement,
and
because of their cohesive strength, they can retain
their shape under
load. The
shear stress transferred
be-
tween the
solid
and
the channel
walls
is
a
function of
the
normal
pressure,
w. The relationship
between
the two is
as
follows:
S
1t
-
tdttrg
--
w
(5-l)
where
{'
:
kinematic
angle of friction between
the solid
and the bin wall
p
:
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
appli-
cations 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
and the
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.
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The Engineering Mechanics of Bins.
Silos and Stacks
arch
lhickness,
T
Figure 5-2. Formatjon
of an
arch.
FR€E
SIJifACE
srREss
{q)
Mass
flow characteristics
1. Material
segregation
problems
are minimized
2.
Fine
Dowders
deaerate
3. Material
flows
unilormly
4.
Smooth steep
hopper
Figure
5-18.
Ideal
flow of
solids-mass flow.
The
strength of
the solid material
is the criterion
for
flow
behavior
in bins. Failure
conditions
ofthe solid oar-
ticles
can result in
arching. no flow. piping
(a
hole
formed
in
the solid formation),
or
limited flow Figure
5-2
illustrates
an arch formed
by
a
solid in
a
hopper.
The
failure
of the arch will
occur when
the major compres-
sive
stress,
R
equals
the unconfined yield
strength, fc. lii)
prevent
arching, the
critical
dimension,
B, ofthe
hopper
opemng
must
De
sTiEss
(L)
sti€ss
t
laLl)
CALCUIATEO
S-IRESS
I
IALL
)
Figure 5-3.
Stress
distributions along
hopper wall
[1].
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 criti-
cal diameter at
which
the
pipe
is unstable is
given
by the
followine:
D
>
4\+
^l
(5-3)
_f-lJ>
'
7(1
+
m)
where
m
:
0 for slot opening
of width
B
m
:
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 ra-
dial
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 func-
tions
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
(5-2)
or
:
IBQ
(54)
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Mechanical
Desisn
of
Process Svstems
z.^
E
=
-to
Figure 5-4.
The criteria
for mass
flow
when
0' < 30".
where
Q
=
2sin0
(s-5)
d
:
angle
of
hopper
slope
o
=
computed stress
function
along
the
wall
Combining
Equations
5-2
and
5-5 we obtain
1>
(r
+
-)e
(s-6)
t"
where
o1lf"
:
flow factor of solid
The critical flow factor for arching in channels
(ff)
is
o(1
+
sin
6)
represented by
n:
(?J".-*,
:
(1
+
m)Q
(s-'t)
'e_
F
I
o
z
igures
5-6-5-9
show the
values
of
ff
for
straight-
walled 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
(5-8)
300
40 50
60
70
ANGLE OF Ii{TERNAL
FRICTON IDEGREESI,Q
Figure
5-5.
Piping factor,
iD,
versus angle of internal friction,
6.
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EFFECIIVE
AI{GLE
OF Ti|cNOfl IOEGf,EESI,
6
Figure
5-6.
Wall
friction
angle,
@',
versus
effective
angle
of
friction,6.
Figure
5-8. Wall friction
angle,
d',
versus
effective angle of
friction,6.
The
Engineering Mechanics of Bins, Silos and
Stacks
2O3.6070
E.rECrrE
^*GLE
OF
FitcT|Ox
roEci€Est,6
Figure 5-7.
Wall
friction angle,
{',
versus
effective
angle
friction,0.
EFFECTTVE
AXCTE Of FFICTION,6
Figure 5-9. Wall
friction
angle,
d',
versus effective angle
friction, d.
5
6ro
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I
t-
(,
=
rl
E
F
(',I
ot
JI
lrJ
I
>l
o
trj
=
-
o
()
z,
=
Mechanical
Design
of Process Systems
--------)-
coNsoLroaTr
G
PRESSURE,
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
of
the
flow of
solid
particles.
This
pressure
is reduced
internally
somewhat
because
as the solid
particles
de-
scend through the
hopper,
a vacuum in the void between
particles
develops
and
produces
a
negative
gauge pres-
sure.
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 hydro-
static
pressure
for
a
liquid head equivalent to the height
ofthe
solid in the bin. Thus,
designing solid bins for
hy-
drostatic 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,
l6
P*:7{'y)*{H)ft
where
"y
:
bulk density of the solid, lb/ft3
H
:
height that solid is stored in bin, ft
(5-
10)
(+)
"
o*o
\r./
.,,,:(,1)",.""=o*o
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
in-
crease
in flow
pressure
because
of
change
in momentum
Table 5-2
Critical
Hopper Dimensions
tor
Material With Flow
Properties
Shown in Figure 5-12
[11
Type
Critical
width
ot
a
slot
opening
lor
arching, ft
Freshly Stored
for
stored
24
hr
Flat
bottom or nonmass
flow
bins
Stainless
lined
hopper
(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
bins
Stainless
lined
conical
hopper
(0'
:
1s",0'
:27")
Mild
steel conical
hopper
(0'
:
15",
d'
:
35')
Critical dimensions
bins
5.6
7.7
+
Dictated only by
porticle
size
or
dynamic conditions.
+*
mese ralues are
the
same
as
the
flat
botrom bin
values because the
mid
steel
conical hopper
when
6' =
35" is too
rough to
proride
flor"'along
the
walls of the cone
when
0'
:
15"
(5-e)
0.2
0*
0,*
1.0
o.4
0.6
2.0
0.9
0.4
0*
0.4*
*
2.O**
CR
ITICAL
STREI{GTH
RoP(e$i{L
.
lrl
<=
ori
F
.I'
-t
aE
()C
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The
internal pressure
in
Equation
5-10
can
be in-
crease.d
by
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-
comes
The Engineering
Mechanics
of Bins,
Silos and Stacks
P.,":77H+Pu;
where
P";.:
air
pressure,
psig
60
e,
z
E
t40
=
o
o--
z
(s-1r
)
The
use of
pneumatic
air in
bins is
often
desirable
and
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'
?
1oo
3
Figure
5.12. Typical
bulk
solid
flow properties
used
to
deter-
mine
critical
dimensions
for piping
and
arching.
coNsoltDAT|NG
PRESSUAE,
q,
Lb/Fr2
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Mechanical Desisn
of
Process Svstems
q,
PSI
+
0 Psl
bin fu
_
bin
haf tu
-
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.
F
I
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 dy-
namic magnification
factor, and
(2)
the solution
to
prob-
lems
induced
by vortex
shedding
are different.
Both of
these
factors are
a
result of stacks
having
simpler
geome-
trres.
The
simpler
geometry
of
the
stack
works
for
and
against
the engineer.
The
positive
aspect comes
as a
re-
sult
of the methods
used
to
break vortex shedding-vor-
tex
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-in-
duced
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.
In
stacks,
lining
is
often
used
where high temperatures
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
gen-
erally
pressure vessel
quality
and require
heat treatment,
such
as
the
Cr-Mo steels described
in ASTM
specifica-
tions 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
con-
servative
values of the logarithmic
decrement
and dy-
namic 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
vor-
tex shedding
caused
by
air
currents, the
elastic strain en-
FUNNEL FLOW
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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
plane
of the
ring).
4.
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
fre-
quencies
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.
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
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 cir-
cular cross
sections. The natural
frequency
of
the
ring
is
siven as
,
_
I
I
Etn2(n2
-
l),
lo5
"
-
t
tpAr6t+
I
+
/t
(s-12)
The lowest
flexural mode
exists when
n
:
2 and
Eoua-
tion
5-12 reduces
to
The Engineering
Mechanics
of Bins,
Silos and Stacks
9
These relationships
were
formulated
by the
great
pio-
neers 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 alter-
nately 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
-
0.2v
'D
Now since f
:2f,
we solve
for
V
and obtain
,,
60f,D
(4-l0l)
(s-14)
"
4.4O9t
E
f'
n=l
n=2
Figure
5-14.
Stack
mode
shapes.
in which
s: the Strouhal
number
(is
equal to 0.2 for
a
wide
range of Reynolds
numbers).
The
value
of V.
is
the
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
tunnel tests.
Now we
come to the
most
practical
aspect of stack
de-
sign-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
fre-
quency,
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
-
(7
x
l0
)v:DrH,
(s-15)
where V"
:
"rnr"u,
,"r"0
velocity (Equation
5-14), fpm
D
=
internal
stack
diameter
at
elevation
under
investigation,
ft
H,
:
stiffening
ring
spacing,
ft
o,
:
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
de-
sirable with
stacks
of
several
diameters.
However,
with
stacks
of
constant
or tapering
cross
section
the
use
of
vortex
strakes
is
becoming
increasingly popular.
(5-
l3)
s
l \
l):
j-r
i,
t
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10
Mechanical Design of Process Systems
Helical Vortex
B?eaker
Strakes
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 cy-
lindrical
towers
has
shown
remarkable results. The
strakes' function
is
to
break up
vortices
such that
flex-
ural frequency
modes are
quickly
dampened.
It is signif-
icant 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:
0.09D<w<0.10D
where D
:
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
a stack.
The helix angle,
{,
should
fall
into the following
range:
54'<d<58"
There are always three strakes
per
stack to counter the
alternate
formation
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
segments, depending
on
the
length of the stack. The
overall
length of the individual strakes that is divided
up
is determined by
S:[(?rD)2+L2]oj
(5-16)
where
D
=
OD
of
stack,
ft
L
:
height of tower
portion
straked
(V:
of
total stack
height),
ft
The number
"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:
a2a2 + 8
(5-17)
. D-
wherea:
--,
lt
z
,L
2rw
r,r
:
number
of
revolutions around
stack
cylinder
made
by
helical strake
(usually
<o
:
1)
An alternative formula, developed
by Dr. Frank Mor-
gan,
and
two
to three
percent
in error of Equation 5-17,
IS
XW
1-)\
S, interior
arc Iensth
of helix
\rhefe A
=
_
:
------:--------:
S" exterior
arc length of helix
aa2
0.090s
W<0.1D
d
=
Helix angle
54o
<C358'
(s-18)
(5-le)
T
L
I
|-,D
Figure 5-15. Cylindrical
strake helix
geometry.
The value Si
is
determined
by using the outside diame-
ter 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].
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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 com-
posed
of two
clamps,
each 45'
from
the
plane
perpendic-
ular
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
Twelve granule
bins
are
to be
designed
to
provide
granules
for the
manufacture
of
roofing
shingles
of Ex-
ample
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 lim-
its
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.
The Engineering
Mechanics
of Bins,
Silos and
Stacks 1t
As seen
in Figure
5-13b,
the minimum
hopper
angle
for
mass flow
is
0
:37.74'1"
From Figure
5-4,
6'
:
l0
From Figure
5-5,
<D
=
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)
zslnd
From
Figure
5-6,
ff
:
1.6
ff=(l+m)Q
Q:
=
=
0.80
).
or
:
7BQ
1
=
90 lb/ft3
B
:
0.667
ft
o1
:
(90)(0.667)(0.80)
:
43.6, tbrtU
From Figure
5-12,
f"
:
s0 lb/fC
(5-5)
(s-7)
Figure
5-17.
Clamping
each
strip
on 45
degree
offsets
and
hot
forming
with
torch
obtains
desired
geometry.
igure
5-16.
Strake fabrication
detail.
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12
Mechanical Design of Process Systems
l--j*---l
t;;-
lr\l
tl \ I
/\
,.T
;l
1
E
Since 0.278
ft
<
0.667
ft
=
8
in.
archins
will
not
form in
the bin
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 mak-
ing the bin
walls
pressurized
components.
For simplicity
and
ease
in calculations, the solid
pres-
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
Thus, the critical arching
dimension is
f{o
B=
'
-
-'
:0.278
ft
r(l
+ m)
(90X2)
:
v{bt
uno
F
:
orPb
at x
=
0, z
:
0
=
*1 o'
unoF
=
orPbatx
=
+a.z
=
b
'
ifu > borz:0.4bif a'( b
Figure 5-18. Granule bin
silo.
(5-2)
(5-20)
(5-21)
In this
problem,
a
:
12.625
ft
and b
=
4.00
ft.
The
pressure
at the bottom
of
the
plate
is
P
:
eo*
(n.6zs)ttffi
:
z,ur
p,r
a 4.000
b
12.625
From Figure 5-19
we obtain
the
following:
*r
:0.030
Vz
=
0.032
The maximum
stress
occurs
at
the
bottom side at x
=
0 and
z:0
_
_
vrPb2
/<.)n\
b
:
12.625
ft:
151.50 in.
For 5.4-516 Gr. 55,
o4
:
13,700
psi.
Solving for t
in
Equation 5-20
we have
/v,pu'\o'
r:
l__-l
here Vr,
V2, 01, and 02 are
in
Figure 5-19
F
:
reaction
force exerted on
the
plate
edge normal to the
plate surface,
lb/in.
P
:
load
per
unit area,
psi
t
:
plate thickness, in.
ko.o:o)(z.ssr)
.\
(rsr.sofin.'lo,
1:l
tn'
|
:0.627
in.
I
r:,eoo
--lb-
I
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The Engineering Mechanics
of Bins,
Silos and Stacks
Deflections of bin
plate"
b
12.625
a 4.O
At
x
=
0,
z
:b
=
12.625
ft
(0.00020)(7.891)
',Jb-
1+t.oy
in.,
D
:
flexural rigidity
of
plate
Et3
12(1
-
v'?)
o
16
13
The
stress at mid-plane
is
v,Pb2
""
t2
z
:
0.4b,
P
:
4.734 psi
,
_
lro.orzlr+.rl+rr
rs
r.
sor'lo
'
=
0.502 in.
Selecting
SA-516 Gr.
70, oat: 17,500
.
_
[ro.o:otr
z. ae1)fl51.50),lo
5
I
--
0.557 in. at bottom
edge
,
_lto.ozzx+.tt+xrsr.sor,lo'
_
=
0.446 in. ar z
=
5.050 fr
Dlb
ln.
I
Figure
5-19.
Rectangular
flat
plate
solutions.
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14
Mechanical Design of
Process
Systems
D
(30.0
>
106x0.562)r
:48:
.b49.25J
12(1
-
0.311
in
which,
w
:7.4565
x
10-o in.
-b
Atx
=
u,z
=
t
w
_
(0.004x7.891)(48.0),
481
,649.253
w
=
1.4913
x
l0-1 in.
For a
e/ro-in.
plate
deflections are negligible and
no
stiff-
eners are
required
for
this
plate
thickness.
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
supported.
The
stress
in
the
plate
is
given
by the follow-
ing:
't,
Ph2
ob
=
'l:-:
and
F
-
QrPb at x
=
0.
z
=
0
\5-22)
t-
Itr
^Ph2
"
:
*,5o'
and
F
-
02Pb ur *
:
tJ.
z'0.4b
(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.
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The Engineering Mechanics
of Bins,
Silos and Stacks 15
F
:
reaction force
exerted on the
plate
edge normal to the
plate
surface,
lb/in.
P
:
load
per
unit area,
psi
t:
plate
thickness, in.
First
Stiffener
Consider b
:8.0
ft,
a/b
:
0.50. From Figure
5-20
we
obtain Vr
=
0.064.
Thus,
from
Equation
5-22
we have
_
_
(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 :
2.0
ft,
o-"-
:
11,475.865
psi
<
allowable
=
17,500 psi
By
a
process
of iteration
we
obtain
a
value
ofb
:
2 ft
8
in.,
in which
o^,
:
17,364.2?9
psi
< 17,500
psi
allowable
Thus, we
place
the first stiffener 2
ft
8
in. above
the
bot-
tom
seam,
Second Stiffener
At 2
ft 8 in. the maximum
pressure
exerted on the bin
wall is
rh / rf':
\
P
-
e0; 2.62s
-
2.667\
ft
ln;-l
=
6.224
psi
Consider b
=
4.0
ft.
a/b
:
1.0 in which
Vr
:
0.192 from
Figure
5-19. Thus,
o-",
='o'n',)lu:?.', '08)2
:
19.s26.e
psi
>
17.500
psi
(0.
141)
By a
process
of
iteration we
arrive at b
=
3
ft
I
in.
in
which
o-""
:
17,502
psi
Third
Stiffener
At the new
elevation, 6.167 ft
above the bottom
seam,
we obtain
the maximum
pressure
exerted
on the
wall.
rhI
P
=
90--l
f
2.625
-
(2.667
-
3.5O)
fcl
:
4.036
psi
-(rq)
The top
portion
ofthe
bin
is
now
a
plate
with
three sides
fixed and
the
top edge free.
Thus, Equations 5-20
and
5-21
hold,
using Figure 5-18. By iteration we
obtain
b
:
6.458 ft,
P
-
4.036
psi,
a/b
=
0.619,
Vr
:0.091
and
o^":15,643
psi
o
17,500 psi
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
/'-TR
I
lt I
Pt l.
| | tco
fi l'
,H1 |
/r
)ll
\q--7891
psi
'Yr
=
0.383
R
:
.yrpb
:
(.383)(7.891X32.0)
:96.712lbhn.
:
w
With
plate pushing
uniformly
on stiffener,
the
latter
will
be analyzed
as
a fixed
end beam
with
uniform loading.
v
u,
ffi
UV
I
STIFFENER
96.712
lb/in
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16
Mechanical
Design
of
Process Systems
w/
M.*:
^-;
W=wf
24
w
:
(96.712X48)
:
4,642.18
tb
M-^.
-
(4'92
181x48
0)
=
9.284.36r
in.-rb
24
:
773.697
ft-Ib
Mc
I
For design
purposes
select
a design
stress
of o
:
17,000
psi.
With
a factor
of safety of 2. This
would
give
a
yield
stress
of
34,000
psi,
which
is conservative.
I:M"
g
Select
a
3-in.
x2-h.
a
t/+-in.
thick,
,
'
(9,284.361)
inlb(.49)
in.
:
0.268 in.a
17,000
lb/in.'?
I of .zr
:0.39
in.a
Therefore,
3-in.
x
2-in.
><
tla-in.
4
is sufficient
Second
Stiffener
Design
P
=
6.224
psi
a:
4ft-}in.;b
:
3 tt-6
in.; a/b
= :
t.t+l
3.5
By
linear interpolation,
1t
:9.349
R:
(0.340)(6.224)
lbl\n.2(42.0)
in.
:
88.879
lb/in.
pr-".
=
{:
w
=
(88.879)
lb/in.(4E.0)
rn.
w
:
4
,266
.192 lb
M
-
@
'266
'1921(48
'ol
=
Rs1?.3E4in.-rb
A-","".
I:M"
q
Select a
2rl2-in.
x
z-in.
x
tl4-in.
4
,
_
(8,532.384)
in.Jb
(0.54)
in.
_
.,
".,,
,-
o
rtun
-
l?soo
rbfinj
I
:
0.37
in.a
Therefore,
Ztlz-in.
x
2-in.
x
t/+-in.
4
is sufficient
Stiffener at
Junction
Point
ot
Bin
P
Hoop
Force
=
-
yD
From
data
provided
by the
client,
P
=
400 lb/ft'z at
junc-
tion
point.
Using a
factor of 7 we have
P
=
7(a00)
=
2,800
lb/ft2
P
:
2,800 rb/rt
(r-lq)
=
re.zt44
psi
UseP
=
20
psi
For bottom
plate,
a:4
ft-0 in.: b:2 ft-8
in., a/b
=
1.500
rr
:
0'383
R
:
(0.383X20.0X32.0)
=
245.
r20 lbl in.
w,
M.*:
=-:
w
=
(245.t20X48.0)
=
11.765.760
Ib
1.+
M
_
(
I 1.765.760X48)
:
1"t
slj.520
injb
A_.-'--
Select
a 3rl2 in.
x
3
in.
x
tla
in.
4
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.
x
r/+-in.
r
is sufficient
with
long side
facing
bin
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:
55.92% of minimum yield
:
30.36% of ultimate
yield
The Engineering
Mechanics of Bins,
Silos and
Stacks
0. | 825(6.31 3X50.928)'
-
(0.438)2
'-'----'''
Therefore, use 716
in.
f,
for bottom
plates
Bending Stress in Bottom Portion
From
previous
information,
P
=
6.313
psi
on triangular plate
A
:
area
of
triangte
=
Ia'20'lro.z*>
=
t0.40
ftj
-
\21
ot A
:
1,497
.589 in.2
=
F
:
(6.3 13)
lb/in.,(I,497.589)
in.2
:
9,454.279
lb
at3
:
(4.244)(12)13
:
16.916
in.
M,
:
F(a/3)
:
160,495.84
in.-lb
Mc
I
thJ r/{O Otl\3
r:-=-:[,007.49Er
l,/.
Iz
17
Bottom Portion
of Bin
Bottom
portion
of bin will be approximated with
four
tdangular
plates
welded together,
as shown
in
Figure
5-18.
Pr
=
7.891 lb/in.2
pz
:
e0 lb/n3(16.50 ft)
[-]q144
:
10.313
psi
At an
angle
ot90o-0:37.7474,
P
:
10.313
sin 37 .747"
=
6.313
psi
By linear interpolation,
B'
:9.3659
o:41
=o.rszs
2
0.1825Pa'z
o=
,,
,
qan
=
l/,JWPSl
m.l8r5x6.rl3x5o.%y
=
u.4rJ
rn.
\l
17.s00
with
t:3/E
in.,
,'
_
0.1825(6.113)(50.928),
=
,t ,4q s?? nci
" - (0it5,- - '''-"
-J-
YJ'
For
SA-516 Gr. 70, minimum
yield
:
38,000
psi
11
*ll
->l
I
Ptt
ll
-tl
ll
--'l'
Y
CROSS
SECTION CUT AT
MIDPLANE
OF
TEIANGLE
--tt
t
La-
t-ll
It-
It;
-il
1$
rJ
-_tt
%
yreld
:
%
yield,
:
21249.532
38,000
21249.532
70,000
with
rhe
in.
f,
,
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18 Mechanical Design
of
Process Systems
,^
50.928
atJ:_=lD.y/orn.
3
(1r,007.498X
,
_
(160.495.84)
in.-lb
(16.976r
in.
_
.,.,,,,
'
-
(r
1,00?/98xr?J00)
i"rlb/i"r
-
"
"'-'
Therefore,
tlrc
in.
t_
is
sufficient.
Vessel
Supports
Consider all trusses as
pin
connected.
Side
Truss
End Truss
For three horizontal plates,
(r2.62s
itx8.0 rt1
=
1 30-1f
-
z,3ts.22JIb
'2
or
for
three
plates,
wt
:
6,945.669 lb
For simplicity and
to
keep things conservative, let us
analyze the
internal
plate
to determine if we need any
supports on
inside
of
structure.
For two outside
plates,
t
:
3/8
in.;
wt
:
(12.625)(8.0)(0.375)(1,14)(.283)
:
1,543.482 Ib
wto'.r
:
3,086.964 lb
For
two
side plates,
Wtt"d
:
2(3,086.964)
=
6,173.9r,
tO
Under
Bins-4
Triangular Plates
For each bin,
/a
qor
\
A
-
4 l-
'"'l
A.244\tt44\
=
5.990.355
in.1 of metal
\21
wt of each bin
-
(5.990.355)(.283)
=
1.695.270 lb
(
160,495.84)(16.976).
o"u
:
17,500
psi
m.
weighr of internal load
:
(t20.24)
lz'z+o
v\
'on'I
,on
/
:
269,337 .60 tb
Weight
of
steel
(Wt):
(12.625
ftx16.0 ftXt)
:
ro*r
:
0.283 lb/in.3
wt:
(16,362.0)(0.283)
(1s
1.s0)(192)(0.s63)
16,362.0 in.3
:
4,630.446 tb
i:\\:-j
w rblfr
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Number
of Bins
:
8
Therefore,
Wtrorur
:
13,562.164
lb
Empty weight
of structure
:
4,630.446
lb
+
6,945.669 lb
+
3,086.964
lb
+
6,173.928
lb
+
13,562.164 tb
:
34
,399
.r7
|
Ib
Wt of
granules
=
269,337
.60 lt:
Total
wt
loaded
:
303,'736.7711b
Total
number
of internal plates
:
4
Total
length
:
4.0 ft
w
-
303'739 771
..
75.934.r93
lb/rt
4.0
:
911,210.313
lb/in.
Considering
the
plate
in
Figure
5-18,
rur
Y,
w
.
(9
.210.313r
lb
92.1 ,n.
E
in.
:
174,952,380.1
lb
M -
(174952'380
1)(192)
=
4
rqx
x\7
r)l,n
-rh
8"
Therefore,
bin
must have
internal
supports
under bot-
aom.
Number
of vertical
supports
=
9
=
R
:
303
'73-6'771
9
=
33,748.530
tb
Number
of
ioint
suDDorts
:
9
tl
tol 716 ?71
F
:
--"'
_-:j____:
:
20,249.118 lb
IJ
The
Engineering Mechanics
of
Bins.
Silos and
Sacks
19
The frame structure
shown in Fieure
5-18 is analvzed
as continuous beams in
the longitudinal
and lateral direc-
tions.
FoR EACH
spAN
wL:
lzsss.+rglli
[+.olrt
:
so,g73.ozo
ro
RA
:
0.393 wt
=
0.393(30,373.676)
=
11,936.3tt
,O
RB:
Ll43
wf:
1. 143(30,373
.676)
=
34,117.rt
b
Rc
:
0.928
wf
:
0.928(30,373.676)
:
28,186.77t
tb
Ro
:
1.143
wf:
1.143(30,373.676)
:34,717.rt
rO
Solr ing
for
reacrion\ in
lateral
plate
FOR
EACH SPAN
WL= 30.373.676
lb
v.*
:
0.607(30,373.676)
tb
V-*
:
18,436.821
lb
RB
=;
(10.373.676X2)
=
37,967.0q5
lb
6
Ra
=
ft.
=
11,390.129
lb
Design each
support
column
for
37,967.095Ib
=
38,000 lb
srde
saructure
The
bin
structural
detail is
shown
in Figure
5-21.
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20 Mechanical
Design
of
Process
Systems
BIN
JUNCTURE
DEIAIL
STIFFENER DETAIL
EXAIIPLE
5-2:
HIGH.PBESSURE
FLARE
STACK
DESIGN
A
high-pressure
flare
stack shown
in
Figure
5-22 is
to
be
designed and construcred
to the
following
specifica-
trons:
Base diameter
:
l0 ft
Height from bottom
of steel
base
to tip of
flare stack
:
200
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
Figuie 5-21. Bin
struclural
frame detail.
Effectlve
Diameters
Add
12
in. for
platforms
and
12
in. for
ladders.
Add
4-2-in. d
lines.
2-in.
g
dia. line
:
2.3'75
in.-Add
t/z
in.
insulation
D
:
(3.375X4)
:
13.50 in.
D"^"".,
=
2(12)
+
13.50
:
37.50 in.
De
:
42
+
37.50
:
79.50
in.
DB
:
90
+
37.50
=
127.50 in.
Dc
:
120
+
37.50
:
157.50
in.
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Height Wind Pressure
(fD
P,
(rb/ftr)
w
=
B
x De x
Pz
lb/tt
The
Engineering Mechanics
of
Bins,
Silos and
Stack
Wind
Load
Moment
(5,270.98X110.5
+
2.5)
+
(2,862.0)
x
(90.0
+
2.5)
+
(10,404.0)(65.5
+
2.5)
+
(13,604.25)(24.2s
+
2.5)
0-30
26
:
to6)( f)tz6):20415
:
ro.olffit:3):25e.88
:
toor(lle)o
:2ee.2s
:
too(l#J(44):34650
:
,0.u,(]?Za)r*)
:
28o.so
/r
r:
so\
=
t0.6tl'-'""1t48t =
306.00
\
12
/
:
ro.orfifJt+t):
reo.8o
:
<o.orit#)or)
=
202.'73
30-40 33
866.25
40-74 38
74-76.5
44
'16.5-125
44
125
159
48
159-t74
48
174-200
51
Wind Load
s.270.98
2,862.00
r0,404.00
Moment
(s,270.98)(13.0
+ .0) +
-0)
+-
o,404
(5,270.98)(28.0
+
x
(7.5
+
34.0)
+
llrl
\21
44 ft-lb
76 ft-lb
(5,270.98)(62.0
+
48.5)
+
(2,862.0)
x
(41.5
+ 48.s)
+
(10,404.0x17.0
+
48.5)
/an s\
+
(13.604.25)
|
-'l
=
1.851.388.35 fr-lb
\2l
l5
34
(1
(2,
(')
.0)
862.00)
169,052.
86rn)
I34.01
\)
I
622,44r.
Figure
5-22.
High-pressure
flare stack;
unless otherwise
indi-
cated,
all dimensions in feet,
design wind
speed
:
100 mph.
51 PSF
48
PSF
__
159
_t
-l
1.
44
PSF
,rO-l
30_
38
PSF
33
PSF
26 PSr
t3,6U.25
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Wind Load
22
Mechanical
Design
of
Process Systems
(5,270.98)(113.0
+
34.0)
+
(2,862.0)
x
(92.5
+
34.0)
+
(10,404.0X68.0
+
34.0)
+
(13,604.25)(26.'75
+
34.0)
+
(866.25)
-
.-.
-
/:+.0\
x
.25 +
34)
+
00.174.5)
l:-jj:
I
\'2 I
:
3,228,045.06
ft-lb
2,598.80
(5,270.98X147.0
+
10.0)
+
(2,862.0)
x
(126.50
+
10.0) +
(10,404.0)(
102.0
+
r0.0)
+
(r3
,6O4.2s)(60.7
5
+
10.0) +
(866.25)
x
(35.25
+
10.0) +
(10,174.5)
/,,r.0\
x
(r7.0
+ t0.0) r
(2.s98.80)
l+-l
\2
t
:3,672,858.86
6,142.50
(5,270.98X157.0
+ 30.0)
+
(2,862.0)
x
(136.50
+
30.0)
+
(10,404.0X112.0
+
30.0)
+
(13,6M.25)(70.7
5
+ 30.0)
+
(866.25)
x
(45.25
+
30.0)
+
(10,174.5)(27.0
+
30.0)
+
(2,598.80)(s.0
+ 30.0)
+
(6,142.50)
For
Section
D
*
(0'875
-
0 125)
:
o.oo6
>
0.00425
120
_
(0.56)(0.006x29.0
x
109
""
tl
+
(0.004x29.0
x
109(30,000)]
:
20,02i.918
psi
For Section C
:
d
(0750
-
o l25)
:
o.oo5
>
o.oo425
120
(0.56X0.005)(29.0
x
109
li
+ 0.004(29.0
x
109/(30,000)l
:
16,684.932
psi
For Section
B
13
d
o,
t"_(0.625-0.125)
d
90.00
o.
=
20,021.918
psi
For Section
A
:0.006
:
d
(0.500
-
0.12s)
=
0.009
o.
=
30.032.877
psi
Section
Weights-Uncorroded
Weight
Section A
i3o'oJ
:
s,
r:t,+rr.zo rt-ru
Allowable Shell
Buckling
Stress
0.56 t"
E
'.E:29
x
'
d
(1
+ 0.004
E/y)
'
''
,[l/€)'-litt\'l',
r
=
(0.2833)
j:
(37.0)(
12)
'n.
'
[\,
/ \2 I
)
-
8,199.69
lb
Section B
wr
-
(02813)
{
rzoo,rz,'
"
[(T)'
- (*,
)']'"'
y
:
30,000
psi
106
psi;
=
45,340.61
lb
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Section
C
The Engineering Mechanics
of
Bins,
Silos and Sacks
Section
A
wt
=
(0.2833)
--ll(30.0)(r2)
in.
"
[(9'
- (r94,)]'"
:
33,397
.r9
tb
Total
wt
:
128,966.580 lb
Required
t
Thickness
16
D" Mr
r(D"'?+Dr'?)@"+D)oE
r(D. + D)oE
Section D
(16)(120.OXs,
138,419.76)(12)
'n
n
[('r),
(ry
ro]l_.,
wr
-
(0.2833);
(44.0X12)'n.
[\, | \
2
l)
:
42,029.09
lb
Section
D
(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)
t.
:
0.052 in.
=
1/z
in.
[ ,
OK
for
buckling
Anchol
Bolt
Design
Try 24-11+-rn.
d
anchor
bolts
=;
dec
:
l2o
+
2(2.50): 125.00
Total tension in each bolt
:
Wn
*,
=
ottl
''] ;01?,tu'
-
l? 'e 6
58
-
76,84r.ros lb
-
24(125.00)
24
oe
:
40,000 psi
A.
-
76'841 109
=
|.921
in.2
<
1.980
in.']
"
40.0(n
:
l3/+ in. dia, 8-thread series
Check
[/av\
1
:
t-wl
^
t\d/
I
AR:-
-
No,
r[(120)'?
+
(1
18.25F](120.0 +
I 1
8.25X14,
182.
19X1.0)
128,966.580
r(120.0
+
118.25X14,182.19)(1.0)
t,
:
0.381 in.
+
7r in.
[
,
OK
for
buckling
Section
C
(4X12X5,138,419.76)
(12s.50)
-
128,e66.58]
r(120.0
+
,
=
0.245
in.
-
I
18.5)(16,684.932X1.0)
t/q
iI^.
'll_
,
OK for
buckling
(16)(120.0X3,672,858.
86)(12)
r1r20)'?
+
(1
18.5F1(120.0
+ I I
8.5)(16,684.932)(1.0)
95,569.39
(24) (40,000)
Ar
=
1.913 in.'?
<
1.980
in.'?
Bearins
pressure
=
P-
=
48Y
+
W
:i- 7rl:in.
nDu'
j
r
Drj
"
^
48(s, r38.419.76)
t28.966.58
'
r( 125.00)'/(7.50)
7r( 125.00X7.50)
Pt
:7\3.734
psi
< Fb
:
1.33(900)
:
1,197
psi
Tr
:
Base
fl
thickness,
T1
:
compression
I
thickness
Section B
(16)(90.0X1.8s1.388.35)(l2l
rl
+
(90),
+
(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
t"
:
"
(;oiltJ
;
e
=
B *
C
:
Z3tqin.
+
Zttcin.
:
5.5o
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24
Mechanical
Design
of
Process Systems
Il,lr r
l
rarl
"t
Te
=
(5.50r
l:j;;:;=l
=
1.800
in.
I
zu.uuj
I
After
K:
:0.151
one iteration,
1
-
[
:twu)
o
l'''
[:1zo.r+r.roenorl''
''
[4(20.000)el
[
4(20.000X5.5)
I
1+
(61,789.8ss)
(10x1,096.373)
1.268.836
psi
B.ownell and
Young Base
f,
Method
Bolt
circle
d
:
125.00 in.
Base
P
:
4
-
125.00
-
212.50\:
130.00
in.
After six
iterations,
K:0.178
f"
=
n
E'
--
lo(1.096.373)
:
t0,963.73
-Eq
t",^
,"8)(t25.0)
+ 7.001
fc,-o,.area,
=
(1.0e6.373)
[46.,rr'l,,rr.*,
I
di
:
130.00
-
2(7
130.00
-
1
(7.00)
:
116.s0
1t.
16.00
:
7.00
in.
-
,. ,..,,
[:r
t,26t.
sto)1"'
-
''
"'
t
,o"ooo
I
:
2.181
in.
(without
gussets)
Using 24
gusset
f,'s,
gusset
spacing
is
-r
lr(
O\
h
=
""-"
"'
=
32.725
in..
|
=
A
=
5.00
in.
t2
n
5.00
b
32.'125
From
tble
4-8,
using linear interpolations,
My:
-
O.467fcrt2
My=
-
0.467
(1,268.836)(5
'00f
:14'813.660
in.-lb
r,
_
l(oJ{l+.6rr.oou)l
=
2.10g in.
-
t
20.000
I
t
=
use
2rls in
base
Brownell
and
Young
External Chair
Design
r
5.00
22
b
:
gusset spacing
=
32.725 in.
t
15
For
|ta-in.O
bolts,
e
-:"
:
t.375
in.
2
with fc,".,
:
1,000;
K
=
0.333
fc(Bc)
:
(1,200)
[
:
559,723.403
A
1.980
in.2
(12)
r,=-
=
-
U.UOI ln.
'
z'd
?r( 125.00)
I
^"
\r/2
I JI. I
L4
-
^1^-l
2(0.333X12s.00)
2(0.333x125.00)
+
7.00
:
1,106.925
psi
For
K
=
0.333;
c"=
1.588;
C,
=
2.316
z:0431l.
j
=
0.782
:
6l,789.855
Fc
=
559,'723.403
+
128,966.58
:
688,689
983
t:
:
7.00
-
0.061
:
6.939
in.
(5.138.419.76)
-
(128.966.58){0.r'''
ll25
00l
.,"\
12
/
688,689.983
r6.e3e
-
(10)(0.06rI
($Q)<r.sasr
rc-
=
1,096.373
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PB
:
max. bolt load on upwind side
:
fsAB
=
(10,963.73)(1.980)
:
21,708.185
lb
\r.
-
2r.708.185[
(t
+
0.30),n Izrs.ool
I
* ,l
4r
t
[z'(L375)J I
=
3,612.549
ir..-lb
.
_
[{6x3612.549)lr" _,
"^.
t
15,000
I
=
lr/+
in.
in.
f,
for
compression
ring
Calculation
of Gusset
f,
Thickness
for
Compression Rings
r,2
[ =
4qr2-r2
=].
withk=%(1.250)=0.469
t2
,
=
[ereL,
]
:0
r35 in.
h:G+H
I21h n.
:9
+
lt/+ in.
i
2t/c in-
=
l2tlz
in.
h
12.500
P
Bolr
Load
r
0.135
18,oo0rtr-Ptt-
htP
:0
I,500
18,000(5.00)t63
-
(21,708.
185)k,
_
(12.500),(21.708.185)
_
0
1,500
qt
-
0.24ltS
-
0.025:0
q
=
0.40
in.
=
r/z-in.
f,
is OK
Skirt-to-Base
Ring
Weld
,:
(#ft)*
(";)'0u."
The Engineering Mechanics of Bins,
Silos
and
Stacks
fw
:
1.33'yn(0.55), for wind or earthquake
fw:
i.33(20,000X0.55)
:
14,639.99
5 154 1)1
Weld size
=
-.'-
---
=
0.396
14,630.00
or
0.396
=
0.198+
Va
in.
minimum
weld each
side
'2
Cantilevel
Vibration
'.
:
(,aJo
o
.
(,$n',
=
5 860
rt
Corroded Stack
weisht
lttt
*,^
:
6nluurf(,sl
-
(91
:6,16'".ze4tb
*,"
:
<arr
oezrl(r1)'
- (r91
:36,323217
tb
*,:,ounn
rl(?l-
(rtl]I|l:
35,o6oe6o,b
23,905.217 tb
101,457.688
lb
Lc
:
8.00 +
5.00: 13.0 ft
r^ rlnn
=
U.UtJ
< U.5
L
200
trl
=
4 4:1688=
=
14.773
<
2r)
LD,2
(200X5.8601
Therefore, vibration
analysis r,?as,
be
performed.
Wa
:
101,457.688
lb,
L"
=
200
-
lr.O *
ff
:
193.50 ft
-
t.648
L?
1.648(
193.501
'
:
5r(ET,
=
o.gaOx:sJt-lItc
:
r'v)) seconds
I
t:
,uB
:
0.511 cps
vc
:3fDrr:3(0.s11X5.860)
:
8.983
mph
,
_
[r+xs.
r:a.+
ro.76x
r2)]
r28.966.58
r-[
--;6
20"0) -l
t
"(t20-00)
=
)'tv+
tzl
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26
Mechanical
Design of
Process
Systems
V:o
:
100 mph
v*
:
(roo)
(*J'"'
:
13r.165
mph
Maximum
gust
velocity
:
13 1.
165(1.3)
:
170.5 l5
mph
k
_
0.0077D,5E
_
(0.0077X5.860)5(29.0
x
106)
L..Ws
(
193.50)1t
0 t.457.688.)
:0.002
<
1
15
Therefore,
the
stack
is
free
from
cantilever vibration.
Static Deflection
^ ^
tt.467V
"f
.-{.,o-
2
_
(
1.0X0.00238X
1.467P(8.983,,
:
0.107
psf
2
,
:
(,$,o.to
-
0.r25)
+
(,$,o.uro
:
0.523 in.
,"
=
(_..)(?
* 0,,,)
*
(,z,|(?..,")
:35.285
in.
i+r
\/
+r
r
o.zs
\ / ss
\/ss.zs
+ o.zs\
'=
\'oo/\
,
/.
\-/l ,
/
:
34."111 ir.
r
:
it{zs.zts),
-
(34.71
lfl
in.a
:
77,307.326 in]
-
P"D,(LF(12)j
D.=
-
-
.
8EI
_
(0.207X5.
86oX l93.so)4(t2f
8(29.0
x
106)(77
,307
.326)
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
:
t
^
7.58r.(E)o
5
''
6oD2
At
42-in.
dia
:
3.50 ft,
r
-
7 58(0'3zs-iq9
0-l-]06t
:
20.826
cps
60(3.50F
fu
=
vortex
shedding
frequency
0.2v
0.2\66,
:D=(35;=r'l/rcPS
2f"=7.54t
.
t,
At
90-in. dia
:
7.5 ft,
-
7.58(0.5x29.0
x
106)0
5
t.:
'
t
:6047
cps
"
60(7
5)2
-'
f
_
0.2(66)
_
|
%n
/.f
2f,:2
(1.760)
=
3.520
<
6.047
cps
At
120-in. dia
:
10
ft,
f
_
7.58(0.625X29.0
x
lfff5
=
a)\).^<
'"
-
6o(to0l--
where
the
uplift load
on each
bolt,
F, is
-
4(5,
r38,4r9.76X
r2)
r0r,457.688
t,:
,2a1us.0ot
a
:
tt't6t
'tztD
_
0.2(66)
10
:
1.320
cps
2t,:2.640
<
4.252
At
bottom
section,
f,
_
7.58(0.751(2?.0
x
t06)05
=
5.102
cps
'
60(10.01
i,:o2t66t=1.320cos
'10
2f,:2.640
. t.rO,
Therefore,
stack is free
from ovaling
vibration.
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
(4-66)
=
0.164 in.
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.\hich
results
in a required bolt torque of
r
:
(0.
rs)
(r.75)(77
,987
.312)
=
20.471.67
in.lb
=
1.706 ft-lb
Use 1,706
ft-lb
torque
with
lubricant
grease
Fel-Pro
C-
5,A,,
or equivalent.
The
skirt base and anchor bolt
detail for the stack
is
hown
in Figure
5-23.
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
,
16) l:/+-in.
anchor bolts
Required
anchor
bolt torque:
1,710
ft-lb
Total
operating weight
=
128,966.580 lb
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. Refer-
ring
to Figure 5-15 we have
the following:-
D:ODofstack:7ft4in.
L:31 ft
6
in.
D
7.333
.i
=
_
=
_
:
J.DO/
L
31.5
_
:
.t
t
{
2ro
2rtl)
\ou,
_ _
a2cu2
+b2
-
--;F-
_
_
(3.66'7)2(r)2
+
(5.013F
-
(356?X1t-
:
=
10.521
ft
(5-17)
The Engineering Mechanics
of Bins,
Silos
and Stacks
ALL
MATERIAL
TO
BE
SA-285
_C
ALL WELD
SIZES IN
INCHES
zl-tci
I
a-tgg-'et.
a THBEAo
sERtEs
BoLTS
BOLTS
TO
STRADDLE
CEI.ITERLINES
trL_u--l
ffi
Figure
5-23. High-pressure
flare
stack base
support detail.
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28
Mechanical
Design of Process Systems
Check
Using the approximate
Morgan equation
we have,
Si
:
interior
arc length
:
[(rDJ'?
+
L2]0
5
:
39.025
ft
52:exterior
arc length
=
[[?r(8.667)]'?
+
(31.5)'?105
:
41.637
ft
x:9:t?'o,T:r.nt
(s-1e)
s.
41.637
\w
r
:
._________
(5-lg)
r
-
(0
937)(0
667)
-
9.966
ft
=
9
ft
i
t.594
in.
|
-
0.937
_
10.521
-
9.966
va
e:,rof
=
ff
=
5.276Eo
errol
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
analy-
sis
must
be
applied
to
obtain Equation
5-13.
The
original
Michell
equation
is
as
follows:
, I rtJrJ
-
'J
f.
=
-r/
.--.-
.
-.
]-
(5-12)
''
2"Y PAf
(n'
+l+/)
where
p
:0.283
lb/in.3 for steel
A:
(t)
in.
x
(1)
in.
f
:
in.a
E
:
lb/in.2
T-
I
-
;
.
per
unit lenpth
ofring.
in.'
t2
z
:
l/r for
steel
I
z7f
BASE PLA?E
- 3/16r
STRIPS
CUT
FRO}I
BASE PLATE
t
0.5ft
+
0,66?ft
=
11.-2.
-
4.409r
E
Ir
:
----
Vt1
386 lb.-in.
rgl
'i-c'
1(36)r(in4)
(0.283)
-.l l
1
in.2 1 in.a
(5.333)
(5-13)
Figure 5-24.
Manufactured strake elements.
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NOTATION
A
:
cross-sectional
area of stack,
in.2
AB
:
anchor
bolt
area,
in.2
a
:
stack
radius
=
D/2,
ft
B
:
critical
arching
parameter, dimensionless
D
:
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
5-
JI
E
=
modulus of elasticity.
psi
f.
:
material
yield
strength,
psi
ff: critical flow
factor for arching
in channels,
di-
mensionless
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;
n-
dius
of
curvature
of vortex strake
(Equation
5-
17),
ft
S
=
over-all
length of vortex strake
(Equation
5-16),
ft
Si
:
interior arc
length of helix
(Equation
5-18), ft
So
:
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
bin walls by solid
(Equation
5-1),
psi
XI
] )
mode
shapes relating
translational
displace-
7.1
ments about
the
x,
y
and z axes,
respectively
Greek
St/mbols
7
:
bulk density of solid.
lb/ftl
6
=
logarithmic decrement, dimensionless
The Engineering
Mechanics
of
Bins,
Silos
and
Stacks
29
Table 5-3
Conservative
Values
for Logarithmic Decrement
and
Dynamic
Magnification Factor tor
Various
Stacks
Low
Oamping
6D
Average
High
Damping
Damping
6D6D
Unlined
Stacks
0.035
90
0.052
60
0.105
30
Lined
Stacks
2"
gunite lining 0.070
4"
gunite
lining
0.117
10
9
31
25
45
27
0.100
0.r25
0.300
0.360
Inw
Danping
=
rocky,
very
stiff soil;
Iow-stressed
pile
suppon, or struc'
tural
Itame
support.
Average Dampin?
=
modetutelt stiff soil; aormol spreadfooting
or
pile
sup-
port
HiBh Damping
:
soft soil;
foundation
on highlJ stressed
Iriction
piles
6
:
piping
factor, dimensionless
0_:
ungle
of
hopper slope, degrees
0
:
modal
shape
relating
to
rotation about an axis
perpendicular
to stack centerline
(Figure
5-14),
dimensionless
p
:
coefficient of friction between the bulk solid
and
the
bin
wall
(Equation
5-1),
dimensionless
d' :
kinematic
angle
of
friction
between the
solid
and
the
bin wall,
degrees
dr
:
consolidating
pressure
for
steady flow
(Equation
5-4\,
tbflft2
ot
:
allowable tensile
stress
of stack material,
psi
or
:
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.
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Fluid movers
and
their
use are vital to the
process
in-
dustries.
This
chapter focuses
on two
basic
types-
pumps
and compressors.
The sizing of these
units and
their interaction with the other components
of
a
process
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
tur-
bine. 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.
PUIIPS
As the
primary
movers
of liquids,
pumps
come in
many
types
and an understanding of the
various kinds is
essential
in
successfully applying them
to
process
sys-
tems.
Pumps
are used to transfer
liquids
from
one
point
to
another.
They basically
fall
under two categories-cen-
trifugal
and
positive-displacement.
The centrifugal
pump
gets
its name from the fact that the
pump's
impeller im-
parts
kinetic energy to the liquid with centrifugal
force
acquired
by the impeller's
rotation.
This simple
mecha-
nism
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 centrif-
ugal
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 ac-
tion.
Ideally, a PD
pump
will
produce
whatever
head is
impressed on
it
by
the
system
restrictions to the flow.
Rotating Equipment
Not all
PD
pumps
are
purely
rotary or reciprocating, but
we
will
focus
our
attention
on
these
types. PD pumps,
by
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
positive-
displacement
pumps.
Typical rotary
positive-displace-
ment
pumps
include screw,
gear,
vane, cam, and lobe.
Reciprocating
positive-displacement
pumps
include
pis-
ton,
plunger,
and diaphragm.
Selecting
the type of
pump
to
use
is
a
function of the
service to be
handled.
Sometimes, the selection
is obvi-
ous;
for
example,
if
you
wanted
to
pump
molasses,
you
would
choose
a
positive-displacement pump.
In the situ-
ation
where neither a standard type
of
pump
is used
for
the
service, nor
is
it
obvious
what
type to use, a
centrifu-
gal
pump
is always considered
first.
The
reason
for
con-
sidering a centrifugal
pump
initially
is because
of its low
initial cost, economical cost
of maintenance, wide range
of
materials of
construction,
and
relatively
large clear-
ances. Factors to be considered in selecting a
pump
are
as follows:
1.
Efficiency
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
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Mechanical
Design
of
Process Systems
10
ro-
F
o
I
J
I
-l
5
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
pres-
sure head
in
the volute.
The
mixed flow
pump
impeller
consists
of
vanes
dou-
bly
curved
or
screw-shaped so
that
the impeller
moves
the
fluid
by both centrifugal
and
pushing
action. The
re-
sult 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.
234
Figure 6-1.
Pump selection
guide.
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 to-
gether
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 ther-
mal
movements
without
causing
shaft
misalignment.
Packing
and seals
on the shaft are the
most common
source
of
failure
for a
pump.
In low-pressure
applica-
tions,
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 configurations-
tandem.
bellows.
and face-to-face.
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.
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Group
I
Standard
Pump
'Pafls
10rtra'y
sl0ck.d by cLsrome.lor e4erqenc/
'Ppd
rs
"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
{01Jackeled cover oral€s are carhon sre€l
(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
I
Duponl deNamoors
&
ComDafiy
Inc
G:oup
ll
and
lll
Standard Pumps
Materials
Common
io all
Alloys Unless
otherwise
Noted
Parl No. Parl
Malerial
104 lmoeller Gasket'
107 Rear Cover
Plate Gasket*
Durabla
108 Bearing
Housing
Adapler
Casl lron
109 Bearinq flousrno
Fool
Casl lron
111
Gland Studs or
F
anqe
Studs
with
Hex
Nuts
3M
S.S./303 S.S
112
Sealcaqe'(E)
PTFE
113 Molded
Rino Packinq'rE)
Kevay'il
114
Inboard 0ellector
PTFE
115 Casino Studs/Hex
Nuls
304 S.S./316
S.S.10
118
Inboard
0ilSeal'
TFSB
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'
Steel
129 outboard
oilseal'
TFSR
130
Shall Couolino
Kev
Steel
131
Beanno
Housrng Adapler' 0"
Binq SBR
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
lor Eearinq
cover Steel
139 Machine Eolts lor
Bearing Housrng Steel
140 CaD Screws
iorAdarterto Cover Sleel
Figure
6-2. Centdfugal
pump
components.
(Courtesy
of the
Duriron
Company.)
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Mechanical Design oI Process Syslems
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
re-
sponsibility of the
pump
manufacturer. In all situations,
the
bearings should be
of
the outboard type
(not
sub-
jected
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
param-
eter
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
pump-
ing temperature.
NPSH
is
the energy that
forces the
liq-
uid into the
pump,
and
is
expressed
in foot-pounds of
en-
ergy
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
atmo-
spheric
pressure
and the
vapor
pressure
of
the
liquid
at
that temperature.
Figure 6-5 helps simplify the calcula-
tion of
the NPSH.
Figure 6-3.
A
seal flush configuration.
(Courtesy
of the
Durametallic
CorDoration.)
In
selecting a
pump
the engineer must
refer to
the
per-
formance curves
the
pump
manufacturer
prepares
for
each
model ofpump. Most
performance
curves
are
plots
of flow
capacity
(gpm)
of
water versus break horse-
power
or
total dynamic
head in
feet.
Such
a curve
is
shown
in
the examples that follow.
As
seen,
the
effi-
ciency 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, be-
cause the capacity
and head change abruptly. Pumps are
normally
selected
to
operate in the area of high effi-
ciency.
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
shut-
off 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 be-
tween
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-
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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.
psra
gpm
gpm
gpm
Flow at ambient temD.
Operating flow at
PT.
Design
flow at
PT.
_
Suction
Source'pressure
Static
(+
headx- lifi)
=
-
APr line loss
Suction
pressure
-
Vapor
pressure
NPSH
avail
NPSH
avail
NPSH req'd
[,lin
NPSH
avail
>
NPSH
req'd
+
2
fl
psra
psi
psi
psra
psra
psra
ft
ft
Terminal
pressure
Static
(head)(lift)
-
APr
discharge
Piping
system
Other
Discharge
press.
-
Suction
press,
TDH
TDH
Discharge
psia
psl
psi
psi
psia
psia
psra
leet
'lnilial
press.,
e.9.,
ATM
or
O
unp at Duty condition
ono"
_
(gpmXTDHXr)
_
(3,e60Xr)
66o.,"
=
(gpm)CrDHXr)
(3,960Xri)
TDH
=
discharge
press.
-
suction
press.
4 =
pump
efficiency,
o/o
PT.
=
pumping
temperature
@
Onp at Maximum Capacity
Condition TDH
=
total
dynamic
head
sphere
is negligible.
The
temperature rise
per
minute is
computed by the following
relation:
42.2(bhp,")
(6-1)
W*Cp
where
At
:
temperature rise
per
minute,
oF/min
bhp,"
:
6.u1" horsepower
at shut-off
W*
:
weight
of liquid in pump,
lb
Co
:
specific
heat of liquid in
pump
The break
horsepower
of the
pump
is
given
by
..
OH"y
bhp
=
-,::--r
(6-2)
J,vou4
Figure
6-5,
Pump
hydraulic
design calculation
sheet.
which is the
power
required
if
the desired head
at the re-
quired
capacity could be
produced
with
zero losses.
For
water
flowing
through the
pump,
conditions be-
come stabilized
and
the temperature
rise is determined
by the following:
".
_
(bhp
-
whp)
2,545
m
(64)
where 2,545
:
Btu equivalent
of
I hp-hr
ir
:
mass
flow rate- lb/hr-
Another variant
of
Equation
6-4 that
relates
the tem-
Derature
rise
to
the
total
head
is
(6-5)
In Equations 64 and 6-5 the compressibility
of
water is
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
^
=
^o(;-,)
here
Q
H
"v
q
:
flow
rate,
gpm
=
total
head,
ft
=
specific
gravity
=
pump
efficiency
(fraction)
The water horsepower is
given
by
who
:
QHI
'
3,960
(6-3)
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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 ap-
proximate
the equivalent water
performance.
The fig-
ures, 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
hori-
zontally
to
the
left
or
right to the viscosity line, and
pro-
ceeding
vertically
upward to the correction-factor curves
for the head and capacity. The equivalent
water-perfor-
mance values
are then obtained by dividing
the viscous-
performance
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 correc-
tion 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 chap-
ter.
Positive
Displacement
(PDl
Pumps
Positive displacement
(PD) pumps
are usually selected
after it
has
been determined that a
centrifugal
design can-
Rotating Equipment 37
not
meet the requirements.
Thus,
PD
pumps
are used
where centrifugals
cannot
operate-under low
NPSH re-
quirements
or
handling
a
highly viscous liquid.
There
are
several types
of
PD
pumps,
as
previously
mentioned,
and
their
positive
attributes are that they
1. Operate at
relatively
high efficiencies when
pumping
viscous liquids.
2.
Operate under
low
NPSH conditions
and
produce
high suction
lifts.
3
. Operate with
high
heads at
a
wide
range
of
capacities
.
4.
Have
a
wide speed range,
which
is limited
by the
liq-
uid's
viscosity.
5.
Are inherently self-priming.
Selecting
the
fype
of rotary
pump
is
primarily
a
func-
tion 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 tim-
ing
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
in-
tercooler before
it
enters the
pump
suction
port.
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Mechanical
Design
of
Process
Systems
l
00
.90
.ao
.70
.60
.50
_40
.30
.20
."n,
B
S9
vrscoslTY-ssu
'.
s
s
u";*t*
g;*1"
I
15
20
25 30 40
50
60
CAPACITY.GALLONS
PER I\4INUTE
(At
bEP)
Figure
6-7. Performance
correction
chart for viscous liquids.
(Courtesy
of
the
Hydraulic
Institute,
Cleveland,
Ohio.)
o
z
.icF
CP
.\$
?p
r_':
\9,
'6
rd
^
3cP
g
1s"
Hp
Zro
o o
-co
g
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Rotating Equipment 39
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
uI
o-l
rr
lrl
I
:l
<l
lrl
I
-l
4
6 810
15
CAPACITY
IN lOO
GPM
Flgure
6-8,
Ferformance
correction chart for viscous
liquids.
(Courtesy
of
the Hydraulic Institute,
Cleveland,
Ohio.)
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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
applica-
tion of
this type
of
pump
is illustrated
in
Example
6-2.
3.
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
vis-
cosities
up to 10
x
107 SSU and
have bearing
and
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
vari-
ety 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
vari-
ous installations
for a
pump.
Some
properties
and
char-
acteristics
illustrated
in
Figure
6-
13
are
Static
suction
lfi-the
vertical distance
in feet
(ex-
pressed 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
(ex-
pressed 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.
Figure
6-10.
The internal
bearing
gear pump
is
a variant
of
the rotary
gear pump in Figure
6-9.
(Courtesy
of
Worthington
Pumps,
Mccraw
Edison
ComPanY.)
Friction
head-the
pressure
(psi)
required
to
over-
come
frictional
resistance
of
a
piping
system.
Velocity
head-expressed
in
psi,
see
Chapter
1.
Tbtal
suction
/r/-the
total
pressure below
atmo-
spheric
(in
Hg
or
psi)
at
the
pump
suction
port
during
pump
operation
and equals
the
following:
1. Static
suction
lift
plus the
frictional
head,
or
2.
Frictional
head
minus
the
static
suction
head
(only
if
the frictional
head is
greater
than the
static
suction
head).
Total suction
head-the
total
pressure
(psi)
above
at-
mospheric
at
the
pump
suction
port when
the
pump is op-
erating
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
differ-
ence
between
the static
suction
lift and
the static
dis-
charge
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'
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Mechanical Design
of
Process
Systems
t|'r$|lhF..Dl$hra
Figure 6-13. The
principal
parameters
of
pump
selection.
(Courtesy
of
Viking
Pump
Division, Houdaille
Industries,
Inc.
)
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.)
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 ex-
pressed
in
feet
of liquid.
However,
the suction lift
practi-
cal
for
actual
pumping
installations is
somewhat less
than
the
theoretical
value.
Figure
6-14 shows the theoret-
ical 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
fluid at a
rate
proportional
to the speed of displacing
ac-
tion and this rate of transfer is independent
of the
pres-
sure
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-
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
such
an arrangement a temperature
sensor
device
is
placed
at the
pump
discharge to detect excessive tem-
peratures.
The intercooler,
or heat exchanger, is
used
to cool the
pumping
fluid.
Normally, temperature be-
comes a
problem
when
the
instantaneous discharge
and
inlet flows
are equal.
Gear and
multiplex
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(plunger,
diaphragm,
and
piston)
pumps
are examples
of
such
pumps
in which
this situation occasionally de-
velops.
2.
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 dis-
charge
piping
and set at a
pressure
slightly
greater
than the
pressure
switch
to
ensure adequate
protec-
tion. 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
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
in-
dustries
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
pro-
cess 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.
Rotating
Equipment
Figure
6-14.
The
theoretical and maximum
recommended
suction lift for water
at
various
temperatures,
'F.
(Courtesy
of
Viking Pump Division,
Houdaille
Industries, Inc.)
(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.
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44 Mechanical Design
of
Process
Systems
2. Lower
operating
and maintenance
cost. The operat-
ing and maintenance
cost
of
a centrifugal is approxi-
mately one-third that
of
a
reciprocating
compressor.
3.
Compactness of
size. Centrifugals
occupy less space
and make
much
less noise.
4.
Simplicity of
piping.
Reciprocating
compressors
can
cause
severe
pulsation
shock response
in
piping
sys-
tems. The
cost
in
preventing
the effects of
pulsation
in
piping
systems
can
entail many hours
of
engineer-
ing 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
and are
often
used
in
series
with
centrifugal
units. Axial-
flow compressors are
governed
by the
same
formulas
that apply to centrifugals.
The axial units
are more
effi-
cient
than
the centrifugals,
but
the latter
have
a
much
wider
operating range.
Axials are
used
primarily
for
clean
gases
such as
air,
because
they are much more
sus-
ceptibie
to corrosion, erosion,
and deposits than
centrif-
usals.
INLET
FLOW,ACF
souRcE:DriroPLot{
t2l
Princlples
of Compresslon
The
general
gas
law
that applies
to
all
gases
can be
written
in several forms:
PV
=
zmRt
(6-6)
zmRt
mw
:
zM.Rt
PV:
zRt
.c"c"
K=---j=
c"
cP
-
1.986
(6-7)
(6-8)
(6-e)
where
P
:
absolute
pressure,
psra
V
:
volume
of
gas,
ft3
z
:
compressibility
factor
for
real
gases
(z
:
1 for
a
perfect
gas)
R
:
R/mw
:
gas constant
of
the
particular
gas
R
:
universal
gas
constant
:
1,545 ft-lbr/lb.
mole
-
'R
t
=
absolute temperature,
'R
:
'F
+
459.7
m
=
mass
of
gas,
lb-
mw
:
molecular weight
of
gas
Mo
:
number of moles of
gas
:
m/mw
v
:
specific
volume
of
gas,
ft3llb.
A very
important
gas
property
is
the specific
heat
ra-
tio, k.
This
property
is determined from the following:
(6-10)
where
C,
:
specific heat at constant volume, Btu/lb.-mole-
=
4.97
Btu/lb,-mole-"F
for ideal monatomic
gases
Cp
=
specific
heat
at
constant
pressure,
Btu/lb,-mole-
:
7.00
Btu/lb.-mole-"F for
most
diatomic
gases
Reverslble Adiabatlc
(lsentropic)
Compression
The reversible
adiabatic
(isentropic)
compression of
an
ideal
gas
is
obtained when no heat
is
added
to, or
re-
moved from,
the
gas
during
compression.
The
process
is
reversible
when no
friction exists.
The
formulations dif-
fer for
a
perfect gas
versus a real
gas.
Perfect Gas
(z :
1)
PrV,K
:
PtYtx
(6-11)
(6-12)
lgure 6-16, Approximate ranges of application for
recipro-
:
l&F
cating, centrifugal,
and
axial-flow
compressors
[2].
tr
\Pr/
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t'
lP:l
"
t'
\Pr/
Real
Gas
(z
*
1)
P1V17
:
P2V2'y
(6-13)
(6-14)
where.
for any
system
of
units
P
:
absolute
pressure
V
:
volume
or specific
volume, v
k
:
specific
heat
ratio
-y
:
isentropic exponent
for
real gases,
Co/Cu
t
:
absolute temperature
subscripts
I
and
2
denote inlet and discharge
conditions,
re-
spectively
To determine the exponent,
T,
real
gas properties
must
be used. These
properties
can
be
obtained
from
gas
property
charts and
used
in
the
following
formulation:
r / \'l
I-I
=*l'*,lSll
(6-15)
-y
JCp
[
\atloj
where
J
:
mechanical equivalent
of
heat
:
'778
ft.-lbrl
Btu
/,el
rate
of
change
of compressibility
facror.
z.
with
re-
ll-l
:
spect
to the required temperature.
t. along a constant
\
d[,l
p
pressure,
P.
path
To determine
a mean value of the isentropic exponent
for
a
real gas,
?,
over
a
compression
range, Equation 6-
15
must be
solved by iteration.
In Equation
6-15 if we
have
a
perfect gas
in
which
l=l
=0andz:1.0
then Equation
6-15 becomes
Rotating Equipment
where
Q
:
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
?
JCP
'v=k
For
a compression
ratio PzlPr <
2.0,
t
is
approxi
mately equal to
k
for most real
gases.
For
isentropic compression
of an ideal
gas
the
theoreti-
cal horsepower
requirement is
as
follows:
_2"*24
:
mean comoressibilitv
factor
z.
:
compressibility factor at
suction
za
:
compressibility factor
at discharge
For a
gas
capacity of
Q
:
100
scfm, Equation 6-16
becomes
[,,,-, ],
h._
=6.42llPdl
k
_rl{r,l_
k-r
l\P,/
-l\520/-
kt
I
In applying
these
formulations
that deal with the isen-
tropic
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:
4"
:
adiabatic
efficiency
:
the isentropic horsepower,
hp1, delivered
by the
actual
horsepower delivered to the gas,
or
hpr
gnp
qn
:
mechanical efficiency
:
the ratio
of
the
actual horsepower
delivered
to the
gas
to
the brake
horseDower.
or
shp
''''
bhp
4,o
:
overall adiabatic
efficiency
:
the
ratio
of
the isentropic horsepower,
hpr, for a
stage
of compression to the brak€ horsepower,
or
hD"
bhp
.
In
defining the
horsepower
input for
a single stage of
compression,
utilize the overall
efficiencv as follows:
R k-1
(6-17)
(6-18)
(6-19)
[,
'*-'
],
hp':ffi|('iJ
,
-'l['',J'
\k/t
t
6'6,
bhP=*=ffi[(,t-']F;'{*)
\
k
/r
(6-20)
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Mechanical
Design of Process
Systems
For bhp
at
100
scfm,
Equation
6-20 becomes
bhp=ffiH=-'l'H
\-o
/1
J
The
isentropic
energy
transmitted
to the
compressed
gas
in
ftJb/lb-
of
gas
represents
the
adiabatic head, or
t \t ,[,,*-,
I
",:
llsl{IlllSlT
-
'la
mw/
\K-
r/
[\Ps/
I
(6-2r)
The compressor
driver
horsepower
(bhp
or
ghp)
is re-
lated
to the
adiabatic
head by
the following:
PV'
:
constant
(6-26)
When
Equation
6-26 is
expressed
between
the initial
and final
conditions
we have
PlVtn
=
PrYro
(6-27)
where
n:
the
polytropic
exponent,
n
+
I orn
+k
Expressing
Equation
6-27
in
terms of
temperature
and
pressure
we have
(6-28)
'
-
/p,\?
t'
-
\P,/
33.0001""
where rir
:
mass flow rate
of
the
gas,
lb./min
The
adiabatic efficiency
can
be defined in terms
of the
polytropic
efficiency
by
the following:
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)
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 inter-
coolers or aftercoolers.
For a multistage compressor,
Equations
6-20 through
6-25 must be applied
separately
for
each stage.
Polytropic Compression
This type of compression
occurs when a
gas
is revers-
ibly
compressed along a
path
that is defined by the fol-
lowins relation:
The
value
ofn depends
on whether
the
gas
is a
perfect
gas (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
expo-
nent.
k. as
follows:
n-1
k-l
lll
\4el
k-1
(6-24)
sincek:
ColC"
;H"
ghp:
bhp
:
33,000a"
frfl,
(6-22)
(6-23)
QCo
(6-29)
(6-30)
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
deter-
mined from real
gas properties
or with
using real
gas
data and using the following
expression:
_R
JCo
n
[z
/a'\]
_t_
+
t l_tl
JCo
lqo \at/l
n-
I
(6-31)
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 fac-
tor for real
gases,
z,
is
divided by the
polytropic
effi-
crency,
?p.
Similarly to Equation 6-15, Equation
6-31
must
be
solved by
iteration for
a mean value of the
polytropic
ex-
ponent,
n,
over
a
compression range.
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6A
70
72
74
POLYTROPIC
767880
EFFTCTENCY
lp
Rotating Equipment
47
Figure 6-17. The relationship
between
the
polytropic
efficiency and the adiabatic
effi-
ciency for a
perfect gas (Z
=
1).
In
Equation
6-31, if
we have
l3l
:
ouno z
=
I fora
perfect
sas
\r/p
then,
n-l:j-:=
@32)
n
JCp4p
,
/r
\
K
l-l
\4pl
For most real
gases
below
a compression
ratio
of
ap-
proximately
2, then
n
-
I
_k
-
1
n
'
ll\
K
l-l
\ql
The
basic horsepower
and head
expressions
for
poly-
fopic
compression
are similar to
those for isothermal
compression,
Equation
6-20. Thus,
we have
*'ffilett'le
''
For
ghp
at
100
scfm,
(,C,tffi
(6.33)
,no
:
H -1J_j1?L
[tfl
(il
t=l
_
]
(,$,,,
H,6.34,
\;/\
k
/t
The
equations for
polltropic
head
are
similar
to those
for adiabatic head.
Equation
6-21. Thus.
.
:
(.*_)t^J
IH(l
FJ
,]
"
(6-35)
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48
Mechanical
Design
of
Process
Systems
If the
polytropic
head
is known,
the compressor
horse-
power
(ghp
or bhp)
can be obtained
from
the following:
mil
Equation
6-43 assumes
that the
heat
of
compression is
fully removed
by
cooling.
In
practice
this
is 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:
bhp
:
ehp
:
33,000a*
riH
(6-36)
(6-37)
(6-3e)
(6-40)
(6-41)
(6-42)
33,00040
P1V1
:
P2V2,
OI
PV
:
constant
bhp
_
hp,
hpr
tlfl- tl:.
N
:
N(Q)o
5
'
H0.75
where N,
:
specific
speed, dimensionless
N
=
speed, rpm
Q
:
capacity
of flow
rate, ft3lsec
H
:
head, ft-lbrilb.
^
D(H)o
25
"":
e*
where D.
:
specific diameter, dimensionless
D
:
diameter
of
impeller
ot
rotor,
ft
H
:
head,
ft-lbr/lb.
(644)
(64s)
(6-46)
(6-47)
where
4oo
:
overall polytropic
efficiency
:
IpI.
The outlet
and inlet
temperatures
for
polytropic
com-
pression
are related
by the following
expression:
=
i&)H
F)
t,
\P,/
(6-38)
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
effi-
ciency
directly
(provided
t,
ta, P,,
P6
and k
are known
values):
7h
where
4,
Ia
:
isothermal
efficiency
:
overall efficiency
:
Itlln
After
applying Equation
644
and determining the
brake horsepower
(bhp)
for
a single stage
of
compres-
sion, 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:
/\
.
I
lk-ll
v
./
-
-t----t
--
4p\
K
/
\p
.
k-l
wnere y
:
k
Normally,
the
value
of
?e
is estimated from
data sup-
plied
by the manufacturer.
For initial
or
preliminary
val-
ues
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 compres-
sion. For
a
perfect gas
in
which z
:
1.0 and
(AzlAip
:
0 we have
The
theoretical horsepower
developed
during
a
revers-
ible isothermal compression
process
is
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
compres-
sor
is
to be used and in cases of uncertainty
or
new
appli-
cations, 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 sepa-
rate
inlet
capacity or head for that stage.
ho,:atz hl&)
"
8.1l0
\P,/
(6-43)
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Rotating Equipment
0.3
0.6
1
30
60 r00 3m 6m
1,000
3,0()()
10,000
Specific speed,
4
Figure
6-18.
The
initial
selection
ofa single-stage compressor
is made using
the
specific
speed
and
specific
diameter
parameters
t3l.
^.
10
E
G
I
Gentffugal
Gompressors
The centrifugal compressor
powered
the
first turbojet-
powered
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
pe-
ripheral
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
re-
peated
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 wa-
ter-cooled
separators
or diaphragms.
The
polytropic
relations,
Equations
6-26
through
6-
40, are usually
preferred
for centrifugal
compressor
cal-
culations. Figure
6-20 shows
why with
a schematic
plot
of
the
centrifugal compression
process
on
a
temperature-
entropy
graph.
Using the adiabatic
(isentropic) process,
the
actual discharge temperature is underestimated
Figure 6-t9A.
Centrifugal compressor-single-stage.
(Cour-
tesy of Dresser Industries, Inc., Roots Blower Operation.)
4
=
N
'/q/Ha1
D,=
DHltalJT'
/V
=
Speed,
rpm
O
=
Flow, fr3/s
D
=
lmpeller
diameter, ft
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50
Mechanical
Design
of Process
Sysrems
1 Discharge
Nozzte
9.
Shaft
17
Intetsection
2. Casing
Cover 10.
Oi
Fterainer
j8.
impe|er
3 Sub
Cov€rSeclion
11
BeartngSrand
j9.
clideVane
Housing
4
Bearing
Stand Cap l2
Coupting
End
Beanng
ZO. In
er
Nozzte
5 SteelShim
13
tmpelerEnd
Bearino
21 cuideVane
6
r'rus
Bed
nq
4.
Or'Ferar-e.
-
22
curoevaneLrtdop
7
- run
Ho-s
nq
5eal t5
Sa.t
23
moe
er End
ptdl;
8. Spaci.g
Fing
16
Votute
24.
Intet
Wearing Fing
Figure
6-198.
Cross-section
of
a
single-stage
centrifugal
compressor.
(Courtesy
of Dresser
Industries,
Inc., Roots
Blower
ODeration.)
(ideal).
Since
the
polytropic
compression
process,
by
definition, is
the
path
connecting
the
inlet
and
actual dis-
charge conditions,
the
polytropic
formulations
are
pre-
ferred
by compressor
manufacturers.
This factor
be-
comes
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
ofundersiz-
ing
the cooler becomes.
Gas inlet
conditions
can change
and when
they do they
affect
a
centrifugal
compressor
differently
frorn
a
posi-
tive-displacement
compressor,
such
as a reciprocating
machine. Table 6-1 lists
the effects
of
changing
inlet
pa-
rameters on a centilugal
compressor
operating at
a con-
stant
volumetric
flow
rate
and a constant
sDeed.
Changing
the speed
of a
centrifugal
compressor
in-
volves
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. The required
power
varies to
the
cube
of
the speed.
3.
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
phe-
nomenon
normally
is
associated
with excess
noise
and
ENTROPY
s
Figure
6-20. Centrifugal compression process.
Atidd:
t2t-tl
At*,-r=t2-tl
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Rotating
Equipment
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52
Mechanical
Design
of
Process
Systems
Table
6-1
E tects
ot
Varying Various
Inlet Parameters
on a
Centrilugal
Compressor
Increasing
Inlet
lncreasing
lnlet
Pressure
Increasing
Molecular
Weight
of
Gas
Increaslng
value
ot
Polytropic
n
or
Adiabatic k
Pressure Differential
Compression Ratio
Inlet
Density
Discharge Pressure
Discharge Temperature
Power Required
Head Developed
Mass Flow
Rate
Deateases
Decreases
Decreases
Decreases
Decreases
Decreases
Constant
Decreases
Increases
Constant
Increases
Increases
Constant
Increases
Constant
Increases
Increases
Increases
Increases
Increases
Increases
Increases
Constant
Increases
Decreases
Decreases
Constant
Decreases
Increases
Constant
Constant
Constant
CONSTIiIT
SPEED
COMPRESSOR
CHARACTERISTI(
B
I
I
I
,
7
I
...
I
c0MPn€ss0F
SURGE LIM I]
I
I
t
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
cen-
trifugal compressor
[4].
vibration of the compressor
and sometimes
the compres-
sor
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
fac-
tors
ease
the
problem
considerably:
1. Throttling at the discharge
flange.
2. Throttling at the
inlet flange, which is usually
more
efficient than throttling at the
discharge flange.
Using
a
variable
speed
driver, usually
accomplished
by
the turbine driver.
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 compres-
sor manufacturer should
be consulted.
Antisurge
devices can be incorporated
into
compres-
sor systems. For nontoxic
or inexpensive
gases
the com-
pressor
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
ex-
changer
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 tempera-
ture 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 perfor-
mance. The manner in
which scfm
and altitude correc-
tion is handled is
discussed later.
Impellers
are critical
in
the selection
of centrifugal
compressors. The three
basic types
of impellers for cen-
trifugal
compressors are shown in
Figure 6-25.
The con-
ventional
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 diame-
ter
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 impel-
ler,
then one must think in
terms of multistage compres-
sors. Each
stage of
compression of
a
multistage
com-
pressor
is
treated as a single
stage compressor and
the
same formulations hold.
r20
0
t0
0
J.
4.
s80
460
o.
40
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Reciprocatlng
Compressofs
These
compressors
normally are sized according to the
adiabatic
expressions
of
Equations
6-11
through 6-25.
Normal
practice
in calculations for reciprocating com-
pressors
is
to use
the adiabatic exponent,
k
=
Cp/C,,
then adjust the results according to the specific
compres-
sor design and
configuration.
The
parameters
that
affect
the compressor horsepower,
cylinder
capacity, and dis-
charge temperature are length
of
stroke, shaft
rotation
speed, cooling efficiency, and fixed clearance of cylin-
ders.
All
of
these
parameters
vary for
each
given
appli-
cation, but have the same basic cylinder design and cy-
Figure
6-23.
comPressor.
Rotating Equipment
cle.
Figure 6-26 shows
the reciprocating
compressor
cycle.
This
cycle
involves
this
displacement
of
gas,
hence the classification of a
reciprocating compressor as
a
positive
displacement
type of unit. The compressor
is
unable
to exhaust
all
gas
from the cylinders and the
re-
sidual
gas
remaining in the compressor at
discharge con-
ditions
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
ca-
pacity
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 com-
pressors
to
vary
the
volumetric efficiency.
These
clear-
ance
pockets
can be sized to affect the capacity of the
compressor,
as in Figure 6-28. Power consumption at
re-
duced
flow rates is minimized by
use
of capacity control.
The
use
of
a
clearance
(additional
clearance
vol-
ume) reduces the
volumetric efficiency
of the
compres-
sor, because
the re-expanding
gas
fills most of the cylin-
der,
and
the
suction
valve opens further
in
the
stroke.
This mechanism is economical, because the energy ex-
pended
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 ef-
ficiency at constant
compression
ratio. The
volumetric
efficiency
for
a
reciprocating
compressor
is
given
by:
(6-48)
inlet
actual capacity
Manual
surge
control
system
for
centdfugal piston
displacement
flow monitor
centrifugal
compressor
Figure
6-24.
Automatic surge control with recirculating
by-
pass.
The
parameters
that affect the volumetric efficiency
are as
follows:
l. The
ratio ofa
relative clearance volume,
e,
which is
the
ratio of
clearance
to theoretical
displacement
ex-
pressed
as
percent.
2.
The compression
ratio, C., of discharge
to inlet
pres-
sure.
3.
The
various exponents
of the
polytropic
curve of
re-
expansion.
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
re-
expansion
oflower compression ratios, Chlumsky
[5]
drscharge
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Mechanical
Design
of Process Systems
OPEN BACKWARD.BLADED
IMPELLER
OPEN RADIAL-BLADED
IMPELLER
CLOSED BACKWARD.BLADED
IMPELLER
BACKWARD
LEANING
B LADED
IMPELLER
(PARAMETER-
%
SPEED)
e
63
s
si
o"o,
EH
o
-4,
?E
100
ao
RADIAL
BLADED
IMPELLER
(PARAMETER.
%
SPEED)
opi-l
RADIALACKWARD
LEANING
IMPELLER
AOJUSTABLE
IN
LET
GU
IDE
VANES
3
1?O
E
100
c'
ao
s
q
E
E
s
Vcc
d>
BLADED
IMPELLER
100
g'g
ro
.-B
so
s9
40
ADJUSTABLE
IN
LET
G UIDE
VAN
ES
20
40 60 80 100
120
oToFATED
INLET
VOLUME
Figure 6-25.
Basic
types of impellers for centrifugal
compressors.
uon.)
20 40 60 BO 100 120
obFATLO
l\-ET
VOIUMF
(Courtesy
of Dresser Industries, Inc., Roots Blower Opera-
'120
100
80
60
40
149
120
40
60
B0
100
120
qoRATEO
INLET
VOLUME
ol
l
ll
GUIDE
V
WIDE
T
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Rotating
Equipment
55
P2
=
receiver
pressure
P1
=
inlet
pressure
Compression
Stages:
O =
start
@ =
comPression
@
=
discharge
@
=
expansion
O
=
intake
-tl
@@
Figure
6-26.
Reciprocating
compressor
cycle.
Clearance
volume
o/o
Clearance
=
Volume
Figute 6-27.
The effect
of clearance
capacity.
(100)
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Mechanical Design
of Process
Systems
Clearance
volume
o/o
Piston
DisDlacement
Figure
6-28. A
clearance
(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.
voLuME -.---------+
sourcE
:
cH
urMsl(Y
l5l
tts
l{-
ts
F
6.
It
rs-
l<\ |
rls
lrlo
I
115
100
CLEARAT{CE
:C
|
0O5L
+
O.Smn,
WHENE
L=STHOKE
L-ETGTH
Figure 6-29.
A
pressure-volume
diagram of a compresor
with clearance
(zero
flow
resistances)
[51.
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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
(64e)
Substituting
Equation 6-49
into the
expression
for
volumetric efficiency,
we have
Rotating Equipment
For
compression
ratios of 4 and higher, the
re-expan-
sion
cannot
be considered as an adiabatic
process.
For
these
compression
ratios
the
polytropic
exponent
m
(where
m denotes
the difference
between the re-expan-
sion
PV'
(constant)
and
the compression
PVn
(constant).
For diatomic
gases,
m
:
1.25.
The
value of the
polltropic
curve exponent,
m, varies
with
pressure.
Chlumsky
[5]
recommends for
a com-
pression
ratio of
3:4
the following values of
m be used:
., ..
/pl,
".
:
""
\p,/
-.[(,*i
-
-
'u'(*o]'
First stage
Second
stage
Third
stage
Fourth stage
Fifth
and further stages
m:l 20
m
:
1.25
m:
1.30
m
=
1.35
m:k
"+v"-v4
,lt
-
-----------=;--
-
or
-
-t
(6-50)
where
e
=
*
:
.utio of
the clearance
volume.
Vo.
to
vp
the
volume swept by the
piston stroke.
v"
V^
?"
=
#
:
expression
for volumelric efficiency.
vp
Equation 6-48, the
ratio of
gas volume
pumped
to
the
volume swept by the
pis-
ton
(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-
c
These values are
given
at different
pressure
levels, as ex-
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)
(6-s
l)
where
4,,
:
theoretical volumetric
efficiency
The
volumeuic
efficiency
for
a
perfect gas
(z
:
1)
with realistic effects.
4":100-cR
-
c(cR'/k
-
l)
Cs
:
compression
ratio
:
PzlPr
(6-s2)
80
I9n
1@Z
Figure
6-30.
Curves
for
determining
volumetric
efficiency
[5].
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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
gas (z
*
1)
with
realistic effects,
lv:
100
_
cr
_
c1(cR)i"
_
I
where
zt, 22:
rnlet and discharge compressibility factors,
respec-
tively
As
stated
previously,
reciprocating compressors
fol-
low 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:
PV
(-o_JhtJ=
-']
(6-54)
The theoretical
horsepower may be found
by
Equation
6-16 or bv the
followine:
6o.
:
(P
Vrrr44 u
[ll,I-
.
rl
[,,
*
,l
33.ooo
k-l
[\Pr/
'l
\
2.,
/
(6-5s)
For an
ideal
ga's,
21
:
22
where P1,
Pz
:
inlet and discharge
pressures, respectively,
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
lncreasing
the compression
ratio,
Cp
2.
Increasing the specific
heat ratio, k
3.
Increasing
the inlet
pressure
at a constant
compres-
slon rate,
4.
Increasing
the 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
ma-
chine element.
In multiple staging of
reciprocating
com-
pressors, increasing the cylinder size
is less expensive
than
increasing the number
of
cylinders,
thus
the
ten-
(6-53)
dency
has been to increase
the cylinder
size using a
smaller
number
of
cylinders.
Multistage reciprocating
compressors
have the
following
advantages:
1.
Operating
at high
speeds,
they
can
be
coupled
di
rectly
at
high shaft
speeds thus
utilizing
cheap
electric
motors.
2.
Better balance
of inertia
forces.
3.
The mass
of
the flywheel,
which rotates
at
high
speeds, can
be
made
smaller, resulting
in
a smaller
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
inter-
cooler
or
oil
separator
are
less, thus
making
these
parts
smaller.
6.
Machines
of
various
capacities
can
be
manufactured
using
identical
parts,
making
interchangeability effi-
crent,
7. 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
in-
cluded, can
be
predicted
by
the
following expression:
(6-56)
where
t
:
absolute
temperature for any system
P
=
absolute
pressure
for any
system
k
:
Cp/C',
adiabatic
exponent
1,
2
:
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
es-
ientially 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 condi-
tions. The
gas
passes
through
the
airfoil
blades
in an ax-
ial 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-
,r
-
/P'\?
t-\Pj
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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
de-
creases 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. Mass
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 mil-
lions of
standard
cubic
feet
of
gas per
day
(MMscfd)
in
the English
system and m3/hr in
the
SI
and
MKGFS
systems.
Iass
Flow
The
method
of defining
the
mass
flow
rate of the
gas
h
terms of the inlet conditions of the comoressor is fa-
r
ored
by
many and
is
mandatory
in
calculating
gas
prop-
enies
between stages. Mass flow rate
,?2uJt
be
specified
as
either dry
gas
or wet
gas.
Ifthe
gas,
for example, con-
rains
water vapor, this could drastically change the com-
pressor
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 sys-
rcm.
An
intuitive
feel
for
any system is essential
to
its
successful
desisn.
Rotating Equipment
Actual
or Inlet Volumetric
Flow
Actual
flow rate conditions
at the inlet to the
compres-
sor
is denoted as
acfm or icfm-acfm
meaning actual
cu-
bic
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
com-
pression 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
ac-
tual 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
inter-
nal
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
sys-
tems.
Standard Volumetric
FIow
Specifying
gas
conditions in terms of standard
volu-
metric
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
tsld
:
temperature at standard conditions
P$d
:
pressure
at standard conditions
Volume
flow is expressed as
Q,ta
:
mV,ro
(6-s8)
where the standard
volumetric
flow
is directly
propor-
tional to the
mass flow rate.
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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."
Unfortu-
nately,
this
is
not
the case
with
using
scfm,
as
the
follow-
ing
"standards" cited
by Lapina
[6]
indicate:
English
system
Metric 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
P",a
=
101.3 k?a
t,ra
:
0'C
P"a
:
101.3 kPa
tsa:15'C
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-
sion.
Properly Specifying Gompressor Flow
Gonditions
To
properly
size or select a compressor, the capacity-
no matter
how
it
is
given-must
be
converted to the
inlet
conditions. To
do this
the
following
expressions are
used:
PrVr
_
P2V2
tflt
tzzz
where
V: volurne
P
:
absolute
pressure
t
:
absolute
Iemperalure
z
:
compressibility
factor
In Equation 6-59, if
z
:
1.0 for
a
perfect gas,
and P
and
t are at standard
conditions, then
acfm
:
e_
=
rirV
: "'
(6-60.)
p
where ri
:
mass
flow
rate,
lb./min
V
:
specific
volume,
ft3llb,,,
p
:
density,
lb./fC
The specific
volume,
V, may be
determined by
/r sas\ /
'
\
v
=
z
l::_:l I::-::l
(6-61)
\
mw
/ \1,14Pl
where,
as before, mw
:
molecular weight
2.
scfm
:
(379.46)mh
(6-62)
60
where mh
=
moles/hour
and
rir
=
(rfi)(mw)
and
finally,
(6-63)
_
[(MMscrdx106)1 1,0
nu)1/f*l*)|/t)
"_*,
clm:
qs
=
t--aOoz,
t
\-pJ\460
+
rJ\il
."
-'
where
lie subscript, s, denotes
properties
at the
inlet
(or
suc-
tion)
conditions.
Equation
6-64
may be
expressed as follows:
e.=acrm=*-tltjHP*.,-J
(6-6s)
where the scfm is
based
on a dry
gas.
To
convert
the standard
volumetric
flow
to
mass
flow
the
following
relations are used:
English system:
(6-66)
Sl/metric system:
rir
:
scfm fP"o
'
ro'\
\zd
R.td t.ld/
(6-61)
PIPING SYSTEilS
FOR
ROTATING
EQUIPMENT
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
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the stalwarts
of
academe
to
join
with industry
in
solving
problems
of
piping
and equipment.
The
two
problems focused
upon here are
nozzle
load-
ings and
pulsation
response
spectra distributed
to the at-
tached
piping
system
by reciprocating
machines.
Nozzle
Loadings
In earlier
years
various rotating
equipment
manufac-
turers 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.
Ulti-
mately, 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 load-
ings
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 engineer-
ing
contractors.
For example,
what
is
valid
for steam
turbines is not valid for
inline
pumps.
Because
steam tur-
bines are
more
fragile than
most types
o[
rotary
equip-
ment, using the
NEMA
standard
produces over-conser-
vative
designs
for
most types
of
rotary equipment.
The American
Petroleum
Institute
(API)
also
has stan-
dards for rotating
equipment:
API 611-General-Pur-
pose Steam
Turbines
For Refinery
Service;
API
612-
Special-Purpose
Steam
Turbines For
Refinery
Service;
,\PI
617-Centrifugal
Compressors
For
General
Refin-
ery 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 equip-
rnent specialists claim
that the
API
standards
are only
in-
tended
for
procurement purposes,
and
the
pipe
stress
en-
gineers,
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 expe-
rience with a
given
piece
of
equipment.
For example,
my
several years
of practical
experience
with turbo
expand-
ers 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 consid-
ered unnecessary.
But "thinning-up"
casings
to
reduce
naterial and
costs makes such
allowables
possible,
al-
rhoush
controversiai
at times.
Rotating Equipment
Table
6-2
Typical
Manufacturer
Allowables
lor
Nozzle
Loadings
tor
Inline
PumPs
Mi=
Li
Mo=
Fo
Lo
PUUP
SIZB
(
in)
Fa lb
t-1
-tb
2x3x6
3x4x6
4000
6000
50
00
60 00
4000
5000
2x3xo
3x4xB
4x6xg
4000
5000
6000
5000
6000
7000
4000
5000
6000
4x6xl0
6x8x
0
5000
8000
7000
9000
5000
8000
6x6x20
| 0x1 0x20
12x12x20
500 0
800
0
r 2000
6000
9000
13000
5000
6 000
10000
F
*Miao * {oact 1 2.g
F"
Mi.o
to,n",
-
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
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62
Mechanical
Design
of Process
Systems
There are three
basic options
to
solving nozzle load-
ings on rotating
equipment.
1. A detailed
finite
element
study of
the equipment.
2.
Destructive testing
of
the
equipment.
3.
Close interface between
the rotating
equipment man-
ufacturer
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
ro-
tating equipment manufacturer
disclose
proprietary
in-
formation often required
in finite
element analyses?
De-
structive testing
poses
the same
question,
who will
pay
for it? The third
option-the
pipe
stress engineer confer-
ring
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 man-
ufacturer can at least
expect extra loadings
and can de-
sign
for
it, if
time
permits.
Thus,
the rotary
equipment
vendor working
as
a team with
the
piping
stress engi-
neer(s) can help to
alleviate most nozzle loading
prob-
lems.
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
prob-
lem comes in modular
skid construction, where the val-
ues
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
manufac-
turers'
allowable
standards is
shown
in Fieure
6-31.
Reasonable nozzle loadings
for
turbo
expandJrs
worked
out by the author
and several
turbo expander manufac-
turers
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
con-
figuration
shown
in
Figure
6-32 is ideal.
PULSATION BESPONSE SPECTRA
INDUCED BY RECIPROCATING
EOUIPI'ENT
Reciprocating machinery
often
induces
pulsation
re-
sponse 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
& MRs
are
resultant moments applied at nozzles
MRO
=
resultant bending moment
about
DM,
=
F"-(0") + FD,(dD) + M"y+ MDy
DM,{
=
F"y(d") + FDy(dD) + l\4"y + l\iDy
tr\arr 12
t\-a
i,
110.5.
.-.-L
LtAr'.-"t_
| lL,/..r,r- )l
-
FFs
=
[Fs2"
+ F , + F .]o5
;
Fno
=
[F2o*
+
FBy + FzD.]o
5
FB
=
greater
of FRs or FFD
*&*^ '*ffi.
z.o
Figure
6-31.
Generalization
of
forces, moments,
and allowable nozzle loadings.
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Rotating Equipment
Table
6-3
Reasonable
Turbo
Expander
Nozzle
Loadings
Nozzle
Size
(in
g9
974
1
too
|,623
1,948
2,272
t
so5
l too
1,948
,
<o7
3,246
3,895
aa \
5,189
1 ?OO
I,948
)
5q1
3,246
3,895
La \
5,189
1,948
)
q))
3,896
4,869
5 R4?
6,817
7
,784
1,624
2,436
7 )47
d n{q
4,871
5,683
6,486
2,436
3,654
4,870
6,088
7
,306
8,524
9,730
M,
3,383
5,074
6,7&
8,455
10,146
11,838
l3,513
4,474
6,710
8,947
I
1,184
13,421
15,658
t7
,870
M,
4
6
8
10
'|.,
t4
l6
Nozzle
Size
(in
F,
4
6
8
10
12
t4
l6
&9
9',14
1
too
1,623
|,948
1 11)
t
so{
r too
1,948
t <o7
3,246
3,895
4,545
5,189
1,299
1,948
,)
<o?
3,246
3,895
A \A\
5,189
1,948
I O))
3,896
4,869
5,843
6,817
7
,784
1,624
2,436
a )L1
4,059
4,87r
5,683
6,486
3,383
5,074
6,7&
8,455
10,146
11,838
13,513
2,436
3,654
4,870
6,088
7
,306
8,524
9,730
4,474
6,710
8,947
11,184
13,42r
15,658
r7
,810
Nozzle
Size
(an
6
8
10
12
t4
l6
l8
20
24
648
972
|,296
|,620
L,944
2,268
, 50?
')
cll5
3,240
3,892
l,080
1,620
2,160
2,699
? )10
3,779
4,3t9
4,859
< 100
6,486
F,
1,080
r,620
2,160
2,699
1r10
3,779
4,319
4,859
< ?oo
6,486
|,659
2,488
3,318
4,147
4,976
5,806
6,63s
7
,464
8,294
9,964
1,620
2,429
l tlo
4,049
4,859
5,669
6,479
7
,289
8,099
9,730
2,699
4,U9
s ?oo
6,748
8,098
9,448
10,798
r2,147
13,497
16,216
2,699
4,O49
s lqq
6,748
8,098
9,448
10,798
12,t47
13,497
16,216
4,147
6,220
8,294
10,367
12,M\
14,514
16,588
18,661
20,735
24,912
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64
Mechanical
Desisn of
Process Svstems
Table 6-3
(continued)
Compressor
Discharqe
Nozzle
Size
(in.) F, F, Fz Fs M, My
M'
Mp
4
6
8
l0
1''
14
16
18
650
974
1,300
1,624
I
q4q
) )74
, sqq
? ol
o
|,444
2,165
2,888
3,610
4 111
{ n{l
6,486
i
rqq
1,949
,
soo
3,249
3,899
4,548
5,198
5,838
2,048
3,072
4,097
5,121
6,145
7
,169
8,193
9,202
1,624
2,436
7 )49.
4,060
4,872
5,684
6,496
'7
1a-l
,
165
?
t4q
\
A1L
6,496
'7
a'7q
8,662
9,730
3,W7
4
at)
6,016
7,5r9
9,023
t0,527
12,030
13,514
4,046
6,070
8,093
10,116
12,139
14,162
16,185
l8,
181
PG:
Planar Guide
lA:
IntermediateAnchot
G: Guide
HEJ:
Hinge
Expansion Joint
GEJ:
Gimbal
Expansion Joint
Figure 6-32.
An expansion
joint
arrangement ideal
for steam
turbines
where nozzle loadings must be kept
low
(almost
al-
ways 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 com-
puter
and
(b)
simulating
it
on a
digital
computer.
Basi-
cally, 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
ma-
chine
or machines.
The
piping
supports
are
moved
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 com-
puting
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
pe-
riod
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
pulsa-
tions
from
a reciprocating
machine. A complete
investi-
gation
of
the
pulsation
frequencies and surge
capacity
is
normally required,
which involves the
compressor
bot-
tles
(surge
drums), compressor
suction header,
and suc-
tion compressor
bottle,
the discharge
header, and dis-
charge
compressor
bottle. Two
companies
are
engaged
separately
in
investigating these
problems-Southern
Gas Association's
compressor analog
computer at South-
west
Research
Institute and the Structural
Dynamics
Re-
search
Corporation
(SDRC).
The compressor
bottle
(or
surge
drum)
acts
as a
pulsation
dampener. A typical
bot-
tle 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 compres-
sor 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-
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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 sev-
eral
years.
In the
days
before
analog
and
digital
simulations,
pul-
sation 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
damp-
eners.
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
in-
stalled
to
process
molasses
into refined
syrup
for break-
fast foods.
A
horizontal
centrifugal
pump is to
be in-
stalled 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
nitrogen
pad because the
tank cannot
be
raised
for higher
head at the
pump.
The
cooking
kettle
is
200
ft
down-
stream and
15
ft above the
discharge
flange
of
the
pump.
It
is
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.
Suction
Llne
Pressure
DloP
Fluid
:
tuel oil
TemDerature
:
90'F
Figure
6-34.
Typical
pulsation
bottle
(or
drum)
configura-
tions
that
act as
pulsation
dampeners.
Pressure
=
50
psig
p
:
54.725
lb^lft3
p:
139.53
cp
:
(139.53)(6.72
x
10-a)
:
0.094
lb./ft-sec
e
:
0.0018
L:1.0ft
Suction
line
=
3
"dSch
40,
Di
:
3.068 in
Q
:
150
gpm
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Mechanical Design
of
Process
Systems
Figure 6-35. Hot-oil pump piping
scheme
for Example
6-1.
fuel
tank
cooking kettle
3" x 1tlz"
burner feed
pump
(r5o)sar
lrj,
ll]]ry\
min
\7.479
gal/
\60
s€c/
Entrance
and exit:
K:1.78
l-3-in.d 90" std ell
:
K
:
0.30
1-3-in.d
gate
valve
:
K
:
0.14
6.51I
ft/sec
(7.393)
in.:
I
t n'
)
\1,14
in.r/
l3
068li.,o.srr,
rt
(s4.72s)l9r
N.-=DVP-\
12l
sec
ft'
-
nur.,
r lh
r0.094;-1\
n-sec
With
NR"
:
969.1, the
flow
is laminar.
From Equation
1-6b
we
compute the
friction
factor as
follows:
6L
6A
f=j_:
-
:0.066
N*"
969.1
K.Values
(Velocity
Heads)
Referring to Figures
1-7 and 1-11 we have
the
follow-
ing:
\-.. *
From
Equation
1-4 we
compute the frictional pressure
drop as follows:
ao,
:
ILL
*
'l-
r.leY
'
\D -
I2e,
oo,
-
fro.ooorrts.oorrtzr,,.rrl
t
(3.068)
I
rsa.72sr
llr(6.511)?
tt2
I
'o',,l
tr
sec2
\144
in.2/
zr:z.zr
n-111
sec'-ln
Ap1
:
L524
psr
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Rotating Equipment
Discharge
Line
Pressure
DroP
The
conditions
are the
same
as
the
suction
line except
for the
following:
Line size
=
2-in.
Schedule 40
for
which
Di
:
2.067
o,,:[ry.0"']
ts+.zzs1$
@.64D'?#Hh)
^."^
^.
fr-lb.
-'--
-'
sec2lbr
or 1l/z-in.
d
pump
discharge,
.
(150)#[+r-J(#,J
";;;m[
For 2-in.
S/40
discharge
line,
fr
=
23.642
:
sec
For
2-in.
d
S/40
pipe,
=r/.lR?
(o.os+)
-.1 .
n-sec
"
64
_
64
_^^^^
Nr"
1,438.3
K-Values
for 11/2-in.
Portion
Entrance
:
K
:
0.78
From
Thble
1-7,
for a 2-\t.
x
lll2-in.
diftuser,
K
:
0.055
E*: o.srt
L
:
3.0 in.,
d
=
1.610
in.
Apr
:
2.982
Psi
K-Values
lor
2-in.
Portion
2-2-in.-std90'
elbows
=
K
=
0.40
exit:K:1.0
EK:
r4o
L-200ft
^
^.
-
[{0.044)r200.0X
t
t,
.,
,.oOl
^r,r
-
[-o
06zr
-.
-l
th.
.
ft2
I
tfr:
I
rS+.225r
'il
r14.343).
_
.z
\raa
in.,]
fr-lh
S€C'-lD1
A*
=
63.72
psi
:
too
high-choose
a
1
r/z-in.
x 3-in'
diftuser
With 3-in.d
Sch
40
PiPe,
(lso)sa,
L+fu)(,**)
(ry)
-
(14.343)A(54.72rk
ft
sec
(7.3e3)
in.2
(r-
*--L)
K-Values
for 3-in.
d
PiPe
2-2-in.-std
90"
elbow
=
K
=
0.54
exit:K:1.00
[('-ryt
-
e3.642t
L,ro.rrr,
hl
r".
-
l\
tz
I
'-
tt'l
=
r.zzo.s
| 10.094;.'"'
I
I
tt-sec
I
@
:0.037
Nt"
Nn"
:
:
969.125
Dr:
t.so
l1 4lr
(6.511)
a,so.tts,
l :
\l2 l
sec
(0.094);lb'
n-sec
6A
f:
-
=
0.066
Nn"
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68
Mechanical Design oI
Process
Systems
^_t
pf_[
(0.066x200.0)(12)
(3.068)
+
r.54]
(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
:
0.78
From
Table l-7
,
for a 3-in.
x
lllz-in.
diffuser,
K
:
0.337
E*:
r.ttt
L
:
3.0
in.: d
:
1.6i0 in.
Nn.:1,720.5;f=0.037
..^.: lQ
ji1Ii0.,
"rl
(1.610)
'-'
l
lh fr2 / rfr?
I
\s4.125)'+
(23.642f
::-
|
'"
,I
Irr sec? \
144
in.2/
V--
fr-1h
)/1t tr "
'"m
sec'-lDl
Apr
:
3.912
Psi
Total
pressure loss in
discharge
linc
-
13.309
-
3.912
=
17.221
psi
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.
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 re-
quirement
of a
centrifugal
pump
is that the
handled
liq-
uid
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 Fig-
ures 6-38
and 6-39
for
determining viscosity
effects.
To
use the charts, the fluid being handled
should be
Newto-
nian. Gels, slurries, asphalt,
and other non-Newtonian
fluids should not be considered
with
these
charts. In han-
dling
such
fluids
a
positive-displacement pump
is
usually
required.
(Example
6-2 is an illustration
of
how
to
han-
dle
such a
liquid.)
To use Figure 6-39 we
must
convert the
absolute
vis-
cosity
io
kinematic viscosity.
This is done as follows:
p
:
139.53 cp at
90'F
w
:
54.725
lb/ft3
io.oooozog\tu-r..
rr-lh
(139.53)cpl
.
--"1
;;--(32.17)
-ij-i: -.
\
rcp
/
r(' rDr-sec'
th
154.'725)=
rt"
f12
z
:
0.0017-:-
sec
or
0.0017
ll
sec
centistokes
0.0000107639
i:
sec
v
:
159
.261 centistokes
Using Table
l-8
we
make
the
viscosity
conversion
from centistoke to SSU as
follows:
rq5
0.226r-::::=v
t
t2
-
704.695t
-
862.832
=
0
t
:
706 SSU
Now, looking at Figure 6-39
we
see
that for 150
gpm,
TDH
:
82
feet,
and
706
SSU
we obtain the
following
coefficients:
Cr:056
Ce:090
Cu
=
0.90 for 1.0
x
Q^*,
where
QNw
is the water
capacity
at which maximum efficiency
is obtained
The corrected
flow
rate becomes
^
sDm
150
Qc
=
"i...
-
:-:
=
166.61
=
167
spm
LO
U.YU
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Rotating
EquiPment
69
O
o
@
(o
<o
{)
5lL
a
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70
Mechanical Design
of Process
Systems
Pump Hydraulic
Design Calculation
Sheet
Liquid
fuel
oil
Viscosity at PT.
(Pumping
Temp.)
139.53
Vapor
pressure
at
PT
0.010
cp
psra
Sp.
gr.
(.y)
at
PT.
o.477
Flow
at ambient
temp. 150
gpm
Operating flow at
PI
150
gpm
Design flow at
PT.
150
_
gpm
Suction
Source
pressure
Static head
-
APr,
line
loss
Suction
pressure
-
Vapor
pressure
NPSH avail
NPSH
avail
NPSH req'd
1.52
65.08
=
-
0.01
=
65.07
_
171
t
=
82.017
64.7
'1.9
psra
psi
psi
psia
psia
psia
ft
ft
1.9
Discharge
Terminal
pressure
=
71-38
psia
Static head
-
APr
discharge
Piping system
Other
17.221
psl
psi
psl
psia
psra
psra
feet
Discharge
press.
=
96.201
-
Suction
press.
=
TDH
3'1.12
bhp at Duty Condition
DnpD
=
The total dynamic head
becomes
TNH
R'
Hc
=
'i-"
=;:91.
=
9l
fr
LH U.YU
Now, referring to the manufacturer's
curve
in
Figure
6-40,
for
Qc
:
167
gpm
and
TDH
:
91
ft,
we
deter-
mine 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-
-
(167)19l)10.877)
-
9.53
ho
3,960
4.
(3,960X0.153)
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.
=ffi =
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.
impel-
ler. In selecting a centrifugal
pump
it is desirable for the
required flow rate
to
fall
in
the middle
of
the
pump
curve.
Avoid extreme
sides
of
the
manufacturer's
perfor-
mance 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 for-
get
the
potential problem
of back
pressure
that
the
pump
could
be
exposed
to under varying conditions. For exam-
ple,
if
the discharge line contained a bypass valve that
diverted
flow
to either the cooking kettle or to
a reser-
voir 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,
result-
ing in a lower TDH. With the same size impeller,
as
the
TDH lowers- the
flow rate increases as
the curve shifts
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Rotating
Equipment
300
26
150
1(n
80
60
40
30
20
15
10
8
10,000
8,000
6,000
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.)
'4,000
3,000
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72 Mechanical Design of
Process Systems
Figure
6-39.
Performance
correction
chaft for
viscous liquids.
(Courtesy
of the
Hydraulic Institute,
Cleveland, Ohio.)
i
F>
*.2
;t
?E
P,Z
E<
o6
;
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Rotating Equipment
Table
6-4
NEMA
Frame
Dimensions
___o
Ir
r--i
F-
E
=q-
E
-->l
H-SIZE
HOLE
Source:
Goulds Pumps,
Inc.
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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
maxi-
mum
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)
:
3.706 or 4 hp with water
'
3.960(0.46)
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.
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
Exam-
ple
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.
Suctaon
Line
Pressure
Drop
N*"
:
DVP
:
{lP}n
(3.78r) a
tes.soer
k
\tzl
sec n"
Fluid
=
coating mix p
Temperature
:400'F
L
Pressure
=
20
psig
a
Suction
line
=
4
in.
Schedule
40
e
:
0.0018
p
:
938.08
cp
=
(938.08)(6.72
:0.6:0
lb'
ft-sec
4
lb.
(0.630)
_'
-
ft-sec
:
193. t 16
From Equation
1-6b we
compute the
friction
factor as
f:
-:-
=
0.332
Nn"
K.Values
(Velocity
Headsl
for
Suction
Line
Referring to Figures
1-7
and 1-11 we have the follow-
tns:
En'irance andexit
:
K
:
1.0 + 0.78
:
1.78
2-4-in.
plug
valves
:
K
:
2(18X0.017)
:
0.612
1-4-in.-90" standard elbow
:
K
:30(0.017):0.510
\-r
LtK
:
2.9O2 velocirv
heads
From Equation 1-4 we compute the
frictional
pressure
droo
as
follows:
oo, [<o.zs:xgo.ox
r2)
*
a.M8l
L
(3.068)
I
(e5.eoe)
k
(6.5ilr
g
F- -,-
fr-Ih
SeC'-lD1
Apr
:
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
vis-
cosity
liquids.
The
pump
manufacturer
has
the
perfor-
mance
curves
rated
in
terms
of
kinematic
viscosity in
SSU. Now converting our
viscosity to SSU's we have
(rso)
sar
(_ri'
)tr_ry
min
\7.479
gat/
\60
sec
:
95.909
lb*/fc
:
11.0 ft
:
150
gpm
+
Dr
=
4.026
in.
x
10-4)
(t2.73)h.2H*l
:
3.781
ftlsec
Ssu
:
ll(.1,]1
635)
(938.08X4.635)
=
1.459.78 SSU
w/g
195.9091
l-l
\
32.2
l
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L)
o
q
o
r)
(o
o
lt
a
z
E
o
o
ro
o
to
N
o
o
GI
o
lo
o
o
o
to
ir
o
o
o o
o
izu(o @sl-
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Rotating
Equipment
Pump Hydraulic
Design
Calculation
Sheet
Liquid
adhesive
mtx
VG;o;itrt
PJ.
(Pumping
Temp.)
938
08
cp
\/.^^r
^;aee,,ra
at
PT
-
PSla
qn
^r
/_ I .r PT
.1.537
rioriat
ihbient
temo. -
not
lEn
Operating
flow at
PT.
j:X
YI:
{^n,.r PT
150
Suction
Source*
pressure
Static
+
(headlift)
-
APr
line
loss
Suction
pressure
-
Vapor
pressure
NPSH avail
NPSH avail
NPSH req'd
2+2=4ltrcqulred
14.7
psia
psi
psi
psia
psra
psia
ft
ft
Terminal
pressure
=
16.70
Static
tift
=
2g.g1-
-
aPr
discharge
Piping system
Other
13.74
Discharge
press.
=
53.75
-
Suction
press.
=
-8.70
psia
psl
psi
psi
psia
psia
psia
feet
-
4.0
-
2.O
=
8.70
=
8.70
ri
na
=
6-90
TDH
TDH
=
67.58
lrin
NPSH avail
>
NPSH
req'd + 2
lt
bhp at
Duty Condition
nr"^
_
(gpm)CrDHXr)
*
(150X67.58X1.537)
=
n
=
3g.g4o/o
(3,960Xrr)
(3,s60X10)
bhp at
Maximum Capacity
Condition
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 Fig-
ure
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)
:
0.496 or 49.6%
'
(3,960)(10)
This efficiency rating
is
quite
common
with a rotary
gear pump
handling
a
highly
viscous
liquid.
Now, refer-
..
(oom)ffDHX'v)
bnp"c
=
:(38;bX4-
TDH
=
total
dynamic
head
TDH
=
discharge
press.
-
suction
press
4
=
pump
efficiency,
o/o
ring to
Table
6-4
one can observe the
classifications
of
electric motors.
From Figure
6-44 we
see
that
the
viscos-
ity
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 re-
quirements,
we select
a
lO-hp motor, because
7llz hp
is
too
small.
Notice that
the
pump
has built-in
jacketed
en-
closures
to match the
piping,
which is hot-oii
traced, to
keep
the
fluid
in the
piping
and
pump
liquid.
These
jack-
eted 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
wa-
ter
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
Figure 6-42.
Pump
hydraulic design
calculation
sheet
for Example
6-2.
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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.)
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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 centrifu-
gal pump
is impractical
because it cannot
handle a non-
Newtonian
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
mix-
ture
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-.
(6-10)
cp.
-
1.986
13.08
=
1.18
13.08
-
1.986
The compressibility
factor
for
the mixture
is deter-
mined
from
the
reduced
pressure
and reduced
tempera-
ture. Thus.
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80
Mechanical Design
of Process Systems
Gas Mol
o/o
Table
&5
Tabulation of Gas
Mixture Properties
P"
(psia)
t"
("R)
Gas
Mixture
Pc
Propane
Ethane
Methane
44.t0
30.07
16.07
17
.64
9.O2
4.81
246.q
212.40
20Q.40
659.20
40
30
30
666
550
343
616
708
668
266.40
6.86
165.00
3.68
102.90
2.54
534.30
13.081.47
Table 6-6
16l
Typical Centrifugal Compressor
Frame Data*
Nominal lnlet Volume Flow
ffi
Frame (icfm)
(m3/h)
Nominal
Nominal
(lt-lbl/lbm)
(k.Nm/kg)
Nominal
Polytropic Rotaiional
Efficiency
Speed
(%)
(rpm)
Nominal
(in,
(mm)
lmpeller Oiameter
English
Metric
B
c
D
E
F
l,000-7,000
6,000- 18,000
13,000-31,000
23,000-44,000
3
3
,000-
65
,000
48,000-100,000
1,700-12,000
10,000-31,000
22,000-53,000
39,000-75,000
56,000-110,000
82,000- 170,000
10,000
10,000
r0,000
10,000
10,000
10,000
l
l,000
7
,700
5,900
4,900
4,000
3,300
406
584
914
1,120
|,370
30
30
30
30
30
30
l6
30
36
44
54
76
76
77
77
78
78
*Wite
this table is based on a survey of currently
available equipment, the instance
of an, machinery duplicating
this table
woud
be
purely
coincidenml.
P
.D
:0.076
0
Computing
the
compression
ratio
we have
^
P,
150
''
Pr 50
Assuming
that we have a
perfect gas
(z
:
l),
we can use
Equation
6-14 to
find
the average
discharge
temperature.
Thus, we
have
(6-14)
Now from
Eouation 6-32
we
have
659.20
t 60
+ 460
534.30
:
4.97 3
Now from
Figure
6-45,
we have
zr
:
0.972:
inlet compressibility factor
Using Equation
6-6
the
inlet
volumetric flow is
-
-
,mRt,
V:
----"
(6-61
(mw)Pi
,,
(0.972x3,000)(
l.545x60
-
460.)
(144)(31.47Xs0)
t1
n-r
/r-
r\
T=\-o
1"
From above,
Y
:
1O,339.276 icfm
(or
acfm at the inlet)
kr
:
l'18
Using Table
6-6
from
Lapina
[6],
we find our
unit
to
ltp'
=
0'76
he a Frame
B
with nominal
values
to be
as
follows:
Thus,
Hp"
:
10,000
ft-lbfnb.
N"
:
7,700
rpm
rp^
:
76%
l0
18\
r0.i6l
-
0.116
u.18/
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from
which
n-I
0116
t?
=
tr(C
"
:
(60
+ 460X3.0)
or
t,
:
590.68'R
:
130.68'F
Now,
the
average
compressibility
for
the
gas
mixture
must
be
obtained.
From
above
the inlet compressibility,
zr
:
0.972
Compression
ratio,
p-
150
rc^r,=:j:
'-"
=
O.228
P,
659.20
Temperature
ratio,
,_,
_tz_560.68
_
r
^<
rR,2-L-534-30-'"-
Using
the
compression
ratio and
pressure
ratio
we de-
termine
the
outlet
compressibility
factor
from
the com-
pressibility
charts
in Appendix
E.
Thus,
zz
:
0'93
v
=zt
zz
_0.972
+
0.93
_
0.95
-22
In determining
the
polytropic
head
we
use
Equation
6-
33,
where
Pz=Pa
and
the average
ratio
of
specific
heat,
k, is
k
=
1.18
=
inlet
conditions,
which
is
an
approximation. Thus,
'
=
(-*-)
(*,{,)
[[&J-"*-"
-'],u
Rotating
Equipment
81
(6-33)
f-
1.00
compressibility
tactor,
Z
=
PV/RT
0.92
0.94
0.91
0.02
0.03 0.04 0.05
0.06
reduced
pressure,
Pr
Figure
6-45.
Compressibility
curves
for
very
low
values of reduced
pressure.
(Reprinted
by
permission of Chemicql Engineering,
Mc-
Graw-Hill
Company,
July
1954.)
N
---1
------J
-t
401
=
2.00
1.60
--
S
=
\
N
\s
iK
(\
S
-->
=
-'----
=
'1
0
\
\-"%_
ii(
><
\
x
-tl
N
ilxl
riP{
/-
x
\
-0.85
>i
'r;{
\*r-1
\l
\t
I
BO
-x
I
0.60
Y
'oS
*al
\"'r
\
\
\
0.01
0.07
0.08
0.09
0.10
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a2
Mechanical Design
of
Process
Systems
from which
r
:
[(t't31srq'01
(8.62r)
r(3.0f
,,6
-
r]
H
=
29,913.143
ft-lbr/lb.
The
required
number
of compressor
stages
is determined
by
where
Ho.
:
maximum polytropic
head per
stage, ft-lb/lb.
(see
Figures
6-46 and
6-47)
Using
Table
6-5, we
have
Thus,
*-
='ni?l
lo'
-
2.ite
=
3
The required
rpm
is
I u
\05
N:N"l
..P
I
'
\Ho.
N.J
(6-10)
I rqqrr
lo'
N
=
r7 TOOr l,:-"'' |
-
7
l3l
rpm
Lr
r t.ooox
r)l
The required shaft
power
is
^
rir
H.
(3,000)(29.913)
r.t:
'
"
33,000
4o
(33,000X0.76)
P,r
:
3,578.11 hp
Using
Table
6-7
to
determine the mechanical
losses, L.,
we find
that
L.
:
(0.02sx3s78.11)
:
99.453 ta
(P.rL"*r
:
P.r
+
L.
:
3,578.11
+
89.453
:3,667.563hp
II
N.,
:
-q
.H-
(6-68)
(6-69)
[t26.
tttm'ntl
I
tzo.
r
lt:
r
.+zr
I
L
krzrrr
I
L(
| . t8
)(0.972)(520t
0
=
1.377
From Figure 6-46,
He.
:
11,000
ft-lbfnb.
12,000
11,000
10,000
9,000
8.000
7,000
6.000
5,000
4,000
3,000
E
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
6:
lNTuw
ltl
I
limit
for miled
yield
slress
I
mpeIers
I
Figure 6-46. Maximum
polytropic
head
per
stage-English
system
[6].
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Rotating
EquiPment
Eru
=32
ot
928
Ezc
e20
o
.-
16
5rz
'i^
't.0
1.l
1.2
1.4
1.5
1.6
1.7
0
Figure
6-47.
Maximum
polytropic
head
per
stage-metric
system
[6]'
Table
6-7
[61
1.9
.8
Approximate
Mechanical
Losses
as
a
Percery
trl
u=@
-
I'n,J,,'*Lon"N
v
krzlTt
ttl
slress
impellers
English
(hp)
Metric
(kw)
Mechanical
Losses,
L,'n
(ohl
0-3,000
3,000-6,000
6,000-10,000
10,000+
0-2,500
2,500-5,000
5,000-7,500
7,500+
3
2.5
2
1.5
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
compres-
sors 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
compres-
sion,
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
insensi-
tive to
the
value
of
k
and
thus
n/(n
-
l).
The discharge
temperature
is
much more
dependent
on
the
value
of k.
Using
the
inlet
value
of k
will
yield
a con-
servative
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].
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84
Mechanical
Design of Process
Systems
EXAMPLE
6-4:
INSTALLING
A
COMPRESSOR AT ELEVATION
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 com-
press
the air to
7
atmospheres, or
102.87
psia.
Now,
r'
/^-
^.
.
rP\
v
:
33.3
r
l3s.314
",1
:
I.175.96 cfm
mtn \
m"i
Compression
ratio:
Pr
=
11.53
psia
Pi
:
102.87
psia
C-
:
t02
g
=
8.92
>
6.
thus requiring two-stage
I l.)J
compresslon
With an
intercooler,
you
must consider the
gas pres-
sure
drop across
it.
The minimum
horsepower is devel-
oped
when the ratios of compression
are
equal
in all cyl-
inders. The
ideal
case
is
with
no intercoolins
in which
Ludwig
[7]
suggests
Pr=Pr=&:...:
P"
Pr
P2
P3
Pn-r
and
with intercooling,
Po1
_
Pa2_ Po3_ Pr.
n
-P__,'-4-
4-'
(6-71)
(6-'72)
where
subscripts 1,2,3, ..., n
:
gas
conditions
across a cyl-
inder in which
I
represents
the
first
stage,
2
represents
the
second
stage, etc.
subscript
d
:
interstage discharge
pres-
sure condition, directly
at
the cylinder
prime
(')
:
represents
the actual
pres-
sure
to
the suction
of the
succeeding
cylinder,
which
rs the interstage
discharge
condition that
is reduced
bY
pressure
drop
over the
in-
tercooler system
subscript
f
:
final
discharge
pressure
from a multistage
machine
t4 t3 t? tl
Alfr
o3ph.ric
Pn33ur., lb./sq.
in.
Figure
6-48.
Atmospheric and barometric
pressures
at
vari-
ous altitudes
[7].
For
a
multiple
stage
unit,
the compression
ratio
is
p.
wnere
LD
:
i
'',
P.
D.
-z
p:
rol
p.
cD-
:
--:l
'.J
Dl
P,
^n
D1
'o.-l
Thus, for two
stages,
/P.
\0.5
t_,21
LRI
:
LR2
:
l;l
\r
l,r
Cnr
:
Crz
-
CR3
:.-":[bJ
(6-73)
(6-74)
Thus, the compression ratio
per
stage
is
approximately
CR:(8.92)05=2.99
and
for
the
first
stage,
Pr
:
11.53
psia
5
Pdr
:
(2.99x11.53)
+
i
=
36.94
psia
For
second stage,
Por
=
(2.99r(11.53)
-
i:
31.97
psia
8p00
2,000
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Pr
:
102
87
Psia
The discharge
temperature
the
first stage
is
by
Equation
6-5s
ta,
:
ttFJ?
for
k
=
1.406,
tu,
:
(85
+ 460)(2.99)0'?8e
='147.94"R
or
tnt
:
287 94"F
The
discharge
temperature
for
the
second
stage
is
based
on the
discharge
temperature
from
the
intercooler.
The
intercooler
cools
the
air to
90'R
which
is the suction
temperature
to the second
stage.
Thus
kz
:
tiiR"G
tvr
=
(90
+ 460)(2.99)0
287
:
754.80'R
tr2
:
294.80"F
Selecting
the
Reciprocating
Gompressor
A reliable
and
quick
method
to
approximate
the
com-
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,,
(*)
(6-75)
where F"n
is determined
in
Figure 6-50,
converting
the
acfm
to MMcfd
we have
MMcrd
=
(r.r75.e6){60x24)
('-lr;(14_:#.
J
:
I,421,068.508
For the
first
stage,
F.,
=
69.6
bhp
:
(6e.6)
Hi+Hfl
:
e8.eo6
hp
For the second
stage,
/,,
..\
1f9_ Jl)
Mcfd
: (
t.421.068.s08\j-r:)
touo
_
uu
/
Rotating
EquiPment
-.
11.203,486.3721
bho
=
(69.6)
l
','-
'=.
l
=
83
763
hp
'
\
l.u
x
lu"
/
Total
horsepower
:
98.906
+ 83.763
=
182.669
or 183
hp
Mechan
Gas
vek
3,000
f
Gas
ref(
intake
I
ical efiiciency,
95j
'city
through
valv€
(
|
(APl
equat(
to
'14.4
psia
.
rfll
$
z
i.?_
2
t
7/.,
/,,/'
v
lllllll
Ratios
below
1-4 are
subiect lo
signiticanl
etror, consult the
manufacturer
foa best
dala.
ttttttl
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
compres-
sors.
(Courtesy
of Ingersoll-Rand
Company.)
1.5
2.0
2.5
3.0
Ratio
of
compr€ssion,
Figure
6-50.
Horsepower
correction
factors
for specific
grav-
ity
[8].
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.
9
I
q:
'
I
60
l:
58fi
561-
:
54f
1
521
50|.-
48r
46r
Ml
o2l
40l-
*l
36
l-
3o
l-
"'l
30
l-
28f
26
l-
24Y
22u
0.60
:1,203,486.372
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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 oper-
ation
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 of
volumetric efficiency we have
where
4"
:
volumetric
efficiencY
Q
:
capacity at
inlet
conditions, acfm
Cp
:
cylinder displacement, ft3/min, where
""
=
I4*l ",)E'|"
\
144
I
\121
(6-77)
where
L
=
piston
stroke, in.
,46"
:
ar€r of
head
end
of
piston,
in.2
A""
:
area ofcrank end
piston
(,46"
minus the area
of
the
piston
rod), in.2
N: Ipm
A convenient
formula
recommended
by
Neerken
[8]
is
n.
=
o.si
-
..
[eU:l
I
zdtzs
I
(6-78)
where
C"
:
cylinder
clearance
Cp
:
compression ratio
k
=
ratio
of
specific
heats
2., za
=
colllpr€ssibility factors at
the
suction and dis-
charge conditions, respectively.
For our
machine
we
have the
following
design:
L
=
220 mm
:
9.661 in.
:
piston
stroke
N
-
500
rpm
Dr
:
500
mm
:
19.685 in.
=
diameter
of first stage
cylinder
Dz
:
300
mm
=
11
.81
1
in.
:
diameter
of
second
stage
cylinder
For the
first
stage,
piston rod
diameter
=
65 mm
:
2.559 in.
/r o
<rs\t
A,-
=
r l'-
"""1
=
304.341 in.2
-
\21
..
=
lrogL:
,2.]2t
)lr
uu'),roo,
"\
t44
l\t2 I
:
1,512.514 ft3lmin
For the second stage,
piston
rod diameter
:
60
mm
:
2.362 in.
o
LD
10e.563
in.2
_
*(.9)'
,n.,
:
105.181
in.'z
10e.563 + ro5.r8r
'l
{gjutl ,roo,
r44
l\
t2
I
(6-i6t
o,.
=
"
(";t")'
:
roe.563
in.?
c":l
:
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
at-
tempting
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 de-
sign reciprocating
compressors is
given
by
Chlumsky
t5l.
EXAMPLE
6.5: NAPHTHA PUMP
SYSTEiI
DESIGN
A
cosmetic
manufacturer
of
women's
lipstick
con-
tracted
a
chemical
company to formulate a chemical that
satisfies certain specifications.
The
chemical
process
en-
gineers
determined that 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.
/r
sso\'
&.
:
304.34r
-
"
\;)
=
2ee.
re8 in.'
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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
manufac-
turer'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
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,
resulting
in
a
colorless
liquid.
Next, the
naphtha
is
pro-
cessed
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
=
141.5:131.5
^tp
7w
where
.yo
:
the specific
gravity
of
the
petroleum
product at
60"F
l*
:
the specific
gravity
of
water at
60"F
(6-79)
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88
Mechanical Design of
Process Systems
9"
g',
g',
$+-Llj
',g',2,-O,g',
9"
5',-O"r
_L
NLL
=
normal liquid level
Figure
6-52. Pump-piping
scheme
of light
naphlha
cut used 10
manufacture women's
lipstick.
(Example
6-5).
The
relationship
between
the
'API,
temperature
is
given
in
Figure 6-53.
For our
case
of
68oAPI,
using Equation
6-79,
we
have
ro:141
5:
o.zo9
7*
199.5
in
which
7o
:
(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
and
p
:
45.55
lb/ff
The
Flow
from
the Reservoir
to
Naphtha
Storage
llank
The reservoir
is of such large
magnitude that
the
head
of
liquid
is 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-
Dresslon:
o
:
rr.os o'(\)"
(6-79)
The velocity
heads
on the
line from
point
@
to
point
@
are as
follows:
Values
of f1
are determined
from
Figure
1-7.
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Entrance:K:0.78:0.78
2-4-in.
plug valve: K
:
18
fr
:
18(0.017X2)
:
0.612
Exit:K:1.00:1.00
sr-
LtK
:
2.392
Rotating Equipment
APr
:
1.223
Ot'
12
ft
of
naphtha
head
=
(12X0.325)
psi
:
3.900
psi
3.90
psi
<
10.5 psi
nitrogen
pad
This
pressure
differential
will
cause the
naphtha to be
forced back
into
the reservoir. The number of feet
re-
quired
to
deliver
the
liquid to
the tank
will now
be deter-
mined.
Since
we already
have
12
ft
in the tank,
then
x
+
3.90
)
10.5
psi
x
=
6.60
psi
=
20.308
ft
Adding
an
additional 26
ft
of
head
we
have
38
ft
:
12.35
psi
-
1.223
psi
:
I l. 127
psi
>
10.5
psi
The new
flow
rate
is
o
ft
:
4.46'1
:::-
sec
-.
DVp
l\Re
:
-
=
p
:
93,088
fi
=
'7
.948
-:-
sec
f
l rnin
I
\oo
r""/
2.640
lb.
I
I
hr
I
ft-hr
\3,600
sec/
r-05:
-2r"r.[+.
rt=*)
(1-6a)
Nr":
0.0884 ft,
(rgl*
(7.e48rx
a
r+s.ss1$
\ul
sec
r"
:
165,633
t-- \
,,,
aP,
=
ILL +
l- x.l4I
t.t
H
|
16
\s I
'Etc
o,,:
[rr1*opu"'
*
r.,nl
t(Hft I
(4s.5s)k
$.46if
##j
fr-lh
SeC"-lDf
"*n
tb
lt* \
-
-
-
ft-hr
\:.ooo
sec/
Applying
Equation
l-6a, f
:
0.0319
r.-"1
aP.
=
l(o.o3l9x1o5.83)
ft
+
2.3921
|
4.026
-
|
|
-n
I
t12J
rrelr'
ft-lb.
SeC'-lOf
AP1
:
3.364
Or'
38
ft
-
APr
=
12.35
psi
-
3.864
psi
:
8.486
psi
8.486
psi
< 10.5
psi
pad
Select a 6-in.
{
Sch
40
pipe
Q
:
1e.65(4.026)
[rrrt*J"
:
177.2
wm
a
=
r. r co [2
4
lb./ft-hrl
:
z.u
lb^
' '\
lcp
/
ft-hr
0.0884
ft,
(1 4|-(a.a67;x
A(45.ss)k
Q
:
1e.6s(4.026)
(#r)0'
:
315.317
gpm
Using Np" to check
the
friction factor,
f:
0.03198
Now,
2.51
(93,088)(0.17875)
(1-4)
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90
Mechanical
Design
of
Process Systems
Repeating
the
hydraulic
analysis
we have
Entrance
and
exit:
K
:
1.78
2-6-in.
{
plug valve: K
:
18
fr
:
18(0.015)
:
0.27
[]-::Yl(a.8a)(a5.55)
N*"=''-';
i
:100.863
2.6401
r
I
\3,600/
f+
:
0.032
(from
Equation
1-6a)
r l.---.
./
r\
or,
-
l,o.orrt,zr.rtr,
* ,.rrnlI
tt'd'*l@
-ll+.oze\
|
2(32'2\
t I
't
I
I
APlo
=
9.5110t'
For a
3-in.
Iine,
L
:
1.0
ft
,rnr,l-l\[)
_
\7.47e1
\601
-
(0.0s130)
-
|
3',0168),s.:0,,+s.:s,
tl".: I}- ..
=
t32.449
2.6401
1
I
\3.600/
8.34 ft/sec
e
:
1e.6s(6.065)
(,
or--)"
=
513.107
gpm
19'ut\,r.rouo,
,r,
\
12,
rr ne
-
--
----7------ -lll
t*tr-oj
f:0.01803
t
rll
l(0.0r803x105.83)
,
^ ^.^lt+s
ssxs
zot'?\r++/
APr:l
-
-r
-.U)Ur-
-
ffi-
I l6.o6sl I
z\rz'z
I
r
\-rzl
I
APr
:
9.939
Ot'
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
pres-
sure
head of naphtha entering
the storage
tank.
Naphtha
Pump
Hydraulics
Suction
Line
For
4-in.
Sch
40
portion
of line, L
:
23.313 ft
K-Values
0.2006
Dr :
z.oso
fr
5.700--
sec
a4
-
1'79
0L')
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 gal-
lons. We select 4.35 hours, which
yields
a flow rate of
s9.990
eat
{+ )
:
re
|
.57
r
=
re2
spm
4.35
hrs
\60 min/
We
will
size a centrifugal
pump
with
192 gpm
capacity. For
192
gpm,
0D(#(*J
:
4.84 ftlsec
(0.0884)
Entrance and
exit:
K
:
1.75
1-4-in.
plug valve: K
:
0.306
4-in.
x
3-in.
reducer: K=0.163
sr-
LtK
=
2.219
For
3-inch
Sch 40
portion
of line:
K-Values
3-in.d
plug valve: K
:
(18)(0.018)
:
0.324
4-in.
x
3-in. diffuser: K:Kr:0.055
D*-*"
f:0.0344
t
la5.5sl,t.r,'(,;)
re,.
=
l(o
ol'l4t(t
or
-
o 3791-
''
l /r.oos\ |
2\32
2)
r
\,2/
r
APi.
=
9.175
ntt
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Rotating
Equipment
The total
pressure
drop
for
the
suction
line
:
AP,
AP.
=
APlo
+ APr3
:
0.686
Psi
Discharge
Line
L
=
60.708
ft,
4-in.
Sch
40
K-Values
(0.0884)
1-4-in.
swing check:
K:
(100)(0.017)
:
170
1-4-in.
gate
valve:
K
:
(8X0.0i7)
:
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
Entrance:K=1.0:i.00
D"
:
o^oto
(45
5r(8
34r(*)
2(32.2)
t
ar,,
=
l(o
ol2'(6oi7o8)
+
o.oro
|
14.0261
t
I
r? |
bhe
-
(19?)(6172)(9
73)
=
3.i
or
a4
hp
motor
(3,960x0.61)
The
Maximum
Capacity
Condition
The small
chemical
company
nearby
that
manufac-
tures
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.
i1,uti,,
,0,,0,
,r,
I 1) |
N^".'"-';
i
=
132'449
-ttl
z
e+o[3
roo/
fi
=
0.0344
rl
aP,,
:
l(o 934'(i
o)
* o.e43l
I lr.068l
I
t
I
17
I
r
AP1,
:
0.460
Psi
The
total
pressure drop
for the
discharge
line
-
APo
APp
=
AP1,
+
APi.
:
|
42'7
+
0
460
:
1
887
psi
From
Figure
6-54,
the
pump
hydraulic
design
calcula-
tion
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
ATM.
pressure
(psia)
+ x
+
static
head
(psi)
/
friction oressure
\
i/
tiquio
uupot
'i
=
\arop
on
suction
line
tAP.rf
=
\preisure
rpsiarJ
where
x
:
minimum
pad pressure required,
pslg
14.7+x+3.557:0.511
+
20.85
+ 21.361
psi
select
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
bhp
:
QHr
(6-2)
3,96Ou
14
026'1,+.
s+x+s.ssr
t*.
=
E*'
too.8b3
2.6401
I
I
\3,600/
f
:
0.032 (from
Equation
1-6a)
APlo
:
1.427
Ot'
For the
3-in.
portion
of
the discharge
line,
L
:
3
ft.
For
3-in.
Sch
40
pipe,
d1
:
3.068
rn.
K-Values
Entrance:
K
:
0.780
4-in.
x
3-in.
reducer:
K:0.163
DK
=
o,sa3
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Mechanical
Design of
Process
Systems
Equivolents
of
Degrees
APl,
Specific
Grovity,
Weight
Pounds Per
Gollon ot
Degrees Boum6,
Densily,
ond
6OF/5OF
Degrees
API
Baum€
Scale
Values
for API
Scale
oil
Values for Baum6
Scale
Liquids Lighter Than
water
Liquids
Heavier
Than
Water
peci6c
s
W€ight
D€nsity,
LblFt3
Pounds
per
Gallon
Specific
Gravity
s
Weight
Density,
Lb
/Ft3
Pounds
pef
Gallon
Specific
Gravity
.s
Weight
Density,
Lb/Ftx
Pounds
per
Gatlon
8.337
8.454
8.574
4.697
4.8L4
8.955
9.0E9
9.XX8
9.371
9.518
L67r
9.828
9.990
10.159
10.332
10.512
10.698
10.891
1r.091
11.297
11.513
11.737
11.969
12.2rO
12,462
12.998
13.244
r3.583
13.895
14.22?
14.924
t5.302
15.699
16.118
..'
'..
l0
t7
I4
l8
0
2
6
8
20
22
'),4
'].6
28
30
32
34
36
38
40
42
46
48
50
54
5E
60
64
66
68
70
7X
78
80
a2
84
E6
88
90
92
94
96
98
100
'.:
,.oooo
0.9861
0.9725
0.9593
0.9465
0.9340
0.9218
0.9100
0.E984
0.8871
0.8762
0.8654
0.8550
0.8448
0.E348
0.8251
0.81 55
0.8063
o
.797 t
0.7883
0.7796
o.77tl
o.7624
0.7547
0.7467
0.7389
0.7313
0.7238
0.7165
0.7093
0.7022
0.6953
0.6E86
0.68r9
0.6754
0.66S0
0.6628
0.6566
0.6506
0.6446
0.6388
0.fl3r.
0.6275
o.6120
0.6166
0.6112
,,.
61.50
60.65
59.83
59.03
57
,87
56.03
54.64
52.69
52.06
5l .46
50.86
50.28
49.7?.
49.
l6
48.62
48.09
47.57
47 .07
46.57
46.08
45.61
45.14
44.64
44.23
43.79
43.36
42.94
47..53
42.12
4t .72
41.33
40.95
40.57
40.20
39.84
39.4E
39-
13
38.79
38.45
38.12
8.337
a.xll
8.108
7
.998
7 .891
7
.787
7.587
7
.490
7
.396
7 .305
7.124
7
.043
6.960
6.879
6.799
6.646
6.499
6.429
6.359
6.292
6.160
6.097
6.034
5.973
5.913
5.854
5.797
5.474
5.424
5.274
5.186
5.r41
5.096
','
1.0000
0.9859
4.9722
0.9589
0.9459
0.9333
0.9211
0.909r
0.4974
0.8861
0.8750
0.8642
0.8537
0.8434
0.8333
0.8235
0.8140
0.8046
0.7955
0.7865
0.7778
0.769X
0.7609
0 .7 527
0.7447
0.7368
0.7292
o.7216
0.7143
o.7071
0.7000
0.6931
0.6E63
0.6796
0.6731
0.6667
0.6604
o.6542
0.6482
0.6422
0.6364
0.6306
0.6250
0.6195
0.6140
0.6087
oa.s
6t.49
60.63
59.80
58.99
58.20
56.70
54.57
53.90
53.L4
5L.60
5t.97
50.76
50.18
49.61
49.05
48.51
47 .97
47.45
46.94
46.44
45.95
45.4E
45.00
44.10
43,66
43.22
42.40
42.34
41.98
41.58
4t.19
40.80
40,42
40.05
39.69
39.33
38.98
3E.63
34.29
37 .96
''.
8.337
E.Zt9
8.105
7 .994
7 .886
7
.781
7 .679
7.579
7.48X
7 .387
7
.295
7 .205
7.117
7 .03r
6.947
6.786
6.708
6.484
6.413
6.344
6.209
6.143
6.079
6.016
5.955
5.836
5.774
5.722
5.666
5.506
5.454
5.404
5.306
s.ttl
5. 1r9
r.0000
1.0140
1.0284
1.0432
1.0584
l.o74l
1 0902
1.1069
1.1240
l.t4t7
l.1600
1.1789
1. 1983
1.2185
1.2393
1.2609
1.2832
1.3063
1.3303
1.3810
|
.4078
|.4356
1.4646
1.4948
1.5591
1.5934
1.619L
1.6667
1.7059
1.7470
1.7901
I . E354
1.EE31
1.9333
,'.
62.36
63.24
64.t4
65.06
66.01
66.99
67
.99
69.03
70.10
7r.20
73.52
75.99
77 .29
7E.64
80.03
8t
.47
42.96
86.13
67.80
89.53
91.34
95. l9
97 .2]
99.37
101.60
103.94
106.39
108.95
I I1.64
r
14.46
t17.44
120.57
Figure
6-53.
Relationship between 'API
and temperature.
(Courtesy
of
Crane Company.)
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Rotating Equipment
Pump Hydraulic
Design Calculation Sheet
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.
Light
Naphtha Cut-68'
API
'1.1
_cp
0.73
20.85
psia
gpm
gpm
gpm
't92
't92
Source
pressure
Static head
-
APr,
line loss
Suction
pressure
-
Vapor
pressure
NPSH
avail
NPSH
avail
NPSH req'd
=
28.248
=
-
20.85
Terminal
pressure
=
Static
head
(litt)
=
-
APi discharge
Piping system
Other
Discharge
press.
=
-
Suction
press.
=
Discharge
6.313
1.887
20.o
44.90
28.244
Suction
25.20
psra
psi
psl
psl
psra
psia
psia
feet
psra
psi
psi
psia
psra
psia
ft
ft
-
0.51
'l
7.398
1.3
bhp at Duty
Condition
bhp at Maximum Capacity Condition
onpo
=
Q{l(IPr)1
onp""
=
QSTrylI1
(3,960Xn)
(3.960Xr)
Figure 6-54.
Pump
hydraulic design calculation
sheet
for
Example 6-5.
Referring
to the
pump
manufacturer's
pump perfor-
mance
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
Referring to
previous
calculations on
the suction side
we
have the
following:
u.
:
{gl
r4.84r
=
io.o8jl
\tvtl
sec
I 1n ORI
N^.
:
l',"i,'l
r100.863)
-
210.062
\
+.d4
/
From
Equation 1-6a we obtain
f
:0.0315
(4s.ss)(ro.osf(1-L;
APr,,
:
2.200
ps
For the
3-in.
portion
of
the suction line,
u.
:
lq)
r8.34r
=
r7.37sa
\t92l
sec
**.
:
(,rr4)
032,44s)
:275,e35
From Equation 1-6a,
f:
0.03395
APr
:
9.759
Ot'
AP,:APso*APi.
AP,:2.29*a.trt
AP,
=
2.959
Ot'
on,.
=
['o
o:'n''lt
o'
*
o
rrnl
rffi l
It
I
2(32.2)
or,.
:
[ro
o1le1'"'r
* r,nl
rffi I
2(32.2)
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Rotating
Equipment
Pump Hydraulic Design Calculation Sheet
Liquid
Viscosity al PT.
(Pumping
Temp-)
Vapor
pressure
at PT
Sp-
gr.
(1)
at
PI
Flow at ambient temp.
Operating flow at PT-
Dosign
flow at P.T.
Light
Naphtha
Cut-68o
API
1.1
cp
psra
gpm
gpm
gpm
20.85
0.73
't92
192
'192
Suction
Source
pressure
=
21.70
Discharge
Static
head
-
APr,
line loss
Suction
pressure
=
-
Vapor
pressure
=
NPSH
avail
NPSH
avail
NPSH req'd
=
3.559
Terminal
pressure
=
Static head
-
aPr
discharge
Piping system
Other
Discharge
press.
=
-
Suction
press.
=
TDH
psia
psl
psi
psra
psia
psra
ft
tt
'16.7
psra
psi
psi
psi
psra
psia
psia
leet
6,313
-
0.51
1
24.744
1.847
-
20.85
12.3
24.744
1.3
20.'152
=
63.77
bhp at
Duty
Condition
bho"
=
(SPmXTDH)(?)
(3,960X4)
bhp at
Back-Pressure
Condilion
bho""
=
(gPm)[rDH)(?)
(3,s60)(a)
Re-evaluation of
pump hydraulic
design
calculation
sheet
of Example
6-5.
igure
6-56,
f:0.03395
v.
:
{g}
(4.84)
=
ro.o8l
\t921
sec
N*
:
(lryrt
(100,863)
:
zto,o6z
II
l(0.03395X3.0)
^ ^.^l
l-h
=
l------l---------
+
U,y4Jl
I l4ql
I
'
\
12
/
J
APlr:1.939
,or.rr,,rr.rrrr(r{)
Discharge
Line
Referring
to
previous
calculations
on
the
discharge
side
we have the
followins:
f:0.0315
t.^
^".-
..^
-^^
l,or.rrxro.oo,{*}
ap,.
_
l(0.031sx60.708) +
6.610l
--"-'--'\r44l
-l
[+.ozo\ |
2(322\
I
IrrI
)
AP6n
:
6.143
O.'
For
3-in.
portion,
*""
:
(,1q;
032,44e)
:275,e35
2(32.2)
APp
:
AP6o
* AP1,
=
6.143
psi
+ 1.989
psi
APo
:
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
indi-
cated
on
the
pump
manufacturer's
curve, Figure
6-55. In
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
re-
quired
NPSH
increases.
As we see
on Figure 6-55, the
available NPSH
of 4.589
ft
is
slightly
exceeded at
400
u,
=
lgl(8.34):
r7.37sa
\t>Ll
sec
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96
Mechanical
Design
of
Process
Systems
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.
0.73
cp
psia
gpm
gpm
4no
Desion flow at
pT.
4uu
gpm
Discharge
Terminal
pressure
=
16.70
Psia
Suction
Source
pressure
=
21.70
Psia
3.559
tatic head
-
APi,
line
loss
Suction
pressure
=
-
Vapor
pressure
=
NPSH avail
NPSH
avail
NPSH req'd
-
2.959
psl
psi
psia
psia
psia
ft
ft
Static
(lifi)
-
APr discharge
Piping system
Other
Discharge
press.
-
Suction
press.
6.313
8.132
=
20.00
=
51.145
psl
psi
psl
psra
psia
psia
feet
TDH
TDH
-
20.85
1.45
4.589
=
22.300
=
24.845
=
91.282
20.85
bhp
at
Duty
Condition
ono"=9##
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
..
(375
x34.0X0.73)
-
J'v'
ttv
'
(3,960X0.65)
A
4-hp
motor is sufficient
for normal and
maximum
ca-
pacity
operations.
Re.evaluation
of Reservoit
Line
Since the
nitrogen
pad
on the
naphtha storage
tank
was
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-
Figure
6-57.
Maximum capacity
re-evaluation
of
pump hydraulic design calculation sheet
of Example
6-5.
bhp at
Maximum
Capacity Condition
.
.
(oom)fiDHXr)
bnp""
=
=.(3GbX4.
necting the
reservoir
to the storage
tank, considering
the
pipe
to be
4-in.
schedule
40, is
as
follows:
(3?r
(ciL)(=*-]
tl+tl
,,
_
"
-'
\min/ \7.a79
eau
\60
sec/
=
9.45j
a
0.0884 ft?
sec
:
196,992
2.640
lb'
fchr
From Equation
l-6a,
f-05
:
-lr"c.
[+
.
*]-tt)
lnr
f:0.031s
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From
Equation
1-4
we
have
aP.:lLL*rrl
Pv'
\d
-
l2e"
or,
=
[,o
olualgrl,o
*
r.rnrl
I
(r flr
I
1+s.ss1
p
1r.+s:;,#
(*q-J
fr-lh
SeC'-lDf
APr
:
5.41f
Or'
With
38 feet
of
head
in
the
reservoir
we have
an entry
pressure
to
the storage
tank of
38ft:12.008psi
Entry pressure
:
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.
NOTATIOl{
acfm
=
actual
cubic
feet
per
minute,
ft3lmin
bhp
:
6.u1"
horsepower, hp
e
:
clearance
volume,
in.3
Co
:
specific
heat
at
constant pressure,
Btu/lb--
mole-"F
C.
:
compression ratio
C"
:
specific heat
at constant volume,
Btu/lb.-
mole-'F
D
:
diametef
of
impeller
or rotor, in.
D"
=
specific diameter,
dimensionless
ghp
=
gas
horsepower
:
horsepower
delivered
to
gas,
hp
H
:
head
:
energy
per pound
of mass,
ft-lb/Ib.,
or better known
as feet
of head, ft
icfm
:
actual
cubic feet
per
minute
at compressor
in-
let, ft?/min
J
:
mechanical
equivalent
of
heat: 778 ft-lbrl
Btu
Rotating Equipment
97
k
:
ratio of specific heats
:
CplC,, dimensionless
m
:
mass,
lb.
and re-expansion
polytropic
expo-
nent
dl
=
mass flow rate, lb-/hr
fiIo
:
moles
of
gas
:
m/mw
mw
:
molecular weight
n
:
polytropic
exponent
N
:
speed, rpm
N,
:
specific speed, dimensionless
NPSH
:
net
positive
suction head, feet or
psia
P:
pressure,
psi
Q
:
flow rate,
gpm
or ft3/sec
R
:
R/mw
:
gas
constant
of
a
particular
gas
R: universal
gas
constant
:
1545
ft-lbr/lb. mole-
scfm
:
standard cubic feet
per
minute, ft3lmin-see
discussion under standard volumetric
flow
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
Greek
Symbols
?
:
specific
gravity,
dimensionless
4
:
efficiency, expressed
as
percent
€
:
ratio of
clearance volume
to the volume sweot
by the
piston
stroke
p
:
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 Hand-
book
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.
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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.)
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FRACTIONING TOWER
(DE
ETHENIZERI
PAOPANE
&
PAOPYLENE
50%
VAPOR
-
50%
L|OUTD
PROPAN€ AND PROPYL€NE
50%
vaPoR
50%
LroulD
PROPANE ANO PFOPYLENE
100% Ltouto
Design
Classifications
of Heat
Exchangers
Typical
shell and
tube
heat
exchangers and their func-
tions
are
as
follows:
Reboiler-transfers
heat to
a liquid
to
produce
a two-
phase, gasJiquid
mixture
used
in
a
distillation
col-
umn.
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
ex-
changer
(reboiler)
into
the
distillation
column.
Condenser-a heat exchanger to
condense
vapors by re-
moving heat from a
gas.
Partial Condenser-only
partially
condenses a
gas
to
provide
heat
to
another medium
to
satisfy a
process
The Mechanical Desien
of
Shell-and-Tube Heat Exchangers
101
Figure 7-3. Iilustration of a
thermo-
s]phon reboiler.
(Courtesy
of
Howell
Training Company.)
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
ap-
plication
of
a
partial
condenser on a distillation col-
umn
is to condense only enough
liquid for the reflux
when
the overhead
product
is
vapor.
Final Condenser-an exchanger where
all
the
gas
is con-
densed
and
all
the heat
is transferred to the other me-
dium.
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.
CONDENSATlON
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102
Mechanical
Design
of Process
Systems
'AIIONARY
HEAD
IYPIS
A
ANO iEA{OVA8TI
COVEP
B
BONNST
(INIEGRAI
COVER)
c
CHANNET INTECFAL
WITH
IU8E.
SHETT
AND
RE/nOVASIE
COVTR
N
CHANNEI
INIEGRAL
WIIH
''UBT-
5HEET
ANO
REITOVABLE
COVER
D
SPEC|AL
hICH
PREsSURE
CTOSUI€
F
WTh LONGIIUOINAT
3AFFIE
G
H
J
K
x
These classifications
are the
major
types of
services
that
shell and tube
exchangers provide
in
the
process
in-
dustries.
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,
changers 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
shell
between
both ends
(E).
Figure
7-4. Nomenclature
of shell and
tube heat
exchangers.
(@1978
by Tlrbu-
lar Exchanger
Manufacturers
Associa-
uon.)
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
I
Uff
'
" SIAIIONARY HEAO
tn
Ul(E
"4"
STATIONARY HEAO
N
LIKE
'1T
STAIIONARY
HEAD
P
OUI5IOE PACKED
FTOA'ING
'IFAO
s
T
PUIT TIiROUGH FIOATIIIG
HE^O
U
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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 ser-
vice,
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 expan-
sion
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
The Mechanical Desisn
of
Shell-and-Tube Heat Exchansers
103
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 U-
tube design is also
very
applicable
to high-pressure ser-
vlces.
Floating
Head
Shell and Tube
Heat
Exchangers
This
type of shell and tube heat
exchanger
has
a float-
ing
head
that
is
designed
to accommodate thermal expan-
sion of the tubes and to
provide
access
to the
tube-side
and shell-side exchangei components.
This
type
of
de-
sign
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-
floating-head
cover
shell
(A)
Packed
lanternring
exchanger
backing ring
flange
(B)
Outside-packed floating
head
exchanger
f
tlange
gasket
floating
tubesheet
floating-head cover
floating-head
cover
shell
cover
floating
tubesheei
gasket
(C)
Internal floating head
exchanger
(D)
Pull-through
lloating head
exchanger
Figure
7-5. Several
configurations
of floating
head exchangers.
gland
tollower
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'lO4
Mechanical Design of
Process
Systems
tures
<
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 lan-
tern
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
packingJantern-
ring 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
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
petroleum-
chemical
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 medium-
sized 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 in-
dustry,
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
di-
rectly
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
pre-
vious 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 ser-
vice the exchanger
will
encounter.
Descriptions
of the
three classes
are
as
follows:
Class
R includes
heat exchangers specified
for the most
severe
service in the
petroleum-chemical
pro-
cessing
industry. Safety and durability
are
re-
quired
for exchangers
designed
for
such
rigor-
ous conditions.
C/css C 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.
-
tbles 7-1 and
7-2
provide
a comprehensive
view
of
the
various types
of heat exchangers
and their
applica-
tions,
so we
can now focus
on the components
of the
shell
and tube design.
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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 vari-
ous 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 exter-
nal to the
tubes. Typical applications
of finned
tubes are
waste heat recovery
exchangers, waste heat boilers,
gas
turbine regenerators,
and air-cooled
exchangers. Exam-
ples
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
Structural
supports
for
the
tubes.
2.
Dampers
against
vibration.
3.
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
The Mechanical
Design
of
Shell-and-Tube Heat Exchangers 1o7
constrained
at
each
baffle. Thus, the hole in
the
baffle,
being larger by
varying amounts than the outside tube di-
ameter,
acts as a limit stop
for
the
tube. In
piping
me-
chanics
(see
Chapter 2)
a
limit stop is
a
restraint
that
lim-
its 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 trans-
late
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
in-
significant.
Thus,
the
baffle
hole acts as a limit stop and
prevents
lateral buckling of the tubes when they are
in-
duced 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 conse-
quences
of strengthened tubes
affect
the integrity
of
tube
joint
connections
in
the
tubesheets and
this
will
be dis-
cussed shortly.
We
see
from
this discussion that the baf-
fle
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
verti-
cally
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
phe-
nomenon 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.
Fie-
ures
7-l
and 7-2 are
examples
of baffles
guiding
or d'i-
recting
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 two-
pass
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,
respec-
tively. With the same inlet
flow
rate, the fluid
velocity
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The Mechanical
Design of
Shell-and-Tube Heat Exchangers 109
Table 7-4
Minimum
Tube Bend Radii
l4l
Tube
Outside
Dia.
(in.)
Bend Radius
(in.)
Center-to-Center Oistance
(in.)
Duplex, all
sizes
*Plain:5/s
I
*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.
Figure 7-7. Baffles
can divert flow horizontally.
(Courtesy
of
Howell Training Company.)
3 times
Tube O.D.
t3/te
1
131t6
6 times Tube OD
15/s
2
2z/s
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 di-
rection.
(Courtesy
of Howell Training
Company.)
VAPOR
IN LET
FLUID
IN LET
FLUIO
OUTLET
CONDENSATE
OUTLET
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1 10 Mechanical
Design
of Process
Systems
increases as the 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
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-New-
tonian fluids are
completely ruled
out.
We will
see
later
in the chapter that the
plate
fin type of
exchanger is supe-
rior 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 baf-
fles
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.
Tie
Rods
These are structural rods that run
oarallel to the ex-
changer tubes through
the
outer perimeter
of
the
baffles.
fastened to the tubesheets such
that they space and sup-
port
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.
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 re-
duce the
possibility
of
a
leak of
the tube-side
fluid.
Dou-
ble
tubesheets
are
quite
common
with
highly
toxic
ser-
vices, 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
Figure 7-9.
Annular orifices
between tube outside surface
and
hole in
baffle
plate
[6].
Figure 7-10. Doughnut and disc type baffles
[6].
Table 7-5
TEMA Tie Rod Standards
(in.)
"c" & "8"
Exchanger
Tie Rod
Dlameter
8-15
r6-27
28-33
34-48
49-60
Nominal
"R"
Exchanger
"R"
Exchanger Tie Rod
ShellDiameter
Dlameter
irinlmum
Number
of
Tie
Rods
3/z
3/t
tlz
tlz
3/a
tlz
rlz
tlz
4
o
o
8
10
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112
Mechanical
Design
of
Process
Systems
for
unsupported
tube lengths
between
two
tubesheets
for
unsupported
tube
lengths between
a
tubesheet and a
baffle
for unsupported
tube
lengths
between two
baffles
Et
:
modulus
of elasticity of
tube material at mean
tube metal
temperature,
psi
4
:
outside
diameter of
tubes,
in.
oc
:
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
de-
veloped by Professor
J. B. Johnson
during the nineteenth
century.
Other
TEMA
formulations
are summarized
in
the
fol-
lowing sections. The
reader is urged
to be
familiar with
the TEMA
standard and
follow
its
guidelines
in
design-
ing a shell and tube heat
exchanger.
TEMA
Formulations
Baffles and
Support Plates
Natural Frequencies
ot
Straight Tubes
on
Multiple
Equal
Spans
3.36C
where
f"
:
tube natural
frequency,
Hz
C
:
mode
constant
from
Thble
7-6
I
:
span
length,
in.
E
=
modulus
of
elasricity. psi
I
=
moment
of
inertia, in.a
(Table
7-3)
W
:
Wr + Wn
+
MWr",
lbs/ft
Wt
:
weight
of empty
tube
(Table
7-3)
Wq
:
weight
of
fluid
inside
tube
0.00545
p1d1,
W6o
:
weight
of
fluid
displaced
by
tube 0.00545
p"d"'?
M
:
added
mass
coefficient
from Table
7-6
p
:
fluid
density,
lbs/ft3
d
:
diameter
of
tube, in
subscripts:
i
:
inside
o
:
outside
r
{o'
['o
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:
-28
a,:ffi
when
C. s
kf/ror
-r
-.
I
s"=\l
r
-
(kur)l
whenc
>kur
21 2C"l
/:*
where
C"
= l/
^
Vsr
Table 7-o
Mode
Constant-C
[21
No.
of
Spans
Extreme
Ends Supported
Fr-l-'-l*,.1
|--___l
/T-7\--lzf-R
Extreme
Ends
ClamDed
,l-r+r
Extreme Ends
Clamped-Supported
r-fr-fr
lst
Mode
2nd Mode lst
Mode
2nd Mode lst Mode
znd Mode
I
2
3
4
5
6
7
a
9
to
31.73
31.73
3r.73
31.73
31,73
31.73
126.94
49.59
&.52
37.O2
34.99
34.32
33.67
33.O2
33.02
72.36
49.59
40,52
37.O2
34.99
34.32
33.67
33.02
33.02
33.02
198.34
72.36
59.56
49.59
44.r9
40.52
38.40
37.O2
34.99
49.59
37.O2
34.32
32.37
31.73
31.73
160.66
63.99
49.59
42.70
39.10
37.O2
35.66
34.99
34.32
33.67
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KT:
yield
stress,
psi,
oftube material
at design metal
temperature used.
radius
of
gyration
of tube
0.25
.vu
+la"
-
2tJ1,
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
spans between two tube-
sheets.
0,8 for unsupported
spans
between
a
tubesheet
and a baffle.
1.0 for unsupported
spans between
two
baf-
fles.
The Mechanical Desien
of
Shell-and-T[be Heat Exchansers 113
quency,
assuming
simple supports
and
for the first mode
only, may
be calculated
as
follows:
2.74C"
=
U-tube natural frequency,
Hz
:
mode constant
for
U-bend
:
bend radius, in.
Note: For
other than simple
support conditions
the calculated
frequency may be
estimated
by multiplying the
above
value
for f,, by
the
appropriate ratio
of mode constants
from Thble 7-6
using single
span values.
ASME
Tube
Joint
Load
Grlteria
The
ASME
Secrion
VItr
Division
I
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:
For
joint
types
a, b,
c, d, e:
F,
:
A,o,11f,
For
joint
types
f,
g,
h,
i,
j,
k:
(7-3)
R2
where fnu
R
Note:
The value
of S"
shall not
exceed the Code allowable
tensile
stress
of
the tube material at desisn metal tem-
perature
used.
Effect
ot Longitudinal Tube
Stress
where fnp
:
tube
natural
frequency in
stressed
condition, Hz
P
=
axial force, lbs
(positive
for tensile,
negative
for
compressive)
Natural
Frequencies of
Straight Tubes on Unequal
Multiple
Spans
f"
:
10.83
t'z
For
a
tube on multiple
unequal
spans
with
the extreme
ends
fixed
and simply supported
at the
intermediate
sup-
ports,
ki can be obtained
by
solving the following
char-
acteristic determinant for
an n span
system.
Natural Frequencies
of
U-Tubes.
It
must be recog-
nized
that
each
tube is
a continuous beam
that has a
sin-
gle
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
fre-
quency
may be
determined from Thble
7-6 using
the ap-
propriate
mode
constant.
The
U-bend
out-of-plane fre-
F,
:
A,o"11f,f"f,
where
Ft
:
oall
:
f=
f.
(no
tesg
=
f,
(teso
:
(7-4)
maximum tube
joint
force, lb1
cross-sectional
metal
area of tube, in.2
ASME maximum
allowable
stress.
psi
joint
reliability
factor
maximum value
without
test
given
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.
Natu-
rally, as
the tube
wall increases,
the
tube stiffens
and,
consequently,
the force exerted
by the
tube on the
tube-
sheet
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 stan-
dard
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-
Dt2
'Er.,j
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114
Mechanical Design
of
Process
Systems
Table 7-7
Reliability Factors, f,
[71
Type
Joint
Descriptions
Notes l.
(tesr)
f,
(no
test)
(1)(7X8)
(1X2)
(1X3)
(1X6)
(1X7X8)
(1X4)(s)
(7)
(
l
)(4)(s)
(7)
(l)(4)(5)
(7)
(l)(4xs)
(l)(4x5)
(l)(4)(5)
a
b
c
d
f
c
h
I
j
k
Welded
only,
a>
1.4r
Welded
only, tsa<L.4t
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
1.00
0.70
1.00
0.50
1.00
0.95
0.85
0.70
0.90
0.80
0.60
0.80
0.55
0.80
0.40
0.80
o.75
0.65
0.50
0.70
0.65
0.50
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), in.
=
tube
o.D_,
in.
=
nominal
thickness of
average
wall tube, 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.
I
sign. One
such formulation to
predict
the critical buck-
ling
load is as
follows:
P.,
- ,
"
q''
,,
t0.5216r
t7-51
I
L**
l'
\Ns
+
t/
where L,u6"
:
total length
of tubei
between tubesheets
NB
:
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 con-
sidered
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 considera-
bly
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 ex-
changers, the
reader is referred
to TEMA.
We will
dis-
cuss tube
vibrations shortly.
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PBOCESS EVALUATION
OF
SHELL AND
TUBE EXCHAI{GERS
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
condi-
tions
of
the entire system is not
our concern
here,
be-
cause 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 over-
lap;
just
as in Chapters 2 and 4
we
saw
how
civil and
The Mechanical Desien
of
Shell-and-Tube Heat
Exchansers
t15
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-conJuc-
tion
and
convection.
In Chapter 3 we considered
heat
transfer
through
pip-
ing
and vessel components
as well
as
jacketed
systems.
As described in Chapter 3,
the
basic expressions
used
in
conveetion are as follows:
q
:
rhcpat
q
:
UA(LMTD)
(3-24)
(3-26)
{1t
Some
ecceptable weld
geometriea
t2l
where t
is
not
less
lhan l.4t
(61
l7l
(81
Figure 7-13. Joint
types
[7].
(Courtesy
of ASME.)
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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
Equation 3-9 is a variant
of Fourier's heat law of con-
duction
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
differ-
ent application. In these
types
of
exchangers
we
are
pri-
marily
concerned
with
the heat
duty
or heat load re-
quired
in the same
general
sense as the
jacketed
vessels
TUBE WALL
THICKNESS Iin|
Figure 7-14.
Tube
joint
loads.
q
=
r;cp(ao
q
:
rimrg
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
math-
ematically with the use of Equation 3-24. Using this rela-
tion
we
have:
(7-7)
(7-8)
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118
Mechanical
Design
of
Process
Systems
r.0
P
.TEMPERATURE
EFFICIENCY
5
o.s
F
2
(l
o -.'
:
oa
o
O.9
F
z
9^"
o
0.7
=
o.6
/tL--.....-.-,
lr-t'
l.-+<_
-l/
LMTD
CORRECTION
FACTOR
I
SHEIL
PASS
EVEN
NUMBER
OF TUBE
PASSES
D
-.:l-J
'
T,-t,
Gl=
r
'2
03
0.5
0.6
P
.
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.)
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'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
.t
-+
r'#
"=
Tr-Tr
o.3 0.4 0.5 0.6
P
=
TEMPERATURE
EFFIoIENcY
LMTD
CORRECTION
FACTOR
6
SHELL PASSES
T2
OR
MORE
EVEN
NUMBER
OF
IUBE
PASSES
9:-]3-J
'
T,-t'
R
=
-l--3
Figure
7-16.
Continued.
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I
o.g
z
P
o.t
o
o.7
F
=
o.6
The Mechanical Desien of Shell-and-Tube
Heat Exchangers
121
P.IEMPERA
LMTD
CORRECTION
FACTOR
SPLIT
FLOW SHELL
2
TUBE
PASSES
e'f{
''r-rE
P
=TEMPERATURE
EFFICIENCY
I
DIVIDED
FLOW
SHELL
PASS EVEN
NUMEER OF TUBE
PASSES
o.
-13--:
'
T,-t,
I-I,
Figure 7.16.
Continued.
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The Mechanical
Desien of Shell-and-Tirbe Heat Exchansers
123
E
g
F
o\
o
o
t\
t-
o
tt
tlll
.9
.f
J
s'
ut
e
3
t-
4
ul
4
=
,l
F
e
3
|'|-
ul
()
e
ul
110
J0
rr|ivr9
'l 'd'v
;l;
lJ
:
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124
Mechanical
Design
of Process
Systems
kn
:
thermal
conductivity
of
foreign
deposits
on
inside
of
tube,
Btu/hr_ftr_.F
T"
=
tube
wall
thickness,
ft
k*
:
thermal
conductivity
of
tube wall,
Btu/hr-ft2-"F
ho
:
outside
tube
film
coefficient,
Btu/hr-ftr-.F
Tro
:
thickness
of
outside
tube
deDosits.
ft
k,o
=
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
re-
fer
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
resis-
tance
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
de-
posited 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
phases
when it
contacts
tube
surface,
resultinq
in
a coat-
ing 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
sur-
faces.
The complexity
of fouling
and
how it
occurs
does
not
easily allow
this
phenomenon
to be treated
analyti-
cally.
There are
far too
many
variables
involved
for
one
to accurately
compute
fouling
factors.
Thus,
this
phe-
nomenon
is treated
in
a more subjective
light, using
ex-
perience
as
a
guideline.
Years
of
experience
with
various
services
have
resulted
in the
use
of accurate
foulins
fac-
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 at-
tachments.
Finned tubes, especially
those
with
fairly
high
fins,
experience
very
little
fouling
unless
the depos-
Its cover
an appreciable portion
of the
fin
height.
With
the normally
accepted
long
periods
between
tube
clean-
ing 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
fac-
tors 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.
At1
=
Temperature
drop
through inside
turbulent
boundary
rayer
Atz
=
Te6p"tu,ur"
Orop through
laminar
boundary tayer inside
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
Direction
+
-----T
Att
Att
Atr
At.
At"
At,
Figure
7-18.
Temperature
profile
through tube wall.
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126
Mechanical
Design
of
process
Systems
where
n
=
0.4 for
heating
n
:
0.3 for
cooling
And
the temperature
differences
are
as
follows:
At
:
pipe
surface
temp-bulk
fluid
temp
At
<
lO'F for
liquids
At
<
100"F
for
gases
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
order
of magnitude
of
film
coefficients.
The
-reader
should
be
aware
that
process
design
is
not
addressed.
Thus,
for
solving problems
dealing
with
condensation,
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
sim-
ple
relationship
is
contrived
by
M.
Jakob
[1]
using
an dy-
ercge Nusselt
number
for
the
gas.
An
empirical version
of
this expression
is
given
by
Nr,
-
hd'
:
C(PJ'/r(NRJn
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 vorti-
ces 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
ana-
lyzed
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:
Kf
hd,
=
C(NIJ"
('7
-2r)
hd,
:
B(pvd"irr.r)"
(7
-23)
where
h
:
average
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
A
variant
of
Equation
7-21
is widely
used for
forced
convection
ofair
normal
to a
cylinder
is
given
by
the
fol-
rowrng:
Table
7-9
Parameters
for
Fluid
Flow
Normal
to
Circular
Cylinders
Range
ol
Reynolds
Numbers
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
min-
imum
distance
is shown
in
Figure
7-19. Tbe
minimum
distance
is expressed
in
terms
of the
tube bundle
geome-
try
for
each of the
four
configurations.
as
follois
isee
Figure
7-19):
pf
:
absolute
viscosity,
lb-/ft-hr
V
:
velocity
of
air,
ft/hr
Nx"
:
Reynolds
number
at maximum
fluid
_
velocity,
V.",
h
:
average
film
coefficient,
Btu/hr-ftr-.F
p
:
air density,
lb./ft3
ki
:
thermal
conductivity
of fluid,
Btu/br-ft-'F
B
and
n
:
constants given
in
Table
?-10
do
=
tube
outside
diameter
Triangular
pitch,
d-,"
:
*
-
.
2''
InJine
triangular pitch,
dni"
=
W
-
d,
InJine
square
pitch,
dmi.
=
W
Diamond
square
pitch,
d.;"
:
P
cos 45'
-
D
:
0.707p
-
D
k1
where
(4,
0.40<
NR"
<4.0
4
<
NR"
<40
40
<
NR"
<
4000
4000<NRe<40,000
40,000
<NR"
<400,000
0.989
0.91
I
0.683
0.193
0.027
0.330
0.385
0.466
0.618
0.805
(b)
(c.l
(d)
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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,
VrAl
:
V2A2
e-24)
where V1
:
velocity
of
fluid at point
I,
ftlsec
Al
:
cross-sectional
area, ftz
we
can deduce
With
all
tubes being placed
at
a
constant
pitch
and
Vr
:
Vr
:
fluid
velocity,
we have
v.,,
=
v'l+l
\o.,"i
'A
</
\@
or staggered and iniine
tube arrays,
o,
=
* [o"
-
p,"
*
9 :
o'10
-
o,yl
,rc
]44
[ " Pn
-
"l
For triangular layouts,
.
B
[^
-
o,^-dr.
..1
.^
n.
=
r++
[D"
-
D,"
+
+---i
(P
-
dJl
,rt'?
where,
DL
=
OD of tube
bundle
D"
=
lD
ol
shell
dr
=
OD of
tube
B
=
baffte spacing
Ar
=
flow
area-cross-llow
area
for
one s€ction
tween
two baffles
Figwe
7-20. Tube
bundle
cross-flow
area.
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
multi-
plied
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
la-
ble 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
im-
pingement
baffles,
channel
and
head
baffle
lanes, must
be
considered.
Table
7
-13
is a compilation
of
various
in-
dustrial 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
flu-
ids. is
as follows:
h"&
-
o
ro lq"o)"'l,9url'
'lu
l'
'
k
\p/
\t/ \pJ
or
h"rD":
o.:orN""f
t,*rr"t
(")o''
Equation
7-26
is divided
into
two
components,
jH
and
Np" in which
(7-2s)
(7-26)
Figure
7-21.
Typical
tubesheet
layouts.
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:iw
The Mechanical
Design of
Shell-and-Tube
Heat Exchangers
j":+H'(,+)
129
('7
-27)
Table
7-1 1
Kays and London
Constants
for
Tube
Bundles
Containing 9 Tubes or Fewer
Number
of Tubes
123456789
In-line
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
where
h.
:
outside tube bundle
film
coefficient,
Btu/hr-ft
"F
G,
:
mass
flow
rate
of
fluid, Iby/hr
k
:
thermal
conductivity of shell-side
fluid,
Btu/hr-
ft-"F
D.
=
shell-side
equivalent tube diameter,
in.
C,
:
sPecific
heat of
fluid,
Btunb-"F
Table
7-'12
Pros and Cons
of
Various Tube
Arangements
Tube Pitch
Arrangement
Advantage
Disadvantage
For a square
pitch
tube arrangement,
l(p:
-
nd;
)
l
i-
?iorn
For
a
60'equilateral
triangular arrangement,
.1(0.-13o:
-
0.5rdi
ilt
D.
:
-_:
in
(7-28)
Yields higher
film Medium
to
h
igh
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.
compact arrange-
ment.
Film
coefficients
are
not as high as
triangular
pitch,
but
greater
than
in-
line square
pitch.
Suitable for fouling
conditions.
Good
for
condi-
tions
requiring low
pressure
drop.
Ar-
rangement allows
for easy
access
of
tubes for mechani-
cal cleaning. Good
for fouling
service.
Better
film
coeffi-
cients
than inline
square
pitch,
but
not
as good
as
tri-
angular or in-line
pitch.
Easy access
for
mechanical
cleaning. Good
for
fouling service.
(.7
29)
uhere
p
:
tube
pitch.
ir.
d,.
=
ID
of shell.
in
a,
:
flow area of
tube bundle, ft:
g
rcB'
ft:
17-30
r
p(144)
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
as
p
:
viscosity
of
the shell-side fluid
at the
ca-
loric temperature,
lb/ft hr
p*
=
viscosity of the shell-side fluid at the
tube
wall
temperature, lb/ft-hr
The
parameter
js
is
plotted
against Nx"
in
Figure
l-22a.
The value ofjH
is determined from
the
figure af-
ter the
Reynolds
number is calculated. Then from
Equa-
tion
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
in-
creased,
the
flow rate increases. Likewise
with
an
in-
creased
flow
rate, the
pressure
drop increases
substan-
tially
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
ap-
proxirnately 44% .
(text
conttuued
on
page
139)
a
(a)
Triangular
Pitch
(b)
In-line
Triangular
Pitch
(c)
InJine
Square
Pitch
Medium
to
h igh
pressure
drop. Can
only
have
chemical
cleaning.
Relative
low film
coefficients.
Relative
low
film
coefficients.
Does
not have as
low-
pressure
drop
as
the
inline square
prtcn
arrangement.
(d)
Diamond
Square Pitch
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130
Mechanical
Design
of Process
Systems
Table
7-13
Tube
Count for
g/a
in.
OD
Tr.rbes
on
13^6-in.
A
pitch
TEMA
TEMA
TEMA
TEMA
LorM
P
Type
s
Inside
ixed
Tubesheet
Outside
Packed
Head
U
U-Tube
ead
No.
ol
Passes
No. of Passes
No, ot
Passes
No.
of Passes
hell
lD in.
5.047
6.065
7
.981
10.02
12.N
13.25
15.25
17
.25
19.25
21.25
23.25
25.00
27
.00
29.00
31.00
33.00
35.00
22
68
0
170
212
283
3&
454
562
668
922
t9
JI
6l
104
151
178
24r
316
396
490
588
812
70
t6
30
28
66
60
106
96
164
148
196
r88
270
252
348
332
440
420
554
524
646
612
18
t2
26
24
52
48
98
84
142
t28
168
156
232
220
798
292
388
3s2
484
456
570
s48
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
1496
1468
1424
902
868
808 764
1230
l2t2
lt72
1590
1560
1516
l106
1092
1040
1438
1430
1336
Tube
Count for
s/s
in.
OD Tubes
on
Z8
in,
A
pitch
TEMA
TEMA
TEMA
TEMA
LorM
Fixed
Tubesheet
P
Outside Packed
Tvoe
S
Inside
U
Head
Head
U-Tube
No.
of Passes
No.
of Passes
No,
ot
Passes
No.
of Passes
hell
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
22
31
61
96
151
187
241
396
482
568
19
26
55
88
130
151
206
270
JJO
418
506
704
92
780
752
1062
1030
1008
13s6
t346
13c4
700 660
18
t6
30
24
s2
48
94
80
138
132
176
168
232
224
302
292
384
352
472
456
554
536
14
t2
26
16
48
44
82
76
124
t12
148
t32
196 184
266
252
334
312
4t6
396
492
472
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
946 930
896
1234
1220
n80
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132 Mechanical
Design
of
Process
Systems
Table
7-13
Continued
Tube
Count for
3/a-in.
OD Tubes
on 1-in. A
pitch
TEMA
TEMA
TEMA
TEMA
LorM
P
s
U
Fixed
Tubesheet
Outside
Packed
Inside
Head
No.
ot
Passes
Head
U-Tube
No.
ol
Passes
No.
ol
Passes
No.
of
Passes
hell
lD in.
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
1026
1000
1152 1134
1090
1273
1259
1222
1485
1461
\434
r72r
1693
1650
1968
l94l
1902
2221
2187
2134
2502
2465
2414
3099 3069
3010
10
108
19
18 16
1652 1620 1586
1894
1861 1820
2142
2101.
2060
2417
2379
2326
29W
29s7
2906
10 104
19
14
l2
2
40
64
98
122
t&
212
270
330
404
482
582
672
64
108
38 36
32 28
37
32 28
26
28
24
&62
6058
61 60
48 46
56
44
95 94 84
78
96 94
80 78
86
72
12L
ll0 100
98 r21
ll8 104
98 106
96
151 146
140 138
163 1&
144
140
148
136
208 196 188 160 216 214 196
158
200
184
258 242 232 230 276 270 260 235 254
240
320 316
296 298
338 338
324
3m
3r4
300
380 372
364 33s
396 396
376
339 388
368
475
466
452
430
460 440
420 4r4
452
432
530 526
508 49s
558 554
536 494
538
524
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
1635
1608 1536
1s04
1632 1s84
1887
tUz
1768
1740 1870
1832
2143
2lA4 2019
1992 2122
2076
2399
2366 2270
2244
2396
2340
2981
2940 2932
2800 2992
2936
Tube
Count for
g/q-in.
OD Tubes
on
f-in.
Pitch
TEMA
TEMA
TEMA
TEMA
LorM
P
Outside Packed
s
U
Fixed
Tubesheet
lnside
No.
ol
Passes
Head
No.
ol
Passes
Head
No.
ol
Passes
U-Tube
No.
of
Passes
hell
lD
in.
5.U7
6.065
7
.98r
10.02
12.00
13.25
).5.25
t7
.25
19.25
2r.25
23.25
25.00
27.N
29.N
31.00
2l
38
61
97
117
158
zlo
262
J10
370
442
524
602
698
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
12 t2
16
16
37 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
4
12
32
12
52
24
76
56
88
80
120
lt4
164 160
208
198
268
260
316
308
392
344
448
424
548
496
612
576
98
16
16
56
52
89 82
104
104
r45
140
188
184
238
236
304
292
344 332
398
386
484
472
554
532
650
@8
4
t2
32
t2
<t
'tA
80
56
96
80
140
tl4
180
160
232
198
284
260
332
308
366
344
468
424
510
496
640
576
64
88
24
20
44
40
68
68
90 88
128
120
176
168
112
108
138
134
340
332
400
388
472
460
554
544
640
624
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
http://slidepdf.com/reader/full/mechanical-design-of-process-system-volume-2shell-and-tube-rotating-equipment-keith 141/252
The Mechanical
Design
of Shell-and-Tube Heat Exchangers
133
Table
7-13
Continued
Tube
Count
lor
s/+-in.
OD Tubes
on
1-in'
n
Pitch
TEMA
TEMA
TEMA
TEMA
LorM
P
Outside
Packed
s
lnside
U
Fixed
Tubesheei
No. of Passes
No. of
Passes
Head
No.
ol
Passes
U-Tube
No. of
Passes
Head
Shell
lD
in.
33.00
782 768
768
35.00
894 892
880
37.00
1004 978
964
39.00
I102
1096
1076
42.00
1283 1285
1270
45.00 1.484
1472
1456
48.00 l70l
1691 1610
51.00
1928 1904
1888
s4.00
2154
2138
2106
60.00
2683
2650
2636
742 732
732
668
'130
112
682
816 8r2
804
760
848 828
824
952 931
928
8'72
931
918
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
668
724
't20
160 836
8L2
8'72 940
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
Tube Count
tor
3/4-in.
Oo
Tubes on
f
in.
'
Pitch
TEMA
TEMA
TEMA
Type
L
or M
Type
P
TYPe
S
TYPe U
Fixed
Outside
Packed
Inside
Tubesheet
Head
Head U-Tube
No.
of
Passes
No.
ol
Passes
No.
of
Passes
No.
ol
Passes
Shell
lD in.
5.047
6.065
7
.981
10.02
12.00
t3.25
t5.25
17 .25
19.25
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
8
16
28
48
84
104
136
184
236
294
352
416
486
568
654
756
850
958
1066
1250
1440
1650
i868
2098
261.2
\2 l0
2r
18
37 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
1118
1092
1298 1269
1500
1470
1714
1681
1939
1903
2173 2135
2692
2651
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
1864 1837
1804
2098
2062
2026
26W
2560 2520
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
608
'720
700
818
796
928
904
1036 1016
1220
rr92
t4t2
1384
804
788
1834 1804
20'72
2036
2584 2544
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
http://slidepdf.com/reader/full/mechanical-design-of-process-system-volume-2shell-and-tube-rotating-equipment-keith 142/252
134 Mechanical
Design of Process
Systems
Table 7-13
Continued
Tube
Count
for
l-in.
OD
Tubes
on 11/a-in.
A
Pitch
TEMA
TEMA
TEMA
TEMA
Type L
or
M
Type
P
Type
S
Type
U
Fixed
outside
Packed
Tubesheet
Floating
Head
Inside
Floating Head
U-Tube
No.
ol Passes
No.
of
Passes
No.
ot
Passes
No.
of
Passes
hell
lD
in.
5.M7
6.065
7 .98r
10.02
12.00
t3.25
15.25
17 .25
19.25
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/.
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
1828
Tube
Count
tor
1-in.
OD
Tubes
on
11/4-in. v
Pitch
TEMA
TEMA
TEMA TEMA
Type
L or
M
Type
P Type S Type U
Fixed
Tubesheet
Outside
Packed
Inside
Floating
Head
Floating Head U-Tube
No.
ot
Passes No.
ot
Passes No. of Passes No. of Passes
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
86
12
l0
24
20
37
32
57
53
70
70
97
90
r29
r20
t62 r52
205 193
238
228
275
264
330
315
379
363
436
422
54
12
l0
2t
18
l) lt
52
46
61
58
89 82
113
1r2
148 138
180
r74
22r
210
261
248
308
296
359
345
418
40r
4
8
l6
28
48
&
84
1t2
142
184
220
256
300
360
410
4
8
16
28
40
56
76
104
128
168
2N
236
286
336
388
00
44108
24
i0
36
32
50
44
70
64
96 88
124
t20
156
152
200 188
232
220
282
268
330
320
382
368
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
http://slidepdf.com/reader/full/mechanical-design-of-process-system-volume-2shell-and-tube-rotating-equipment-keith 143/252
{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
135
TEMA
TEMA
TEMA
Type
L
or
M
Type
P
Type
S
Type
U
Fixed
Tubesheet
Outside
Packed
Floating Head
lnside
Floating Head U-Tube
No, of Passes
No.
ol
Passes
No.
ol
Passes No. ol Passes
Shell
lD in.
33.00
35.00
37.00
39.00
42.00
45.00
48.00
51
.00
54.00
60.00
495
478
472
556
552
538
632
613
598
705
685
672
822
'799
786
946 922
912
1079 1061 1052
1220 t159
1176
1389 1359
1330
1714
l69t
t6&
477 460
448
540 526
508
608 588
568
674 654
&O
788 765
7s6
910
885
866
1037
1018 1000
1181 1160 1142
1337 1307
1292
1658 1626
1594
440
424
498
484
562
548
630
620
144
728
872
852
1002
980
1138 1116
1292
12@.
r@4
1576
Tube
Count
lor
1-in.
OD
Tubes
on
1tA-in. Pitch
TEMA TEMA
TEMA
Type L or
M
Type
P
Type S
TEMA
Type U
Fixed
Tubesheet
Outside
Packed
Floating Head
lnside
Floating Head
U-Tube
No.
of
Passes
No.
ol
Passes No.
ot
Passes
No. ot
Passes
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
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
106l
l0,l0
1218 1202
tt92
1370 1354
1350
1701
1699
1684
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
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
http://slidepdf.com/reader/full/mechanical-design-of-process-system-volume-2shell-and-tube-rotating-equipment-keith 144/252
136 Mechanical
Design of Process Systems
Table
7-13
Continued
Tube Count
tor 11/4-in, OD Tubes
on 1sfi6-in.
A
Pitch
TEMA
Type
L
or
M
Type
P
TyPe
S
TYPe
U
Fixed
Tubesheel
Outside
Packed
Inside
Floatlng
Head
Floating
Head
U-Tube
No. of
Passes
No. of
Passes
No. ol Passes
No.
ol
Passes
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
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
000-
764-
14
148-
22
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
1116
00
00
64
14
12
22
20
32
28
48
44
64
60
86
80
tt4
104
138
132
t62 152
196
184
232
220
268
256
310
296
356
3M
4M
388
452
440
534
522
626
6t2
720
700
822
800
930
908
1160
1140
Tube Count
for
11/4-in,
OD
Tubes on
11fi6-in'
Pitch
TEMA
fvoe U
TEMA
Tvpe
S
TEMA
l'vDe
P
TEMA
LorM
Fixed
Tubesheet
Outside
lnside
rtinq
Head
Packed
I
Head
No.
of
Passes
No. ol
Passes
No.
ol
Passes
No. of Passes
Shell
lD in.
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
0000000
6640664
t2 12 lZ 0r2 12
4
21
16
16 12
21
12
8
32
32 32
18
29
28
16
38
38
32
24 38
34
34
52
52
52
48 52
48
44
70
7o
68
s0
70 66
56
89
88
88
80
85 84
70
rr2 112
ll2 96
108
108
100
138 138
130
114
136
128
128
164 l@
156
136
154
rs4
142
444
664
12 12
12
24 22
16
37 34
32
45
42
42
61 60
52
80
76
76
97
95 88
t24
124
t20
t45
145
144
172 168
164
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
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
http://slidepdf.com/reader/full/mechanical-design-of-process-system-volume-2shell-and-tube-rotating-equipment-keith 145/252
The Mechanical
Design
of
Shell-and-Tube Heat
Exchangers
'137
Table 7-13
Continued
Tube
Count
lor
'l'tlq-in.
OD
Tubes on l/rs-in. Pitch
TEMA
TEMA
Type L
or M
Type
P
TEMA
TEMA
Type
S
Type
U
Fixed
Tubesheet
Outside
Packed
Floating Head
lnside
Floating
Head
U-Tube
No. of
Passes
No. of
Passes
No, of
Passes
No. of
Passes
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
210 202
202
24r 234
230
272
268
268
310 306
302
356
353
338
396 387
384
442 438
434
518 518
502
602 602
588
682 681
676
7'.70
760
756
862 860
8s6
1084 1070
1054
193 184
184 172 184 180
158 r12
176
176
224 224
216 198 2t7
212 204 198 200
196
258 256 256 236
252 248 234 236
232
232
296 296 282 264
289
2',76
270 264
272 268
336 332 332 304 329
316 310 304
312 296
378
3'70
370 358
312 368 354 340
348 348
428 426 414
408 420
.102
402 392
396 392
492 492 4U
464 485 116 468 464 472
456
570 566 556
544 565 55J 5+6 544
552
536
658 648 648
620 653 616 628 620
628 620
742
'729
722 7t2 738 126 ?20
',705
'7t2
708
838 823 810 804 837 820
811
80.+
808 804
1042 t034
1026 1008 1036
l0lE i0r2
1008
l0t2
992
Tube
Count
tor
1tlc-in.
OD
Tubes on
1el16-in.
,
Pitch
TEMA
Type L or
M
TEMA
Type
P
TEMA
Type
S
TEMA
Type U
Fixed
Tubesheet
Outside
Packed
Floating Head
lnside
Floating Head
U-Tube
No, of
Passes
No.
ot
Passes
No.
of
Passes
No.
ol
Passes
Shell
lD
in.
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
544664
13 108
24 20 16
37 32
28
45 40
40
60 56
56
'79
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
< ,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
0000
44
12
t2
20
20
26
24
40
36
56
52
74
68
96 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
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Sallle Pilch
or Stoci.q
The Mechanical Design
of
Shell-and-Tube
Heat
Exchangers 139
Kern
[9],
where
the expression
for the shell-side
pres-
sure drop is
given
as follows:
iGlD.(NB
+ 1)
Polh
ot
Fluid
A.
Shell side fluid baffling
showing
segmental cut baffles.
Fluid Flo13
Poroll.lhTubrs
os,t
Po3r.3
/From
one
Bolll.d A..o
io N.rr.
;9
]
eorrrr
"wintoi'
or
"co'l
O
O
J
Eac$ed
03
%cu ,{hkh
is
(5.22X10)roD"7
r
where
(p/p,,).
G,,
D.,
D.
NB
^l
t.
(7
31)
:
are
previously
defined
:
number of bafiles
=
specific
gravity
of
shell-sidc
fluid
:
combined friction
factor deter
mined
from Figure
7
23
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
differ-
ent
problenr.
Chapters
I and
,1
were primarily
concerned
with Yorte\
sheddrng.
This
chapter
covers vortex
shed-
ding and sereral
olher t\pes of vibration
phenomena.
Also.
the
problen
is difterent from
rhat
in Chapter 4 be-
cause
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
preven-
tion of
tube vibrations. Here
we
will
outline the causes
of
the
phenomena
and
present
some quanlitative
ap-
proaches
to the
problems.
Presented
first is a simple
and
quick
approach to
pre,
dict
tube vibrations
caused
by
shell-side
flow.
This
ap-
proach
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
shell-
side 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
{%XSherl
10.).
Ner
Fror
Ateo
ol Wiido* is
Full
Windor A/.0 Diius
Ar.o
B. Segmental
baffles
showing window
are
for
fluid flow.
Iilol.:Ar0o Avo,l0bla
tor Cror Flor L3ed
Cort,r, rr r
.'
peler*ce
I
. oth.t
i:l:1if.'
4,i
*,
orhe'
a,,olq -e.rt
ro
ooh
.
E3se"',- ||e
so-.
C. Cross
flow
area
for iube
layouts.
Figurc
7-228.
Various
baffle
*indou
schemes
[,1].
Baffles
neveq
except for unusual
designs such as ori-
fice baffles,
extend a
full
360" around
the
shell.
The
baf-
fle
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
percent-
ages of
the
entire
circular shell
area. Figure
7-22b illus-
trates
various
baffle window
schemes.
Shell-Side
Pressure
Drop.
There
are several methods
to calculate
the
frictional
pressure
drop across tube
bun-
dles,
and the reader
is referred
to
Ludwig
[4]
or Kern
[9]
who give
comprehensive
discussions
of
the
various
tech-
niques.
The method
we will
use is
the one developed
bv
Boftr.s
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'142
Mechanical Design
of Process
Systems
F.
:
aFrL
^
bFI L4
EI
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 re-
suit 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 ef-
fective resistance
against collapse.
Thus, Equation 4-2
predicts
the amount
of
tube
wall
that effectively resists
the baffle wall reaction,
and
is written
as
(4-2)
(7
-32)
(7
-33)
The
values
for a and b
are dependent upon the bound-
ary
conditions of
the
continuous beam. Typical values
are
presented
in Figure
7-25
and
are
fairly
comprehen-
sive 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.
a:11{
+
:ol
180
\12 I
Continuous
Beams
dmar br"r
I
2
3
4
5
6
l .200
0.550
1.100
1.223
0.572
1.143
0.0059
0.0099
0.0069
0.0094
0.0097
0.0065
4
[.r.
(0,130
r fton A]
=
t.005r ,rrlsl
il.r.
(0.tt
, tioE
^
.'
o)
a
0,00n &,4/El
a
r.&
o.raa
I
rroi
A o.
D)
-
0,0rl r.
r
A rr.r.
(0,415
r koh E,
5
o.m a
r./al
€
comtruous
BEAM-FoUR
Eeual spaNs-LoAD
FtRsr aND THrRo spANs
a
tl.r.
(t
az
rlr.n A)
E
0.6tt {,r/al
6.
coNTlNuous
BEAM-FoUR EeuAL
spANs--{LL spaNs
LoAoEo
^
.L
(Gaa
I lr.h A
.na
a)
-
O.Ol5 d./s
Figure 7-25.
Boundary conditions
of
continuous
beams
u5l.
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where
d
=
angle of contact
A
=
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
that neither
the tube
nor
baffle hole
will
deform
to
re-
duce
stfesses, which
is the worst
condition. For
deter-
mining
contact
stresses between
the
two
bodies,
Ti-
moshenko
[16]
has
shown
that for the case in
Figure 7-26
the
diameter
of
the circle
of contact
is
d
:
1.76E(qi_e")g4"
l"'
[
2EEB(d, +
dJl
Q-34)
From Equation
7-34 one
can
deduce
that
the tub€-baf-
fle interface
should
be
alLalyzed
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
ts
*.
(#,.
J"L,,*',J'
Q-3s)
Evaluating
the
relationship
for shear
in Equation
7-32
we
have
F.
=
aaFrl-
The
Mechanical Design
of
Shell-and-Ttbe Heat
Exchangers
149
where
q
:
constant that
represents
the
amount of effective re-
sisting tube wall
area
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
=
(7-36)
(7-37)
z,
=
hisson
ratio
for
the tube
material,
dimension-
less
/B
=
hisson ratio
for the
baffle
plate
material,
di-
mensionless
E =
modulus of
elasticity for
tube
material,
psi
Ea
:
nodrlus of
elasticity
for
baffle
plate
material,
pst
c
=
constant, in./lbr
cr
:
constatrt,
dimensionless
To
arrive at the modified
damage
numtrr
for
baffle
damage we solve
for
F1 in Equation
7-32:
Now dividing
this relation
into
Equation
4-80 we obtain
Cpd,p\Palc
_
2g"F.
Letting the baffle
damage
number
be
represented by
Nss,
a dimensionless
parameter,
we have:
EB
F,:
F"
-
o'al-
1.0
*,
-
Cpd.pV2alcv
^""
- --fdE-
Q-38)
where
Nss
(
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
param-
eter,
NsD,
which
governs
tube
damage
induced
by exces-
sive displacements
in
tube movements,
is
similar to that
for
the
baffle
damage
parameter.
Solving
for
F1
in Equa-
tion
7-33 we
determine F1
as
follows:
Figule
7-26. Fluid
foroe
causing
tube
to impinge
on baffle
F"
:
E
plate.
"
bL4
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144
Mechanical Design of Process Systems
Dividing this expression
into Equation 4-80
we have
Ded,pV'?bLa
_
1.0
2g.6E,I
We define N6p as
rrcD
-
CDd,pv2bL4
(7
-39)
where
NcD
<
1.0
Once again,
if
NcD
>
1.0,
then thicker
tubes should
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 dimen-
sionless,
they do
not
have the same firm
basis as do di-
mensionless
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
un-
equally),
one can simulate the
tube displacements.
How-
ever, since
we are
not dealing with
a single
tube, vortex
shedding
around tube bundles
can
presently
only
be ac-
counted
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-in-
duced
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
re-
sult
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
"whirl-
ing"
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 syn-
onymously
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.
Turbu-
lence 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.
2g.6E I
F-+
6=
futr)
p
=
p_(t) where
t=
iime
Figure
7-28.
The magnitude
of
the
direction
of
the fluid
strik-
ing
the
cylinder
can
be
thought
of mathematically
as
a
forcing
function,
F-,
mapping
a
pressure
distribution
around the
cyl-
inder
over
region
R.
(r\
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146 Mechanical Design
of
Process
Systems
V
:
fluid
velocity
of
fluid
external
to
tubes, ft/sec
m
:
mass
density of fluid external to tubes, slug/ft
dr
:
tube OD,
ft
L
:
tube
length
between
baffles, ft
Lr
:
total
length of
tube
between tubesheets,
ft
fN
:
fundamental natural frequency
of
tube
portion
between
baffles,
Hz
I
:
sum
of
structural damping
and
the
fluid
dynamic
damping
x
:
distance along tube,
ft
d"
:
4Rs
:
4(hydraulic
radius)
:
4
(flow
area between tubes)
wetted perimetel
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
sim-
plest
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 sol-
idly 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 com-
ponents
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
fol-
lowing expressions:
-
;]
-
".
tubes on an equilateral
triangular pitch
of
P
_
+0,
[/r\
-;
t\-dJ
-
f]
-
ro.,"0", on a square
pitch
ot
P
-
pv':d,
-.
16,l
ru
:
--
N"
l=l
'
zE"
\o,/
/\
."
_
pv'0,
6" 16,l
^
2e,
"
\d,/
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 con-
sidered 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 K,
:
Kr:
2T-
D
/nV r
l:l for
:
)
\T/
D'
tn
T
l
5
<
1.5
(7 -4s)
(7
-46)
(P\'",
r
\T/
D
t2
o*":
E-Cp1*-y
(7-42)
where Ce
:
drag coefficient of tube
surfaces
6.*
:
2.586.-,
(for
x
:
L/2)
(7-43)
Equation
7-42 represents the maximum tube deflec-
tion
to be
incurred.
The factor 2.58 represents the
ampl
tude
of the highest one
percent
of cycles.
The
value
for
the
natural frequency
at
the tube in
Equation
7-41 takes on several forms. The easiest
to
use
is the
formulation
developed
by Blevins
[18]:
K,
=
C'(D/T)
-(,n)'.,(,n)'
"7(
N
-
;;;
6L-
F
i,l2
-L
,lZ r0
5
where E,
:
modulus of elasticity of tube metal,
psi
mr
:
mass
density
of
tube metal.
slugs/ftl
4
=
tube OD, in
dti
=
tube
ID,
in.
TEMA
gives
a listing
of expressions for
the
natural
frequencies of the
tubes based
on several types
of
sup-
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.
Ex-
periments
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 deter-
mine if those deflections
are acceptable.
After determin-
(7
-44)
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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.
Un-
fortunately,
at the current
state
of technology,
there are
no critical values to
decide whether the whirling
parame-
ter 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
stag-
gered
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
The Mechanical
Design
of Shell-and-Tube Heat
Exchangers 147
more
efficient
than the
shell and tube
exchanser because
the comparable shell and
tube exchanger
req-uired
to
re-
place
a
plate
fin would be eight
times the volume
and
twenty-four times the weight
of the
plate
fin
if
con-
structed
of
aluminum. The reason for
this is that
if
the
plate-fin
is made
of
brazed
aluminum,
the
aluminum
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
expen-
sive
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
ex-
changer 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
load-
ing in
excess
of
differential
temperatures
of
50'F
that
in-
ternal 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-
1
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.)
--loF
\JT
rl-L
o
Oo
./
,-7
./
-rl-
-
i,
.
-2
.
5,onr-3ro'2
'
(0,1,3
A
---_
xY
-lDt'3
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M
o
"F
A
o
,r1
1'h
.-
>;
-/l
--r.
h
--
u+
I
o
o
o
148 Mechanical
Design
of Process
Systems
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
fatigue.
The
aluminum flanges
used
on
these
units
are
de-
signed
per
ASME Section VIII
Division
I
and,
quite
commonly, are identical to ANSI 816.5 flanges.
For
further
discussion on the thermal analysis and de-
sign 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
de-
signed. The exchanger
is
to
be used
to
exchange heat
be-
tween a hydrocarbon
process gas
and a
gas
used for re-
generation.
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,
Table
7-14
Maximum Recommended
Shell-Side Velocities
All liquids in
10
fusec
Gases and
Vapors-in fl/sec
Pressure Molecular
Weight
(psi)
18
30 50 100
150
200 400
2'7
-tn.(vac) 250
185 160 110
100 90
77
15-in.(vac)
130
100 85 65
60 52
45
0 100
80 70 50 45
40
35
50 65
55 45 35
30 25
20
100
200
500
1000
55 45
35 25 20
18 16
50 40
30 23 19
t7
40
30
20
20
15
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 rectan-
gular
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 thick-
ness, depending
on
the
pressure
of
the service.
This
de-
sign is commercially available
at a temperature and
pres-
sure
of approximately
-
452"F at
1,400
psig.
975'F
200'F
750'F
625"F
GTTD:775"F tiITD
:
125'F
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.M
Figure 7-32. The
plate-fin
exchanger.
(Courtesy
of Albraze
International, Inc.)
The
Mechanical Design
of
Shell-and-Tube Heat Exchangers
'7'75
-
125
:356"F
h
(E,l
u25/
Turning
Distributor
Fin
q
:
riCo(LMTD)
The shell-side
mass
flow
rate
:
22,050
lb,/hr
for
the shell-
side
gas,
Co
:
1. 10 Btu/lb.-'F.
The
required
heat
duty of the
unit
is
q
=
122.050r
l
rr. ror
j'l=
1:so.r"r
'
hr lb",-'F
Rfr
I
q
:
8.634.780
--
nt
The available tube area in the exchanger is
determined
as
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.
Available area
=
(0.3171)
T
(ZS:),u0.,
(tr)
,,
'ft
=
1.38E.95 it:
ng
Sh€el
Bar
149
LMTD:
now,
Figure
7-33. Tubular channels in
plate
surfaces result in excellent
heat
transfer
in
plate-fin
heat
exchangers.
(Courtesy
ofAlbraze
International. Inc.)
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150
Mechadcal
Design of Process
Systems
HEAT EXCHANGER
SPECIFICATION
SHEET
I
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
50
52
53
57
5a
59
6l
T"b"-T,rb".h".t
J.i.t
Bundle
Entranc€
Bundtc Erir
Figure 7'34.
Heat
exchanger specification
sheet.
(O1978
Tubular
Exchanger
Manufacturers
Association.)
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The
Mechanical
Design
of Shell-and-T[be
Heat Exchangers
For the
tube-side
gas, 1%-in.-11
gauge
tubes
Np"
:
0.7,
obtained
ftom
Process
data
k
:
0.03
Btu/hr-ftL'F
P
=
0.01 Cp
:
0.024
lb/ft-hr
Tirbe-side
mass flow
rate
=
41,884 lb./hr
For each
tube,
.
-
41:qq4
9./hr
:
148 rb-ihr
--
283 tubes
P
:
O.1524lbJft3
'
4
=
l'25
in"
di
:
1'010
in';
Ar
:
0.8012
in''?
:
48.48 ff/sec
151
sa-tua-600
osME)
r.gu;riil{
sa-ra8-6lrt
(^snE)
Flgure
7-35.
Vertical
gas-gas exchanger.
Shell-side
nozzles
C and
D are
16
in.
in diametel
which
makes the
flow
area
o.os
r
n.396) ft,
ftr
From Table
7-14 we observe
that this
is a
reasonable
velocity.
ftrbe.Slde
Film
Coellicient
For turbulent
flow
inside tubes
we use Equation
7-19,
the Sieder-Thte
correlation,
From
Table 7-14
this
velocity is
reasonable
_-
(48.4D
a
(1.oro)
in.
ffi
,o
tou
*
l.
=
a'(16)'z=
2ol.o6
in.2
:
t.396
ftz
Shell-side
mass
density
:
p.
:
0.09 lb./ft3
rr.
/ rr,.
\
22,050
+ l=.:;r-l
nr Ijbtt, secl
v
:
-------
j::--l:i:-
:
48.75 ff:/sec
:
ro lt
Btu
--
--
hr-ft2-"F
Shell-Side
Fllm Goefficlent
Nu"
=
0.027(NrJ03(Np.)18
(rJrJ''4
N.,"
:
?
=
o.:o
(Ps,
)"'rN*,',,
(;)"
Nr"
:
93,278
>
10,000
and Equation 7-19
applies
Nr"
:
0.027(93,278)0.8(0.7)t/3(1.0)
:
226.78
h..1.
Nr"
::+:1
From
which,
Q-26)
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152
Mechanical Design of Process
Systems
For
60"-4
arrangement,
p
:
1.75 rn.
^
_
8[0.43P'z
-
0.52'd"'z/4]
""
-
"dr,
^
_
8[0.43(1.75)7
-
0.5rr1.25r']l41
_,/1rr-
'
r(l .25)
or
D"
:
0.119
ft
c
=
tube clearance
:
L75
-
1.25
:
0.50
in.
B
:
distance between baffles
._
-.
-
-^.
ln.
n
B:
tnnll
1.r.
=
1100) l^',',"=l t0.8tr/\tt
\u.
r
lvl
Btu
-- -
hr-ft2-o
F
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,
(7-2e)
IT
_
:
22.50 rn.
I
_
+
0.001
80.83
Btu
I
:
l/'\l-
-
"
--
hr-ft2-'F
+
0.001
+
I
23.40
8,634,780
+
r
^rn
as
8 baffles
Computing the
flow
area of tube bundle
=
a,,
D.(cXB)
. ,
a\=-ll-
(7-301
"
p(t44)
(40)
in.
(0.50)
in.
(22.50)
- l. t9 rt'
in
2
(1.75xt44)
-
t'
For the shell-side
gas, p
:
0.09 lb-/fC
average
for tem-
peratures
specified,
and
p
:
0.05 lbm/ft-hr
lh
rt n <n
'"m
c"
-
.=^.+
=
12.348.00-15
"
1.79
11'
hr-ft2
^,
_
D.G,
_
{0.119)
fr
(12.J48.00)
lb./hr-ttz
_.
4
0.05 lb./ft-hr
NR":29,388.24
The
exchanger
has
baffles with
25
%
cut,
thus from
Fig-
ure
7-22,
jn
:
100
/
\o
t+
n"
:
ff
rr.re,r"t
[aJ
r
Area required
:
1tz.st,)
.
j\
1.lso;"n
hr-ftr-"F
:
1,384.91
ft':
From
previous calculation,
Available
area
:
1,388.95
ft'z
In most applications
the available
area should
not
be
10%
greater
than
the required area, such
material is
not
wasted.
Shell.Side
Pressu:e
Drop
Ap-
f
C.rD,(l_.,t8__t
t)
(7_Jt)
(5.22X10) oD"1d
Ns
=
8 baffles
D.
:
shell
ID
:
40 in.
:
3.333
ft
G,
:
12,348.00
lb./hr-ft2
For
Np"
=
29,388.24,
f
=
0.0022
from Figure 7-23.
For
plain
and bare
tubes,
f
f,=::=0.00t8
t.1.
D"
:
0.119
'y
:
specific
gravity
of shell-side
gas
=
0.9
Np.
=
0.8
from
process
data
/ \o
t+
d
:
r.0:
tl]
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-
The Mechanical
Design
of
Shell-and-Tube Heat Exchangers 153
From Equation
7-35 we
compute the
shear
force induced
aP"
=
(0.0018)(12,348.00f
(3.333X8
+ 1)
(5.22X10)ro(0.
l 19)(0.9X1.0)
AP.
=
0.0015
psi
<
<
10
psi
allowed
on data sheet,
Figure
7-34
EXAIIPLE 7.2:
VIBRATION
CIIECK
FOF
REGENERATED
GAS
EXCHANGER
The exchanger in Example 7-l is to be checked
for
possible
vibration
problems.
To
accomplish this we com-
pute
the damage numbers
of
equations
7-38 and 7-39.
B
=
tube
span
between
baffles
:
22.50
in.
Shell-side
gas
density
=
0.09 lb-/ft3
4
:
1.25 in.
From ASME
Section VIII Div. I
(see
Chapter
4)
for the
tube
rnaterial at design temperature,
o"n,
:
18,052
psi
at
shell-side conditions
ds
=
1.25
in. *
1/o+
in.
=
1.156, where
t/e+
in.
is the baffle hole
clearance
(s€e
Figure 7-34)
From Figure
7-20 we compute the
shell-side
gas
velocity
bgtween
tubes.
D.
:
210.0
in.,
D,o
:
37.125, P
=
1.75
A,
:
+ [o,
-
o," +
D'=
d'te
-
al
nz
t44t
"
*
P
I
on the
tube at the baffle hole,
I
^"
\ /-
V
R:l#kltto-.tnr]
(7-35)
"=
t=''
+
--l
--f",&:
Es
=
27.0
x
1trpsi
qEB
c
_
2(1.00
-
0.?33)
=
4.941
x
10_E
27xlop
'.
=
[.'
?]il''"l,o
*
*,0-',
(oryJ
=
16.015
lbr/ft
Frorn Figure 7-25, a
:
1.10 and b
:
0.0069
Fr:
crPP4
<olito.ri
p
orr.rrur$
(9
o
z1tzz1
":
ft=
tDf
-
SeC"
Fr.
:
1.200 lbr/ft
F.
:
eaF,
L =
q:
F
aFrL
16.015
lbf/ft
^,
=#[oo
-
rr.,r,
.tf#6.?s
-
r.2s)]
Ar
:
2.051
ft2
l|1 lh
G":
18,522.0
-;l
:5.14s
.:"'
tt'-hr
ft'-sec
(5.145)
5
(2.0s1)
ft,
n'-sec
0.0e
5
:
117.236
A
betwe€n
tubes
sec
Nse
(7-38)
(7-39)
2(32.,
-:
J-(l6.0lt
+
lDf
-
SeC- n
(1.
1ox1.2oo)
+
(zig*")
-
^,
-
CpdlpV2ale
rtBE
-
------;-----
zE"r
'
=
6.471
,
rr.rr
(lJoJ
ft6.471)
NeB
:
1.00
",
_
Cedp\Pbla
,.."
_
_EJE;_
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154
Mechanical
Design
of Process
Systems
^
bF,
L4
E,I/\
(o.oo6ex
t.2o)
ry l]i I
(22.50)a
fr
rt
\Lz ln.i
th-
(27
\
106)::]
(0.06881
in
4
f(
6
:
9.520
x
l0-5 in.
N.o
:
Nco
:
1.000
With
NBE
and NcD not
exceeding 1.0,
we do not expect
vibration
trouble.
To be certain
we compute
the
maxi-
mum tube deflections
as
follows:
For
the
tube-side,
M,:1.448f:o.o+sf
0,..
:
o.o36cV2d,
H
(;9"
[.J",r [.)
d,
=
1.25
in.
=
0.
104
ft
dt
:
1.084
in.
:
0.090
ft
'"
-
8(rrjo4:
(7
-4r)
(1-44)
Shell-side
(hot
oil)
Tube-side
(chlorine
gas)
GTTD
:
250'F in.
176'F out
77"F
in.
158'F out
173'F
LTTD:
l8"F
(27
x.
ro6)-,-]k
ttt.zsF
in.2 +
(1.084)2
in.2
LMTD
=
crrD
-
LTTD
_
173
-
t8
:68.496.F
. /crro\
irz:\
'"
\tttol
'n
\-tr
/
(with
a
parallel
exchanger no
correction
is
needed
for LMTD)
Tube-Side
Film
Goefficient
For
chlorine
gas,
Co:0.
l16
Btu/lb.-'Fi
p:
|.667
rb-/fc
q
:
rirCog-Uf O;
",
lb.
-
fr
I
9.520
x
l0-5
d-,
:
0.036
r4.94r
x
t0-)(t,r.rru,2
lit,ltl F
ol
\
12
/ \0.04s/
6..,
:
7.553
x
l0
7
ft
:
9.063
x
10-6 in.
With
this
magnitude
of
tube
displacement
and
Nss and
Nsp being
in
the
safe zone,
we
conclude
that
the
ex-
changer
will
not
have
vibration
problems.
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
tube-
tubesheet
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.
rt2 /rr <n\n
tItT.236f
"
,
(0.00691
l':::l
fi.
sec'
\
12
|
.,
,0""
lb.
/
r ,rug
\
/rzza
in.r\
"
"*-
*l
1:z-z
ruJ
\--
ft-/
f"
=
1.710
Hz
For shell-side
fluid,
,'^ /,^,..^\
p
=
o.oe
r: ,llils
|
:
o.oo3:15
'
frr
\
32.2
lbJ
ft'
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I
2
3
5
6
7
a
9
to
ll
72
14
t5
l6
t7
l8
l9
20
2l
22
23
21
25
26
27
2E
29
30
3l
32
33
31
35
36
37
3a
39
1to
4l
4Z
13
11
45
46
47
4a
49
50
5l
The Mechanical
Desisn
of
Shell-and-Tube
Heat
Exchansers
155
55
57
59
50
5l
H
EAT
EXCHANGER
SPECIFICATION SHEET
Add.€ss Prcposal No.
Plaht
Locarion Dale Rev.
Siz. TypG
(Horlvert)
Connected
In
Pa.allet
Series
Surf/Unii
(Gross/Eff.)
So Ft: Shells/ Unit
Surr/Sh.ll
(Gross/Eft.)
So rl
PERFORMANCE OF ONE UNI'I
ShcllSid€
Tube Side
Ur:T
otL
EEDfuflE
GA-
Ffuid
Ouantitv. Total
Lb/Hr
Liquid
T€mper.tur.
(lnlo l)
,
'F
7{6
soecific
cravitv lC
^IEg
I
^fiO
Viscosity,
Liquid
Cp
Molecular W6isht,
Vapor
Molecular
Weighl Noncondensable
Specitic
Heat
Btu/Lb
"F
o.+zao
O.11to
Thermal
Conducalvity Btu Ftltlt Sq
Fr
'
F
Latent Heat
Btu,/Lb
@ "F
Inlet
Pressure
Psia
Ftls
Pressur€
Drop, Allow.
Calc. Psi
Foulins
Resisranc.
(Min.)
Heat
Exchansed
(D
O
O.OOO
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
t /,79
DesiEn
TemD€rature
'F
No.
Passes
Der
Shell
Corrosion Allowance
ln,
Sizo
&
Ralins
ln
Out
rube No.,5O
op
I
In.;rhk
(Min/^vs)
In.r r€nsrh
r5Ff':
Ft; Pitch
If{
In. +30
a.50€-so
€>a5
Tsbe
Type
Material
Shell
Channel or Bonnet
Tubesh€ct-Stationary
Tubesheet.Floating
FloatinE Head Cover
lmpins€menr Protectio
Bafites.cross
b
TvDe
4h
%
cut
(Diam/area)
1
.j/4"spacine:
cuc tnlet
In
Supports-Tube U-Bend
Type
Bypass
Seal
Arransem€nt Tube-Tubesheet Joint
Bundle Exit
Gaskers-Shell Side
Code Reo0irem€nts
TEMA
Class
Weight/sherl
Lb
Figure
7-36. Chlorine
superheater heat exchanger
specification sheet.
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156
Mechanical Design
of
Process
Systems
700,000
P
ft:
nr
:
9.116
_
Btl,
(68.496).F
rDm-
-r
88.0ee.783'u.(
t*
)
^
hr
\3600
sec/
lh
| .667
:
ftr
For each of
the
150-l-in.-14
BWG
tubes,
ft3
14,680
:
v
=
-........-
J9c
=
25.'796
ft/sec
-
Reasonable
(0.0037941ft
2(
I
50)tubes
Nq.
=
j:l;
I
=
0.0148
Cp
=
0.036
lb./[t-hr
r2s.7e6t
Llg{'o)
',
(1.667r
r
{:ooo
"''l
sec\12
/
ftr
\
lhr
/
88,099.733
5
nr
frl
14.680
i-
sec
(0.036)
lb'
'
'frhr
:298,860.527
u".:l.Cp,k=5.0x to-r-gu
'
k
hr-fc'F
ro.036r
lb'
,0.116r
Btu
--
ft-hr
'
lb^-'F
r'
=_ _____ =Aal(
(5.0
x
l0
3)
Btu
'
'hr-ft-"F
N*"
:
0.027(NrJo
tN.,l,'
(re)'
'',
0.7
<
Np,
<
17,000
^
_
8[0.43
p')
-
0.5rd 4]
Nn.
=
NN"
=
0.027(298,860.527)0E(0.835)r/3(1.01
:
619.a64
N",:\ i
=h,
(610.464r(5.0
t
l0-,)
Bt'
'
hr-ft-'F
r(1.0)
D"
:
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
(
18.00)(0.25
X30)
I
=
_-
:
t-t.11
ll.
-"
p(144)
\1.2s)(t44)
^rn
as
lh .a^
(6.664)
iI
(3.600):::
^
sec hr
--
lh
G.
:
______=-_:=_______j::
:
31.987.20
.+
(J.
/) rt'
hr-tt'
lqi,t\n
\12 l
h,
=
41.866
-+-
r-n'-
-f
Shell.Slde
Film
Goefficient
q
:
fiCP(LMTD)
cp
:
0.426
Btu/lb,-"F;
lh
p
:
62
46
-;T:
k
=
0.077
Btu/hr-ft-'F
(.42o
d+
(68.4e6).F
:
6.664
r
sec
6.664
l9r
E9
:
0.10? ft3/sec
For 60" A
arrangement,
Tdo
8(0.43)(1.2sf
-
0.5 r(l.0)z
l
4l
th
62.46=
ftr
The smallest shell-side nozzle is the
3-in. outlet, where
Ar
:
7.393
in.'?:0.051
ft2
fr3
v
:
_--
g
:2.092:
-
Very reasonable
0.051
ftr sec
r'l'.:
&,
u
=
2.544ltt^tft-hr
12.5+4t
lb^
ro.426r
Btu
Np,
=
ft-hr
lb.-'F
=
t4.075
0.077
Btu
hr-ft-
"F
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,0#
P
z.su
lb^
ft-hr
The
exchanger
has
baffles with
45
%
cut, so
from Figure
1-JJ
in=
12
I \0.14
U
=Jx 11-trr:l
Pl
"
D.'
"'
\p",
h
-
(l2xo.o77)
64.025)r/36)
Btu
-
o.o59
tt
t
tt
;$:F
Since both
gases
are
relatively
clean, the fouling
factors
for
both
sides are
0.0001.
1
*
o.oor
+
o.ooo8
*
,1 ..
37.779
43.866
U=19
700,0m#
The Mechanical
Design
of
Shell-and-T\rbe Heat Exchangers
'v
=
1.001
d=1.0
Aa
:
ratio of OD
to ID of tube
Ar
=
1.199
r,.-
:
h'
=
73'629
-
ot.+os
Blu
Ar l.l99
--"-'br-ftL'F
h
=
196.720
-
6r.M
(196.720
-
99.680)
61.,109
+
107.480
t*
=
161.436"F
Maximum allovable
tube
joint
load
=
L"*"
1..*
=
A,ouf,
For SB-l6l-2fi) at
162"F,
o"n:
10,000
psi
r
-,
:
(0.239)in.1lo,m)
g
(1.0)
=
2,3e0.00 lbr
tn.'
The tube wall tenperature
is used in a method devel-
oped
by
Miller
[21],
which is
a
more exact approach
than most and
consequerdy results in a more economical
design.
P,
:
shell-side
pressure
:
100
psi
At
=
tw
-
ta; ta
=
ambient
air
temperaturo
:
70oF
At
:
161.436"F
-
70'F
:
91.436'F
D.
:
shell
ID
=
Ds
-
CA
CA
=
corrosion
allowance
=
0 for
pure
helium
(inert)(ero-
sion
is negligitle)
D"
=
18.0
-
0.0
:
18.0
in.
,
.
..
=
PR
- (looxg'o)
=
0.0558
in.
'st'ctt
-
og
-
qfp
<te"zooltt.ol
-o.ettool
Use
ta'a
=
34rc-in.
=
0.1875 in.
For the shell,
F.+
=
27.546
x
lffpsi
at 161.436'F
aPs
=
(0.w2zs)(3r,987.20f(1.5x6
+ l)
(s.22X10)ro(0.059)(1.00lx1.0)
=
0.008
psi
which is acceptable
Nn"
:
=
741.842
G
_
(o'059)ft(31'987.
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.
Plessure
Drop
f"G.,D"(N" + l)
^''
=
iSzrl
o)'D.rd
\
:
6
baffles
D,
:
shell
ID
=
18
in.
=
1.5
ft
C"
:
ft,gSZ.Z0,l\.
nr-n'
f
f"=
i=
0.w225
D"
=
0.059
ft
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158
Mechanical
Design
of
process
Systems
Tube
Metal
Temperature
For
parallel
flow,
Atn:259-77:173.F
At: tla
-
158
:
lS.F
At": 18
=o,no
Atn
113
For hot
end,
Ul:
600,000
where
E1,
:
modulus
of elasticity
of
tubesheet
metal
T
:
tubesheet
thickness
:
1.1875
in.
ar
:
cross-sectional
area
of tube
(see
Table
7-3)
:
0.239
in.2
n:
number
of
tubes
:
150
na,
:
(ls0)(0.239)
:
35,850
in.2
rr lR Or2
A
=
':A
=
254.469
in.2
:
shell
cross-secrional
area
4
rt I Ol2
c
-
/rtr'vr-
tljOt
:
86.394 in.z
-
total
cross-sectional
4
Area or
tube holes
B
=
{
(Di"
-o3r
=
I
Ul8.J75P
.{l8.r2s),J
:
7 .1668
in.2
A
-
C
:
254.469
in.2
-
86.394
in.2
:
168.075
in.2
The ratio
of
the
inside
shell bore
area
to
the net
tube-
sheet
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
expressed
as
(A-C)
tl
:--
^
Ler
I
=
4a,
-
(13.79q
^
106X35.850)
- ) sosr
'
E,B
t21.546
y
106X7.1668)
Let APn
=
equivalent pressure
difference.
psi
:6.794
(s
10.510x173)
For
cold
end,
g-
=
6oo'o00
=
6s )q^
'
(s
10.510)(18)
ltl
^
_
luh
-u"l
_
6.794
-
65.2e41
'-l
U[
,-i-5i%
l=u6eo
From
Figure
7-1"1,
F"
:
O.28
Lr,=tr,o*F.(tr-tm)
t"i
-
176
+
(0.28X250
-
176)
:
r96.jZO.F
L":
t"i
+
F"(t""
-
t"i)
t-=77
+
(0.28X158
-
711
=
99.6t0",
t*=t"i,-,
.
tt.n-r".t
n,o +
n.
ct
:
coefficient
of thermal
expansion,
in./in.-.F
For
the shell
material,
o,
:
6.090 x
10-o
in./in.-'F
at 161.436"F
Pri
:
tube-side
(channel-side)
pressure
:
100
psi
At
=
161.436'F
-
70"F
:
91.436.F
dt
=
0.834
:
100
-
100
-
(100)(35
850)
168.075
(7-11)
(7
-t2)
D
rri
n
ar
:
-21.3298
psi
Computing
the differential
thermal expansion
:
Ac
Aa=e,A,-o,A.
4*:
(7.010
x
10
6X91.436)
-
(6.090
x
t0
9(91.436)
:0.000084
PE
:
the effective
pressure
differential induced
by the
equiva-
lent pressure
difference,
APs,
and thermal
expansion,
Aq
P,:P+(ao)
qna'
A_C
(7
47)
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fl
The
Mechanical Desien of Shell-and-Tube Heat Exchansers
159
Pe:
-2r.32e8
+
(0.000084)
(13
7e?l
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): 153.375 in.
Defining
the
dimensionless
parameter,
tr, as
|
-
t025
\
:
1.08
l---
:rr-l
D.
[Lr
-DTdA
-
L,J
(748)
1.08
'10.25
I
(18.125)
4[(2.50s8X1.ss) +
3.12]
o.1."";
:
-1,418.659
compression <
16,?00
psi
allowable
for the tubesheet material
"I
(13.799 x
i09(3s.8s0)
(153.37sX1.
12sf(27.s46
x
109(168.075)
\:2.696
q,(.-r
:
-415.968
psi
for
|
:
f+
:
-0.046
4r-*r
:
-415.968
psi
is well below the maximum allowable
stress, which means that the tubesheet
is of
sufficient thick-
ness.
One could
repeat the
process
if
it
was desired to use a
thinner tubeshe€t.
Had o.1-o*1
exceeded the maximum
al-
1oo
lowable stress
for
the.tubesheet material,
then
a
greater q
tubesheet
thickness would
have
to
be selected and
the-
process
repeated.
From Figures
'7
-37
,
7
-38,
7
-39
,
and 7 40:
f
I
:
1.55; lz:3.12l,
l:
:
-0.046;
f+
=
1.970
The
maximum
radial stress
in
the tubesheet is expressed
as
.'-.,,ffi11,9'
(7-4e)
4(Vfr
+ fr)
l,o,o.,,
-{
I00){2s4.469X2.sOs8)
I
(rg.rz5\t
f-"
--
(168.07s)
I \
1.125
i
a
4
6 A 1ot2
14
16
\
Figure
7-37. Tube stress
factor Ir versus
\.
2
4
6
a lo12
14',r6
|a
X
Figure 7-38.
Tube stress factor 12
versus tr.
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160
Mechanical Design
of Process Systems
The maximum
stress
in the tubes is the
sreater of the follow-
ins:
:u-[^,.-
na,
I
",
(n,
-
A_C
APt*
or
(7-50)
(7
-sr)
o.2
q
o.o
-o2
-ot
-0.6
-oa
-1.O
[
",{t"
-:t'e
]l
=A
_clAP,_
-\-
(A-crl
nu,[
-
(*
+
|.4)
I
;.lr"-l-,,,,n
,lrr^ ro^
-
t-"
-'
T
Figure
7-39.
TUbe
stress
factor
f3 versus
\.
2
4 6 8 rO12
14
16
18
I
Figure
7-40. Tube stress factor f4
versus
\.
(2.5058
+
1.970)
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 ex-
changer
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 counter-
flow.
The
process
is described
in Example 3-6. The
ex-
changer
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)
TLrbe-side
(asphalt
coating
mix)
650"F
in
500'F
out
550'F
out
425'F
rt
GTTD:
150'F
LTTD:
125"F
LMrD:
crrP
-
qrp
_
l5o_-
l?5
:
r.7.t2"F
. lcrrDl ,
11501
'"\rt-/
'\*/
({
+
lr)
(100x254.469X2.50s8)
168.075
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The Mechanical
Design of Shell-and-Tube
Heat Exchangers
161
HEAT
EXCHANGER
SPECIFICATION SHEET
Job No.
Addr€ss Proposal No.
Plant Location Date Rev.
Siz. Type
(Horlv€rt)
Connected
In Parall€l
Se.i€s
Surf/Unit
(Gross/E
f.) Sq Ft: Shells/Unit
Su.r/Shell
(G.oss/Efi
.)
So
Ft
PERFORMANCE
OF ONE
UNIT
ShellSide
HOT
otr-
ASHJNLTCd'NN6FNIf,
Ffuid
OuantitY,
Total
Lb/Hr
Liquld
Tsmpe.ature
(lnlout)
//.60
5=
4z€
sDecific
cravirv
@ 656cp
t.60
a
7
l-lz,
Viscosity,
Llquid
Cp
h.4) a.7>
q3*
q4?
Molccula. Weipht.
Vaoo.
Molccula. Weisht,
Noncondensable
Specitic
Heat
gtu/Lb
"F
0.52b
d.<2b
a.7b
t
D:47
Thermal
conductivity
Btu
Ft Hr Sq Ft
'
F
Latent
tleaa
Btu/Lb
@
'F
Inlet
Pressurc Psia
Ftls
Pressure
Drop,
Allow.,/Calc.
Psi
IO
I
tO
t0
b
Foulins
Resisranc€
(Min.)
Heat
Exchanaed
atu/Hri
MIO
(Correcied)
"F
r-".r". n"r",
S"-i."
so
rt
"
r
CONSTRUCTION
OF
ONE
SHELL
Sketch
(Bundle/No:?le
Orientation)
Shell
Side
DeEisn/TestPressurc
Psis
l<D r
221
EO /
226
O.sasn Temperature
No.
Passes
D€r Shcll
Corrosion
Allowanc€
ln.
Si2G
&
Ratins
Out
luge
o.
5gt
op
74
In.:rhk
(Min/^ve
lIl 8ly6
In.;
Len$h
20
Fr;
Pitch
I.A
In.
<- 30
fgl+119
9
Tubc
Type
Material
sh€l
274l
tp op
In.
lshen
cover
0nt€s.)
(Rernov.)
Channel
or
Eonnet I
Channel Cover
Tubesheel-StationarY
Tubesheet-FloatinE
Flo.lina
Head
Cover
lmoineement P.otection
o/o
Cur
(Dia6lA.ezt
Spacina:
c/c
Inlet
In
Baftles-Lorg
Seal Typ€
Supports-Tube
U'Bend
Type
Bypass Seal ArranAem€nt
Tub€-Tubesh.et Jolnt
pvt-lnlet
Nozzl€
Bundle
Entranc€
Bundle
Exit
Gaskets"shelr side
Tube side
-FloatinE
Head
codc
Requirements
TEMA Class
I
2
5
6
7
a
9
to
t1
t2
t3
t1
77
t8
l9
20
2l
22
23
24
25
26
27
2a
29
30
3l
32
31
35
36
3a
39
40
41
42
11
16
47
4a
49
50
5l
53
55
59
50
61
Figure
7-41. Asphalt
heater heat
exchanger specification
sheet.
l@1978
Tubular
Exchanger Manufacturers
Association.)
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6s0
-
425
=
0.333;
R
:
500
-
425
From
Figure 7-16,
F
:0.93.
Thus,
the corrected
LMTD becomes
LMTD
:
(0.93X137.12)
:
127
.522"F
Tube.Side Film
Coefficient
For
asphalt coating
mix
at 450'F we have
the follow-
ing
properties:
Cp
:
0.368
Btu/lb.-'F;
p
:
89.2321b.ift3;
p
:
933
"O
2,251.20 tb^/ft-hr
q
:
fiCo
(LMTD)
=
1,000,000 Btu/hr
P=
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.
500
-
425
650
-
550
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.
Nn"
:
DiV2
-
ip
(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
catastro-
phe.
At
the current state-of-the-art
there are no
simple
answers for
such
complicated
subjects
such as non-New-
tonian
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 veloc-
ity
gradient
ofthe fluid
particles
are
linearly related. For
a
Bingham
plastic,
n in Equation 1-7
is
l-4x13*xal3
1-xa
where x
:
ratio of
the
fluid particle yield
stress
to the shear
stress
in
the
fluid
particles
at the tube wall
Lab tests reveal that x
:
0.5 and
1
:
3.9 for
which
.
4
.^
-.
(0.5r
I
-
-
(U.))
+
-:--------
n=
1
:=
=:;
"
=
O.378
l
-
(u.)f
Now,
€r
th
(0.584)0
r78(0.059)?-"
-1
(89.232)
+
N.-
=
sec n"
:
0.092
'*
8.0
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.
1,ooo,ooo
9
hr
:
2l,309.196
lb^/hr
rO 16Rr
-i:L
r
l t? {t)\oF
---'''lh
-oF
--
'---'
'
/\
th I thf I
21.309.196
"'
l
' '"
I
^
hr
\3600
sec/
^
^,,
tt3
i
u.uob
_
lh
sec
co,'tt'"m
It,
We
will
try
594-3lq-in.
tubes-14
BWG.
tube wall thickness
for internal
pressure,
PD)
t-,":
o"11E
-
0.6P
where
o1
:
maximum
allowable
stress
for tube material, psi
E
:
tube weld
joint
efficiency
:
l.g
P
:
internal pressure,
psig
ID
:
tube
ID,
in.
(
150)(0.584)
t-,"
=
:0.005
in.
"-
(17.s00x1.0)
-
0.6(
150)
t""r4
:
0.083 in.
Flow
velocity
through each
tube is
fi3
0.066
i-
v
=
--
-
=j L
:
0.059 frlsec
(0.0019)ft'z(594)tubes
Checking
the
150 psig
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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
N".:
f
(2251.20\
lb'
,0.368'
Btu
ft-hr
lb--"F
(o.lo)
Btu
'
-
hr-ft-"F
Np,
=
8284.416
For laminar flow,
the Sieder-Tate correlation
is
N",
=
T:
,
eo
[6*.16.,;[n)]'' kl''
N",
:
r.86
[,o.or,,rrro.o,u,
ffi]"',t.,
o
lt-
c
.9
.9
u-
hrD
=
k
2.r85
Meizner Reed
Reynolds Number' Re"*
Figurc 7-42. Friction factors for
flow
of non-Newtonian
flu-
ids
[22].
For our velocity
heads we use the
entrance
and
exit
loses
and
get
f
:
O.ZS
+
1.00
:
1.78
(see
Figure l-1
l)
Using Equation
1-4
we compute
the
pressure
drop over
a
Shell-Side
Film
Coef
ticient
q
:
rirCp(LMTD)
For the
hot
oil
at 600"F the following
properties
exist:
Ce
:
0.526
Btu/lb--'F;
p:
(O.997)(O.a)
:
62.213
tb^/tt'
Rr,r
(-
j6)
){{l
ll
-
hr-ft-'F
"L_,|
10.5841
^
\
12
/
Btu
'-''
hr-ft2-'F
2O-ftJong
tube as
op,
:
ILL
*
r* )qr
\d
-
lze,
(t
-4)
ae,
:
p g(zo{l?I'*
*
r.zr
]
(8e.82)k(o.o5eFg(,-iI--J
2(32.2)
It-lD;T
aP,
=
2.47gpsi
:
Acceptable
sec'-rDl
Looking
at
this
pressure
drop one realizes that a flow
velocity
of 0.059 ft/sec is not
so slow for
a
bulky
fluid
m
:
0.076
Btu/hr-ft-'F;
p
:
0.30
cp
:
0.720
lb.ift-hr
_/-\
t.000.000
l'tu
I
t
nr
I
hr
\J.600
sec/
,
...
lb-
Rf
{0.526)
"'-
1127.522\'F
tb.-'F
th
4.141
:
sec
^ ^.-
ftt
:
U.UD/
-
h
Sec
62.213
+
tt'
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,,.,
-
ACp
rrpr
_
k
164
Mechanical Design
of
Process
Systems
The smallest
nozzle
shell-side is
a
3-in. nozzle, making
the maximum shell-side velocit)
fr3
0.067
i:
sec
'
-
boslF
:
1.305 ftlsec
-
Very reasonable
h-
=
155.959
Btu
"
hr-fta'F
Fouling factors
are as
follows:
Asphalt coating
mix
:
0.01
Hot
oil
:
0.004
1
rl
_
+
0.004
+
0.01 +
155.959
4.695
Elr,r
"
-"
hr-ft2-'F
1,000,000
nr
Area required
:
Tlr,r
(4.284)
-'.-
-
i27.s22f
F
nr-rt'-
-|:]
:
1,830.308
ft'?
Available area
:
(0.1963)
i
(zo)
rt
694)
:
2,332.94^
tt
It
Twenty-seven
percent
of the
excess
area
can
be elimi-
nated
by
reducing the
number
of
tubes.
This
would in-
crease
the
flow
rate
in
each
tube
and
thus the
pressure
drop,
which
already
is
at
2.5
psi.
For
non-Newtonian
fluids,
properties
can vary from
sample
to
sample and
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 heat-
ing
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.
(0.720)
lb'
ro.526r
Btu
ft-hr lh
-oF
(o.o76t
Btu
'
'hr-ft-'F
Fora60'Aarrangement,
n
810.43
p']-
0.5rdl/41
810.4311.00)
-
0.5rrl.0r/41
r4
-
"(0
?t
D"
=
0.127 or De
:
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
D.(c)B
(27.00X0.25X
15.0)
^
-^^
"
,
"
144p
(1.00)(144)
.
4.t41jl
t3,600r
l
^msechr
<=-:
as 0.703 fl
th
=
21.201
.920
:'*L
nr-n'
*,
_
D.G,
_
1\Rc---
p
(0.011)
fr
(2t,201.9201
5
nr-It"
lh
' '
ft-hr
From Figure'1-21
jH:
12
for
baffles
with
15%
cut
=
323.918
/ \o
rq
n"
=
lo4rNr,f
':[aJ
From
laboratory
tests it
2.0.
(
l2)(0.076)
Btu- ft
hr-ftr-'F
was
determined
thar
plp*
=
Shell-Side
Pressure
Drop
^.
_
tGiD,{NB
+ l)
(slt(t0t6.1d
Ns
=
16
baffles
D.
=
shell ID
:
27 in.
:
2.25 ft
G,
=
21,201.92
lb./hr-ft2
Nr"
=
324 and
from Figure 7-24, f
=
O.0O75
0.011)
ft
(4.983)'/r(2.0)o
r4
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For
plain
and bare tubes,
f o
nn75
F_'-"'"--nnn<t<
'
t.2 1.2
D"
=
0.011
ft
"y
:
specific
gravity
:
0.997
The Mechanical Design
of
Shell-and-Tube Heat Exchangers
165
:
L(t)
:
0
when
t
:
a,
and
if
the ratio of dT(t)/dt
to
dl(t)/dt
exists, then
T(t):(200-0-(140-60)
dT(t)
-:
_l
dt
L{r,
=
ln l2oo
-
t\
\80/
dl(r)
/
ao
\/-r\
dr
\200
-
ri
\80i
200-t
1
I'Hospital's
rule states that
,.
T(t.)
..
dT(r)/dt
1.'t
L(t)
i-=
d
dl(r)/dr
or,
witha
:
120'R
Now
using
Equation 3-23 we have
to-Ro
o
LMTD:
. /so\
o
lnt 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
r1
|
-1
|
liml
l=
lim
(200
-
t)
80"F
r.al
_I
I
t-uu
troo -
tl
Therefore, LMTD
:
80'F
With this value
of
LMTD,
the exchanger can be de-
signed,
using the correction
factor
in the case
of
a coun-
terflow
unit.
NOTATION
A
:
tube surface
area, ft2
At
:
cross-sectional
area of tube, in.2
a
=
constant
for
a continuous beam shear,
dimen-
sionless
b
:
constant
for
a continuous
beam
deflection
c
=
tube
clearance,
in.
c
:
constant,
in.2/lb1
(Equation
7-37)
C
:
constant
:9.7
x
10
a(sec)05/(ft)'5
(Equa-
tion
741)
g"
=
12fE
t
or)o
5
(Equation
7-2)
Cp
:
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.
Tube-side
Shell-side
1141P
:
T(t)
:
Lt)
200'F
in
120'F
out
at:
80'F
(200-0-(140-60)
.
1200
-
rl
ln l-l
\80/
140"F out
60'F
in
At
=
80'F
As temperature t approaches a certain
value
such
that
T(t)
and
L(t)
become zero being
divided
by
zero.
The de-
rivatives 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)
/
\o
t+
d:
1.0:
(E
(0.0062s)(2
r,20 l. 9D,
Q.2s)
(r7
)
(s.22)(10)'0(0.01
1)(0.997)(1.0)
:
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
confectionar-
ies. 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.
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166
Mechanical
Design
of
Process
Systems
do
:
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 im-
mersed body,
lbg
F,
:
shear force
against
tube
at baffle, lbr
; I
constants
used in
determining
tubejoint force,
i'
I
lbs
(Equations
7-3
and
7-4)
f"
1
fundamental
natural
frequency
of tube, Hz
gc
:
gravitational
constant
:
32.2
lb.-ftilbr-sec,
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
tube
surfaces
temperature,
Btu/hr-ftl'F
I
:
moment
of inertia,
in
a
Ir
:
moment
of inertia
of
tube cross
section, in.a
k
:
structural
constant,
dimensionless
(Equation
7-2)
k
:
equivalent
effective
unsupported length
of the
tube,
in.
k*
:
coefficient
of thermal
conductivity
of tube
wall, Btu/hr-ft-'F
kr
=
thermal conductivity
of
fluid, Btu
kn
:
thermal
conductivity
of
foreign deposits in-
side 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
(Equa-
tion
7-39)
Np,
:
Nusselt number,
dimensionless
Np.
:
Prandd
number,
dimensionless
Nr"
:
Reynolds number,
dimensionless
P
:
axial force,
lbl
p
:
tube
pitch,
in.
q
:
rate
of heat transfer,
Btu/hr
r
=
radius of
gyration
of tube,
in.
(Equation
7-2)
T
:
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 ex-
changer,
Btu/hr-ft2-'F
U,
:
the value
of
the overall heat
transfer
coeffi-
cient
at the caloric
temperature. Btu/hr-ft2-.F
V
:
flow
velocity,
ft/sec
Greek
Terms
ct
:
factor of effective
tube resistant
area,
dimension-
less
6
:
deflection
or displacements,
in.
p
:
dynamic viscosity
of
the fluid inside
tube,
lb./ft-
hr
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
(Equa-
tions 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,
Houston. Texas.
1975.
2.
Snndnrds
of
the Tubular
Exchanger Manufacturers
Association
(TEMA),
6th Edition,
Thrrytown, New
York,
1978.
3.
Rubin.
F. L.
.
"What's
the
Difference
Between
TEMA
Exchanger
Classes," Hydrocarbon Process-
ing, 59,
June
p.
92,
1980.
4. Ludwig, E . E., Applied Process
Design
for
Chemi-
cal
and
Petrochemical
Plants, Volume
3.
Second
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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
Engineers, New York.
8.
Colburn,
A. P., Ind. Eng. Ch.em.,35,
pp.873-877,
1933.
9.
Kern, Donald
Q.,
Process
Heat
Tlansfer,
McGraw-
Hill
Book
Company,
New York,
1950.
10. McAdams, W. H., Heat hansmission, Third
Edi-
tion, McGraw-Hill
Book
Company,
New
York,
1954.
ll.
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.
The Mechanical Design of Shell-and-Thbe Heat Exchangers 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 ofElas-
tr:ciry, Second
Edition,
Engineering
Societies
Mono-
graph,
McGraw-Hill
Book
Company, 1951.
17.
Coit, R. L.,
C.
C. Reak, and
A.
Iohmeier,
"De-
sign and Manufacturc
of
Large
Surface Condens-
ers-Problems
and Solutions,"
American
Fower
Conference, April
1965.
18. Blevins, R.
D., Flow-htduced
Wration,
Van Nos-
trand
Rheinhold Company,
New
York,
1977.
19. lbmbsganss,
M.
W.,
and S.
S.
Chen,
"Tbntative
Design Guide for
Calculating
the Vibration Re-
sponse
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.
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External
Loadings on
Shell
Structures
In a book about the mechanical design of
process
sys-
tems it is impossible to ignore the
phenomenon
of exter-
nal
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 de-
sign of
piping
supports in
Chapter 2.
Vessels
require a
simiJ.ar analysis, but the
phenomenon
is
different be-
cause
in
a vessel
the
loadings are more
localized.
partic-
ularly in
a
large vessel.
In
the case
of external
loadings
on vessel nozzles one must consider
primary
stresses in-
duced
by
internal
pressure
and
secondarv
stresses
in-
duced
by
the
external loadings.
In
the design
of
the lift-
ing lugs only secondary
stresses need
to be considered,
since vessels
being
lifted almost never have internal
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 cylin-
drical
shells. Neither
WRC
107 nor
WRC
297 are
con-
sidered 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 Bul-
letin
when
the
ratio
of the dianeter
of
the branch to the
diameter of
the
header
is
between 0.5
and
1.0.
exoressed
mathematically
as
0.5 <
db/DH
<
1.0
=
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
pres-
sure. 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
so-
lution is impractical. Discontinuity
stresses
at the
nozzle-
shell
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 us-
ing the following expression for
internal
pressure
stress:
(8-1)
:
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
as-
sume
that
such
pads
remove
discontinuity
stresses at the
nozzle-shell
juncture.
While
this is true, one must real-
ize 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 mem-
brane
stresses
occurring
at the nozzle-shell
juncture
(as-
suming the circumferential bending
stresses
are negligi-
ble compared
with
the membrane
stresses).
As
Figure
8-1b shows
that as the reinforcement thickness increases,
where
db
DH
P(ID)k"
"n
2t
where P
ID
I
kP
169
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c
170
Mechanical
Design of
Process
Systems
M-'x'i€m5'mm'n'|ll
ll
I
--------|-
B
w> 1.6s(arf.
ll
r5
l
HI
_-____1---r
R-r
I
I
i
II
tN_
and
finite element
studies.
--'_;J
Figure 8-1. simple
schematic
of maximum
combined
stress
disribution,
as
supported
by field
tests
F----'1 |
ti
tl
r
ryrcJ
r,
I
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
rein-
forcement
edge-shell
juncture
point,
shown
in Figure
8-
lc. Considering
this it
would intuitively
appear
that
a ta-
pered
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 stud-
ies,
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
trans-
ier
the
maximum
loading to
the
pad
edge
as shown
in
Figure
8-1c,
resulting
in
crack
propagation or
even
rup-
tuie.
Caution
should
be taken
in working
with thin-
walled
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
if
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
setting
the
equipment
in one operation
without
readjust-
ing oi
re-rigging
the
crane or
other
equipment'
and
pro-
teit
equipment
and
personnel. The lugs
must
not inter-
fere
with
vessel components,
such
as
platforms, ladders,
or
piping.
Thi
advantage
to lifting
lug design
is that
only
second-
ary 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.
Consequently,
the
AISC
Manual
of Steel
Constructi.on
[4]
can
be used
in
which
the
factor of
safety
is
2:
I
(unlike
ASME's
4:l).
The
vessel
is
to
be considered
as
a simply
supported
horizontal
beam.
All
non-shell
components,
head,
lad-
ders,
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 fol-
lowing
examples.
EXAMPLE
8-1:
LIFTING
LUG
DESIGN
At{D
LOCATION
A 96-in.
ID
shell
and tube
heat exchanger
is
to be
lifted
from
a dock
onto an
offshore
structure'
The
ex-
changer
weighs
158,750
lbs,
which
is the total
erection
weight.
The
objective
is
to locate
and design
the lifting
lugs,
and
determine
the
minimum
chocker
length
and
maximum
chocker
angle.
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172
Mechadcal
Design
of
Process Systems
1
T
A
norizontal
lili
"1" or
"W"
beam
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)
+
(346x44.000)
+
(2,283)(40.7
s)
+
(346)(2.542)
-
(2,094)(46.7
5)
+
(1s1,587)(23.27
r)
Rr
:
75,888.874 lb
and
Rr.
:
75,698'
126
lb
For
lug supporting
the
fulI
vessel weighing
158,750
lb,
referring
to Table 8-1
we write
t
t
+
.l
J\
U
Figure 8-3. Lifting
lug and erecting
procedure
(moments
in-
duced
by
lift
load at choker angle d can
be avoided
with a
spreader bar
or with the
lug
design
in Figure
8-28.
A
=
16.50in.,B
:
6.50in.,
C
:
4.50in.,
D
:
4in.,
E
:
6.50 in.
Hole
diameter
:
a
=
(4.50
+ 0.125)
:
4.625 in.
:
mmlmum
Lug width
:
Wr
:
3a
:
3(4.50)
:
13.50 in.
:
minimum
Lug
Thickness,
t1
wL
_
13.50
88
=
1.688 in.
r/
use 1.75
in.
w
_
158,750
1.6ao,
(1.6X4.625X38,000)
=
0.565
in.
+
tL
:
Larger
of
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174
Mechanical
Design
of
Process Systems
Table 8-1
Anchor Shackles
For lug
material
SA-516-GR
7O,
o,
=
38,000
psi
Lug
Height
(assume
2
in.
fireProofing)
"
:
|
*
(?.,)['
-
(".
;'
;f
-
")']"
lug
height,
in.
insulation
thickness
shell
outside
radius,
in.
(a)
screw
Pin
n
tl
ll
/\
f-et
r
D'
(b)
round
Pin
n
tl
|l
1"b
lvt
t+l
where,
H:
R":
t:?
*({*
\2
,\
-)
"["-(
50.0
+
50
JO
6.
n
1.75
50-00
-
4.00
I'
Pin Dia.
THWP,
(in.)
(in.)
(in.)
(in.)
(in.) Load-|9
rh
trys
rlz
shd
tllrc
.79-9-
q*
lttn
71rc
ls
r3/rc
1'100
,1"
Itl,
5/s
llrc
|
1,675
,l*
lrl^
3/c
rlz
lrlrc
2,200
,1, lrl, r'lrc 5/a Lslrc
2,900
tl"
2rltu
ltlrc
3lc
le/rc
4,500
t1o
ZIz
lh
1ls
|1ha
6,400
,t"
Yt^
171rc |
2tla
8,700
1
33lq
111/to
1Vs
23lg
1I
'4OO
-/"
4r1o
tt3lrc
ltlc
25lL
___J3_5W
1tl4
43h
Ztlta
13/e
3
16'500
rr-r"
stlo
2tls
lvz
351rc
2 ,59q
lrlz
53lq
2tlq
lslt
35la
u,w
1t/"
1
27lt
2
451rc
33,600
2
7rl"
3tlc
211+
5
44,800
zrh
-9V^
3?'1"
2tlz
5Vq
56,000
it, - tou qu" 23lq 6
67
'2w
i1o
tluz
4lz
3
6t/+
81,ooo
6tlz
100,800
33/q
63/q
125,000
3t/z
15Vz
t
50,000
16l lz
41lt
r79,200
lTtlz
6tlz
7)lz
200,000
4118
181/z
43/q
224,N0
313,600
r,
)
*.
where R
=
greater
of
RR or
R; for
horizonal
or
w'
vessel
R
:
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
13
D
Safe
Lilting
H
:
19.690
in.
Check
lug thickness
Minimum
Weld
Size
R[0.47
+
0.45(h/w)]
re(wr)(0.707)
r*
=
0.426
in.
minimum
Actual
weld
size
:
t*u
where
ra
:
allowable
shear
stress
in
weld
:
0 3q*
o,*
:
weld
minimum
yield
stress/
in
tension
I rr2jry\l
(7s888.874)
[o
ot
.
o.ot
\ir.roo1
15
tl+
6tlq
(0.30)(70,000)(13.50)(0.707)
4tlz
5t/z
21
6tt/rc
5tlz
73lc
448,000
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f
t,
-
t/ro
in.
r*a
:
Larger
ot
I
,,
_
,t,u
in.
and twr
>
h
where
t, =
vessel
thickness, in.
In this
case, tL
>
tv, so
that
t*"
=
1.75
in.
-
0.0625
=
1.688
For
each side of weld
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
A,B,C,D,E
:
Ds:
du:
H:
Kp:
L.:
Ml=
Mr:
External
Loadings on Shell
Structures 175
NOTATIOil
constants
(Figure
8-6)
header
diameter, in.
branch diameter,
in.
constant
(Thble
8-l)
internal
pressure
stress
concentration
factor,
dimensionless
minimum chocker
length,
ft
moment
resolved about
the left end
(Figure
84),
ft-lb
moment resolved
about
the
right
end
(Figure
8-4), ft-lb
U:
"r*rI
(38,000x13.50)(1.75F
R"
,
50.00
t"
:
12
rin
(4.90t
=
'+6'/rl
n
Because of height
restrictions,
the lug had
to be low-
ered
from
19.690 in.
to 11.00 in. Thus,
we now have
the
following:
" I
(38.ooox
l3.soxl.7sy
I
.:qrt.grt-l
lrrtst.zso.ooy
{rt.oo
* ro.so
*
4ll
t
\
zll
0
:
6.327'
and
LC:
A
=
16t/z in.,
B
=
61/z
in.,
C
=
4 z in., D
=
4
in..
E
=
6t/z in.
Figure
&6.
Detail of
choker and shackle.
3(1,58750.00)
(rn.uno
* r6.s0
+
4t0)
0:4.905"
I.:
:
minimum choker
lensth
12 sin
d
=
37.807
ft
12
sin
(6.327)
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176
Mechanical
Design
of
Process
Systems
:
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,*
:
minimum
weld
yield
stress
in
tension,
psl
7A
:
allowable
shear stress
in
weld,
psi
0
=
chocker angle,
degrees
REFERENCES
Welding
Research Council,
Welding Research
Coun-
cil Bulletin
WRC 107 bcal Stresses
in
Spherical
and
Cylindical
Shells Due to External
Inadings,
Match,
New
York,
1979.
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.
Forman.
B. Fred.
Incal Stresses
in
Pressure
Vessels,
Second
Edition,
Pressure
Vessel
Handbook
Publish-
ing,
Inc.
Tirlsa,
OK., 1979.
American
Institute
of
Steel
Construction,
Manual
of
Steel
Constructior,
Eighth
Edition,
AISC,
Chicago,
Illinois,
1980.
P
RL
R"
RR
t
t1
t*
wL
z.
t.
J.
A
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178 Mechanical
Design
of
Process
Systems
(a)
Figure
A-2. Partial volume
of
vertical
hemispherical
head.
(B)
Partial
volume
of
horizonral hemispherical
head.
PARTIAL
VOLUMES
OF SPHERICALLY
DISHED
HEADS
Horizontal
Head
The
partial
volume
of a horizontal
head
(Figure
A-3) is
Example-Spherically
Dished
Horizontal
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
:
16.786 in.
(Figure
A-5),
p
:
108 in.
l14
-
)/t o\
R:
"
-
.'"'=
56.0in.
'2
e:
159.43"
:
2.78
L
:
108
-
16.786
:
91.21 in.
-_T---T
-+l
i
ln'
tv
I
tl
tf
Figure
A-3. Partial volume
of
spherically
dished
horizontal
neaos.
Vertical Head
The
partial
volume
of
a
vertical
head
(Figure
.,
nv(3x2
+
vr)
v='
-
6
ot
..
nv2(3o
v)
y:
-
.
3
atl
P"l
x
v----i-
-v----T
\:-7lTv
llDD
-<--E--------i-:--r
I
Figure A-4.
Partial volume
of
spherically
dished vertical
heads.
(A-3)
A-4) is
(A-4)
--
J___
--.-{,>--
_
(A-5)
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Appendix A: Pressure
ry'essel
Formulations
179
Yr =
6.786"
Flgure
4"5.
_
(9t.2r)(562
-
6.7862)
V
:
38,893.21 in.3
=
168.37
gal
Example-
Spherically
Dlshed
Vertical
Head
For the
same head
above, determine
the
partial
volume
of
a head
of liquid
of 9 in.
x
:
55.456 in.
u
-
zr(9)[3(55
416)'? +
9'z]
=
A.874
in.t
=
64.4
gal
6
"'
PARTIAL
VOLUIIES
OF
ELLIPTICAL
HEADS
The exact
partial
volume
of
a
horizontal
elliptical
head
lV(r08,
--i86at
-
v?ro8r
-
5-dF
.,-
IJ
(Figure
A-6)
is
as
follows:
..
(IDD)q
Venical
Elliptical
Heads
Volume
of top
portion
@
of
Figure
A-7 is
-a
v,.'
=
'Ri'
l"
-
Y'
I
'"
2
l'
3(rDDFl
Volume
of
bottom
portion
O
is
. ,
2r(IDD)R,2
rRl I
u3
I
-
"-----:
lw
2
(
3(rDDll
t\
Itr
t\
t\
l
ti
;;=*--:-__T,
_-
(A-6)
(A-7)
End
View of Horizontal
Head
Figure A-6. Partial volume
of horizontal elliptical
head.
Figure 47,
Partial volume
of
vertical
ellipticat
head.
(A-8)
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180
Mechanical
Design
of Process
Systems
Horizontal
Head
Example
Find
the
partial
volume
of a 2:
I
(R;/IDD
=
2)
ellipti-
cal
head
that is 108-in.
OD. The
level
of
the liquid is 35
in.,
and
the
head
is
spun
from
l-in.
plate.
IOR
-
?rl
O\
IDD
--
'"-______:rr:',
=
26.50 in.
From
Equation
,4-6
and
Figure A-8
we
have
the
follow-
lng:
y
=
(IDDI
a
vm7
--tl'-
6R,
a
=
138.80"
=2.42
v
_
(
19.0)(2.42t
463r-
*
{Iqy-rr
6(53)
V
:
17,512.94 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:
.,
_
2a'(IDD)R1'?
o
A
vertical head
KR
IDD
-x
B
horizontal
head
c
vertical
knuckle
region
H=IDD-KR
D
horizontal
knuckle
region
Figure A-9. Partial volumes
of torispherical heads:
(A)
verti-
cal,
(B)
horizontal,
(C)
vertical
knuckle region,
(D)
horizontal
knuckle resion.
v
_
2?r(26.s0x53.01
_
1(5i.0)
[,o
n
_
trq.or,
]
6
2
t--"
3(26.s0),.j
V
=
77,951.81 in.3
-
13i0.75 in.3
Y
:76,641.06
in.3
:
331.78 gal
Figure
A-8.
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PARTIAL
VOLUIIES
OF
TORISPHERICAL
HEADS
For Figures A-9
and
A-10,
Vk
:
knuckle
volume
y
:
height of liquid
Vo
:
dish
volume
IDD
:
inside depth
of
dish
KR
=
knuckle
radius
p
=
inside
dish
radius
For vertical
heads
(Figure
A-9c) the knuckle-cylinder
Dartial volume
is
Appendix A: Pressure Vessel Formulations
Figure
A-1o.
end view
of dish
volume
Flgure
A-11, Sketch for example
partial
volume calculation
of horizontal torisoherical
head.
Flgure
A-12.
The
partial
volume
ofthe dish region of
a
vertical head
is
v*:
?rtJ
+
4ry2
+
r,2;
uo
=
"[#
+
Ri-
KR)
+
(R,-
KRr]
., -
?ry(3x2
+
y2)
vD_-6-
The
total
partial
volume in
a
verticil
head is
,,
nH
,.
.
Ty(3x2
+
y2l
vu
:
-6-
(ro'
+ 4rM' + ri') +
-----6-------:-
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,)
|
,o_,r.,
JZ
Volume of Knuck-Cylinder Region
@
(Figure
A-12)
(A-e)
(A-
l0)
(A-ll)
(A-13)
The total
partial
volume
for
a horizontal
torispherical
head
is
as
follows:
V1
:
V6+
V6
.
"lry
+
Ri-
KR)
+
(&
-
KR),]
wherel:
p
_
IDD
-
.vG,
-
R-iT
L(Rr2
-
yi2)
(A-14)
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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.
deter-
mine the
partial
volume.
From
the vessel
head
manufacturer's
catalog
and Fig-
ure
A-12
we
determine
the
following:
p
:
96
in.,
KR
:
6.125
in.,
IDD
:
17.562
in.
ltut
R,
=
:
=
50in..
L
=
96.0
-
17.562
=
78.438 in.
z
From Equation
A-14
we
have
vr
:
Q.532)
,4%t_
1s+
_\@6r:50it
_
(78.438X50'
-
ls)
r
r-
/,''
<1r,
14(6.125)
|
[
J?r'
+
(5o.oo
-
6.12s) +
(s0.00
-
6.l25fl
'J
Vr
=
34.093.44 in.r
=
147.59
ga.
Vertical
Head
Example
A
138-in.
d
OD
F&D
(flanged
and
dished)
head
nor
made
to ASME
specifications
is
spun from
I
l/z-in.
plate.
The
head
is
vertical
and
the liquid
level
is 18-in.
Deter-
mine
the
partial
volume.
From
the vessel
head
manufacturer's
catalog we
deter-
mine
the following:
p
:
132
in.,
KR
:
3 in., IDD
:
20.283 in.
l?R
-
trl 5l
R,
=
'-"
=-"'-'
=
67.50
in.;
2
x
:
67 .50
-
(3f
-
H2lo
5
=
66.446
in.
For
knuckle-cylinder
region,
ro:
Ri
=
67.50; 11
=
Ri
-
KR:67.50
-
3.00:64.50
in.
67.50
+
@.50
r.=
,-
=
ob.u;
h
:
120.283
-
(3.0
+ 15.0)l
:
2.283
in.
+() 19,4\
Yv
=
"
-;-"-'l(67.501
+ 4(66.0),
+
(64.5011
b
*
r(I'1
.283)[3(64.500)'?
+
(17.283)2]
6
vv:31,247.726
in.3 +
115,645.832
in.3
Vv
:
146,893.558
in.3
:
635.903 gal
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I
INTERNAL PRESSURE
ASME
FORMULATIONS
WITH OUTSIDE DIMENSIOI{S
Cylindrical
Shelt
Longitudinal
Joint
Appendix
A:
Pressure
Vessel
Formulations
183
-
oEt
R
-
0.4t
Circumterential
Joint
.PR
oE +
O.4P
r=
PRo
2oE
+
'1.4P
^
2oEt
Ro
-
1.4r
2:1
Ellipsoidal
Head
r=
PDo
2oE
+ 1.8P
^
2oEt
Do
-
1.8t
-
2oEt
R.
-
0.8r
-2rE+0,8P
s
=
0'885P1
oE
+ 0.8P
Sphere and Hemispherical Head
ASME Flanged
and Dished
Head
when UR
=
164s
r
=-
0.885L
-
0.8t
When UB
<
16ry3
t=
PLM
2oE+P(M-0.2)
r=
PDo
-
2 cos o(oE
+ 0.4P)
Section
^
2SEt
cos d
^
2oEt
ML-(M-0.2)
Do
-
0.8t
cos
o
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184
Mechanical
Design
of
Process
Systems
FOR VALUES
OF
M
SEE
SUPPLEMENT
INTERNAL
PRESSURE
ASME
FORMULATIONS
WITH
INSIDE
DIilENSIONS
1-\
i-
-----T;-'-
,-il
/l\
{,;ft
<=]li
}<T-t"._
PRi
'-rE-O.6P
t=
PRi
2oE
+
O.4P
oc-v.tr
pt
tu
Cylindrical Shell
Longitudinal Joint
Circumferential Joinl
2i'l Ellipsoidal
Head
Ri
+
0.6t
^
2oEt
Ri
-
0.4t
^
2oEl
Oi
+ 0.2t
-
2oEt
R +
0.21
P=
oEt
0.885L
+ 0.1t
<
164s
2^tr1
LM + 0.2t
Sphere and Hemispherical
Head
ASME Flanged
and Dished
Head
when
UR
=
1 6?3
I
Ft
-./L-
\
#+\
\-__=-2,
F---
q--l
F.-t
When
UR
Conical Section
PDr
p
=
2oEt
cos
o
Di
+ l.2l
cos
d
cos
d(oE
-
0.6P)
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Appendix
A:
Pressure
Vessel Formulations
Supptement
for
ASME
Formulations
185
'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
effi-
ciencv
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).
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
4.
1-5(e).
5. Foian
ASME
flangsd
and dished
haad
(torispherical
head)
when
Ur<
164r the
tollowing
values
ot
M
shall
be used:
'
The maximum allowed
ratio:
M=
1
L-r
=
D
When
L/r
>
162/3
(non-ASME Code
construction), the
values
ot
M may be
calculated by
'('.
Values
ot
Factor
M
Ul
M
Ur
M
1.00
1.00
7.00
1.41
1.25
1.03
7.50
1.44
1.50
'1.06
8.00
1.46
1.75
1.08
8.50
1.48
2.00
'1.10
9.@
1.50
2.25
1.13
9.s0
1.52
2.50
1
.15
10.0
1.54
2.75
1.17
10.5
1.56
3.00
1.18
'|
1.0
1.58
3.25
1.20
11.5
1.60
3.50
1.22
12.O
1.62
4.00
1.25
r3.0
'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
1.36
16?s
1.77
6.50
1.39
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A
standard is a
collection
of current
practices, past
ex-
periences,
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 ma-
terials.
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
devel-
oped
to
represent the
needs
and interests
of their
respec-
tive areas and are written
in legal language
to
be
incor-
porated
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
na-
tional in
perspective.
For
this
reason,
one must be cer-
tain
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
de-
sign. 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
para-
graph
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
stan-
dard. What
all
this
implies
is that
one may follow
the
guide
of
the ANSI
standard's appendix
or use
another ra-
tional
analysis,
which includes
another
wind
standard.
Thus, one
care
use another
standard
for design
purposes.
Appendix B
National Wnd Design
Standards
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
fac-
tors 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 dif-
ferent
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 rough-
ness,
which
reduces its
velocity
and changes
its direction
and
turbulence. A
secondary
criterion,
except
for
ex-
treme
wind
conditions,
is
the
temperature
gradient,
which
affects the vertical
mobility
of
turbulent
eddies
and therefore influences
the surface velocitv
and
the era-
dient 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
147
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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"
:
annual probability
of
exceedance
(reciprocal
of
the
mean
recurrence
interval)
n
:
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 De-
riod
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
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
mile
wind
speed
is
I I
54t
"
:
tffil
(100y
rnp6
=
118.4
mph
for
a 2-sec
gust.
For
I l0 mph,
the
values
becomes
V:
(l.l8x1l0)
mph
=
129.8mph
Table
B-1
Probability
of
Exceeding
Wind
Design
Speed
Pr
=
1-(1
-
PJ"
PA
0.
l0
0.05
0.01
0.00s
r
5
l0
0.100
0.410
0.651
0.0s0
0.226
0.401
0.010
0.049
0.096
0.005
0.025
0.049
15
25
50
0.794
0.928
0.995
0.537
0.723
0.923
0.140
0.222
0.395
0.072
0.rr8
0.222
100
0.999
0.994
o.634
o.394
Figure
B-1.
Cup generator
anemometer
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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
Edition
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
Standard
Building
Code
Basic
Building
Code
Standards
Association
of
Australia
British
Standards
Institution
Building
Research
Establishment
National
Research
Council
of
Canada
National
Research
Council
of
Canada
American
National
Standards
Institute
International
Conference
of Building
Officials
Southern Building
Code
Congress
International
Building
Officials
and
Code
Administrators
International,
Inc.
Address
Standards
House
80 Arthur
Street/North
Sydnev.
N.S.W.
Australia
British
Standards
Institution
2 Park
Street
London,
WlA
285,
England
Building
Research
Station
Carston,
Watford,
WD2
7JR,
England
National
Research
Council
of
Canada
Ottawa,
Ontario
KIA
OR6
Canada
1430
Broadway
New
York,
New York
10018
5360
South Workman
Mill Road
Whittier,
California
9060
I
900 Montclair
Road
Birmingham,
Alabama
35213
17926
South
Halsted
Street
Homewood,
Illinois
60430
1983
t972
1974
1980
1980
t982
1982
1982
with
1983
rev.
1984
Table
B-3
Reference
Wind
Speed
Australian
British
Canadian
United
States
Beletence
Averaging
time
1
1
2-3
second
gust
speed
I18.4
2-second
gust
speed
1
18.4
Mean
hourly
76.9
1
Fastest
mile
100
I
Equivalent
reference
wind
speed
to fastest
mile
100 mph
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Appendix B: National Wind
Design
Standards
Table
B-4
Parameters
Used
in the Maior National Standards
191
Parametel
Australian
Brltlsh
(sAA,
1983)
(BSr,
re72)
Canadian
(NRCC,
1980)
Unlted States
(ANS|,
1982)
Wind
Speed
Terrain
roughness
Local terrain
Height variation
Ref.
speed
Wind Pressure
Pressue coefficients
Gusts
Magnitude
Spatial correlation
Gust frequency
Analysis
procedure
2-sec
gusts
tbles in
appendix includes
figures
Gust speed
Reduction
for
large
area
Dynamic consideration
for
h/b
>
5
This
standard is consid-
ered
by many
the
best
for
us€
in
the
process
industries. Figures
and
tables
are easy to
read.
The
standard actually
provides
the user with
equatrons to curves.
The
analysis
procedure
is straight-forward.
z-sec
gusts
Tables, includes
figures
Gust
speed
None
Dynamic
consideration
not
included
Overall
a very
good
code,
its weakest
part
is the
lack of
dynamic
consideration.
3
None
Yes
Mean
hourly
Figures and
tables
in
commentaries
Gust effect factor
Gust effect factor
Dynamic
consideration
for h/b
>
4
in. or for
h>400ft
An excellent wind
standard. The
analysis
procedure
is
straight-forward
and the
docu-
ments-code
and
supplement con-
tain tables and
fig-
ures easy
to
read,
None
Yes
Fastest
mile
Tables,
figures
and
notes
Gust
response
factor
Area
averaging
Dynamic
consideration
for
h/b
>
5
Although
the appendix
is technically
not con-
sidered a
part
of
the
standard, it
contains
figures difhcult to read,
namely
Figure
6.
For
many structures the
data extend beyond the
limis of
the curves
in
Figures
6 and 7. In the
method
in the appendix,
one
must
assume
an
ini-
tial natural frequency,
resulting
in
an
iterative
process.
This
method is
extremely
difficult
in
designing
petrochemical
towers
without the
use
of
a computer.
4
Yes
Yes
Yes
Yes
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192
Mechanical
Design
of
Process
Systems
Table
B-5
Limitations
of Codes
and
Standards
Code
or
Standard
statement
ot Limitation
Location
Australian
Standard
I170,
Part
2
1983
National
Buildinq
Code
of Canada
-
(NRCC,
r980)
British
CP3
"Minimum
Design
Loads
on Structures"
"...EssentiallyaSer
of Minimum
Regulations
.
.
."
".
. .
Does Nor
Apply
to
Buildings.
.
. Thdt'Are
of
Unusual
Shape
or Location
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
minimumstandards.._"
"The
Basic
Minimum
Wind
Speeds
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 Design-
of
Structures
Not Includedln
This
Section."
United
States
ANSI
A58.I
Uniform
Building
Code
Basic
Building
Code
(BOCA,
1984)
Standard
Building
Code,
1982
(SBCCI,
t982)
Title
Guide
to the
Use
of the
Code
Section
I
(Scope)
TitIE
Paragraph
6.1
Section
102
Section
912.1
Preface
Article
1205.2(a)
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194
Mechanical
Design
of
process
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dreo
of Estcrl
(Equa.e
nocles)
d
=
inside
dida€ter
(iach€6)
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didnete
(bchos)
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=
lodiu
ol
gFotior
(irches)
t
: pip€
wdU
thicloess
(inchss)
DoEinol
piF
rize
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diclmeter,
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Bchedul€
wcll
thick-
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in-
io"ia.
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il|3id€
sur{dc6,
per
lt
weight
Fr
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lbf
lr'6ight
ol
wcler
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lt,
lb
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ol
inertio.
a6clioE
Erodu.
lus,
lodiu
gYrd-
UorL
in
%
0.405
40
80
std
xs
l0s
40s
0.049
0.068
0.095
0.307
0.269
0.215
0.0740
0.0568
0.0364
0.0548
o.0720
0.0925
0.r06
0.106
0.r06
0.0s04
0.070s
0.0563
0.186
0.245
0.3ts
0.0321
0,0246
0.0157
0.00088
0,00106
0.00I22
0.00437
0,00525
0-00600
0.1271
0.1215
0.1146
%
0.540
;;
80
std
l0s
40s
80s
0.065
0.088
0.119
0.410
0.364
0.302
0.1320
0.1041
0.0716
0.0970
0.12s0
0.1s74
0.141
0.I4t
0.141
0.1073
0.0955
0.0794
0.330
0.425
0.535
0.0572
0.04s1
0.0310
0.002?9
0.00331
0.00378
0.01032
0.01230
0.0r395
0.1594
0.1628
0.1547
%
o.675 40
80
t;
xs
ss
l0s
{0s
80s
0.065
0.(E5
0.091
0.t26
0.710
0.54S
0.493
0.423
0.396
0.2933
0.19t0
0.1405
0.1582
0.1246
0.1670
0.2173
0.220
0.t77
o.t77
0.t77
0.1859
o.t427
0.1295
0.1r06
0.538
0,423
0.568
0.739
0.1716
0.t011
0.0827
0.0609
0.01197
0.00586
0.00730
0.00862
0.0285
0.01737
0.02160
0.02554
0.2150
0.2159
0.2090
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%
0.840
40
80
160
;;
XS
xxs
l0s
40s
80s
0.065
0.083
0.109
0.147
0.187
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0.710
o.6't4
0.622
0.546
0.466
o.2s2
0.3ss9
0,357
0.304
0.2340
0.1706
0.u99
0.1583
0.1974
0.2503
0.320
0.383
0.504
0.220
0.220
o.220
0.220
0.220
0.220
0.I859
0.1765
0.1628
0.1433
0.t220
0.0660
0.538
0.671
0.851
1.0€8
r,301
't.7t4
0.17t
0.rs47
0.1316
0.10I3
0.0710
0.0216
0.0120
0,01431
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0.02010
0.022\3
0-t2125
0.0285
0.0341
0.0407
0.0478
o.0527
0.0577
o.2750
0.2692
0.2613
0.2505
o.2102
0.2t92
1.050
40
80
160
;;
xs
xxs
l0s
10s
80s
0.065
0.083
0.1l3
0.I54
0.2t8
0.308
0.920
0.884
0-s21
o.?42
0.614
0.434
0.655
0.6t4
0.533
0.432
0.2961
0.1479
0.2011
o.2521
0.333
0.435
0.570
0.718
o,275
0,273
o.275
0.275
o.275
o.275
0.2409
0.2314
0.2157
0.1943
0.1607
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37
0,684
0.857
l.l3t
t.414
1.937
2.441
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0.2661
0.2301
0.1875
0.1284
0.0541
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0,0448
0.0527
0.0579
0.0467
0.0566
0.0706
0,0853
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0.349
0.343
0.334
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0.2810
I
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80
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xs
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40s
80s
0.065
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0.133
0.1?9
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0.358
1.185
1.097
1.049
0.957
0.815
0.599
1.103
0.945
0.864
0.719
0.s22
0.2818
0.2553
0.113
0.4s4
0.639
0.836
1,076
0.344
0.344
0.344
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0.3{{
0.341
0.310
0.2872
o.2716
0.2s20
0.2134
0.1570
0.858
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1.679
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3.659
0.478
0.{09
0.374
0.311
0.2281
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0.0500
0,0757
0.0874
0.I056
o.1252
0.1405
0.0760
0.ll5l
0.1329
0.1605
0.1900
0.2137
0.443
0.42A
0.42t
0.407
0.387
0.361
r%
J.660
{0
80
160
;;
xs
xxs
55
r0s
40s
,::
0.065
0.109
0.t{0
0.250
0.382
1.530
t.442
r.380
1.27a
1.160
0.896
r.839
r.496
r.283
1.057
0.63r
0.326
U.53I
0.669
0.8b
I
1.107
1.534
0,434
0.434
0.434
0.434
0.134
0.434
0.401
0.378
0.361
0.335
0.304
0.2346
1.r07
1.805
2.273
2.997
5.2t4
o.797
0-7al
0.648
0.458
0.2732
0.1038
0.1605
0.1948
0.2418
0.2839
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0.1934
o.2346
0.2913
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0.564
0.550
0.540
0.524
0.506
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r%
1.900
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0.06s
0.t09
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1.682
2.461
0.37s
0.613
0.197
0.497
0.469
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2.085
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tCt,kne\) ,'f ITT
Ctinkll.
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
http://slidepdf.com/reader/full/mechanical-design-of-process-system-volume-2shell-and-tube-rotating-equipment-keith 203/252
Appendix
C: Properties
of PiPe
195
PROPERTIES
OF
PIPE
(Continued)
noEitrol
prpe
rir.
outside
diomelet
ia.
rchedule
qumber'
wcll
thick-
646.
in.
inrid€
diqa-
iriide
3q.
in.
metol
rq.
rD.
eq lt
outsido
suatcce,
po.
ft
rq
It
itrlide
EurIqce,
pe.Il
rrreight
per
lt.
w€isht
ol wsler
p€r
It,
lb
oI
in€diq,
in..
a6ctioE
rnodu-
lus,
inJ
rodiue
gYrc-
tio|1.
q
b
1%
L90{)
40
80
160
srd
xi
xxs
.:
40s
8os
0.I45
0.200
0.281
0.400
0.52S
0.650
1.6r0
1.500
1.338
1.I00
0.850
0.600
2,036
1.767
r.406
0.950
0.567
0.283
0.799
r.058
I.{29
1.885
2.247
2.551
0.497
0.497
0.497
0.497
0.497
0.{97
o,42r
0.3s3
0.350
0.288
o.223
0.I57
2.7t8
3.631
1.859
6.40€
7.7tO
8.6?8
0.882
0.765
0.608
o.4tz
0.246
0.t23
0.310
0.39r
0.483
0.568
0.6140
0.6340
0.326
0.{12
0.508
0.598
0.6470
0.6670
0.623
0.50s
0.58I
0.549
0.5200
0.4980
2
2.375
;;
80
160
;;
xs
xxs
5'S
los
{0s
80s
0.06s
0.109
0.154
0.218
0.343
0,436
0.s62
0.687
2-245
2.157
2.081
I.939
1.689
l.5m
r.251
1.001
3.96
3.65
3.36
2.953
2.210
1.774
t,229
0.787
0.472
o.176
r.075
1.411
2.1s0
2.556
3.199
3.641
0-622
0,622
D-622
0.822
0.622
0.822
0.622
0,622
0.588
0.565
0.541
0.508
0.442
0.393
0.328
0.262
1.60d
2.638
3.653
5.O22
7.444
9.029
t0.882
12.385
r.715
1.582
1.455
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0.311
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0,561
0.731
0.979
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0.817
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0.6710
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;;
80
160
.''.
";;
s
)o(s
l0s
40s
80s
0.083
0.120
0.203
0.274
0.3?5
0.552
0.675
0.800
2.r09
2.635
2.469
2.323
2.L25
t.771
1.525
t.275
4.19
4.24
3.55
2.184
1.826
1.276
o.724
1.039
r.704
2.945
4.03
4.663
s.2t2
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
2.175
3.531
5.793
7.661
I0.01
13.70
15.860
t1-729
2.499
2.361
2,016
1.837
1.535
1.067
0.792
0.554
0.710
0.988
1.530
1.925
2.872
3.0890
3.2250
0.4s4
0.68t
1.064
1.339
l.ss8
2.I4S0
2.2430
0.988
0.975
0,947
0.924
0.894
0.844
0.8140
0.7860
3.500
1;
80
160
;;;
xi;
10s
40s
80s
0.083
0.120
0.2I6
0.300
0.437
0.600
0.725
0.850
3.334
3.260
3.068
2.900
2.626
2.300
2.050
r.s00
8.73
8.35
7.39
6.6r
5,12
4.15
3.299
2,5,13
0.89r
1.2?4
2.224
3,02
1.2L
5.4t
6.317
7.O73
0.916
0.916
0.916
0.916
0.916
0.916
0.916
0.916
0.873
0.s53
0.803
0.75S
0.687
0.602
0.537
o.171
3.03
4.33
7.58
10.25
tl-32
18.58
zt-447
24.0s'l
3.78
3.6r
3.20
2.864
2314
1.801
1.431
1.103
1.301
LazZ
3.02
3.90
5,03
5.39
6.50r0
6.8530
o.111
r.041
t.724
2-226
2.476
3.43
3.7t50
3.9160
1.208
t.t96
1.154
1.136
1.094
1.0,17
1.0140
0.9810
3h
1,qn
40
80
i;
xs
xrs
10s
40s
80s
0.083
0.I20
0.226
0.318
0.636
3.834
3,760
3.548
3.364
2.72A
11.10
9.89
8.89
5,845
1.021
1.463
2.680
3.68
a,721
t.o47
1.047
1.047
t.o41
1.047
1.004
0.984
0.92S
0.881
0.7t6
3.41
4.91
9.r
12.51
22.850
5.01
4.81
4.28
3.8S
2.S30
1.960
2.756
4,19
6.28
s,8d80
0,980
1.378
2.394
3.14
4.9240
1.38s
L.312
1,337
1.307
1.2100
4'JU)
;;
80
120
r60
;;
xs
:o,s
IGS
40s
s0s
0.083
0.r20
0.188
0,237
0.337
o.437
0.500
0.531
0.674
0.800
0.925
4.334
4.260
4.L24
4.026
3,826
3.626
3.S00
3.138
3.152
2.900
2.650
14.7S
11.25
13.357
t2.73
It.50
r0.33
s.521
s.28
7.80
6.602
5.513
2.547
3.17
4,41
6.283
6.62
8.10
9.294
10.384
1.178
t.178
1.178
1.178
1.178
1.178
r.178
1,178
1.178
1.r78
t.178
l.ll5
1.082
r.054
1.002
0.94S
0.916
0.900
0.825
0.759
0.694
3.92
8.560
10.79
14.98
r8.96
21.360
21.54
31,613
35.318
6.40
5.800
5.51
4.98
4.48
4.160
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3.38
2.864
2.391
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3.96
5.8500
123
11.65
t2.17tO
13.27
15.29
16.66t0
t7.?130
t.249
L.762
2.6000
3.21
4.27
5.6760
5.90
6,79
7.4050
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1.562
1.549
1.5250
t,510
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1.3380
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;;
80
t20
160
;;;
xs
)o(s
r0s
4os
80s
0.109
0.134
0.258
0.375
0.500
0.62S
0.7s0
0.875
1.000
5.34S
5.29S
5.(X7
1.813
4.563
4.313
4.063
3.813
3.553
22.44
22.02
20.01
18.19
I6.35
14.6r
t2.97
rt.4l3
1.868
2,285
4.30
6.ll
7.95
9.70
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12.880
1t.328
1.456
t.456
1.4s6
1.456
1.456
1.456
1.455
l.{s6
1.156
1.399
1.386
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1.260
1.t95
1.129
r.064
0.998
0.933
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7.77
l{.62
20-74
27.O4
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9.73
t.89
7.(x)
6.33
s.62
{.951
4.232
6.95
8.43
15.17
20.68
25.74
30.0
36.6450
39.lll0
2.494
3.03
5.15
7.13
9.25
10.80
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13.1750
11.0610
1.920
1.878
1.839
1.799
1.760
1.6860
1.5s20
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
http://slidepdf.com/reader/full/mechanical-design-of-process-system-volume-2shell-and-tube-rotating-equipment-keith 204/252
196
Mechanical
Design
of
Process
Systems
PROPERTIES
OF PIPE
(Continued)
pipe
Biz€
in.
schedule
wall
thick-
inside
diom-
rn.
inside
sq.
in.
tItetol
3q.
rL
aq lt
outside
pe
It
sq
ft
inBide
surrcc
per
lt
weighl
per It,
lbf
w€ighl
per
It,
tb
oI
inertia,
luB,
rddius
gyra-
tion,
in.
6
40
80
t20
160
sia
xs
xxs
l0s
40s
80s
0.109
0.134
0.219
0.280
0.432
0.562
0.7I8
0.864
L000
L
t25
6.407
6.357
6.187
5.761
5.50r
5.189
4.897
4.62S
4.37S
32.2
3t.7
30.r00
28.89
26.07
23-77
18.83
16.792
Is.02s
2.231
2.733
4.4I0
5.58
8.40
10.70
15.64
t7.662
19.429
1.734
1.734
t.734
t.734
I.734
1.734
1.734
1.734
t.734
t-734
r.677
1.664
1.620
1.588
1.508
L440
1.358
r.282
r.211
1.t45
5.37
9.29
15.020
18.97
28.57
36.39
45.30
s3.16
60.076
66.0S4
r3.98
t3.74
r3.100
12.51
It.29
I0.30
8.17
7.284
ll.8s
14.40
22.6600
28.\4
40.5
49.6
5S.0
66.3
72.r190
76.5970
3.58
4.35
6.8400
8.s0
t2.2s
14.98
r7.8I
20.03
21.7720
23.t240
2.304
2.295
2.2700
2.245
2.I95
2.153
2.r04
2.060
2.0200
1.s850
8
8.625
20
30
40
60
80
a;;
XS
I0s
4;;
80s
0.109
0.I48
0.219
0.250
0.27',|
0.322
0.406
0.s00
4.407
8.329
8.187
8.125
8.07r
7.991
7.813
7.625
s4.s
52.630
51.8
51.2
50.0
47.9
45.7
2.916
3.94
5.800
6.58
8.40
10.48
t2.78
2.258
2.258
2.258
2.258
2.258
2.25A
2.258
2.25A
2.2A1
2.180
2.150
2.t27
2.1t3
2.089
2.045
1.996
9,91
r3,40
19.640
22.36
24.70
28.55
35.64
43,39
24.07
23.59
22.500
22.48
22.t8
21.69
20,79
19.80
26.4S
35.4
sr.3200
63.4
88.8
r05.7
6.13
8.2I
ll.s000
I3.39
t4.6S
r6.81
20.58
24.52
3.0r
3.00
2.9700
2.962
2.953
2.938
2.S09
2.578
I
8.625
100
t20
l{0
160
0.593
0.718
0.8I2
0.906
1.000
7.439
7.18S
7.001
6.813
6.625
6.375
43.5
40.6
38.5
34.454
3L903
14.96
t7.44
19.93
2t.9?
23.942
26.494
2.25a
2.258
2.2s8
2-2s8
2.258
2.258
L948
1.882
L833
1.784
t.?34
r.669
50.87
60.63
74.69
81.437
90.1r4
18.84
17.60
r6.69
15.80
14.945
13.838
t21.4
140.6
1s3.8
177.t320
r90.62I0
28.t4
32.6
35.7
38.5
4r.0140
44.2020
2.847
2.807
2.117
2.7 4A
2.7I90
2.68I0
l0
)0.750
;;
30
40
60
80
100
120
140
I60
;,;
xs
l0s
40s
80s
0.134
0.t 65
0.219
0.250
0.307
0.365
0.500
0.593
0.718
0.843
0.87S
L000
t.125
1.2s0
1.500
t0.482
r0.420
r0-312
10.250
r0.r38
10.020
9.750
s.564
9.314
9.064
9.000
8.7S0
8.500
8.250
7.750
86.3
85.3
83.52
82.s
80.7
78.9
'14.7
7t.8
68.I
64.5
60.1
56.7
s3.45
47.r5
4.52
5.49
7.24
9.25
10.07
l l.9l
16. t0
t8.92
22.63
26.24
27.t4
30.6
34.0
37.3r
43.57
2.815
2.815
2.815
2.815
2.815
2.81s
2.815
2.815
2.815
2.815
2.815
2.815
2.815
2.815
2.8I5
2.744
2.728
2.70
2.683
2.654
2.623
2.5S3
2.504
2.438
2.373
2.36
2.:91
2.225
2.16
2.03
r8.70
24.63
28.04
34.24
40.48
54.74
64.33
76.93
89.20
92.28
104.13
t26.42
148.19
37.4
36.9
36,2
35.8
35.0
34.1
32.3
31.1
28.0
27.6
26.1
24.6
23.2
20.5
63.7
76.9
100.46
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137.S
160.8
2t2.0
244-9
248.2
324
333.46
368
399
428.t'I
478.59
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21.I6
25.57
29.90
39.4
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53.2
60.3
62.04
58.4
74.3
79.66
89.04
3.75
3.74
3.72
3.7r
3.69
3.53
3.60
3,56
3.52
3.50
3.47
3.43
3.39
3.31
t2
12.750
;i
30
40
;;
80
I00
t20
l{0
150
;;;
.-.
l0s
4;;
80s
0.156
0.180
0.2s0
0.330
0.375
0.406
0.500
0.562
0.687
0.7s0
0.843
0.87s
1.000
r,125
1.250
r.3t2
12.438
12.390
2.250
12.0S0
12.000
11.938
u.750
I1.626
11.376
1r.250
11.064
I1.000
10.750
10.500
10.250
10.126
rzt-4
r20.6
u7.9
ll4_8
I
t3.l
llt.9
108.{
106.2
r0t.6
99.40
96.t
95.00
90.8
86.6
82.50
80.5
7.11
9.84
r2.88
14.58
1s.74
19.24
2t-s2
26.04
.28.27
31,5
32.64
36.9
4l.l
45.16
41.1
3.34
3.34
3.34
3.34
3.34
3.34
3.34
3.34
3.34
3.34
3.34
3.34
3.34
3.34
3.34
3.34
3.24
3.21
3.17
3.14
3.08
3.04
2.978
2,94
2.897
2.88
2.8t4
2.749
2.68
2.651
20.99
24.20
33.38
43-77
49.S6
53.53
65.42
73.16
88.51
96.2
07.20
t0.9
25.49
39.68
53.6
4D.27
52.7
52.2
5r.l
19.1
4S.0
48.5
47.0
46.0
44.0
43.1
41.6
4I.l
39.3
3?.S
35.8
34.9
t22.2
I40.S
191.9
248.S
279-3
300
362
401
475
510.7
562
578,5
642
70r
755.5
781
19.20
22.t3
30.1
39.0
43.8
47.1
56.7
62.8
? 4.5
80.1
90.7
100.7
I09.9
118.5
122.8
4.45
4.44
4.42
4.39
4.38
4.37
4.33
4.31
4.27
4.25
4.22
4-21
4-t7
4.I3
4.09
4.01
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
http://slidepdf.com/reader/full/mechanical-design-of-process-system-volume-2shell-and-tube-rotating-equipment-keith 205/252
'1
Appendix C: Properties
of
Pipe
197
PROPERTIES OF
PIPE
(Continued)
aoniaal
pipo
riz.
outtide
rchedule
woll
thicL-
11646,
iD.
iDsid€
diqn-
iD-
inside
3q.
h.
metal
sq.
it .
sq It
outside
rurlqce,
Frlt
sq lt
ingide
rurldce,
per
lL
weight
per
lL
lbt
woisht
trrr
fL
tb
trlo|ne|''t
ol
i|'ertiq,
iD..
aectiorr
modu-
luB,
in.t
rcdiu6
9Yra-
tioD.
i -
l{
t1.000
to
;;
;;
40
;;
80
100
120
140
180
l0s
0.1s6
0.188
0.2r0
0.219
0.2s0
0.281
0.312
0.344
0.375
0.437
0.469
0.500
0.ss3
0.625
0.750
0.937
1.093
1.2s0
1.406
13.688
13,624
13.580
r3.562
t3.s00
13.438
13.312
13.250
13.126
13.082
13,000
12.8I4
12.750
12.500
12,t28
It.8l4
I1.500
lI.l88
147.20
145.80
141.80
144.50
143.I
141.80
140.5
139.20
137.9
I35.3
1s4.00
t32-7
129.0
t27.7
t22.7
109,6
103.9
98.3
6,78
8.16
9.10
9.48
10.80
l2.tt
t3.42
14,76
16.05
18.62
19.94
24.94
26,26
31.2
44.3
50,1
55.6
3.67
3.67
3.67
3.67
3.67
3.67
3.57
3.67
3.67
3.67
3.67
3.6'r
3.58
3.57
3.55
3.53
3.52
3.50
3.48
3.4J
3.44
3.42
3.40
3.35
3.34
3.27
3.17
3.09
3.01
2.929
23.0
27.1
30.9
32.2
36,71
4t.2
45.68
s0.2
s1.57
63.37
67.8
72.09
84.91
89.28
106,13
130.73
150.67
t10,22
I89.12
63.1
62.8
62.1
6I.5
60.9
50.3
59.7
58.7
s8.0
57.5
55.9
53.2
s0.0
47.5
45.0
42.8
r62.6
194.6
2t8,2
225.1
285-2
3r4
34{.3
429
456.8
484
562
s8s
687
825
tr21
I0l7
27.8
30.9
t2.2
36.S
40.7
14.9
49.2
53.3
61.2
55.3
69.1
80.3
81.1
94.2
117.8
132.8
146.8
159.5
4.90
4.88
1.87
4.47
4.86
4.85
4.84
4.8s
4.82
1.80
1-79
4.18
4.14
4.73
4.69
4.63
1.58
4,53
4.18
16.0U)
i;
20
30
40
60
80
100
120
t40
t60
;;
xs
l0s
0.16s
0.188
0.250
0.312
0.37S
0.500
0.656
0.843
1.03r
1.218
1.437
1.593
IS.670
15.624
r5.500
1s.376
1s.250
15.000
14.688
14.314
13.938
13.564
13.126
12.814
I92.90
191.70
188.7
185.7
182.6
t76.7
169.4
160.9
1s2.6
144.5
t35.3
129.0
8.21
9.3{
t2.3?
15.38
18.4I
24.35
40.1
48.5
65,7
72.1
4.
ts
1.19
4.19
4.IS
4.I9
4.19
4.19
4.19
{.19
4.19
4.19
4.I9
4.10
4.09
4.06
4.03
3.99
3,93
3.85
3.75
3.65
3.55
3.44
28
32
42.05
52.36
62.58
42.71
10r.50
136.45
164.83
192.29
223.81
245.11
83.5
8S.0
81.8
80.s
79.1
73.4
89.7
66.1
58.5
25?
292
384
473
562
?32
933
ll57
1365
I?60
1894
36.5
48.0
59.2
?0.3
9t.s
114,6
170.6
194.5
220.0
236.1
s.60
5.59
5,{8
5.43
5.37
5.21
5.17
5.12
t8
18,000
;;
20
30
;;
80
r00
I20
140
r60
5S
l0s
0.r65
0.188
0.2s0
0.312
0.375
0.437
0.500
0.562
0,750
0.937
r.r56
1.375
1.562
1.781
17,670
t7.624
I7.500
u.376
17.250
17.126
17.00
16.876
16.500
16.126
r5.688
r5.250
r4.876
14.438
245.20
243.90
240.5
237,r
233.7
230.4
227.0
223.7
213.8
204.2
193.3
182.6
173.8
163.7
9.24
r0.52
13.9{
t7,34
20.76
24.11
21.49
30.8
40.6
s0,2
61.2
71.8
80.7
90.7
4.71
4.',1L
4.71
4.71
4.71
4.71
4.71
1.7r
4.71
4.7
r
4-71
4.7 |
4.7
4.63
4.61
4.58
4.55
4.52
4.48
{.45
4-42
4.32
4.22
4.ll
3.9S
3.89
3.78
36
41-39
59.03
70.59
82.06
93.15
r04.75
138.17
t70.75
207.96
244.14
274.23
308.5I
106.2
105.7
104.3
102.8
t01.2
99,9
98.{
97.0
92.7
88.S
83.7
79.2
75,3
7
r.0
368
4t7
5{9
678
807
93r
1053
rt72
1834
2180
2499
2',150
3020
40.8
46.4
61.0
75.S
89.6
103.4
117.0
130.2
168.3
203.8
242.2
z'17.6
306
335
6.31
5.30
6.28
6.25
8.23
6,21
6.19
6.10
6.01
s.97
5.90
5.84
5.77
20
20,000
l0
20
30
40
60
80
100
s;
l0s
0.188
0.218
0.250
0.375
0.500
0.s93
0.812
0.875
1.031
1.281
I9.634
19.564
r9.500
r9.250
t9.000
18.814
I8.376
18.2s0
17.938
17.438
302.40
300.60
298.6
291.0
283.5
278.0
265,2
261.6
252.7
238.8
I1.70
23.t2
30.6
36.2
48.9
52.6
61.4
s.21
5.24
s.24
s.24
5.24
5.24
5.24
5.24
5.24
5.24
5.14
5.12
5.ll
5.0{
4.97
4.93
4.8r
4.78
4.70
4,57
40
46
s2.19
78.60
104.I3
r22.91
I66.40
178.73
208.87
256.10
131.0
r30.2
129.5
126,0
t22.8
120.4
115.0
Ir3.4
109.4
103.{
574
663
7S?
1I l4
t457
1704
2257
2409
2772
3320
57.4
7S-7
lll.4
145.7
170.4
225.?
240.9
277.2
332
7.00
6.99
6.98
6.94
6.90
6.79
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
http://slidepdf.com/reader/full/mechanical-design-of-process-system-volume-2shell-and-tube-rotating-equipment-keith 206/252
198
Mechanical
Design
of
Process
Svstems
PROPERTIES
OF PIPE
(Continued)
nominol
pip6
rire
schedule
wcll
lhick-
in.
inaide
dicm-
iD.
inside
sq
in.
metdl
aq rr'"
Bq
lt
oubide
gurlqce,
per
lt
sq lt
in8ide
surlcce,
perlt
lreight
per
Il,
tbt
n
eight
per
lt,
tb
lnoEent
oI
inerlid,
rection
Erodu-
lus,
rqdiur
9yra.
lion,
in.
20
20.ooo
r20
140
160
1.500
1.750
t.968
17.000
16.500
16.064
227.0
213.8
202.7
87.2
I00.3
lll.s
s.24
5.24
s.24
4.45
4.32
4.21
296.37
341.10
379.01
98.3
92.6
87.9
4220
4590
376
422
459
6.56
6.48
6.41
22
22.004
l0
20
30
;;
80
r00
120
140
160
;;;
xs
5S
I0s
0.188
0.218
0.250
0.37s
0.500
0.625
0.750
0.875
l.t2s
1.37s
r.875
2.t25
2r,624
21.564
2r.500
2t.250
21.000
20.750
20.s00
20.250
I9.750
19.2s0
18.7S0
r8.250
17.750
367.3
363.1
354.7
346.4
339.2
330.r
322.1
306.4
291.0
276.1
26t.6
247.4
12.88
14.92
17.18
25.48
33.77
41.97
50.07
58.07
13,7A
8S.09
104.02
118,55
132.68
5.76
5.76
5.?6
5.76
5.76
5.76
5.76
5.56
5.50
5.43
5.37
5,30
5,17
5.04
4.91
4.78
44
5l
87
lls
t43
1?0
I97
2Sl
303
351
403
45t
r59.t
1s8.2
157.4
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132.8
t26.2
119.6
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756
885
l0l0
1490
1953
2400
2829
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6054
69.7
80.4
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237
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295.0
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432.6
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7.t5
7.07
24.000
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20
30
io
;;
80
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150
XS
0.250
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23.500
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22.064
21.s64
20.938
20.376
1s.876
19.314
434
425
415
4
406
402
398
436.1
388.6
382
365
344
326
310
293
18.65
21.83
36.S
41.{
45.9
50.3
54.8
16.29
63.54
70.0
87.2
108.1
126.3
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159.4
6.28
6.25
6.28
6.28
6.28
6.28
6.2S
6.28
6.28
5.28
6.28
6.28
6-28
6.28
6.28
6.r5
6,09
6.O2
5.99
s.96
5.92
5.89
6.17
5.83
5.78
5.48
5.33
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5.06
63.41
s4.62
125.49
140.80
156.03
t7t.I?
186.24
55
216
238.11
2S6.36
367.40
429,39
483.13
541.94
188.0
183.8
180.1
178.1
t76-2
174.3
172.4
r88.9
168.6
r55.8
158.3
149.3
141.4
t34.S
t27.0
1316
1943
2550
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4256
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6850
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212.5
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285.2
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96.0
354.7
388
t73
571
719
788
8.10
8.35
8.31
8.29
a.z7
8.25
8.22
8.41
8.18
8.15
8,07
7.95
7.47
7.79
7.10
28
26.000
t0
20
srd
0.2s0
0.3I2
0.37s
0.500
0.625
0.750
0.875
1.000
1.t25
2S.s00
25.376
25.250
2s.000
24.750
24.500
24.250
24.000
23.7s0
510.7
505.8
500.7
490.9
481.1
471-4
461.9
452.4
443.0
19.8S
25.18
30.19
40.06
49.82
59.49
69.07
78.54
87,91
6.8r
6.81
6.81
6.81
6.81
6.81
6.8I
6.81
6.68
6.64
6.54
6.48
6.41
6.35
6.28
6.22
88
I03
202
235
267
299
22t.4
2t9.2
217,1
2t2-8
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204-4
200.2
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ts2.t
1646
2076
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6813
126.6
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190.6
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308.7
364.9
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473.0
524.1
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9.08
9.06
9.02
8.98
8.93
s.89
8,85
8.80
2A
28.000
l0
20
30
std
xs
0.250
0.3r2
0.375
0.500
0.625
0.750
0.875
r.000
1.r25
27.500
27.376
27.250
27.000
26.750
26.500
28.250
26.000
2s.750
594.0
588.6
583.2
572.6
562.0
s51.5
541.2
530.9
520.8
21.80
z',t.t4
32.54
43.20
53.75
64-21
74.s6
84.82
94.98
'1.33
7.33
7.G)
7.33
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7.t7
?.13
7.07
7.00
6.34
6.87
6.74
71
92
lll
t17
183
2tg
253
288
323
2s1.3
2S5.0
252.6
248.0
243.4
238.9
234.4
230.0
225.6
2098
2601
3l0s
4085
5038
5964
6855
714D
8590
149.8
185.8
22t-A
23 1.8
359.8
426.0
490.3
6t3.6
9.81
9.79
9.77
9.68
9.61
9.60
s.55
9.51
30
30.000
l0
20
30
std
xs
t0s
0.250
0.3I2
0.375
0.500
0.62S
29.s00
29.376
29.250
29.000
28.750
683.4
477.8
672.O
660.5
649.2
23.37
29.19
34.90
46.34
57.68
7.85
7.85
7.85
7.8s
7.8s
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
258S
3201
3823
s033
6213
t72.3
2t3.4
254.8
335.5
4t4.2
10.52
10.50
10.18
I0.43
10.39
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Appendix
C: Properties
of
Pipe
199
PROPERTIES
OF PIPE
(Continued)
nominol
pipe
size
oulside
didmeteL
schedule
wcll
thick-
inside
dicm-
irBide
sq.
in,
metal
Bq.
in,
sq It
outside
per
It
sq
It
inside
per
rl
weighl
pe
ft,
lbt
weight
per
It
lb
ol
ilrerlio.
lus,
in.3
(rdiug
gvrq-
iion,
30
30.000
40 0.750
0.875
I.000
l.l2s
28.500
28.250
28.000
27.',750
637.9
620.7
615.7
6D4.7
68.92
80.06
9t.Il
r02.05
7.85
7.85
7.85
7.85
7.46
7.39
7.33
'1.26
234
272
310
347
276.6
271.8
2E',t.O
242.2
137 |
84S4
9591
10653
491.4
566.2
639.4
7 t0.2
10.34
10.30
10.26
t0.22
32
32.000
l0
20
30
40
std
xs
0.250
0.312
0.375
0.500
0.625
0.688
0.750
0.87s
1.000
L l25
31.500
31.250
31.000
30.750
s0.624
30.500
30.250
30.000
29.?50
'179.2
773.2
766.9
7 54.7
7
42.5
736.6
730.5
718.3
706.8
694.7
24.93
3I.02
37.25
49.48
61.59
67.68
73.63
85.52
s7.38
109.0
8.38
8.38
8.38
8.38
8.38
8.38
8.38
8.38
8.38
8.38
8.2S
8.21
B.l8
8.l l
8.05
8.02
7.98
7.92
7.85
7.',19
85
106
t27
168
209
230
250
291
33t
371
337.8
335.2
332.5
321.2
321.9
319.0
316.7
306.4
301.3
3l4 t
38gl
4656
6140
7578
8298
8990
10372
I
I680
I3023
196.3
243.2
291.0
383.8
473.6
518.6
561.9
648.2
730.0
814.0
11.22
11.20
11.18
u.l4
I1.09
11.07
I1.05
lr.0l
l0.ss
10.92
34
34.A00
t0
20
30
40
st;
XS
0.250
0.312
0.375
0.500
0.62s
0.688
0.750
0.875
1.000
t.125
33.500
33.376
33.250
33.000
32.7s0
32.624
32.500
32.250
32.000
3t.750
881.2
874.9
867.8
s5s.3
841.9
835.S
829.3
816.4
804.2
791.3
26.50
32.99
39.61
52.82
65.53
72.00
78.34
91.01
I03.67
lI5.I3
8.90
8.90
8.90
8.S0
8.90
8.90
LS0
8.90
8.90
8.90
8.1',|
8.7 4
8.70
8.64
8.57
8.54
8.51
8.44
8.38
8.31
90
1r2
t79
223
245
266
310
353
395
382.0
379.3
370.8
365.0
3M.l
359.5
3S4.1
348.6
343.2
3173
4680
sssT
7385
9124
9992
1082s
12501
l4l t4
15719
22t.9
2',t5.3
329.2
434.4
535.7
587.8
637.0
735.4
830.2
924.7
IL33
I t.9I
11.89
r 1.s5
I1.80
I
I.78
11.76
tt.12
I1.67
I1.63
36
36.000
l0
20
30
40
XS
0.250
0.312
0.37s
0.500
0.625
0.750
0.875
I.000
1.125
35.500
35.376
3s.2s0
35.000
34.750
34.500
34.250
34.000
33.750
s89.7
982.S
s75.8
962.1
948.3
934.7
920.5
907.9
a94.2
28.11
34.95
42.D\
55.76
69.50
83.0I
96.s0
109.96
123.19
L42
9.42
L42
9.42
9.42
9.42
9.42
9.42
9.42
9.29
9.26
9.23
9.16
9.10
9.03
8.97
8.90
8.89
96
lIs
143
190
236
242
324
374
419
429.1
426.1
423.1
417.l
4lt.t
405.3
399.{
393.6
387.9
4491
5565
6654
8785
10872
12898
I4903
I6S5I
18763
24S.5
309.1
310.2
488.1
504.0
7I6.5
82',t.9
936.2
t042.4
t2.84
12.62
12.59
12.55
12.51
12.46
t2.42
I2.38
12.34
42
42.000
2i
30
40
std
XS
0.250
0.375
0.s00
0.62S
0.750
1.000
1.250
1.500
41.500
41.250
41.000
40.7s0
40.500
40.000
39.500
39.000
1352.6
1336.3
t320.2
1304.r
1288.2
1256.6
t225.3
1194.5
32.82
4S.08
65.18
81.28
97.23
128.81
160.03
190.85
10.99
10.99
t0.99
r0.99
I0.99
10.99
t0.99
10.99
10.86
10.80
10.73
10.67
10.60
10.47
10.34
10.21
tt2
I67
222
276
330
438
s44
649
586.4
s79.3
s't2.3
565,4
558.4
544.8
531.2
517.9
7 r28
I0627
I4037
17373
20689
210a0
33233
39181
339.3
506.r
668-4
427.3
985.2
r2s9.5
rs82.5
1865.7
14.?3
t4.7r
t4.67
14.62
14.59
14.50
14.41
14.33
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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.
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.
Nominal
Pipe Size
Nominal
Insulation
Thickness
1%"
2rt"
3%"
4%"
5t4"
I
1%
1%
2
.051
.066
.080
10
12
ll
l4
.21
.21
.23
.29
.29
.31
.30
.38
.40
.39
.48
.47 .59
214
3
3%
4
.09r
.10
.r9
.17
.24
.31
.30
.36
.34
,41
.39
.46
.44
.58
.56
.63
.70
.68
.78
.83
.81
.96
.s7
1.10
6
8
10
. 7
.24
.34
.43
.34
.38
.59
.45
.o.t
.66
.58
.64
.80
.93
.71
.83
t.12
.88
.97
1.17
1.04
1.13
1.36
1.54
1.20
1.34
1.99
t2
l4
16
18
.50
.6{
.68
.70
.78
.87
.88
.90
1.0r
l.t2
1.07
1.1I
1.24
1.37
1.34
1.49
1,64
1.52
1.57
1.92
1.74
1.81
2.01
r.s9
2.07
2.29
2.24
2.34
2.58
2.82
2.50
2.62
2.88
3.14
20
24
.70
.83
.96
1.13
1.44
1.50
1.77
t.7s
2.10
2.09
2.44
2.40
2.80
3.16
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.
%
lz
V+ %
1
.1ya,
ry4
1y4
2
2l+
2 2y4
3 3r/t
3
Root
Area of
Thread,
sq.
in.
.068 .126
.202 .302 .419
.693 .889 1.293 1.144 2.300 3.023
3.719 4.619 5.621 6.124
?.918
Max, Safe Load,
lbs.
at
Rod
Temp.
of 650'F
610 1130 1810
27t0
3770 4960 6230 8000 11630 15?00
20700 21200 33500 41580
50580 71280
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202 Mechanical
Design
of Process
Systems
PIPE
r.660"
o.D.
Tempcrature
Renge
'F
Fiber-
Sodium
WEIGHTS
OF
PIPING
MATERIALS
Yn"
w'
4\
di
t_L_,
z
F
z
F
z
F
z
-J
tr
Nr$
ts-ts$
{l.-.-tis
Boldface
.ty"pe
is
\eight
in
pounos.
Lrghflace
t)pe
benexth
weight. is weight
factor
for
Insulation
thicknesses
and
weights arc
based
on averaqe
mnditiors
and
do Dot
constituie
a recommendation
for
specific
thicknesses of
materials-
Insula-
tion lveights are
based
on.85/p
magnesra
ano
nl drous
c3lclum
silicate
at
11
lbs/cubic
foot. The
listed thicknesses and
neights
of
combination
coverinq are
ihe
sums of
ihe
inner
layer of dia-
tomaceous
earth
&t 2l
lbs/cubic
foot and
the
outer
laycr
at
1l lbs/cubic foot.
Insulation
weiqhts include al-
lowances
for wiri,
cement,
can-
vas,
bands and
paint,
but
not
special surface 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-
mate. When
possible,
-dbtain
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,
,41
/A
#
,N
Jrtd
@
@
IrtJ
@
FsO
Nom.
Thick.,In.
*
16
lb
cu.
ft,
density.
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.IVEIGHTS
OF
PIPING
X{ATERIALS
Appendix
C:
Properties
of Pipe
203
r.eoo'o.D.
l/2"
erce
Schedule No.
40
80 160
Wall
De,<igna.tion
std.
NS
xxs
lhickness-In.
.145
.200 .281
.400
Pipe-Lbs/Ft
2.72
3.63 4.86
6.41
lVatcr-Lbs/Ft
.88 .77
.61 .41
{,1
t2
nuj
>f\
i t />
LLP
e tij
i
-1/
4,
q---
1_
-0
dti
L.R.
90"
Elbow
.8 1.1
1.4
I.E
S.R. 90' Elbow
.6
.3
.7
.3
L.R.
45"
Elbow
_5
.2
.2
.E
.2
1
.2
Tee
.6
2.5
.6
3.L
.6
3.7
.6
Latera.l
1.3
5.4
Reducer
.6
,2
.7
.2
.9
.2
.2
c"p
.3
.5
.3
.7
.3
.7
Temper&ture
Range
'F
t00-199 200,29e
300,3c0
.100-.199
;00-it)9
000-0119 ;00-;,1,1
s00-sf)1r
1t00- r 9
11000-1099
1100-L:00
Nlaqnesia
Caliium
:
Siili.crp
\om. Thick., In. 1
I \)t 2 2
214
tl
i
3
Lbs,/Ft
.84
.84 1.35
2.52
3.47 4.52
4.s2 4.52
{
Combina-
z
\om. Thick.,In.
2tt 21
;
2)1
3
3 3
Lbs/Ft,
1.t0
1.20
1.20 5.62
5.62
5.62
Fiber-
Sodium
Nom.
Thick.,
In.
1
1%
1ta
2
2\l 2%
3 3
LbslFt
1.07
1.07
1.01 1.8s r.85 3.50
3.50 4.76
4-16
6.16
,MS
A rtr
za|
lg
tsrj_ri}
{rrTs
PressLrre
Ratiig
ps'
Casl
lron
blecl
Roldf.rcc tlpe is weight
in
pounds.
Lightfi.ce
tl
pc
bene&th
rveight is
rveight
iactor
lor
insulation.
Insul&tion thickncsses rnd
*eights
^te
based
on
:rverage
conditions
and
do
not constitutc
r rocommcnd&tion for spocilic
thicknesses
of
m"rtorial-q.
Insula-
tion
Neishts :rre
bstxl
on
85f6
mrgnesia ud
hrrlrous lrrlcium
l -.. , ,,,,1,i
^
f^^r Tl-
125
250 i
j;0
300
400
000
900 r500
2500
Screled
or
SIip-On 1.5
7
1.5
1.5 1.5
9
1.5
9
l9
1.:)
l9
1.5
\Yelrling
\eck
L5
I \2
1.5
l2
1.5
l9
1.5
l9
1.5
34
1.5
Lap Joini
1.5
8
9
1.5
9 t9
1.5
19
31
Rlind
3.5
1.5
7
I
5
3.5
t.5
9
1.5
10
1.5
l0
1.5
l9
1.5
19
3l
..4
a
/:)
Z
tt 4\
-
?41
| /A
3,\
S.R. 90"
nlbow
10
3.7
t2 23
3.8
26
3.9
46
listcd
lhiclinesses
orxl
\\'cights
of
combinltion
covering rte
the
sums
of the inner l.rver of dir-
tomaceous errth at
21
lbs .ubic
foot anrl the outcr
hl cr
at
11 ltls/cubic foot.
Insuhtion
\\'ci,ahts
inrluclc
cl-
louanr:rs
for \\'iro, ccmcnt. ern-
vlt'\, 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,
multiplt
thc
rveight f.|rtor
l)y
thc
rvcight
lrcr
fooi
of
covcrir)g
uscd
or) strLright
pipe.
\'.rlvt} \ 0iJahts lrre appro\i-
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
ioints.
L.R. 90' Elbow
4
45'Elbow
9
ll
23
39
Tee
t7
5.6
20
30
5.8
70
6
j=<l
s
k3J
lltn
++I
FrO
Ilanged
lJonnet
G:rt{
6.8
1.2
70
.l.il
125
Flanged
tsonnet,
GLrlrc
or
Angle
40
4.2
45
.t.2
t70
5
Irlanged
Bonnet
Clheck
30
4.1
35
.1.1
40
I l0
I)tessure
Seal
Borrrret-(-irte
42
1.9
t.2
Pressurc
Seal
Ilonnet
Giobe
*
16
h
cu.
ft.
density-
joints.
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2O4
Mechanical
Design of Process
Systems
2"
ptpn
z',s,,
o.D-
wErcHTS
oF
pIprNG
MATERTALS
A
Schedule
No.
40
80
160
Wall
Designation
std.
XS
xxs
Thickness-In.
.154
.218
.343
.436
Pipc-Lbs/tr
1,
5.02
7.41 9.03
I4'ater-Lbs/Ft
1.46
1.2E
q
t -/
zf.
F t/>
w
'HJ
^
_l--__,
\i/
L.R. 90"
Elbow
1.5
.5
.5
2.9
.5
S.R. 90'
Elborv
1
1.3
.3
L.R.
45' Elbow
.E
.2
r.1
.2
1.6
1.8
Tee
.6
.6
.6 .6
Lateral
5
1.4
7.8
1.4
Reducer
1.2
.3
1.6
1.9
crp
.5
1.2
,+
t,2
.+
Temperaiure
Range
"F
100-199
200-299
300-399 400-499
500-5s9 600-699
700-7c9
800-899
900-9s9 1000-1099
1r00-1200
Megnesia
z
Calcium
I silicate
Nom.
Thick.,In.
I
I
L% 2%
2%
3
3
3
3%
Lbs/Ft
1.01
1.01
t.7l 2.53
2.53
3.48
3.48
4.42
4,42
4.42
*
uomDlnx-
;
tion
z
Nom,
Thick.,
In.
2%
2%
3
3
3%
Lbs/Fb
4.28 4-2E
5,93
5.93
7.80
Fiber-
Sodium
Silicate
Nom.
Thick.,In.
I
I I
1%
1% 2
2
214
3
3
Lbs/Fb
1.26
1.26 1.26
2.20
2.20
4.57
4.57
5.99
5.99
sffi
d-ir
Z
trLrlS
6N_l-M
ryi:-s
Pre-ssure
Rating
psl
Cast Iron
Steel
Boldface
type
is
weieht
in
pounds.
Ligh[flce
type
bineath
weigii.
is
yreight
factor
for
lnsul&llon.
fnsulotion
thicknesses
and
weights
a,re based
on average
COnOrtlons ancl
do
not
constitute
a
recommendation
for
specific
thicknesses of materials. I-nsula-
tion weights
are
based
on.85/,
magnes,a
anct
nydrous
c&lctum
silicate
st 11
lbs/cubic
foot.
The
listed
thicknesses and weiqhts
of
combination
coverins arl
the
sums of the
inner
Iajer
of dia-
tomaceous
eerth st 21 lbs/cubic
foot
and
the
outet layer
at
l1
los/cuorc
loo .
Insulation
weishts include al-
lowances
for
wird,
cement,
can-
vas, b&nds and
paint,
but
not
special
surface finishes.
To find
the
weisht
of coverins
on
flanqes.
valvds
or
fittincs]
muhipltth weisht factor
by tle
wergnt.per
too
ol coverrng usecl
on srrargn
prpe.
V&lve
weishts
are aooroxi-
mete.
When
possible,
-dbtain
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 to
make
uD
s.ll
ioints.
250
150
300 400
600 900 1500
2500
Scre* ed
or
SIip-On
9 6
9
ll ll
32 32
4E
'|1'elding
Neck
10
13
t3
3l
1.5
3l
{E
Lap Joint
9 12
1.5
4E
Blirrd
6
10 4-8
l0
t2
1.5
3l
3l
49
,h
,-{l
2t4xJ
i rlt
E,N
e
/9S
z
t?.4
E
II'
Y
ll_______.rl
S.R.
90'
Elbow
16
3.8
3.8
19
3.8 3.8
35
83
4,2
L.R. 90'
Elbow
1E
27
4.r
22
4.1
3l
4.1
45"
lllbow
14
3.4
l6
3.4
73
3.9
1'ee
23 37 41
6
129
ru
",1.{l
3m
+<f
rc
I'langed
Bonnei
Gat€
6.9 7.1
40
4
EO
4.5
190
5
Flanged
Bonnet
Globe or Angle
30
7
64
30
3.8
45
4 4.5
235
Flanged
Bonnet
Check
26
7
5t
3.8
40 60
4.2
300
5.8
Pressure SeaI
Bonnet-Cste
150
Pressure
Seal
Bonnet-Clobe
165
3
o make
up all
joints.
'
16
lt
cu.
ft.
density.
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
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A
. -f
w
fl\
F-:l
-2t"
---i
/-\
-L-t
(--r..}
\.u
z
F
z
J
'
WEIGHTS OF
PIPING
MATERIALS
Appendix
C:
Properties
of Pipe
2o5
2.875'o.D. 2/2"
Ywn
Boldface
type
is seight in
pounds.
Lightfece type
beneai,h
\r'eight is
weight factor
for
insulation.
Insulation thicknesses
and
weights
are
besed
on
everage
conditions and do
not
constitute
a
recommendatioD
for specific
thicknesses
of
materials-
Insula-
tion
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
dia-
tomaceous
earth
at
2i
lbs,'cubic
foot and the outer l:r|cr
at
11 lbs/cubic foot.
Insulation
weights
include
al-
lowances
for
wirc,
cemcnt,
can-
vrs,
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.
Valve
*eiftrts
are approxi-
mate- 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.
z
I
)
z
Temperature Range
'F
Magnesb,
Calcium
Combina-
tion
Fiber-
Sodium
,ffi
9+
i
${lit$
N-ls$
N
/A)
,4"1
,N
g 4
l-{
@
flt'
)
+€
|<IJ
()
z
I
z
.t
*
16
lb
cu.
ft.
density.
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
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rt?
uf
/\
{_0
{l}
L:-I
-{\
fl-\
ri\
{----fr
\iJ
8
z
F
F
z
B
206
Mechanical Design
of Process
Systems
3
tt
"tpr
B.boo" o.D.
WEIGIITS
OF
I'IPING
NIATERIALS
l cnrpentLurc Rcngc
"F
Magnesia
Calcium
(--oDlbi
r-
tron
Fiber-
Sodium
z
F
z
z
z
a
-
ffi
${rn$
Njs
qN
Boldface type
is
weight
in
pounds.
Lightface type beneath
weight is weight Jactot Jor
insuLation.
Insulation ihicknesses and
weights
are based
on
average
conditions and
do not
constitute
a recommendation
for specific
thicknesses
of materials. Insula-
tion
$eights are
based
on 85/p
magnesia
and
hydrous
calcium
silicate
at ll
lbs/cubic foot.
The
listed thicknesses
and weights
of
cornbinetion
covering
are
the
sums
of the inner layer of
dia-
iomrceous
eerth
at 21
lbs/cubic
foot
and the
outer
la]
e. at
11
lbslcubic foot.
Insul{rtion Ncights include
al-
lorvarrces for \\'irc, cenrent, can-
vas,.bands-
and
prlitrt,
but not
speclsL
suf
tace
hnrshes,
-
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-
mete.
Wben-
possible,
-dbtain
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.
/A
-11
,N
/9N
49 S
t<t
@
0
J{
Fs3
Nom.
Thick.,
In.
*
16
lb
cu. ft.
deDsity.
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208
Mechanical Design
of Process Sl
stems
4"
ptpn
4.boo'
o.D.
WEIGHTS
OF PIPING MATERIALS
'li,mtx'nrluro
I
rngo
"I
trlagnesia
Calcium
ComLirur-
iioIl
Iiber-
Sodium
z
k
o
7
F
z
1
/a)
tu
&?
h
:
,t
{l\
tr;:I
tr:JI
/\
\JJ
z
z
3
NrS
{Nj+ln}
N_ts
rx:w
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.
Insula-
tion 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
dia-
tomaceous
earth at
21 lbs/cubic
foot and the
outer ieter'at
ll
Ibs/cubic fooi,
Insulation
weights
includc
al-
lowances
fo wire,
cement,
can-
vas, bands
and
paint,
but
not
speciel
surlace
6nishes.
-
To find
the
weighl
of
cover;ng
on
flanges,
velves
or
fittings,
multiply
the
weight
frcior
by the
seight
per
foot
of
covcring
uscLl
on
str{righi
pipe.
Vrlve weights are
approri-
mate.
When
possible,
obtoin
$eights
from
thc
mxnufacturer.
Cast
iron
valve Ncights are
for
flanged end
valves
i
steel $eights
for
rveldinq
end
valves.
All flanged fitting,
flrnged
valve
and
flangc wcights
includc
the
proporbionxl
\\eiglrt
of
bolts
or
studs
to mrke
up
all
joinbs.
,.'Nl
/ ,l)
,41
N
/\
F<3
@
fi\
+<l
F<U
\\'stcr-Lhs/l
t
\om.
'l'hick.,
In.
Nom. T)rick.,In.
I
16 li cu.
ft.
density.
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
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Appendix
C: Properties
of Pipe
209
WEIGIITS OF PIPING
MATERIALS
5.56:J"
O.D.
5"
pge
on t5%
rot.
The
righrs oi
of die-
rl er
Di
.lurie
rl-
hut
noi
co\,enng
)r
DJ
rnc
lng
used
approxi-
\reights
flanged
r include
of
bolts
ll
ioints.
Schedule
No.
40
80
120 160
Wall
Designation std.
XS
xxs
Thickness-In.
.258 .500 .62'r
Pipe- Lbs/ Ft, t4.52
20.78
27.M 32.96 38.55
Water-Lbs/Ft
8.66
7
.89 7.09
6.
J3
5.62
ul
,a
g.I/
zf\
F li
E4\
o
f'+
3 4/4-
LJ---.D
{---J--r
\tJ
L.R.,90" Elbow
14.7
1.3
21
1.3
S.R.
C0"
Elbow
9.8
.8
13.7
.8
L.R.
45'
Elborv
7.3
.5
r
0.2
.5
15.6
.5
t7
.7
.5
Tee
t9.E
1.2
26
1.2
39
1.2
43
Laterel
3l
2.5
50
Reducer
6
.4
E.3
.1 .4
t4.2
cop
.7
.7
ll
.7
1l
.7
Tcmpereture ll.enge
"F
00-199 200-20s 300-399 400+s9 500-599 000-699
700,;9c 800-Ec3
900-999
1000-1009
1100,1200
Fiber-
Z Sodium
9
Silicate
Nom.
Thick.,In.
1 1%
2
2ra
2%
3r/t, 3rl 4
4
Lbs/Ft 1.86 2.92 2.92 4.08 6.90 8.41
E.41 10.4
10.4
F-
B
tion
Nom. Thick., In.
2ra
3
3tl
3ti
4
4
Lbs/Ft
7.01 9.30
I1.8 I1.8
14.9 14.9
85%
Iagnesia
Calcium
Nom.
Thick.,In.
I
I
|
1,t;
11,.i
2% 2%
3 3
4
4
Lbs/Ft
2.34 2.34 2.34
3.76
9.31
9.31 14.31
14.37
,ffi
O
-'r-
i
sli19
N-l,Ns
El:::lr$F
Pressure
Rctiltg
psr
Casi,
Stecl
Boldf&ce type is
$eight
in
pounds.
Lightf.rce type
benerth
rvcight
is rveight factor ior
insulrtion.
Insuiation
thicknesses
and
\reights.rre
brsed on
rverage
condirions and do
not
constitute
3 rocommendrtion
for
specihc
thicknesses
of materials.
lnsuh-
tion
wcights
rre
brsed
on t5%
mrgnc-.ia
antl hydrous crlcium
silicatc at
11lbs,/cubic
foot.
The
listed
thickncsses
3nd rreighls oi
combination
covering
lrre
lhe
-cums
of the
inner later
of
dir-
tomrceous
errih
rt
2I
lbs cubic
foot
end the outer
irl er
Dt
ll
lbs/cubic foot.
Insulation
\\0ighis inclurie
rl-
lorvances
for
\\'ire,
cement, crn-
vns,
bends
xnd
p.rint,
hut not
soecial
surfxco
linishes.
1o
hnd
tlrc
$Lrglrt
ol
coverlne
on
llenges, lll\'fs or
littings,
muitiplt thc
\reight
fsctor bl
th.
rveight
per
foot o[
covering
used
on,str.riqht
t,ifo.
\' ive \\'.rqh is rrc
x||ro\l-
mrtc.
\\-hen
possiblc,
oblarn
weiglrts fronr the mllnufrcLurer-
C.rst
iron
vrlve
rvcishis
l|re fol
fluged end
vrlves;steel
\reightl
for
$cLdirrq
end
vlrlvcs.
,\ ll
fianee(l
fittiDs,
flanged
vol\c .rn.l ILrngc
wprgl,ts includ€
tl,c
t,rol,ortionxl
\eight
of bolt
or
siuds to make
up all
joints
125 250
i50
300 400
600 s00
1500
2|rc/..)
Screu
ed
or
Slip-On
20
1.5
32
1.5
l8
1.5
l
5
1.5
73
1.5
100
1.5
162
1.5
259
1.5
'|r,\'elLling
Ncck
22
1.5
49
713
1.5
103
162 293
1.5
Lap
Joini
18
1.5
32 7l
98 168
1.5
Blind I.5
37
t.5 l 5
39
1.5
50
1.5
78
104
1.lr
172
1.5 1.5
0
/a
F ,an
|
/,$
3,\
z
Et\
E
II'
Y
S.R.
90"
Elbo*
58 94 80
t l3
4.3
t23
205
268
4.8
435
5.2
L.R. 90'
Elbow
68 105
9l
t2a
45" Elbow
51
3.3
E3
3.8
66
3.8
98
t23
4
130
350
Tee
90 t45
6.5
ll9
0.4
t72
6.4
179
6.8
304
7
415 665
1-{
-
FdJ
JiLII
;hJ
+<i
rc
Flanged
Bonnct
Cet,e
138 264
7.9
150
4.3
4.9
3r0
455
5.5
615
6
1340
7
Flanged Bonnet
Globe
or
Angle
138 )47
8
ls5
2t5
5
5.2
515 950
6
Flanged Bonnet
Check
llE
7.6
210
E
110
4.3
165
5
1E5
5
350 560
6
1150
7
Pressure
Scal
Bonnet-Cate
350
3.1
520
3.8
865
4.5
Pressure Seal
Bonnet {ilobc
280
4
450
4.5
'
16 lb
cu.
ft. density.
up
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2'10
Mechanical
Design
of
Process Systems
6"
pr""
6.625,
o.D.
WEIGHTS
OF PIPING
X{TTERIALS
Tempcraturc
Ilange
"F
Magnesia
Calcium
Combins-
t)on
Fiber*
Sodium
u/
AX
w
{T\
LilI
t---1
\JJ
z
'.
z
F
sq-,$
#r|&
N-S
dISrsS
-Xl
t#
rA
kL
,N
/>
lt'
'{
l-dl
@
ru
1-<i
rc
z
t
z
z
z
z
.|
Boldface
type
is weight in
oounds.
Liehtiace
trpe benea,th
iveight. is
-
tleight
'
iactor
for
Insulation
thichnesses
and
weights are
based
on average
conditions and do
not
constitute
a
recommendation
for
specific
thicknesses
of
materials.
Insula-
tion
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
dia-
tomaceous
es,rth
at
21
lbs/cubic
foot
and
the
outer layer
at
l1
lbs/cubic
foot.
Insulation
$eights include
aI-
Iowrnces
for
\aire,
cement, can-
vas,
bands
and
paint,
but not
special surface
finishes.
To
find
the
weight of covering
on
flanges, valves or
fiLtings,
multiplt; the
weight fxctor
bl the
rveight
per
foot of
covering used
on
straight
pipe.
Valve ueights xre
sppro\i-
mete.
When
possible, obtrin
weights
from ihe
mrnuf&cturer-
Clst
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.
\\'eter-Ils/Irt
*
16
lb
cu. ft. density.
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,qR
Appendix C: Properties of
Pipe
211
WEIGHTS
oF
PIPING
MATERIALS
8.625.
o.D.
8''
"T"e
2
i.
z
B
2
F
-
z
2
F
t'-
r_ j
w
{t}
E:I
,4\"
A
--l-r
\tJ
Temperature
Range
'F
Magnesia
Calcium
Combina,-
tron
Fiber-
Sodium
Boldfnce
tlpe
js
Neiaht in
pounds.
Lighilirce
tvpe bineeth
Neight.
is veight Jactor
lor
Insulation
thicknesscs
cnd
\reights
are based
on average
conditions and do not
constitute
a recommendation
for specific
thicknesses
of materiols. Insula-
tion
rveights
are
based
on
85%
magnesio
and
hJ'drous
calcium
silicate
at 11lbs/cubic foot. The
Iisted
thicknesses
aod
$'eights
of
combinetion covering
are
the
sums of the inner layer of dia-
tomaceous
earth
at 21
lbs/cubic
foot
and
the
outer la]'er at
11
lbs/cubic
foot.
,
Insulation
rveights
include al-
lowances lor
wDe,
cemenl,
c&n-
vas,
bands and
paint,
but
noi
soecial surface finishes.
'
-
To find
the weight
of covering
on
flanges, valves
or
frttings,
multiply
the weight f&ctor by
the
Neight.per folt
of
covering used
on
slrarghl
prpe.
Yalve rveights
are approxi-
mcte. lYhen
possible,
obtcin
lleights from
thc
manufrcturer.
Cast
ilon
valve
weiehts
are
for
flanged
end valves; sGel
\\'eights
Ior
seldinq
end
valvcs.
AII flcneed
fitting,
flanged
valvc
and llangc
rveights
include
tlrc
nroDortioDrl
\eiqht
of bolts
or stu,li
to make ut all
joints.
z
a
7
d
ffi$
ffi
$\
is
d
<,fs$
A
/A
A
gilq
j.43
t4
r\
+<i
FsO
Nom.
Thick.,In.
|
16
lb
cu.
ft.
density.
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
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212 Mechanical
Design of
Process
Systems
10"
prpn
lo.zbo,
o.D.
IVDIGIITS OF
PIPING tr{ATDRIALS
lrmpcr:rturc
lirnge'F
Magnesia
Calaium
Combina-
iion
Fiber-
Sodium
(,
z
(,
z
z
F
P
z
z
.
z
Ih
fl\
L:J
.4'4^
L:-
-l_,
\]J
ffi$
qFl
rr$
N-|s
ryrTqJr
Boldfece t{pe is l\'eight in
pounds.
Lightface
t1'pe
benerth
*eight
is rveight
foctor
ior
insulation.
Insulation thicknesscs and
rveights are based
on average
conditions and do not constit,ute
a
recommcndetion
for specific
thicknesscs
of
materials.
Insula-
tion 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 dia-
tomaceous
earth at 2I lbs/cubic
foot and
ihe outer
lsyer
at
11
ibs/cubic
foot.
Insr-rlation Neights
include
al-
lowances
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
rr
ciglrts
from
thc
nrnnufrcturcr.
(lxst
iron
vrlYc
\\'ciglrts
arc
for
lllngcrl
cnd
vrlrcs:
stcoi
teights
fol
lcldilg cnd
vrlves.
-\)l
fl.rngcd fitting,
flnngcd
'rlvc : nd
l]3nge \\'eights include
tlru
prolroriioDxl scislrt
of
l)olts
or
studs
to mrkc
up:rlL
joints.
Ai
/AJ
,-11
,N
/>
lN'
'{
tHt
@
ff1
+<i
f<o
\om.
Thick.,
ln.
\Yelding
Neck
*
16
lb
cu.
ft.
derxity.
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
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WEIGHTS
OF
PIPING
MATERIAI,S
Appendix
C: Propenies
oi PiPe
213
rz.lso'o.D.
12"
Pwr:
30
Schedulc
)io.
|
20
40
60
80
100
120
1{0
Wall
Designation
sid.
XS
Thickness-In.
|
.250
.330
.375
.406
.500
.562
.687
.843
1.000
l-J
Pipe-Lbs/Ft
33.3E
43.8
49.6
53.5
65.4
EE.5
t07
.2
r25.5
139.7
t58
3
Wsier-Lbs/Ft
5l .10
49.7
49.0
48.5
47
.O
46.0
44.0
4
r.6 39.3
{,)
IJJ
f4
.
(_ -f
2n^
F
flIT
Eji1
o
t-
-:
-t
i />"
3tr-
d_l\
L.R. 90'
Elbow
119
3
t51
3
3
S.R.
90"
Elbow
80
2
104
2
L.R.
45" Elbow
60
7E
181
;
1.o
l
Tee
r32
2.5
167
360
2.5
Lateral
1E0
5.4
273
Reducer
33
,|
44
'|
9,1
cap
30
3E
E9
1.5
Temperature
Range
"F
100-199
200-299
300-399
400-49S
500-5s9
600-699
700-799
800-E99
900-999
1000-1099
1100-1:to
Nom.
Thick.,
In.
1)4
114
2
2t/4
3
3
3rlt
4
4
4%
z Calcium
9 silicate
,-
s|
Combina-
;
iron
z
Lbs/Ft
6.04
6.04
8.13
10.5
t2.7
12,1
15.r
17.9
17.9
20.4
20.4
Nom.
Thick.,In.
3
3%
4
4
414
1)i
Lbs/Ft
17.7
21.9
26.7
26.7
31.1
3l,
r
Fiber-
Sodium
Nom.
Thick.,In.
t%
1rt
1r/1,
l1/r,
2\/r,
216
4
4
5
c
Lbs/Ft
14.20
14.20
24.&
4.64
32.&
32.40
,ffi
;+
z #rils
'$$js
{N
Pressure
Rating
psr
Cast
ffi
125
250
150
300
400
600
900
1500
|
2500
Screwed
or
Slip-On
71
1.5
r37
|
72
|
r44
1.5 |
1.5
|
1.5
164
1.5
261
r.o
3EE
820
1611
l.c
Welding
Neck
88
I
163
1.5 I 1.5
212
1.5
434
1.5
843
1.5
1919
1.5
Lap
Joint
72
|
164
1.5
|
1.5
ta7
1.5
286
1.5
433
902
1.5
1573
t.5
Blind
96
177
lllE
r.5 |
1.5
209 261
1.5
341
475 92E
1775
I.D
a4
a
lAl
,
/..4
A,N
I /}
z@
E IP
'{
S.R.
90'
Elbow
265
5
453
5.2
345
5
509
5.2
669
El5
5.8
t474
6.2
L.R.
90' Elbow
6.2
6.2
485
6.2
624
6.2
159E
6.2
45' Elbow
235
4.3
383
2E2
414
4.3
469
4.5
705
4.7
1124
4.8
Tee
403
6E4
7.8
5r3
754
7.4
943
8.3
1361
a.7
r92E
s.3
Flanged
Bonnet
Gate
6E7
7.8
1298
8.5
635
4
1015
5
1420
5.5
215s
7
2770
7.2
4650
8
Fhnqed
Bonnet
Globi
or
Angle
808
9.4
1200
9.5
7t0
5
1410
Flanged
Bounet
Checlc
674
9..1
ll60
9.5
560
720
1410
7.2
2600
8
3370
8
Pressure
SeeI
Bonnet-Gate
1975
2560
6
45r5
7
Pressure
SeaI
Bonnet-Globe
*
16
lb
cu,
fi.
densrty.
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
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214
Mechanical
Design of Process System:
14"
,trr.
14'o.D.
WEIGHTS
OF
PIPING
]IATERIALS
Tcmpcrature Range
'F
Alagnesia
Calcium
Conlbina-
tion
z
|.
z
t
z
F
t
z
1
z
z
{.f
t
/)
fl\
fJJ
-t
c---r---l
\L"J
ffi
S{r-rM
N]s
{N
Boldlace
l\'pc
is
Ncight
in
pounds.
Lightface
tl
pc
l)eneath
*eight
is lYcight
lactor
for
insulation.
Insulation
thicknesses
and
$eights are based
on
lverage
conditions
and
do
not constitutc
a recommendation
for spccific
thicknesses of
rnaterials. Insula-
tion $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
dia-
tomaceous
e:irlh at
21
lbs/'cubic
foot and the outer la] er at
11
lbs/cubic foot.
Insulation
\reights include
al-
lorvances for lvire,
cement,
can-
vas, bands and
ptint,
but
not
special su
ace finishes.
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.
Valve
s
eights are
spnro\i-
mate. 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,
/.4
--ll
,4
,N
i>
0,
.{l
ru
@
0
+<i
FSO
Nom. Thick.,In.
Nom.
Thick.,In.
*
16
lb
cu.
ft.
density
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
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il
tl
Appendix C: Prop€rties of
Pipe
215
WEIGHTS
OF
PIPING
MATERIALS
re"
o.o.
16t'
plpu
Boldfxce
tvDe
is
rveielrt in
pounds.
Lighifirc
tt
pe
benesth
teight
is rveight factor
for
insulation.
Insulrtiod
thicknesses
and
weiqhts
are
bascd
on averase
conditions
and do
not constituie
&
recommend&tiol
for
spccific
thicknesses
of
materials-
Irrsuh-
tion
weights
ere
bosed
on
85%
magnesir
and hydaous
cnlcium
silicate
&t ll lbs/cubic foot. The
listed
thicknesses
&nd \yeights oi
combiortion
covering
are
the
sums oI the
inner layer
oI
dia-
tomaceous
earth
at 2l
lbs/cubic
foot
and
the
outer layer at
rr rDs/cuDLc
ioot.
,
Instrlati<.rn
weights
irclude
al-
low&nces
Io $alrc, cement,
ca
vas,
bands
and
pcint,
but Dot,
specilll
surlace
fi nishes.
To find
the
weight of
coverbg
on
flanges,
v&Ives or
fittings,
multiply
the weight
frctor
by
the
r
eight
per
foot of covering used
on
str&ight
pipe.
Valve Neights are
approxi-
matc. 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.
S$
stjjs
$$l.M
qr\ssF
A
.A
A
B
@
i[I
@
t4
v
z
z
;
z
F
z
z
z
z
1
t
A.
lJj
i\
w
{T\
1-5:I
J,1
E=_:ir
t .+r
fl\
\iJ
Temperature
Ra.nge
'F
I\Iagnesia
Calcium
Combina-
tion
'ih.r-
Sodium
l 100-1200
Flenged
Bonnet
*
16
lb
cu.
ft.
density.
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216 Mechanical Design
of
Process
Sy:,rems
18"
plpr
18"
o.D.
WEIGI{TS
OF PIPING
MATERIALS
'fcnpcnturc
ll
Dgc
'I,'
Magnesia
Calcium
Combin.r.-
tion
Fiber-
Sodium
z
z
F
z
E
z
t-
Z
F
z
LLl
f^
'4r
fl\
H'
UL,
c.=-=I
IA
\JJ
ffi
ffi
Nl$
si)\r'|\s
Boltlface
tvne
is lcicht in
pounds.
Lig)rifrce
t5
pe
b-enerth
reiglrt. is
\cjght fschor
for
Instrlation
thicknesses
aod
rvciglrts
flrc
l,rsr:d
on r,vcrrge
conditions ltnrl do
not
(oustituta
a
r-ccommcndrtion
for specific
thicknesscs
of matcricls. Insula-
tion
\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
dia-
tomaceous
eorth
at 21
lbs/cubic
foot
and
the
outet laver at
11
lbs/cubic foot.
Insulation s'cights include al-
Iolanr:cs for \rirc,
cemcnt,
con-
ves,
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
\eight
pcr
foot of
covering
used
on
stroight
pipe,
Vrlvc
\rriqhts
rre aptrroxi-
mate.
\l'hen possil,le,
-dt,tain
lscights
from
the m$nufacturer.
Cast
iron valve \yciqhts
are
for
flanged
end
velves;
st-eel \\eights
Ior
welding end
valves.
All
flanged
fitting,
flanged
valve
and
flange
scights
include
thc
proDortionrl
\\ci(lrt
of
bolts
or
si,udi
to
meke
up
all
joints.
/'a
IA
rA
,N
/$
4444
@
iln
+<t
rc
a
Il,s
/
Iit
\om.
Thir,k.,
In.
\om. Thitk.,
In.
*
16
lb
cu.
ft.
deDsity.
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
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&Jj
Ih
\-.1-_t
{l\
r'-:
-'t
F4
, ^
*J----
z
F
i:
z
Appendix
C: Propen:*
:: l-
21
1VEIGIITS
OF
]'IPING
}I.\TDRI,\LS
20,,o.D
20" e-,rz
l{t)
3;9
Ll
'17
9
4l.:
'Icmpcraturc
Renge
"F
z
o
F
z
I{agnesia
Calcium
Combina-
tion
Fiber-
Sodium
2a.l
{-1-
1
Roldfrrce
tYpe
is
r..r:
: .:
poun(ls.
Lighthcc
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..
:.:
:,
.
.
\lrgllt
l)ff
iL_'r:
.: '
I
: _.
-
onstfrLigi,:r:
f.
\_rtlvc Li,:::.:.
.:.
-
nlrtr'. \\
'.1:
..
\fi{)its
ir,r:r :].- r..
,
-
(,Lst
ir,:r'. ....
:
--
.- :.-
43.r
fl:LrLgcrl
i r:
i
iot $r:Lli:-ir::- .. :
..
.\ll
:l:,r..r.
:
:
::
:
_' :
vrh-c
rrri i
::.,::r':
r.
::r
-.
tlrc
prorl:l:,:.1-
.::
:
::
or studi i1r ::r:i:
.: ; ,.-
.:
1-1.03
z
g
J
ffi
sm$
N+s
gr(\i.x$
z
F
(,
z
/A
/41
/,+
A\
/>
€4 4
@
fln
J-<f
rc
Pip€'-Lbs./I,t
\\'at.r Lbs/
I,t
300-3c3
100+cc
i00-;9u
1000-6e0
\om.
Thick.,In.
Pressure
Rnting
|
(last.Ir('n
psr
ll25 l2s
l'langed
tsonnet
Globe
or Anglc
*
16
lb
cu. ft.
deDsity,
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
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218 Mechanical Design
of
Process
Systems
24"
prpr.
24"
o.D. \T UIGI I1'S
OF
I'IPI\G
}IATEITIALS
Icnrpcrlturc llongc
'F
Magnesia
Calciun
Combinc-
tion
Fiber-
Sodium
Z
F
z
e
z
::
z
ui
f><
w
{T\
trJ-t
-/A
J]\
___-l____-
z
F
p
z
z
ffi
qN
trs
Njs
EN,fr\l
Boldfsce
troe
is weicht
in
pounds.
Liehifl.ce
tvDe
b;neath
ireight.
is
-
rreight'iactor
for
Insulation
thicknesses
and
$'eights
are based
on averaqe
conditions
and do
not, constitule
a
recommendation
lor
specific
thicknesses of
materials.
lnsuh-
tion ucights are
bused
on.85/e
m3gnesla ano nyorous
cstclum
silicate
at ll
lbs/cubic foot.
The
listed
thicknesses
and
lr'eiqhts
of
combinotion covering
arl
the
sums of the inner layer
of
dia-
tomaceous
earth
at 2l lbs/cubic
foot and the
outer
lsyer
at
ll
lbs,/cubic
foot.
d
,N
/D
tt,
.rl
IH
\Y.ltcr-Lbs/It
*
16
lb
cu.
ft.
density.
l=<[J
@
e
++J
rc
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{:
Appendix
C:
Properties
of Pipe
219
WEI(IHTS OF PIPING
MATERIALS
za"
o.o
26t'
prps
Llj
/\
Iit
{1\
E--I
J'\
-:I
-I_'
\"J
z
F
F
a
z
t
Temperature
Range
'F
Ilagnesia
z
Calcium
o
brUcate
F
3
combina-
3
tion
3;m::;-
Fiber-
Sodium
z
z
F
ffi
s.{-n$
N-is
fFq.s
Boldface
type is
weight in
pounds.
LiEhtface
type
be-
neath weight is weight
factor
for insulation.
Insulation
thicknesses
and
weights
are
based
on
average
conditions and do
not consti-
tute 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
thick-
nesses and weights of
combi-
nation
covering
are the
sums
of the
inner layer of diatoma-
ceous
earth
at
21
lbs/cubic
foot
and the outer layer
at
11 lbs/cubic
foot.
Insulation weights
include
allowances
fo wire. cement,
canvas, bands and
iaint,
but
not special surface ffnishes.
To-find the weiqht of cover-
ing on flanges,
v-alves
or
fit-
tings, multiply
ihe
weight fac-
tor
by
the weight
per.foot of
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
valve and flange weiRhts
in-
clude
the
propo-rtionaf
weight
of
bolts
or
studs to make up
all
joints.
| ,41
AI
/r+
,N
&"f
n'
l
u:-Ji
t<t
@
fi)
+<i
rc
*
16 Ib cu.
ft. deDsitt'.
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220
Mechanical Design
of Process
Syslems
28"
prpn
28-
o.D.
WEIGHTS
OF PIPING MATERIALS
Tempelature
Range
"F
nlagnesia
Calcium
Combina-
tion
Fiber-
Sodium
F
B
z
F
F
z
W
/4
{.J-f
Ih
t-+J
{1}
trJ:I
\IJ
ffi$
ffi
ds]-s
iN
,-a
A
tr'
.{
B---Jl
t=<3
@
0
+<i
rc
Boldface type is weight in
pounds.
Lightface
type
be-
neath weight is weight
factor
for insulation.
Insulation
thicknesses
and
weights
are
based
on average
conditions and do not co[sti-
tute 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
[nlck-
nesses
and
weights of combi-
nation covering are
the
sums
of the inner laver of
diatoma-
ceous earth
ai
21
lbs/cubic
foot
and
the
outer layer at
11 lbs/cubic
foot,
Insulation
weights
in€lude
allowances for
wire,
cement,
canvas, bands and
paint,
but
not special surface
finishes,
To find
the weight of
cover-
ing on
flanges, valves
or fft-
tings, multiply
the
weight
fac-
tor
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
for
flanged end
vslves;
steel
weishts forweldinsend
valves.
A-ll flanged fftting, flanged
valve and flahge weights in-
clude
the proportional weight
of
bolts
or
studs
to
make up
all
joints.
*
16
lb
cu.
ft.
derBity.
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F
z
'
t
z
z
u-f
Ih
fl\
E-I
4',q
E::l
L--r-----U
\L/
Appendix
C: Properties
of
Pipe
221
WEIGHTS
0I'
PIPIN(}
MATERIALS
Bo"
o.D.
30"
prpe
Boldface type
is weight
in
pounds.
Lightface
type be-
neath weight
is
weight factor
for insulation.
Insulation
thicknesses
and
weights ale
based
on average
conditions and do
not consti-
tute 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 thick-
nesses
and
weights
of combi_
nation covering are
the
sums
of
the
inner layer
of diatoma-
ceous 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 cover-
ing on
flanges,
valves
or
fit-
tinss. multiDl\.the weieht fac-
toibl
the rieight
per-foot of
covering
used on straight
piPe.
Valve weights are approxF
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 in-
clude
the
proportional
weight
of
bolts
or
studs
to
make
up
all
joints.
Ilagnesia
Oalcium
Fiber
SodiLtm
tlon
Temperature
Range
'F
G
@
CD+
ffi
E lr-'$
Nls
CI-]-\}
*
16
lb
cu.
ft. density.
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222
Mechanical
Design
of
Process
Systems
32"
prcn
sz,
o.D.
WEIGHTS
OF PIPING
MATERIALS
Temperature
Range
.F
Magnesia
Calcium
z
Silicate
{
uomDlna-
5
llon
Fiber-
Sodium
tu?
tg
f\
l_p
{T\
LJJ-
4',4
{-r-,
lr-f-r
\L/
z
7
,@$
3*
3
euls
Boldface
type is
weight in
pounds.
Lightface type be-
neath
weight is weight
factor
for
insulation,
Insulation thicknesses
and
weights are
based
on
average
conditions and do
not
consti-
tute a lecommendation
for
speciflc
thicknesses of mate-
rials. Insulation
weights
are
based on 857.
magnesia
and
hydrous calcium silicat€
at 11
lbs/cubic foot.The listed thick-
nesses
and weights of eombi-
nation covering are
the
sums
of
the
inner
laye of
diatoma-
ceous
earth
at
21
lbs/cubic
foot
and
the outer layer
at
11 lbs/cubic
foot.
Insulation
weiEhts
include
allowances
for
w-ire.
cement.
eanvas, bands and
paint,
but
not special surface
finishes.
To find the weieht of
cover-
ing
on
flanges, valves
or
fit-
tings,
multiply
the weight
fac-
tot
by
the weight
per
foot of
covering
used,on
straight
pipe.
v
alve
wergn s
are approxl-
mate.
When
Dossible. obtain
weights from- manufacturer.
Cast
iron valve weiehts are
for
flanged
end
vatves;
steel
\
eights
f
or
. rrelding
end
valves.
All
flanged
fitting,
flanged
valve and
flange
weights
in-
clude the
orooortional
weieht
of
bolts oi stluds to make-up
all
joints.
,-11
/A
.A
A
4
t"{3
@
m
+<i
t€
z
F
tr
z
lt
fsls
J: i.\\
*
16
lb
cu.
ft.
density.
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\
Appendix
C: Properties
of Pipe
223
WEIGHTS OF
PIPING MATERIALS
s4"
o.D.
34"
*trc
G
/.^
u-/
b
/-i\
rT
-r
2,1
c_=_=r
"t\
{---t-r
\IJ
z
F
I
z
F
Temperature
Range
"F
Magnesia
Calcium
Fiber-
Sodium
tion
2
{
z
z
{
z
3
a"
z
3
ffi
ffi
Njis
N
Boldface
type
is
weight
in
pounds.
Lightface
tYPe
be-
ireath
weight
is
weight factor
for insulation.
Insulation
thicknesses
and
weishts
are
based
on
average
conditions
and
do not
consti-
tute 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
thick-
nesses and
weights
of
combi-
nation covering
ale
the sums
of
the
inner
layer of
diatoma-
ceous earth at
21
lbs/cubic
foot
and
the outer
layel
at
11 lbs/cubic
foot.
Insulation
weights
include
allowances
for v/ire, cetnent,
canvas, bands
and
paint,
but
not special surface
frnishes'
To
find
the
weisht
of cover-
ine on ffanees,
v-aives or
fit-
tinles. 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 in-
clude
the
proportional
weight
of
bolts
or
studs
to
make
up
all
joints.
-l)
/A
AI
//
N
/>
+.{
@
m
+<i
rc
*
16
lb
cu. ft.
density.
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W
uj
f\
w
{T\
t=l
_/A
--i
A
\iJ
z
F
EI
3
224
Mechanical Design
of Process
Systems
36"
"t"u
s6" o.D.
WEIGHTS OF
PIPING MATERIALS
Temperature
Range'F
Fiber-
Sodirm
I\{agnesia
Ctllcitm,
ffi
6{fliN$
N-S
{raT,s
z
z
F
z
Boldface type is
weight in
pounds.
Lightface type be-
neath
weight
is
weight faetor
for insulation.
Insuiation thicknesses
and
['eights
are
based
on
averag:e
conditiods and do not consti-
tute a
recommendation
lor
specific
thicknesses of mate-
rials. Insulation
weights aae
based on
85% magnesia
and
hydrous calcium silicate
at 11
lbs/cubic foot.
The
listed thick-
nesses
and
weights of
combi-
nation covering are
the
sums
of
the
inner
layer of diatoma-
ceous
earth
at
21
lbs/cubic
foot
and
the
outer
layer
at
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
fit-
tirigs,
multiply
the
weig-ht
fac-
tor
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 in-
clude
the
proportional
weight
of bolts or
studs
to
make up
all
joints.
,tA
4t
/A
/t\
l|'
tl
6l
.lk{
l-<J
lli'l
+q]
@
Nom.
Thick., In.
Nom.
Thick,,
In.
*
16 ]b cu.
ft. derNity.
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Appendix
D
Conversion
Factors
225
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226 Mechanical Design of
Process Systems
TO
CONVERT
INTO
Alphabetical Conversion Factors
MULTIPLY
BY
TO CONVERT
tNt0
MULTIPLY
BY
gram-cal/sec
norsepower-hrs
watts
toot-lbs/sec
horsepower
kilowatts
waIls
watts/sq
in.
Cubic Cm,
cu ft
cu In.
cu meters
laters
pecks
pints (dry)
quarts (dry)
Abcoulomb
Acre
acres
acres
actes
acres
acre-feet
acre-feet
amperes/sq cm
amperes/sq
cm
amperes/sq
in.
amperes/sq
In.
amperes/sq
meler
arnperes/sq 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
un it
An8stron un
it
Angstrom unit
Ares
ares
Astronomical
LJnit
Atnospheres
atmospneres
atmospheres
atmospneres
atmospheres
atmospneres
atmospheres
atmospheres
Barrels
(U.S.,
dry)
Barrels
(U.S.,
dry)
Barrels
(U.S.,
liquid)
barrels
(oil)
oars
bars
bars
bars
bals
Baryl
Eolt
(US
Cloth)
BTU
8tu
Btu
Btu
Bttr
Btu
t'(U
Btu
8tu
Btu/hr
A
Statcoulombs
Sq. chain
(Gunters)
Rods
Square links
(Gunters)
Hectare
or
sq.
hectometer
sq
feet
sq
mete6
sq mrles
sq
yards
cu feet
gaflons
amps/sq In.
amps/sq
neler
amps/sq cm
amps/sq
meter
amps/sq cm
amps/sq In.
coulombs
faradays
gilberts
amp{urns/in.
amp{urns/neter
gilberts/cm
amp-turns/cm
amp-turns/meter
grlberts/cm
amp/turn5/cm
amp-turns/ in.
gilberts/cm
I ncn
Meter
l\4
icron
or
(i.,lu)
Acre
(US)
sq.
yards
acres
sq meters
Kilometers
Ton/sq. inch
cms
of mercury
ft
of water
(at
4'C)
In.
of mercury
(at
0"C)
kgs/sq
cn
kgs/sq
meter
pounds/sq
jn.
tons/sq
ft
B
cu. tnches
quarts (dry)
8al
tons
gallons (oil)
arrnospnetes
dynes/sq
cm
kgs/sq
meter
pounoS/sq
In.
Dyne/sq.
cm.
Meters
Liter-Atmosphere
ergs
foot-lbs
graln-caloneS
horsepoweahrs
ioules
kjlogram,calories
krlografi-meters
kilowatt-hrs
foot,pounds/sec
2.998 x
10ro
10
160
I x 1Cl'
.4047
43,560.0
4,O47.
1.562
x
10-:
4,840.
43,560.0
3.259 x 1Cl'
6.452
10.
0.1550
1,550.0
I0
I
6.452 x
10-.
3,600.0
0.03731
|.257
2.540
r00.0
t.257
0.3937
39.37
0.4950
0.01
0.0254
0.01257
3937
x
10-'
1x
10-ro
1x 10-.
.0247 |
I19.60
o.o247
|
100.0
1.495 x 101
.007348
76.0
33.90
29.92
1.0333
l0,332.
t4.70
1.058
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
10-'
o.2t62
Btu
/hr
Btu/hr
Btu
/hr
Btu/min
8tu/min
Btu/man
Btu/min
Btu/sq ftlmin
Bucket
(Br.
dry)
bushels
bushels
bushels
bushe,s
bushels
bushels
bushels
Calories,
gram
(mean)
Candle/sq.
cm
Candle/sq. inch
centares
{centiares)
Centigrade
centiglams
Centiliter
Centiliter
Centiliter
centiliters
centimeters
centimeters
centrmeters
cent,meters
centimeters
centimeters
centimeters
centrmeters
centimeter-dynes
centimeter-dynes
centimeter-dynes
centimeter-grams
centimeter-grams
centimeter-grams
centimeters
of mercury
centimeters
of mercury
centimeters of mercury
centirneters of mercury
centimeters
of rnercury
centimeters/s?c
centameters/sec
centameters/sec
centimeters/sec
centimeters/sec
centlmeters/sec
centimeters/sec
centimeters/sec/sec
centimeters/sec/sec
centarneters/s€c/sec
centimeters/sec/sec
Chain
Chain
Chains
(surveyors'
or
Gunter's)
circular
mils
circular
Inils
Circumference
circular
mils
Cords
Cord
feet
Coulomb
coutomos
c
B.T.U.
{mean)
Lambeats
Lamberts
sq meters
Fahrenheit
glams
Ounce
fluid
(US)
Cubic inch
drams
liters
feet
inches
kilometers
meters
m
es
mallimete6
m ils
yards
cm-grams
meter-xgs
po nd.feet
cm-dynes
rneter-kgs
poundJeet
atmospheres
feet
of water
kgs/sq meter
pounds/sq
tt
pounds/sq
in.
feet
/
min
feet/sec
kilometers/hr
xnotS
mete6/min
miles/
hr
miles
/
rn in
feet/sec/sec
kms/hr/sec
meters/sec/sec
miles/hrlsec
Inches
meters
yards
sq
clns
sq mils
Radians
sq Incnes
cord
feet
cu.
teet
Statcoulombs
faradays
0.0700
3.929 x
l0
'
0.2931
12.96
0.02356
0.01757
t7.57
o.r22r
1.818
x 10'
1.2445
2,150.4
o.03524
4.0
64.0
32.0
3.9685
x
10
I
3.142
.4870
1.0
(C'x9/5)+32
0.01
.6103
2.705
0.01
3-281 x l0-'
0.3937
10-
5
0.01
6.214 x lO-.
10.0
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
o.02237
3.728 x l0-r
0.03281
0.036
0.01
o.02237
792.00
20.12
22.O0
5.057
r
10-.
0.7854
6.283
7.854 x
10-'
8
l6
2.998
x
10'
1.036
x 10-'
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Appendix D: Conversion
Factors
(Continued).
Alphabetical Conversion
Factors
I ULTIPLY 8Y
TO CONVERI
IN?O
MULTIPLY
8Y
227
TO
CONVERT
INTO
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 feet
cubic feet
cubic
feet
cubic feet
cubic teet
cubic
feet
cubic feet/min
cubic
teet/min
cubic
teet/min
cubic teet/min
cubic feet/sec
cubic teet/sec
cubic
inches
cubic
inches
cubic
inches
cubic
inches
cubic inches
cubic inches
cubic inches
ctibic
inches
cubic inches
cubic
meters
cubic 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
coulombs/sq in,
coulombs/sq meter
coulombs/sq
cm
coulornbs/sq
meter
coulombs/sq
cm
coulombs/sq
in.
cu
feet
cu inches
cu mete6
cu
yards
Sallons
(U.
S. liq.)
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.
'iq.)
uarts (u.s.
liq.)
cubic
ftlsec
Sallons/sec
liters/sec
0
Gram
seconds
grams
tlers
meters
quadrants
radrans
seconds
64.52
10.
1,550.
l0-.
6.452
x t0-l
3.531
x
10-'
0.06102
10-.
1.308
x 10-'
2.542 x lO-'
0.001
2.113 x l0-
1.057
x
10-
0.8035
-
2A32O.O
t,72A.O
o.02832
0.03704
7.4a0s2
2432
59.84
472.0
0.t247
0.4720
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
2,1r3.0
1,057.
7.646
x
IO'
27.O
46,656.0
0.7646
202.0
764.6
1,615,9
807.9
0.45
3.367
t2.74
oramS
oramS
otams
Dyne/cm
oyne/sq. cm.
Dyne/sq. cm.
Dyne/sq. cm.
dynes
dynes
dynes
dynes
dynes
dynes
oynes/sq
cm
EII
Etl
Em,
Pica
Ern, Pica
*glsec
ergs
ergs
erSs
ergs
ergs
ergs
ergs
ergs
ergs
erg5/sec
ergs/sec
farads
Faraday/sec
faradays
faradays
Fathom
Iathoms
feet
leet
feet
feet
teet
feet
leet
feet
ol water
feet of
water
leet of water
Srams
grains
ounces
Erglsq.
millimeter
Atmospheres
Inch of Mercury at
0'C
Inch of Water at
4'C
grams
JOUTeS/Cm
joules/meter
(newtons)
kilograms
poundals
pounds
bars
Cm.
Inches
Inch
Crn.
Dyne
-
cm/sec
Btu
dyne-centimeters
foot'pounds
Srarn-calo
es
Sram-cm5
Joules
Kg-carofles
Kg-melers
kilowatFhrs
watt-houts
Btu/min
ft-lbs/min
ft-lbs/sec
kg-calories/min
kilowatts
microfarads
Ampere {absolute}
ampere-hours
coulombs
l{eter
feet
centimeters
krlometers
meters
rniles
(naut.)
miles
(stat.)
millimeters
mr
ls
armospnere5
an. of mercury
Kgs/sq
cm
0.01745
0.1667
2.778 x
10
1
r0.0
10.0
10.0
0.r371429
0.125
3.6967
1.7714
27.3437
0.0625
.01
9.869 x
10-'
2.953 x
l0-'
4.015 x
10-'
1.020
x
10
I
10-'
10-
'
1.020
x
10
6
7.233 r 10-5
2.248 x 10-'
10-6
114.30
45
.4233
1.000
9.480 x l0-rr
1.0
7.367 x
10-l
0.2389 x
10
'
1.020
x
10
3.7250 x
10-r'
10-
'
2.389 x
l0
-rl
1,020
x
10-'
O.277ax
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
lcr
26.4O
9.649
x
l0
1.828804
6.0
30.48
3.048
x 10
'
0.3048
1.645 x l0-.
1.894 x
10
.
304.8
1.2 x
lg
0.02950
0.8826
0.03048
degrees/sec fadians/sec
degrees/sec revolutaons/min
degrees/sec
revolltions/sec
oeKa8rams
gtams
dekaliters
liters
dekamete6
meters
Drams
(apothecaries'
or troy)
ounces
(avoidupois)
Drams
(apothecarieS'
or
troy)
ounces
(troy)
Drams
(U,S.,
fluid or apoth.)
cubic cm.
Dalton
days
decrgrams
deciliters
oecrmelers
degrees
(angle)
degrees
(angle)
degrees
{angle)
1.650 x l0-1.
86,400.0
0.1
0.1
0.1
0.01111
0.01745
3,600.0
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
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228 Mechanical Design
of
Process
Systems
TO
CONVERT INTO
(Continued).
Alphabetical
Conversion
Factors
MULTIPLY
BY
TO
CONVERT
INTO
MULTIPLY 8Y
teet of water
feet
of
water
feet of water
teet/m
in
feet/ min
feet/ min
feet/ min
feet/min
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
Foot
-
candle
foo pounds
foot-pounds
loot.pounds
foot-pounds
foot-pounds
foot-pounds
foot-pounds
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
Furlongs
turlongs
furlonBs
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
Sills
Grade
Grains
kgs/sq
meter
pounds/sq
ft
Pounds/sq
in.
cms/sec
teet/sec
kms/hr
meters/min
miles/hr
crns/sec
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
Btu
ergs
grarl1-calofles
np-nrs
JOules
kg'calories
kg-meters
kilowatt-hrs
Btu/min
foot-pounds/sec
hotsepowel
kg-calories/min
kilowatts
Btu/hr
Btu/min
horsepower
kg-calories/min
kilowatts
miles
(u.S.)
rooS
feet
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
pints
(liq.)
Radian
drarns
(avoirdupois)
304.8
62.43
0.4335
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
1.0
10.764
1.286 x 10-3
1.356 x 10'
0.3238
5.050 x l0-'
1.356
3.24
x 1.0
.
0.r383
3.766 x l0-'
1.286 x l0-3
0.01667
3.030
x 10
-5
3.24
x
lO-.
2.260 x l0-5
o.o77 17
1.818 x
l0-'
0.01945
1.356 x 10-'
o.125
40.0
660.0
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
grains
(troy)
grains
(troy)
Srains
(troy)
giains
(troy)
Srains/U.S.
gal
grains/U,S.
8al
grains/lmp.8al
Srams
Srams
Sralns
Srams
Srams
grams
grams
grams
grams
g,ams
grams/cm
Slams/cu
cm
gr-arns/cu
cm
Srams/cu
cm
grams/
liter
grams/
liter
grams/liter
grams/liter
grams/sq
cm
gram-calones
gram-calories
Sram-catones
Stam-catofles
Sram-calories
gram-calones
gram-caloraes/sec
gram-centimeters
gram-centimeters
gram-centrmeters
gram'centametels
grafi-centimeters
Hand
nectares
nectares
neclograms
hectoliters
hectometers
hectowatts
henries
Hogsheads
(British)
Hogsheads
(U.S.)
Hogsheads
(U.S.)
hoasepower
holsepower
horsepower
horsepower
(met.ic)
(542.5
ft
lb/sec)
horsepower
(550it
lb/sec)
horsepower
ho15epower
horsepower
horsepower
(boiler)
horsepo',ver
(boiler)
horsepower-hrs
horsepower-hrs
horsepower-hrs
horsepower-hts
norsepower-nrs
grains (avdp)
grams
ounces
(avdp)
pennyweight
(troy)
parts/million
pounds/million
gal
parts/rnillion
oynes
Slarns
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
pounds/cu
ft
parts/nillion
pounds/sq
ft
6tu
foot-pounds
horsepowet-hrs
kilowatt-hrs
watt-hr9
Btu/hr
Btu
ergs
joules
kg-cal
xg-meters
Cm.
acres
sq feet
grams
liters
meters
watts
millihenries
cubac ft.
cubic
ft.
gallons
(U.S.)
Btu/min
foot-lbs/min
foot-lbs/sec
horsepowet
(550
ft lb/sec)
horsepower
(metric)
(542.5
ft lb/sec)
kg.calories/min
kilowatts
watts
Btu/hr
kilowatts
Btu
ergs
footl
bs
gram.calol|es
JOU
leS
1.0
0.06480
2.0833
x
10-t
0.04167
17.118
142.56
14.286
980.7
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
-'
10.15
2.471
1.076 x 103
100.0
100.0
100.0
100.0
1,000.0
10.114
8.42184
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'
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
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Appendix D:
Conversion
Factors
(Continued),
Alphabetical
Conversion
Factors
TO
CONVERT
229
TO COI{VERT
tt{To
ilIULTIPLY
BY
INTO
HULTIPLY BY
ho.sepower-hrs
horsepower-hrs
horsepower-hrs
nours
houls
HundredweiShts
(long)
Hundredweights
(long)
Hundredweights
(short)
Hundredweights
(shortl
Hundredweights
(short)
Hundredweights
(short)
inches
inches
inches
inches
Inches
inches
inches of
mercury
atmospheres
inches
of
mercury
feet of water
inches
of
mercury
kgs/sq cm
inches
of
mercury
kgs/sq meter
inches
ot
mercury
pounds/sq
tt
inches of mercury
pounds/sq
an.
inches of water
(at
4'C) atmospheres
inches of watet
(at
4'C)
inches
of
mercury
inches of water
(at
4'C) kgs/sq cm
inches of
water
(at
4'C)
ounces/sq
in.
inches
of water
(at
4'C)
pounds/sq
ft
inches
of water
(at
4'C)
pounds/sq
in.
International
Ampere
Ampere(absolute)
InternationalVolt
volts(absolut€)
Inte.nationalvolt
Joules(absolute)
lniernational
volt Joules
kg.calories
l(g-meters
kilowatt-hrs
qays
pounds
tons
(long)
ounces
(avoirdupois)
pounos
tons
(metric)
tons
(long)
I
centimeters
meIels
miles
millimeters
mils
yaros
641.1
2.7X7 x lU
o.7457
4.167 x
10-r
5.952
x l0-r
t12
0.0s
t600
100
0.0453592
o.0446429
2.540
2.540x
10-t
1.578 x 10-5
25.40
1,000.0
2.77a x
rO-'
0.03342
0.03453
345.3
70.73
o.4912
2.458 x
10-
0.07355
2.540
x
l0-1
0.5781
5.204
0.03613
.9998
1.0003
l-593
x
10-''
9.654
x
l0'
kilograrns/sq
cm
kilograms/sq
cm
kilograms/sq cm
kilograms/sq rneter
kilograms/sq
meter
kilograms/sq meter
kilograms/sq meter
kilograms/sq
meter
kalograms/sq meter
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
kilolines
kiloliters
kilometers
kilometers
kilometers
kilometers
kilometers
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
kilowatt-hrs
knots
knots
l(nots
knots
inches of mercury
pounds/sq
lt
pounos/sq
In.
atmospheres
oars
teet ot water
inches ot mercury
pounds/sq
ft
pounds/sq
in.
kgs/sq meter
Btu
foot-pounds
hp-h.s
joules
kg-meters
kilojoules
kilowatt-hrs
Btu
foo pounds
JOUIeS
kg-calories
kilowatt-hrs
liters
centimetels
{eet
inches
meterS
miles
millimeters
yards
cms/sec
feet/min
teet/sec
knots
meters/nin
miles/hr
cms/sec/sec
ft
/sec/sec
meters/sec/sec
miles/hrlsec
Btu/min
foot-lbs/min
foot-lbs/sec
norsepower
kg-calories/min
Btu
foot-lbs
24.
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
l0-'
10.
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'
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
0.6214
lCl'
1,094.
27.74
54.68
0.9113
0.6214
27.74
0.9113
0.2774
0.6214
4.426
\ W
737.6
1.341
14.34
1,000.0
3,413.
3.600
x 10r'
2.655 x 10.
JOUIeS
joules
joules
ioules
joules
joules
joules/cm
ioules/cm
joules/cm
.loules/cm
ioules/cm
Btu
9.480
x
10-'
ergs
107
footpounds
0.7376
kg-calories 2.389
x
l0-'
kg-meters 0.1020
watlhrs 2.77Ax lO-'
grams
1.020
x 10.
dynes
10'
joules/meter(newtons)
100.0
poundals
723.3
pounds
22,44
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
K
dynes 980,665.
grams
1,000.0
joules/cm
0.09807
joules/meter(newtons)
9.807
poundals
70.93
pounds
2205
tons
(lond
9,842 x 10-'
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
oynes
980,665
atmospheres
0.9678
feet
of
water 32.81
gram-calories
859,850.
horsepower-hrc
1,341
joules
3.6
x
lcl.
xg.carofles
5bu.5
k8-meters
3.671
x
10'
pounds
ot water
evaporated from and
at212'F.
3.53
pounds
ot water raised
frcm62"
to 212"
F.
22.75
feet/hr 6,080.
kilometers/hr
1.8532
nautical
miles/hr
1.0
statute
miles/hr
1.151
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
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Mechanical Design
of
Process
Systems
(Continued).
Alphebetical Conversion
Factors
TO
CONVERT INTO
MULTIPLY
BY
TO
COI{VERT
INTO
IT.IULTIPLY BY
230
knols
knots
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
maxwells
megaltnes
megohms
megohms
fieters
meters
metets
meters
metels
meters
meters
meters
metets
meters/m,n
meters/man
meters/mrn
meters/min
metels/min
meters/min
meters/sec
mete6/sec
meters/sec
meters/sec
mere6/sec
metels/sec
meters/sec/sec
meters/sec/sec
mete6/sec/sec
mete6/sec/sec
meterkilograms
meteFkilograms
meteFkilograms
microfarad
micrcgrams
micrchms
yards/hr
feet/5ec
L
miles
(approx.)
Miles
Kilometers
gausses
Sausses
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
tl
kilolines
webels
maxwells
microhms
ohms
centimeters
leet
anches
kilometers
miles
(naut.)
miles
(stat.)
millimeters
yards
cms/sec
feet/min
teet
/sec
kms/hr
knots
miles/hr
feet/ m in
feet/sec
kilomete15/hr
kilometers/min
miles/hr
miles/min
ft/sec
/sec
kms/hrlsec
rniles/hrlsec
cm-dynes
cm-grams
pound-feet
farads
glams
megohIns
2,027.
1.589
5.U
5.9
x
10rr
9.46091
x
10"
1.0
0.1550
1.550
x
l0-'
l0-l
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
0.001
10-l
1Cl.
10u
10.
100.0
39.37
0.001
5.396
10-1
6.214
x 10-'
1,000.0
1.094
1.179
1.567
3.281
0.05458
0.06
0.03238
0.03728
195.8
3.281
5,O
0.06
0.03728
r00.0
3.281
9.807 x 19
lCr'
l0-.
10-.
10-rl
microhms
micrcliters
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)
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
mil-feet
milliers
Millimicrons
Milligrams
milligrams
milliSrams/litet
millihenrie5
milliliters
millimeters
millimeters
millimeters
millimeters
millimeters
millimete6
millimeters
millimelers
million
gals/day
mils
mils
mils
mils
mils
miner's
incheg
Minims
(British)
Minims
(U.S.,
flu;d)
minutes
(angles)
minutes
(angles)
minutes
(angles)
minutes
(angles)
myriagrams
myriameters
myriawatts
ohms
liters
mererc
feet
kilometers
meters
miles
(statute)
yards
centametels
feet
inches
kilometers
meterc
miles
(naut.)
yards
cms/sec
leet/man
feet/sec
kms/ht
kms/min
knots
meters/min
miles/min
cms
/
sec/sec
feet
/
sec
/sec
kms/hr/sec
meters/sec/sec
cms/sec
teet/sec
kms/min
knots/min
miles/hr
cu
inches
kiloSrams
meters
g|a
Ins
grams
parts/million
henries
liters
centimetels
feet
inches
kilometers
meters
miles
mrls
yards
cu
ftlsec
centimeters
feet
anches
kilorneters
yaros
cu
ft/min
cubic
cm.
cubac cm.
oeSrees
quadrants
radians
seconds
kilograms
kilometers
kilowatts
10-.
10-.
I
x
10-'
6,04O.27
1..'J5
1,853.
1.1516
2,027.
1.509
)(
1Cl'
5,280.
6.336
x 10
r.609
1,509.
0.8684
1,760.
M.70
8&
t,467
1.609
o.o26a2
0.8684
26.42
0.1667
44.70
L.467
1.509
0.4470
2,642.
88.
0.8584
60.0
9.425
x
10-'
1,000.
I
x
lo-t
0.01543235
0.001
1.0
0.001
0.001
0.1
3.281
x 10-t
10-.
0.001
6.214
x 10-'
1.094
x l0-'
1.54723
2.540 x
10-t
8.333
x
10-
0.001
2.540
x
10-'
2.77Ax
lO-'
t.5
0.059192
0.0516r2
0.01667
1.852 x 10-'
2.909
x l0-.
60.0
10.0
10.0
10.0
8.686
1x105
N
decibels
Dynes
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232 Mechanical Design
of
Process
Systems
TO CONVERT
INTO
(Continued).
Alphabetical
Conversion
Factors
MUI.TIPLY
BY
TO
COI{VERT
INTO
MULTIPLY
BY
revolutions/min/min
revolutions/min/min
revolutions/min/min
revolutions/sec
revolutions/sec
revolutions/sec
revo,utions/sec/sec
revolutions/sec
/sec
revolutions/sec/sec
Rod
xoo
Rods
(Surveyors'
meas.)
rods
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
square feet
square
Inches
square
Inches
square
Inches
square
Inches
square
inches
square
k'lometers
square
kilofleters
square
kilometers
square
kilorneters
square
kilometers
square
kilometers
square
kalometers
square
meters
square
meters
square melers
square
meters
square
meters
square
meters
square
meters
square
miles
square
miles
square
miles
square
mrles
square
millimeters
square
millimeters
square
millimeters
square
millimeters
square
rn ils
radians/sec/sec
revs/sec/sec
oegrees/sec
radians/sec
radians/sec
/sec
revs/min/min
revs/man/sec
Chaan
(Gunters)
Meters
yards
feet
s
gra,ns
minutes
quaoranls
radians
Kilogram
Pounds
Steradians
circular
lnils
sq feet
sq rnches
sq miles
sq
millimeters
sq
yards
acres
circular
mils
sq
cms
sq inches
sq mrles
sq millimeters
sq
yaros
circu lar
mils
sq cms
sq teet
sq millimeters
sq mils
sq
yards
acreS
sq
cm5
sq
ft
sq mrles
sq
yards
sq cns
sq
feet
sq miles
sq millimeters
sq
yards
actes
sq feet
sq xms
sq meters
sq
yards
circular mils
sq
cms
sq feet
sq inches
circular mils
1.745
x
10-r
0.01667
2.778 x 10-.
360.0
6.283
50.0
3,600.0
60.0
.25
5.029
20
2,778\ lO
.
0.01667
3.087 x 10-6
4.848 x l0-l
14.59
32.17
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
3.587 x
l0-r
9.290 x lCr
0.1111
1,273
x
106
6.452
6.944 x
l0-3
10.
7.716 x
10-.
247.1
10x
10.76 x 106
1.550 x 10'
106
0.3861
1.196 x
106
2.471 x lO-.
10.
10.76
1,550.
3.861 x 10-'
1Cp
1.196
640.0
27.88 x 10.
2.590
2.590 x 10d
3.098
x 106
1,973.
0.01
1.076 x 10-r
1.550
x 10-
1.273
square mrls
squate nrl5
square
yards
square
yards
square
yards
square
yards
square
yards
square
yards
square
yards
6.452 x 10-6
10-6
2.066 x 10-.
8,361.
9.0
't
,296.
0.8361
3.228
x 1O-,
8.361
x l0'
.39370
.003336
temperature
("F)-32
temperature
('C)
5/9
tons
(long)
kilog€ms
1,016.
tons
(long) pounds
2,240.
tons
{long)
tons
(short)
1,120
tons
(metric)
kilograms
1,000.
tons
(metric) pounds
2,205.
tons
(short)
kilograms
907.1848
tons
(short)
ounces 32,000.
tons
(short)
ounces
(troy)
29,166.65
tons
(short) pounds
2,000.
tons
(short)
pounds
(troy)
2,430.56
tons
(short)
tons
(long)
0.89287
tons
(short)
tons
(metric)
0.9078
tons
(short)/sq
ft
kgs/sq
meter
9,765.
tons
(short)/sq
ft
pounds/sq
in.
2,000,
tons
of
water/24
hrs
pounds
of
water/hr
83.333
tons
of
water/24
hrs
gallons/min
0.16643
tons of water/24
hrs
cu
ltlhr
1.3349
tempemture
("c)
+273
temperature
('c)
+
r7.78
temperalure
("F)
+460
Volt/
inch
Volt
(absolute)
watts
walls
watts
watts
Watts
(Abs.)
Watts
(Abs.)
watt'hours
watt-hours
watt-hours
watt'hours
watt-hours
watt-hours
watt-hou.5
watt-hours
Watt
(lnternational)
sq
cns
sq Inches
acres
sq cms
sq inches
sq meters
sq males
sq millimeters
T
absolute
temperature
('C)
1.0
temperature
('F)
1.8
absolute temperature
('F)
1.0
v
Volt/cm.
Statvolts
w
Btu/hr
Btu/min
eags/sec
foot-lbs/min
toot'lbs/sec
horsepower
horsepower
(metric)
kg-calories/min
kilowatts
B.T,U.
(mean)/man.
joules/sec.
Btu
erSs
foofpounds
gram-caloneS
horsepolver-hrs
kilogram-calories
kalogram-meters
kilowatt-hrs
Watt
(absolute)
kilolines
3.4129
0.05688
107.
44.27
0.7374
1.341
x
l0-1
1.360
x
10-
0.0t 433
0.001
0.056884
I
3.413
3.60
x
10'o
2,656.
859.85
1.341
x l0-1
0.8605
0.001
1.0002
1Cp
10,
8/9/2019 Mechanical Design of Process System Volume-2(Shell and Tube Rotating Equipment)-Keith Escoe
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Appendix
D:
Conversion Factors
2Sg
Synchronous
Speeds
Frcqusncy r
120
syncnronou3
sPc.o
- T;;Ei;;-
FIEQUEiICY
60.ycle
50
.y.lc
50 Gycl.
142.9
136.4
130.4
r25
t20
5.a
||t.l
t
o7.l
103.5
100
96.8
93.7
90.9
88.2
85.7
83.3
8r.l
78
-9
76.9
75
6
8
l0
l2
II
t6
t8
2l
26
28
30
32
31
36
38
10
3600
r800
1200
900
600
5r 4.3
150
400
360
327
.2
300
276.9
257
.1
210
225
2n.8
200
t89.5
r80
3000
t
500
1000
750
600
500
124.6
375
300
272.7
250
230.8
211.3
200
187.5
175.5
166.7
157
-9
150
| 500
375
300
250
214.3
187.5
166.7
t50
136.4
lt5.a
t 07. t
100
93.7
88.2
83.3
78,9
75
12
11
a6
18
56
60
62
61
66
58
72
71
76
80
171.1
|
63.6
|
56.5
l50
111
t38.5
133.3
128.6
t21.1
120
rr6.t
2.5
t0t. I
r
05.9
102
-9
t00
97 .3
91.7
92.3
?0
Courtely
Ingersoll-Rand
Co.
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234
Mechanical Design
of
Process
Systems
Temperature
Conversion
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.
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
to
d.gr..r
fobr.nhi.t,
thc
oniy€r
$ll
b.
fo'rnd in
the
column
on
thc
right.
C.ntigrodc Fohrenhcil
Centigrode
enlisrod.
C.ntlgrod.
5t.t
60.0
62.8
65.6
68.3
71.1
73.9
76.7
79.1
s2.2
85.0
82.8
90.6
93.3
96.1
93.9
100.0
t02
t04
t07
I
l0
ll3
I t6
I
l8
l2l
121
127
129
132
135
138
t{
143
lt6
l,a9
154
t60
t66
t71
177
182
t88
r93
t99
201
210
216
221
266
2e1
293
3ll
t20
-273.17
-a59.f
-268 -r50
-262
-aao
-257
-{30
-25t
-420
-216 -aro
-210
-,100
-231
-390
-229
-3r0
-223
-370
-2t8
-360
-212
-350
-207
-3{0
-20t
-330
-t96
-310
-190 -3ro
-t81
-300
-179
-290
-173
-2t0
-f69
-2f3
-168 -rro
-t62
-260
-157
-250
-tsf
-rao
-116
-230
-f10
-220
-t34
-210
-129
-2oO
-123 -r90
-I8
-tlo
-l
12
-tto
-107
-r50
-tot
-t50
-96
-lao
-90
-r30
-8{
-120
-79
-ll0
-73.3
-I00
-67
-S
-90
-62.2
-r0
-59.r
-56.7
-53
.9
-51
.l
-18.3
-15.6
-/2.9
-,40.0
-31.1
-3t
.7
-28
.9
26.1
formulor
ol
lh. .isht hoy oho
bc ured
(ony€rling
Ceotigrcdc
or
foh.enhcil
125.6
127.1
12r.2
r3l .0
r
32.8
| 34.6
| 36.4
| 38.2
l{0.0
l4r.8
t 13.6
I t5.4
117.2
149.0
t
50.8
152
.6
154.4
|
56.2
158.0
159.8
161 .5
163.4
165.2
167
.O
168.8
170.6
t72.1
171.2
't76.O
177
.8
t79.6
l8l .,a
I83.2
185
.0
186.8
|
88.6
|
90
.,4
192.2
194.0
| 95.8
197
.6
r
99.4
201 .2
203.0
204.8
206,6
208.4
21o.2
212
.0
221
230
239
218
257
Dcqree' Fohr.,
'F
=
fc
+
.ot
-.0
esr€e'
cent,'.=|et
+
,ot
-ro
=
|
et-r'r
Degreca KeMn,'K:'C
+
273.2
-75
-ro
-55
-50
- l
-50
a5
-40
-35
-25
-20
-ll
-t0
-159.1
-151
-136
-4t8
-100
-382
-361
-316
328
-292
-271
-256
-238
-220
-202
-181
-t66
-148.0
-t
30.0
-t
l2 .0
-t
03.0
91.0
-65.0
-75,0
-67
.0
-58
.0
-49.0
10.0
-31.0
-22.0
-t3.0
-4.0
.4.0
-20.6
-16.7
-t6.1
-15.0
-14.1
-13.t
-r3.3
-t2.8
-t2.2
-
.l
-10.6
-10.0
-8
.9
-8
.3
6.7
-6.1
-1.1
-3
.9
1.7
0.0
0.6
LI
1.7
2.2
3.9
4.1
5.0
5-6
6.1
6.7
8.3
8.9
9.1
10.0
l0 .6
23
-O
32.0
35.6
37.1
39 .2
al.0
t2.a
lt.6
16.4
18.2
50.0
5r.8
57 .2
59.0
60
.8
62.6
61.1
66.2
d8.0
69.8
71.6
73.1
75.2
77 .O
80.6
8?
.,{
81.2
86.0
82.8
89.6
9t.,(
93.2
95.0
96.8
98.6
100.,{
102.2
104
.0
105.8
to7
.6
109.1
l]1.2
113.0
114.8
| 16.6
118.,(
120.2
122.O
t23.9
.l
11.7
12.2
I2.8
13.3
t3.9
14.1
15.0
l5 .6
16.
r
t6.7
t7 .2
l, .8
|
8.3
l8 .9
I9..{
20.0
20.6
2t.r
2t .7
22.2
22.8
23.9
21.1
25.0
25.6
26.1
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200
205
210
212
215
220
225
230
235
240
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233
260
255
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Altitude
and Atmospheric
Pressures
Hs
Ab3.
Aooendix
D:
Conversion
Factors
235
Kelrq
H9 Abr.
PSIA
-5000
,{500
,{000
-3500
-3000
2500
-2000
-1500
-1000
t0,000
t5,000
20,000
25,000
30,000
35,000
40,000
15,000
50,000
55,000
60p00
20.000
80,000
90,ooo
t00,000
120,000
t,(0,000
160,000
180,000
200p00
220,000
2,{0,000
260,000
280,000
300,000
,(00,000
500,000
600,000
900,000
tp0o,ooo
1.200,000
1,400,000
1,600,000
l,8oo,ooo
2,000,000
-1526
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15S
-305
763
915
1068
1220
1373
l83l
2136
2111
2716
3050
6102
7628
9153
1o,679
12,201
13.730
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18,306
21,357
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27.159
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0
36,612
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73,221
79,326
85,128
91,530
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3500
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6000
7000
8000
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Mechanical Design
of Process
Systems
I
9
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Index
American
Society
of
Mechanical
Engineers. 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 limit
of, 59
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
degradation
flow
condition,
1
design of, reasons
for inefficiency,
1
flow,
erratic,
I
flushing of, 1
funnel
flow in,
1,
6,
8
hoop
pressure
in,
rnaximum,
6
hooper
angle,
3
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
piping
factor, 304
pneumatic gases
in, 7
pressure
vessels,
differences 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
stresses in, 13- 14
truss design, 18-20
wall friction
angle,
4-5
Blowers
and fans, 59
Bulk
solid
properties
bins, in, 1, 6
bulk density,
3,
6
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,
3
Centrifu
gal
compressors
actual, or inlet,
flow
rate,
80
advantages
of, 43-44
affinity laws, 50
237
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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
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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
standard
volumetric
flow,
59-60
mass
flow,
conversion
to
standard
volumetric
flow,
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
Fans
and
blowers,
59
Flow
of solids,
problems of, 1-3
Gas
compressibility
tactor,
44
general
gas
law,
44
specific
heat
ratio
for,
44
universal
gas
constant,
44,
59
Gear
pumps, 37,
40
Heat
transfer,
convection
of,
air
normal
to cylindeq
126
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
Non-Newtonian
fluids,
162
Nozzle
reinforcing
pads
disadvantage
of
pads,
170
pad
width,
maximum,
170
Nusselt
number,
125-126,
156
Petroleum
fractions
API hydrometer
for, 87-88
Plate-fin
heat
exchangers
advantages
of,
147
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24O
Mechanical Design of Process
Systems
applications
of,
99
disadvantages
of, 147
illustrated, 149
Kays
and
London
coefficients,
148
thermal shock
and fatigue, 148
uses of, 147- 148
vacuum brazing of, 148
Polytropic
compression
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
types of, 3l
uses
of, 31
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
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fr
lnder
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
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,
58
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
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
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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, 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 of, 115
McAdams correlation,
125
outside 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
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
reboiler,
99, l0l
kettle
type,
99
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
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 of,
129
tube
bundle, 99, 126, 128
flow area
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
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{
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
fot
103
vaporizer,
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,
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244
Mechanical
Design
of
Process
Systems
recommendations
for,
1
10
uses
of,
110
tube
joint
load
formulations,
113
tubes,
minimum
bend
radii,
109
stress,
allowable
compressive, I
12
tubesheets,
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