FLOW OF FLUIDS
THROUGH
VALVES, FITTINGS, AND PIPE
By the Engineering Department
I CRANEJ
©1988 -
Crane Co.
All rights reserved. This publication is fully protected by
copyright and nothing that appears in it may be reproduced,
either wholly or in part, without special permission.
Crane Co. specifically excludes warranties, express or implied, as
to the accuracy of the data and other information set forth in this
publication and does not assume liability for any losses or
damage resulting from the use of the materials or application of
the data discussed in this publication.
I~
CRANE CO.
100 First Stamford Place
Stamford, CT 06902
Technical Paper No. 410
PRINTED
IN
U.S.A.
('TWenty Fifth Printing-J991)
Reprinted 12/00 5000 HunterPacific
Bibliography
IR.A. Dodge & M. J. Thompson. "Fluid Mechanics";
McGraw-Hili Book Company, Inc .. 1937; pages 193.288.
and 407.
'H. Rouse. "Elementary Mechanics of Fluids"; John Wiley
&·Sons. Inc .• New York. 1946.
aB.F. Grizzle, "Simplification of Gas Flow Calculations by
Means of a New Special Slide Rule"; Petroleum Engineer.
September, 1945.
'H. Kirchbach, "Loss of Energy in Miter Bends"; Transactions of the Munich Hydraulic Institute, Bulletin No.3,
American Society of Mechanical Engineers, New York,
1935.
S"Dowtherm Handbook"; Dow Chemical Co., Midland,
Michigan, 1954; page 10.
6R.J.S. Pigott, "Pressure Losses in Tubing, Pipe, and Fittings"; Transactions of the American Society oj Mechanical
Engineers, Volume 72, 1950; pages 679 to 688.
7"Handbook of Chemistry and Physics", 44th Edition,
1962-1963, Chemical Rubber Publishing Co., Cleveland.
8R.F. Stearns, R.M. Jackson, R.R. Johnson, and c.A.
Larson, "Flow Measurement with Orifice Meters" iD. Van
Nostrand Company. Inc., New York, 1951.
'''Fluid Meters"; American Society of Mechanical Engineers. Pan l-6th Edition, New York, 1971.
IOR.G. Cunningham, "Orifice Meters with Supercritical
Compressible Flow"; ASME Paper No. 5O-A-45.
u"Air Conditioning Refrigerating Data Book-DeSign."
American Society of Refrigerating Engineers. 9th Edition.
New York, 1955.
aw.L. Nelson, "Petroleum Refinery Engineering"; McGrawHill Book Co., New York, 1949.
13Lionel S. Marks, "Mechanical Engineers Handbook";
McGraw-Hili Book Co., New York. Fifth Edition.
14"ASME Steam Tables" (page 298). American Society of
Mechanical Engineers, New York, 1967.
ISJ.B. Maxwell, "Data Book on Hydrocarbons"; D. Van
Nostrand Company, Inc., New York, 1950.
IOC.I. Corp and,R.O. Ruble, "Loss of Head in Valves and
Pipes of One-Half to Twelve Inches Diameter"; University
of Wisconsin Experimental Station Bulletin, Volume 9, No.
I, 1922.
17G.L. Tuve and R.E. Sprenkle. "Orifice Discharge Coefficients for Viscous Liquids"; Instrumen/s. November, 1933;
page 201.
18L.F. Moody, "Friction Factors for Pipe Flow". Transactions of the American Society of Mechanical Engineers.
Volume 66. November. 1944; pages 671 to 678.
I'A. H. Shapiro. "The Dynamics and Thermodynamics of
Compressible Fluid Flow"; The Ronald Press Company.
1953. Chapter 6.
2°V,L. Streeter. "Fluid Mechanics", 1st Edition, 195 L
UK.H. Beij. "Pressure Losses for Fluid Flow in 90 Degree
Pipe Bends"; lournal of Research of the National Bureau
of Standards. Volume 21. July, 1938
22"Standards of Hydraulic Institute", Eighth Edition, 1947.
13Bingham, E.C. and Jackson, R.F .. Bureau of Standards
Bulletin 14; pages 58 to 86 (S.P. 298, August. 1916)
(1919).
"T. R. Weymouth, Transactions of the American Society of
Mechanical Engineers. Volume 34, 1912; page 197.
uR. J S. Pigott. 'The Flow of.Fluids in Closed Conduits,"
Mechanical Engineering, Volume 55, No.8, August 1933.
page 497.
2·Emory Kemler, "A Study of Data on the Flow of Auids
in Pipes," Transactions of the American Society of Mechanical Engineers, Vol. 55, 1933, HYD-55-2.
FOREWORD
The more complex industry becomes, the
more vital becomes the role played by Huids
in the industrial machine. One hundred
years ago water was the only important f1uid
which was conveyed from one point to another in pipe. Today, almost every con:
ceivable fluid is handled in pipe during its
production, processing, transportation, or
utilization. The age of atomic energy and
rocket power has added fluids such as liquid
metals
i.e., sodium, potassium, and
bismuth, as well as liquid oxygen, nitrogen,
etc .... to the list of more common fluids
such as oil, water, gases, acids, and liquors
that are being transported in pipe today.
Nor is the transportation of fluids the only
phase of hydraulics which warrants attention now. I-Iydraulic and pneumatic mechanisms are used extensively for the controls
of modern aircraft, sea-going vessels, automotive equipment, machine tools, earthmoving and road-building machines, and
even in scientific laboratory equipment
where precise control of fluid f10w is required.
So extensive are the applications of hydraulics and fluid mechanics that almost every
engineer has found it necessary to familiarize himself with at least the elementary
laws of fluid flow. To satisfy a demand for
a simple and practical treatment of the
subject of f10w in pipe, Crane Co. published
in lq35, a booklet entitled Flow of Fluids
and Heat Transmission. A revised edition
on the subject of Flow of Fluids Through
Valves, Fittings, and Pipe \vas published in
Ig42.· Technical Paper No. 410, a completely new edition with an all-new format
was introduced in Iq57 In T.P. 410, Crane
has endeavored to present the latest available information on flow of fluids, in summarized form with all auxiliary data necessary to the solution of all but the most
unusual Huid flow problems.
From Ig57 until the present, there have been
numerous printings of Technical Paper No.
410. Each successive printing is updated,
as necessary, to reflect the latest flow in-
CRANE
formation available. This continual
updating, we believe, serves the best interests of the users of this publication
The fifteenth printing (Iq76 edition) presented a conceptual change regarding the
values of Equivalent Length "Lj D" and
Resistance Coefficient "K" for .valves and
fittings relative to the friction factor in pipes.
This change has relatively minor effect on
most problems dealing with How conditions
that result in Reynolds numbers falling in
the turbulent zone. l-lowever, for flow in
the laminar zone, the change avoids a significant overstatement of pressure drop. Consistent with this conceptual revision, the resistance to now through valves and fittings
is now expressed in terms of resistance coefficient "1<" instead of equivalent length
"Lj D", and the coverage of valve and fitting
types has been expanded.
Further important revisions included updating of steam viscosity data, orifice coefficients, and nozzle coefficients. As in
previous printings, nomographs are included
for the use of those engineers who prefer
graphical methods of solving some of the
more simple problems.
Insofar as general arrangement is concerned,
theory is presented in Chapters I and 2. . . . .
practical application to How problems in
Chapters 3 and 4 .... physical properties of
Huids and flow characteristics of valves, fittings, and pipe in Appendix A .... and conversion units and other useful engineering
data in Appendix B.
Most of the data on flow through valves and
fittings were obtained by carefully conducted
experiments in the Crane Engineering Laboratories. Liberal use has been made, however, of other reliable sources of data on this
subject and due credit has been given these
sources in the text. The bibliography of
references will provide a source for further
study of the subject presented.
CO.
Table of Contents
CHAPTER
CHAPTER 2
Theory of Flow in Pipe
Flow of Fluids
Through Valves and Fittings
page
Introduction .................................................................... 1-1
page
Physical Properties of Fluids ...................................... 1-2
Viscosity .................................................................... 1-2
Weight density ........................................................ 1-3
Specific volume ........................................................ 1-3
Specific gravity ........................................................ 1-3
Introduction ............................................................. .
2-1
Types of Valves and Fittings
Used in Pipe Systems ............................................. .
2-2
Nature of Flow in PipeLaminar and Turbulent.. .............................................. 1-4
Mean velocity of flow .............................................. 1-4
Reynolds number ...................................................... 1-4
Hydraulic radius ..................................................... 1-4
Crane Flow Tests
Description of opparatus used ...
Water flow tests.
Steom flow tests ..
General Energy EquationBernoulli's Theorem .................................................... 1-5
Relationship of Pressure Drop
to Velocity of Flow ..................................................... . 2-7
Resistance Coefficient K, Equivalent Length
Lj D, and Flow Coefficient C v ..................................... . 2-8
Measurement of Pressure.......................................
1-5
Darcy's FormulaGeneral Equation for Flow of Fluids ........................ 1-6
Friction factor .......................................................... 1-6
Effect of age and use on pipe friction.........
1-7
Principles of Compressible Flow in Pipe ................. . 1-7
1-8
Complete isothermal equation ....
Simplified compressible flowgas pipe line formula .............. .
1-8
Other commonly used formulas for
1-8
compressible flow in long pipe lines .....
Comparison of formulas for
compressible flow in pipe lines ......... .
1-8
Limiting flow of gases and vapors ....................... . 1-9
Steam-General Discussion .................................... .
1-10
Pressure Drop Chargeable
to Valves and Fittings ................................................ . 2-2
2-3
2-4
2-5
Laminar Flow Conditions
2-11
Contraction and Enlargement ..
2-11
Valves with Reduced Scats ..
2-12
Resistance of Bends
2-12
Resistance of Miter Bends
2-13
Flow Through Nozzles and Orifices
General data
Liquid flow ...
Gas and vapor flow ...
2-14
2-14
2-14
Maximum flow of compressible
fluids in a nozzle .................................................. 2-15
Flow through short tubes................................
2-15
Discharge of Fluids Through
Valves, Fittings, and Pipe
Liquid flow ............................................................ . 2-15
Compressible flow ......................................... .
2-15
CHAPTER 3
Formulas and Nomographs for Flow
Through Valves, Fittings, and Pipe
CHAPTER 4
Examples of Flow Problems
page
Introduction ............................................................... 3-1
Summary of Formulas ......... .
................ ... 3-2 to 3-5
Formulas and N omographs
for Liquid Flow
Velocity.....
........................... 3-6
Reynolds number; friction factor for
clean steel and wrought iron pipe ................... 3-8
Pressure drop for turbulent flow..........
3-10
Pressure drop for laminar flow........
3-12
Flow through nozzles and orifices................
3-14
Formulas and Nomographs
for Compressible Flow
Velocity ......................................... .
3-16
Reynolds number; friction factor for
clean steel pipe .............................. .
3-18
Pressure drop ..................
..................... .
3-20
Simplified flow formula ...................................... .
3-22
Flow through nozzles and orifices ....................... . 3-24
page
Introduction ....... .
4-1
Reynolds Number and Friction Factor for
Pipe Other than Steel or Wrought Iron..
4-1
Determination of Valve Resistance in L,
Lj D, K, and Flow Coefficient C v .... ........................... 4-2
Check Valves; Reduced Port Valves............................ . 4-3
Laminar Flow in Valves, Fittings, and Pipe
4-4
Pressure Drop and Velocity
in Piping Systems ....
..................
4-6
Pipe Line Flow Problems.....................................
4-10
Discharge of Fluids from Piping Systems....
4-12
Flow Through Orifice Meters .................................... 4-15
Application of Hydraulic Radius
to Flow Problems....
.. ........................ ..
Determination of Boiler Capacity ....
...... 4-18
APPENDIX A
APPENDIX B
Physical Properties of Fluids
and Flow Characteristics of
Valves, Fittings, and Pipe
Engineering Data
page
Introduction ., .,,,. __ ,,,.,,.,, ... __ ,____________ ''''' ____ .____ .,,'
page
Introduction ......... ,"'''''''"."''_,,. ___ " ___ """.,," ..
A-I
Physical Properties of Fluids
A-2
Viscosity of steam
A-2, A-3
Viscosity of water" .. " .... " .. " .. "."""",,.,
Viscosity of liquid petroleum products ...... _
A-3
Viscosity of various liquids
A-4
A-5
Viscosity of gases and hydrocarbon vapors
Viscosity of refrigerant vapors
A-5
_.. ,_, _______ A-6
Physical properties of water..
S peci fic gravity-temperature
relationship for petroleum oils"
Weight density and specific
gravity of various liquids"".,,,
Physical properties of gases""""""""
Volumetric composition and
specific gravity of gaseous fuels_, ..
Steam-values of isentropic exponent, k
Weight
and specific
volume
gases and vapors
Properties of Fluids
Saturated steam and saturated water..
Superheated steam
Superheated steam and compressed water..
A-7
A-7
" A-8
_, ___ "A-8
A-9
A-IO
A-12
_______ A-16
A-19
Flow Characteristics of
Nozzles and Orifices
. Flow coefficient C for nozzles"
A-20
Flow coefficient C for
A-20
square edged orifices .,,",,'"
Net expansion factor Y
for compressible flow"".""."",,,, .. ,,,,
A-21
Critical pressure ratio, rc
for compressible flow,,_. _"." ...... "" "" .. ""-,,,_ A-21
Flow Ch'aracteristics
of Pipe, Valves, and Fittings
Net expansion factor Y for compressible
flow through pipe to a larger flow area ""'" A-22
Relative roughness of pipe materials and
friction factor for complete turbulence" .. , "_,,A-23
Friction factors for
A-24
a'ny type of commercial
Friction factors for clean
commercial steel pipe ."." ..... " .. " .. ,," """""."." A-2S
Resistance Coefficients (K)
for Valves and Fittings-"K" Factor Table
Pipe friction factors,,,,,,,
Formulas; contraction and enlargement.
Formulas, reduced port valves and fittings
Gate, globc, and angle valves" '
Check valves ____ ._
Stop-check and foot valves."",
Ball and butterfly valves __________ __
Plug valves and cocks._ ,
Bends and flttings._
Pipe entrance and exit._,
Lengths Land L/ D and Resistance
Coefflcicnt I< ~omograph __
Equivalents of Resistance CoeffIcient K and Flow
Coefficient C v Nomograph ..
A-26
A-26
A26
A-27
A-27
A28
Equivalent Volume and Weight
Flow Rates of Compressible Fluids _________ ,
,__ B-2
Equivalents of Viscosity
B-3
Absolute
Kinematic """ __ , __ "''' ___________ . ___ ,__ ".' __ ""_". __ , __ """ __ " B-3
Kinematic and Saybolt UniversaL,. __ ,, ______________ . B-4
Kinematic and Saybolt Furol
B-4
Kinematic, Saybolt Universal,
B-5
Saybolt Furol, and Absolute".
Saybolt Universal Viscosity Chart.
B-6
Equivalents of Degrees API,
Degrees Baume, Specific Gravity,
Weight Density, and Pounds per Gallon __ ,
B-7
Steam Data
Boiler capacity _______________ ,,_,, __ "' ____ , __ '''',, __ '''' __ __
B-3
Horsepower of an engine
______ " __ , __ ". ______ ,,
B-8
Ranges in steam consumption
by prime movers ,,,, ____ ,__ ,,, __ . '''''' ______________ , B-8
Power Required for Pumping"
B-9
Equivalents (General)
::\feasure __ ,__ ,__
, __ ". __ ." ____ ,,.,,''' ______ ''' __ .,, ___ ,,__
B-lO
Weight __ """" __ ."" __ "" __ "." __ .".,,",,. __ .,,",,. __ "" _____ B-1O
________ ,,,.,, __ ., __ "' __ "'''' __ , __ , .
B-I0
Velocity
Density __ ,_______ " ___________________________________ ,,,"_____
B-1O
B-IO
Physical constants __ ," __ ,,""" ________ ,, ____ ''' ______ ''''
Temperature ____ ." __ ". ________ ,, ____ ,,. __ , _________ "
____ B-IO
Prefixes __ "" __ ." ____ ",,. __ ,, __ ,,
,. __ ,, ___________ ,, __ "" __ B-IO
B-lI
B-II
Liquid measures and
Pressure and head __ , ______ __
Four-Place Logarithms to Base 10 ____ __
B-12
Flow Through Schedule 40 Steel Pipe
\Vater _
___ """".,, ____ .__________ __
Air "''' __
B-15
Pipe Data-(Carbon and
Alloy Steel; Stainless Steel)
Sizes Ys thru 3-inch
Sizes 3 Y2 thru 12-inch, _______________ ,, ___ "
Sizes 14 thru 22-inch __
Sizes 24 thru 36--inch """".,, ____ . __ . _________ _
B-16
B-17
B-18
[3-19
Fahrenheit-Celsius Temperature Conversion,
B,--20
B-14
MISCELLANEOUS
A-28
A-29
A-29
A--29
Illustrations of Typical Valves
Globe, angle, and stop-check,
lift and swing check,
Tilting disc check and foot.
Gate, ball, and butterfly,
Cocks, '
A-30
Bibliography. ,
Foreword
A-31
B-1
Nomenclature
" 3-26
2--7 and 3--26
326
A-32
A--32
see second page of book
see third page of book
see next page
Unless otherwise stated, all symbols used
in this book are defined as follows:
Nomenclature
A
= cross sectional area of pipe or orifice, in
square feet
a = cross sectional area of pipe or orifice, or flow
area in valve, in square inches
rate of Aow in barrels (42 gallons) per hour
B
Aow coefficient for orifices and nozzles
C
= discharge coefficient corrected for velocity of approach = Cd / ,,-~fj4
discharge coefficient for orifices and nozzles
flow coefficient for valves: expresses flow
rate in gallons per minute of 60 F water
with 1.0 psi pressure drop across valve
internal diameter of pipe, in feet
D
internal diameter of pipe, in inches
d
base of natural logarithm = 2.718
e
friction
factor in formula hL = f L v2 / D 2g
f
=
friction
factor
in zone of complete turbulence
JT
g
acceleration of gravity = J 2. 2 feet per
second per second
H
total head, in feet of fluid
h
static pressure head existing at a point, in
feet of Auid
total heat of steam, in Btu per pound
loss of static pressure head due to fluid
flow, in feet of Auid
static pressure head, in inches of water
resistance coefficient or velocity head loss
in the formula, hL = KV 2/2g
k
ratio of specific heat at constant pressure
to specific heat at constant volume =
cp/c"
L
length of pipe, in feet
L/D
equivalent length of a resistance to Aow,
in pipe diameters
Lm
length of pipe, in miles
M
molecular weight
MR
uni versa I gas constant = I 545
n
exponent in equation for polytropic change
(p'\!: = constant)
P
pressure, in pounds per square inch gauge
P'
pressure, pounds per square inch absolute
(see page 1-5 for diagram showing relationship belween gauge and absolute pressure)
p'
Q
q
q'
q'a
,
q h
q'm
R
pressure, in pounds per square foot absolute
rate of flow, in gallons per minute
rate of Aow, in cubic feet per second at
flowing conditions
rate of Aow, in cubic feet per second at
standard conditions (14.7 psia and 60F)
rate of flow, in millions of standard cubic
feet per day, MMscfd
rate of flow, in cubic.feet per hour at standard conditions (14.7 psia and ooF), scfh
rate of flow, in cubic feet per minute at
flowing conditions
rate of flow, in cubic feet per minute at
std. conditions (14.7 psia and 60F), scfm
individual gas constant
MR/M
154)/M
Reynolds number
RH
hydraulic radius, in feet
rc = critical pressure rauo for cumpressible flow
S
specific gravity of liquids at specified temperature relative to water at standard temperature (60 F)
So
specihc gravity of a gas relative to air =
the ratio of the molecular weight of the
gas to that of air
T
absolute temperature, in degrees Rankine
(460
t)
temperature, in degrees Fahrenheit
V
specific volume of Auid, in cubic feet per
pound
\/
mean velocity of flow, in feet per minute
Va
volume. in cubic feet
v
mean velocity of Aow, in feet per second
v,
sonic (or critical) velocity of flow of a gas,
in feet per second
WI
rate of flow, in pounds per hour
W
rate of Aow, in pounds per second
Wa
weight, in pounds
x
percent quality of steam
100 minus per
cent of moisture
Y
net expansion factor for compressible flow
through orifices, nozzles, or pipe
Z
potential head or elevation above reference
level, in feet
+
Greek LeHers
Beta
ratio of small to large diameter in orifices
and nozzles, and contractions or enlargements in pipes
(3
Delta
6,.
differential between two points
Epsilon
absolute roughness or effective height of
pipe wall irregularities, in feet
t
Mu
,
absolute (dynamic) viscosity, in centipoise
absolute viscosity, in pound mass per foot
second or poundal seconds per sq foot
absolute viscosity, in slugs per foot second
or pound force seconds per square foot
"
,,'
kinematic viscosity, in centistokes
kinematic viscosity, square feet per second
iJ.e
Nu
Rho
p
p'
weight density of Auid, pounds per cubic ft
density of fluid, grams per cubic centimeter
Theta
fJ
angle of convergence or divergence in enlargements or contractions in pipes
Subscripts for Diameter
(I) ... defines smaller diameter
(2) ... defines larger diameter
Subscripts for Fluid Property
(I) ... defines inlet (upstream) condition
(2) .. ,defines outlet (downstream) condition
.~
1• 1
Theory of Flow
In Pipe
CHAPTER 1
The most commonly employed method of transporting fluid from one point to another is to force the
fluid to flow through a piping system. Pipe of circular section is most frequently used because that
shape offers not only greater structural strength, but
also greater cross sectional area per unit of wall surface than any other shape. Unless otherwise stated,
the word "pipe" in this book will always refer to a
closed conduit of circular section and constant
internal diameter.
Only a few special problems in fluid mechanics ....
laminar flow in pipe, for example .... can be entirely
solved by rational mathematical means; all other
problems require methods of solution which rest, at
least in part, on experimentally determined coefficients. Many empirical formulas have been proposed
for the problem of flow in pipe, but these are often
extremely limited and can be applied only when the
conditions of the problem closely approach the
conditions of the experiments from which the formulas were derived.
Because of the great variety of fluids being handled
in modern industrial processes, a Single equation
which can be used for the flow of any fluid in pipe
offers obvious advantages. Such an equation is the
Darcy* formula. The Darcy formula can be derived
rationally by means of dimensional analysis; however, one variable in the formula .... the friction
factor .... must be determined experimentally. This
formula has a wide application in the field of fluid
mechanics and is used extensively throughout this
paper.
*The Darcy formula is also known as the Weisbach formula or the DarcyWeisbach formula; also. as the Fanning formula, sometimes modified
so that the friction factor is one-fourth the Darcy friction factor.
1-2
CRANi
CHAPTER 1 - THEORY OF FLOW IN PIPE
Physical Properties of Fluids
The solution of any flow problem requires a knowledge of the physical properties of the fluid being
handled. Accurate values for the properties affecting
the flow of fluids ... namely, viscosity and weight
density ... have been established by many authorities for all commonly used fluids and many of these
data are presented in the various tables and charts
in Appendix A.
Viscosity: Viscosity expresses the readiness with
which a fluid flows when it is acted upon by an external force. The coefficient of absolute viscosity
or, simply, the absolute viscosity of a fluid, is a
measure of its resistance to internal deformation or
shear. Molasses is a highly viscous fluid; water is
comparatively much less viscous; and the viscosity
of gases is quite small compared to that of water.
Although most fluids are predictable in their viscosity, in some, the viscosity depends upon the
previous working of the fluid. Printer's ink, wood
pulp slurries, and catsup are examples of fluids
possessing such thixotropic properties of viscosity.
second and is equivalent to 100 centistokes.
II
(centistokes)
IJ.
(centipoise)
pi (gn:imspercu--'b-ci-c-cm------)
By definition, the speCific gravity, S, in the foregoing formula is baseci upon water at a temperature
of 4 C (39.2 F), whereas specific gravity used
throughout this paper is based upon water at 60 F.
In the English system, kinematic viscosity has
dimensions of square feet per second.
Factors for conversion between metric and English
system units of absolute and kinematic viscosity are
given on page B-3 of Appendix B.
The measurement of the absolute viscosity of fluids
(especially gases and vapors) requires elaborate
equipment and considerable experimental skill. On
the other hand, a rather simple instrument can be
used for measuring the kinematic viscosity of oils
and other viscous liquids. The instrument adopted
as a standard in this country is the Saybolt Universal
Viscosimeter. I n measuring kinematic viscosity
with this instrument, the time required for a small
volume of liqUid to flow through an orifice is determined; consequently, the "Saybolt viscosity" of the
liquid is given in seconds. For very viscous liquids,
the Saybolt Furol instrument is used.
Considerable confusion exists concerning the units
used to express viscosity; therefore, proper units
must be employed whenever substituting values of
viscosity into formulas. In the eG.s. (centimeter,
gram, second) or metric system, the unit of absolute
viscosity is the poise which is equal to 100 centi- Other viscosimeters, somewhat similar to the Saybolt
poise. The poise has the dimensions of dyne seconds but not used to any extent in this country, are the
per square centimeter or of grams per centimeter Engler, the Redwood Admiralty, and the Redwood.
second. It is believed that less confusion concerning The relationship between Saybolt viscosity and
units will prevail if the centipoise is used exclusively kinematic viscosity is shown on page B-4; equivaas the unit of viscosity. For this reason, and since lents of kinematic, Saybolt Universal, Saybolt Furol,
most handbooks and tables follow the same pro- and absolute viscosity can be obtained from the
cedure, all viscosity data in this paper are expressed chart on page B-5.
in centipoise.
The ASTM standard viscosity temperature chart for
The English units commonly employed are
per liquid petroleum products, reproduced on page B-6,
foot second" or "pound force seconds per square is used to determine the Saybolt Universal viscosity
foot"; however, "pound mass per foot second" or of a petroleum product at any temperature when the
"poundal seconds per square foot" may also be en- viscosities at two different temperatures are known.
countered. The viscosity of water at a temperature The viscosities of some of the most common fluids are
given on pages A-2 to A-5. It will be noted that,
of 68 F is:
with a rise in temperature, the viscosity of liquids
poise
decreases, whereas the viscosity of gases increases.
1 centipoise*
0.01 gram per cm second
1 dyne second per sq cm
The effect of pressure on the viscosity of liqUids and
perfect
gases is so small that it is of no practical
[0.000 672 pound mass per foot second
JJ-e
interest in most flow problems. Conversely, the
\ 0.000 672 poundal second per square foot
viscosity of saturated, or only slightly superheated,
, (0.000 0209 slug per foot second
vapors is appreciably altered by pressure changes, as
lJ.e
lo.ooo 0209 pound force second per square ft indicated on page A-2 showing the viscosity of steam.
Unfortunately, the data on vapors are incomplete
Kinematic viscosity is the ratio of the absolute vis- and, in some cases, contradictory. Therefore, it is
cosity to the mass density. In the metric system, expedient when dealing with vapors other than
the unit of kinematic viscosity is the stoke. The steam to neglect the effect of pressure because of the
stoke has dimensions of square centimeters per lack of adequate data.
·Actually the viscosity of water at 68 F is 1.005 centipoise.
CRANE
CHAPTER I
1-3
THEORY OF FLOW IN PIPE
Physical Properties of Fluids Weight density,
specific volume, and specific gravity: The weight
density or specific weight of a substance is its weight
per unit volume. In the English system of units,
this is expressed in pounds per cubic foot and the
symbol designation used in this paper is p (Rho).
In the metric system, the unit is grams per cubic
centimeter and the symbol deSignation used is p'
(Rho prime).
The specific volume
being the reciprocal of the
weight density, is expressed in the English system
as the number of cubic feet of space occupied by one
pound of the substance, thus:
In the metric system, the number of cubic centimeters
per gram of a substance can readily be expressed as
the reCiprocal of the weight density, that is.
The variations in weight density as well as other
properties of water with changes in temperature are
shown on page A-6. The weight densities of other
common liquids are shown on page A-7. Unless
very high pressures are being considered, the effect of
pressure on the weight of liquitls is of no practical
importance in Row problems.
The weight densities of gases and vapors, however,
are greatly altered by pressure changes. For the socalled "perfect" gases, the weight density can be
computed from the formula:
144 P'
p=~
The individual gas constant R is equal to the universal gas constant, MR 1545, divided by the molecular weight of the gas,
R = 1545
M
Values of R, as well as other useful gas constants,
are given on page A-8. The weight density of air
for various conditions of temperature and pressure
can be found on page A-IO.
continued
In steam Row computations, the reciprocal of the
weight density, which is the specific volume, is commonly used; these values are listed in the steam
tables shown on pages A-12 to A-19. A chart for determining the weight density and specific volume of
gases is given on page A-II.
Specific gravity is a relative measure of weight denSity. Since pressure has an insignificant effect upon
the weight density of liquids, temperature is the
only condition that must be considered in designating the basis for specific gravity. The specific gravity of a liquid is the ratio of its
density at
specified temperature to that of water at standard
temperature, 60 F.
f any liquid at
S = p l specified temperatu re f
p
(water at 60 F)
A hydrometer can be used to measure the specific
gravity of liquids directly. Three hydrometer
scales are common in this country .... the API scale
which is used for oils .... and the two Baume scales,
one for liquids heavier than water and one for liquids
lighter than water. The relationship between the
hydrometer scales and specific gravity are:
For oils,
F)
S (60
IJ \. 5
+ deg. API
For liquids lighter
than water,
S (60
F)
14 0
;3'0+ deg.'Baume
For liquids heavier
than water,
S (60 Fj60 F)
145
145 - deg. Baume
For convenience in converting hydrometer readings
to more useful units, refer to the table shown on
page B-7.
The specific gravity of gases is defined as the ratio
of the molecular weight of the gas to that of air, and
as the ratio of the individual gas constant of air to
that of the gas.
s = R (air)
U
R (gas)
M (gas)
M (air)
CRANE
CHAPTER 1 - THEORY OF FLOW IN PIPE
Nature of Flow in Pipe -
Figure 1-1
laminar Flow
Actual photograph of colored filaments being
carried along undisturbed by a stream of
water.
Laminar and Turbulent
Figure 1-2
Flow in Critical Zone, aetween
laminar and Transition Zones
At the critical velocity, the filaments begin to
break up, indicating flow is becoming
turbulent.
A simple experiment (illustrated above) will readily
show there are two entirely different types of flow
in pipe. The experiment consists of injecting small
streams of a colored fluid into a liquid flowing in
a glass pipe and observing the beha vior of these
colored streams at different sections downstream
from their points of injection.
If the discharge or average velocity is small, the
streaks of colored fluid flow in straight lines, as
shown in Figure I-I. As the flow rate is gradually
increased, these streaks will continue to flow in
straight lines until a velocity is reached when the
streaks will waver and suddenly break into diffused
patterns, as shown in Figure 1-2. The velocity at
which this occurs is caned the "critical velocity".
At velocities higher than "critical", the filaments
are dispersed at random throughout the main body of
the fluid, as shown in Figure 1-3.
The type of flow which exists at velocities lower
than "critical" is known as laminar flow and, sometimes, as viscous or streamline flow. Flow of this
nature is characterized by the gliding of concentric
cylindrical layers past one another in orderly fashion. Velocity of the fluid is at its maximum at the
pipe axis and decreases sharply to zero at the wall.
Figure 1·3
Turbulent Flow
This illustration shows the turbulence in the
stream completely dispersing the colored
filaments a short distance downstream from
the point of injection.
Reynolds number: The work of Osborne Reynolds
has shown that the nature of flow in pipe, . , . that
is. whether it is laminar or turbulent , ... depends
on the pipe diameter. the density and viscosity of
the flowing fluid. and the velocity of flow. The
numerical value of a dimensionless combination of
these four variables, known as the Reynolds number, may be considered to be the ratio of the dynamic
forces of mass flow to the shear stress due to viscosity. Reynolds number is:
Equalion '.2
}I.e
(other forms of this equation; page 3-2.)
For engineering purposes. flow in pipes is usually
considered to be laminar if the Reynolds number is
less than 2000, and turbulent if the Reynolds number
is greater than 4000. Between these two values lies
the "critical zone" where the flow .... being laminar,
turbulent, or in the process of change, depending
upon many possible varying conditions . . . . is
unpredictable. Careful experimentation has shown
that the laminar zone may be made to terminate at
a Reynolds number as low as 1200 or extended as
high as 40,000, but these conditions are not expected
to be realized in ordinary practice.
At velocities greater than "critical", the flow is tur- Hydraulic radius: Occasionally a conduit of nonbulent. In turbulent flow, there is an irregular circular cross section is encountered. In calculating
random motion of fluid particles in directions trans- the Reynolds number for this condition. the equivaverse to the direction of the main flow. The velOCity lent diameter (four times the hydraulic radius) is subdistribution in turbulent flow is more uniform stituted for the circular diameter. Use friction
across the pipe diameter than in laminar flow. Even factors gi ven on pages A-24 and A-25.
_cross sectional flow area
though a turbulent motion exists throughout the
R
greater portion of the pipe diameter, there is always
wetted perimeter
a thin layer of fluid at the pipe wall .... known as This applies to any ordinary conduit (circular conthe "boundary layer" or "laminar sub-layer" .... duit not flowing full. oval. square or rectangular)
which is moving in laminar flow,
but not to extremely narrow shapes such as annular
or elongated openings, where width is small relative
Mean velocity of flow: The term "velOCity", unless to length. In such cases, the hydraulic radius is
otherwise stated. refers to the mean. or average, approximately equal to one-half the width of the
velocity at a given cross section, as determined by passage.
the continuity equation for steady state flow'
H---~--~---~
v=3..=~
A
Ap
wV
Equolion ,.,
(For nomenclature, see page preceding Chapt.er I)
"Reasonable" velocities for use in design work are
given on pages 3-6 and 3-16.
To determine quantity of flow in following formula:
q = 0043 8d2
fh:15
'\jJr
the value of de is based upon an equivalent diameter
of actual flow area and 4RH is substituted for D.
CIANI:
1·5
CHAPTER J - THEORY OF FLOW IN PIPE
General Energy Equation
Bernoulli's Theorem
The Bernoulli theorem is a means of expressing the
application of the law of conservation of energy to
the flow of fluids in a conduit. The total energy at
any particular point, above some arbitrary horizontal
datum plane, is equal to the sum of the elevation
head, the pressure head, and the velocity head,
as follows:
If friction losses are neglected and no energy is added
to, or taken from, a piping system (i.e., pumps or
turbines), the total head, H, in the above equation
will be a constant for any point in the fluid. However, in actual practice, losses or energy increases
or decreases are encountered and must be included
in the Bernoulli equation. Thus, an energy balance
may be written for two points in a fluid, as shown in
the example in Figure 1-4.
PI x 144.
p
Note the pipe friction loss from point 1 to point 2
is hL foot pounds per pound of flowing fluid; this is
sometimes referred to as the head loss in feet of fluid.
The equation may be written as follows:
Arbitrary Horizontal Datum Plane
Eq ua';on J·3
Z + I 44Pz + v~
Figure 1.4
Energy 8alance for Two Poinl. in a Fluid
2
P2
2 g
+h
L
All practical formulas for the flow of fluids are derived from Bernoulli's theorem, with modifications
to account for losses due to friction.
By permission, from Fluid Mechanics l * by
R. A. Dodge and M. J. Thompson. Copyright
1937; McGraw-Hili Book Company, Inc.
Measurement of Pressure
Any Pressure Above Atmospheric
e
e
"
'"
1;3
'"
'"
et_
.,
i
::I
Q)
et
.g
Q)
At Atmospheric Pressure Level-Variable
E
~
co
+
""
~
Q)
""II
""
E
~-
'"
;,.
Barometric pressure is the level of the atmospheric
pressure above perfect vacuum.
"Standard" atmospheric pressure is 14.696 pounds
per square inch, or 760 millimeters of mercury.
An~ Pressu re Below Atmospheric
Q)
~
Figure 1-5 graphically illustrates the relationship
between gauge and absolute pressures. Perfect
vacuum cannot exist on the surface of the earth, but
it nevertheless makes a convenient datum for the
measurement of pressure .
e
11e
'"
et
Q)
~-
=-
"0
'5
~
~
..0
..:
Absolute Zero of Pressure-Perfect Vacuum
Figure 1·5
Relationship 8etween
Gauge and Absolule Preuures
Gauge pressure is measured above atmospheric pressure, while absolute pressure always refers to perfect
vacuum as a base.
Vacuum, usually expressed in inches of mercury, is
the depression of pressure below the atmospheric
level. Reference to vacuum conditions is often
made by expressing the absolute pressure in inches
of mercury; also millimeters of mercury and microns
of mercury .
• All superior figures used o. ",ference morle. refer to tbe Bibliogropby; see second poge of boole.
1-6
CRANE
CHAPTER 1 - THEORY OF FLOW IN· PIPE
Darcyls Formula
General Equation for Flow of Fluids
Flow in pipe is always accompanied by friction of
fluid particles rubbing against one another, and consequently, by loss of energy available for work; in
other words, there must be a pressure drop in the
direction of flow. If ordinary Bourdon tube pressure
gauges were connected to a pipe containing a flowing
fluid, as shown in Figure 1-6, gauge PI
would indicate a
higher static pressure
Figure 1·6
than gauge P 2 •
The general equation for pressure drop, known as
Darcy's formula and expressed in feet of fluid, is
hL = jLv 21D 2g. This equation may be written to
express pressure drop in pounds per square inch, by
substitution of proper units, as follows:
L:::.P =
Eq uation J-4
(For other forms of this equation, see page 3-2.)
The Darcy equation is valid for laminar or turbulent
flow of any liquid in a pipe. However, when extreme
velocities occurring in a pipe cause the downstream
pressure to fall to the vapor pressure of the liquid,
cavitation occurs and calculated flow rates will be
inaccurate. With suitable restrictions, the Darcy
equation may be used when gases and vapors (compressible fluids) are being handled. These restrictions are defined on page 1-7.
Equation 1-4 gives the loss in pressure due to friction
and applies to pipe of constant diameter carrying
fluids of reasonably constant weight density in
straight pipe, whether horizontal, vertical, or sloping.
For inclined pipe, vertical pipe, or pipe of varying
diameter, the change in pressure due to changes in
elevation, velocity, and weight density of the fluid
must be made in accordance with Bernoulli's theorem
(page 1-5). For an example using this theorem, see
page 4-8.
Friction factor: The Darcv formula can be ration-
ally derived by dimensional ~nalysis, with the exception of the friction factor, j, which must be determined experimentally. The friction factor for laminar flow conditions (Re < 2000) is a function of
Reynolds number only; whereas, for turbulent flow
CRe > 4000), it is also a function of the character of
the pipe wall.
A region known as the "critical zone" occurs between
Reynolds number of approximately 2000 and 4000.
In this region, the ft.ow may be either laminar or turbulent depending upon several factors; these include
changes in section or direction of flow and obstructions, such as valves, in the upstream piping. The
friction factor in this region is indeterminate and
has lower limits based on laminar flow and upper
limits based on turbulent flow conditions.
At Reynolds numbers above approximately 4000,
flow conditions again become more stable and definite
friction factors can be established. This is important because it enables the engineer to determine
the flow characteristics of any fluid flowing in a
pipe, providing the viscosity and weight density at
flowing conditions are known. For this reason, Equation 1-4 is recommended in preference to some of
the commonly known empirical equations for the
flow of water, oil, and other liquids, as well as for
the flow of compressible fluids when restrictions
previously mentioned are observed.
If the flow is laminar CR. < 2000), the friction factor may be determined from the equation:
j
= ~:± = 64 J.le
Re
D vp
vp
If this quantity is substituted into Equation 1-4,
the pressure drop in pounds per square inch is:
L:::.P = 0.000668
Lv
Equation J·5
which is Poiseuille's law for laminar flow.
When the flow is turbulent CRe > 4000), the friction
factor depends not only upon the Reynolds number
but also upon the relative roughness, tiD . ... the
roughness of the pipe walls (e), as compared to the
diameter of the pipe CD). For very smooth pipes
such as drawn brass tubing and glass, the friction
factor decreases more rapidly with increasing Reynolds number than for pipe with comparatively
rough walls.
Since the character of the internal surface of commercial pipe is practically independent of the diameter, the roughness of the walls has a greater effect
on the friction factor in the small sizes. Consequently, pipe of small diameter will approach the
very rough condition and, in general, will have
higher friction factors than large pipe of the same
material.
The most useful and Widely accepted data of friction
factors for use with the Darcy formula have been presented by L. F. Moody 18 and are reproduced on pages
A-23 to A-25. Professor Moody improved upon the
well-established Pigott and Kemler 25 , 26 friction factor
diagram, incorporating more recent investigations
and developments of many outstanding scientists.
The friction factor, j, is plotted on page A-24 on
the basis of relative roughness obtained from the
chart on page A-23 and the Reynolds number. The
CRANE
1-7
CHAPTER I - THEORY OF FLOW IN PIPE
Darcy's Formula
General Equation for Flow of Fluids value of f is determined by horizontal projection from
the intersection of the E/ D curve under consideration with the calculated Reynolds number to the left
hand vertical scale of the chart on page A-B. Since
most calculations involve commercial steel pipe, the
chart on page A-25 is furnished for a more direct
solution. I t should be kept in mind that these figures
apply to clean new pipe.
Effect of age and use on pipe friction: Friction
loss in pipe is sensitive to changes in diameter and
roughness of pipe. For a given rate of flo\\' and a
fixed friction factor, the pressure drop per foot of
pipe varies inversely with the flith power of the
diameter. Therefore, a 2~c reduction of diameter
continued
causes a II % increase in pressure drop; a 5 reduction of diameter increases pressure drop 29%. In
many services, the interior of pipe becomes encrusted
with
dirt, tubercules or other foreign matter;
thus. it is often prudent to make allowance for expccted diameter changes.
Authorities 2 point out that roughness may be expected to increase with use (due to corrosion or
incrustation) at a rate determined by the pipe
material and nature of the fluid. IppenlB, in discussing the effect of aging, cites a 4-inch galvanized
steel pipe which had its roughness doubled and its
friction factor increased 20% after three years of
madera te use.
Principles of
Compressible Flow in Pipe
An accurate determination of the pressure drop of a
compressible fluid flowing through a pipe requires a
knowledge of the relationship between pressure and
specific volume; this is not easily determined in
each particular problem. The usual extremes considered are adiabatic flow (p'vt
constant) and isothermal flow (p'Va = constant). Adiabatic flow is
usually assumed in short, perfectly insulated pipe.
This would be consistent since no heat is transferred
to or from the pipe, except for the fact that the
minute amount of heat generated by friction is
added to the flow.
Isothermal flow or flow at constant temperature is
often assumed, partly for convenience but more often
because it is closer to fact in piping practice. The
most outstanding case of isothermal flow occurs in
natural gas pipe lines. Dodge and Thompsonl show
that gas flow in insulated pipe is closely approximated
by isothermal flow for reasonably high pressures.
Since the relationship between pressure and volume
may follow some other relationship (p'\l~ = constant) called polytropic flow, specific information in
each individual case is almost an impossibility.
The density of gases and vapors changes considerably
with changes in pressure; therefore, if the pressure
drop between PI and P 2 in Figure 1-6 is great, the
density and velocity will change appreciably.
When dealing with compressible fluids, such as air,
steam, etc., the following restrictions should be
observed in applying the Darcy formula:
I. If the calculated pressure drop (PI
P z) is less
than about 1O~;~ of the inlet pressure PI, reasonable accuracy will be obtained if the specific
volume used in the formula is based upon either
the upstream or downstream conditions, whichever are known.
2. If the calculated pressure drop (PI
P 2 ) is
greater than about 10%, but less than about 40%
of inlet pressure Pl. the Darcy equation may be
used with reasonable accuracy by using a specific
volume based upon the average of upstream and
dO\\flstrcam conditions; otherwise, the method
given on page I-q may be used.
3, For greater pressure drops. such as are often
encountered in long pipe lines, the methods given
on the next two pages should be used.
(continued on the ned page)
CRANE
OF flOW IN PIPE
Principles of Compressible Flow in Pipe
(continued)
Complete isothermal equation: The flow of gases
in long pipe lines closely approximates isothermal conditions, The pressure drop in such lines is often
large relative to the inlet pressure, and solution
of this problem falls outside the limitations of
the Darcy equation, An accurate determination of
the flow characteristics falling within this category
can be made by using the complete isothermal
equation:
Equation 1·6
144 g /V
.
[ -; (fL
'" 1
0
Pi)
+ 210ge P~
] [CPiF - (P~)2]
Pi
The formula is developed on the basis of these
assumptions:
1.
2,
],
4.
5.
Isothermal flow.
No mechanical work is done on or by the system.
Steady flow or discharge unchanged with time.
The gas obeys the perfect gas laws.
The velocity may be represented by the average
velocity at a cross section.
6. The friction factor is constant along the pipe.
7. The pipe line is straight and horizontal between
end points.
Simplified Compressible Flow~Gas Pipe Line
Formula: In the practice of gas pipe line engineering, another assumption is added to the foregoing:
8.
Then, the formula for discharge in a horizontal pipe
may be written:
u,2 - [144.
-
g DA2] rep')"~
-_
l' P')~]
, 1.7
_~ _
~_
EquatIon
\/1 fL
Pi
This is equivalent to the complete isothermal equation if the pipe line is long and also for shorter lines
if the ratio of pressure drop to initial pressure is
small.
Since gas flow problems are usually expressed in
terms of cubic feet per hour at standard conditions,
it is convenient to rewrite Equation 1-7 as follows:
d:'
Equation 1·70
Other commonly used formulas for compressible flow in long pipe lines:
Weymouth formula 24 :
q' h =
28,0 d
2. m
Equation
Equotion 1·9
q' h = 36.8 E d2.6182
0.5394
The flow efficiency factor E is defined as an experience factor and is usually assumed to be 0,92 or
92
for average operating conditions, Suggested
values for E for other operating conditions are given
on page 3-3.
Comparison of formulas for compressible flow
in pipe lines: Equations 1-7, 1-8, and 1-9 are derived from the same basic formula, but differ in the
selection of data used for the determination of the
friction factors.
Friction factors in accordance with the Mood y 18 diagram are normally used with the Simplified Compressible Flow formula (Equation 1-7). However, if
the same friction factors employed in the Weymouth
or Panhandle formulas are used in the Simplified
formula, identical answers will be obtained.
The Weymouth friction factor 24 is defined as:
Acceleration can be neglected hecause thc pipe
line is long.
!
Panhandle formula 3 for natural gas pipe lines 6
to 24-inch diameter, Reynolds numbers 5 x 10 6 to
14 X 10 6 , and
0,6:
r.8
f
This is identical to the Moodv friction factor in the
fully turbulent flow range for lO-inch I.D. pipe only.
Weymouth friction factors are greater than Moody
factors for sizes less than 20-inch, and smaller for
sizes larger than 20-inch.
The Panhandle friction factor 3 is defined as:
.
j= 0.1225
(
d )0.1461
~
qh a
In the flow range to which the Panhandle formula is
limited, this results in friction factors that are lower
than those obtained from either the Moody data
or the Weymouth friction formula. As a result, flow
rates obtained by solution of the Panhandle formula
are usually greater than those obtained by employing
either the Simplified Compressible Flow formula with
Moody friction factors, or the Weymouth formula.
An example of the variation in flow rates which may
be obtained for a specific condition by employing
these formulas is given on page 4-11.
CRANE
1·9
CHAPTER 1 - THEORY Of fLOW IN PIPE
Principles of Compressible Flow in Pipe
(continued)
Limiting flow of gases and vapors: The feature
not evident in the preceding formulas (Equations 1-4
and 1-6 to 1-9 inclusive) is that the weight rate of
flow (e.g., lbs/sec) of a compressible fluid in a pipe,
with a given upstream pressure, will approach a certain maximum rate which it cannot exceed, no matter how much the downstream pressure is further
reduced.
The maximum velocity of a compressible fluid in pipe
is limited by the velocity of propagation of a pressure wave which travels at the speed of sound in
the fluid. Since pressure falls off and velocity increases as fluid proceeds downstream in pipe of uniform cross section, the maximum velocity occurs in
the downstream end of the pipe. If the pressure drop
is sufficiently high, the exit velocity will reach
the velocity of sound. Further decrease in the outlet pressure will not be felt upstream because the
pressure wave can only travel at sonic velocity, and
the "signal" will never translate upstream. The
"surplus" pressure drop obtained by lowering the
outlet pressure after the maximum discharge has
already been reached takes place beyond the end of
the pipe. This pressure is lost in shock waves and
turbulence of the jetting fluid.
The maximum possible veloci.ty in the pipe is sonic
velocity, which is expressed as:
Equation '.10
v.
" kg RT = "kg 144 P'
The value of k, the ratio of specific heats at constant pressure to constant volume, is 1.4 for most
diatomic gases; see pages A-8 and A-9 for values of
k for gases and steam respectively. This velocity
will occur at the outlet end or in a constricted area
when the pressure drop is sufficiently high. Th~
pressure, temperature, and specific volume are those
occurring at the point in question. When compressible fluids discharge from the end of a reasonably
short pipe of uniform cross section into ail area of
larger cross section, the flow is usually considered to
be adiabatic. This assumption is supported by experimental data on pipe having lengths of 220 and
130 pipe diameters discharging air to atmosphere.
Investigation of the complete theoretical analysis of
adiabatic f1ow 19 has led to a basis for establishing
correction factors, which may be applied to the
Darcy equation for this condition of flow. Since
these correction factors compensate for the changes
in fluid properties due to expansion of the fluid, they
are identified as Y net expansion factors; see page
A-22.
The Darcy formula, including the Y factor, is:
U'
" !6P
= 0·525 Yd - VKV 1
(Re~istuncc coefficient K
Equotion I-r I
is defined on page 2-8)
I t should be noted that the value of K in this equation is the total resistance coefficient of the pipe line:
including entrance and exit losses when they exist,
and losses due to valves and fittings.
The pressure drop, 6P, in the ratio 6P/P't which
is used for the determination of Y from the charts on
page A-22, is the measured difference between the
inlet pressure and the pressure in the area of larger
cross section. In a system discharging compressible
fluids to atmosphere, this 6P is equal to the inlet
gauge pressure, or the difference between absolute
inlet pressure and atmospheric pressure. This value
of 6P is also used in Equation 1-11, whenever the
Y factor falls within the limits defined by the resistance factor K curves in the charts on page A-22.
When the ratio of 6P/P\, using 6P as defined
above, falls beyond the limits of the K curves in the
charts, sonic velocity occurs at the point of discharge
or at some restriction within the pipe, and the limiting values for Y and 6P, as determined from the
tabulations to the right of the charts on page A-22,
must be used in Equation I-II.
Application of Equation I-II and the determination
of values for K, Y, and 6P in the formula is demonstrated in examples on pages 4-13 and 4-14.
The charts on page A-22 are based upon the general
gas laws for perfect gases and, at sonic velocity
conditions at the outlet end, will yield accurate
results for all gases which approximately follow the
perfect gas laws. An example of this type of flow
problem is presented on page 4-13.
This condition of flow is comparable to the flow
through nozzles and venturi tubes, covered on page
2-15, and the solutions of such problems are similar.
1 • 10
CHAPTER 1
THEORY OF FLOW IN PIPE
CRANE
Steam
General Discussion
Substances exist in anyone of three phases, , , .
solid, liquid, or gas, When outside conditions are
varied, they may change from one phase to another.
Water under normal atmospheric conditions exists
in the form of a liquid, When a body of water is
heated by means of some external medium, the temperature of the water rises and soon small bubbles,
which break and form continuously, are noted on the
surface. This phenomenon is described as "boiling",
The amount of heat necessary to cause the temperature of the water to rise is expressed in British Thermal Units (Btu), where, I Btu is the quantity of heat
required to raise the temperature of one pound of
water from 60 to 61 F The amount of heat necessary to raise the temperature of a pound of water
from 32 F (freezing point) to 212 F (boiling point)
is 180, [Btu. When the pressure does not exceed 50
pounds per square inch absolute, it is usually permissible to assume that each temperature increase
of 1 F represents a heat content increase of one Btu
per pound, regardless of the temperature of the
water.
Assuming the generally accepted reference plane for
one pound of water at
zero heat content at 32
212 F contains 180.17 Btu, This quantity of heat is
called heat of the liquid or sensible heat. In order to
change the liquid into a vapor at atmospheric pressure (14.7 psia), 970,3 Btu must be added to each
pound of water after the temperature of 212 F is
reached, During this transition period, the temperature remains constant. The added quantity of
heat is called the latent heat of evaporation, Consequently, the total heat of the vapor, formed when
water boils at atmospheric pressure, is the sum of
the two quantities ... , 180, I Btu and 970,3 Btu, or,
1150.5 Btu per pound,
If water is heated in a closed vessel not completely
filled, the pressure will rise after steam begins to form
accompanied by an increase in temperature.
Saturated steam is steam in contact with liquid
water from which it was generated, at a temperature which is the boiling point of the water and the
condensing point of the steam. I t may be either
"dry" or "wet", depending on the generating conditions. "Dry" saturated steam is steam free from
mechanically mixed water particles. "Wet" saturated steam, on the other hand, contains water
particles in suspension, Saturated steam at any
pressure has a definite temperature.
Superheated s'eam is steam at any given pressure
which is heated to a temperature higher than the
temperature of saturated steam at that pressure.
2 ·1
Flow of Fluids
Through Valves and FiHings
CHAPTER 2
The preceding chapter has been devoted to the
theory and formulas used in the study of fluid flow in
pipes. Since industrial installations usually contain a considerable number of valves and fittings, a
knowledge of their resistance to the flow of fluids
is necessary to determine the flow characteristics of
a complete piping system.
Many texts on hydraulics contain no information on
the resistance of valves and fittings to flow, while
others present only a limited discussion of the subject. In realization of the need for more complete
detailed information on the resistance of valves and
fittings to flow, Crane Co. has conducted extensive
tests in their Engineering Laboratories and has also
sponsored investigations in other laboratories. These
tests have been supplemented by a thorough study of
all published data on this subject. Appendix A
contains data from these many separate tests and the
findings have been combined to furnish a basis for
calculating the pressure drop through valves and
fittings.
Representative resistances to flow of various types
of piping components are given in the "K' Factor
Table; see pages A-26 thru A-N.
The chart on page A-30 illustrates the relationship
between equivalent length in pipe diameters and in
feet of pipe for flow in the zone of complete turbulence.
resistance coefficient K. and pipe size.
The chart on page A-3l may be used to readily determine the Cv flow coefficient of any valve for which the
resistance coefficient is known or can be determined
from the data presented in the "K" Factor Table.
A discussion of the equivalent length and resistance
coefficient K, as well as the flow coefficient Cv methods of calculating pressure drop through valves and
fittings is presented on pages 2-8 to 2-10.
2-2
CHAPTER 2
flOW OF FLUIDS THROUGH VALVES AND FITTINGS
CRANE
Types of Valves and Fittings
Used in Pipe Systems
Valves: The great variety of valve designs precludes
any thorough classification.
If valves were classified according to the resistance
they offer to flow, those exhibiting a straight-thru flow
path such as gate, ball, plug. and butterfly valves
would fall in the low resistance class, and those having
a change in flow path direction such as globe and angle
valves would fall in the high resistance class.
For photographic illustrations of some of the most
commonly used valve designs, refer to pages 3-26 and
A-32. For line illustrations of typical fittings and
pipe bends, as well as valves. see pages A-26 to A-29
Fittings: Fittings may be classified as branching,
reducing, expanding, or deflecting. Such fittings
as tees, crosses, side outlet elbows, etc., may be
called branching fittings.
Reducing or expanding fittings are those which
change the area of the fluid passageway. In this
class are reducers and bushings. Deflecting fittings
.... bends, elbows, return bends, etc ..... are those
which change the direction of flow.
Some fittings, of course, may be combinations of any
of the foregoing general classifications. I n addition, there are types such as couplings and unions
which offer no appreciable resistance to flow and,
therefore, need not be considered here.
Pressure Drop Chargeable
To Valves and Fittings
When a fluid is flowing steadily in a long straight
pipe of uniform diameter, the flow pattern, as indicated by the velocity distribution across the pipe
diameter, will assume a certain characteristic form.
Any impediment in the pipe which changes the direction of the whole stream, or even part of it, will
alter the characteristic flow pattern and create turbulence, causing an energy loss greater than that
normally accompanying flow in straight pipe. Because valves and fittings in a pipe line disturb the flow
pattern, they produce an additional pressure drop.
The loss of pressure produced by a valve (or fitting)
consists of:
1. The pressure drop within the valve itself.
2. The pressure drop in the upstream piping in
excess of that which would normally occur if
there were no valve in the line. This effect
is small.
J. The pressure drop in the downstream piping in
excess of that which would normally occur if
there were no valve in the line. This effect
may be comparatively large.
From the experimental point of view it is difficult to
measure the three items separately. Their combined
effect is the desired quantity, however, and this can
be accurately measured by well known methods.
I."'----c----·I
..
Figura 2-1
Figure 2-1 shows two sections of a pipe line of the
same diameter and length. The upper section contains a globe valve. If the pressure drops, !:::'P 1 and
!:::,P 2, were measured between the points indicated,
it would be found that !:::,p[ is greater than !:::'P z.
Actually, the loss chargeable to a valve of length "d"
is !:::'P 1 minus the loss in a section of pipe of length
"a + b". The losses, expressed in terms of resistance
coefficient" K' of various valves and fittings as given
on pages A-26 to A-29 include the loss due to the
length of the valve or fitting.
CRANE
CHAPTER 2
2-3
FLOW OF FLUIDS THROUGH VALVES AND FITTINGS
Crane Flow Tests
Crane Engineering Laboratories have facilities for conducting water, steam, and air flow
tests for many sizes and types of valves and
fittings. Although a detailed discussion of all the
various tests performed is
beyond the scope of this
paper, a brief description
of some of the apparatus
will be of interest.
The test piping shown in Figure 2-3 is unique
in that 6-inch gate, globe, and angle valves or
90 degree ells and tees can be tested with
either water or steam. The vertical leg of the
angle test section permits testing of angle lift
check and stop check valves.
~,. ,~t
,,- '*'
Saturated steam at 150 psi is available at flow rates
up to 100,000 pounds per hour. The steam is throttled to the desired pressure and its state is determined at the meter as well as upstream and downstream from the test specimen.
For tests on water, a steam turbine driven pump supplies water at rates up to 1200 gallons per minute
through the test piping.
Static pressure differential is measured by means of
a manometer connected to piezometer rings upstream
and downstream from test position 1 in the angle test
section, or test position 2 in the straight test section. The downstream piezometer for the angle
test section serves as the upstream piezometer for
(or 12~
.~ ..Gh.
the straight test section. Measured pressure drop
for the pipe alone between piezometer stations is
subtracted from the pressure drop through the valve
plus pipe to ascertain the pressure drop chargeable
to the valve alone.
Results of some of the flow tests conducted in the
Crane Engineering Laboratories are plotted in Figures 2-4 to 2-7 shown on the two pages following.
Exhaust to
Atmosphere
Determination of
State of Steam
Outlet
Control
Valves
Steam Flow
Orifice Meter
Manometer
\
\
Stop Valve
Water Header
(Metered Supply from
turbine driven pump)
Figura 2-3
Tast piping ClppClrCltus for meClsuring
the pressure drop through vCllves Clnd
fittings Cln steClm or wClter linas.
Determination of
State of Steam
Elbow Can Be Rotated to _ _ _'"
Admit Waler or Steam
CRANE
CHAPTER 2 - FLOW OF FLUIDS THROUGH VALVES AND FITTINGS
2-4
Crane Water Flow Tests
IO--~-.-.'-,,-'-'-rTl--
10
9
8
7
6
__~~
9--~~~~~4-~4-4-+-~--~~~~
8~4-~-+~4-~4-4-+-~--fh~hM~
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14 '-15
3
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1
2
Water Velocity, in Feet per Second
Fluid
F~e
o.
1
2
3
4
5
Figure 2-4
Water
{;
7
8
9
10
11
12
Figure 2-5
13
14
15
16
17
18
•.
•
I
6 7 8 9 10
4
20
Water Velocity. in Feet per Second
Figure 2·5
Figure 2·4
Curve
No.
J'I 3
0...
Water Flow Tests - - Curves 1 to 18
Size,
Valve Type·
Inches
3A
2
4
Class 150 Cast Iron Y-Pattern Globe Valve,
Flat Seat
{;
1%
2
2%
3
1%
2
2'h
3
Class 150 Brass Angle Valve with Composition Disc,
Flat Seat
Class 150 BrassConventional Globe Valve
With Composition Disc-Flat Seat
%
%
3A
Class 200 Brass Swing Check Valve
1tA
2
6
Class 125 Iron Bodv Swing Check Valve
*Except for check valves at lower velocities where curves (14 to 17) bend, all valves were tested with disc fully lifted.
CRANE
2·5
CHAPTER 2 - FLOW OF FLUIDS THROUGH VALVES AND FITTINGS
Crane Steam Flow Tests
10
9
8
7
6
.r:
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-=e
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en
a'
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6 7 8 9 10
20
30
I I
6 7 8 9 10
20
Steam Velocity, in Thousands of Feet per Minute
Steam Velocity, in Thousands of Feet per Minute
Figure 2-6
Figure 2-7
Steam Flow Tests
Fluid
I
.r:
-=e
I
I
.4
'20
'-
" '-"
'" "
"
I
.5
'-
2 I VIV
V~ /
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I
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e
I
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/'
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.... r--.... V V H V
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3
r-,
/
I
Figure
Curve
No.
30
Curves 19 to 31
No.
Size,
I
Inches
Valve· or Fitting Type
19
20
21
22
2
6
6
6
Class 300 Brass Conventional Globe Valve ............... Plug Type Seat
Class 300 Steel Conventional Globe Valve ................ Plug Type Seat
Class 300 Steel Angle Valve ............................. Plug Type Seat
Class 300 Steel Angle Valve ........................... Ball to Cone Seat
23
24
25
26
6
6
6
6
Class 600 Steel Angle Stop.Check Valve
Class 600 Steel Y·Pattern Globe Stop.Check Valve
Class 600 Steel Angle Valve
Class 600 Steel Y.Pattern Globe Valve
27
28
29
30
31
2
90° Short Radius Elbow for Use with Schedule 40 Pipe
6
6
6
6
Class 250 Cast Iron Flanged Conventional 90° Elbow
Figure 2·6
Saturated
Steam
50 psi
gauge
Figure 2-7
Class 600 Steel Gate Valve
Class 125 Cast Iron Gate Valve
Class 150 Steel Gate Valve
·Except for check valves at lower velocities where curves (23 and 24) bend, all valves were tested with disc fully lifted,
2-6
CRANE
CHAPTER 2 - FLOW OF FLUIDS THROUGH VALVES AND FITTINGS
Figur. 2·8
Flow te.t piping
for 2'12 -inch co.t
.teel ang/. valve.
Figur. 2·9
Steam capacity te.t
of a V2 -inch bran
relief valve.
Figur. 2.10
Flow te.t piping for
2·inch fabricated .teel
y-pattern globe valve.
CRANE
2-7
CHAPTER 2 -- flOW Of flUIDS THROUGH VALVES AND fiTTINGS
Relationship of Pressure Drop to Velocity of Flow
Many experiments have shown that the head loss due
to valves and fittings is proportional to a constant
power of the velocity. When pressure drop or head
loss is plotted against velocity on logarithmic coordinates, the resulting curve is therefore a straight
line. In the turbulent flow range, the value of the
exponent of v has been found to vary from about
1.8 to 2.1 for different designs of valves and fittings.
However, for all practical purposes, it can be assumed that the pressure drop or head loss due to
the flow of fluids in the turbulent range through
valves and fittings varies as the square of the
velocity.
This relationship of pressure drop to velocity of flow
is valid for check valves, only if there is sufflcient
flow to hold the disc in a wide open position. The
point of deviation of the test curves from a straight
line, as illustrated in Figures 2-5 and 2-6, defines the
flow conditions necessary to support a check valve
disc in the wide open position.
Most of the difflculties encountered with check valves,
both lift and swing types, have been found to be due
to oversizing which results in
operation and premature wear of the moving parts.
Referring again to Figure 2-6, it will be noted that
the veloCity of 50 psig saturated steam, at the point
where the two curves deviate from a straight line, is
about 14,000 to15 ,000 feet per minute. Lower velocities are not sufflcient to lift the disc through its full
stroke and hold it in a stable position against the
stops, and can actually result in an increase in pressure drop as indicated by the curves, Under these
conditions, the disc fluctuates with each minor flow
''''leIf".1/>..2
__ . ~'I>r litlld ~_I!;> hi/.iI*
~<>td~ 1>'1> fbh
Figure 2-11
Y-Partern
Swing Check Valve
lift Check
Valve
pulsation, causing noisy operation and rapid wear of
the contacting moving parts.
The minimum velocity required to lift the dis: to the
full-open and stable position has been determined by
tests for numerous types of check and foot valves,
and is given in the "K' Factor Table (see pages A-26
thru A-29). I t is expressed in terms of a constant times
the square root of the specific volume of the fluid being
handled, making it applicable for use with any fluid.
Sizing of check valves in accordance with the specified
minimum velocity for full disc lift will often result in
valves smaller in size than the pipe in which they are
installed; however, the actual pressure drop will be
if any, higher than that of a full size valve which
is used in other than the wide-open position. The
advantages are longer valve life and quieter operation.
The losses due to sudden or gradual contraction and
enlargement which will occur in such installations
with bushings, reducing flanges, or tapered reducers
can be readily calculated from the data given in the
"K' Factor Table.
CRANE
CHAPTER 2 - flOW OF FLUIDS THROUGH VALVES AND FITTINGS
Resistance Coefficient K, Equivalent Length L/D,
And Flow Coefficient Cv
Pressure loss test data for a wide variety of valves
and fittings are available from the work of numerous
investigators. Extensive studies in this field have been
conducted by Crane Laboratories. However, due to
the time-consuming and costly nature of such testing,
it is virtually impossible to obtain test data for every
size and type of valve and fitting.
It is therefore desirable to provide a means of reliably
extrapolating available test information to envelope
those items which have not been or cannot readily be
tested. Commonly used concepts for accomplishing
this are the "equivalent length LID", "resistance
coefficient K", and "flow coefficient Cv ".
Pressure losses in a piping system result from a number of system characterist ics, which may be categorized
as follows:
1. Pipe friction, which is a function of the surface
roughness of the interior pipe wall, the inside
diameter of the pipe, and the fluid velocity,
density and viscosity. Friction factors are discussed on pages 1-6 and 1-7. For friction data,
see pages A-23 thru A-25.
2. Changes in direction of flow path
3. Obstructions in flow path.
4. Sudden or gradual changes in the cross-section
and shape of flow path.
The same loss in straight pipe is expressed by the
Darcy equation,
Equation 2·3
I t follows that,
Equation 2-4
The ratio LID is the equivalent length, in pipe diameters of straight pipe, that will cause the same pressure drop as the obstruction under the same flow conditions. Since the resistance coefficient K is constant
for all conditions of flow, the value of LID for any
given valve or fitting must necessarily vary inversely
with the change in friction factor for different flow
conditions.
The resistance coefficient K would theoretically be a
constant for all sizes of a given design or line of valves
and fittings if all sizes were geometrically similar.
110wever, geometric similarity is seldom, if ever,
achieved because the design of valves and fittings is
dictated by manufacturing economies, standards,
structural strength, and other considerations.
12-INCH SIZE
1/6 SCALE a=
Velocity in a pipe is obtained at the expense of static
head, and decrease in static head due to velocity is,
hL =
v2
,
2g
E~a';011 2.1
which is defined as the "velocity head". Flow
through a valve or fitting in a pipe line also causes a
reduction in static head which may be expressed in
terms of velocity head. The resistance coefficient K
in the equation,
hL =K
v2
2g
,
Equation 2·2
Figure 2-13
Geometrical dissimilarity between 2 and
I 2·lnch standard cast Iron flanged elbows
therefore, is defined as the number of velocity heads
lost due to a valve or fitting. It is always associated
with the diameter in which the velocity occurs. In
most valves or fittings, the losses due to friction (Category I above) resulting from actual length of flow path
are minor compared to those due to one or more of the
other three categories listed.
An example of geometric dissimilarity is shown in
Figure 2-13 where a 12-inch standard elbow has been
drawn to 116 scale of a 2-inch standard elbow, so that
their. port diameters are identical. The flow paths
through the two fittings drawn to these scales would
also have to be identical to have geometric similarity:
in addition, the relative roughness of the surfaces
would have to be similar.
The resistance coefficient K is therefore considered as
being independent of friction factor or Reynolds number, and may be treated as a constant for any given
obstruction (i.e., valve or fitting) in a piping system
under all conditions of How, including laminar flow.
Figure 2-14 is based on the analysis of extensive test
data from varioLls sources. The K coefficients for a
number of lines of valves and fittings have been plotted
against size. It will be noted that the K curves show
a definite tendency to follow the same slope as the
(contillued on IIe"t page)
CRANE
CHAPTER 2
2-9
FLOW OF FLUIDS THROUGH VALVES AND FITTINGS
Resistance Coefficient K, Equivalent Length L/D,
And Flow Coefficient Cv - continued
'-,
.r.r.
10.0
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6
H-WIo
K - Resistance Coefficient
r"'
r"'.
-----
Figure 2-14, Variation of Resistance Coefficient K (
Symbol
0
0-
9
-0
6
-0-
¢
-9d
tI.
~
*fr
Product Tested
I LID) with Size
Authority
30/T)* .... . Moody A.S.ME. Trans, Nov.-1944 Is
Univ. of Wisc. Exp. Sta. Bull., Vol. 9, No.1, 1922 16
. ...... Crane T es(s
..... Pigott A.S.ME. Trans. 19506
" . Pigott A.S.ME. Trans, 1950. Pigott A.S.ME. Trans, 1950"
Class 600 Steel Wedge Gate Valves, Seat Reduced ........ Crane Tests
Class 300 Steel Venturi Ball·Cage Gate Valves.
. . Crane-Armour Tests
Class 125 Iron Body Y.Pattern Globe Valves.
. Crane-Armour Tests
Class 125 Brass Angle Valves, Composition Disc ..
, Crane Tests
Class 125 Brass Globe Valves, Composition Disc.
. Crane Test s
Schedule 40 Pipe, 30 Diameters Long (K
Class 125 Iron Body Wedge Gate Valves
Class 600 Steel Wedge Gate Valves ..
90 Degree Pipe Bends, R/D = 2.
90 Degree Pipe Bends. R/ D = 3 ....
90 Degree Pipe Bends. R/ D = 1, ..
friction factor for flow in the zone of complete turbulence; see page A-26.
(coflfinued from the preceding page)
j(LI D) curve for straight clean commercial steel pipe
at flow conditions resulting in a constant friction
factor. I t is probably coincidence that the effect of
geometric dissimilarity between different sizes of the
same line of valves or fittings upon the resistance coefficient K is similar to that of relative roughness, or
size of pipe, upon friction factor.
Based on the evidence presented in Figure 2-14, it can
be said that the resistance coefficient K, for a given
tends toward a constant for the various sizes of a given
line of valves or fittings at the same flow conditions.
On the basis of this relationship, the resistance coefficient K for each illustrated type of valve and fitting
is presented on pages A-26 thru A-29. These coefficients are given as the product of the friction factor for
the desired size of clean commercial steel pipe with
flow in the zone of complete turbulence, and a constant, which represents the eqUivalent length LID for
line of valves or fittings, tends to vary with size as
the valve or fitting in pipe diameters for the sam~ flow
does the friction factor. j, for straight clean commercial
steel pipe at flow conditions resulting in a constant
friction factor, and that the equivalent length LID
conditions, on the basis of test data. This equivalent
length, or constant, is valid for all sizes of the valve or
fitting type with which it is identified.
2·10
CHAPTER 2 - flOW OF FLUIDS THROUGH VALVES AND fITTINGS
---------------------------------------------
CRANE
Resistance Coefficient K, Equivalent Length LID,
And Flow Coefficient Cv - continued
When a piping system contains more than one size of
valves, or fittings, Equation 2-5 may be used
to express all resistances in terms of one size. For
this case, subscript "a" relates to the size with reference to which all resistances are to be expressed,
and subscript "b" relates to any other size in the
system. For sample problem, see Example 4-14.
The friction factors for clean commercial steel pipe
with flow in the zone of complete turbulence (iT), for
nominal sizes from 1/2 to 24~inch, are tabulated at the
beginning of the "K" Factor Table (page A-26) for
convenience in converting the algebraic expressions of
K to arithmetic quantities.
There are some resistances to flow in piping, such as
sudden and gradual contractions and enlargements,
and pipe entrances and
that have geometric
similarity between sizes. The resistance coefficients
(K) for these items are therefore independent of size,
as indicated by the absence of a friction factor in their
values given in the "K" Factor Table.
It has been found convenient in some branches of the
valve industry, particularly in connection with control valves, to express the valve capacity and the
valve flow characteristics in terms of the flow coefficient Cv . The Cv coefficient of a valve is' defined as
the flow of water at 60 F, in gallons per minute, at
a pressure drop of one pound per square inch across
the valve.
As previously stated, the resistance coefficient K is
always associated with the diameter in which the
velocity in the term v2j2g occurs. The values in the
"K" Factor Table are associated with the internal
diameter of the followin~ pipe schedule numbers for
the various A'JSI Classes of valves and fittings.
By the substitution of appropriate equivalent units
in the Darcy equation, it can be shown that,
Cy~
Class 300 and lower ..................... Schedule 40
Class 400 and 600 ...................... Schedule 80
Class 900 .............................. Schedule 120
Class 1500 ............................. Schedule 160
Class 2500 (sizes }1 to 6/1) ............••...•.... XXS
Class 2500 (sizes 8/1 and up) .............. Schedule 160
Q ~ Cy
Equation 2-6
vi (6:. 4)
vi D.:
D.P
Equation 2-7
Q = 7.Q Cy
and the pressure drop can be computed from the
same formula arranged as follows:
An alternate procedure which yields identical results
for Equation 2-2 is to adjust K in proportion to the
fourth power of the diameter ratio, and to base values
of velOCity or diameter on the internal diameter of the
connecting pipe.
P
62·4
(Q)2
Cy
Equation 2-7
Since Equations 2-2 and 2-7 are simply other forms
of the Darcy equation, the limitations regarding
their use for compressible flow (explained on page 1-7)
apply. Other convenient forms of Equations 2-2 and
2-7 in terms of commonly used units are presented on
page 34
Equation 2·5
Subscript "a" defines K and d with reference to
the internal diameter of the connecting pipe.
Subscript "b" defines K and d with reference to the
internal diameter of the pipe for which the values of
K were established, as given in the foregoing list of
pipe schedule numbers.
*
vR
Also, the quantity in gallons per minute of liquids of
low viscosity* that will flow through the valve can be
determined from:
When the resistance coefficient K is used in flow equation 2-2, or any of its equivalent forms given in Chapter 3 as Equations 3-14,3-16,3-19 and 3-20, the velocity and internal diameter dimensions used in the
equation must be based on the dimensions of these
schedule numbers regardless of the pipe with which
the valve may be installed.
*
2q.qd2
*When handling highly viscous liquids determine flow
rate or required valve C v as described in the ISA
Handbook of Control Valves.
*
*
*
CRANE
CHAPTER 2
2 - 11
FLOW OF flUIDS THROUGH VALVES AND FITTINGS
Laminar Flow Conditions
In the usual piping installation, the flow will change
from laminar to turbulent in the range of Reynolds
numbers from 2000 to 4000, defmed on pages A-24 and
A-25 as the critical zone. The lower critical Reynolds
number of 2000 is usually recognized as the upper
limit for the application of Poiseuille's law for laminar
flow in straight pipes,
hL = 0.Oq62 (~;:)
Equalion 2.8
which is identical to Equation 2-3 when the value of
the friction factor for laminar How, f = 64/ R., is factored into it. Laminar flow at Reynolds numbers
above 2000 is unstable, and in the critical zone and
lower range of the transition zone, turbulent mixing
and laminar motion may alternate unpredictably.
Equation 2-2 (h L Kv 2/2g) is valid for computing the
head loss due to valves and fittings for all conditions
of How, including laminar flow, using resistance coefficient K as given in the "K" Factor Table.
When Equation 2-2 is used to determine the losses in
straight pipe, it is necessary to compute the Reynolds
number in order to establish the friction factor, j, to
be used to determine the value of the resistance coefficient K for the pipe in accordance with Equation
2-4 (K fL/D). See Examples, pages 4-4 and 4-5.
Contradion and Enlargement
The resistance to flow due to sudden enlargements
may be expressed by,
Kl =
0.5
o <: 45° ..... , .. Ce = 2.6 sin 2o Equalion 2-12
If, 45° < 0 <: 180° .... C.
(I
(I -~::)
Equation 2-10
Subscripts 1 and 2 defme the internal diameters of
the small and large pipes respectively.
I t is convenient to identify the ratio of diameters of
the small to large pipes by the Greek letter {3 (beta).
Using this notation, these equations may be written,
The losses due to gradual contractions in pipes were
established by the analysis of Crane test data, using
the same basis as that of Gibson for gradual enlargements, to provide a contraction coefficient, Cc , to be
applied to Equation 2-10.
The approximate averages of these coefficients for different included angles of convergence, 0, are defined
as follows:
IC,0<:45°···.·· ... Cc
Sudden Enlargement
Kl = (I - (32)2
.~
0.5 (r - (32)
Equation 2-10.1
Equation 2-9 is derived from the momentum equation together with the Bernoulli equation. Equation
2-10 uses the derivation of Equation 2-9 together with
the continuity equation and a close approximation of
the contraction coefficients determined by Julius
Weisbach. 2G
. 0
I. 6 sm2
Equolion 2.13
. /.
Equolion 2·13.1
0
V Sin;:
Equa/ion 2-9.1
Sudden Contraction
KJ
Equalion 2·12.1
Equallon 2-9
and the resistance due to sudden contractions, by
Kl
Ic,
The resistance coefficient K for sudden and gradual
enlargements and contractions, expressed in terms of
the large pipe, is established by combining Equations
2-9 to 2-13 inclusive.
Sudden and Gradual
Enlargements
Equalion 2-14
. 0
2. 6 sm-
o <: 45° ......... K2 = - - - - - : 2: : : - - - - -
The value of the resistance coefficient in terms of the
larger pipe is determined by dividing Equations 2-9
and 2-10 by {3\
K2 = Kl
{34
Equallon 2.11
The losses due to gradual enlargements in pipes were
investigated by A. H. Gibson, 22 and may be expressed
as a coefficient, C, applied to Equation 2-9. Approximate averages of Gibson's coefficients for different
included angles of divergence, 0, are defined by the
equations:
Equation 2-14.1
Sudden and Gradual
Contractions
Equalion 2·15
0.8 sin §.
(I - (32)
2
0<: 45° ......... K2 = ----f34~--Equation 2.15.1
0·5 V~ (I - (32)
f34
2 ·12
CHAPTER 2
CRANE
FLOW OF FLUIDS THROUGH VALVES AND FITTINGS
Valves with Reduced Seats
Valves are often designed with reduced seats, and the
transition from seat to valve ends may be either
abrupt or gradual. Straight-through types, such as
gate and ball valves, so designed with gradual transition are sometimes referred to as venturi valves.
Analysis of tests on such straight-through valves indicates an excellent correlation between test results and
calculated values of K based on the summation of
Equations 2-11, 2-14, and 2-15.
Valves which exhibit a change in direction of the flow
path, such as globe and angle valves, are classified as
high resistance valves. Equations 2-14 and 2-15 for
gradual contractions and enlargements cannot be readily applied to these configurations because the angles
of convergence and divergence are variable with respect to different planes of reference. The entrance
and exit losses for reduced seat globe and angle valves
are judged to fall short of those due to sudden expansion and contraction (Equations 2-14.1 and 2-15.1
at fJ = 180°) if the approaches to the seat are gradual.
Analysis of available test data indicates that the factor {3 applied to Equations 2-14 and 2-15 for sudden
contraction and enlargement will bring calculated K
values for reduced seat globe and angle valves into
reasonably close agreement with test results.
In the
absence of actual test data, the resistance coeffIcients
for reduced seat globe and angle valves may thus be
computed as the summation of Equations 2-11 and
{3 times Equations 2-14.1 and 2-15.1 at fJ
180°.
The procedure for determining K for reduced seat
globe and angle valves is also applicable to throttled
globe and angle valves. For this case the value of {3
must be based upon the square root of the ratio of
areas,
where:
al ... defines the area at the most restricted point
in the flow path
a2 ... defines the internal area of the connecting
pipe.
Resistance of Bends
Secondary flow: The nature of the flow of liquids
in bends has been thoroughly investigated and many
interesting facts have been discovered. For example,
when a fluid passes around a bend in either viscous
or turbulent flow, there is established in the bend a
condition known as "secondary flow". This is rotatmotion, at right angles to the pipe axis, which is
superimposed upon the main motion in the direction
of the axis. The frictional resistance of the pipe
walls and the action of centrifugal force combine to
produce this rotation. Figure 2-15 illustrates this
phenomenon.
Resistance of bends to flow: The resistance or head
loss in a bend is conventionally assumed to consist
of . . . . (I) the loss due to curvature.. . (2) the
excess loss in the downstream tangent. .. and (3)
the loss due to length, thus:
Equo/;on 2·16
where:
hi = total loss, in feet of fluid
h p = excess loss in downstream tangent, in feet of
fluid
he
loss due to curvature, in feet of fluid
hL loss in bend due to length, in feet of fluid
if:
hb = hp + he
;(
-----
Equation 2-17
then:
hI = hb + hL
However, the quantity hb can be expressed as a function of velocity head in the formula:
I
(
hb
Figur. 2·15
Secondary Flow In Bends
=
Kb
.,p
2g
Equation 2-18
where:
Kb the bend coefficient
v
velocity through pipe, feet per second
g = 32.2 feet per second per second
CRANE
CHAPTER 2 - flOW OF FLUIDS THROUGH VALVES AND FITTINGS
Resistance of Bends -
2-13
continued
.6r---~---.----r----r--~----.----.-=--r---'---~----'
°O~--~---+----~--~--~10'---~12,---h14--~1~6--~18~--~--~'
Relative Radius.
r/fl
Figure 2-16, Bend Coefficients Found by Various In"estlgoton (leW')
from ""'.lIvre Lo.... for fhHd Flow in 90° Pip.. Bend," by K. H. "ij.
Cowte • ." af Journal of ReHartb of Notionol B\lreau of Standard•.
Investigator
Diameter
Symbol
Balch ..
Davis.
Brightmore ..
Brightmore.
Hofmann.
Hofmann.
Vogel..
... =..=.=.=..=.=
..=.=)-=in=c=h=.= = = = = =
•
. .. ,-inch.
. ...... J-inch. .
.4-inch.
. 1. 7-inch (rough pipe) .
. . I. 7-inch (smooth pipe) .
.0.8. and lo-inch..
. ...... 4-inch.
The relationship between Kb and rid (relative radius*)
is not well defined, as can be observed by reference
to Figure 2-16 (taken from the work of Beij21). The
curves in this chart indicate that Kb has a minimum
value when rid is between 3 and 5.
•
C
...
D.
...
•
made up of continuous 90 degree bends can be determined by multiplying the number (n) of 90 degree
bends less one contained in the coil by the value of K
due to length,
one-half of the value of 1< due to
bend resistance, and adding the value of K for one 90
bend (page A-19).
Values of K for 90 degree bends with various bend
ratios (rid) are listed on page A-29. The values (also
based on the work of Beij) represent average conditions of flow in 90 degree bends.
The loss due to continuous bends greater than 90
degrees, such as pipe coils or expansion bends, is less
than the summation of losses in the total number of
90 degree bends contained in the coil, considered separately, because the loss h p in Equation 1-16 occurs
only once in the coiL
The loss due to length in terms of K is equal to the
developed length of the bend, in pipe diameters, multiplied by the friction factor /T as previously described
and as tabulated on page A-16.
Equation 2-20
Subscript 1 defmes the value of 1< (see page A-29)
for one 90 degree bend.
Example:
A 2" Schedule 40 pipe coil contains five complete
turns, i.e., twenty (n) 90 degree bends. The relative
radius (rid) of the bends is 16, and the resistance coefficient Kl of one 90 degree bend is 42fT (42 x .019
.80) per page A-29.
Find the total resistance coefficient (1<8) for the coil.
K8 = (20-1) (0.25 x 0.019 7r x 16 + 0.5 x 0.8) + 0.8
Equation 2-19
In the absence of experimental data, it is assumed
that hp he in Equation 2-16. On this
the
total value of K for a pipe coil or expansion bend
=
13
Resistance of miter bends: The equivalent length
of miter bends, based on the work of H. Kirchbach4,
is also shown on page A-29.
*The relative radius of a bend is the ratio of the radius of the bend axis to
the internal diameter of the pipe. Both dimensions must be in the same units.
2·14
CRANE
CHAPTER 2 - flOW OF flUIDS THROUGH VALVES AND FITTINGS
Flow Through Nozzles and Orifices
Orifices and nozzles are used principally to meter rate of flow, A portion
of the theory is covered here, For more complete data, refer to Bibliography sources 8, C), and 10 , , , or to information supplied by the meter
manufactureL
Orifices are also used to restrict flow or to reduce pressure, For liquid
flow, several orifices are sometimes used to reduce pressure in steps so as
to avoid cavitation. Overall resistance coefficient K for an orifice is given
on page A-20, For a sample problem, see page 4-7.
The rate of flow of any fluid through an orifice or
nozzle, neglecting the velocity of approach, may be
expressed by;
q
may be taken from page A-20 if hL or 6.P in Equation 2-23 is taken as the upstream head or gauge
pressure,
Equation 2-21
Velocity of approach may have considerable effect on
the quantity discharged through a nozzle or orifice.
The factor correcting for velocity of approach,
Flow of gases and vapors; The flow of compressible fluids through nozzles and orifices can be expressed by the same equation used for liquids except
the net t::xpansion factor Y must be included,
q
may be incorporated in Equation 2-21 as follows:
A
q
Equat/oll 2-22
Equation 2 -24
The expansion factor Y is a function of:
I. The speCific heat ratio, k.
2. The ratio (p) of orifice or throat diameter to
inlet diameteL
3, RatIO of downstream to upstream absolute
pressures.
The quantity
This factor~·lo has been experimentally determined
on the basis of air, which has a specific heat ratio of
14. and stcam
specIfic heat ratios of approximately 1.3. The data is plotted on page A-21.
is defined as the flow coefficient C. Values of C
for nozzles and orifices are shown on page A-20, Use
of the flow coefficient C eliminates the necessity for
calculating the velocity of approach, and Equation
2-22 may now be written:
Values of k for some of the common vapors and gases
are given on pages A-8 ancl A-9, The specific heat
ratio, k, may vary
for c!iffere:lt pressures and
temperatures, but for most practical problems the
values
\\ill provide reasonably accurate results
Equation 2-23
q
CA
=
CA
Orifices and nozzles are normally used in piping systems as metering devices and are installed with
flange taps or pipe taps in accordance with ASME
specifications, The values of hL and 6.P in Equation
2-23 are the measured differential static head or
pressure across pipe taps located J diameter upstream
and 0.5 diameter downstream from the inlet face of
the orifice plate or nozzle, when values of C are taken
from page A-20, The flow coefficient C is plotted
for Reynolds numbers based on the internal diameter
of the upstream pipe.
Flow of liquids; For nozzles and orifices discharging incompressible fluids to atmosphere, C values
Equation 2-24 may be usce: for orifices discharging
compressible :1uios to atmosphere by using:
1. Flow coefficient C given on page A-20 in the
Reynolds number range where C is a constant
for the given diameter
fr
2. Expansion factor Y per page A-21.
3. Differential pressure 6.P, equal to the inlet
gauge pressure,
This also applies to nozzles discharging compressible
fluids to atmosphere only if the absolute inlet pressure is less than the absolute atmospheric pressure
divided by the critical pressure ratio rc; this is
discussed on the next page. When the absolute inlet
pressure is greater than this amount, flow through
nozzles should be calculated as outlined on the
follOWing page.
CRANE
2 ·15
CHAPTER 2 - FLOW OF FLUIDS THROUGH VALVES AND FITTINGS
Flow Through Nozzles and Orifices Maximum flow of compressible fluids in a nozzle: A smoothly convergent nozzle has the property
of being able to deliver a compressible fluid up to the
velocity of sound in its minimum cross section or
throat. providing the available pressure drop is
sufficiently high, Sonic velocity is the maximum
velocity that may be attained in the throat of a
nozzle (supersonic velocity is attained in a gradually
divergent section following the convergent nozzle,
when sonic velocity exists in the throat),
continued
Equation 2-24 may be used for discharge of compressible fluids through a nozzle to atmosphere, or
to a downstream pressure lower than indicated by
the critical pressure ratio r c, by using values of:
Y , , . , minimum per page A-21
C . . . , page A-20
l:c,.P ... , p I 1 (l
re); r. per page A-21
p ., .. weight density at upstream condition
The critical pressure ratio is the largest ratio of
downstream pressure to upstream pressure capable
of producing sonic velocity. Values of critical pressure ratio r e, which depend upon the ratio of nozzle
diameter to upstream diameter as well as the specific
heat ratio k. are given on page A-21.
Flow through short tubes: Since complete experimental data for the discharge of fluids to atmosphere through short tubes (LID is less than, or equal
to, 2.5 pipe diameters)1 are not available, it is suggested that reasonably accurate approximations.may
be obtained by using Equations 2-23 and 2-24, with
values of C somewhere between those for orifices
and nozzles, depending upon entrance conditions.
Flow through nozzles and venturi meters is limited
by critical pressure ratio, and minimum values of Y
to be used in Equation 2-24 for this condition, are
indicated on page A-21 by the termination of the
curves at pl21 P't = re.
If the entrance is well rounded, C values would tend
to approach those for nozzles, whereas short tubes
with square entrance would have characteristics
similar to those for square edged orifices.
Discharge of Fluids Through Valves, Fittings, and Pipe
Liquid flow : To determine the flow of liquid through
pipe, the Darcy formula is used. Equation 1-4 (page
1-6) has been converted to more convenient terms in
Chapter 3 and has been rewritten as Equation 3-14.
The form of Equation 3-14 which is most applicable
to liquid flow is written in terms of flow rate in
gallons per minute.
h L = _o_.O_O_2~c---"'-
Solving for Q, the equation can be rewritten,
Equation 2-25
Equation 2-25 can be employed for valves, fittings,
and pipe where K would be the sum of all the resistances in the piping system, including entrance and
exit losses when they exist. Examples of problems
of this type are shown on page 4-12.
Compressible flow: When a compressible fluid flows
from a piping system into an area of larger cross section than that of the pipe, as in the case of discharge
to atmosphere, a modified form of the Darcy formula.
Equation I-II developed on page 1-9, is used.
Figure 2.17
Pressure measurements made at strategic points
in a valve in order to establish optimum design.
The determination of values of K Y. and l:c,.P in this
equation is described on page 1-9 and is illustrated
in the examples on pages 4-13 and 4-14.
2· 16
CHAPTER 2
flOW OF FLUIDS THROUGH VALVES AND FITTINGS
"'-'!If "I1J on
p~.l_ drop
CRANE
3 -1
Formulas and Nomographs
For Flow Through
Valves, Fittings, and Pipe
CHAPTER 3
Only basic formulas needed for the presentation of
the theory of fluid flow through valves, fittings, and
pipe were presented in the first two chapters of this
paper. In the summary of formulas given in this
chapter, the basic formulas are rewritten in terms of
units which are most commonly used in this country.
This summary provides the user with an equation
which will enable him to arrive at a solution to his
problem with a minimum conversion of units.
l\"omographs presented in this chapter are graphical
solutions of the flow formulas applying to pipe. Valve
and fitting flow problems may also be solved by means
of these nomographs by determining their equivalent
length in terms of feet of straight pipe.
Due to the wide variety of terms and the variation in
the physical properties of liquids and gases, it was
necessary to divide the nomographs into two parts:
the first part (pages 3-6 to 3-1 5) pertains to liquid flow,
and the second part (pages 3-16 to 3-25), pertains to
compressible flow.
All nomographs for the solution of pressure drop problems are based upon Darcy's formula, since it is a
general formula which is applicable to all fluids and
can be applied to all types of pipe through the use of
the Moody Friction Factor Diagram. Darcy's formula also provides a means of solving problems of flow
through valves and fittings on the basis of equivalent
length or resistance coefficient. Nomographs provide
simple, rapid, practical. and reasonably accurate solutions to flow formulas and the decimal point is accurately located.
Accuracy of a nomograph is limited by the available
page space, length of scales, number of units provided
on each scale, and the angle at which the connecting
line crosses the scale. Whenever the solution of a
problem falls beyond the range of a nomograph, the
slide rule or arithmetical solution of the formula must
be employed.
3-2
CHAPTER 3
CRANE
fORMULAS AND NOMOGRAPHS fOR fLOW THROUGH VALVES, fiTTINGS, AND PIPE
----------~------
Summary of Formulas
To eliminate needless duplication, formulas have
been written in terms of either specific volume V
or weight density p, but not in terms of both, since
one is the reciprocal of the other.
p=
p
These equations may be substituted in any of the
formulas shown in this paper whenever necessary,
• Head loss and pressure drop
in straight pipe:
Pressure loss due to flow is the same in a sloping,
vertical, or horizontal pipe, However, the difference in pressure due to the difference in head
must be considered in pressure drop calculat ions:
see page 1-5,
Equation 3-5
Darcy's formula:
fLQ2
• Bernoulli's theorem:
Z +
0,0311 ~
3·'
Equation
2
144 P
P
+ v
H
2g
fLpV2
0,000 000 359
0,000 216
• Mean velocity of flow in pipe:
(Continuity Equation)
=
'V
= 0,286 B
V
0,001
V
Equation 3·2
A
IBn
=
q'h T
wV
A
0086 5
q'h T
q'hS.
--;J.2
R,
12 3,9
47NP
-R H/;.-
\\7
DI'
If
R,
Equation 3-3
Dvp
R. = 22 700 ~:
j
f
For limplilled compreuible fluid
formula, lee page 3·22,
3,06(12-
0,2 J3
P'cP
Dvp
6,3 1
q'hS.
'XIV
2,4 0 --a-
q'hS.
dv
1211
,
q
4 1 9 000 ---
lid
• Viscosity equivalents:
dvp
Qp
50 ,6(l;
0,482 --~-
(1];
J 5-4
Bp
-er;;-
dv
7740 - -
"
3 160
fL T(q' h )2S.
--(li.p-'---
_
0,000 000 00 i '26
--;;J2
'XIV
qm
R,
L:,.P
0,003 8 9
44 -P'd2
• Reynolds number
of flow in pipe:
R,
fL;sQ2
q
v
V
d-
II~
WV
394
-;(J
Equalion 3-4
• Head loss and pressure drop
with laminar flow in straight pipe:
For laminar flow conditions CR, < '2000), the friction
factor is a direct mathematical function of the
Reynolds number only, and can be expressed by
the formula f = 64/ R e , Substituting this value of
f in the Darcy formula, it can be rewritten:
~Lv
hL
0,09 62 (1£p
hL
17 65 _!,Lq
hL
002 75
,
~LQ
00393 (Ji p
d 4p
~U3
L:,.P
0,000668,
L:,.P =
0,000
L:,.P =
0.0000340
E"",,'ion 3-6
~L\\?
0,004 90 -(14p2
~Lv
(j2
2i3~;.Q..
~LW!
0, 122 5
~Lq
-J4'
0.000 19 1
/lLB
----;J'4
CRANE
3-3
CHAPTER 3 - FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, FITTINGS, AND PIPE
Summary of Formulas -
continued
• Empirical formulas for the flow
of water, steam, and gas
• Limitations of Darcy formula
Non-comprassibla flow; liquids:
The Darcy formula may be used without restriction
for the flow of water, oil, and other liquids in pipe.
However, when extreme velocities occurring in pipe
cause the downstream pressure to fall to the vapor
pressure of the liquid, cavitation occurs and calculated flow rates are inaccurate.
Comprnsible flow; gases and vapors:
Although the rational method (using Darcy's formula) for solVing flow problems has been recommended in this paper, some engineers prefer to use
empirical formulas.
Hazen and Williams
formula for flow of wale"
When pressure drop is less than 10% of PI, use p or
V based on either inlet or outlet conditions.
When pressure drop is greater than 10% of PI but
less than 40% of PI, use the average of p or V
based on inlet and outlet conditions, or use Equation 3-20.
When pressure drop is greater than 40% of PI, use
the rational or empirical formulas given on this
page for compressible flow, or use Equation 3-20
(for theory, see page I-q).
Equation 3-9
where:
= 140 for new steel pipe
C
130 for new cast iron pipe
C l i O for riveted pipe
C
Equation 3· 10
(deleled)
• Isothermal flow of gas
in pipe lines
Equation 3·7
Spilzglass formula for low pressura gas.
Equation 3· 1 I
(pressure less than one pound gauge)
t:,.hU' do
355 0
J
- _...(
Su L
I+ 3
6
d + C.03 d
)
Flowing temperature is 60 F,
• Simplifled compressible flow
for long pipe lines
w
~
Equation 3-70
J( ;::i) (
Way mouth formula
for high prassura gas:
Equation 3-12
Panhandle formula' for nalural gas
pipe linn 6 to 24-inch diametar
and Ie = (5 X 106 ) to (14 x JC)6).
Equation 3· J 3
(P'.)' P', (P")')
q' ~
• Maximum (sonic) velocity of
compressible fluids in pipe
The maximum possible velocity of a compressible
fluid in a pipe is equivalent to the speed of sound
in the fluid; this is expressed as:
7'"'
.~
v. = .JkgRT
v.
.Jkg 144pt V
V.
68.1
Eq uation 3·8
= 36 .8£ d2.6182 ( (P' I )2 ~ (PI 2)2
)0
'
5394
where: gas temperature = 60 F
Su
0.6
£
flow efficiency
£
1,00 (100%) for brand new pipe without
any bends, elbows, valves, and change
of pipe diameter or elevation
£
0,95 for very good operating conditions
E
0.92 for average operating conditions
E
0.85 for unusually unfavorable
operating conditions
3-4
CHAPTER 3 - fORMULAS AND NOMOGRAPHS fOR flOW THROUGH VALVES, FITTINGS, AND PIPE
Summary of Formulas • Head loss and pressure drop
through valves and flHings
Head loss through valves and fittings is generally
given in terms of resistance coefficient K which
indicates static head loss through a valve in terms
of "velocity head", or, equivalent length in pipe
diameters LID that will cause the same head loss
as the valve.
•
continued
Resistance coefficient, K, for sudden and gradual
enlargements in pipes .
If, e <: 45°,
Kl = 2.6 sin f3 (I -
2g
and head loss through a valve is:
(32)2
*Equation 3·17
2
Ir, 45° < f3 <: 180°,
Kl = (I -
From Darcy's formula, head loss through a pipe is:
2
hL
f L -v
Equation 3·5
CRANE
•
(32)2
*Eqllotion 3·17.1
Resistance coefficient, K, for sudden and gradual
contractions in pipes
Ir, e'< 45°,
Equation 3·14
Kl = 0.8 sin! (I
therefore:
*Equatioll 3-18
2
Equation 3·15
Ir, 45° < (j <: 180°,
To eliminate needless duplication of formulas, the
following are all given in terms of K, Whenever
necessary, substitute (f LID) for (K),
KQ2
0.002 59 (fI'
Equation 3·14
KB2
D.P
KW2\12
0.001 270 ~ =
0.0000403
0.000 1078 K pv2 =
0.00000003 00 KpV2
Kpq2
3·62
-([I =
Kl
0·5
V
sin :- (I
'Equation 3-18.1
*Note: The values of the resistance coefficients (K)
in equations 3-17, 3-17.1, 3-18, and 3-18.1 are
based on the velocity in the small pipe. To determine K values in terms of the greater diameter,
divide the equations by {34.
KpQ2
0.00001799----;:J4
• Discharge of fluid through valves,
flHings, and pipe; Darcy's formula
KpB2
0.000 008 82 ~
KW2V
D.P = 0.000000 280 -~0.000 000 000 60 5
0.000 000 001 633
K(q\)2 T Su
d 4 pI
K (q/~)2 S/
d4 p
For compressible flow with hL or t;P greater than approxi.
mately 10% of Inlet absolute pressure, the denominator
should be multiplied by Y'. For values of Y, see page A-22.
CompressIble flow:
•
Equation 3·20
Pressure drop and flow of liquids of low
viscosity using flow coefficient
D.P
(QCv Y
p
Equation 3·16
62.4
I
Q Cv~ D.P 6: 4 = 7.90Cv~ ~P
d
d2
Cv
QJ D.P (62-4) .y29.9
f LID
qm
q'
2
p
K
89 1 d 4
(CV)2
w
Values of Yare shown on page.A-22, For K, Y. and
t:,.p determination. see examples on pages 4-13 and 4-14.
CHAPTER 3
FORMULAS AND NOMOGRAPHS FOR FLOW THROIroH VALVES. FITTINGS. AND PIPE
CRANE
3-5
...
....- - - . -..- - - - - . . .
... _ - - . . . .
... _ - - ... - - - - - - - -
-
-----.~
Summary of Formulas •
Flow through nozzles and orifices
(hL and llP measured across pipe taps
at 1 diameter and 0.5 diameter)
liquid:
concluded
• Specific gravity of liquids
Any liquid:
Equalion 3-25
any liquid at 60 F.
Equalion 3·21
s
p ( unless otherwise specified
p
(water at 60 F)
=
q = AC.j2g hL
Oils:
Equalioll 3·26
S (60 F /60 F)
q
13 1
Liquid$ lighler than wate"
Q
Comprenibl. fluids:
S (60 F/60 F) =
16P P't
40 700 Y d1 C\j TJ S,
q' h
Yd12 C - 24 700 ---:S;-" 6P P!
q'm
6 8 Yd2C
,
412
2
7
Equalioll 3·28
145
Deg Baume
145
Equalion 3·22
qh
qm
130 + Deg Baume
Liquids heavier than water:
Values of C are shown on page A·20
I
EqualiOIl 3·21
140
S (60 F /60 F)
w
)
1
•
i 6 P pI!
\/
T! Sa
Specific gravity of gases
Sa
R (air)
R (gas)
Sq
M (gas)
M (air)
EqUOlioll 3·29
53·3
R (gas)
M
29
2
Y d1 C .J6PP;
• General gas laws for perfect gases
q'
p'V"
q'
RT
Wa
p
W
w
Wa
Va
Equatioll 3·30
p'
RT
'44 pI
R
189 1 Y d12 C
144 P'
Ifr
Equation 3-31
Equatioll 3·32
---;;r-
Equatiall 3-33
/6P
\j VI
n.MRT = na 1545T
Values of C are shown on page A-20
Values of Yare shown on page A-21
EquatiOIl 3-34
• Equivalents of head loss
and pressure drop
p
Equalion 3·23
=
where:
n. =
6P
• Changes in resistance coefficient, K,
required to compensate
for different pipe I. D.
Eq ualion 3-24
(see poge A·30)
Subscript a refers to pipe in which valve will be installed.
Subscript b refers to pipe for which the resistance coefficient
K was established.
p'M
P'M
1545 T
10·72
·w./M
P'S,
2.70
T
number of mols of a gas
• Hydraulic radius·
Equatioll 3-35
cross sectional flow area (sq. feet)
wetted perimeter (feet)
Equivalent diameter relationship:
D = 4RH
d
48R H
·See page 1·4 for limitations.
CHAPTER 3-FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, FITTINGS, AND PIPE
3·6
CRANE
Velocity of Liquids in Pipe
The mean velocity of any flowing liquid can be calculated
from the following formula, or, from the nomograph on the
opposite page. The nomograph is a graphical solution
of the formula.
v =
(For values of d, see pages 8-16 to B-19)
The pressure drop per 100 feet and the velocity in Schedule 40 pipe, for water at 60 F, have been calculated for
commonly used flow rates for pipe sizes of Y8 to 24-inch;
these values are tabulated on page 8-14.
w
d
p
Qq
Example 1
Example 2
Given: NO.3 Fuel Oil at 60 F flows through a 2inch Schedule 40 pipe at the rate of 45,000 pounds
per hour.
Given: Maximum flow rate of a liquid will be 300
gallons per minute with maximum velocity limited
to 12 feet per second through Schedule 40 pipe.
Find: The rate of flow in gallons per minute and
the mean velocity in the pipe.
Find. The smallest suitable pipe size and the
velocity through the pipe.
Solution:
Solution:
I.
. page A-7
p
Connect
2.
W= 45000
J.
Q = 100
Connect
Read
1.
p
= 56 .0 2-
Q= 100
2.
2"
Sched 40
V
= 10
).
Q = 300
I
12
d = 3.2-
3lj2" Schedule 40 pipe suitable
Q =3 00
I 3>1" Sched 40
Reasonable Velocities
For the Flow of Water through Pipe
Service Condition
v =
Read
Reasonable Velocity
Boiler Feed. . . . . .
. . . . . . . . .. .. 8 to I 5 feet per second
Pump Suction and Drain Lines ... 4 to 7 feet per second
General Service ... ' . . . . . . . .
4 to 10 feet per second
City ........................ , , ,. to 7 feet per second
v = 10
CRANE
3-7
CHAPTER 3 - FORMULAS AND NOMOGRAPHS FOR FlOW THROUGH VALVES, FITTINGS, AND PIPE
Velocity of Liquids in Pipe
(continued)
d
3/8
Q
q
40000
100
80
W
10000
8000
30000
6000
20000
4000
V2
60
2000
10000
8000
.6
.7
40
3/4
30
3000
.5
.8
.9
t!J
1.0
6000
P
/',
4000
1000
,800
3000
600
2000
10
8
6
L5
1~
4
;;
Q;
200 2
<>
~llO
-:;
'"
co
'"'"
'"
"0
=
tC>
~,
'"
100 V>
co
C>
80 :;;;200
<:J
60
40
30
""'"
=
.8
t!J
.6
;;: 100
-:; 80
~
2
.4 U=>
-:;
2
'" 60
I
20
8
co
.2 LI..
.!!:
t;»4O
'"
LI..
<>
.3
30
10
~-
Q;
c.
'"
t:t:
.1
.08 """'
.06
.04
2
.,'"
-'=
40
II
t!J
15
10
8
6
4
3
0;
t:t:
-:;
.!!:
co
i
~~
LI..
.,8
VI
:i400
a.
co
600
'"co
"0
=>
r'
100
80
60
2
=>
c::
Q.
.~
1000
800
300
<>
=
40
I'
400
~
37
1%
1
.8
.6
.4
.3
.2
'-'
co
co
co
.,'-'
.,;
<>
VI
;;;
Q.
0;
.,
LI..
co
2
-;;
<>
2Yz
2.5
8
4
3
2
.•01
.008
.006
.004
.003
~
.3
co
;;
c.
Q
a.
'0
""
'"
:;
..,
..c::
..,
3Yz
3.5
2..,
"0
c.
'"co
"0
=>
C>
a.
'"
~
Cl
'-'
-:;
«i
c'"
>
;,:;;
.,
«i
"
-.:;
E
4
'"
N
==
.!!:
co
c
e
C>
z
I
6
6
50
co
VI
£.
45
=>
'"c:::
:::;
.,.
55
'0;
i!!=
..",
<:l.
60
65
.1
9
.02
.8
.4
u
,!:-
10
10
6
3
.6
.=
<>
.03
10
2
.0
<.>
..;
a.
LI..
.,
'"
-<=
.8
14
16
15
18
t!J
20
.OQ2
24
.6
.5
12
25
.001
70
W
I
Reynolds number may be calculated from the formula
below, or, from the nomograph on the opposite page.
The nomograph is a graphical solution of the formula.
R.
22
700
=
50.6
CD
~: = 6.31 ~
(For values of d, see pages B-16 to B-19)
n
::J:
>
."
The friction factor for clean steel pipe can be obtained
from the chart in the center of the nomograph. Friction
factors for other types of pipe can be determined by using
the calculated Reynolds number and referring to pages
A-23 and A-24.
...
m
'"...
I
0
"'1'1
'"3:c:
Q. '<
'"
>
~
:::I, CD
cr 0
qQ
:::I
W
:::I
p
--......
"'1'1
Q
ii:
CIt
'"0 ZC
Example 2
Given: Water at 200 F flows through 4-inch Schedule
40 steel pipe at a rate of 415 gallons per minute.
Given.' Fuel Oil No. 3 at 60 F flows through 2-inch
Schedule 40 steel pipe at a rate of 100 gallons per minute.
Find: The flow rate in pounds per hour, the Reynolds
number, and the friction factor.
Find: The flow rate in pounds per hour, the Reynolds
number, and the friction factor.
Solution:
Solution:
0
3:
0
G>
>
'"
."
CD
-...
0
0
CD
Q
0
.a'
C
_.
'"0c:
tr
...
n
Example 1
z0
z
3
0
f
);:
:::I
VII
r-
m Q..
"'1'1
:! 0
"0
CD
~
::J:
'"
...'"
~
...::J:
G>
:x:
<
>
<
m
~
.,.
::;
::!
z
1.
p
60.107
. page A-6
1.
P
56 .02
.page A-7
2.
I"
0.3 0
page A-3
2.
I"
9·4
.page A-3
G>
~
>
z0
."
Connect
Read
3·
Q
4·
W
5·
6.
R.
4 15
200000
=
60. 107
200000
3·
Read
:;;
m
= 56.02
Index
4·
Index
Re = 1000000
._---
5'.
R.
14
1000000
f = 0.017
6.
f
0.03
n
,..
~
Z
rn
)
)
)
)
)
q
Q
20000
10 000
8000
6000
10
B
6
4
3
2
4000
3000
2000
1000
800
600
"0
""
0
.!!:!
..,'-' .B1
400 ~
;;:;
300 ::
..,
(,?
-..,..,
Q.
"'-'
.Q
:::>
U
0:::
.6
"'-
.4
.3
.2
",,0
lL.
.1
~ .OB
OJ
Oi .06
0::
.04
<.:::r< .03
I
.02
.01
.008
.006
.004
.003
.002
200 ..,
<:
0
'"
<.:)
10000
8000
6000
10
8
6
4
3
2
1
.B
.6
24
~IB
~l'
R,
10 000
6000
4 000
1000
BOO
400 :;
<::>
300 :l:
;;;
Q.
200 VI
"0
<:
,.
<::>
100 Il..
so
60
~
'"
'"'"
"0
0:::
:::>
0
=
I-
4
3
2
1
.8
.6
.4
.3
.2
2
\1
'" 1 000 1=
"0
"" 600 t-'",.'" 400
0
.c
I-
?i
"~
..
.!!:!
0::
-1
3/4
~
1/2
~.
-"
.Q
:::>
z
'"
<:>
..,""»
"0
0::
I
I
.'\ 1\\
20
10
6
4
2
~
.6
.4
.2
•J
~
I-IYI
200
"" 100
60
OJ
40
E
<:
~
10
8
6
3
2000
GOO
20
I
Index
2000
~
0'
Internal Pipe
Diameter, Inches
4000
3 000
40
30
20
)
w
100.=
BO ?i
0
60 lL.
40 ..,
'"
30 0::
)
.\.
Ni
.01
.02
.03
.04 .0
f . Friction Factor lor Clean
Steel Pipe
)
)
)
)
)
w
...o•
The pressure drop of flowing liquids can be
calculated from the Darcy formula that follows, or, from the nomograph on the opposite
page. The nomograph is a graphical solution
of the formula.
0. 12 94
jpv 2
·····d
4350
Example 1
Given: Water at 200 F flows through 4-inch Schedule 40
new steel pipe at a rate of 200,000 pounds per hour.
Find: The pressure drop per 100 feet of pipe.
n
%
j~f
)0.
.. '"...
Solution:
(For values of d. see pages 8-16 to 8-19)
I.
P
60. 107
..... ............. page A-6
2.
P-
0.30
0.017
4 15
.........
J.
j
4·
Q
j
=
Index 1
7·
Index 2
C
i
. Example I, page 3-8
..
c
.. Example I. page 3-8
0.017
6.
c.c.-
...... page A-3
1 P
60. 107
Index 1
4 15
4" Sched 40
Index 2
Q
I
J
0
Read
Connect
).
."
CD
.6.Ploo = 3.6
"-::I
....
.iiC
a:
Given: No. 3 Fuel Oil at 60 F flows through a 2-inch
Schedule 40 pipe at a velocity of 10 feet per second.
When flow rate is given in pounds per hour (W), use the
following equation to convert to gallons per minute (Q).
or use the nomograph on the preceding page.
W
Q =S.02P
For Reynolds number less than 2000, flow is considered
laminar and the nomograph on page 3-13 should be used.
Find: The pressure drop per 100 feet of pipe.
1.
P
-....
2.
Q
J.
j
0
....
C
C
..
... .............. page A-7
::!!
.. Example I. Step 3; page 3-6
0
~
., ... Example 2. page 3-8
)0.
z
z
1:1
i0
0
'"....
)0.
%
en
:E
Ci"
,
~
c.-
::I
56 .02
100
0.030
~
....
-::I
V
Solution:
.,.I
0
i!l
CD
Example 2
:!I
m
'".,.
6
...
%
i3
c
0
%
~
:;:m
~
.,.
3
i
0
~
)0.
Z
1:1
...
:;;
m
""'-
The pressure drop per 100 feet and the velocity in
Schedule 40 pipe, for water at 60 F, have been calculated
for commonly used flow rates for pipe sizes of Ys to
24-inch; these values are tabulated on page 8-14.
4·
100
).
Index 2
n
.6.P1oo = 10
6.
:ID
:J>
Z
m
-:
)
)
)
)
))
)
)
)
)
I
)
)
"
)
)
)
')
)
)
)
)
)
v
Index 2
q
Q
50
40
dl 000
n
P
Z
65
30
20
.05
.06
d
Index 1
2000
1000
"0
c:
.05
aoo
8
'"
(/)
;;;
,04
""
-;;;
I
'" .8
I.L.
.03 E'-'
'"
I.L.
c:
0
'Z;
.02
'-'
.c
u
.4
"j;- .3
'-'
~
I.l..
'-.
':;
.2
~
'"
0::
.015
400
300
I
<:::-
200
.I
.08
.06
.04
.03
9 ""
'-'
100
80
2*
2
60
1*
.004
.• 003
'-'
L:)
::J
u
;;;
a.
<II
-0
':;
I::
<l)
0..
50
'"
a.
101::
'"
8 :;;;
3/8
V4
;; VB
4
E
I.L.
':;
Oa.
~a:
2 -;;;'"
'-0
""I
.:: :;
10>
z'B
::>
0
1
;;;
a.
Q.
""..,co
3:
.8
.7
.6
.5
<l)
~
E
0
..,
C
'"'"
~
<J
40
.a
C
!:':
:::J
-..
CD
CIt
0
..,'">
:c
'"0
,.
...
0
...~
,.:c
a
<
Y'
...
....
=<
~
z
::!!
!"
0
(
a
:;:m>
CD
:::J
30
Z
!!:
cr
C
20
z
....
..
10
c:
c:
Cl
:c
C
40
50
60
.2
"
a
0
5
6
0..
is
' .3
!::
4
::J
.:(
.4
CD
3
!!:
":::J-.
...S·:::s'" a:.
'"
'"I
,.0
..
!:':
........
m
;:
'">
0
0
'"
0
I::
- .,
Cil
0..
c::
:='!
'"
C
.4
.5
.6
.8
I::
...
CiCItl
CIt
.3
'"
"0
<=>
<l)
45
1/2
a.
>.
I
dl=
::;;;
;;:;
"";;:;
I.l..
I::
E
2 '"
~
3/4
::J
cr
c:
-:::;
~
;:;;
>
..,
."
C
::>
0
1\4
30
0
0
I.l..
0
40
6 c:
.006
55
8 c
7 c::
6 .,;
,s!5 0..
5
'-"
.01.008
..,
0;
<II
.02
.2
""c::<.>
109;
4
::>
-.01
5
aJ
18
16
14
12
c:
I.L.
I
.6
::>
12
10
8
600
r"\
:c
24
24
dl
16
f
.08
.1
30
4000
3000
m
c".Pwo
10000
a000
6000
10
8
6
,.'"
~
Cl
z>
0
..,
:;;
m
80
100
"'"",
"iii..,
w
5'"
0'"
'"
.I
37
-...
3-12
CHAPTER 3
CRANE
FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, FITTINGS, AND PIPE
Pressure Drop in Liquid Lines for Laminar Flow
Pressure drop can be calculated from the formula below,
or, from the nomograph on the opposite page, only when
the flow is laminar. The nomograph is a graphical
solution of the formula.
Flow is considered to be laminar at Reynolds number of
2000 or less; therefore, before using the formula or nomograph, determine the Reynolds number from the formula on page J-2 or the nomograph on page J-9.
f).P lOO
p.V
=
0.0668 '([2
p.Q
p.q
=
12.25 (F
0.0273(F
=
(For values of d, see pages B-16 to B-19)
d
Qq
Example 1
Example 2
Given: SAE 30 Lube Oil at 60 F flows through a
6-inch Schedule 40 steel pipe at a rate of 500 gallons per minute.
Given: SAE 10 Lube Oil at 60 F flows in a J-inch
Schedule 40 pipe at a velocity of 5 feet per second.
Find: The pressure drop per 100 feet of pipe.
Find: The flow rate in gallons per minute and the
pressure drop per 100 feet of pipe.
Solution:
Solution.
1.
P
56.02
2.
p.
450
J.
R.
550
4·
Since R. < 2000, the flow is laminar and the
nomograph on the opposite page may be
used.
.
, ,page A-7
, .. , ,page A-3
.,
.. , .....
Connect
5·
6.
p.
'. page 3-9
Q
Index
6" Sched 40
500
95
.. ' ... page A-3
P
2.
page 3-7
J.
J.I.
4.
R.
5·
Since R. < 2000, the flow is laminar and the
nomograph on the opposite page may be
used.
Read
= 450
' . , , ,page A-7
Q
54.64
115
I.
Index
6.
6PlOO = 4.5
7·
I .I 00
... page 3-9
,~
CRANE
CHAPnR 3 - FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH
AND PIPE
Pressure Drop in Liquid Lines for Laminar Flow
/'
(continued)
Q
p.
/'
2000
Index
1000
900
d
800
700
25
GOO
20
500
400
/~
15
300
10
9
8
7
200
150
1000
24
20
18
16
14
12
GOO
500
400
10
300
8
200
6
100
5
5
100
80
70
4
4
80
GO
312
GO
50
3
50
3
0>
'"
0
30
Q.
'"
u
.=
(..)
2
2
c::
0>
U
/"'
20
c::
a,"
,:,!Q..
?;o
':;
'"
.2!
1.5
lY.:
c::
c::
0
U
."
10
8
7
S
5
>
.2!
:::>
0
."
"""
...;
'"E 1.0
c""
.9
-;;;
E
.2!
t::
I
::t
"1:::l
40
.2!
:::>
:: 30
:::;;
Q.
;;;
~20
Q..
0
a;
<=
1\4 0.... :;; 15
OJ
15
c.!:I
::;
c::
'"'"
;; 10
2
b.PlOo
1.5
0.1
1.0
.8
.2
.6
.5
.4
.3
.;:::
'-'
V>
.=
1.1..
8
'"
6
5
.8
3/4 ':; ':;
.7
'"
N
.S
1/2 ~ t:r:'"
'"c::
.5
3/8 z~
~
.5
•.2
.6
.7
.8
.15
.10
.08
'"
.06
.05
.04
.03
.02
.01
3
.OOS
.005
.004
r-
1.0
.B
.15
.6
.5
1.5
/'
.8
.7
.6
.5
.4
~
.3
.2
.4
.10
.09
.08
.07
1.5
2
u
.Q
.3
.2
.OS
4
':;
.2!
6
7
8
9
10
.1
S
0:;
Q.
Q.
E
c
e
:::>
'"'"
~
Q..
I
:5
15
.002
.0015
30
.001
40
.0008
50
.0003
c::
0>
al
.0006
.0005
.0004
0
Q..
c::>
5
~
c
1.1..
c::
'"
'"
-0
Q;
:::>
;;
.=
1.1..
""r::T
:::I
:::I
.003
-VB
.2
1.0
'"
t::
~
Q.
Q;
1.1..
u
0:;
'"
Q;
.t::
."
V>
Q;;
1/4
2
.9
1.0
U
.008
.4
.3
t::
0
U
~
4
3
.4
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212 .t::
0>
.t::
4
150
6
40
r---
1500
q
60
70
SO
90
100
~
<J
3-14
CRANE
CHAPTER 3-FORMUlAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, FITTINGS, AND PIPE
--------
Flow of Liquids Through Nozzles and Orifices
Example 2
Given. The flow of water, at 60 F through a 6-inch
Schedule 40 pipe, is to be restricted to 2.25 gpm by
means of a square edged orifice, across which there
will be a differential head of 4 feet of water when
measured across taps located I diameter upstream
and 0.5 diameter downstream.
The flow of liquids through nozzles and
orifices can be determined from the following formula, or, from the nomograph
on the opposite page. The nomograph is
a graphical solution of the formula.
Find. The size of the orifice opening.
Solution.
U
l::.P hI" I
1.
p
62·37I
2.
}J.
1.1
3·.
Re
6.
d1
0.50 d2
7·
C
0.62
I ' ... '
........... page /\-6
· . page /\-3
105 000
(1. 0 5 X
Assume
a
{3
ratio,
say
0.50
4·
6. 06 5
5· d2
I
(0·5° x 6. 06 5)
· . page 3-9
... rage B-17
3. 0 33
... page A-20
8.
9·
An orifice diameter of 3 inches wiJi be
satisfactory, since this is reasonably close
to the assumed value used in Step 6.
11. . I f the value of dj determined from the nomograph is smaller than the assumed value
used in Step 6, repeat Steps 6 to 10 inclusive, using
reduced assumed values for d1 until it is in reasonable agreement with the value determined in Step 9.
10.
Example 1
Example 3
Given: A differential pressure of 2.5 psi is measured across taps located I diameter upstream and
0.5 diameter downstream from the inlet face of a
2.ooo-inch 1.0. nozzle assembled in a 3-inch Schedule
80 steel pipe carrying water at 60 F.
Given: A differential pressure of 0.5 pSJ IS measured across taps located rdiameter upstream and
0.5 diameter downstream from the inlet face of a
I.ooo-inch I.D. square edged orifice assembled in
174-inch Schedule 80 steel pipe carrying SAE 30
lubricating oil at 60 F.
Find. The !low rate in gallons per minute.
Find.' The now rate in cubic feet per second.
Solution
l.
d2
Solution:
2.
.. 3" Schcd 80 pipe; rage 13-16
(3
2.900)
J.
C
I. I 3
4·
p
6z. 37I .
0.69
. turbulent now a;;sumcd; page A-20
. .. page /\-6
I.
P
........ ' ... page /\-7
.. n.l" Schcd 80 pipe, page 8-16
I. 278) = 0.783
2.
d2
J.
(3
1.2
(1.000
4·
}J.
45 0
.. suspect now is laminar since
yiscosity is high; page 1\-3
5.
C
1.05
.... assumed; page A-20
5
6.
6.
7·
7·
8.
Calculate R, based on I D. of pipe (2.9°0").
9·
}J.
I. 1
. . page A-3
.. page 3-9
10.
R, =
2. I X 105 ..
JJ •
C
I .13 correct for R, = 2. I X 105 ; page A-20
When the C factor assumed in Step J is not
in agreement with page A-20, for the Reynolds number based on the calculated flow, the
factor must be adjusted until reasonable agreement'
is reached by repeating Steps 3 to 11 inclusive.
12.
8.
9·
Calculate Re based on JD. of pipe (1.278/1) .
· . page 3-9
= i 15
.correct for R.
110; page A-20
C = 1.05
12.
When the C factor assumed in Step 5 is not
in agreement with page A-20, for the Reynolds number based on the calculated flow. it must
be adjusted until reasonable agreement is reached
by repeating Steps 5 to I I inclusive.
10.
[ I .
R,
w
The mean velocity of compressible fluids in pipe can be
computed by means of the following formula, or, by using
the nomograph on the opposite page. The nomograph
is a graphical solution of the formula.
wv
V=
f
W
,------,
d
p
).06 W
n
d2p
:J:
......
~
..
m
'"
(For values of d, see pages 8-16 to B-19)
I
Example 1
Given: Steam at 600 pounds per square inch gauge
and 850 F is to flow through a Schedule 80 pipe at a
rate of 30,000 pounds per hour with the velocity limited
to
feet per minute.
Find: The suitable pipe size and the velocity through
the pipe.
i:onnp{'t
850 F
600 psig
:::;:
'<
-
Given: Air at 400 pounds per square inch gauge and 60 F
flows through a 1 Y2-inch Schedule 40 pipe at the rate of
144,000 cubic feet per hour at standard conditions
(14.7 psia and 60
0
n
0
3
\/= I. 22
I
Read
vertically to
600 psig
horizontally to
V =
W
=
1.22
Index
)0000
1.
W
2.
p
11 000, using So
" ,page R-2
1.0
Index
8000
d
3·7
Index
4/1 Sched 80 pipe
lV
J.
7600
-------
,--
4·
p
= 2. 16
Index
\'(1 =
c..
CIt
-.
:s
11000
~
1 Y2 /I Sched 40
G)
...'"
~
:l:
...
-c:
Connect
4/1 Schedule 80 pipe is suitable.
5·
6.
V
0
~
0
i"
."
"page A-IO
2.16
z
z
0
!:!!.
D'"
Solution:
~
c:
'"
0
...'"
Cil
CIt
-------
4·
;;:
'"~
n
Example 2
Find: The flow rate in pounds per hour and the velocity
in feet per minute.
c-'"
J.
0
'U
Solution:
1.
<
CD
'0
'U
CD
0
:E
:l:
'"0c
G)
:l:
<
~
<
m
!:"
...
...:::;Z
G)
!:"
»
z
Reasonable Velocities for Flow of Steam
Condition
of
Steam
.. ----;-----------------=----=----,-"'-.. - - - _..
Pressure
Service
0
...:;;
Reasonable Velocity
(V)
(P)
m
Minute
Heating (short lines)
Saturated
25 and up
Power house equipment, process piping, etc.
6000 to 10000
200 and up
Boiler and turbine leads, etc.
7 000 to 20 000
---------~-----~-+-------
Superheated
n
lID
~
Z
m
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
17
Specific Volume of Stearn
)
)
Index
p
)
)
)
W
d
1500
.8
.9
.03
1000
.04
800
20--.05
600
500
400
lJ
.06
.08
)
)
)
)
n
:Ia
l>
.,
z
m
lO
1.2
l.4
/"I
Z
.......»
..,
1.6
m
1.8
2
IlO
<
!..
ZOO
'"
...,
Li..
,;::;
:.
u
:;;
Q.
'"c
"0
:I
'"
D..
c
:6
-'"'"
Il
.,.., ZO
Li..
10
6
-0
4
'"'" 3
2
'"
.."
.4
:6
...,
.,
3:
I
~
80
c
.6
~
., .2
>
I
::.
•1
Co
'":.
"0
60
50
40
lJ
'"
15
10
8
6
5
4
.,'"
<.>
3.5
<=
4
.c::
.5
-
.!!!-
CI)
D..
'"c::
~
V>
:I
~
'"
t-
...
'"
.,
e
c
'fI:~
;;;
-
E
Li..
~
.,<:>
I
-;;;
0::
0
Cl
0
-- OJ
or 4.5
c::
~
n
0
3
-
"<
3
'"
'"
D..
.c::
ZO
:::;
.~
100 :;;
:I
t-
c
5
6
60
:;; 40
Co
.,c::
CI)
4
V
'"
::t:
0:::
n
0
"0
:I
::r.
CIt
c:
CD
!!.
aCD
:I
5
!:
6
""C
a:
8
CIt
9
10
:::I
::!
~
It
c
O.
:;
~
=>
c
::IE
I
.,0
'"»
0
2.5
150
~
)
"0
CD
>
z
0
Z
~
~
z...
'"0
...'"
0
~
....
z
.,
0
c:::
Cl
z
»<
<
m
~
...
~
z
Cl
~
~
»
z
15
0
::!!
'"
m
3
ZO
2
am
IlO
500
400
t
-
600
700
800
900
1000
Temperature, in Degrees Fahrenheit
1100
1200. 10 -
10
1.5
25
Il
~~'i?> ~ ~~~~
Schedul e Numbe r
w
.....
W
...
I
C»
The Reynolds number may be determined from the formula below or from the nomograph on the opposite page.
The nomograph is a graphical solution of the formula.
The friction factor for clean steel pipe can be obtained
from the chart in the center of the nomograph. Friction
factors for other types of pipe can be determined by using
the calculated Reynolds number and referring to pages
A-2) and A-24.
n
:J:
»
~
m
~
W
Find: The flow rate in pounds per hour, the Reynolds
number, and the friction factor.
Solution:
."
C
IJ.
fit
Z
- "i
CA
CD
fit
!.. !!.
IT
::!! CD
" CD
."
0
~
= 0.011
Z
0
a 3
::J
.. " .. page B-17
.... pageA-2
Z
0
0
n n
CD 0
Find: The Reynolds number and the friction factor.
til
»
-.. .
0
Given: Steam at 600 psig and 850 F flows through a
4-inch Schedule 80 steel pipe at a rate of )0,000 pounds
per hour.
'"c
0
3:
-. -..
Example 2
Read
Connect
].
-
"0 3IT
CD
Solution:
L
d = ).826
2.
IJ. = 0. 02 9
69000, using S, = 0.75 .... page B-2
..... page A-5
0.011
2.
):
a
Given: Natural gas at 250 psig and 60 F, with a specific
gravity of 0.75, flows through an 8-inch Schedule 40
clean steel pipe at a rate of 1,200,000 cubic feet per hour
at standard conditions (scfh).
W
::::!. 0
::J
Example 1
1.
0
3:
C"r ii:
f
(For values of d, see pages B-) 6 to 8-19)
...
CD
'<
::J
."
Re = 6.)1 dlJ.
...'"I
0
G')
»
'"...
:J:
til
...'"
0
:e
...
:J:
'"
0
c
G')
:J:
<
»
,...
<
m
.tII
...
:3
iG')
.!"
»
].
z
0
...
::!
4·
4·
5·
f = 0.014
m
5·
Note: Flowing pressure of gases has a negligible effect
upon viscosity, Reynolds number, and friction factor.
n
:Ia
)II>
Z
m
))
')
)
)
)
)
)
)
)
)
1000
W
)
)
)
) )
Index
Z
.008
In
.4
500
400
.009
Internal Pipe Diameter
in Inches
300
.5
.010
.6
36
200
.8
.9
.012
.013
80
.014
60
50
~
.015
i .016
-'"'"
~ .017
u
.: .018
£. .019
.~ .0211
"'"
'"'"o'"
.c
I;
'-'
>'"
I-
~
10
'"
6
5
3/4
.
'"
.c
~
m
.030
;:ICII
CD
.,,-<
'"I
:::J
1.5
u
c
c
'"
CL.
-
.035
.040
3
'"
'"e 4
'"
~
2 .:
2li .;
~
3 ~
'"
3li ::;
4 ~
.",
'-'
<'>
7
8
9
10
'"c:
8 :;
z:
10
15
211
14
16
18
Q. 3
-
r
'"I
.n
.. 0-'"I
o
n
D
0
3
'U
~ C;
:::J
".
l 0'"~,
>z
o
~'">-
."
::z:
'"(5
...'"
~
....
::z:
1;
c:
(;'l
::z:
~
<:m
...
-a'
CD ."
~
yo
~
z
~
>z
o
::!!
."
m
211
24
.045
.6
.3
z
D
c;;
E
~ 6
.8
.5
.4
Z
." C
0-
~
c
E
:::J
2
I
o
a:~
C;" ..
12
2
'"
G>
~
3
~
LO
I
4
n
Q
'"'" .025
~
B
1/2
.7
.011
24
18
100
211
,..,.n
,3
60()
40
)
d
800
30
)
)
)
}
30
.01
.02
.03
.04
f - Friction Factor for Clean
Steel Pipe
.05
.050
w
40
-0
w
•
~
The pressure drop of flowing compressible fluids can be
calculated from the Darcy formula below, or, from the
nomograph on the opposite page. The nomograph is a
graphical solution of the formula.
w
W2
J W2V = 0.000)36 Jd$p
0.000)36~
n
....."'
:J:
)io
0,000 001 q5q
J (q' )2 S 2
cF. p
'"...
0
(For values of d, see pages B-16 to B-19)
."
When the flow rate is given in cubic feet per hour at
standard conditions (q' h), use the following equation or
the nomograph on page 8-2 to convert to pounds per
hour (W).
tit
tit
W
a
a
C
= 0.0764 q' h So
~
~
_.
Cl
n
3
Given: Steam at 600 psig and 850 F flows through a 4inch Schedule 80 steel pipe at a rate of 30,000 pounds
per hour.
Given: Natural gas at 250 psig and 60 F flows through
an 8-inch Schedule 40 pipe at a rate of 1,200,000 standard
cubic feet per hour; its specific gravity is 0.75.
'V
Find: The flow rate in pounds per hour and the pressure drop per 100 feet of pipe.
i"
Find: The pressure drop per 100 feet of pipe.
Solution:
}J.
J.
J
3. 826
0.029
0.017
.... page B-17
...... page 3-17 or A-17
1.22
4·
Connect
5·
6.
J.
W
g"'II
0-
r.:
::J
0
~
:J:
3c
Cl
:J:
<
»
....
<
m
.!"
...
:z
0.011
..... page A-5
3·
J
0.014
..... page 3-19
»
4·
P
1. 0 3
................ page A-IO
...
:;
W
Connect
Read
Index 2
J = 0.017
Index I
6.
69 000 8/1 Sched 40 pipe
Index~ 2
J = 0.014
6PIOO = 7.5
J.
Index I
1.22
tit
}J.
.... using So = 0.75; page B-2
5·
\1=
'"......
2.
69000
Index 2
Index I
CI>
is
W
= 3. 826
d
:J:
a .
!!.
~
Read
30000
Index 2
»
...'"
T.
. . . . . . . . .... page A-2
. ..... - .......... page 3-19
z
3
0
2.
»
'V
100 feet of Schedule 40 pipe, for air at 100 psig and 60
see page 8-15.
Solution:
T.
d
...
1:7
Air: For pressure drop, in pounds per square inch per
Example 1
~
c
~
C
::J
Example 2
I
is
p =
1.03
Index I
6P 100 = 0.68
CD
tit
:t
fh
z
1:7
m
n
•»
z
m
)
)
)
)
)
))
)
)
)
)
)
)
P
,02
50
.5
40
.6
.7
.8
Index 1
Index 2
30
.04
.05
d
30
20
6 :g
~
(..)
."
-g .2
:::J
~
.E .3
.z:.
.~
5 .E
4
3 ~
'jl
.4
-
~ .5
~ .7
I .8
.9
Q.. 1.0
2
u
.-~
.04
20 ~
(I.)
c.
0:::
5
u
~
I
.7
,6
I:::"
.5
x
15~
<J
20
",. .8
.7
.6
.5
.015
3 ~
I
.3
.2
40
~
~
~
=
:r
~
~...
:r
3c
Cl
:r
<
...<»
m
~
...
:i
z
~
.01
»
z
1:1
."
:;;
m
.4
.3
30
z
1:1
en
5 '0
2
'"
»
o
o
o
.......
.02
-=_I .91
...
»
."
: ~4
(5
~
c
»
:::II
10 .E
c::
....
.9 t5-
.8
=:
(I.)
c;;
~
.05
£ 4
1.5.=!
r.;::
1.0 .~
'"w
:r
I
(I.)
$?
200
n
»
8
2 '0
E
m
f
~
.....
c;:
1000
800
600
500
400
300
10 ~
7
-=
6
.E
0
4 -:v~
5 g
1/8
.2
4
5
..c
c::
.4
3
§
l>
Z
10
~ 9
Q..
o
(I.)
c ..5
~
3
n
:lilt
I
24
20
16 ~
14 ~
12 .§
9
8~
)
100
80 ....
60 5
50
40 ~
30 ~
c::
10
7 u
)
1600
15
....
)
W
.9
1.0
20
)
)
)
l:::.PUIO
.4
j7
.03
)
50
Co)
.1
I
~
3 ·22
CRANE
CHAPTER 3 - fORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, fiTTINGS, AND PIPE
Simplified Flow Formula for Compressible Fluids
Pressure Drop, Rate of Flow, and Pipe Si:z:e
The simplified flow formula for compressible fluids is
accurate for fully turbulent flow; in addition, its use
provides a good approximation in calculations involving
compressible fluid flow through commercial steel pipe for
most normal flow conditions.
Values of C1
w
If velocities are low, friction factors assumed in the
simplified for.mula may be too low; in such cases: the
formula and nomograph shown on pages 3-20 and 3-21
may be used to provide greater accuracy.
2S00
1000
2000
lS00
The Darcy formula can be written in the following form:
W2(0.00~5336f)v
b.P IOO
(33 6;iof)v
(\\;121
C1
W
.1
10
1000
900
The simplified flow formula can then be written:
C1C2
.15
800
.2
700
.25
p
G\
.3
5
0
::x::
1000
900
800
700
600
500
400
600
llO
(;j
c.
.4
'"c::
SOD
200
'0
C1
discharge factor from chart at right.
size factor, from table on next page.
Cz
The limitations of the Darcy formula for compressible
flow, as outlined on page 3-3, apply also to the simplified
flow formula.
.6
'0
'"c::
()
-c
'"'"
-<=
a
'"::::
3.5
:::l
Q)
0
(ij
f-
>
.:::
Example 1
Given: Steam at 345 psig and 500 F flows through 8-inch
'0
Schedule 40 pipe at a rate of 240,000 pounds per hour.
.l!l
c::
'"
Find: The pressure drop per 100 feet of pipe.
::t:
Solution:
C1
200
.5
:::l
0
a..
0
Q)
250
100 (ij
90 >
80
70
60
50
2.5
'.
lIlO
40
30
ISO
1.5
.. page3-17or A-16
12
.002
57 x 0.146 x 145 =
25
20
.0015
15
8
Example 2
1.0
Given: Pressure drop is 5 psi with 100 psig air at 90 F
.9
.oooa
.8
.0007
.0006
flowing through 100 feet of 4-inch Schedule 40 pipe.
Find: The flow rate in standard cubic feet per minute.
Solution:
C1
0.5 6 4
(5.0 x 0.5 64)
W
23000
P
q'm
q'm
.001
.0009
9
10
100
10
.. page A-1O
5.17
0.545
W -+ (4.58 S.)
. page B-2
23000 -+ (4.58 X 1.0) = 5000 scfm
For C, valves and on example on "determining pipe size",
.Jee the opponle pOGe.
v
:::l
57
0.146
1·45
100
'"
300
1.5
2.5
400
.7
.8
.9
1.0
CRANE
CHAPTER 3- FORMULAS AND NOMOGRAPHS fOR FLOW THROUGH VALVES, FlmNGS, AND PIPE
3-23
Simplified Flow Formula for Compressible Fluids
Pressure Drop, Rate of Flow, and Pipe Size -
continued
Va Iues 0 f \.2
Nominal
Pipe Size
Inches
Schedule
Number
Value
of C,
Nominal
Pipe Size
Inches
Schedule
Number
Va
408
80x
7920000.
26200000.
5
14
408
80x
1590000.
4290000.
408
80x
120
160
... xx
1.59
2.04
2.69
3.59
4.93
%
408
80 x
319000.
718000.
6
112
408
80 x
160
... xx
93500.
\86100.
430000.
11180000.
408
80 x
120
160
... xx
0.610
0.798
1.015
1.376
1.861
20
30
40 s
60
80 x
0.133
0.138
0.146
0.163
0.185
100
120
140
, xx
160
0.211
0.252
0.289
0.317
0.333
20
30
40s
60x
80
0.0397
0.042 I
0.0447
0.0514
0.0569
100
120
140
160
0.06,52
0.0753
0.0905
0.1052
20
30
5
40
'" x
60
0.0157
0.0168
0.0175
0.0180
0.0195
0.0206
80
100
120
140
160
34
1
114
1112
405
80x
160
... xx
21200.
36900.
100100.
627000.
40s
80x
160
... xx
5950.
9640.
22500.
114100.
40s
80x
160
. xx
1408.
2110.
3490.
13640.
408
80 x
160
, .. xx
627.
904.
1656.
4630.
8
10
2
40s
80 x
160
xx
161}.
236.
488.
S99.
2%
40s
SO x
160
.. , xx
66.7
91.8
146.3
380.0
3
408
SOx
160
... xx
21.4
2S.7
48.3
96.6
3%
408
80 x
10.0
' 13.2
4
40 s
80 x
120
160
... xx
6.75
8.94
11.80
18.59
12
14
5.17
Value
of C2
Nominal
Pipe Size
Inches
Schedule
Number
Value
of C,
16
10
20
30s
40x
60
0.00463
0.00483
0.00504
0.00549
0.00612
80
100
120
140
160
0.00700
0.00804
0.00926
0.01099
0.012 44
10
20
.. s
30
.. x
40
0.00247
0.00256
0.00266
0.00276
0.00287
0.00298
60
80
100
120
140
160
0.00335
0.00376
0.00435
0.00504
0.00573
0.00669
10
205
30x
40
60
0.00141
0.00150
0.00161
0.00169
0.00191
80
100
120
140
160
0.00217
0.00251
0.00287
0.00335
0.00385
0.0231
0.0267
0.0310
0.0350
0.0423
10
20s
,x
30
40
60
0.000534
0.000565
0.000597
0.000614
0.000651
0.000741
10
20
305
40
, .. x
60
0.00949
0.009 96
0.01046
0.01099
0.011 55
0.012 44
80
100
120
140
160
0.000835
0.000972
0.001 119
0.001274
0.001478
SO
100
120
140
160
0.01416
0.01657
O.OIS 98
0.0218
0.0252
18
20
24
Note
The letters s, x, and xx in the 001umns of Schedule Numbers indicate
Standard, Extra Strong, and Double
Extra Strong pipe respectively.
Example 3
Given: An 85 psig saturated
steam line with 20,000 pounds
per hour flow is permitted a
maximum pressure drop Of.IO
psi per 100 feet of pipe.
Find: The smallest size of
Schedule 40 pipe suitable.
= 4.4 ...... ,page3-17orA-I3
!::"P100 = \0
C2 = 10 -;- (0.4 x 4.5) = 5.5 6
C1 = 0.4
Reference to the table of C 2 values above shows that the 4-inch size is
the smallest Schedule 40 pipe having a C 2 value less than 5.56.
The actual pressure drop per 100 feet of 4-inch Schedule 40 pipe is:
!::"P100 = 0-4 x ;.17 x 4·4 = 9.3
Solution:
3_24 __________C=H=A~PT~e~R~3_-~F~O=RM~U~L~A~S~A~N~O~N~O~M~O~G~RA~P_H~S~F~O_R_F_LO_W__TH_R_O_U_G_H_V_A_LV_E_S,_F_IT_T_IN_G_S_,_AN_O__P_IP_E________C_R_A
__N
__E
Flow of Compressible Fluids Through Nozzles and Orifices
The flow of compressible fluids through nozzles and
orifices can be determined from the following formula, or, by using the nomograph on the next page.
The nomograph is a graphical solution of the
formula.
--
W
d
p
x x
UJ UJ
a a
!!
J1:,.P
= 0.525 Y d21 C..J 1:,.P PI = 0·525 Y 21 C '\j VI
W = 189 1 Y d21 C
Y d21 C 11:,. P
'\j VI
(Pressure drop is measured across taps located I
diameter upstream and 0.5 diameter downstream from the inlet face of the nozzle or orifice)
Example 1
Given: A differential pressure of I 1.5 psi is measured across taps located I diameter upstream and
0.5 diameter downstream from the inlet face of a
l.ooo-inch I.O. nozzle assembled in a 2-inch Schedule
40 steer pipe, in which, dry carbon dioxide (C02 )
gas is flowing at 100 psig pressure and 200 F.
Find: The flow rate in cubic feet per hour at standard conditions (scfh).
Solution:
R = 35.1 }
Sg = 1.5 16 ............ forCO.gas;pageA-8
3. k
1.28
I.
2.
Steps 3 through 7 are used to determine the Y factor.
4· P't
P + 14·7
100 + 14·7 = 114·7
5· 1:,.PjP'l = 11·5 + 114·7 = 0. 100 3 :. ,'r;
6. d2
2.067 ........ 2" Sched 40 pipe; page 8-16 ',t.,
7· {3
1.00 + 2.067 = 0.484 ~
8. Y
0.93 ........................ page A-21
9. C
1.02 .. turbulent flow assumed; page A-20
10.
T
460 + t = 460 + 200
660
.... page A-IO
0·71
~
Ii
1:,.P
Read
13·
Index I
0·71
C = 1.02
Index I
14·
Index 2
dl
1.000
Index 3
15·
Index 3
Y = 0·93
W = 5000
12.
16. q' h
=
11·5
PI
=
Index 2
44 000 scfh .................. page B-2
0.018
................. page A-5
R.
860000 or 8.6 x 105 . . . . . . . . page 3-2
1.02 is correct for
19· C
R. = 8.6 x 105 ... page A-20
20.
When the C factor assumed in Step 9 is not
in agreement with page A-20. for the Reynolds number based on the calculated flow, it must
be adjusted until reasonable agreement is reached
by repeating Steps 9 through 19.
17·
18.
fJ.
Example 2
Given: A differential pressure of 3 psi is measured
across taps located I diameter upstream and 0.5
diameter downstream from the inlet
of a 0.750inch I.O. square edged orifice assembled in I-inch
Schedule 40 steel pipe, in which, dry ammonia (NH 3)
gas is flowing at 40 psig pressure and 50 F.
Find: The flow rate in pounds per second and in
cubic feet per minute at standard conditions (sefm).
Solution:
1.
2.
3·
R = 90.8 }
Sg :
0.5 8 7 ............ for NH3 gas; page A-B
k -
1.29
Steps 3 through 7 are used to determine the Y factor.
4· P'l
P + 14·7 = 40 + 14·7 = 54·7
5· 1:,.P/P'l = 3. 0 + 54·7 = 0.0549
6. d 2
J .049 ........ 1" Sched 40 pipe; page 8-16
0.71 6
0.75 0 + 1.049
7· {3
8
8. Y
. ...................... page A-21
0.9
I
C
..
turbulent flow assumed; page A-20
0·7
9·
T
60
10.
510
4
+ t = 460 + 50
PI
II.
0.17 ........................ page A-IO
Read
Connect
13·
1:,.P = 3·0
Index I
14·
Index· 2
15·
Index 3
d1 = 0·75
Y
0.98
16.
Index 3
Y
12.
1.7· q'm
18.
fJ.
W
4·5 8S ,
= 0.010
= 0.17
Index I
C = 0.7 1
Index 2
Index 3
W=
W= 520
PI
0.98
0.145
52 0
8 = 195 .. page B-2
4·5 x 0·5 7
8
. ...................... page A-5
3 J 0 000 or 3. lOX 105
...... page 3-2
20.
C
0.702 is correct for
R. = 3.10 X 105 .. page A-20
21.
When the C factor assumed in Step 9 is not
in agreement with page A-20. for the Reynolds number based on the calculated flow, it must
be adjusted until reasonable agreement is reached
by repeating Steps 9 through 20.
19.
R.
.-.'
CRANE
3-25
CHAPTER 3 - FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, FITTINGS, AND PIPE
Flow of Compressible Fluids
Through Nozzles and Oriflces
(continued)
L::,.p
d1
600
500
r'-
JI
6
13 W
III
1)00
800
&10
<UOO
400
5
4
~-,
3
60
'"0"
:::I
:;;
50 ""
2.5
40 "C
'"c:
.~
30
0
'"
<>
0..
c:
2
Q;
~
15 '"
'"
'"~
~
1.5
Q...
4
.6
•6
.4
4
1.0
3
.9
><
'"c::
"C
r-.
1.5
.8
'".,><
"'"
c:
;U
Q.
'"c::
'"
0..
'"
"0
<:>
c::>
c::>
.7
1.0
.6
~
.5
.co
.4
.3
.55
;;,....
.5
OJ
0-
~3
"C
t.)
.3
.;
e
'"
04
>
..,
'"
t
,!;-5
'"
I
N
I;::" 6
OJ
N
<>
OJ
eN
9
~
'0
'0
~
J;
0::
'"
0::
I
I
lI..
'"
3
-
•
().,
7
~
'"
c'"
".,"""
.2
c::
.,'"'"
<.>
.E
,;
~
.25 .~
"C
::>
""
.:
OJ
"0
.4
'"c::
;0
c:
I
"0
<>
'"c::
'"'"
0..
:z:
.45
0
Q.
Q..
'"
t.)
lI..
c::
I..U
<>
<>
lI..
.4
8
OJ
"";;:;
.5
OJ
-
<.>
c:
=
G;
""
~
'"c: .6
.1
~
lI..
.5
0..
.2
'"
-..,
~2
:::I
.3
'"><
.4
.3
"'"c:
.7
c::
t t
<>
:t:
<>
0..
..,
2
1.0
.8
.7
1.5
.6
4
3
2
:::I
2
.8
-.;
6
/'
10
8
6
.!!!
''is
<I
.9
10
8
6
J;
.7
.6
aJ
.8
10
8
1.0
1.0
c:
1.0
Y
GO
40
30
3
:::
1.0
.8
'"
0
OJ
1.1
.8
.e..,
lI..
'"
~
e
20 0e
Q..
'"
.9
1.0
100
80
<U
..,.;
1.3
1.2
.9
40
1)
.:
.:
--
Q.
~
1.1
400
300
GO
.,'"
""..,
OJ
.75
.8
.9
100
80
100
""..,
80 .:
moo
<Uo
<UO
150
P
aoo
GOO
200
1.24
1.2
1000
300
V
C
lz
.35
..,
.<:;
10
.,
.1
.09
u'"
.08
51:
~
lI..
I
u
15
16
.07
.0625
3-26
CHAPTER 3
fORMULAS AND NOMOGRAPHS fOR FLOW THROUGH VALVES, FITTINGS, AND PIPE
CRANE
Types of Valves
(For other valve types, see page A·32)
Conventional Globe Valve
Y·PaDern Globe Valve
With Stem 45 degrees from Run
Conventional Swing Check Valve
Conventional Globe Valve
With Disc Guide
Globe Stop-Check Valve
Clearway Swing Check Valve
Conventional Angle Valve
Angle Stop-Check Valve
Globe Type Lift Check Valve
4·1
Examples of
Flow Problems
Theory and answers to questions
regarding proper application of
formulas to flow problems can
be presented to good advantage by the solution of practical
problems. A few simple flow
problems were presented in
Chapter 3 to illustrate the use
of the nomographs.
Other
problems, both simple and complex, are presented in this
chapter.
CHAPTER 4
Many of the examples given in this chapter employ the basic
formulas of Chapters I and 2; these formulas were rewritten in
more commonly used terms for Chapter 3. Use of nomographs,
when applicable, are indicated in the solution of these problems.
The controversial subject regarding the selection of a formula
most applicable to the flow of gas through long pipe lines is
analyzed in Chapter I. It is shown that the three commonly used
formulas are basically identical, the only difference being in the
selection of friction factors. A comparison of results obtained,
using the three formulas, is presented in this chapter.
An original method has been developed for the solution of problems involVing the discharge of compressible fluids from pipe
systems. Illustrative examples applying this method demonstrate
the simplicity of handling these, heretofore complex, problems.
Reynolds Number and Friction Factor
For Pipe Other Than Steel
The example -below shows the procedure in obtaining the Reynolds
number and friction factor for smooth pipe (plastic). The same
procedure applies for any pipe other than steel such as concrete,
wood stave, riveted steel, etc. For relative roughness of these
and other piping materials, see page A-z 3.
Example 4-1 ••• Smooth Pipe (Plastic)
Given: Water at 80 F is flowing through 70 feet of
l-inch standard wall plastic pipe (smooth wall) at
a rate of 50 gallons per minute.
Find: The Reynolds number and friction factor.
Solution:
I.
R.
50 .6 Qp
dJ.'
. .... page 3-2
p=
62.220
................... page A-6
3·
d = 2.067
................... page 8-16
4·
J.' = 0.85
5·
R.
2.067 X 0.85
Re = 89600 or 8.96 x 10 4
f = 0.0182 for smooth pipe
2.
6.
.............. page A-3
50.6 X 50 X 62.220
. .. page A-24
4-2
CRANE
CHAPTER 4 - EXAMPLES OF flOW PROBLEMS
Determination of Valve Resistance
In L, L/D, K, and Flow Coefficient Cv
Example 4-2 ••• L, L/D, and K from Cv for
Conventional Type Valves
Example 4-3
continued
Given: A 6-inch Class 125 iron Y-pattern globe valve
has a flow coefficient. Cv. of 600.
5·
Cv = 2q.q X 3. 8 26 = 274
Find: Resistance coefficient K and equivalent lengths
L/ D and L for flow in zone of complete turbulence.
6.
L = 2·55 = 150
D 0.017
7·
L = 150 X 3.826 = 47.8
12
Solution:
1. K. L/ D. and L should be given in terms of 6inch Schedule 40 pipe; see page 2-10.
2.
3·
4·
5·
_ 89 1 d 4
K - Cv2
V2.55
rfor graphical solutions
. .... j of steps 5 thru 7. use
lpages A·30 and A·31
................. page 3-4 or A·31
d = 6.065
d 4 = 135 2.8
D = 0.5054
K = 89 1 X 1352.8 = 3.35
600 2
L K
D=T
...... page B-17
..... {based on 6"
Sched 40 pipe
. . . . . . . . . . . Poage 3-4
. . . . {for 6.065" 1.0. pipe in fully
turbulent flow range; page A-2S
6.
i= 0.015
7·
!::.= K= ~ = 223
D i
0.015
8.
2
L= (~)D =
Example 4-4 ..• Venturi Type Valves
Given: A 6 x 4-inch Class 600 steel gate valve with
inlet and outlet ports conically tapered from back
of body rings to valve ends. Face-to-face dimension
is 22" and back of seat ring to back of seat ring is
about 6" .
Find: 1<.2 for any flow condition. and L/D and L for
flow in zone of complete turbulence .
Solution:
1.
K 2 • L/D. and L should be given in terms of 6inch Schedule 80 pipe; see page 2-10.
223 X 0.5054 = 113
2.
Kl = 8
iT
...................... page A·27
K2 = Kl + sin ~ [0.8 (I - (32) + 2.6 (I - (32)2]
(34
L
L K
K = i D or 15 = iT
Example 4-3 ... L, L/D, K, and Cv for
Conventional Type Valves
Given: A 4-inch Class 600 steel conventional angle
valve with full area seat.
(3 -- ~
d
............. page 3·4
....................... page A.26
2
d1 = 4.00
· .............. Valve seat bore
Find: Resistance coefficient K. flow coefficient Cv.
and equivalent lengths L/ D and L for flow in zone of
d2 = 5.761
· . . . . . . 6" Sched. 80 pipe; page B·17
complete turbulence..
jT=0.015
· ........... for 6" size; page A·26
Solution:
3·
4·
4.00
61 =0.69
(3 = 5.7
(32 = 0.48
1.
K. L/ D. and L should be given in terms of
2.
4- in ch Schedule 80 pipe; see page 2- I O.
K = 150 iT
.................... page A.27
tan!!" __
0 .....t..5.. .:("'-5-'. .7. . ;. 6_1_----74;:..:.0::..;:0'-'-)
2 0.5 (22 - 6)
V 2C:;
tan!!' = .110
C
:2 ..................
=
L
L
K
K = i D; or 15 = iT
page 3.4
............ page 3·4
2
5·
(subscript "T' refers to flow in zone of complete
turbulence)
3·
4·
d=3· 826
.................... pageB-17
iT ~
.................... page A·26
0. 01 7
K = 150 X 0.017 = 2.55
based on 4"
. . . .. {Sched. 80 pipe
(34 = 0.23
= sin!!.. approx.
2
K _ 8 X 0. 01 5 + 0.110 (0.8 X 0.52 + 2.6 x 0.52,2)
0.23
2 -
K2 = 1.06
6.
7·
L _ 1.06 _ 70
D-o.oIs-
. .. diameters 6' Sched. 80 pipe
L ~ 70 X 5.761 = 34 ..... feet of 6" Sched. 80 pipe
12
CRANE
CHAPTER..
4-3
EXAMPLES OF FLOW PROBLEMS
Check Valves
Reduced Port Valves
Determination of Size
Velocity and Rate of Discharge
Example 4-5 .. . lift Check Valves
Example 4-6 . . . Reduced Port Ball Valve
Given: A globe type lift check valve with a wing-
Given: Water at 60 F discharges from a tank with
guided disc is required in a 3-inch Schedule 40 horizontal pipe carrying 70 F water at the rate of 80
gallons per minute.
Find: The proper size check valve and the pressure drop. The valve should be sized so that the
disc is fully lifted at the specified flow; see page 2-7
for discussion.
Solution:
L
. . . . . . . . . . . . . . . . . . page A·27
Vmin = 40VV
0·408 Q
d2
V
. . . . . . . . . . . . . . . . . page 3·2
I1P _ 18 X 10-6 KpQ2
d4
K1
600 fT
K2 _ K1 + {j [0·5 (I - (j2) + (I
fj4
d1
J;
2.
d2
3.068
V
0.01605
. . . . . . . . . 70 F water; page' A.6
p
62.3 0 5
· . . . . . . . . . . 70 F water; page A·6
Vmin = 40 VO.OI605 =
v
K1 +.8 sin!!. (I _ (j2) + 2.6 sin 8 (I
4·
f·
6.
[.I
0.408 X 80
3. 0682 = 3·5
= 2·46q
J.068
8
o. 0
600 x .018 +.8 [0.5 (I - 0.64) + (I - 0.64)2J
0·41
K2 = 27
6.
{j = ~ = 2·375 = 0.77
d2 3.068
sin 8/2 = sin 8° = 0.14
sin 8/2 = sin 15° = 0.26
{j2)2
2
. . . . . . . . . page A·26
......... valve inlet
. ...... valve outlet
......... for 3" valve
{j2 = 0.64
f·
2
5·1
0.408 x 80
v=
6q2 = 5· J 5
. . . . . . for 2%" valve
2·4
Based on above, .a 2Yz-inch valve installed in J-inch Schedule 40 pipe with
reducers is advisable.
fJ
•••• page 3·2
K = 0.5
K = 1.0
K2 =
.... valve
Inasmuch as v is less than Vmin, a J-inch
valve will be too large. Try a 2;Y2-inch size.
4·
. . . . . . . . page 3·4
.............. entrance; page A·29
. . . . . . . . . . . . . . . . . . exit; page A·29
h = 0.018
................... page A·26
J.
For K (ball valve), page A-28 indicates use of
Formula 5. However, when inlet and outlet
angles (8) differ, Formula 5 must be expanded to:
2.
· .. for 3" Schoo. 40 pipe; page 8-16
· .... for 2%" or 3" size; page A·26
v2
• /2gh L
hL = K 2g or v = V ~
v = 0.408 ~ or Q = 2.45 I vd 2
· .for 2%" Schoo. 40 pipe; page 8-16
h = 0.018
J.
{j2)2J .. page A.27
. . . . . . . . . . . . . . . . . . . . . . page A·26
.1 ~ 2·46q
I.
........... page 3·4
................... page A.27
-
22-feet average head to atmosphere through:
200 feet- J " Schedule 40 pipe
6- J H standard qoO threaded elbows
1-3" flanged ball valve having a 2%" diameter seat, 16° conical inlet, and
30° conical outlet end. Sharp-edged
entrance is flush with the inside of
the tank.
Find: Velocity of flow in the pipe and rate of discharge in gallons per minute.
Solution:
2
6
I1P = 18 X 10- X ;.~8~2. J 0 5 X 80 = 2.2
K = 6 X 30h = 180 X 0.018 = 3.24
!::
K fD
8.
9.
. .. 6 elbows; p. A·29
0.oI8x200XI2
8
3.068
= 14. 0
pipe; p. 3-4
Then, for entire system (entrance, pipe, ball
valve, six elbows, and exit),
K = 0.5 + 14.08 + 0.58 + 3.24 + 1.05 Iq.4
v
V(64.4 x 22) + Iq.4 = 8.5
Q 2.451 x 8.5 X 3.0682 ~ 196
Calculate Reynolds number to verify that friction factor of 0.018 (zone of complete turbulence) is correct for flow condition ... or, use "vd"
scale at top of Friction Factor chart on page A-25.
vd 8.5 x 3.068 = 26
I I.
Enter chart on page A-25 at vd = 26. Note f
10.
for J-inch pipe is less than 0.02.
Therefore,
flow is in the transition zone (slightly less than fully
turbulent) but the difference is small enough to
forego any correction of K for the pipe.
4·4
CHAPTER"
CRANE
EXAMPLES OF FLOW PR08LEMS
Laminar Flow in Valves, Fittings, and Pipe
In flow problems where viscosity is high, calculate the Reynolds
Number to determine whether the flow is laminar or turbulent.
Example 4·7
Example 4-8
Given: S.A.E. 10 Lube Oil at 60 F flows through the
system described in Example 4-6 at the same differential head.
Given: S.A.E. 70 Lube Oil at 100 F is flowing at
the rate of 600 barrels per hour through 200 feet
of 8-inch Schedule 40 pipe, in which an 8-inch conventional globe valve with full area seat is installed.
Find: The velocity in the pipe and rate of flow in
gallons per minute.
Solution:
Find: The pressure drop due to flow through the
pipe and valve.
Solution:
r.
....................... page 3-4
........... page 3-4
1.
R.
Q
v ~ 0.408 d2
35.4 pB
K 1 = 340 fT
. . . . . . . . . . . . . . . . . . . . page 3-2
Q ~ 2.45 1 vd 2
R.
2.
. . . . . . . . . . . . . . . . • . . . page 3-2
j.A.
. . . . . . . . . . . . . . . . . . . . . . . " . pipe
f - R.
· ......... pipe, laminar flow; page 3·2
K=f!5
.................... pipe; page 3-4
2.
K2
0.58
. . . . . . . . . . . . . valve; Example 4-6
K
3.24
............. 6 elbows; Example 4·6
K =0.5
· ............. entrance; Example 4·6
K = 1.0
· . . . . . . . . . . . . . . . . exit; Example 4·6
P ~ 54. 64
.
S = O.go at 100 F
. . . . . . . . . . . . . page A-7
3·
4·
64
......... pipe
V
64 .4 x 22 _ 5.13
V
5·
Q=2.45IX5·13x3·0682
118
"Note; This problem has two unknowns and, therefore, requires
a trial·and.error .solution. Two or three trial assumptions wilt
usually bring the solution and final assumption into agree·
ment within desired limits.
4.76
0.20 X 200 X 12
7·g81
60.14
K = 4.76 + 60.14 - 64.g
5·
t:.P = 8.82 X 10-6 X
t:.P
53·8
. . . . . . . . . . . . . . . . . . . . pipe
0.20
KI - )40 x 0.or4
K = 48.5 + 0.58 + 3.24 + 0.5 + 1.0
4·
. . . . . . . . . . . page A.26
)5·4 x Qoo X 56 . 1
8
- 3I
7.g8 ! X 470
-
f = JIB
K
................... entire system
... . . . ..
R. < 2000; therefore flow is laminar.
. . . . . . . . . . . . . . pipe
K = 53 .8
. . . . . . . . . . . . . . . . . . . . . . page A·3
p = 62.371 X o.go = 56. I
R.
*Assume laminar flow with v - 5.
0.062 X 200 X 12
8
K =
= 4 ·5
3
= 470
fT = 0.014
. . . . . . . . . . . . . . . . . . . . . Example 4-6
R.
. . . . . . . . . . . . . page A·7
j.A.
. . . . . . . . . . . . . . . . . . . page A-7
124 x 3·068 x 5 x 54.64
100
= 1040
S=0.gI6at60F
. . . . . . 8" Sched. 40 pipe; page 8·17
. . . . . . . . . . . . . . . . . . . . . . . page A-3
3.
. . . . . . . . . . . . . . valve; page A-27
. . . . . . . . . . . . . . . . . . . pipe; page 3-4
dvp
124-
_ 64
. . . . . . . . . . . . . . . . . . . page 3.2
dj.A.
2.85
............ valve
. . . . . . . . pipe
....... total system
CRANE
CHAPTER"
EXAMPLES OF FLOW PROBLEMS
Laminar Flow in Valves, Fittings, and Pipe -
continued
In flow problems where viscosity is high, calculate the Reynolds
Number to determine whether the flow is laminar or turbulent.
Example 4-9
Given: S.A.E. 70 Lube Oil at 100 F is flowing
through 5-inch Schedule 40 pipe at a rate of 600
gallons per minute, as shown in the following sketch.
5" Class 150 Steel Angle
Valve with full area
seat-wide open
5" Class 150 Steel Gate
Valve with full area
seat-wide open
T Elevation 50'
50'
__
-l--==~~- ~I----~'l-I----_+-_l Elevation 0
1 7 5 ' - - - -...- - 75'
Find: The velocity in feet per second and pressure
difference between gauges PI and P 2 •
Solution:
I.
0.408 Q
~
v
_ 50. 6Qp
Re -
/:;.P
2.
d~
hLP
144
. . ..
. . . . . . . . . . . . . . . page 3·2
4·
loss due to flow; page 3·4
5·
loss due to elevation change; page 3·5
6.
. . . . . . . . . . . . . gate valve; page A·27
K= 20fT
. . . . . . . . . . . . . . . elbow; page A·29
5·047 X 470
R. < 2000; therefore flow is laminar .
.. . ' . . . . . . . . . . . . . . . . . page 3.2
Kl 8/T
Kl = 150/T
R. = 50 .6 X 600 X 56 . 1 = 718
64
718
/ = -- =
0.08q
Summarizing K for the entire system (gate
valve, angle valve, elbow, and pipe),
K = (8 X 0.016) + (150 X 0.016) + (20 X 0.016)
. . . . . . . . . . angle valve; page A·27
+ (0.08q x 300 x (2) = 66.
5.047
. . . . . . . . . . . . . . . ... . pipe; page 3·4
7·
v=
0.408 x 600
2
5·047
3
9.6
. . . . . . . . . . . . . . . . . . . pipe; page 3.2
3·
d = 5.047
...... S" Sched. 40 pipe; page 8.17
S = o.ql6 at 60 F
.............. page A·7
S
o.qo at 100 F
.............. page A.7
~ =
470
. . . . . . . . . . . . . . . . . . . . . . page A·3
P =62·371 X o.qo = 56.1
/T = 0.016
8.
/:;.P = _I_8_x_I0_-_6...:.x_6_6-"..3...:.X~5_6_.I_x...:....;6...:.oo
__2 + 50 x 56. I
5.047 4
/:;.P = 56.6
144
. . . . . . . . . . . . . . . . . . . . . . . . total
4·6
CHAPTER..
CRANE
EXAMPLES OF flOW PROBLEMS
Pressure Drop and Velocity in Piping Systems
Example 4-10 ... Piping Systems-Steam
Example 4·11 ... Flat Heating Coils-Water
Given: 600 psig steam at 850 F Rows through 400
feet of horizontal 6-inch Schedule 80 pipe at a rate
of go,ooo pounds per hour.
Given: Water at 180 F is flowing through a Rat
heating coil, shown in the sketch below, at a rate
of 15 gallons per minute.
The system contains three go degree weld elbows
having a relative radius of 1.5, one fu \ly-open 6 x 4inch Class 600 venturi gate valve as described in
Example 4-4, and one 6-inch Class 600 y-pattern
globe valve. Latter has a seat diameter equal to O.g
of the inside diameter of Schedule 80 pipe, disc
fully lifted.
1" Schedule
40 Pipe
2'
Find: The pressure drop through the system.
4" r
Solution:
Find: The pressure drop from Point A to B.
. . . . . . . . . . . page 3·4
I.
2.
Solution:
For globe valve (see page A-27),
K _ KJ + I' [0·5 (I
1'4
2 -
. . . . . . . . . . . . page 3·4
1.
1'2) + (1_1'2)2]
. . . . . . . . . . . . . . . . . . . page .3·2
Kl=551T
I' = o.g
3·
L
K-ID
4·
5·
6.
. . . . . . . . . . . . straight pipe; page 3·4
K = 14 IT
. . . . . . . 90° weld elbows; page A·29
rid = 4
. . . . . . . . . . . . . . . . . . . pipe; page 3·4
W
R. - 6·3 I d/J.
. . . . . . . . . . . . . . . . . . . page 3·2
d = 50761
. . . . . . 6" Sched. 80 pipe; page B·17
V
I.2I6
.... 600 psi steam, 850 Fj page A·17
/J. = 0.027
. . . . . . . . . . . . . . . . . . . . page A·2
IT - 0. 01 5
.................... page A·26
. . . . . . 90° bends; page A·29
KB
For globe valve,
1.44
R
6·3 1 x 9 0 000
3·
6
p = 60·57
· . . . . . . . . . water, 180 F; page A·6
/J. = 0·34
. . . . . . . . . . . water, 180 Fj page A.3
d
1.049
· . . . . . 1" Sched. 40 pipe; page B·16
IT = 0. 02 3
· ..... I" Sched. 40 pipe; page A.26
R, = <-----"-----'-'- = I. 3 X 105
I.049 X 0·34
6
e=5.76IXO.027 =3· 5XIO
1=0. 02 4
I = 0.0 15
K
K
................ pipe; page A·25
0.015 x 400 X 12
= 12·5
5.7 6 I
K - 3 X 14 X 0.01 5 ~ 0.63
... pipe
3 elbows; page A·29
4·
Summarizing K for the entire system (globe
valve, pipe, venturi gate valve, c1nd elbows),
K = 1.44 + 12.5 + 0.63 + I.44 - 16
8.
fl.p = 40.1
. . . . . . . . . . . pipe
18' straight pipe
K = 2 X 14 X 0.023 - 0.64
For seven 180° bends,
... two 90° bends
KB = 7[(2-1) (0.257r X 0.023 X 4) +
...... 6 x 4" gate valve; Example 4-4
7·
r
(n-I) (.25 niT d + ·5 Koo) + K90
....... 180° bends; page A.29
2.
K2
. . . . . . . . . . . . . . pipe bends
(0·5 X 0.J2) + 0.J2~
3.87
5·
KTOTAL = 4·94 + 0.64 + 3. 8 7 = 9.45
6.
fl.p = 18 X 10-6 X 9-45 X 60.57 X 15
1.04g
4
2
=
1.91
CRANE
4·7
CHAPTER'" - EXAMPLES OF FLOW PROBLEMS
Pressure Drop and Velocity in Piping Systems -
continued
Example 4·12 ... Orifice Size for Given
Pressure Drop and Velocity
Example 4·13 ... Flow Given in International
Metric System (51) Units-Oil
Given: A 12-inch Schedule 40 steel pipe 60 feet
long, containing a standard gate valve 10 feet from
the entrance, discharges 60 F water to atmosphere
from a reservoir. The entrance projects inward into
the reservoir and its center line is 12 feet below the
water level in the reservoir.
Given: Fuel oil with a density of 0.815 grams per
cubic centimeter and a kinematic viscosity of 2.7
centistokes is flowing through 50 millimeter I.D.
steel pipe (30 meters long) at a rate of 7.0 liters per
second.
Find: The diameter of thin-plate orifice that must
be centrally installed in the pipe to restrict the
velocity of flow to 10 feet per second when the gate
valve is wide open.
Find: Head loss in meters of fluid and pressure
drop in kg/cm 2, bar, and megapascal (MPa).
Solution: I. Define symbols in S1 units as follows:
A ... cross-sectional area of pipe, in meters'
D ... internal diameter of pipe, in meters
g ... acceleration of gravity = 9.8 meters/sec/sec
hL . .. head loss, in meters of fluid
L ... length of pipe, in meters
q ... rate of flow, in meters3/second
v ... mean velocity of flow, in meters/second
p ... fluid density, in grams/centimeter 3
tl.P (kg/em') ... pressure drop, in kilograms/centimeter'
tl. P (bar) ..... pressure drop, in bars
tl.P (MPa) .... pressure drop, in mega pascals
Solution:
I.
v2
2ghL
hL = K - or System K = -22g
R. =.:..1-.:. 23"-...:zq.. .:.d:..:.v-,,-p
2.
. . . . . . . . . . . . . . entrance; page A·29
K = 1.0
· . . . . . . . . . . . . . . . . . . exit; page A-29
Kl = 8/T
· . . . . . . . . . . . . . gate valve; page A.27
L
2.
· . . . . . . . . . . . . . . . . . . . pipe; page 3-4
d = I I.q38 ..................... pipe; page B·17
/T = 0. 01 3
.................... page A-26
P = 62.371
.................... page A·6
R. = 123·q X I I.q3 8 X 10 X 62·371
1.1
A column of fluid one square centimeter in crosssectional area and one meter high is equal to a
pressure of o. I p kg/ cm 2 ; therefore:
= 8.4 X 105
t1P (kg/cm 2) equals ... O. I P h L
t1P (bar) equals ..... 0.q8067 t1P (kg/cm 2)
f = 0.014
5·
.................... page A·25
Total K required = 64.4 X 12 + 102 = 7.72
K 1= 8 x 0.013 = 0.10
. . . . . . . . . . . gate valve
K = 60 x 0.014 = 0.84
. . . . . . . . . . . . . . pipe
Use metric-imperial equivalents as indicated below and on pages B- I 0 and B- I I .
meter (I) = 3.28 feet = 3q.37 inches
bar = 0.q8067 x kg/cm 2
megapascai = 0.oq8067 x kg/cm 2
· . . . . . . . . . . . . . . . . . . . . . . page A·3
J.L = I. I
4·
. . . . . . . . . . . . . . . . . . page 3·2
K - 0.78
K=f75
].
.... page 3-4
V
t1P (MPa) equals .... o.oq8067 lip (kg/cm 2)
3
].
Then, exclusive of orifice,
v _!l =
7 x 10=
66
-A (7r+4)X502 XIO-6 3·5
... page 3·2
Ktotal = 0·78 + 1.0 + O. I + 0.84 = 2.72
~
6.
Korifice =
7·
1 --,- (32
K()ri~ce '"'-' C2(34
7.7 2 - 2.7 2 = 5
v
v
...... page 3·2
....... ' ... page A-20
6
.------
~
8.
9
~
10.
.. C= 0·7
page A-20
.. (3 is too large
Assume (3 = 0.65 .. C = 0.67
page A-20
then I< '"'-' 7. I
.. (3 is too small
Assume (3 = 067 .. C = 0.682
page A-20
then I< ~ 5.8
II.
R. = 0.05 0 x 3.5 66 x 10 = 6.6 X Id
2·7
. .............•••... page A·25
f = 0. 02 3
Assume (3 = 0·7
then I< '"'-' 43
.. use (3 = 0.68
Orifice size ~ 11938 x 068 = 8.1"
4·
662 = 8.95
hL = fL ~ = 0. 02 3 X 30 X 3.5
D 2g
0.050 X 2 X q.8
. . . . . . . . . . . . . . . page 3·4
t::,.p (kg/cm') = 0.1 x 0.815 x 8.g5 = 0.729
t1P (bar) = 0.q8067 x 0.72q = 0.715
t1P (MPa) = 0.oq8067 X 0.72q = 0.0715
4-8
CHAPTER 4
CRANE
EXAMPLES OF flOW PROBLEMS
Pressure Drop and Velocity in Piping Systems -
continued
Example 4-14 ... Bernoulli's Theorem~Water
Given : Water at 60 F is flowing through the piping
system, shown in the sketch below, at a rate of
400 gallons per minute.
5" Welding Elbow
5" Schedule 40 Pipe
P,
.'i" Sched. 40 pipe; page B .. J7
fr
4·
{3 ~
o.olb
. .......... 5" size; page A·26
5·047
~ 0.80
1"----150' ---~
5" Schedule 40 Pipe
VI
_ _ _Eltvation ZI':' 0
10.08
.............. 4" pipe, page 8·14
... 5" pipe, page 1)·]4
5" X4# Reducing Welding Elbow
10.08 2
Find: The velocity in both the 4 and 5-inch pipe
sizes and the pressure differential between gauges
PI and P 2 •
2g
j.
2 X 32.2
For Schedule 40 pipe,
Solution:
I.
~ 2.85 X 105
Use Bernoulli's theorem (see page 3-2) :
.......... 4" pipe
+
Since, PI
PI
2.
P2
Rc = 50.6~300X 6~ 371
5.047 X 1.1
P2
.......... 5" pipe
=1:4 (Z2
h _ 0.00259 K Q2
d4
I~ -
5:0 . 6 Qp
dp.
K
fl:::
D
fL
f
. . . . . . . . . . . . . . ~page 3-4
K
............ 90° elbow; page A·29
q.6
K
5.q
K= 14 X 0.016
0.22
0.36 2
0.22 + ~84
0·54
K
sistance is conservatively estimated to be equal to the summation
of the resistance due to a straight size elbow and a sudden
enlargement.
7.
KTOTAL
8.
...... . 5u 90 elbow
Q
.... 5x4 u 90° elbow
Then, in terms of 5-inch pipe,
. . . . . . . . . . . . . . . . . . . . . page A·26
. . . . . . . . . . . . . . . . . . . page A·6
. . . . . . . for 110' of 4" Sched. 40 pipe
With reference to velocity in 5" pipe,
Note: In the absence of test data for increasing elbows, the reo
P ~ 62·371
... for 225' of 5" Sched. 40 pipe
X 110 X 12
,or
J< = 0.018 4·026
. . . . . . . . . . . . . . . . . . . . . . . page 3-4
small pipe, in terms of
. . . . . . . . .. { larger pipe; page 2·11
.4 or 5" pipe; page A-2S
0.018
K ~ 0.018 X 22 X 12 , or
5·047
K
. . . . . . . . . . . . . . . . . . . page 3·2
K ~ D{:J4
14fT
6.
reducing 90°
. . . .. { elbow; page A.26
3·
- 0.94 feet
q.6 + 144 + 0.22 + 054 = 248
hL = 0.002
15.8
. . . . . . . . . . . . . . . . . . . . . . page A·]
.. 4" Sched. 40 pipe; page B-17
9·
144
(75 - 0·Q4 + 15.8) = 39.0
CRANE
4-9
CHAPTER" - EXAMPLES OF FLOW PROBLEMS
Pressure Drop and Velocity in Piping Systems -
continued
Example 4-15 • .. Power Required for Pumping
For 500 feet of 3-inch Schedule 40 pipe,
Given: Water at 70 F is pumped through the piping
system below at a rate of
100 gallons per minute.
Elevalion Z, 400'
IJ----
3" Schedule 40 pipe
Elevation 2,
-
And,
2.16 + 0.14 + 27.0 + 41.06 + I
9,
N
Find: The total discharge head (H) at flowing conditions and the brake horsepower (bhp) required for a
pump having an efficiency (e p ) of 70 per cent,
Solution' J, Use Bernoulli's theorem (see page
2,
P
2
144 2 V 2 h
+ V 1 = Z2 + -- + + L
PI
2g
P2
2g
Since PI Pz and VI = V2, the equation can be
rewritten to establish the pump head, H:
P
J.
.. , ... , . , ...... page 3-4
Given " Air at 65 psig and I 10 F is flowing through
75 feet of I-inch Schedule 40 pipe at a rate of 100
standard cubic feet per minute (scfm).
Find: The pressure drop in pounds per square inch
and the velocity in feet per minute at both upstream and downstream gauges.
Solution: J. Referring to the table on page B-15,
read pressure drop of 2.21 psi for 100 psi, 60 Fair
at a flow rate of 100 scfm through 100 feet of I-inch
Schedule 40 pipe.
, . . . . . . . . . . . . . . . page 3,2
fJ.
v = -'-;---'"
..
).
K = 30fT
K 1 =8/r
L
K =f D
. . . . . . . . . . . 90° elbow; page A-29
K = 1.0
, ........ , , ....... exit; page A,29
6.
...... 3" Sched. 40 pipe; page B,16
62.3 0 5
. . . . . . . . . . . . . . . . . . . page A-6
....... , ....... , .... ,pageA-3
fT = 0.018
. . . . . . . . . . . . . . page A-26
v = --'-------
4·33
......... , .... , . page A-25
K=4X30XO.oI8
K = 27.0
(Z5) (100 + 14.7) (4 60 + 110)
100
65 + 14.7
520
2.61
To find the velocity, the rate of flow in cubic
feet per minute at flowing conditions must
be determined from page B-15.
=
(14:;':
p)
(1~~~~)
At upstream gauge:
qm = 100(
1
4 .7
) (4 60 + 110) = 20.2
5 20
14·7 + 6 5
At downstream gauge:
fJ. = 0·Q5
K 1 = 8 X 0,018
2.n
qm = q'm
........ straight pipe; page 3-4
f = 0,021
7.
J.
=
, ..... , . gate valve; page A-27
d = 3.068
P
Correction for length, pressure,
and tem'perature (page B-1 5) :
!:::'P
!:::'P
. page 3,2
. . . . . . . . . . . , . . . . page 13--9
4·
421
21
Example 4-16 . .. Air lines
2.
dvp
Re = 123,Q--
H = 400
bhp = _10_0_-'-_ _-"--'- = 15.2
24700 x 0,70
installed with reducers in 3" pipe
2
71.4
8.
2\1 Globe Uft Check Valve with wing-guided disc
PI
41,06
0
__- - - 7 0 ' - - - - 0 1
Zl +
=
3
KTOTAL
Four 3" Standard 90'
Threaded Elbows
12
K = 0.021
0, 14
2.16
qm =
4·
100[-1-4-'7-+-(~I;"-5~7-2.-'6-1,,-)J( 46~:~ 10) =20.9
v = '1",-
5·
A
A = 0.006
6,
V = -~~
, .. page 3-2
. page B-I&
3367
. , .. at upstream gauge
V = 20·9 = 3483
0.006
,at downstream gauge
0.006
.. four 90° elbows
.......... gate valve
lift check valve with
. . .. {reducers; Example 4,5
Note: Example 4-16 may also be solved by use of the pressure
drop formula and nomograph shown on pages 3-2 and 3-21
respectively or the velocity formula and nomograph shown
on pages 3-2 and 3-17 respectively,
4·10
CRANE
CHAPTER" - EXAMPLES OF FLOW PROBLEMS
Pipe Line Flow Problems
Example 4·17 .. . Sizing of Pump for Oil Pipe Lines
Given: Crude oil 30 degree API at 15.6 C with a viscosity
of 75 Universal Saybolt seconds is flowing through a 12inch Schedule 30 steel pipe at a rate of 1900 barrels per
hour. The pipe line is 50 miles long with discharge at an
elevation of 2000 feet above the pump inlet. Assume the
pump has an efficiency of 67 per cent.
Find: The brake horsepower of the pump.
Solution:
after converting B to Q.
{ or,
use nomograph on page 3-11
~EqUation
I.
1.8 to + J2
3-5 on page 3-2
........... page B-10
Bp
.... ' page 3-2 or 3-8
R. = 35·4 d,..
...... page 3-5
brake horsepower =
2.
J.
4.
QHp
· page B-9
247000 ep
t = (1.8 X 15.6) + J2 = 60 F
p = 54·64
.... page B-7
S = 0.8762
· page B-7
d
· page B-17
12.09
5
d = 258 30 4
5.
75 USS = 12.5 centipoise
35·4 x 1900 x 54.64
-~----'-'-----' = 24 JOO
12.09 x 12.,5
6.
1·
8.
' ...... page B-5
f = 0. 02 5
..... page A-25
.6. P = _0_.0_0_0_1---"_ _ _-'----"-~-'-"-----<-'---'----~
.6.P = 53J
9·
10.
The total discharge head at the pump is:
H = 1405 +2000 = 3405
II.
12.
Q
(
1900bbl..)
-k
(42*bbI...gal) ( ~)
mm
60
13)0
Then, the brake horsepower is:
13)0 x 3405 x 54.64
6
1500
247000 x 0.67
= 149 ,or say
CRANE
4·11
CHAPTER'" - EXAMPLES OF FLOW PROBLEMS
Pipe Line Flow Problems -
continued
Example 4·18 ... Gas
Given: A natural gas pipe line, made of 14-inch
Schedule 20 pipe, is 100 miles long. The inlet
pressure is 1300 psia, the outlet pressure is 300
psia, and the average temperature is 40 F.
~
The gas consists of 75% methane (CH 4), 21 %
ethane (C 2H s), and 4% propane (C 3Hs).
q
10.
R. =
12.
Solutions: Three solutions to this example are
presented for the purpose of illustrating the variations in results obtained by use of the Simplified
Compressible Flow formula, the Weymouth formula, and the Panhandle formula.
1 J.
Simplified Compressible Flow Formulo
(see page 3.3)
I
ooooook
= 107.8
day
0.482 q' hSD
..... page 3-2
d/J
/J=0.011
11.
Find: The flow rate in millions of standard cubic
feet per day (MMscfd).
K)
'a = (449 0000 ft3) (24
9·
.estimated; page A·5
R. = 0.4 82 X 4 49 0 000 x 0.693
13.376 x 0.011
R. = 10 190000 or 1.019 x 1'0 7
f = 0.0128
.............. page A-25
Since the assumed friction factor (j = 0.0128)
is correct, the flow rate is 107.8 MMscfd.
I f the assumed friction factor were incorrect, it
would have to be adjusted and Steps 8, 9, 12, and 13
repeated until the assumed friction factor was in
reasonable agreement with that based upon the calculated Reynolds number.
14.
Weymouth Formula
(see page 3.3)
2.
d = 13.376
d5 = 428 185
. .page B·]8
J.
f = 0.0128
turbulent flow assumed; page A·25
4.
).
6.
T = 460 + t = 460 + 40 = 500
Approximate atomic weights:
Carbon. . . . .. C = 12.Q
Hydrogen. . .. H = 1.0
16. d2.6S7 =
17·
1009
q'h= 28.0 x 1009
18.
Approximate molecular weights:
Propane (C3Hs)
M = (3 x 12.0) + (8 x 1.0) = 44
Natural Gas
M = (16 x 0.75) + (30 x 0.21) + (44 x 0.04)
M = 20.06, or say 20. I
8.
D
M (air)
~
29
93
... page 3·5
(13002 - 3002) 428 185
0.0128 x 100 x 500 x 0.693
q\ = 4490000
q\ = 114·2
-
3002) (525000)
q
Id
= (4 380000 ft3) (24.h-r) = 105.1
I oooooo.hr
day
Panhandle Formula
(see page 3·3)
Ethane (C 2H s)
M = (2 X 12.0) + (6 x 1.0) = 30
S = M (g~s) = 20.1 = 0.6
002
q' h = 4 380 000
Methane (CH4)
M = (I X 12.0) + (4 x 1.0) = 16
7·
/(13
'\J 0.693 x 100
PI )2
Lm (PI
)2J 0 5394
.
19.
q' h = 36.8 E d2.61S2 [(
20.
Assume average operation conditions; then
efficiency is 92 per cent:
E = 0.92
21.
22.
1
2
d2 . 6IS2 = 889
I
q h = 36.8 X 0.92 x 889
(13002 - 3002) 0.5394
100
q' h = 5 570 OQO
2J.
I
q
a = (5 570000 ft 3) (24
I
oooooohr
.hr). = 133.7
day
CRANE
CHAPTER 4 - EXAMPLES OF flOW PROBLEMS
4·12
Discharge of Fluids from Piping Systems
Example 4·19 ... Water
Given: Water at 60 F is flowing from a reservoir
through the piping system below. The reservoir has
a constant head of [[.5 feet.
K =
0.018 X 10 X 12
68
= 0·70
3. 0
.. 10 feet, 3" pipe
For 20 feet of 2-inch pipe, in terms of 3- inch
pipe,
Water
at 60 F
Standard Gate Valve - Wide Open
11.5'
3" Schedule 40 Pipe
10'
Bend
K = O.O[q X 20 X 12 =
2.067 X 0.674
[o.q
2" Schedul e 40 Pipe
For 2-inch exit, in terms of 3-inch pipe,
K = I + 0.67 4 = 5.0
---II. . ---- - - + - -....
20'
For sudden contraction,
_ 0·5 (I - 06i) ([) _
K 26 4
-1.37
Find: The flow rate in gallons per minute.
O. 7
Solution:
_ 50.6 Qp
Re dp.
{3 = d1/d 2
2.
. . page 3-4
I.
and, KTOTAL = 0.5 + 1.08 + 0.[4 + 0·70 +
lo.q + 5.0 + 1.37 = Iq·7
. . . . . . . . . . . . . . . . . . . page 3-2
. . . . . . . . . . . . . . . . . . . . . page A-26
5
Q = [q.65 X 3.0682 VI 1.5 + Iq7 = [4 1
(this solution assumes Aow in fully turbulent zone)
K = 0.5
· . . . . . . . . . . . . . . entrance; page A·29
K = 60fr
. . . . . . . . . . . . mitre bend; page A·29
K 1= 8fT
· . . . . . . . . . . . . . gate valve; page A·27
Calculate Reynolds numbers and check friction
factors for flow in straight pipe of the 2-inch
size:
· . . . . . . . . . . . . . straight pipe; page 3-4
R _ 50.6 X 141 X 62·371
6.
c -
I.q6 x 105
2.067 x I. I
f = 0.021
. . . . . . . . . . . page A·25
and for flow in straight pipe of the 3-inch size:
50.6 x [41 x 62·37[
5
R c=
68
=[·3 2X [0
3.0 Xl.[
.... sudden contraction; page A·26
small pipe, in terms of
. . . . . . . . . . .. { larger pipe; page 2·5
f = 0.020
exit from small pipe
. . . . . . . . . . . . .. { in terms of larger pipe
3·
d = 2067
· . . . . . . 2" Sched. 40 pipe; page B·16
d = 3068
· . . . . . . 3" Sched. 40 pipe; page 8·16
p. = I. I
4·
7.
Since assumed friction factors used for straight
pipe in Step 4 are not in agreement with those
based on the approximate flow rate, the K factors for
these items and the total system should be corrected
accordingly.
. . . . . . . . . . . . . . . . . . . . . . . page A·3
p = 62.37[
.................... page A·6
fr = O.Olq
· . . . . . . . . . . . . . 2" pipe; page A·26
fT = 0.018
· . . . . . . . . . . . . . 3" pipe; page A-·26
_ 0.020 X 10 X [2 _
K 68
-0.78
3. 0
K = 0.02 I X 20 X [2
2.067 X 0.67 4
· . . . . . . . . . . . . . . . . . . . . 3" entrance
. . . . . . . 3" mitre bend
Kl= 8 X 0.018 = o. '4
. . . . . . . . . 3" gate valve
.. 10 feet, 3" pipe
For 20 feet of 2-inch pipe, in terms of 3-inch
pipe,
{3 = 2.067 + 3.068 = 0.67
K = 60 X 0.018 = 1.08
. page A·25
[2.[
and, KTOTAL = 0.5 + 1.08 + 0.[4 + 0.78 +
[2.[ + 5.0 + 1.37 = 21.0
8.
Q = [q.65 X 3.0682 V[ 1.5 + 2[ = 137
CRANE
4·13
CHAPTER ,. - EXAMPLES OF FLOW PR08LEMS
Discharge of Fluids from Piping Systems -
continued
Example 4-20 . .. Steam at Sonic Velocity
Given: A header with 170 psia saturated steam is feeding
a pulp stock digester through 30 feet of 2-inch Schedule
40 pipe which includes one standard 90 degree elbow and a
fully-open conventional plug type disc globe valve. The
initial pressure in the digester is atmospheric.
Find: The initial flow rate in pounds per hour, using
both the modified Darcy formula and the sonic velocity and
continuity equations.
Solutions-for theory, see page 1-9:
Sonic Velocity and Continuity Equations
Modifled Dorey Formula
1.
page 3-4
W
L
D
K=f2.
].
K
30 fT
... globe valve; page A-27
............. 90° elbow; page A-29
K
0.5
..... entrance from header; page A-29
K
1.0
. . . . . . . . . . exit to digester; page A-29
k = 1.297 or say I.J
d 2 = 4. 272
fT = O.Olg
VI
V d2
. page 3-3
.. Equation 3-2; page 3-2
pipe; page 3-4
K 1= 340 fT
d = 2.067
"j kg 144 P' V
9·
2.673 8
.......... page A-9
10.
P' = P't - b.P
P' = 170 - 133.5 = )6.5
b. P determined in Step 6.
11.
hQ = 1196
12.
At 36.5 psia, the temperature of steam with
total heat of I Ig6 Btu/lb equals 3 I 7 F, and
... 2" pipe; page 8-16
... . . . . . . . . . . . . ..
.. 170 psia saturated steam; page A-14
............. pages A-\3 and A-16
. . page A·26
. . . . . . . . . . . . . . . . . . . page A.14
1 ].
V,
V.
I.J X )2.2 X 144 X
5 X 12-4
1652
12
4·
K - ------'--"'-'-'---7-....:.:..~ = J. 3 I . . . . . . . 30 feet, 2" pipe
K 1 = J40 X O.Olg = 6.46
K = J.JI + 6.46 + 0·57 + 0.5 + 1.0 = 11.84
b. : = - " - - - " - ' - = 155·J = 0.9 1 4
P 1
170
170
Using the chart on page A-n for k = I. J, It IS
found that for K = II. 84, the maximum
b.PjP't is 0.785 (interpolated from table on page
A-22). Since b.Pjp I l is less than indicated in Step
), sonic velOCity occurs at the end of the pipe, and
b.P in the equation of Step 1 is:
•
b.P = 0.785 X 17 0 = 133.5
6.
7·
Y = 0.71 0
8.
W = 1891 X 0.71 X 4.272
... (interpolated from
\table; page A-22
I:~
4 2.6738
'\/ 1 I.
W= 11780
=
0.05Dq X 12-4
11180
...... 2" globe valve
K = JO X O.Olg = 0.57
. . . . . ... 2" 90° elbow
and, for the entire system,
).
W =
X
NOTE
In Steps II and 12 constant total heat hg is assumed.
But the increase in specific volume from inlet to outlet
requires that the velocity must increase. Source of the
kinetic energy increase is the internal heat energy of
the fluid. Consequently, the heat energy actually decreases toward the outlet. Calculation of the correct
hg at the outlet yields a flow rate commensurate with
the answer in Step 8.
CHAPTER .c - EXAMPLES OF FLOW PROBLeMS
4·14
CRANE
Discharge of Fluids from Piping Systems -
continued
Example 4·22 . .. Compressible Fluids
Example 4·21 ... Gases at
at Subsonic Velocity
Sonic Velocity
Given: Coke oven gas having a specific gravity of
0.42, a header pressure of 125 psig, and a temperature of 140 F is flowing through 20 feet of 3inch Schedule 40 pipe before discharging to atmosphere. Assume ratio of specific heats, k = 1.4.
20' of 3" Schedule 40 Pipe
Given: Air at a pressure of 19.3 psig and a temperature of 100 F is measured at a point 10 feet
from the outlet of a Yz-inch Schedule 80 pipe discharging to atmosphere.
Find: The flow rate in standard cubic feet per
minute (scfm).
Solution:
1.
L
K=/ D
2.
J.
..... page B-16
K ." /~ = 0. 01 75 x 20 ." 1 6
D
0.2557
·3 9
l:!.P
...... total
Using the chart on page A-21 for k == 1.4, it
is found that for K = 2.87, the maximum
l:!.P/P'1 is 0.657 (interpolated from table on page
A-22). Since l:!.P/P'1 is less than indiCated in
Step 6, sonic velocity occurs at the end of the pipe
and l:!.P in Step ] is:
7·
l:!.P ." 0.657 P'I - 0.6; 7 x 139· 7 ." 91.8
Y - 0.637
]0.
q'h is equal to:
....... , ..... {interPOlated from
table; page A-22
40700 xo.b37 x 9 ...P3 /
~1.8 ~ 139·7
-V 2. 7 x 00 X 0.42
q'h == 1028000
19·3 + 14·7 = 34. 0
d = 0.546
cP = 0.2981
... page B-16
D == 0.0455
5·
/ = 0.0275
6.
K = / ~ = 0.0275 x 10 = 6.0
D
0.0455
4
.. fully turbulent flow; page A-25
. . for pipe
K = 1.0
..... for exit; page A-29
K = 6.04 + 1 = 7.04
.............. total
7.
l:!.;
=
PI
19·3 = 0.568
34.0
8.
Y = 0.7 6
9·
Tl - 460 + tl .... 460 + 100 = ;60
10.
139·7 - 14·7 = \25. 0 == 08
139.7
139.7' 95
9·
l:!.P = 19.3
.. page 3-4
.. for pipe
... forentrance; pageA-29
........ for exit; page A-29
K= 1.369+0.5+1.0=2.87
6.
J.
.. page A-25
d = 3.068 cP·"" 9.413
D." 0.2557
K 0.5
K '" 1.0
P'I
...... page 3-4
Nate: The Reynolds number need not be calculated since gas discharged to atmosphere
through a short pipe will have a high Re. and
flow will always be in a fully turbulent range.
in which the friction factor is constant.
4·
2.
4·
/=0.0175
.... page 3-4
K=/D
.. page 3-4
p') = 12 5 + 14·7 = 139·7
Ydl~~~I~;
L
Find: The flow rate in standard cubic feet per
hour (scfh).
Solution-for theory, see page 1-9:
Il:!.P P'
1.
q'n 40700 YcP-V K TI S:
q' no = 678
q'",-678xo.76xo.2981
q'm == 62.7
......... page A-22
I 19.3X~4.0
-V 7·04 X 5 0 X 1.0
CRANE
4-
CHAPTER .. - EXAMPLES OF FLOW PROBLEMS
Flow Through Orifice Meters
Example 4-24 . .. laminar Flow
Example 4-23 . .. Liquid Service
I n flow problems where the viscosity is high. calwlate
the Reynolds number to determine the type of flow.
Given: A square edged orifice of 2.0-inch diameter
is installed in a 4-inch Schedule 40 pipe having a
mercury manometer connected between taps located
I diameter upst(eam and 0.5 diameter downstream.
(a) The theoretical calibration constant
for the meter when used on 60 F water and for the
flow range where the orifice flow coefficient e is
constant ... and (b), the flow rate of 60 F water
when the mercury deflection is 4.4 inches.
Find:
Solution - (a)
R _ 50 .6 Qp
e -
2.
where:
].
"
j.
6.
7·
8.
9·
. page 3-5 or 3-15
page 3-2 or 3-1'
dp.
.. page 3-5
12 X 144
t:.h m = differential head in inches of mercury
The weight density of mercury under water
equals PW(SHg - Sw), where (at 60 F).
' .. page A-6
PU'
density of water = 62.371
.. page A-7
SHg = specific gravity of mercury = 13.57
SIC = specific gravity of water
4·
1.00
=
l:::.P = l:::.h m(784) = 6.454l:::.hm
12 X 144
•
c4. = 4.026
.. l '
d
2.00
I
- 1 = - - = 0·497
d2 4.026
•
e = 0.625
p. = 38
].
d2 3. 068
d1
2.15
.
- = - - = 0·70
d2 3. 068
4·
5·
6.
50.4" 4.4 =: 106
...... : . page A-3
R. = 50.6 x 106 x 62·371
12.
4.026 x 1.1
Re = 75 500 or 7.55 x 10 4
I].
e 0.625 is correct for Re = 7.55 X 10 4, per
page A-20; therefore, the flow rate through
the pipe is 106 gallons per minute.
T4.
When the C factor on page A-20 is incorrect,
for the Reynolds number based on calculated
flow, it must be adjusted until reasonable agreement is reached by repe<}ting Steps 9, 10, and [2.
... suspect laminar Aow; page A-3
e = 0.8
.. page B-16
.... [page A-20; assumed value
,based on laminar Aow
S = 0.876 at 60 F
S 0.87 at 90 F
. ... page A-7
.... page A-7
7·
p = 62.4 x 0.87 = 54.3
8.
Q=23 6 x2.15 2 xO.S/
9·
[0.
10.454 l:::.hm
) 2 xO. 6 2 5.\, 62.34
Q =23 6 x (2.0
'
Q 50.4" l:::.h m
.... calibration constant
page 3-5 or 3-15
.... page '3-2 or 3-8
2.
page B-17
..... page A-20
Il:::.P
23 6 d 12 e'\J -p-
50 . 6 Qp
dp.
page A-6
And P of Hg under H 20 = 62.371 (lJ. 57 - 1.00)
784 Ib/ft 3
Solution - (b):
10.
Q 50.4" l:::.h,,,
II.
p. = 1.1
Q
p
To determine differential pressure
across the taps,
l:::.P =
Solution:
T.
Q=236d12e'\I~P
1.
Given: SAE 10 Lube Oil at 90 F is flowing through
a 3-inch Schedule 40 pipe and produces 0.4 psi pressure differential between the pipe taps of a 2. I 5-inch
to. square edged orifice.
Find.' The flow rate in gallons per minute.
. page A-7
O 4
.
~ 54·3
R,
=75
50 .6 x 75 x 54·3 = 1768
3.068 x 38
e = o.q for R. = 1768
...... page A-20
Since the assumed e value of 0.8 is not correct, it must be adjusted by repeating Steps
5, 8, 9, and 10.
11.
e
[ 2.
Q=236x2.152xO.87 /0.4 =81.5
[ ].
0.87
.... assumed; page A·20
~ 54·3
R, = 50 . 6 x :1.5 x 54·3 = Iq20
3.0 8 x 38
e 0.87 for R. lqzo
.. page A-20
Since e = 0.87 is correct for the flow, the
flow through the meter is 81.5 gallons per
minute.
CRANE
CHAPTER .. - EXAMPLES OF flOW PR08LEMS
Application of Hydraulic Radius to Flow Problems
Example 4-25 • .. Rectangular Duct
Given: A rectangular concrete overflow aqueduct. 25 feet
high and 16.5 feet wide. has an absolute roughness (E) of
0.01 foot.
16.5' WI de
1060'
Find: The discharge rate in cubic feet per second when
the liquid in the reservoir has reached the maximum height
indicated in the above sketch. Assume the average temperature of the water is 60 F.
5·
2.
v=!L
2
(10·5+25)
497 ft.
6.
Equivalent diameter relationship:
D=4RH=4X4·97= 19. 88 .............. page 3-5
d = 48R. 1l = 48x497 = 239 .............. page 3-5
7·
Relative roughness. E/ D = 0.0005 . page A-23
A
J.
_~6.:L~2L.
R.u
. .. page 3-4
I-'~
q=8.05 A \I' ---K, + Ka
8.
f
9·
q = 8.05 X2) x 16.5
K.
resistance of entrance and exit
resistance of aqueduct
To determine the friction factor from the !v1oody
diagram, an equivalent diameter four times the
hydraulic radius is used; refer to page 3-5.
{O.
p = 61.·371
12.
~
15·
Assuming a sharp edged entrance.
... page A-29
Assuming a sharp edged exit to atmosphere,
K
I .0
.. page A-29
Then, resistance of entrance and exit,
K,=0·5+ 1.0 1.5
=
0.0 17 for q = 30 500 cfs Row.
... page A-6
. page A-3
1.1
4.97 X I. I
R, 164000 000 or 1.64 x 10 8
f = 0.017
.. for calculated R,; page A-24
page 3-2
K = 0·5
Calculate R.
and check,
ll.
I J.
R _ cross sectional Row area
H - - wetted"perimeter--
X 1000
30 500
q
where; K,
.. ffully turbulent Aow
',assumed; page A-23
0.017
Since the friction factor assumed in Step 8
and that determined in Step 14 are in agreement, the discharge flow will be 30500 cfs.
If the assumed friction factor and the friction
factor based on the calculated Reynolds number were not in reasonable agreement, the former
should be adjusted and calculations repeated until
reasonable agreement is reached.
16.
CRANE
CHAPTER 4
4 - 17
EXAMPLES OF FLOW PROBLEMS
Application of Hydraulic Radius to Flow Problems -
continued
Example 4-26 . .. Pipe Portiolly Filled
With Flowing Woter
Given: A cast iron pipe is t\vo-thirds full of
,
uniform flO\\-ing water
F).The
has an inside
diameter of 24 inches and a
of
per
foot. Note the sketch that follows.
[0
The cross sectional flow area equals;
A+B-'-"C= 22,6+22,b-:--275 = 32 0 . 2 in~
C=32 0 -2 =2,22 ft 2
B
A
144
20.2
X
12
The wetted perimeter equals:
Find: The flow rate in gallons per minute.
1r
Solution:
1.
o_06 25 rt per f t
0·75
-- =
1r
" Ih
6 d
Q =1 9 ,5"\/
40 J
1r
12
1J.
0
=
II.
d (~8'94)
24 (
360
218. 94)
360
= 45·9 m.
459
" ft.
- = 3.03
1)
I:1
page 3-4
R
Since pipe is flowing partially full an equivalent
diameter based upon hydraulic radius is SubSllwted
for D in Equation I (see page 1-4)
15·
39 3
Equivalent diameter d = 48R H ..
. .•...
page 3-5
27 8
Relative roughness ~ = 0.00°36 .. , , . page A-23
17,
. . . . . page 3-5
X
d=48(0,580)
. page 3-5
D=4RH ... ,." .. , .... , .. ,." .. ·
2.22
H=3· 8 3=o·5,-O
18 .
/
.... {assuming fully turbu.lent flow; page
= 0, 01 55
10.0625 X 0. 580
0. 01 55
Q=393 X 408 \j
Q=24 500 gpm
1,054
4·
5
. , . , .. , , , , . page 3- 2
19.
Depth of flowing water equals;
20.
p = 62.J7I
2
21.
J.L =
16 in.
3
6.
Calculate the Reynolds number to check the
friction factor assumed in Step 17.
Cos
4
() = ±
r
12
22.
0·333
.... , ............... page A-6
, , . , .. , ' .. , . page A-3
1.1
R _ j,054 X2 4 500 X62 '37I
e-
---0. 5
X-I-.1 - - 80
R.= 2 520 000 or 2,52 X 10 6
()
2J.
7·
8.
b
9·
Area A
4
II.) I
Area B
(4 b)
Area A or B
in,
. ..... , .... , , , .... , . , . page A-24
24.
Since the friction factor assumed in Step 17
and that determined in Step 23 are in agreement, the flow rate will be 24500 gpm.
25.
If the assumed friction factor and the friction
factor based on the calculated Reynolds num-
AreaC
Area C
/ = 0 . 01 55
ber were not in reasonable agreement, the former
should be adjusted and calculations repeated until
reasonable agreement is reached.
2 2.6 in~
4 -18
CRANE
CHAPTER ... - EXAMPLES OF FLOW PROBLEMS
Determination of Boiler Capacity
Example 4-21
Given: A steam boiler operating at 300 psia saturated
steam has a maximum capacity of 100,000 pounds per
hour.
Find: The boiler capacity in both kilo Btu per hour and
in boiler horsepower.
Solutions:
Kilo Btu per Hour:
1.
Boiler capacity = W(h q
2.
hu = total heat of steam
h,)
1000
, ..... , page B-8
",' page A-15
h q = 1202·9 Btu/lb
3,
h, = heat of liquid
, , , ... , . page A-J 5
h, = 394. 0 Btu/lb
4,
,100000
= ----'--------"Bo I'ler capacity
1000
= 80 890 kilo Btu/hr
Boller Horsepower:
W (h - h,)
97 0 .3 x )4.5
5·
Boiler horsepower = _....:....!u'-----':.:..
6.
For values of hu and hr, see Steps 2 and J.
.
100 000 1202·9B oller horsepower = - - - - ' - - - - - - - - ' - = - - - ' 97 0 .3 x )4.5
=
2420
,page B-8
A-l
Physical Properties of Fluids
and Flow Characteristics of
Valves, Fittings, and Pipe
APPENDIX A
The physical properties of many commonly used
fluids are required for the solution of flow problems.
These properties, compiled from many varied reference sources, are presented in this appendix. The
convenience of a condensed presentation of these
data will be readily apparent.
Most texts on the subject of fluid mechanics cover in
detail the flow through pipe, but the flow characteristics of valves and fittings are given little, if any,
attention, probably because the information has
not been available. A means of estimating the resistance coefficients for valves, deviating in minor
detail from the standard forms for which the coefficients are known, is presented in Chapter 2.
The Y net expansion factors for discharge of compressible fluids from piping systems, which are presented
here for the first time, provide means for a greatly
Simplified solution of a heretofore complex problem.
A·2
AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
APPENDIX
CRANE
Viscosity of Steam and Water
Viscosity of Steam and Water ~ In Centipoise II'I
Temp.
····1J;.2--I~~
F
psia
psia
psia
---
-,-----.
-~-
_L~~aI~~~aJJ~m 1,:~~_I]~~ L~~f~lJ,~~~
.017
.042
.040
.039
.038
.037
.094
,019
.042
.041
.040
.038
.037
.078
.023
.042
.041
.040
.039
.038
.197
.013
.041
.040
.039
.038
.037
.164
.014
,041
,040
.039
.038
.037
.138
.015
.041
.040
.039
.038
.037
.lIl
.667
Sat.
Sat. steam .010
.041
15000
.040
1450
.039
1400
1350
.038
1300
.037
.524
.010
.041
.040
.039
.038
.037
.388
.0Il
.041
.040
.039
.038
.037
.313
.012
.041
.040
.039
.038
.037
.255
.012
.041
.040
.039
.038
.037
1250
1200
1150
!l00
1050
.035
.034
.034
.032
.031
.035
,034
.034
.032
.031
.035
.034
.034
,032
.031
.035
.034
.034
.0:32
.031
.03,'}
.034
.034
.032
.031
.035
.034
.034
.032
.031
.035
.034
.034
.032
,031
.036
.034
.034
.032
,031
.036
.035
.034
.033
.032
.036
.035
.034
.033
.032
.037
.036
.034
.034
.033
1000
950
900
850
800
.030
.029
.028
.026
.025
.030
.029
.028
.026
.025
.030
.029
.028
.026
.025
.030
.029
.028
.026
.025
.030
.029
.028
.026
.025
.030
.029
.028
.. 026
.025
.030
.029
.028
.027
.025
.030
.029
.028
,027
.025
.030
.029
.028
.027
.026
.031
.030
.028
.027
.026
750
700
650
600
550
.024
.023
.022
.021
.020
.024
.023
.022
.021
.020
.024
.023
.022
.021
.020
.024
,023
.022
.021
.020
.024
.023
.022
.021
,020
.024
.023
.022
.021
.020
.024
.023
.022
.021
.020
.024
.023
.022
.021
.020
.025
.023
.023
.021
.020
500
450
400
350
300
.019
.018
.016
.015
.014
.019
.018
.016
.015
.014
.019
.018
.016
.015
.014
.019
.018
.016
.015
.014
.019
.017
,016
.015
.014
,019
.017
.016
.015
.014
.019
.017
.016
.015
.182
.018
.017
.018
lli
183
.131
.153
.183
250
200
ISO
100
50
.013
.012
.Oll
.680
1.299
.013
.012
.Oll
.680
1.299
.013
.012
.427
.680
1.299
.013
.012
.427
.680
1.299
.013
.300
.427
.680
1.299
.228
.300
.427
.680
1.299
.228
.300
.427
.680
1.299
.228
.300
.427
.680
1.299
.680
1.299
.680
1.298
32
1.753
1.753
1.753
1.753
1.753
1.753
1.753
1.752
1.751
1.749
~~~~ J~~~~~~I~~i~O
~
.043
.048
.047
.047
.046
.045
.050
.049
.049
.049
.048
.042
.041
.041
.040
.040
.045
.045
.045
.045
.047
.048
.048
.049
.050
.052
.032
.031
.029
.028
.027
.039
.038
,037
,037
.036
.03,'}
.035
.035
.035
.040
.041
.042
.045
.052
.062
.049
.052
,057
.064
.071
.055
.059
.064
.070
.075
.025
.024
.023
,021
.019
.095
.057
.071
,082
.091
,101
.071
.079
.088
,096
.105
.078
.085
.092
.101
.109
.081
,086
.096
.104
.113
.103
.116
.132
.154
.184
.105
,118
.134
.15.5
.185
.111
,123
.138
.160
.190
.114
.127
.143
.164
.194
.119
.131
.147
.168
.198
.122
,135
.150
.171
.201
.301 I•..301
.2~
229
.427
.428
.231
.303
.429
.680
1.296
1.74,'}
.235
.306
.431
,681
1.289
.238
.310
.434
.682
1.284
.242
.313
.437
.683
1.279
.245
.316
.439
.683
1.275
1.733
1.723
1.713
1. 705
Values directty below underscored viscosities are lor water.
~
.044
.043
.042
.041
.040
.046
.045
.044
.044
® Critical point,
,-
-
..
~,
CRANE
APPENDIX A - PHYSICAL PROPERTIES Of flUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
A·3
Viscosity of Water and
Liquid Petroleum Products8, 12,23
4000
3000
2000
1. Ethane (C,H,J
1000
800
600
2, Propane (C,H,)
3, Butane (C,Hld
400
300
4. Natural Gasoline
200
6. Water
5, Gasoline
7. Kerosene
(l)
v>
0
100
80
60
8. Oistillale
9. 48 Oe9. API Crude
Cl.
.....
c
(l)
u
c
i3
10. 40 Oeg. API Crude
40
30
20
11. 35,6 Oe9. API Crude
12. 32.6 Oeg. API Crude
13. Salt Creek Crude
v>
0
u
v>
>
I
:::t
14. Fuel 3 (Max.)
10
8
15, Fuel 5 (Min.)
6
16. SAE 10 lube (J 00 V.I.)
4
3
2
17. SAE 30 lube (100 V.I.)
18. Fuel 5 (Max.) or
Fuel 6 (Min.)
19. SAE 70 lube (100 V.I.)
1.0
.8
20. Bunker C Fuel {Ma x.J and
M.e. Residuum
.6
21. Asphalt
.4
.3
.2
Data extracted in part
by permission from the
Oil and Gas Journal.
.1
.08
,06
.04
.03
10
20
30 40
60 80 100
200 300 400
t - Temperature, in Degrees Fahrenheit
600 800 1000
ExalTIple: The vis~osity of \\ater at
125 F is 0.52 centipoise (Curve No.6).
A-4
APPENDIX A - PHYSICAL PROPERTIES OF flUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
~--=----.
CRANE
Viscosity of Various Liquids 5 , 8, 11
10
I( \
6.0
5.0
18\\
II
16~
2.0
~ "'
'\
Vl
'0
Q.
:;:::
C
(I)
c..:>
7
~5/
12
"-
IVo"'"
1\..,
.5
4
0
u
Vl
:>
ro...
........
.3 ~ ~
I
.2
'",..... r-... "-
"" ~ "'-
3~
:::l
"- ,.."-
I\..
~
;:;. .4 ~\.
'Vi
~
""
'" "" " "'"
"
"'1"""1"- "-.....
6
L
"
c
~
~
"" ~
","
~
,
.,
I' ' ' '
"
~\\
s..
.9
.8
.7
.6
"\\ \
\
~ ,\
\\ ' ~
3.0
(I)
~
l{\
4.0
1.0
It 1~
1'\""
i"
"- "-
~~
'" ~
~ r-....
~ '........
~ t:::::::
.............
~
"""""
~
"""-
~ r--
---.... ~
1 - - - -~
,
1\
0.1
.09
.08
.07
\
\
.06
\
.05
-40
......
""
,
\
.04
.03
'"""
o
~
~
~
......
\
40
80
120
160
200
240
280
320
360
t - Temperature, in Degrees Fahrenheit
I. Carbon Dioxide •• CO,
2. Ammonia •••••••• NHs
3. Methyl Chloride •• CHaCl
4. Sulphur Dioxide •• SO,
5. Freon 12 ........ F- 12
6. Freon 114 ....... F-I14
7. Frean 1 1. ....... F.1l
8. Freon 113 ....... F-113
9. Ethyl Alcohol
10. Isopropyl Alcohol
11. 20% Sulphuric Acid •••••• 20% H,SO.
12. Dowtherm E
13. Dowtherm A
14. 20% Sodium Hydroxide •• 20% NaOH
15. Mercury
16. 10% Sodium Chloride Brine ••• 10% NaCI
17. 20% Sodium Chloride Brine ••• 20% NaCI
18. 10% Calcium Chloride Brine •• 10% CaCl,
I 9. 20% Calcium Chloride Brine •• 20% Co CI,
Example: The viscosity of ammonia at 40 F is 0.14 centipoise.
CRANE
A·5
APPENDIX A- PHYSICAL PROPERTIES Of flUIDS AND flOW CHARACTERISTICS Of VALVES, FITTINGS, AND PIPE
Viscosity of Gases and Vapors
Viscosity of Various Gases
The curves for hydrocarbon vapors and
natural gases in the chart at the upper
right are taken from Maxwell lS ; the
curves for all other gases (except helium 7)
in the chart are based upon Sutherland's
formula. as follows:
=
0
iJ.
/-La =
l'
To
C
I
viscosity, in centipoise at
temperature To.
absolute temperature, in degrees Rankine (460 + deg, F)
for which viscosity is desired.
•
.032
I
:~ .028
I
o'"
<l>
,~
>
I
.01
IV'A 1/1/ /./ /1;:; v/
0
~7 / V
v/
6~ / /. /- t/
V
.~
I
HYDRO
CARBON
VAPOR
AND
<;y
NATURAL
GASES
,
8~
1/
......-'~
V
/
/"
I
I
i
V'
-
~
a 100 200 300 400 500
600 700 800 900 1000
t - Temperature, in Degrees Fahrenheit
Viscosity of Refrigerant Vaporsll
0,
Air
127
120
.018
Nz
III
.017
CO,
CO
S0,
240
.016
(saturated and superheated vapors)
.019
'
,,\)~
1
118
!
VV
I
/
:
~ *015 !'
I"
I
~ .014
u
, /'
J!:;o
'iii
.01 IV
.010
.009
I /" / ' V
P"
.007
-40
I
l/
~
-
~ f....- n
I
\'~~~
,... 1c...- r;\t;;:;
~
C\\3~
~
.........
".
:
~ -1"-1\3
~
--::::::
.......... ~ ?- ~ V
.....~
::--f--
V
.008 I-""
~
/'
/'"
,./"
i
8 .012
'"
;;;
V
i-'
V
71
I
.:=_ .013
I
::I.
/'
1
.~
of carbon dioxide gas (C0 2) at about 80
F is 0.015 centipoise.
IV /. ?/
1/V/~ ~
27/ ~/
.00
.5
NH 3
,/
V/
Fluid
Lower chart example: The viscosity
.... 8(/
/
<;0
I
.01
Approximate
Values of "C"
of sulphur dioxide gas (S02) at 200 F
is 0.016 centipoise.
I
./
/.
pressure is small for most gases. For
gases given on this page, the correction
of viscosity for pressure is less than 10
per cent for pressures up to 500 pounds
per square inch.
Upper chart example: The viscosity
// V;V //V
V/ bf//V/ /
v
/
'" .020
Note: The variation of viscosity with
370
72
I
...
Sutherland's constant,
NH,
H.
.)
Helium
/ )
/ / / Air
/ / / 1"/
L / / / ~I
/ / / / 0-V I
V
~, =.75
~
0 ~ 9CO//
LOa
V
;; 'h f" v/ 1-/ d ~, "
::::
'§ .024
absolute temperature, in degrees Rankine, for which viscosity is known.
416
I
I
,
:l::
viscosity, in centipoise at
temperature 1'.
i
.036
555 To
where:
/-L
.040
+ C) ('f )%
0.555 l' + C
70
(0.
I
~
V
."".
~ ~~
~
~
~~ ~
V
~~
i
II
o
40
80
120
160
t - Temperature, in Degrees Fahrenheit
200
240
APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
Physical Properties of Water
Tem'\Vrature
of ater
Saturation
Pressure
Specific
Volume
Weight
Density
I
P'
V
p
Degrees
Fahrenheit
Pounds per
Square Inch
Absolute
Cubic Feet
Per Pound
Pounds per
Cubic Foot
Pounds
Per Gallon
0.08859
0.12163
0.17796
0.25611
0.016022
0.016019
0.016023
0.016033
62.414
62.426
62.410
62.371
8.3436
8.3451
8.3430
8.3378
32
40
50
60
I
70
80
90
100
0.36292
0.50683
0.69813
0.94924
110
120
130
140
1.2750
1.6927
2.2230
2.8892
150
160
170
180
190
.
i
I
Weight
I
I
0.016050
0.016072
0.016099
0.016130
62.305
62.220
62.116
61.996
8.3290
8.3176
8.3037
8.2877
0.016165
0.016204
0.016247
0.016293
61.862
61.7132
61.550
61.376
8.2698
8.2498
8.2280
8.2048
3.7184
4.7414
5.9926
7.5110
9.340
0.016343
0.016395
0.016451
0.016510
0.016572
61.188
60.994
60.787
60.569
60.343
8.1797
8.1537
8.1260
8.0969
8.0667
200
210
212
220
11.526
14.123
14.696
17.186
0.016637
0.016705
0.016719
0.016775
60.107
59.862
59.812
59.613
8.0351
8.0024
7.9957
7.9690
240
260
280
300
24.968
35.427
49.200
67.005
0.016926
0.017089
0.017264
0.01745
59.081
58.517
57.924
57.307
7.8979
7.8226
7.7433
7.6608
350
400
450
500
134.604
247.259
422.55
680.86
0.01799
0.01864
0.01943
0.02043
55.586
53.648
51.467
48.948
7.4308
7.1717
6.8801
6.5433
550
600
650
700
1045.43
1543.2
2208.4
3094.3
0.02176
0.02364
0.02674
0.03662
45.956
42.301
37.397
27.307
6.1434
5.6548
4.9993
3.6505
I
I
I
I
Specific gravity of water at 60 F
Weight per gallon is based on 7.48052 gallons per cubic foot
All data on volume and pressure are abstracted from ASME Steam
Tables (1967), with permission of publisher, The American Society of
Mechanical Engineers, New York, N. Y
CRANE
CRANE
APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND flOW CHARACTERISTics OF VALVES, fiTTINGS, AND PIPE
A-7
Speciflc Gravity-Temperature Relationship for Petroleum OilS 12
(Reproduced by permission from the Oil and Gas Journal)
,.-.,.
lJ..
<::;)
<.0
~
ro
<E
('C!
:l:
-"""';:::--1-_-1- A PIG RA VI T Y
0
" '0
~
0.8
w
......
<L>
c:::
~
::;:)
C'Cl
<E
Q..
E:
<L>
I>.
J.6
<:::
«
.....
(l;l
0.5
>.
>
;::: 0.4 '--~--I---j
<:.::J
<..>
......
'u
<L>
~,
~
or 0.3
cr;
""
~
0.2 ;;"'0-.l....-~l~OO=---L-----:l:20~O---l-.."J30:-:-0-~~4~OO~~~50~o--L--::6L"OO-L----='="70::-0----1--::8L"Oo-L-~9::l:-00".--...l...-~IOOO
C2He =Ethane
C3Hs =Propane iC.H10=I.obutane
C.H1o=Butane iC 6H12 = I.apentane
Example; The specific gravity
of an oil at 60 F is 0.85 The
specific gravity at 100 F = 0.83.
Temperature, in Degrees Fahrenheit
To find the weight density of a petroleum oil at its flowing temperature
when the specific gravity at 60 F /60 F is known, multiply the specific
gravity of the oil at flowing temperature (see chart above) by 62.4, the
density of water at 60 F.
Weight Density and Specific Gravity* of Various Liquids
Liquid
Temp. Weight Specific i
Density Gravity •
p
S
Liquid
iTemp'l Weight Specific
.
Density Gravity
IpS
"Liquid at specified temperature relative to water
at 60 F.
tMilk has a weight density of 64.2 to 64,6.
tlOO Viscosity Index.
,..-
.~
Fuel 3 Max.
Fuel 5 Min.
Fuel 5 Max.
Fuel 6 Min.
- GasOIine---~
Gasoline, Katural
Kerosene
M. C. Residuum
80.6
52.99
5602
60.23
61.92
I 6192
46.81
42.42
50.85
58.32
I
1014
1.292
0.850
0898
0.966
0993
0.993
0751
0.680
0.815
0.935
Milk
Olive Oil
Pentane
SAE 10 Lubd
SAE 30 Lubet
SAE 70 Lubd
Salt Creek Crude
32'.6° API Crude
35.6" API Crude
40° AP I Crude
48° API Crude
59
59
60
60
60
60
60
60
60
60
54.64
5602
57.12
52.56
5377
52.81
51.45
49.16
0.919
0.624
0.876
0.898
0.916
0.843
0.862
0.847
0.825
0788
Values in the table at
the left were taken
from Smithsonian
Physical Tables,
Mark's Engineers'
Handbook, and 12Nelson's Petroleum Refinery Engineering,
A-8
CRANE
APPENDIX A-PHYSICAL PROPERTIES OF fLUIDS AND fLOW CHARACTERISTICS Of VALVES. fiTTINGS. AND PIPE
Physical Properties of Gases
iS
'(Approximate values at 68 F and 14.7 psia)
Cp =
C. =
Name
of
Gas
Chemical
Formula
or
Symbol
specific heat at constant pressure
specific heat at constant volume
Specific Heat I Heat Capacity
Specific: !IndiGravity vidual
per
atRoom
I
Rela- , Gas
Temperature
Cubic Foot
Btu/Lb of
tive ,Constant
to Air '
APprox., Weight
Molecu-, Density,
tar
! Pounds
WeMight
I.
C~hlc
k
equal
to
cplcf)
Foot
p
Sg
R
Cp
c"
26.0
29.0
17.0
39.9
.0682
: .0752
.0448
I .1037
0.907
1.000
0.596
1.379
59.4
53.3
91.0
38.7
0.350
0.241
0.523
0.124
0.269
0.172
0.396
0.074
.0239
.0181
.0234
.0129
.0184
.0129
.0178
.0077
1.30
1.40
1.32
1.67
Butane
Carbon dioxide
Carbon monoxide
Chlorine
58.1
44.0
28.0
70.9
.1554
.1150
.0727
.1869
2.067
1.529
0.967
2.486
26.5
35.1
55.2
21.8
0.395
0.205
0.243
0.115
0.356
0.158
0.173
0.086
.0614
.0236
.0177
.0215
.0553
.0181
.0126
.0162
1.11
1.30
1.40
1.33
Ethane
Ethylene
Helium
Hydrogen chloride
30.0
28.0
4.0
36.5
.0789
.0733
.01039
.0954
1.049
0.975
0.1381
1.268
51.5
55.1
386.3
42.4
0.386
0.400
1.250
: 0.191
0.316 , .0305
0.329 ! .0293
0.754
.0130
0.135
.0182
.0250
.0240
.0078
.0129
1.22
1.22
1.66
1.41
2.0
34.1
16.0
50.5
.00523
.0895
.0417
.1342
0.0695
766.8
1.190
45.2
0.554
96.4
1.785 I 30.6
3.420
0.243
0.593
0.240
2.426
0.187
0.449
0.200
.0179
.0217
.0247
.0322
.0127
.0167
.0187
.0268
1.41
1.30
1.32
1.20
19.5
30.0
28.0
44.0
.0502
.0780
.0727
.1151
0.667
1.037
0.967
1.530
79.1
51.5
55.2
35.1
0.560
0.231
0.247
0.221
0.441
0.165
0.176
0.169
.0281 I .0221
.0129
.0180
.0127
.0180
.0194
.0254
1.27
1.40
1.41
1.31
32.0
44.1
42.1
64.1
.0831
.1175
.1091
.1703
1.105
1.562
1.451
2.264
48.3
35.0
36.8
24.0
0.217
0.393
0.358
: 0.154
0.155
0.342
0.314
0.122
.0180
.0462
.0391
.0262
.0129
.0402
.0343
.0208
1.40
Acetylene (ethyne)
Air
Ammonia
Argon
Hydrogen
Hydrogen sulphide
Methane
Methyl chloride
NH3
I
A
I
:
Natural gas
Nitric oxide
Nitrogen
Nitrous oxide
NO
N,
N,O
Ii
Oxygen
Propane
Propene (propylene)
Sulphur dioxide
I
I
I
i
i
1.15
1.14
1.26
Molecular Weight. Specific Gravity, Individual Gas Constant, and Specific Heat values were
abstracted from, or based on, data in Table 24 of Mark's "Standard Handbook for ~1echanical
Engineers" (seventh edition).
Weight Density values were obtained by mUltiplying density of air by specific gravity of gas,
For values at 60 F, multiply by 1.0154.
Natural Gas values are representative only. Exact characteristics require knowledge of specific
constituents.
Volumetric Composition and
Specific Gravity of Gaseous FuelsiS
-
-~------.
-"'-- . - ....- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ; 0 - - Chemical Composition
Percent by Volume
-----
Hydro- Carbon I
Paraffin
'Ill
.
gen
Mon-' Hydrocarbons'
umlOants
Type of Gas
oxide
IMeth-!
Eth- EthYl~1 Ben-'
ane
ane
ene
zene
~====~==========~==~==~
~?'i~~~~;;~~;t.:,inouo~,II,::: ;;:~ 8;::
Blue Water Gas from Coke
Carbureted Water Gas
Coal Gas (Cont. Vertical Retorts)
Coke-Oven Gas
Refinery Oil Gas (Vapor Phase)
Oil Gas, Pacific Coast
I
47,3
"40.5
54.5
37.0
1.3
34.010.2
10.9
24.2
46.5
13.1
48.6
6.3
1.2
12.7
32.1
23.3
26.3
15
1
.'1 j ...
Oxygen
1 0.6
Specific
Gravity
Relative
Nitro- Carbon to Air
gen
DioxS"
ide
v
1 ::::
I,::; :::
----',-0-,-7-+-8-.3--:1,--353-:·-~4-T.-11--=0-'-.5.:..::7'--
21.7
6.12.8
1.5
1.3
0.5
0.2
2.9
4.4
3.5
39.6
2.7
0,8
1.0
0.3
8.1
0.5
1.1
3.6
0.63
0.42
I ~2:'721 I
0,44
0.89
0.47
CRANE
APPENDIX A- PHYSICAL PROPERTIES Of flUIDS AND flOW CHARACTERISTICS Of VALVES, fiTTINGS, AND PIPE
A·9
Steam
14
Values of Isentropic Exponent, 1c
1.34
, I
1 1
I
/
1.32
r"""""'--
i
~
C
Q,)
1.30
...F_ _
~o.Q
~OQ.L
1---
I
---
1,/ I I
r,
'-
~
- - - -------- - _... - :.~
1---- -
-.... .................
--
'0.
I
"
<ll
'"I
\
~
-- --- -~
!
120.0. F
1.26
I
...
!
----
1400. F
I
--"
/
/
/
",/
/
\
1;/
~
I
I
/
"<.,
, ....
,
/ /I
~
"
-"\
,100.0. F
r - - 1 - - - - 1 - - - --- I---~
c:
if ;
I.
~~T-- - - - - - - - --- I-~~ "-,- - "!~
(j
,g 1.28
;'I I
I
--- ="
'""-
_ I- _ _ I- _ _
70.0. F
1.
V~POR
--- --- ~
-
I
L.U
r---- ~
~o.o. F
c::
2-
><
30.01:. _ _
1-- -
SATURATED
I
/
-- !
I
i
1.24
..... 1
2
5
10
20
50
100
200
500
pi _ Absolute Pressure, Pounds per Square Inch
For small changes in pressure (or volume) along an isentropic, pv k = constant
i
A-l0
APPENDIX A- PHYSICAL PROPERTIES Of flUIDS AND FLOW CHARACTERISTICS Of VALVES, FITTINGS,AND PIPE
CRANE
Weight Density and Specific Volume
Of Gases and Vapors
The chart on page A-I I is based on the formula:
144 p'
p
MP'
= ~ = 10·72
p' =
where:
2.70 p' Sg
=~""-T-'
14.7
+P
Problem: What is the density of dry CH 4 if the temperature is 100 F and the
gauge pressure is 15 pounds per square inch?
Solution: Refer to the table on page A-8 for molecular weight, specific gravity',
or individual gas constant. Connect 96.4 of the R scale with 100 on the temperature scale, t, and mark the intersection with the index scale. Connect this
point with 1 5 on the pressure scale, P. Read the answer, 0.08 pounds per cubic
foot, on the weight density scale p.
___. . __ . . __ . ___ . __ . . _
_ _-..-__..._ _..~.. _ _ _ _ _~...._ _.._
We~ht Density of A:~
~ ~.
Weight Density of Air, in Pounds per Cubic Foot
For Gauge Pressures Indicated
(Based on an atmospheric pressure of 14.696 and a molecular weight of 28.97)
Air 1/
Temp.
Deg F.
~~ ~I~I:I:':I:I:!:I:I:I:I~I:I:
: :
.302 " .357
.41i-I·467~I2-1·578~1-:-633T-:688-~7~1 :798
.853 1 .909
, .0811 1.1087 i .13631 .IMs .247
.0795 .1065· .1335: .1876 .242
.295: .350
.404
.458
.512
.566
.620
.674
.728
.782
.836
.890
.0782 .10481.131 41.1846 .238
.291 1.344
.397
.451
.504
.5571 .610
.663
.717
.770
.823
.876
.284
.336
.388, .440
.492
.544
.596
.648
.700
.752
.804
.856
.0764 .1024 .128 4 .1804 .232
.0750 i .1005 .126o .1770 .228
.279
.330
.381 1 .432
.483: .534
.585: .636
.687
.738
.7~_ .840
.0736 .0986 .1236' .173Y--1.2:i~-' :324~1:~:474--:Si~4
.624
.674
.724
.774
.824
.269
.318
.367
.416 . . 465
.515 . . 564
.613
.662
.711
.760
.809
.0724 .0968 .121 4 .1705 .220
.1192 .1675 .. 216
~0709 .0951
.264 " .312
.361·, .4091' .457
.505 . . 554
.602
.650 . . 6'l8
.747
.795
.259· .307
.354
.402
.449
.497 1 .544
.591
.639 1 .686
.734
.781
.0647 .0934 .117 1 .1645 .. 212
1
.1617
.208
.255
i
.302
.348
.395
.441
.488·
.535
.581
.628·
.674
.721
I
.768
.0918 .lI5.
.0685
..
.09021 .113fT.1590-:205
.251: .296 1 .342
:~.434 1~4~525
.571
.617 --:663"'~'" .755
.0887 .• 11131.1563 .201
.246, .291
.337
.382
.427:.472: .517
.562: .607
.652
.697
.742
.0873. .1094 .1537 .1981 .242 1.287 :,.331
.375
.420
.464 'I .508
. 553 1 .597
.641
.686
.730
.0834 .1051 .1477 .1903 .233
.275
.318
.361
.403
.446
.488
.531
.573
.616
.659
.701
.0807 1 .10'11 .1421 .1831 .224 : .265
.306
.347
.388
.429 I .470
.511
.552
.593
.634
.675
.07771.0974 .13691.1764 .216~ .295
.334
.j74-.413--:45~::m--:~:5~.6TiJ
.650
.0750: .0940 .1321 .1702 I .208
.246 : .284
.322
.361: .399
.437
.475
.513
.551
.589
.627
.0724,.0908 .1276 .. 16441.201 ,.. 238 1.275
.311
.348,.385
.422
.459
.495
.532
.569
.606
.0700 .0878 .1234 .1590 .1945 .230
.266
.301·1 .337
.372
.408
.443
.479
.515
.550
.586
~3~50~..;r..:..;.0490
.0657 .0824 .1158 i .1491 .1825 .216
.249
.283
.316
.349
.383
.416
.449
.483
.516
.550
400
.0462 .06191.0776 .1090, .1405~7I9T.203- '.235 : .266 i~:i98 .329-:3601 .392----:-4f:f
.455
.486
.518
450
.0436 .0585 •. 0733 .1030,: .1327 .1624! .1921 .222
.252' .281
.311
.341
.370
.400 I· .430
.459
.489
500
.0414 .0555 i .0695 .0977, .1258 .1540, .1821 .210
.238
.267
.295
.323
.351
.379
.407
.436
.464
550
.0393 .0527: .0661 .0928 .1196 .14641.1731 .1999 •. 227
.253
.280
.307
.334
.360
.387
.414
.441
600
.0375 .0502 1.0630 .0885 .1140 .1395 .1649 .1904 i .216
.241
.267
.292
.318
.343
.369
.394
.420
30·
40
50
60
70
80
90
100
110
120
130
140
150
175
200
225
250
275
300
I'
~--~---.----
----.------~
'I
I,
1
175 , 200 1 225
250
300
400 I 500 1 600 I 700
800
900
1000
I~I~
~
~
~
~
~
~
~
~
~
~
I
30· :,1.047 1.185 1.323- 1.460 11.73612.192:84 13.391' 3.94 ···14.49~---s:60
i
40
:1.026 1.161 1.296 1.431 1.702: 2.24 2.78 3.32
3.86
4.40
4.95 5.49
50 11'1.009 1.142 1.275 1.408 :11.674 ',2.21
2.74 3.27
3.80
4.33 4.87 5.40
60
.986 1.116 1.246 1.376 1.636 2.16 .2.68 3.20
3.72
4.24
4.76 5.28
70
.968 1.095 1.223 1.350 1.605 2.12 12.63 ! 3.14 3.65 • 4.16
4.67 5.18
80
:950 ! 1.075 • 1.200 1.325· 1.575 2.08
2.58 3.08 3.58
4.084.58 5.0890
.932.1.055 1.178 1.301: 1.547 2.04
2.53 3.02 3.51
4.00 I· 4.50
4.99
100
.91611.036 1.157 1.27811.519 2.00
2.48 2.97 3.45. 3.93 4.42 4.90
110
.900 1.018 1.137 1.255 1.492 1.967 '2.44 2.92
3.39
3.86 4.34 4.81
120
.884 i 1.001 1.117 1.234 1.467 1.933 2.40 2.86 3.33
3.80 4.26 -1.73
.869
.984 1.09811.213 1.442 1.900 /2.36 12.82----ri73.7~94_:65
130
140
.855
.967 1.080 1.193 1.418 1.868 2.32 : 2.77 3.22
3.6714.12
4.57
150
.841
.951 1.062 1.173 1.395 1.838 2.28
2.72 3.17
3.61
4.05
4.50
175
.807
.914 1.020.1.127 1.340 1.765 2.19 i 2.62 3.04
3.47 3.89 4.32
200
.777
.879
.982 1.084 1.289 1.698.2.11 : 2.52
2.93
3.34 3.75 4.16
225
.749
.847
.946 1.044,1.242 1.636 2.03 .2.4312.82
3.21 --;r.6i~o
250
.722
.817
.913 1.08811.198 1.579 1.959 2.34 2.72
3.10 3.48 3.86
275
.698
.790
.881
.973 1.157 1.525 1.893 2.26
2.63
3.00 3.36 3.73
300
.675
.764
.852
.941 1.119 1.475 1.830 2.19 2.54
2.90 3.25
3.61
350
.633
.716
.800
.883 1.050 1.384 1.717 2.05 : 2.38
2.72 3.05
3.39
400.- . 59 6 ' ": •. 667358
.753' .8321 .989 1.303: 1.618 1.93212.25 I 2.56 2.87 i 3.19
56
450
.712,• . 786: .934 1.232 .1.529 1.826 2.12
2.42
2.72 3.01
500
.534
.604
.675
.745
.886.1.167 1.449 1.731 2.01 12.29 2.58
2.86
550
.50831 ,575
.641
.708
.842 : 1.110 1.377 1.645: 1.912 2.18
2.45
2.72
600
.484
.547
.611
.675. .802 1 1.057 1 1.312,1.567· 1.822 2.08
2.33
2.59
'I
I·
1
I:
Air Density Table
The table at the left is calculated for the perfect gas
law shown at the top of the
page. Correction for supercompressibility, the deviation from the perfect gas
law, would be less than
three percent and has not
been applied. .
The weight density of gases
other than air can be determined from this table by
multiplying the density
listed for air by the specific
gravity of the gas relative
to air, as listed in the tables
on page A-8.
CRANE
A ·11
APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
,~,
Weight Density and Specific Volume
Of Gases and Vapors M
R
1
~
150
continued
Sy
0.35
p
,~
0.4
.015
Index
.02
iT
60
50
p
0
40
.03
0.5
15
90
.05
.06
.07
.08
(5 .09
0
lL. .l0
u
:c
0.6
80
2
0.7
::;:)
c.:>
70
VI
"0
c:
.c:
:::>
0
<:>II
'Q)
31:
~~
~
-
::;
u
-
Q)
~
I
~
VI
60
~
0.9
~
(!'
::;:)
1.0
'0
~
<5
u
Q)
Q.
V')
50
=
'0
j
rJ;
I
~
~
.::;:
.~
~
30-:~
c...
.2
c:
4
~
.3
VI
c:
Q)
-- .4
i'c
'Q)
;;::
I
Q,
.5
.6
.7
.8
1
40
2
~
50
-.:::s
10 c:
0
9 c...
8 Q)
0.
7 ...
...
6 lL.
u
5 :c:::>
T
::;:)
c.:>
c:
3
.c:
c:
160 ~
~
$ 60
--
~
Ilf ...E
....
::>
~
2
0
-Ow «
Q)
550
1
::;:)
."
40 .c:
u
=
4>
50 ro:::>
t:::r
50
49
.9
.8
.7
.6
.5
V')
~
Q)
60
1
I;::,. E....
1
QO
(!'
-- 70
80
0.
.c
40
30
E
.......
'I
...
VI
I
Q..,
150
200
3
2.0
300
60
for application of chart, ref.r to th.
• xplanation on th• preceding pog••
70
2.5
Molecular weight, specific gravity, and individual
~
78
20
2.7
tOn.,at"S for various gases ar. given on page A-8~
c:
::;:)
a:
~
~
0.
VI
"'0
0
80 c...
c:
90 ...100 ~
.4
30
...
...- 60 Q)
100 :;
0.
V')
30
C
:::>
.J:l
:::>
"0
VI
lL.
140 ...VI
<:>II
120 ...
Q)
U
20
t
200
180 ~
0.
c
1.5
~
10
4
.9
/"'
20
--
Q)
0.
0.8
--
5
.04
100
~
30
400
A-12
CRANE
APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
Properties of Saturated Steam and Saturated Water*
Absolute Pressure
Lbs. per
Inches
Sq. In.
of Hg
1
Vacuum
Inches
ofHg
Degrees F.
i
I
0.02
0.20
0.31
0.41
0.51
0.61
0.71
0.81
0.92
1.02
1.22
1.43
1.63
1.83
2.04
2.44
2.85
3.26
3.66
4.07
4.48
4.89
5.29
5.70
6.11
7.13
8.14
9.16
10.18
11.20
12.22
13.23
14.25
15.27
16.29
17.31
18.32
19.34 .
20.36
22.40
24.43
26.47
28.50
29.90
29.72
29.61
29.51
29.41
29.31
29.21
29.11
29.00
28.90
28.70
28.49
28.29
28.09
27.88
27.48
27.07
26.66
26.26
25.85
25.44
25.03
24.63
24.22
23.81
22.79
21.78
20.76
19.74
18.72
17.70
16.69
15.67
14.65
13.63
12.61
11.60
10.58
9.56
7.52
5.49
3.45
1.42
Pressure
Lbs. per Sq. In.
Absolute
Gage
pI
Heat of
the
Liquid
Latent Heat Total Heat
of
of Steam
Evaporation
t
pI
0.08859
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.60
0.70
0.80
0.90
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
11.0
12.0
13.0
14.0
Temperature
Temperature
32.()lS
35.023
45.453
53.160
59.323
64.484
68.939
72.869
76.387
79.586
85.218
90.09
94.38
98.24
101.74
107.91
113.26
117.98
122.22
126.07
129.61
132.88
135.93
138.78
141.47
147.56
152.96
157.82
162.24
166.29
170.05
173.56
176.84
179.93
182.86
185.63
i 188.27
190.80
i 193.21
197.75
i 201.96
I 205.88
209.56
Degrees F.
I
i
i
i
i
I
i
I
:
I
I
Heat of
the
Liquid
t
P
...
Steam
Cu: ft. per lb.
Cu. ft. per lb.
Btu/lb.
0.0003
3.026
13.498
21.217
27.382
32.541
36.992
40.917
44.430 .
47.623
53.245
58.10
62.39
66.24
69.73
75.90
81.23
85.95
90.18
94.03
97.57
100.84
103.88
106.73
109.42
115.51
120.92
125.77
130.20
134.26
138.03
141.54
144.83
147.93
150.87
153.65
156.30
158.84
161.26
165.82
170.05
174.00
177.71
1075.5
1073. S
1067.9
1053.5
1060.1
1057.1
1054.6
1052.4
1050.5
1048.6
1045.5
1042.7
1040.3
1038.1
1036.1
1032.6
1029.5
1026.8
1024.3
1022.1
1020.1
1018.2
1016.4
1014.7
1013.2
1009.6
1006.4
1003.5
1000.9
998.5
996.2
994.1
992.1
990.2
988.5
986.8
985.1
983.6
982.1
979.3
976.6
974.2
971.9
1075.5
1076.S
1081.4
1084.7
1087.4
1089.7
1091.6
1093.3
1094.9
1096.3
1098.7
1100.8
1102.6
1104.3
1105.8
1108.5
1110.7
1112.7
1114.5
1116.2
1117.6
1119.0
1120.3
1121.5
1122.6
1125.1
1127.3
1129.3
1131.1
1132.7
1134.2
1135.6
1136.9
1138.2
1139.3
1140.4
1141.4
1142.4
1143.3
1145.1
1146.7
1148.2
1149.6
:
Btu/lb.
Water
Btu/lb.
Latent Heat, Total Heat
of
of Steam
EVaporation
h
Btu/lb.
V
ha
Btu/lb.
I
Specific Volume
I 0.016022
i
0.016020
0.016020
0.016025
0.016032
0.016040
0.016048
0.016056
0.016063
0.016071
0.016085
0.016099
0.016112
0.016124
0.016136
0.016158
0.016178
0.016196
0.016213
0.016230
0.016245
0.016260
0.016274
0.016787
0.016300
0.016331
0.016358
0.016384
0.016407
0.016430
0.016451
0.016472
0.016491
0.016510
0.016527
0.016545
0.016561
0.016577
0.016592
0.016622
0.016650
0.016676
0.016702
I
I
I
2945.5
2004.7
1526.3
1235.5
1039.7
898.6
792.1
708.8
641.5
540.1
466.94
411.69
368.43
333.60
280.96
243.02
214.33
191.85
173.76
158.87
146.40
135.80
126.67
118.73
102.74
90.64
83.03
.73.532
67.249
61.984
57.506
53.650
50.294
47.345
44.733
42.402
40.310
38.420
35.142
32.394
30.057
28.043
Specific Volume
V
g
Water
,
Steam
Btu/lb.
Cu. ft. per lb.
I
Cu. ft. per lb.
14.696
0.0
212.00
180.17 I
970.3
1150.5
0.016719
15.0
0.3
213.03
181.21
969.7
1150.9
0.016726
16.0
1.3
216.32
184.52
1152.1
0.016749
967.6
17.0
2.3
219.44
187.66
1153.2
965.6
0.016771
18.0
3.3
222.41
190.66
963.7
1154.3
0.016793
19.0
4.3
225.24
193.52 I
961.8
1155.3
0.016814
20.0
5.3
227.96
196.27
960.1
1156.3
0.016834
21.0
6.3
230.57
198.90
958.4
1157.3
0.016854
22.0
7.3
233.07
201.44
956.7
1158.1
0.016873
23.0
8.3
235.49
203.88
955.1
0.016891
1159.0
24.0
9.3
237.82
206.24
953.6
1159.8
0.016909
i
25.0
10.3
240.07
208.52
952.1
1160.6
0.016927
26.0
11.3
242.25
210.7
950.6
1161.4
0.016944
27.0
12.3
244.36
212.9
0.016961
949.2
1162.1
28.0
13.3
i
246.41
214.9
0.016977
947.9
1162.8
29.0
14.3
248.40
217.0
946.5
1163.5
0.016993
30.0
15.3
250.34
218.9
945.2
1164.1
0.017009
31.0
16.3
252.22
220.8
943.9
0.017024
1164.8
32.0
17.3
254.05
222.7
942.7
1165.4
0.017039
33.0
18.3
255.84
224.5
941.5
1166.0
0.017054
i
34.0
19.3
257.58
226.3
940.3
1166.6
0.017069
*Abstracted from ASME Steam Tables (1967), with permission of the publisher, The American
Society of Mechanical Engineers, 345 East 47th Street. New York. New York 10017.
I
! 3302.4
i
26.799
26.290
24.750
23.385
22.168
21.074
20.087
19.190
18.373
17.624
16.936
16.301
15.7138
15.1684
14.6607
14.1869
13.7436
13.3280
12.9376
12.5700
12.2234
(continued on
tne next page)
eRA N E
A _ 13
APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND flOW CHARACTERISTICS OF VALVES, FITTI NOS, AND PIPE
-------~--------~----------------~==~~~~~~~~----~~
Properties of Saturated Steam and Saturated Water-continued
Pressure
Lbs. per Sq. In.
Absolute
Gage
P'
35.0
36,0
37.0
38.0
39.0
40.0
41.0
42.0
43.0
44.0
45.0
46.0
47.0
48.0
49.0
50.0
51.0
52.0
53.0
54.0
55.0
56.0
57.0
58.0
59.0
60.0
61.0
62.0
63.0
64.0
65.0
66.0
67.0
68.0
69.0
70.0
71.0
72.0
73.0
74.0
75.0
76.0
77.0
78.0
79.0
80.0
81.0
82.0
83.0
84.0
85.0
86.0
87.0
88.0
89.0
90.0
91.0
92.0
93.0
94.0
95.0
96.0
97.0
98.0
99.0
100.0
101.0
102.0
103.0
104.0
105.0
106.0
107.0
108.0
109.0
I
P
20,3
21.3
22.3
23.3
24.3
25.3
26.3
27.3
28.3
29.3
30.3
31.3
32.3
33.3
34.3
35.3
36.3
37.3
38.3
39.3
40.3
41.3
42.3
43.3
44.3
45.3
46.3
47.3
48.3
49.3
50.3
51.3
52.3
53.3
54.3
55.3
56.3
57.3
58.3
59.3
60.3
61.3
62.3
63.3
64.3
65.3
66.3
67.3
68.3
69.3
70.3
71.3
72.3
73.3
74.3
75.3
76.3
77.3
78.3
79.3
80.3
81.3
82.3
83.3
84,3
85.3
86.3
87.3
88.3
89.3
90.3
91.3
92.3
93.3
94.3
Temperature
I
...
I
I
t
Heat of
the
Liquid
Degrees F.
Btu/lb.
Btu/lb.
Btu/lb.
259,29
260.95
262.58
264.17
265.72
267.25
268.74
270.21
271.65
273.06
274.44
275.80
277.14
278.45
279.74
281.02
282.27
283.50
284.71
285.90
287.08
288.24
289.38
290.50
291.62
292.71
293.79
294.86
295.91
296.95
297.98
298.99
299.99
300.99
301.96
302.93
303.89
304.83
305.77
306.69
307.61
308.51
309.41
310.29
311.17
312.04
312.90
313.75
314.60
315.43
316.26
317.08
317.89
318.69
319.49
320.28
321.06
321.84
322.61
323.37
324.13
324.88
325.63
326.36
327.10
327.82
328.54
329.26
329.97
330.67
331.37
332.06
332.75
333.44
334.11
228,0
229.7
231.4
233.0
234.6
236.1
237.7
239.2
240.6
242.1
243.5
244.9
246.2
247.6
248.9
250.2
251.5
252.8
254.0
255.2
256.4
257.6
258.8
259.9
26Ll
262.2
263.3
264.4
265.5
266.6
267.6
268.7
269.7
270.7
271.7
272.7
273.7
274.7
275.7
276.6
277.6
278.5
279.4
280.3
281.3
282.1
283.0
283.9
284.8
285.7
286.5
287.4
288.2
289.0
289.9
290.7
291.5
292.3
293.1
293.9
294.7
295.5
296.3
297.0
297.8
298.5
299.3
300.0
300.8
301.5
302.2
303.0
303.7
304.4
305.1
939,1
938.0
936.9
935.8
934.7
933.6
932.6
931.5
930.5
929.5
928.6
927.6
926.6
925.7
924.8
923.9
923.0
922.1
921.2
920.4
919.5
918.7
917.8
917.0
916.2
915.4
914.6
913.8
913.0
912.3
911.5
910.8
910.0
909.3
908.5
907.8
907.1
906.4
905.7
905.0
904.3
903.6
902.9
902.3
901.6
900.9
900.3
899.6
899.0
898.3
897.7
897.0
896.4
895.8
895.2
894.6
893.9
893.3
892.7
892.1
891.5
891.0
890.4
889.8
889.2
888.6
888.1
887.5
886.9
886.4
885.8
885.2
884.7
884.1
883.6
1167,1
1167.7
1168.2
1168.8
1169.3
1169.8
1170.2
1170.7
1171.2
1171.6
1172.0
1172.5
1172.9
1173.3
1173.7
1174.1
1174.5
1174.9
1175.2
1175.6
1175.9
1176.3
1176.6
1177.0
1177.3
1177.6
1177.9
1178.2
1178.6
1178.9
1179.1
1179.4
1179,7
1180.0
1180.3
1180.6
1180.8
1181.1
1181.4
1181.6
1181.9
1182.1
1182.4
1182.6
1182.8
1183.1
1183.3
1183.5
1183.8
1184.0
1184.2
1184.4
1184.6
1184.8
1185.0
1185.3
1185.5
1185.7
1185.9
1186.0
1186.2
1186.4
1186.6
1186.8
1187.0
1187.2
1187.3
1187.5
1187.7
1187.9
1188.0
1188.2
1188.4
1188.5
1188.7
I
I
Latent Heat Total Heat
of
of Steam
Evaporation
hg
I
Specific Volume
V
~-Water
Cu. ft. per lb .
0,017083
0.017097
0.017111
0.017124
0.017138
0.017151
0.017164
0.017177
0.017189
0.017202
0.017214
0.017226
0.017238
0.017250
0.017262
0.017274
0.017285
0.017296
0.017307
0.017319
0.017329
0.017340
0.017351
0.017362
0.017372
0.017383
0.017393
0.017403
0.017413
0.017423
0.017433
0.017443
0.017453
0.017463
0.017472
0.017482
0.017491
0.017501
0.017510
0.017519
0.017529
0.017538
0.017547
0.017556
0.017565
0.017573
0.017582
0.017591
0.017600
0.017608
0.017617
0.017625
0.017634
0.017642
0.017651
0.017659
0.017667
0.017675
0.017684
0.017692
0.017700
0.017708
0.017716
0.017724
0.017732
0.017740
0.01775
0.01776
0.01776
0.01777
0.01778
O.Ol77Q
0.01779
0.01780
0.01781
Steam
Cu. ft. per lb.
1
I
11.8959
11.5860
11.2923
11.0136
10.7487
10.4965
10.2563
10.0272
9.8083
9.5991
9.3988
9.2070
9.0231
8.8465
8.6770
8.5140
8.3571
8.2061
8.0606
7.9203
7.7850
7.6543
7.5280
7.4059
7.2879
7.1736
7.0630
6.9558
6.8519
6.7511
6.6533
6.5584
6.4662
6.3767
6.2896
6.2050
6.1226
6.0425
5.9645
5.8885
5.8144
5.7423
5.6720
5.6034
5.5364
5.4711
5.4074
5.3451
5.2843
5.2249
5.1669
5.1101
5.0546
5.0004
4.9473
4.8953
4.7947
4.7459
4.6982
4.6514
4.6055
4.5606
4.5166
4.4734
4.4310
4.3487
4.3087
4.2695
ti~gi
4.1560
4.1195
4.0837
A-14
APPENDIX A
CRANE
PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
Properties of Saturated Steam and Saturated Water-continued
Pressure
Lbs. per Sq. In.
Absolute
Gage
P'
P
110.0
111.0
112.0
113.0
114.0
115.0
116.0
117.0
118.0
119.0
120.0
121.0
122.0
123.0
124.0
125.0
126.0
127.0
128.0
129.0
130.0
131.0
132.0
133.0
134.0
135.0
136.0
137.0
138.0
139.0
140.0
141.0
142.0
143.0
144.0
145.0
146.0
147.0
148.0
149.0
150.0
152.0
154.0
156.0
158.0
160.0
162.0
164.0
166.0
168.0
170.0
172.0
174.0
176.0
178.0
180.0
182.0
184.0
186.0
188.0
190.0
192.0
194.0
196.0
198.0
200.0
205.0
210.0
215.0
220.0
225.0
230.0
235.0
240.0
245.0
95.3
96.3
97.3
98.3
99.3
100.3
101.3
102.3
103.3
104.3
105.3
106.3
107.3
108.3
109.3
110.3
111.3
112.3
113.3
114.3
115.3
116.3
117.3
118.3
119.3
120.3
121.3
122.3
123.3
124.3
125.3
126.3
127.3
128.3
129.3
130.3
131.3
132.3
133.3
134.3
135.3
137.3
139.3
141.3
143.3
145.3
147.3
149.3
151.3
153.3
155.3
157.3
159.3
161.3
163.3
165.3
167.3
169.3
171.3
173.3
175.3
177.3
179.3
181.3
183.3
185.3
190.3
195.3
200.3
205.3
210.3
215.3
220.3
225.3
230.3
I
I
!
I
I
i
I
i
Temperature
t
Degrees F.
334.79
335.46
336.12
336.78
337.43
338.08
338.73
339.37
340.01
340.64
341.27
341.89
342.51
343.13
343.74
...
344.35
344.95
345.55
346.15
!
346.74
347.33
I 347.92
348.50
349.08
349.65
350.23
I
350.79
351.36
351.92
352.48
353.04
i
353.59
354.14
354.69
355.23
355.77
356.31
356.84
357.38
357.91
358.43
359.48
360.51
361.53
362.55
363.55
364.54
365.53
366.50
367.47
368.42
369.37
370.31
371.24
372.16
373.08
373.98
374.88
375.77
376.65
377.53
378.40
379.26
380.12
380.96
381.80
383.88
385.91
387.91
389.88
391.80
393.70
395.56
397.39
399.19
I
I
I
I
i
I
i
Heat of
the
Liquid
ILatentof Heat I Total
Heat
of Steam
Evaporation!
h
Btu/lb.
Btu/lb.
Btu/lb.
305.8
306.5
307.2
307.9
308.6
309.3
309.9
310.6
311.3
311.9
312.6
313.2
313.9
314.5
315.2
315.8
316.4
317.1
317.7
318.3
319.0
319.6
320.2
320.8
321.4
322.0
322.6
323.2
323.8
324.4
325.0
325.5
326.1
326.7
327.3
327.8
328.4
329.0
329.5
330.1
330.6
331.8
332.8
333.9
335.0
336.1
337.1
338.2
339.2
340.2
341.2
342.2
343.2
344.2
345.2
346.2
347.2
348.1
349.1
350.0
350.9
351.9
352.8
353.7
354.6
355.5
357.7
359.9
362.1
364.2
366.2
368.3
370.3
372.3
374.2
I
\
I
883.1
882.5
882.0
881.4
880.9
880.4
879.9
879.3
878.8
878.3
877.8
877.3
876.8
876.3
875.8
875.3
874.8
874.3
873.8
873.3
872.8
872.3
871.8
871.3
870.8
870.4
869.9
869.4
868.9
868.5
868.0
867.5
867.1
866.6
866.2
865.7
865.2
864.8
864.3
863.9
863.4
862.5
861.6
860.8
859.9
859.0
858.2
857.3
856.5
855.6
854.8
853.9
853.1
852.3
851.5
850.7
849.9
849.1
848.3
847.5
846.7
845.9
845.1
844.4
843.6
842.8
840.9
839.1
837.2
835.4
833.6
831.8
830.1
828.4
826.6
I
I
i
I
I
I
Specific Volume
V
g
1188.9
1189.0
1189.2
1189.3
1189.5
1189.6
1189.8
1189.9
1190.1
1190.2
1190.4
1190.5
1190.7
1190.8
1190.9
1191.1
1191.2
1191.3
1191.5
1191.6
1191.7
1191.9
1192.0
1192.1
1192.2
1192.4
1192.5
1192.6
1192.7
1192.8
1193.0
1193.1
1193.2
1193.3
1193.4
1193.5
1193.6
1193.8
1193.9
1194.0
1194.1
1194.3
1194.5
1194.7
1194.9
1195.1
1195.3
1195.5
1195.7
1195.8
1196.0
1196.2
1196.4
1196.5
1196.7
1196.9
1197.0
1197.2
1197.3
1197.5
1197.6
1197.8
1197.9
1198.1
1198.2
1198.3
1198.7
1199.0
1199,3
1199.6
1199.9
1200.1
1200.4
1200.6
1200.9
Water
Steam
... Cu. ft. per lb.
i
I
i
I
I
i
I
0.01782
0.01782
0.01783
0.01784
0.01785
0.01785
0.01786
0.01787
0.01787
0.01788
0.01789
0.01790
0.01790
0.01791
0.01792
0.01792
0.01793
0.01794
0.01794
0.01795
0.01796
0.01797
0.01797
0.01798
0.01799
0.01799
0.01800
0.01801
0.01801
0.01802
0.01803
0.01803
0.01804
0.01805
0.01805
0.01806
0.01806
0.01807
0.01808
0.01808
0.01809
0.01810
0.01812
0.01813
0.01814
0.01815
0.01817
0.01818
0.01819
0.01820
0.01821
0.01823
0.01824
0.01825
0.01826
0.01827
0.01828
0.01830
0.01831
0.01832
0.01833
0.01834
0.01835
0.01836
0.01838
0.01839
0.01841
0.01844
0.01847
0.01850
0.01852
0.01855
0.01857
0.01860
0.01863
Cu. ft. per lb.
I
I
4.0484
4.0138
3.9798
3.9464
3.9136
3.8813
3.8495
3.8183
3.7875
3.7573
3.7275
3.6983
3.6695
3.6411
3.6132
3.5857
3.5586
3.5320
3.5057
3.4799
3.4544
3.4293
3.4046
3.3802
3.3562
3.3325
3.3091
3.2861
3.2634
3.2411
3.2190
3.1972
3.1757
3.1546
3.1337
3.1130
3.0927
3.0726
3.0528
3.0332
3.0139
2.9760
2.9391
2.9031
2.8679
2.8336
2.8001
2.7674
2.7355
2.7043
2.6738
2.6440
2.6149
2.5864
2.5585
2.5312
2.5045
2.4783
2.4527
2.4276
2.4030
2.3790
2.3554
2.3322
2.3095
2.28728
2.23349
2.18217
2.13315
2.08629
2.04143
1.99846
1.95725
1.91769
1.87970
CRANE
APPENDIX A - PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
A·15
Properties of Saturated Steam and Saturated Water-concluded
Pressure
Lbs. per Sq. In.
Temperature
I
Heat of
the
Liquid
Latent Heat Total Heat
of
of Steazn
Evaporation •
h
Specific Volume
V
g
250.0
255.0
260.0
265.0
270.0
-235.3
240.3
245.3
250.3
255.3
400.97
402.72
404.44
406.13
407.80
376.1
378.0
379.9
381.7
383.6
825.0
1201.1
0.01865
1.84317
823.3
1201.3
0.01868
1.80802
821.6
1201.5
0.01870
1.77418
820.0
1201.7
0.01873
1.74157
818.3
1201.9
0.01875
1.71013
-----:2;;:7;;:;5-';;.o:---l--~26~0~.3~-L-409:45 ~-~385X
816.7
1202.1
0.01878
1.67978
280.0
265.3
411.07
387.1
815.1
1202.3
0.01880
1.65049
412.67
388.9
813.6
1202.4
0.01882
1.62218
285.0
270.3
290.0
275.3
414.25
390.6
812.0
1202.6
0.01885
1.59482
295.0
280.3
415.81
392.3
810.4
1202.7
0.01887
1.56835
300.0
285.3
417.35
394.080S.9 .... r--u02.9 --+---;;0~.0~1-:<:88;c;9:---+---:-1'-;;.5-:-42~7i:4-320.0
305.3
423.31
400.5
802.9
1203.4
0.01899
1.44801
340.0
325.3
428.99
406.8
797.0
1203.S
0.01908
1.36405
345.3
434.41
412.8
791.3
1204.1
0.01917
1.28910
360.0
365.3
439.61
418.6
785.8
1204.4
0.01925
1.22177
380.0
400.0
385.3
444.60
424.2
780.4
1204.6
0.01934
1.16095
420.0
405.3
449.40
429.6
775.2
1204.7
0.01942
1.10573
440.0
425.3
454.03
434.8
770.0
1204.8
0.01950
1.05535
460.0
445.3
458.50
439~8
765.0
1204.8
0.01959
1.00921
480.0
465.3
462.82
444.7
760.0
1204.8
0.01967
0.96677
500.0
I
485.3
467.01
449.5
755.1!
1204.7
0.01975
0.92762
520.0
505.3
471.07
454.2
750.4.
1204.5
0.01982
0.89137
540.0
525.3
475.01
458.7
745.7
1~2i.oo.4j.:4~
0.01990
0.85771
560.0
545.3
478.84
463.1
741.0
0.01998
0.82637
565.3
482.57
467.5
736.5
0.02006
0.79712
580.0
--;6;";;0i.0:";;.0-+-~58~5":';.3<-+-;4;;::8;':6.~2;;"0-+--7.47;;1-':;.7;'-'-+-~73f.O
! 120~3;-;.7;---f--;;0-;.0"'2""01;-:;3:----r--AO".77:69;;;;;7;;:;5-620.0
605.3
489.74
475.8
727.5
I!
1203.4
0.02021
0.74408
625.3
493.19
479.9
723.1
1203.0
0.02028
0.71995
640.0
660.0
645.3
496.57
483.9
718.8
1202.7
0.02036
0.69724
665.3
499.86
487.8
714.5
1202.3
0.02043
0.67581
680.0
700.0
685.3
503.08
491.6
710.2
1201.8
0.02050
0.65556
720.0
705.3
506.23
495.4
706.0
1201.4
0.02058
0.63639
725.3
509.32
4-99.1
701.9
1200.9
0.02065
0.61822
740.0
745.3
512.34
502.7
697.7
1200.4
0.Q2072
0.60097
760.0
780.0
765.3
515.30
506.3
693.6
1199.9
0.02080
0.58457
-----:8~0~0~.0~~-~78~5~.3~+~5~178'-;;.2-:-1-4--~50~9~.8~-+-~6~8~9~.6~-~--:-11~9~9~.4.--+~6.~0~20~8~7-~1·.--;0~.~56;..;;8~96~--820.0
805.3
521.06
513.3
685.5
1198.8
0.02094
I'!
0.55408
825.3
523.86
516.7
681.5
1198.2
0.02101
0.53988
840.0
860.0
845.3
526.60
520.1
677 6 ~
1197.7
0.02109
0.52631
_----:8;:-:;8~0_;;.0:--~_~86;o.;5,.:,.3~---r---;5.-:;279-;;.3.;.0--+---;;-52""'3,.-,.4;;---+----;~67~~3::6~ _
1197.0
0.02116
00 . 5501039331
900.0
885.3
531.95
526.7
1196.4
0.02123
920.0
905.3
534.56
530.0
1195.7
0.02130
0.48901
925.3
537.13
533.2
661.9'
1195.1
0.02137
0.47759
940.0
960.0
945.3
539.65
536.3
658.0
1194.4
0.02145
0.46662
980.0
965.3
542.14
539.5
654.2
1193.7
0.02152
0.45609
1000.0
985.3
544.58
542.6
650.4
1192.9
0.02159
0.44596
1050.0
1035.3
550.53
550.1
640.9
1191.0
0.02177
0.42224
1100.0
1085.3
556.28
557.5
631.5
1189.1
0.02195
0.40058
1150.0
1135.3
561.82
564.8
622.2
1187.0.
0.02214
0.38073
1200.0
1185.3
567.19
571.9
613.0
1184.8
0.02232
0.36245
-~1:-;2:.;5.;;.;0.~0-+-----:-12:=.;3:.;5,:.:;.3~+--;;5,;72:::-=..;.38~-+--5;;7.-:;8~.8,----+--·~663:8;....---1-....:1:.:1·.::.,82;.:..6:::.--!i, ~0;::.0:-;2~2;.:50~-+--...,,0"-::.3;-;4""55~6-1300.0
1285.3
577.42
585.6
594.6
1180.2
0.02269
0.32991
1350.0
1335.3
582.32
592.2
585.6
1177.8
0.02288
0.31536
1385.3
587.07
598.8
567.5
1175.3
0.02307
0.30178
1400.0
1450.0
1435.3
591.70
605.3
567.6
1172.9
0.02327
0.28909
-~15~0~0-';;.0:--~--'1~48~5":'.3~-r--;5'-:;976~.2~0-~-76~11;-;.7;;---+-'5~5~8A.4'--+--'11~7~0~.I--+-~0.~02~3~476-~'--'0~.2~7~7~19~--1600.0
1585.3
604.87
624.2
540.3
1164.5
0.02387
0.25545
1700.0
1685.3
613.13
636.5
522.2
1158.6
0.02428
0.23607
1800.0
1785.3
621.02
648.5
503.8
1152.3
0.02472
0.21861
1885.3
628.56
660.4
485.2
1145.6
0.02517
0.20278
1900.0
-~20~0~0~.0:---+--:'1-:<:98~5~.3~+~6;':';;-35.~£I0--l--.o-,67ii2;-.1;--+--4"676--;;.2:---+-.;.113=8-,.3:---+-0:;;··.··0·2565
0.18831
642.76
683.8
446.7
1130.5
0.02615
0.17501
2100.0
2085.3
2185.3
649.45
695.5
426.7
1122.2
0.02669
0.16272
2200.0
2285.3
655.89
707.2
406.0
1113.2
0.02727
0.15133
2300.0
2385.3
662.11
719.0
384.8
1103.7
0.02790
0.14076
2400.0
2485.3
668.11
731.7
361.6
1093.3
0.02859
0.13068
2500.0
2600.0
2585.3
673.91
744.5
337.6
1082.0
0.02938
0.12110
2685.3
679.53
757.3
312.3
1069.7
0.03029
0.11194
2700.0
2800.0
2785.3
684.96
770.7
285.1
1055.8
0.03134
0.10305
2885.3
690.22
785.1
254.7
1039.8
0.03262
0.09420
2900.0
--~30~0~0-;.0;---r---;;2~98~5~.3~-+----:6~9~5'.3~3--,---~80Ml~.g~-+--~2«1~8A.4,--+--.1~02~0~.3~~--~0~.0~3~42~8:----}---~0.~0~85~0~0---3100.0
3085.3
700.28
814.0
169.3
993.3
0.03681
0.07452
3185.3
705.08
875.5
56.1
931.6
0.04472
0.05663
3200.0
3193.5
705.47
906.0
0.0
906.0
0.05078
0.05078
3208.2
,I
I
l'.
I
1
I
1
I,
APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
CRANE
Properties of Superheated Steam *
V
Pressure
Lbs. per
specific volume, cubic feet per pound
total heat of steam, Btu per pound
Sat.
TelTIp
Total TelTIperature-Degrees Fahrenheit (t)
Sq. In.
Abs.
pI
Gage
P
3500
t
15.0
0.3
213.03
20.0
5.3
227.96
30.0
15.3
250.34
40.0
25.3
267.25
50.0
35.3
281.02
60.0
45.3
292.71
70.0
55.3
302.93
80.0
65.3
312.04
90.0
75.3
320.28
100.0
85.3
327.82
120.0
105.3
341.27
-V
hg
V
hg
400 0
500
0
31.939 33.963 37.985
1216.2 1239.9 1287.3
6000
7000
8000
900
0
1000°
37.458 40.447 43.435
1432.9 1483.2 1534.3
28.457 31.466 34.465
1286.9 1334.9 1383.5
15.859
1213.6
16.892
1237.8
18.929 20.945
1286.0 1334.2
11.838
1211.7
12.624
1236.4
14.165
1285.0
15.685
1333.6
17.195
1382.5
18.699 20.199 21.697
1432.1 1482.5 1533.7
9.424
1209.9
10.062
1234.9
11.306
1284.1
12.529
1332.9
13.741
1382.0
14.947
1431.7
16.150
1482.2
7.815
1208.0
8.354
1233.5
9.400
1283.2
10.425
1332.3
11.438
1381.5
12.446
1431.3
6.664
1206.0
7.133
1232.0
8.039
1282.2
8.922
1331.6
9.793
1381.0
5.801
1204.0
6.218
1230.5
7.018
1281.3
7.794
1330.9
5.128
1202.0
5.505
1228.9
6.223
1280.3
hg
V
4.590
1199.9
4.935
1227.4
5.588
1279.3
V
V
hg
-
V
hg
-
V
hg
V
hg
-
V
hg
-
V
hg
22.951 24.952 26.949
1383.0 1432.5 1482.8
46.420
1586.3
52.388
1693.1
V
hg
140.0
125.3 353.04
26.183
1692.7
29.168
1803.0
17.350
1533.4
18.549 20.942
1585.6 1692.5
23.332
1802.9
13.450
1481.8
14.452
1533.2
15.452
1585.3
17.448
1692.4
19.441
1802.8
10.659
1430.9
11.522
1481.5
12.382
1532.9
13.240
1585.1
14.952
1692.2
16.661
1802.6
8.560
1380.5
9.319
1430.5
10.075
1481.1
10.829
1532.6
11.581
1584.9
13.081
1692.0
14.577
1802.5
6.917
1330.2
7.600
1380.0
8.277
1430.1
8.950
1480.8
9.621
1532.3
10.290
1584.6
11.625
1691.8
12.956
1802.4
6.216
1329.6
6.833
1379.5
7.443
1429.7
8.050
1480.4
8.655
1532.0
9.258
1584.4
10.460
1691.6
11.659
1802.2
3.7815 4.0786
1195.6 1224.1
4.6341 5.1637
1277.4 1328.2
5.6813
1378.4
6.1928
1428.8
6.7006
1479.8
7.2060
1531.4
7.7096
1583.9
8.7130
1691.3
9.7130
1802.0
3.4661
1220.8
3.9526 4.4119
1275.3 1326.8
4.8588 5.2995
1377.4 1428.0
-
V
hg
160.0
145.3 363.55
V
hq
180.0
200.0
165.3
373.08
185.3 381.80
23.194
1585.8
220.0
205.3
389.88
225.3 397.39
245.3
404.44
..
...
2.6474 3.0433 3.4093 3.7621
1213.8 1271.2 1324.0 1375.3
-
...
...
2.3598
1210.1
2.7247 3.0583 3.3783 3.6915 4.0008 4.3077
1269.0 1322.6 1374.3 1425.5 1477.0 1529.1
...
2.1240
1206.3
2.4638
1266.9
1.9268
1202.4
2.2462 2.5316
1264.6 1319.7
2.8024
1372.1
3.0661 3.3259 3.5831 3.8385
1423.8 1475.6 1527.9 1580.9
.,
2.0619 2.3289
1262.4 1318.2
2.5808
1371.1
2.8256
1423.0
.
1.9037 2.1551
1260.0 1316.8
2.3909 2.6194 2.8437 3.0655
1370.0 1422.1 1474.2 1526.8
V
-
V
...
-
V
-
V
hg
280.0
265.3
411.07
5.7741 6.5293
1582.9 1690.5
V
hg
260.0
4.2420 4.6295 5.0132 5.3945
1376.4 1427.2 1478.4 1530.3
6.6036 7.4652 8.3233
1583.4 1690.9 1801.7
hg
hg
240.0
3.0060 3.4413 3.8480
1217.4 1273.3 1325.4
..
5.7364 6.1709
1479.1 1530.8
-
hu
,
.
-
V
hg
V
58.352
1803.3
34.918 38896
1692.9 1803.2
28.943 30.936
1534.0 1586.1
-
hg
1500°
41.986 45.978 49.964 53.946 57.926 61.905 69.858 77.807
1335.2 1383.8 1433.2 1483.4 1534.5 1586.5 1693.2 1803.4
23.900 25.428
1215.4 1239.2
-
1300°
11000
,
4.1084
1426.3
7.2811
1801.4
4.4508 4.7907 5.1289 5.8014 6.4704
1477.7 1529.7 1582.4 1690.2 1801.2
2.7710 3.0642 3.3504 3.6327 3.9125
1321.2 1373.2 1424.7 1476.3 1528.5
4.6128 5.2191
1581.9 1689.8
5.8219
1800.9
4.7426 5.2913
1689.4 1800.6
4.1905
1581.4
4.3456
1689.1
4.8492
1800.4
4.0097 4.4750
1688.7 1800.1
3.0663 3.3044 3.5408
1474.9 1527.3 1580.4
3.2855 3.7217 4.1543
1579.9 1688.4 1799.8
2.4407 2.6509 2.8585 3.0643 3.4721 3.8764
1421.3 1473.6 1526.2 1579.4 1688.0 1799.6
1.7665
1257.7
2.0044 2.2263
1315.2 1368.9
..
1.6462
1255.2
1.8725
1313.7
2.0823
1367.8
2.2843
1420.5
2.4821 2.6774
1472.9 1525.6
2.8708 3.2538 3.6332
1578.9 1687.6 1799.3
.,
1.5399
1252.8
1.7561
1312.2
1.9552
1366.7
2.1463
1419.6
2.3333
1472.2
2.5175
1525.0
2.7000 3.0611 3.4186
1578.4 1687.3 1799.0
1.4454
1250.3
1.6525 i 1.8421
1310.6 1365.6
2.0237
1418.7
2.2009
1471.5
2.3755 2.548212.8898 3.2279
1542.4. 1577.9 1686.9 1798.8
*Abstracted from ASME Steam Tables (1967) with permission of the publisher, the
American Society of Mechanical Engineers, 345 East 47th St reet. New York, N. Y. 10017.
(eontinued on
the next page)
300.0
285.3
417.35
hg
320.0
305.3
423.31
V
hg
340.0
325.3
428.99
V
hq
360.0 I 345.3 434.41 I ~ i
...
i
i
CRANE
APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS Of VALVES, fiTTINGS, AND PIPE
Properties of Superheated Steam -
A-17
continued
\/ = specifk volume, cubic feet per pound
hq = total heat of steam, Btu per pound
Pressure
Lbs. per
Sq. In.
Abs.
pI
380.0
Sat.
Temp.
Total Temperature-Degrees Fahrenheit (t)
Gage
P
t
365.3
439.61
V
hq
400.0
385.3 444.60
V
hg
420.0
405.3
449.40
V
425.3
454.03
445.3
458.50
465.3 462.82
485.3
467.01
505.3
471.07
560.0
525.3
475.01
545.3 478.84
565.3
482.57
585.3 486.20
635.3
494.89
750.0
685.3 503.08
735.3
510.84
1.6499
1363.4
1.8151
1417.0
785.3
518.21
835.3
525.24
885.3
531.95
2.0790
1575.9
2.2203
1630.4
2.3605
1685.5
2.4998
1741.2
2.6384
1797,7
V
1.0939
1236.9
1.2691
1302.5
1.4242
1360.0
1.5703 1.7117 1.8504 1.9872
1414.4 1468.0 1521.5 1575.4
2.1226
1629.9
2.2569
1685.1
2.3903
1740.9
2.5230
1797.4
1.0409
1234.1
1.2115
1300.8
1.3615
1358.8
1.5023
1413.6
1.6384
1467.3
1.7716 1.9030 2.0330 2.1619
1520.9 1574.9 1629.5 1684.7
2.2900
1740.6
2.4173
1797.2
0.9919
1231.2
1.1584 1.3037
1299.1 1357.7
1.4397
1412.7
1.5708 1.6992
1466.6 1520.3
2.3200
1796.9
0.9466
1228.3
1.1094
1297.4
1.3819
1411.8
1.5085
1465.9
-
V
V
V
935.3
538.39
985.3
544.58
1035.3
550.53
1085.3
556.28
1135.3 561.82
2.0746
1684.4
2.1977
1740.3
1.6323 1.7542 1.8746
1519.7 1573.9 1628.7
1.9940
1684.0
2.1125 2.2302
1740.0 1796.7
1355.3
1410.9
1465.1
1519.1
1573.4
1628.2
1683.6
1739.7
1796.4
V-
0.8653
1222.2
1.0217
1293.9
1.1552
1354.2
1.2787
1410.0
1.3972
1464.4
1.5129
1518.6
1.6266
1572.9
1.7388
1627.8
1.8500
1683.3
1.9603
1739.4
2.0699
1796.1
V
0.8287
1219.1
0.9824
1292.1
1.1125
1353.0
1.2324 1.3473
1409.2 1463.7
1.4593
1518.0
1.5693
1572.4
1.6780
1627.4
1.7855
1682.9
1.8921
1739.1
1.9980
1795.9
0.7944
1215.9
0.9456
1290.3
1.0726
1351.8
1.1892
1408.3
1.4093
1517.4
1.5160
1571.9
1.6211
1627.0
1.7252
1682.6
1.8284
1738.8
1.9309
1795.6
-
V
1.3008
1463.0
V 0.7173 0.8634 0.9835 I 1.0929 1.1969 1.2979 1.3969 1.4944 1.5909 1.6864 1.7813
1207.6
V
hg
...
V
·.
V-
V
...
·.
V
V
·
.
V
V-
..
VV-
I hu I
1285.7
1348.7 . 1406.0
1461.2
1515.9
1570.7
1625.9
1681.6
1738.0 1794.9
0.7928 0.9072
1281.0 1345.6
1.0102
1403.7
1.1078
1459.4
1.2023 1.2948
1514.4 1569.4
1.3858
1624.8
1.4757
1680.7
1.5647
1737.2
1.6530
1794.3
0.7313
1276.1
0.8409
1342.5
0.9386
1401.5
1.0306
1457.6
1.1195 1.2063
1512.9 1568.2
1.2916
1623.8
1.3759
1679.8
1.4592
1736.4
1.5419
1793.6
0.6774
1271.1
0.7828
1339.3
0.8759
1399.1
0.9631
1455.8
1.0470
1511.4
1.1289
1566.9
1.2093
1622.7
1.2885
1678.9
1.3669
1735.7
1.4446
1792.9
0.6296
1265.9
0.7315
1336.0
0.8205
1396.8
0.9034 0.9830
1454.0 1510.0
1.0606
1565.7
1.1366
1621.6
1.2115
1678.0
1.2855
1734.9
1.3588
1792.3
0.5869
1260.6
0.6858
1332.7
0.7713 0.8504
1394.4 1452.2
0.9998
1564.4
1.0720
1620.6
1.1430 1.2131
1677.1 1734.1
1.2825
1791.6
0.5485
1255.1
0.6449
1329.3
0.7272 0.8030 0.8753 0.9455
1392.0 1450.3 1507.0 1563.2
0.9262
1508.5
1.1484
1733.3
1.2143
1791.0
1,0266
1675.3
1.0901
1732.5
1.1529
1790.3
0.4821 0.5745 0.6515 0.7216 0.7881
1243.4 1322.4 1387.2 1446.6 1503.9
0.8524 0.9151 0.9767
1560.7 1617.4 1674.4
1.0373
1731.8
1.0973
1789.6
0.4531
1237.3
0.8121 0.8723 0.9313 0.9894
1559.4 1616.3 1673.5 1731.0
1.0468
1789.0
0.4263 0.5162 i 0.5889 0.6544 0.7161 0.7754 0.8332l 0.8899 0.9456
1230.9 1315.211382.2 1442.8 1500.9 1558.1 1615.2 1672.6 1730.2
1.0007
1788.3
1.0142 1.0817
1619.5 1676.2
0.5137 0.6080 0.6875 0.7603 0.8295 0.8966 0.9622
1249.3 1325.9 1389.6 1448.5 1505.4 1561.9 1618.4
hq
1150.0
1.9507
1629.1
1295.7
hu
1100.0
1.8256
1574.4
1225.3
hQ
1050.0
1.9363
1522.1
V 0.9045 1.0640 1.2010 1.3284 1.4508 1.5704 1.6880 1.8042 1.9193 2.0336 2.1471
hQ
1000.0
1.2504
1356.5
1.7918
1468.7
hQ
hq
950.0
i
1.6445
1415.3
hq
900.0
2.7515 2.9037
1741.9 1798.2
1.4926
1361.1
hq
850.0
2.2901 2.4450 2.5987
1576.9 1631.2 i 1686.2
1.3319
1304.2
hQ
800.0
1.9759 2.1339
1470.1 1523.3
i
1.1517
1239.7
hq
700.0
1.4763
1307.4
2.8973 3.0572
1742.2 1798.5
V
hg
650.0
1.2841
1245.1
2.7366
1686.5
2.5750
1631.6
2.6196 i 2.7647
1741.6 1798.0
hu
600.0
2.4124
1577.4
1500°
2.4739
1685.8
hg
580.0
1.7410 1.9139 I 2.0825 i 2.2484
1364.5 1417.9 1470.8 1523.8
1400°
2.3273
1630.8
hQ
540.0
1.5598
1309.0
1 1
13000
0
1200
2.1795
1576.4
hu
520.0
1.3606
1247.7
9000
1.7258 i 1.8795 2.0304
1416.2 1469.4 1522.7
hQ
500.0
11000
0
1.5676
1362.3
hQ
480.0
10000
I 800
1.4007
1305.8
hg
460.0
700
1.2148
1242.4
hg
440.0
0
5000 I 600 0
...
"
.
0.5440
1318.8
0.6188
1384.7
0.6865
1444.7
0.7505
1502.4
A.
APPENDIX A - PHYSICAL PROPERTIES OF flUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
Properties of Superheated Steam V
Abs.
Gage
p'
P
Sat.
Temp.
6500
567.19
1300.0
577.42
1285.3
Total Temperature-Degrees Fahrenheit (t)
t
1200.0 1185.3
1385.3
V
no
587.07
1500.0
1485.3
596.20
1600.0
1585.3
604.87
1700.0
1685.3
b13.13
1800.0
1785.3
621.02
1900.0
1885.3
628.56
2000.0
1985.3
635.80
2100.0
2085.3
642.76
2200.0
2185.3
649.45
2300.0
2285.3
655.89
2400.0
2385.3
662.11
2500.0
2485.3
668.11
2600.0
2585.3
673.91
2700.0
2685.3
679.5~~
2800.0
2785.3
684.96
2900.0
2885.3
690.22
3000.0
2985.3
695.33
3100.0 3085.3 700.28
3200.0 3185.3 705.08
-
v
3400.0
3385.3
..
.. .
0
I 750
0
800 0
9000
10000
1l00°
12000
1
0.5615 0.6250 0.6845 0.7418
1379.7 1440.9 1499.4 1556.9
0.4497
1271.8
0.4905
1311.5
0.5273
1346.9
0.4052
1261.9
0.4451
1303.9
0.4804 0.5129
1340.8 1374.6
0.5729
1437.1
0.6287
1496.3
0.6822
1554.3
0.7974 0.8519
1614.2 1671.6
0.9055
1729.4
0.9584
1787.6
0.7341
1612.0
0.8345
1727.9
0.8836
1786.3
0.7847
1669.8
V 0.3667 0.4059 0.4400 0.4712 0.5282 0.5809 0.6311 0.6798 0.7272 0.7737 0.8195
no
1251.4
1296.1
1334.5
1369.3
1433.2
1493.2
1551.8
V
0.3328
1240.2
0.3717
1287.9
0.4049
1328.0
0.4350
1364.0
0.4894
1429.2
0.5394
1490.1
0.5869 0.6327 0.6773
1549.2 1607.7 1666.2
0.7210 0.7639
1724.8 1783.7
V
0.3026
1228.3
0.3415 0.3741 0.4032 0.4555 0.5031
1279.4 1321.4 1358.5 1425.2 1486.9
0.5482 0.5915 0.6336
1546.6 1605.6 1664.3
0.6748 0.7153
1723.2 1782.3
V
0.2754
1215.3
0.3147
1270.5
0.3468
1314.5
0.3751
1352.9
0.4255
1421.2
0.47ll
1483.8
0.5140
1544.0
0.5552
1603.4
0.5951
1662.5
0.6341
1721.7
0.6724
1781.0
V
0.2505
1201.2
0.2906
1261.1
0.3223
1307.4
0.3500
1347.2
0.3988
1417.1
0.4426
1480.6
0.4836 0.5229
1541.4 1601.2
0.5609
1660.7
0.5980
1720.1
0.6343
1779.7
V
0.2274
1185.7
0.2687
1251.3
0.3004 0.3275 0.3749
1300.2 1341.4 1412.9
0.4171
1477.4
0.4565
1538.8
0.4940
1599.1
0.5303
1658.8
0.5656
1718.6
0.6002
1778.4
0.2056
1168.3
0.2488
1240.9
0.2805
1292.6
0.3072 0.3534 0.3942
1335.4 1408.7 1474.1
0.4320
1536.2
0.4680 0.5027 0.5365 0.5695
1596.9 1657.0 1717.0 1777.1
no
-
no
no
no
no
-
V
no
1609.9
1668.0
1726.3
1785.0
V 0.1847 0.2304 0.2624 0.2888 0.3339 0.3734 0.4099 0.4445 0.4778 0.5101 0.5418
no
1148.5
1229.8
1284.9
1329.3
1404.4
V
0.1636
1123.9
0.2134
1218.0
0.2458
1276.8
0.2720
1323.1
0.3161 0.3545 0.3897
1400.0 1467.6 1530.9
ng
.,
0.1975
1205.3
0.2305
1268.4
0.2566
1316.7
0.2999
1395.7
V
,
..
"
,
0.1824
1191.6
0.2164
1259.7
0.2424
1310.1
0.2850 0.3214
1391.2 1460.9
'
..
no
-
V
no
V
1470.9
1533.6
0.3372 I 0.3714
1464.2 1528.3
0.3545
1525.6
1594.7
1655.2
1715.4
1775.7
0.4231 0.4551
1592.5 1653.3
0.4862
1713.9
0.5165
1774.4
0.4035
1590.3
0.4344
1651.5
0.4643
1712.3
0.4935
1773.1
0.3856
1588.1
0.4155
1649.6
0.4443
1710.8
0.4724
1771.8
0.1681 0.2032
1176.7 1250.6
0.2293 0.2712 0.3068 0.3390 0.3692 0.3980 0.4259 0.4529
1303.4 1386.7 1457.5 1522.9 1585.9 1647.8 1709.2 1770.4
'\7
0.1544
1160.2
0.2171
1296.5
V
0.1411 0.1794
1142.0 1231.1
0.2058 0.2468 0.2809 0.3114
1289.5 1377.5 1450.7 1517.5
0.3399
1581.5
0.3670 0.3931 0.4184
1644.1 1 1706.1 I 1767.8
...
...
0.1278 0.1685
1121.2 1220.6
0.1952
1282.2
0.2358
1372.8
0.2693
1447.2
0.2991
1514.8
0.3268
1579.3
0.3532
1642.2
0.3785
1704.5
0.4030
17b6.5
...
0.1138
1095.3
0.1581 1 0.1853
1209.6 1274.7
0.2256
1368.0
0.2585
1443.7
0.2877
1512.1
0.3147
1577.0
0.3403
1640.4
0.3649
1703.0
0.3887
1765.2
0.0982
1060.5
0.1483
1197.9
0.1759
1267.0
0.2161
1363.2
0.2484
1440.2
0.2770
1509.4
0.3033
1574.8
0.3282
1638.5
0.3522
1701.4
0.3753
1763.8
..
., .
0.1389
1185.4
0.1671
1259.1
0.2071
1358.4
0.2390
1436.7
0.2670
1506.6
0.2927
1572.6
0.3170
1636.7
0.3403
1699.8
0.3628
1762.5
..
...
. ..
. ..
0.1300
1172.3
0.1588
1250.9
0.1987
1353.4
0.2301
1433.1
0.2576
1503.8
0.2827
1570.3
0.3065
1634.8
0.3291
1698.3
0.3510
1761.2
no
.. .
.
. ..
0.1213
1158.2
0.1510
1242.5
0.1908 0.2218
1348.4 1429.5
0.2488
1501.0
0.2734
1568.1
0.2966
1623.9
0.3187 0.3400
1696.7 1759.9
V
...
. ..
.. ,
0.1129 0.1435
1143.2 1233.7
0.1834 0.2140
1343.4 1425.9
0.2405
1498.3
0.2646 0.2872
1565.8 1631.1
0.30881 0.3296
1695.1 1758.5
no
no
no
~;
no
V
no
,. ,
V
...
V
...
no
no
-
V
no
.
3300.0 3285.3
700
I
no
1400.0
concluded
specific volume, cubic feet per pound
total heat of steam, Btu per pound
ho
Pressure
Lbs. per
Sq, In.
CRANE
v
...
,
,
0.1909
1241.1
0.2585
1382.1
0.2933
1454.1
0.3247
1520.2
0.3540 0.3819
1583.7 1646.0
0.4088 0.4350
1707.7 1769.1
~
no
,
...
CRANE
A-19
APPENDIX A- PHYSICAL PROPERTIES OF flUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
Properties of Superheated Steam and Compressed Water*
v = specific volume, cubic feet per pound
ho = total heat of steam, Btu per pound
Absolute
Pressure
Total Temperature-Degrees Fahrenheit (t)
Lbs. per
Sq. In.
3500
2000
-V
ho
3600
V
hq
3800
-
V
ho
4000
4200
4400
4600
4800
5200
5600
6000
6500
7000
7500
8000
9000
10000
11000
12000
13000
15500
178.1
178.5
179.0
179.9
180.8
181.7
182.9
V 0.0163
h9 i 184.0
-
V 0.0163
185.2
0.0182
379.8
0.0223
606.9
0.17641 0.2066
1338.2 1422.2
0.1463
1311.6
0.1996 0.2252 0.2485 0.2702
1418.6 1492.6 1561.3 1627.3
0.2470 0.2645
1682.6 1748.0
0.0182 0.0197 0.0222 0.0282
380.1
758.6
487.8
606.4
0.0945
1151.6
0.1362 0.1647 0.1883
1300.4 1396.0 1475.5
0.2093 0.2287
1547.6 1616.1
0.0182 0.0197 0.0222
380.4 487.9 605.9
0.0278
754.8
0.0846
1127.3
0.1270 0.1552 0.1782
1289.0 1388.3 1469.7
0.1986 0.2174 0.2351 0.2519
1543.0 1612.3 1679.4 1745.3
0.0182
380.7
0.0197 0.0221
487.9 605.5
0.0274 0.0751
751.5 1100.0
0.1186
1277.2
0.0182 0.0196 0.0220
380.9 488.0 605.0
0.0271 0.0665
748.6 1071.2
0.2071
1608.5
0.2242 0.2404
1676.3 1742.7
0.1109 0.1385 0.1606
1265.2 1372.6 1458.0
0.1800 0.1977
1533.8 1604.7
0.2142 0.2299
1673.1 1740.0
0.1244 0.1458
1356.6 1446.2
0.1642 0.1810
1524.5 1597.2
0.1966 0.2114
1666.8 1734.7
0.1465 0.1691
1380.5 1463.9
0.0181
381.5
0.0196 0.0219 0.0265
488.2
604.3
743.7
0.0181
382.1
0.0195 0.0217 0.0260 0.0447 0.0856 0.1124
488.4 603.6
739.6 975.0 1214.8 1340.2
0.0180 0.0195
382.7 488.6
0.0216 0.0256
602.9
736.1
0.0531
1016.9
0.0973
1240.4
0.0397 0.0757
945.1 1188.8
0.1020
1323.6
0.1508 0.1667 0.1815
1515.2 1589.6 1660.5
0.1221
1422.3
0.1391 0.1544 0.1684 0.1817
1505.9 1582.0 1654.2 1724.2
0.0252
732.4
0.0358
919.5
0.0655 0.0909 0.1104
1156.3 1302.7. 1407.3
0.1266 0.1411
1494.2 1572.5
0.1544 0.1669
1646.4 1717.6
0.0180 0.0193
384.2
489.3
0.0213
601.7
0.0248
729.3
0.0334
901.8
0.0573
1124.9
0.0816 0.1004
1281.7 1392.2
0.1160 0.1298
1482.6 1563.1
0.1424 0.1542
1638.6 1711.1
0.0179 0.0193
384.9
489.6
0.0212 0.0245
601.3
726.6
0.0318
889.0
0.0512 0.0737
1097.7 1261.0
0.0918
1377.2
0.1068
1471.0
0.1200 0.1321
1553.7 1630.8
0.1433
1704.6
0.0989
1459.6
0.1115
1544.5
0.1230
1623.1
0.1338
1698.1
0.0724 0.0858
1333.0 1437.1
0.0975
1526.3
0.1081
1607.9
0.1179
1685.3
0.0178
387.3
0.0191 0.0209
490.9 600.3
0.0288
864.7
0.0568
1204.1
0.0177
388.9
0.0189 0.0207 0.0233
491.8
600.0
717.5
V 0.0161
190.9
V 0.0161
hq
193.2
V 0.0161
hg
195.5
V 0.0160
197.8
-
V 0.0160
200.1
V 0.0159
0.0176 0.0188
390.5
492.8
0.0205
599.9
0.0237
720.4
0.0229
715.1
0.0402
1037.6
0.0276 0.0362 0.0495
854.5 1011.3 1172.6
0.0267
846.9
0.0335 0.0443
992.1 1146.3
0.0633
1305.3
0.0757 0.0865
1415.3 1508.6
0.0963 0.1054
1593.1 1672.8
0.0562 0.0676 0.0776 0.0868
1280.2 1394.4 1491.5 1578.7
0.0952
1660.6
0.0176 0.0187 0.0203 0.0226
392.1
599.9 713.3
493.9
0.0260 0.0317
841.0
977.8
0.0405 0.0508 0.0610
1124.5 1258.0 1374.7
0.0704 0.0790
1475.1 1564.9
0.0869
1648.8
0.0175
393.8
0.0186 0.0201
495.0 600.1
0.0223
711.9
0.0253
836.3
0.0302
966.8
0.0376 0.0466
1106.7 1238.5
0.0558
1356.5
0.0645 0.0725
1459.4 1551.6
0.0799
1637.4
0.0174
395.5
0.0185 0.0200
600.5
496.2
0.0220. 0.0248
710.8
832.6
0.0291
958.0
0.0354
1092.3
0.0432
1221.4
0.0515
1340.2
0.0595
1444.4
0.0670
1538.8
0.0740
1626.5
0.0198 0.0218 0.0244 0.0282
829.5
950.9
600.9
710.0
0.0337
1080.6
0.0405 0.0479 0.0552 0.0624
1206.8 1326.0 1430.3 1526.4
0.0690
1615.9
0.0603
1520.4
0.0668
1610.8
0.0174 0.0184
397.2
497.4
hg
202.4
V
0.0159 0.0173
203.6 i 398.1
hg
0.1954
1729.5
0.0180 0.0194 0.0215
383.4 488.9 602.3
V 0.0162
hg
0.1889
1538.4
0.1331
1434.3
0.0671 0.0845
1241.0 1362.2
188.6
0.3106
1755.9
0.2601 0.2783
1685.7 1750.6
0.0306 0.0465
879.1 1074.3
186.3
0.2908
1692.0
0.2210 0.2411
1552.2 1619.8
0.0179 0.0192 0.0211 0.0242
385.7
490.0 600.9 724.3
hq
0.2995 0.3198
1693.6 1757.2
0.1752 0.1994
1403.6 1481.3
V 0.0162
hg
15000
177.6
V 0.0163
hg
1500"
0.0287 0.1052
763.0 1174.3
V 0.0163
ho
14000
0.2326 0.2563 0.2784
1495.5 1563.6 1629.2
1400°
0.0198
487.7
177.2
V 0.0163
hg
13000
0.0294 0.1169 0.1574 0.1868 0.2116 0.2340 0.2549 0.2746 0.2936
768.4 1195.5 1322.4 1411.2 1487.0 1556.8 1623.6 1688.9 1753.2
V 0.0164
hg
12000
0.0198 0.0224
487.7
607.5
V 0.0164
hg
11 000
0.0164 0.0183
176.7 379.5
V 0.0164
ho
10000 i
0.0302 0.1296 0.1697
775.1 1215.3 1333.0
-
hg
900 0
0.0198 0.0225
487.6 608.1
V 0.0164
hg
800 0
0.0183
379.3
V 0.0164
hq
0
0.0164
176.3
-
hg
I 600° I 700
0.0199 0.0225 0.0307 0.1364
487.6
779.4 1224.6
608.4
V 0.0164
hq
500 0
0.0164 0.0183
37,9.1
176.0
-
hq
4000
0.0184
498.1
0.0198 0.0217
601.2 709.7
0.0242! 0.0278 0.0329 0.0393
828.2
947.8 1075.7. 1200.3
*Abstracted from ASME Steam Tables (1967) with permission of the publisher, The
American Society of Mechanical Engineers, 345 East 47th Street, New York. N.Y. 10017
0.0464
1319.6
0.0534
1423.6
A-20
APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
Flow Coefficient C for Nozzles'
1.2Q
LIB
I
LI6
Ll4
U2
LID:
oi
Flow_
C
Cd
VI-{:J4
Example: The flow coefficient C for a diameter ratio
Reynolds
number of 20,000 (2 X 104)
equals 1. 03 .
{:J of 0.60 at a
Flow Coefficient C for Square-Edge Orifices 9 ,17
c
It, - Reynolds Number based on d 2.
Flow_
C
I
Korifice"""'"
{:J2
C2{:J4
D.641--+-l-+++
H.., - ReynQlds Number based on d 2
CRANE
CRANE
Net Expansion Factor, Y
Critical Pressure Ratio, rc .
For Compressible Flow through
Nozzles a nd Orifices!!
For Compressible Flow through
Nozzles and Venturi Tubes!!
Ie = 1.3 approximately
.64
......
(for CO 2 , 502 , H 20, H 2S, NH s, NzO, Oz, CH 4, C 2H z, and CZH4J
.........
10
i'-- r-....
.. _JiO
Q.
............
"'"
'''' .........
Q.
If
.18 .........
"'" .......... .........
..........
0.95
~ "",~'r", f3. .
~
-~ r---...
......... r-....
........
J".. ............
...............
...... ......... r-....
R: ~,
I
.54
0.75 J---+--+--..,..1E~~,ld---+------l
•
Nozzle 01
Venturi Meter
fl=0.2
0.1Il I---t-:: ~.~ ~~~+-~-"d-->n;"'-+------l
=0.1
=0.75
,.25
0.65 J - - - + - - + - - - I - - - f ' - - - + - - - - j
0.60
I....L..l...L.J....I....I...J...J..J....J...J......L.JL....J.....J....L...L...I....J....J....I-1-.J....I....J..J......L.J..J.....J
o
0.2
0.4
Ie
0.6
b:.P
Pressure Ratio
1.4 approximately
(for Air, Hz, Oz. N 2 • CO, NO. and HO)
1.0
0.95 1--~.........!iIIIoo::+---+---+---!----!
0.90 I----+W~+_--"~~,.;:--t---t---t
Square Edge Orifice
[l = 0.2
.B
~
I
.52
085 I---+-....;-\:-"~-+--~.....,.~~-;;;>'"""-.\./
c::
.2
~ 0.80 I----t---+-~~~--+---t--"'........o:-I
'"x
Q.
L.U
0.75 f----+-i-
0.10 J---+--+------l--'on-~~+_----t
0.65 r---I----+------l---/---+----f
0.2
Pressure Ratio
0.6
0.4
b:.P
pI
I
=0.5
=0.6
0.1
0.75
I
-
~
...........
u
A-21
APPENDIX A- PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
~
~
.............
~
,
t;:::
.......
"'<
~I
..........
.............
I
/~
/'~
r........
"'"
i'-.
'<
..........
.m
...
......... I'< ....--- <w
~~ :::...... V ~."
v __
~~
i<-"
I
1.31
I
1,4
APPENDIX A- PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
A-22
CRANE
Net Expansion Factor Y for Compressible Flow
Through Pipe to a Larger Flow Area
k
(k
1.0
0.95
0.85
=;'H)[\rflX
I~ "-
0.90 I
1.3
'"""
'\
I
~~
I
I
I
I
I
I
I
I
i
I
I
~
f\.~ ~ ~ ~
I
I I I
I
i
I
I
.~ ~.~ ~ ~ ~
~
~ ~ \..~ ~
~ ~ ~ ~ ~ ::::-......
"-
I
0.80
"-
I
0.75
1
0.70
0.65
'\ '\ "Q
I
~
0.2
0.3
0.4
\\
?
?'O'
!'~ r
0.5
I:::.P
(,\
.,. t i
f--"
I
I
0.1
I
I
I
i
1
I
,
\\. \'
1'- "'0.,. I
\\-
0.6
I~o 1'0
I
"i'o!
';0'
I
.
I
,
i
I
0.7
K
--
6.P
P'I
Y
1.2
1.5
2.0
.525
.550
.593
.612
.631
.635
3
4
6
.642
.678
.722
.658
.670
.685
8
10
15
.750
.773
.807
.698
.705
.718
20
40
100
.831
.877
.920
.718
.718
.718
\\'-
"'-0 i"o.,. I'"\\ \\1'0 ~"[ tb Vo -00
'\~ I\.~ "'" ~
,\ Q>
r--.
2'\'_6''':'0.
I
o
Ie = 1.3
I
.
0.60
0.55 ::----i---
:
""r'R~~~
I
~ ~ ~.,.~~, :~ ~ ~~
I
I
!
~
~ ~~~
~~ ~::::~ ~ ~
I
I
Limiting Factors
For Sonic Velocity
I
I
I
Y
I
II
I
t'-....
[
I
0.8
0.9
1.0
P{
k = 1.4
(k = approximately 1.4 for Air, Hz, O 2 , N z, CO, NO, and l'-!Cl)
I,D ~r--r--T-"':-T-r--T~-r-,;,-,-:~,:,-:::,:",,~,,:,;==,,:,:,::,~.,--...,..----,
Limiting Factors
For Sonic Velocity
Ie = 1.4
K
6.P
P't
Y
1.2
1.5
2.0
.552
.576
.612
.588
.606
.622
3
4
6
.662
.697
.737
.639
.649
.671
8
10
15
.762
.784
.818
.685
.695
.702
20
40
100
.839
.883
.926
.710
.710
.710
CRANE
APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND
OF VALVES, FITTINGS, AND PIPE
Relative Roughness of Pipe Materials and Friction Factors
For Complete Turbulence
.00002
18
..... ~.009
~-4--+-+-~I'~~~rr~r+~---+--~~-r~+-r+4Hr~r"~~v+--+-+~~
~,
ffi+-t-++++-w="
~~
.-
.00001 ~~=t::t::~:t:t+~itI~,·~~;:==+::.~t:::
008
.000008 f----i--+--+-+-+........t-+-+-+'"...".o;:+--+--+--t=:~~~t::j
<?'~oO;--+---i--lI""'+Ir-++t-++.....
1 .......~
':c--+--t--'--+-+-+++-t-t"•000006 I---+-I--+-+-+-t-H-t-++-tl
tlres
I
.000005 1
2
3 4 5 £ 8 10
20 30 40 5060 80 100
200 300
...
Pipe Diameter, in Inches
l)lltu extracted
/,'ric/wn
Faclors Jor Pipe
bv L.F.
l'v10od:;, with pcrmi,s!(m 01 the
publisher, The ;\merican ::;oci~
ctv 01 ~vlcchanical Engineers,
d
Problem; Determine absolute and relative roughness, and friction factor, for fully turbulent flow in lo-inch cast Iron pipe (1.0. = 10.16/1).
Solution: Absolute roughness (E)
0.00085 ..... Relative roughness
(f/D) = 0.001. " .. Friction factor at fully turbulent flow (f) = o.olq6.
VALUES OF (lid) FOR WATER AT 60· F (VELOCITY IN Fl./SEC. X DIAMETER IN INCHES)
0.1
0.4
0.2
0.1
0
4
6
0.1
I I I
.09
.08
.07
Fi
'MI~A~
rtf
'Z~I
-
60
ru
---
200
.Of
'"'-~
I
I
HPIIES
R('~
ttttlt
.03
o§>'"
'
",,,,"'#
10'
fo'
1
I
".
m
Z
1:7
)(
.04
".
.."
...:z:I
::!•
.03
til
:::r.
-<
VI
.....
n".
:::I
.02
.-l
.."
-
-N
r-_~,-
!"-oo
.....
E
IIIiI
~
"-
"" .....
!"-...
~
~
.02
•
~
......
........
~
~
-
~)o.
2
3 4 5
~ , 4ttitlO'
=D
.0 01
0008
.0 006
Re - Reynolds Number
Dv
~
...0
l>
....
0
VI
'<
1:7
."
c:
:::I
".
z
-t
."
'<
0
-
n
:z:
~
i'~
.0 004
...
~~
f~r 4 56
~ ~
ij 107 ,.
2
.!...
D
n....
,.m
ii>
....
n
VI
0."
CD
.0 001
o.a
.0 0005
::!
"
......
,.
".
".
n
0
3
3
.0 002
......... -l"'-
3 4 5 6 "10'
-
m
0
<
".
:;:m
~
."
::;
"U
CD ....
"III
2
::!
VI
"U
CD
....
E
.009
Relative
,004 Roughness
r-~
m
VI
.006
...
.
...3,.
0
.002
:--..
<-;
.0 I
-...
.0 1
.0 08
....
!"-oo
.,e,., ~~I'
.015
atil
.01
•
""'II~ :""'1'-0.
10'
....
....
os
0
.025
.OOB
..
±tilli:t
\
f
Friction
Factor
","
<f
600 800 ....
\
.05
.04
•
400
80 100
• ET~ Tl,IR~U
'.
... ~
.06
~
•
;Ri
I_~r
an
20
8
::!
Z
0
00
~
.00001
56
.!. = .000,005
".
Z
)8
1:7
~
."
m
D
,.n
fat othet fotms of the R, equation, see page 3·2.
Problem:
Determine the friction factor for iO-inch cast iron
pipe (10.16" I .D.) at a Reynolds number flow of 30 ,000.
)
)
)
)
)
lIQ
Solution: The relative roughness (see page A-I3) is
0.00 I.
Then, the friction factor (J) equals 0.026.
)
)
)
Z
m
)
)
)
)
)
)
)
)
)
)
)
)
)
n
:a
VALUES OF (vd) FOR WATER AT 60· F (VELOCITY IN FT./SEC. X DIAMETER IN INCHES)
)-
'1.<1'
Z
m
»
....
....m
Z
Nominal
Pipe
Size,
+-++-lH-l++1H-l-++i Inside
+-++-lH-l-++lI-l-l-Hi Diameter,
.20
H*,;m;J;1fn~fE;J;1mffmt;;;t;f~;t!m ~nChes
Inches
.~
r+~~HH+r-r~HH+H~~~-+~+H++~O .25
~~~~H+-+~+++H~~~~~H+~~O .30
f
Friction
Factor =
:;;.;.-
II8
II4
~~~~~~~~#=~~~~O .40
~~~~~~-H~~##=*4*~~~~~~~0 .50
3/8
II2
3/4
.75
1
0
I~
1
5
2
.-
2V,
~~
4
5
I)
8
!~
~ggg6~l~
o
0
0
Schedule Number
."
..
»
,,"
-
:I:
c;"
'"
n
."
....
1\
;::
X
::::I
.12
0
-..
CIt
0
n
i'"
12
::::I
I
....
-<
~
'"0
'"m~
'"
~
."
.-
c:
CJ
'"
»
zCJ
."
6
n
0
3
3
~
n
:I:
.o·
CD
1\
»
'"
»
n
;ri
'"
CA
'"n....
'"
CD
CD
<
»
::!
"
CD ....
.01 Httt--t-+++tt+H+HH--+-l-H+H++H-H~1.009
0
14
CJ
00
~
<:
m
~
."
:::;
~
z
0
~
103
2 3 4 5 6 810 4
2 3 4 5 6 8 105
2 3 4 5 6 8106
2 3 4 56 8107
2 3 4 5 6 8 108
»
z
0
Re - Reynolds Number = p..
Problem: Determine the friction factor for 12-inch Schedule 40 pipe at a flow having a Reynolds number of 300 ,000.
For other forms of the R. equation, see poge 3-2.
Solution:
The friction factor (f) equals
0.016.
...
~
A-26
CRANE
APPENDIX A- PHYSICAL PROPERTIES OF flUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
UK" FACTOR TABLE-SHEET 1 of 4
Representative Resistance Coefficients (K) for Valves and Fittings
(UK" ;s based on use of schedule pipe as listed on page 2- 10)
PIPE FRICTION DATA FOR CLEAN COMMERCIAL STEEL PIPE
WITH FLOW IN ZONE OF COMPLETE TURBULENCE
Nominal Size
Friction
---..tactor (fr)
Vl"
%"
1"
11,4"
1 Y2"
.027
.025
.023
.022
.021
;:p:v"
3" i 4"
.0 18
17
2"
.0 19
l.O
5"
6"
8-10"
12-16"
18-24,,1
.016
.015
.014
.013
.012
FORMULAS FOR CALCULATING uK" FACTORS·
FOR VALVES AND FITTINGS WITH REDUCED PORT
(Ref: Pages 2-11 and 3-4)
• Formula 1
• Formula 6
0.8
1<2 =
~in-!1 (I - f32)
1<2 = 1<1 -l- Formu Ia 2 + Formula 4
2
f34
f34
• Formula 2
0·5 (I - (32)
1<2 = ~..
VSin: 1<1
=
(34
• Formula 7
(3 (Formula 2 + Formula 4) when()= 1800
1<1 (3 [0, 5 (I - (32) + (I - f32) 2]
1<2=------------~----------• Formula 4
• Formula 5
1<2 = ~1 + Formula I + Formula 3
Subscript I defines dimensions
and coefficients with reference to
the smaller diameter.
Subscript 2 refers to the larger
diameter.
• Use UK" furnished by valve or fitting supplier when available.
SUDDEN AND GRADUAL CONTRACTION
f
d
/
I
a,
?
i2
G
~
?
e
)
I
~S
I
d,
I
I
\
3,
"1
I
6
If: () <' 45° ... , , ... 1<2 = Formula I
45° < 8 <: 180° .. ,1<2
Formula 2
SUDDEN AND GRADUAL ENLARGEMENT
-If: 8
, a,
/
I
1,-
,
\
!
/
I
d,
I
C
\e d,
/
45°,·,,·," .1<2
0
!
III ,
/
\
a,
I
I
J
\
"
,/
?
5
Formula 3
45° < () <' 180 , , ,1<2 = Formula 4
I
A-27
APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
"K" FACTOR TABLE-SHEET 2 of 4
Representative Resistance Coefficients (K) for Valves and Fitti.,gs
(for formulas and friction data, See page A-26J
(UK" is based on use of schedule pipe as listed on page 2-10)
GATE VALVES
Wedge Disc, Double Disc, or Plug Type
SWING CHECK VALVES
K
If:{3
100
fr
Minimum pipe velocity
for full disc lift
1,0=0.
Minimum pipe
Cfps) for full disc lift
I''''''~
.K2 ~ Formula 5
0
(3 < 1 and 45° < 0'< 180 . . K2
Formula 6
{3 < 1 and 0 <: 45°···
35 v V
I~····
60 V V except
U IL Iiste~ = 100
vV
LIFT CHECK VALVES
GLOBE AND ANGLE V ALVES
If:
{3
I .. KJ
600fT
{3 < I .. . K2 ~ Formula 7
Minimum pipe velocity (fps) for full elise lift
~ 46 {32
vV'
~
id" a, :
1..-"""........- ~
If
{3
IKJ
55fT
KJ = 55 fr
~ Formula 7
Minimum pipe velocity (fps2Jor full disc lift
If:
{3
I.
{3 < I .
~ 140 {32
vV'
TILTING DISC CHECK VALVES
If:
{3
All globe and angle valves,
whether reduced seat or throttled.
If: {3 < I . . . K2 Formula 7
Sizes 1, to 8".. K
Sizes 10 to 14" ... K
Sizes 16 to 48" ... K
Minimum pipe velocity
(fps) for full disc lift =
/-=-
80 V V
30
VV
A·28
APPENDIX A
CRANE
PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
UK" FACTOR TABLE-SHEET 3 of 4
Representative Resistance Coefficients (K) for Valves and Fittings
(for formula. and friction data, see page A-26)
(UK" is based on lise of scheduled pipe as listed on page 2- 10)
STOP·CHECK VALVES
(Globe and Angle Types)
FOOT VALVES WITH STRAINER
Poppet Disc
Hinged Disc
t--d-:l
If:
If:
{3 = 1 . . . Kl - 400 fr
{3 < I .. :K2 Formula 7
{3
I ,. Kl = 200 fT
{3 < I .. . K2 = Formula 7
Minimum pipe velocity
for full disc lift
Minimum pipe velocity
for full disc lift
- 55 {32VV
= 75 {32 VV
Minimum pipe velocity
(fps) for full disc lift
=
Minimum pipe velocity
(fps) for full disc lift
15 VV
=J5
BALL VALVES
rf:
If:
{3 = I ... Kl = JOo fT
{3 < I .. . K2 = Formula 7
{3 = I .. ,K l
35 0 fT
{3 < I . , . K2 = Formula 7
If:
Minimum pipe velocity (fps) for full disc lift
= 60 {32 VV
{3 = I, 0
0., ... , . . . . . . . . Kl = 3
BUnERFLY VALVES
If:
{3 = I ... Kl
55 fT
f3 < I .. . K2
Formula 7
If:
f3- I. .. Kl = 55fT
f3 < I .. . K2 = Formula 7
Minimum pipe velocity (fps) for full disc lift
=
140 /1 2
VV
fr
/1 < 1 and 0 <' 45° .... , .... K2 = Formula 5
{3 < I and 45° < 0 <: 180°. , .K2 = Formula 6
Sizes 2 to 8" .. , K = 45 /T
Sizes 10 to 14" ... K = J5 fr
Sizes 16 to 24" . .. K - 25 IT
CRANE
A·29
APPENDIX A- PHYSICAL PROPERTI~S OF FLUIDS AND FLOW CHARACTERISTICS OF VAlV~S, FITTINGS, AND PIPE
UK" FACTOR TABLE-SHEET 4 of 4
Representative Resistance Coefficients (K) for Valves and Fittings
(for formulas and friction doto, see poge A-26)
("K" ;s based on use of schedule pipe as lis led on page 2- 10)
PLUG VALVES AND COCKS
Straight-Way
[~J
GJ
If:
90·
45°
@
0
3-Way
View X-X
If: {3 I,
KI = 18 fT
STANDARD ELBOWS
d,
ClJcBJ
If:
{3 =
K
K
30 fT
16fT
If:
I,
Kl = JofT
Kl
{3 < I .. . K2 = Formula 6
STANDARD TEES
MITRE BENDS
0(
K
O·
2 fr
4 {r
8 {r
15 {r
25 {r
40 {r
60 fr
15°
30·
45°
60·
75°
90°
~-
Flow thru run .. :.,. ,K = 20fT
Flow thru branch, ... K 60 fT
PIPE ENTRANCE
90° PIPE BENDS AND
FLANGED OR BUTT-WELDING 90· ELBOWS
I
rid
K
rid
K
1
20 {r
1.5
14 {r
2
3
4
6
12 £T
8 24 IT
10 30 {T
12 i 34 {T
, 12 {r
i 14 {r
i 17 (r
14 138 fT 1
16 42 fr
20 50 IT
Inward
Projecting
Flush
rid
K
0.00*
0.5
0.02
0.28
0.04
0.24
0.06
. 0.15
0.Q9
• 0.10
0.04
0 . 15 & up
I
1
The resistance coefficient, K n , for pipe bends other
than '10. may be determined as follows:
J(B=(n-l)
,--.
K = 078
*Shorp.edged
For K,
see table
(0.2 5 7rfrJ. 0.5K)+K
n
number of 90 0 bends
K = resistance coefficient for one 90° bend (per table)
PIPE EXIT
CLOSE PATTERN RETURN BENDS
Projecting
Sharp-Edged
Rounded
~ ----1 ~
~
..
K = 1.0
K
1.0
K
1.0
A-30
CRANE
APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
Equivalent Lengths Land L/D and Resistance Coefficient K
d
L
LID
10000
8000
6000
5000
4000
000
50
III
40
Q.)
.r;
u
-=,:
30
<Ii
N
c;:;
2000
Q.)
Q.
0:: 24
Q
..,.
20
.!!
:::J
"0
Q.)
.r;
c:
u
.r;-
c.o?
bo
c:
7il
...J
'5
0
z
c:
Q.)
C
Q.)
200 7il
>
10
I..LJ
9
'S
c:r
100 I
80 ....:j
60
50
40
30
8
III
7 .r;
u
Q.)
-=
6 ,:
Q.)Q.
5 a..
'+-
0
4 .E:l
Q.)
E
<0
Q
3 -c
Q.)
'Vi
~
2 2
2
lYl
1~
1.0
0.9
3/4 0.8
0.7
li2 0.6
% 0.5
0.1
SIZE, INCHES
Solution
Problem: Find the equivalent length in pipe
diameters and feet of Schedule 40
meretal steel pipe, and the resistance
for 1, 5, and 12-inch fully-opencd
with flow in zone of complete
-=
I
~
CRANE
A·31
APPENDIX A - PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS. AND PIPE
Equivalents of Resistance Coefficient K
And Flow Coefficient Cv
CV
K
0.1
891 d
K
C;
0.15
Cv =
0.2
29.9 d
d
60,000
50,000
40,000
30,000
4
24
20
2
20,000
"K
15
0.4
0.5
10
8
8
7
2000
<Il
OJ
GOO ............
<l.>
0
()
<l.>
u
1.5 §
VI
'iii
<l.>
0::::
I
~
3
4
..........
...... ......
...... ......
......
.......
.......
.......
.......
..............
.......
...... .......
.......
.......
.......
...... ......
.......
.......
.............
...... ......
......
......
....
500 _
400
24
<l.>
'0'
300 -=
.... .c
u
c::
c::
6
5
5
4
0:
'0
3~
Q:;
c..
-
lJ..
c:::I
2~
100 I
80
:2
<l.>
<Il
2
<l.>
.c:
c.n
ro
2
<l.>
N
c;;
ro
c::
'e0
z
l~
1.0
1-
.9
.8
K = 340/T .... ,. . . . . . . . . . . . .. page A-27
0.015 ..... ..... " ..... . .. page A-26
/T
K
340 X 0.15 = 5.1
Cv
490 ...... ... . .. dotted lines on chart
<l.>
-c
u
E
20
Solution:
~
::::I
3
<l.>
~
10
0:
0
1.5
Problem: Find the flow coefficient Cv for a
6-inch Class 125 cast iron globe valve with
full area seat.
c::
c..
<Ii 4
c::
u
<l.>~
::
0
<l.>
0
()
<l.>
.c:
.5
3
200
3/4
.7
.6
2
20
c::
......
............
§..
1~
5
15
~ ....
1000
800
0.8 1:
(I.l
0.9 'u
1.0 iE
6
7
8
9
10
16
10
9
0.6
2
20
18
14
12
10,000
8000
6000
5000
4000
3000
0.3
24
.5
.4
1/2
3/8
A·32
APPENDIX A-PHYSICAL PROPERTIES OF flUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE
CRANE
Types of Valves
(For other valve types, see page 3-26)
Wedge Gale Valve
(Bolted Bonnet)
High Performance Butterfly Valve
Flexible Wedge Gale Valve
(Pressure-Seal Bonnel)
Ball Valves
Tilling Disc Check Valve
Butterfly Wafer Valve
Fool Valves
Poppel ond Hinged Types
Three-Way Cock
Sedional and Outside Views
8·1
Engineering Data
APPENDIX B
Flow problems are encountered in many fields of
engineering; therefore, a wide choice of terminology
prevails. Terms most widely accepted in the fluid
dynamics field have been employed in this paper.
In the event problems are expressed in units other
than used in this paper, tables and nomographs are
provided for conversion.
Other useful engineering data are presented to provide direct solutions to frequently recurring factors
appearing in flow formulas, as well as complete
solutions to water and air flow pressure drop
problems.
CRANE
APPENDIX B - ENGINEERING DATA
B-2
Equivalent Volume and Weight
Flow Rates of Compressible Fluids
g'm
gh
1000
800
60,000
g~
1000
800-
600
600-
400
400-
300
2.7
10,000
8000
40,000
300-
Sg
W
30,000
6000
5000
4000
20,000
3000
2.5
W = 4.58 q'm Sg
W= Pa q' h Sg
W= 0.0764 q' h Sg
W= J 180 q'd Sg
where:
Pa = weight density of air at
standard conditions
(14.7 psia and 60 F)
2000
200
10,000
200-
8000
100
<::
0
80-
fA
:3 60
- :0
<::
"0
<::
0
c..:>
-ero
"t:I
<::
en'"
1U
60- 840
- -e
.g 30
40-
:::>
'" 20- :E
~
- ~
0.
<..>
c..:>
W-:g
_ c..:>
-
".0
[J:
'0
.l!:l
'"
0:::
I
tJ)
"t:I
c
10
If
400
300
:g
3- [J: 2
- '0
2- .l!:l
0:::
- '"I
-
_~
;:;,-
1.0
fA
0.8
0.8
0.60.40.3-
0.6
0.4
20
0.2
10
8
0.20.1
30
20
I-
~
0
.c:
Q
"*
0:::
I
-"'0<"
ro
- __
- -- -- -- --
t3
-- --- - -
~
<..>
'"
0.
en
~
1.
0.9
'0
_.-
"*
0.7
".0
--~"" 0
0:::
I
~
0.6
2
0.6
0.5
0.4
0.3
0.2'
6
4
0.5
1.0
0.8
.08
0.1
~
[J:
10
8
6
5
4
3
.i:::'
.:;:
___
40
30
0.3
40
0
.c:
.:
60
0
tJ)
'0
0
100
80
<::
:::>
a..
.!::
=>
".-
tJ)
50-'0 __
tJ)
200
~
0.
"0
c..:>
0
3
-
100
80
60
I-
"8
ro
Ic
0
ro
tJ)
..c
::;
::I:
r:;;
'"
6- '"
:::> 4
4-
200
<::
<..>
8-- '0 6
c:
0
c..:>
"t:I
600
'"
<..>
~
-e
ro
-
1.5
300
'E
2000
ii
10
.!::
<::
3000 :,g
0.
1.1...
'"
.S:
:E
fA
1[00 ::;
0
::I:_
800
c:
Cl
'0
600
500
400
4000
'"
- r:;;
30- :; 20
>.
:c
=>
6000
80
100
fA
1000
800
2.0
0.1
Problem: What is the rate of flow in
pounds per hour of a gas, which has a
specific gravity of 0.78, and is flowing at
the rate of 1,000,000 cubic feet per hour
at standard conditions?
Solution: W = 60,000 pounds per hour
0.4
0.3
r-'.
CRANE
APPENDIX B - ENGINEERING DATA
8·3
.~------------------~--~~
Equivalents of Absolute (Dynamic) Viscosity
TO OBTAIN
\WLTIPLY
-
Centipoise
Gram
CmSec
Dyne Sec
BY
1
~
rP'Tltipoisp'
-tPound~
~
Poise
[
·Pound, Sec
Ft 2
Ft Sec
Poundal Sec
Ft 2
Cm z
()J.)
(100 )J.)
()J.' .)
()J.e)
1
0.01
2.09 (10- 5)
6.72 (10-4)
f',.,
Poise
Gram
CmSec
Dyne Sec
Cm2
(100 )J.)
100
1
2.09 (10- 3 )
0.0672
Slugs
Ftsec
'Pound, Sec
Ft%
()J.' ,)
47900
479
1
g or 32.2
.l
or .0311
g
1
tpoundm
Ft Sec
Poundal Sec
Ft 2
-[
I
14.87
1487
(1-'.)
i
I
*Pound,= pound of Force
To convert absolute or dynamic viscosity from one
set of units to another, locate the given set of units
in the left hand column and multiply the numerical
value by the factor shown horizontally to the right
under the set of units desired.
tPound m= Pound of Mas~
As an example, suppose a given absolute viscosity of
2 poise is to be converted to slugs/foot second.
By
referring to the table, we find the conversion factor
to be 2.09 (10- 3). Then, 2 (poise) times 2.09 (10- 3)
4.18 (10- 3)
0,00418 slugs/foot second.
Equivalents of Kinematic Viscosity
TO OBTAIN---""
~
'-......
Centistokes
Ft 2
Sec
(v)
1
0.01
1.076 (10-5)
MULTIPLY
i
:
Stokes
Cm 2
Sec
(100 v)
Centistokes
(v')
Stokes
Cm 2
Sec
(100 ")
100
1
1.076 (10-3 )
Ft2
Sec
(v')
92900
929
1
To convert kinematic viscosity from one set of units
to another, locate the given set of units in the left
hand column and multiply the numerical value by
the factor shown horizontally to the right, under
the set of units desired.
As an example. suppose a given kinematic viscosity
of 0.5 square foot/second is to be converted to centistokes. By referring to the table, we, find the conversion factor to be 92,900. Then, 0.5 (sq ft/sec)
times g2,gOO = 46,450 centistokes.
for conversion from kinematic to absolute viscosity, see page B·5.
1·4
CRANE
APPENDIX 8- ENGINEERING DATA
Equivalents of Kinematic
anJ Saybolt Universal Viscosity
Kinematic
Viscosity,
Centistokes
v
Equivalent Saybolt
Universal Viscosity, Sec
At 100 F
Basic Values
Equivalents of Kinematic
and Saybolt Furol Viscosity
Kinematic
Viscosity,
At 210 F
Centistokes
At 122 F
At 210 F
v
1.83
2.0
4.0
32.01
32.62
39.14
32.23
32.85
39.41
48
50
60
25.3
26.1
30.6
25.2
29.8
6.0
8.0
10.0
15.0
20.0
45.56
52.09
58.91
77.39
97.77
45.88
52.45
59.32
77.93
98.45
70
80
90
35.1
39.6
44.1
34.4
39.0
43.7
25.0
30.0
35.0
40.0
45.0
119.3
141.3
163.7
186.3
209.1
120.1
142.3
164.9
187.6
210.5
100
125
150
175
48.6
60.1
71.7
83.8
48.3
60.1
71.8
83.7
95.0
106.7
118.4
130.1
95.6
107.5
119.4
131.4
50.0
55.0
60.0
65.0
70.0
232.1
255.2
278.3
301.4
324.4
233.8
257.0
280.2
303.5
326.7
200
225
250
275
300
325
350
375
141.8
153.6
165.3
177.0
143.5
155.5
167.6
179.7
75.0
80.0
85.0
90.0
95.0
347.6
370.8
393.9
417.1
440.3
350.0
373.4
396.7
420.0
443.4
400
425
450
475
188.8
200.6
212.4
224.1
191.8
204.0
216.1
228.3
100.0
120.0
140.0
160.0
180.0
463.5
556.2
648.9
741.6
834.2
466.7
560.1
653.4
500
525
550
575
235.9
247.7
259.5
271.3
240.5
252.8
265.0
277.2
200.0
220.0
240.0
260.0
280.0
926.9
1019.6
1112.3
1205.0
1297.7
600
625
650
675
283.1
294.9
306.7
318.4
289.5
301.8
314.1
326.4
700
725
750
775
330.2
342.0
353.8
365.5
338.7
351.0
363.4
375.7
300.0
3'20.0
340.0
360.0
380.0
1390.4
1483.1
1575.8
1668.5
1761.2
800
825
850
875
377.4
389.2
400.9
412.7
388.1
400.5
412.9
425.3
400.0
420.0
440.0
460.0
480.0
500.0
1853.9
1946.6
2039.3
2132.0
2224.7
2317.4
900
925
950
975
424.5
436.3
448.1
459.9
437.7
4.'iO.l
462.5
474.9
1000
1025
1050
1075
471.7
483.5
495.2
507.0
487.4
499.8
512.3
524.8
1100
1125
1150
1175
518.8
530.6
542.4
554.2
537.2
549.7
562.2
574.7
1200
1225
1250
1275
1300
566.0
577.8
589.5
601.3
613.1
587.2
599.7
612.2
624.8
637.3
Over 1300
*
t
Over 500
Saybolt Seconds
equal
Centistokes
times 4.6673
Saybolt Seconds
equal
Centistokes
times 4.6347
Note: To obtain the Saybolt Universal viscosity
equivalent to a kinematic viscosity determined at t,
multiply the equivalent Saybolt Universal viscosity
at 100Fby 1+ (t - 100) 0.000064.
For example, 10 v at 210 F are equivalent to 58.91
multiplied by 1.0070 or 59.32 sec Saybolt Universal
at 210 F.
These tables are reprinted with the permission of
the American Society for Testing Materials (ASTM)
The table at the left was abstracted from Table I,
D2161-63T. The table at the right was abstracted
from Table 3, D2161-63T.
*OVER 1300 CENTISTOKES AT 122 F:
Saybolt Fluid Sec = Centistokes x 0.4717
tOVER \300 CENTISTOKES AT 210 F:
Log (Saybolt Furol Sec
2.87) =
1.0276 [Log (Centistokes)] - 0.3975
CRANE
APPENDIX 1\
ENGINeeRING DATA
Equivalents of Kinematic, Saybolt Universal,
Saybolt Furol, and Absolute Viscosity
v
~
1000 10 000
900··_ _-="- 2000
800
700
600
500
1000
~.
~
~
J.Le
.05
900
400 _..:!Yl<"-=*, 800
.04
700
300
-~>L~"F 600
'"
.03
500
.02
V)
"c::w
The empirical relation between Saybolt Universal Viscosity
and Saybolt Furol Viscosity at 100 F and 122 F, respectively,
and Kinematic VIscosity is taken from A.S.T.M. D2161-63T.
At other temperatures, the Saybolt Viscosities vary only
slightly.
0
2000
Saybolt Viscosities above those shown are given by the relationships:
V>
c::
~,
~
Saybolt Universal Seconds
Saybolt Furol Seconds
V)
.~
0
400
w
.~
Centistokes x 4.6347
Centistokes x 0.4717
>
<3 1505
300
LL.
.01
.009
.008
w .007
a .006
.005
0
-1
Dl 100-90
80
70
~ ~ .004
60
~
0
500
50 ---':'::'::--L-IOO ~ '& .003
90 8c: "~
400
40 -----C.::..:....---'-811:; ~ .002
70 ~~
.g,
~
s:
V)
/"'.
~
~
.::----......
w
,~
o
V)
:;: '"
o
.~ i;; .001
~ :;: .0009 l.!' 2 .0008
;0:: ~ .0007
I
~ .0006
:::.
I .0005
26
200
-£ .0004
100
w 90
V>
'"c:: 80
V)
"0
200 '"
V)
'15
S
1::
u
1.3
.e-
'"
100 90 ~
80 ~
70 .~
1.2
1tr<
o"'_ - _ _
50.2
V)
:iI
~
1.1
_
--- . . . . . . ..............
-
10
.......
- - - - - - -_
:~
20 a::
«
c:;
~
30
>- 0.9
---............ _
c::
0
~.
-
~ 0.8
V>
'iii
0
40
'u
.0002
I
\
0.7
~
.0001
.00009
.00008
.00007
.00006
.00005
=>
~
<3
>ro
.0
"" 40
.00004
~
.00003
35
2
.00002
Problem I: Determine the absolute viscosity
of an oil which has a kinematic viscosity of 82
centistokes and a specific gravity of 0.83,
Solution I: Connect 82 on the kinematic viscosity scale with 0,83 on the specific graVity
scale; read 67 centipoise at the intersection on
the absolute viscosity scale .
Problem 2: Determine the absolute viscosity of
an oil having a specific gravity of 0.83 and a
Saybolt Furol viscosity of 40 seconds.
Solution 2: Connect 0.83 on the specific gravity
scale with 40 seconds on the Saybolt Furol scale;
read 67 centipoise at the intersection on the
absolute viscosity scale.
70
80
0.6
0.5
""
Cl
c::
~
60
'":>
'c
~
50 ·s
'f;
w
V)
:>
ro
'"
Q.)
Q.)
~-........
.0003
b
0
90
100
'"
<.1i
TEMPERATURE. DEGREES FAHRENHEIT
-30
100000
-20
-10
AMERICAN STANDARO
ASA No. ZIl.J9.I~39
10
SO 000
A.s.T.M. STANDARD VISCOSITY·TEMPERATURE CHARTS
FOR LIQUID PETROLEUM PRODUCTS (0 3411
20 000
CHART B: SAYBOLT UNIVERSAL VISCOSITY, ABRIDGED
10 000
(This A.S.T.M. chart is used to determine the viscosity of a
petroleum product at any temperature if its viscosity in two
different temperatures is known. When the Saybolt Universal
VlScosity-Tempcrature relationship of an oi!" is plotted on
this chart, the resulting Curve is a straight line. Consequently,
if the viscosity-temperature relationship is known at two
points, then all points will fall on thc line connecting the
two given points. The line may be extended in either dIrection
beyond thc two known points, provided that the temperature
range is between the cloud point and the initial boiling point.)
(This chart 'waS reproduced by permission of
the American Society for Testing Materials.)
5000
4000
3000
2000
1500
1000
750
III
500
400
z
300
Vl
a
"<
500
400
0
0
..,u
III
..J
<
III
0::
IT
0
If)
0
z
8
IIJ
If)
200
200
150
ISO ~
0::
..J
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-30
-20
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30
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Pri,IO<! in U.S.A.
70
-
250 260 270 280 290 300 310 320 330 340 350
80
TEMPERATURE, DEGREES FAHRENHEIT
)
,.'"
Z
Copyrigllt, 1939
AMERICAN SOCIETY FOft TESTING MAtERIALS
1916 RACE Sr., PHILADELPHIA 3, PA.
)
m
)
B·7
APPENDIX B- ENGINEERING DATA
CRANE
Equivalents of Degrees API, Degrees Baume,
Specific Gravity, Weight Density, and
Pounds Per Gallon at 60 F/ 60 F
...............
~
~
Degrees
on
API
or
Baunle
Scale
0
2
4
6
8
Values for Baunle Scale
Values for API Scale
Specific
Gravity
Weight
Density,
Lb/Ft3
S
p
,
"
,
"
,
"
.
"
,
"
,
"
"
.
.
'
Liquids Heavier Than Water
ighter Than Water
Oil
Pounds
per
Gallon
"
.
~ecific
ravity
Weight
Density,
Lb/Ft 3
S
p
"
"
'
'
' ,
'
"
Weight
Density,
Lb/Ft3
S
p
.
1.0000
1.0140
1.0284
1.0432
1.0584
62.36
63.24
64.14
65.06
66.01
8.337
8.454
8.574
8.697
8.824
,
' ,
"
'
,
"
,
"
"
,
"
'
'
'
Pounds
per
Gallon
Specific
Gravity
Pounds
per
Gallon
:
10
12
14
16
18
1.0000
0.9861
0.9725
0.9593
0.9465
62.36
61.50
60.65
59.83
59.03
8.337
8.221
8.108
7.998
7.891
1.0000
0.9859
0.9722
0.9589
0.9459
62.36
61.49
60.63
59.80
58.99
8.337
8.219
8.105
7.994
7.886
1.0741
1.0902
1.1069
1.1240
1.1417
66.99
67.99
69.03
70.10
71.20
8.955
9.089
9.228
9.371
9.518
20
22
24
26
28
0.9340
0.9218
0.9100
0.8984
0.8871
58.25
57.87
56.75
56.03
55.32
7.787
7.736
7.587
7.490
7.396
0.9333
0.9211
0.9091
0.8974
0.8861
58.20
57.44
56.70
55.97
55.26
7.781
7.679
7.579
7.482
7.387
1.1600
1.1789
1.1983
1. 2185
1.2393
72.34
73.52
74.73
75.99
77.29
9.671
9.828
9.990
10.159
10.332
30
32
34
36
38
0.8762
0.8654
0.8550
0.8448
0.8348
54.64
53.97
53.32
52.69
52.06
7.305
7.215
7.128
7.043
6.960
0.8750
0.8642
0.8537
0.8434
0.8333
54.57
53.90
53.24
52.60
51.97
7.295
7.205
7.117
7.031
6.947
1.2609
1.2832
1.3063
1.3303
1.3551
78.64
80.03
81.47
82.96
84.51
10.512
10.698
10.891
11.091
11.297
40
42
44
46
48
0.8251
0.8155
0.8063
0.7972
0.7883
51.46
50.86
50.28
49.72
49.16
6.879
6.799
6.722
6.646
6.572
0.8235
0.8140
0.8046
0.7955
0.7865
51.36
50.76
50.18
49.61
49.05
6.865
6.786
6.708
6.632
6.557
1.3810
1.4078
1.4356
1.4646
1.4948
86.13
87.80
89.53
91.34
93.22
11.513
11.737
11.969
12.210
12.462
50
52
54
56
58
0.7796
0.7711
0.7628
0.7547
0.7467
48.62
48.09
47.57
47.07
46.57
6.499
6.429
6.359
6.292
6.225
0.7778
0.7692
0.7609
0.7527
0.7447
48.51
47.97
47.45
46.94
46.44
6.484
6.413
6.344
6.275
6.209
1.5263
1.5591
1.5934
1.6292
1.6667
95.19
97.23
99.37
101.60
103.94
12.725
12.998
13.284
13.583
13.895
60
62
64
66
68
0.7389
0.7313
0.7238
0.7165
0.7093
46.08
45.61
45.14
44.68
44.23
6.160
6.097
6.034
5.973
5.913
0.7368
0.7292
0.7216
0.7143
0.7071
45.95
45.48
45.00
44.55
44.10
6.143
6.079
6.016
5.955
5.895
1.7059
1.7470
1.7901
1.8354
1.8831
106.39
108.95
111.64
114.46
117.44
14.222
14.565
14.924
15.302
15.699
70
72
74
76
78
0.7022
0.6953
0.6886
0.6819
0.6754
43.79
43.36
42.94
42.53
42.12
5.854
5.797
5.741
5.685
5.631
0.7000
0.6931
0.6863
0.6796
0.6731
43.66
43.22
42.80
42.38
41.98
5.836
5.778
5.722
5.666
5.612
1.9333
120.57
16.118
·.
80
82
86
88
0.6690
0.6628
0.6566
0.6506
0.6446
41.72
41.33
40.95
40.57
40.20
5.577
5.526
5.474
5.424
5.374
0.6667
0.6604
0.6542
0.6482
0.6422
41.58
41.19
40.80
40.42
40.05
5.558
5.506
5.454
5.404
5.354
90
92
94
96
98
100
0.6388
0.6331
0.6275
0.6220
0.6166
0.6112
39.84
39.48
39.13
38.79
38.45
38.12
5.326
5.278
5.231
5.186
5.141
5.096
0.6364
0.6306
0.6250
0.6195
0.6140
0.6087
39.69
39.33
38.98
38.63
38.29
37.96
5.306
5.257
5.211
5.165
5.119
5.075
84
For Formulas, see page '.3.
I
'
.
..
·.
...
,
..
"
..
. ..
..
...
"
., .
,
.
...
.
,
..
·.
.. ,
'
..
. ..
B-
CRANE
APPENDIX B- ENGINEERING DATA
Steam Data
Horsepower of an Engine
Boiler Capacity
P
The output of a steam generating plant is often expressed
in pounds of steam delivered per hour. Since the steam output may vary in temperature and pressure, the boiler capacity is more completely expressed as the heat transferred in
Btu per hour. Boiler capacity is usually expressed as kilo
Btu (kB) /hour which is 1000 Btu/hour, or mega Btu (mB) /
hour which is 1,000,000 Btu/hour. The boiler capacity is:
L
A
N
Mean effective pressure per square
inch of the steam on the piston
Length of stroke, in feet
Area of piston, in square inches
Number of strokes per minute
then,
W (h g - h,) m
. k'lI 0 B tu lour
'h
--'--"'---'1000
Horsepower =
h g - h, = change in enthalpy, Btu/lb
An older expression of boiler capacity in terms of an irrational unit called "boiler horsepower" may be expressed:
W (h p - h,)
, 97 0 .3 x 34,5
That is, one boiler horsepower is equivalent to 34,5 pounds
of water evaporated per hour at Standard Atmospheric
Pressure and a temperature of 2 I 2 F.
boiler horsepower = (horsepower) (13,1547)
I boiler horsepower
33475 Btu/hr
horsepower
550 ft-lb/sec,
I Btu
77'8.2 ft-lb
I Btu
252 calories
I kw-hr = 1412.20 Btu
PLAN
33000
The approximate mean effective pressure
in the cylinder when the valve cuts off
at:
7.l stroke, equals steam pressure x/·597
73 stroke, equals steam pressure/x ,670
% stroke, equals steam pressure x .743
Y2 stroke, equals steam pressure x .847
% stroke, equals steam pressure x .919
% stroke, equals steam pressure x .937
% stroke, equals steam pressure x .966
Ys stroke, equals steam pressure x .99 2
Ranges in Steam Consumption by Prime Movers
(For Estlmatinll Purposes)
Simple Non-Condensing Engines ....... , .. , .. , 29 to 45 pounds per H. P. hour
Simple Non-Condensing Automatic Engines .... 26 to 40 pounds per H. P. hour
Simple Non-Condensing Corliss Engines. . . . . . .. 26 to 35 pounds per H. P. hour
Compound Non-Condensing Engines .... , . . . . .. 19 to 28 pounds per H. p, hour
Compound Condensing Engines ... , . , ..... , , ,. 12 to 22, pounds per H. P. hour
Simple Duplex Steam Pumps. . . . .. . ....... ,. 120 to 200 pounds per H. P. hour
Turbines, :--Jon-Condensing ...... , ...... , .. , .. 21 to 45 pounds per H. P. hour
Turbines, Condensing ... , ......... , , . , . . . . . .. 9 to J2 pounds per H. P. hour
Quality of Steam ... oX
(h Q -
h,) 100
h Iv
where,
h,
heat of liquid, in Btu/lb
h,p = latent heat of evaporation, in Btu/lb
hp
totaL heat of steam, in Btu/lb
8·9
CRANE
"
.i'/clV;: 7
'
t~~~eq~i¥~J2'6'mL~~o)r-~ -.r~
Theoretical Horsepower Required to Raise Water (at 60 F)
To Different Heights
~
,,",,
,~
,~
/"",
25
30
35
40
0.032
0.038
0.044
0.051
0.063
0.076
0.088
0.101
0.095
0.114
0.133
0.152
0.126
0.152
0.177
0.202
0.158
0.190
0.221
0.253
0.190
0.Z27
0.265
0.303
0.221
0.265
0.310
0.354
0.253
0.303
0.354
0.404
0.284
0.341
0.398
0.455
0.316
0.379
0.442
0.505
0.379
0.455
0.531
0.606
0.442
0.531
0.619
0.707
0.505
0.606
0.707
0.808
0.568
0.682
0.796
0.910
0.632
0.758
0.884
1.011
45
50
60
70
0.057
0.063
0.076
0.088
0.114
0.126
0.152
0.177
0.171
0.190
0.227
0.265
0.227
0.253
0.303
0.354
0.284
0.316
0.379
0.442
0.341
0.379
0.455
0.531
0.398
0.442
0.531
0.619
0.455
0.505
0.606
0.707
0.512 0.568
0.568
0.682'
0.796 0.884
%:~i!
0.682
0.758
0.910
1.061
0.796 0.910
0.884 1.011
1.06' 1.213
1.238 1.415
1.023
1.137
1.364
1.592
1.137
1.263
1.516
1.768
80
90
100
125
0.101 0.202
0.114 0.227
0.126 0.253
0.158 .0.316
0.303
0.341
0.379
0.474
0.404
0.455
0.505
0.632
0.505
0.568
0.632
0.790
0.606
0.682
0.758
0.947
0.707
0.796
0.884
1.105
0.808
0.910
1.011
1.263
0.910
1.023
1.137
1.421
1.011
1.137
1.263
1.579
1.213
1.364
1.516
1.895
1.415
1.592
1.768
2.211
1.617
1.819
2.021
2.526
1.819
2.046
2.274
2.842
2.021
2.274
2.526
3.158
150
175
200
250
0.190
0.221
0.253
0.316
0.379
0.442
0.505
0.632
0.568
0.663
0.758
0.947
0.758
0.884
1.0n
1.263
0.947
1.105
1.263
1.579
1.516
1.768
2.021
2.526
1.705
1.990
2.274
2.842
1.895
2.211
2.526
3.158
2.274
2.653
3.032
3.790
2.653
3.095
3.537
4.421
3.032
3.537
4.042
5.053
3.411
3.979
4.548
5.684
3.790
4.421
5.053
6.316
300
350
400
500
0.379
0.442
0.505
0.632
0.758
0.884
1.011
1.263
1.137
1.326
1.516
1.895
1.516
1.768
2.021
2.526
1.895
2.211
2.526
3.158
1.137 1.326
1.326 1.547
1.768
5
1.
1.8 • 2.211
2.274 1, 2.653
2.6531 3.095
3.0321 3.537
3.~01 4.421
3.032
3.537
4.042
5.053
3.411
3.979
4.548
5.684
3.790
4.421
5.053
6.316
4.548
5.305
6.063
7.579
5.305 6.063 6.821 7.579
6.190 7.074 7.958 8.842
7.074 8.084 9.095 10.11
8.842 10.11 11.37 12.63
150
175 • 200
1
250 'j 300 1 350
400
/'[U'
JJ?
f~$~"
HORSE~OW::: 33
l
~f~. ~~ (;~ 1b ~
0.316~~.:3?9 ~4421 0.50(' It ~Tc'>I"! i1~I\il~ :) -
GaI8'11125
.~
~
.-..
~.
"""
,.......
.~
1
5
10
15
20
0.1 8
0.316
0.474
0.632
0.190
0.379
0.568
0.758
0.221
0.442
0.663
0.884
0.253
0.505 0.632 tr.758 0.884 1.011
0.758 0.947 1.137 1.326 1.516
1.011 1.263 1.516 1.768 2.021
25
30
35
40
0.790
0.947
1.105
1.263
0.947
1.137
1.326
1.516
1.105
1.326
1.547
1.768
1.263
1.516
1.768
2.021
1.579
1.895
2.211
2.52q
45
50
60
70
1.421
1.579
1.895
2.211
1.705
1.895
2.274
2.653
1.990
2.211
2.653
3.095
2.274
2.526
3.032
3.537
2.84:i 3.411 3.979 4.548
3.158 3.790 4.421 5.053
3.790 4.548 5.305 6.063
4.4211 5.305 6.190 7.074
80
90
100
125
2.526
2.842
3.158
3.948
3.032
3.411
3.790
4.737
3.537
3.979
4.421
5.527
4.042 5.0~3 6.063 7~074 8.084
4.548 5.684 6.821 7.958 9.095
5.053 6·i_ 6 7.579 8.8.42 10.11
6.316
9.474 11.05 12.63
150
175
200
250
4.737
5.527
6.316
7.895
11.37
5.684 6.632 7.579 ~
6.632 7.737 8.842 I1.Q5 13.26
7.579 8.842 10.11 12.~ 15.16
9.474 11.05 12.63 115.;9, 18.95
13.26
15 .•7
17.~
22.11
15.16
17.68
20.21
25.26
300
350
9.474 11.37
n.05 13.26
12.63 15.16
15.79 18.95
13.26 15.16 18 ;95' 22.74
15.47
26.53
17.68 17.
20.21 25.26 1 30.32
22.11 25.26 31.58 37.90
26.53
30.95
35.37
44.21
30.32
35.37
40.42
50.53
400
500
1.895
2.274
2.653
3.032
7~4:
"1"'1/1.
2.211
2.653
3.095
3.5i7
Specific gravity of water ••• •.•..••••.•••••• page A·6
Specific gravity of liquids other than water • ••• page A·7
2.526
3.032
3.537
4.042
000
. "ft~lb/min
0
55
. . , .ft Ib/sec
_ -l-ov.I~Pf"l)
= 2544·,,8 ... Btu/hr
0.. - t
=
745·7 .,. watts
(whp) = QHp -;- 247000 = QP -;- 1714
(bhp) = (whp) -;- ep = QHp -;- 247000 ep
(e p )
= QH p -;- 247 000 (bhp)
where: (whp) = water horsepower
H = pump head in feet
(bhp) = brake horsepower
ep
= pump efficiency
Overall effiCiency (eo) takes into account all
losses in the pump and driver.
eo = ep eD eT
where: e D = driver efficiency
eT = transmission effiCiency
ev = volumetric efficiency
ev
(o/c) - actual pump displacement (Q) (100)
0
theoretical pump displacement (Q)
Note.' For fluids other than water, multiply
table values by specific gravity. In pumping
liquids with a viscosity considerably higher
than that of water, the pump capacity and
head are reduced. To calculate the horsepower for such flUids, pipe friction head must
be added to the elevation head to obtain the
total head; this value is inserted in the first
horsepower equation given above.
B - 10
CRANE
APPENDIX B - ENGINEERING DATA
Equivalents
Measure
Weight
I in.
I in.
Imm
I film
I micron
25.4 mm
2.54 cm
0.03937 in.
0.00328 ft
0.000001 meter
I torr
10-' torr
mm mercury
1 ntom mercury
I ft
I ft
304.8 mm
30.48 cm
I sq. in.
I sq cm
I sq cm
I sq ft
6.4516 sq cm
0.155 sq in.
0.00108 S4 ft
929.03 sq cm
Circumference
of a circle
Area of a circle
I kg = 2.205 Ib
I cu in. of water
(60 F)
I cu in. of mercury (32 F)
I cu in. of mercury (32 F)
0.073551 cu in. of mercury (32 F)
13.596 cu in. of water (60 F)
0.4905 Ib
Velocity
I ft per sec
I m per sec
0.3048 m per sec
3.2808 ft per sec
Density
211"r
11" d "-
4
I Ib per cu in.
I gr per cu cm
I Ib per cu ft
1 kg per cu m
27.68 gram per cu cm
0.03613 Ib per cu in.
16.0184 kg per cu m
0.06243 Ib per cu ft
Physical Constants
Base of Natural Logarithms (e)
Acceleration of Gravity
(g) ,
Pi (71") .. '
Absolute Zero
Water Freezing Point (14.696 psia) ,
Water Boiling Point
(14.696 psia) ,
.32.174 ft/sec'.
...........
Degree:;
1"e1vin
0
273.15
373.15
Degrees
R8nkinc
0
491.67
671.67
2.7182818285
, , , (980.665 cm/sec')
3.1415926536
Degrees
Celsius
- 273.15
0
100
Degree:;
Fahrenheit
- 459.67
32
212
~.
-,
Equivalents of Temperature
To convert degrees Celsius to degrees Fnhrenheit:
t = 1.8 tc + 32
To convert degrees Fnhrenheit to degrees Celsius:
t - 32
tc =
1.8
\\·hcrc.
tcnlpcruturL', in degrees C:c}:..;ius
Prefixes
atto ..... a .... one-quintillionth .................... .
femto ... f .. ,,' one-quadrillionth ................... .
pi co .... p .... one-trillionth ....................... .
nano ... n .... one-hillionth ....................... .
micro .. }1 .••• one-millionth ........................ .
0.000 000 000 000 000 001. .. 10- 18
0.000 000 000 000 001 ....... 10'-10
0.000 000 000 001. ........... 10- 12
0.000 000 001 ................ 10- 9
0.000 001 .................... IO- G
milli .... m ... one-thousandth ..................... .
centi. ... c .... one-hundredth ...................... .
Lleci .... d .... one-tenth ........................... .
tlni .......... one. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
deka .... da ... ten ..................................
0.001
0.01
0.1
1.0
10.0
hecto ... h .... one hundred ........................ 100.0
kilo ..... k .... one thousand ....................... 1 000.0
mega ... M ... one million .......... _......... 1 000 000.0
giga ..... G ... one hillion ................. 1 000 000 000.0
tera ..... T ... one trillion ............ l 000000000000.0
· ................... 10-'
· ................... 10- 2
· ................... 10- 1
· ................•.. lOll
· ................... 10 1
· .. , ................ 10"
· ................... 10:l
· ................... lOU,
· ................... 10 9
· ................... 10"
,~
CRANE
8·11
APPENDIX B-ENGINEERING DATA
Equivalents of
Liquid Measures and Weights
----------
- - - - - - - _.....
TO OBTAIN
\1ULTIPLY
BY
U.S.
Gallon
LS. Gallon
U.S.
Pound
Water*
r.S.
U.S.
Cuhic
Liter
Cubic
\Ieter
8.
8.:-\37
0.13368
2:31.
3.78.')33
0.003785
9.607S2
10.
0.160.'>4
277.42
·L~4.'>96
0.004546
1.042
0.01671
28.875
0.473166
0.000473
0.016035
27.708
0.45405
0,0004S4
21Ul702
0.028317
0.016387
0.0000164
Imperial
Gallon
U.S.
Pint
0.8:n
Imperial Gallon
1.2009
l'.S. Pint
0.125
0.1041
U.S. Pound Watpr"
0.1199.'>
0, I
0.%96
U.S, Cubic Foot
7.480.~2
6,22888
.'>9.8442
62,36.')
U.S. Cubic In('h
0.004329
0,0036]
0.0:346:32
0.03609
0.0005787
Litpr
0.2641779
0.2199756
2,ll.j423
2.202
0.0:353154
Cubi" \1('!pr
219,969
264.170
2113,34
1728 .
:35.:)1446
2202.
0.001000
61.02509
999.972
6102:'\,38
1 Barrt'l = 42 gallon" (pt'lrolt'ulll llwa,urt')
'Watpr at 60 F 11:;.6(;)
Equivalents of Pressure and Head
.-
TO OBTAIN
MULTIPLY
-Ib/in'
Ib/fl 2
B\
Atmos-
1
fl.
kg/em,1
on,
bar
Fit
0,00689.)
0.000479
0.0000479
760.
1.01325
0.101325
735,559
0,98067
0,098067
0.073556
0.000098
0.0000098
0.073430
1,8651
0,00249
0.000249
I
0.88115
22.3813
0.029839
0,0029839
0.1926
0.01605
0, 01 4J:l9
10332.27
407.484
33.9570
29.921
1
10000.
;;9438
3VI650
28.959
0.003287
0.002896
0.08333
0.070307
I
0,000473
0.000488
1.0332
(MPa)~
0.06895
2.3106
0.068046
megapascal
(32 Fit
27.7276
144.
mm
kg/m'
I
pheres
\
Ibitn 2
----
703.070
4.88241
0.35913
Iblft'
0.0069445
Atmospheres
14.696
2116,22
1
kg/em'
14.2233
2048.15"
0.96784
kg!m'
0.001422
0,204768
0,0000968
0.0001
1
in. wafer-
0.036092
5.1972
O.OO24S4
0.00253
25.375
1
fi. water·
0.432781
62.320S
0.029449
0.03043
:l04.275
12.
in. mereuryt
0.1911S4
70,7262
0.03:1421
O.034S3
345,316
13,6185
1.1349
1
2S.40005
0,033864
0.0033864
mm mercuryt
0.0193,>68
2.78450
0.0013158
Q,0013595
1:1,59509
0,5:1616
0.044680
0.03937
I
0.001333
0.0001333
bart
14.5038
2088.55
0.98692
1,01972
10197,2
402,156
;>:>.5130
29.s:l00
7:;0,062
I
MPa~
14~.038
20885.5
9.8692
10.1972
101972.0
4021.56
335,130
290.300
7500,62
~-----
,,,,,,,,,-
L ..."
• Water at 68 F (20C)
0.03944
10.0
-"
tmercury at 32 F (0 C)
tl MPa (megapascal) = 10 bar = 1,000,000 N /m 2 (newton/meler»
To convert from one set of units to another, locate Ihe given unil in
the left hand column, and multiply the numerical value by Ihe foetor shown horizontally to the r;ghl, under Ihe set of units desired.
0.10
1
1-12
CRANE
APPENDIX B - ENGINEERING DATA
Four-Place Logarithms to Base 10
The logarithms to base 10 of numbers between 1 and 10, correct to four
places, are given in the tables shown on this and the following page.
I f the decimal point in the number is moved n
places to the right (or left), the value of n (or -n)
is added to the logarithm, thus:
the fourth figure, as read in the proportional parts
section of the table,
Thus, the logarithm of 3, 1416 is found as follows:
3,14 =0.4969
log 314,
=0.4969+2 or 2.4969
log
,0314=0.4969-2, which may be written 2.4969
or 8.4969 - IO
If the given number has :nore than four significant
figures, it should be reduced to four figures, since
those beyond four figures will not affect the result
in four-place computations.
The logarithm of a number having four significant
figures must be interpolated by adding to the logarithm of the three figure number, the amount under
log ab
a. Reduce the number to four significant
: 3.142
b. The log of J. [4 is .4969
c. The value of the proportional part under 2
(the fourth figure) is 3
d, Then, the log 3,142 0.4969+,0003 or 0.4972
Natural1ogarithms: Many calculations make use
of natural logarithms (Base e
2,7183), To convert base 10 (common) logarithms to natural logarithms, multiply the value for the former by 2,30258.
Natural logarithms are also called Hyperbolic or
Naperian logarithms.
log an=n log a
n[log a
log "Ii a=-n
log a+ log b
a
log b=log a-log b
•
1
2
3
4
5
6
1.'
1.1
1.2
1.3
1.4
0000
0414
0792
1139
1461
0043
0453
0828
1173
1492
0086
0492
0864
1206
1523
0128
0531
0899
1239
1553
0170
0569
0934
1271
1584
0212
0607
0969
1303
1614
1.5
1.6
1.7
1.8
1.9
1761
2041
2304
2553
2788
1790
2068
2330
2577
2810
1818
2095
2355
2601
2833
1847
2122
2380
2625
2856
1875
2148
2405
2648
2878
2.'
2.1
2.2
2.3
2.4
3010
3222
3424
3617
3802
3032
3243
3444
3636
3820
3054
3263
3464
3655
3838
3075
3284
3483
3674
3856
2.5
2.6
2.7
2.8
2.9
3979
4150
4314
4472
4624
3997
4166
4330
4487
4639
4014
4183
4346
4502
4654
3.'
3.1
3.2
3.3
3.4
4771
4914
5051
5185
5315
4786
4928
5065
5198
5328
3.5
3.6
3.7
3.8
3.9
5441
5563
5682
5798
5911
N
•
~
I
Proportional Parts
!
7
8
9
0253
0645
1004
1335
1644
0294
0682
1038
1367
1673
0334
0719
1072
1399
1703
0374
0755
1106
1430
1732
4
4
3
3
3
8 12 17 21 25 29 33 37
8 11 15 19 23 26 30 34
7 10 14 17 21 24 28 31
6 10 13 16 19 23 26 29
6 9 12 15 18 21 24 27
1903
2175
2430
2672
2900
1931
2201
2455
2695
2923
1959
2227
2480
2718
2945
1987
2253
2504
2742
2967
2014
2279
2529
2765
2989
3
3
2
2
2
6
5
5
5
4
8 11 14 17 20 22 25
8 11 13 16 18 21 24
7 10 12 15 17 20 22
7 9 12 14 16 19 21
7 9 11 13 16 18 20
3096
3304
3502
3692
3874
3118
3324
3522
3711
3892
3139
3345
3541
3729
3909
3160
3365
3560
3747
3927
3181
3385
3579
3766
3945
3201
3404
3598
3784
3962
2
2
2
2
2
4
4
4
4
4
6
6
6
6
5
4031
4200
4362
4518
4669
4048
4216
4378
4533
4683
4065
4232
4393
4548
4698
4082
4249
4409
4564
4713
4099
4265
4425
4579
4728
4116
4281
4440
4594
4742
4133
4298
4456
4609
4757
2
2
2
2
1
3
3
3
3
3
5
5
5
5
4
4800
4942
5079
5211
5340
4814
4955
5092
5224
5353
4829
4969
5105
5237
5366
4843
4983
5119
5250
5378
4857
4997
5132
5263
5391
4871
5011
5145
5276
5403
4886
5024
5159
5289
5416
4900
5038
5172
5302
5428
1
1
1
1
1
3
3
3
3
3
4
4
4
4
4
6
6
5
5
5
7 9 10 11 13
8 10 11 12
7 8 9 11 12
6 8 9 10 12
6 8 9 10 11
5453
5575
5694
5809
5922
5465
5587
5705
5821
5933
5478
5599
5717
5832
5944
5490
5611
5729
5843
5955
5502
5623
5740
5855
5966
5514
5635
5752
5866
5977
5527
5647
5763
5877
5988
5539
5658
5775
5888
5999
5551
5670
5786
5899
6010
1
1
1
1
1
2
2
2
2
2
4
4
3
3
3
5
5
5
5
4
6
6
6
6
5
1
2
3
4
5
6
7
8
9
I
I
I
I
1 2 3 4 5 6 7 8 9
8 11 13 15 17 19
8 10 12 14 16 18
8 10 12 14 15 17
7 9 11 13 15 17
7 9 11 12 14 16
7 9 10 12 14 15
8 10 11 13 15
6 8 9 11 13 14
6 8 9 11 12 14
6 7 9 10 12 13
7
7
7
7
7
7
7
9 10 11
8 10 11
8 9 10
8 9 10
8 9 10
1 2 3 4 5 6 7 8 9
CRANE
B·13
APPENDIX B - ENGINEERING DATA
continued
Four-Place Logarithms to Base 10
Proportional Parts
0
N
2
1
3
4
5
7
6
8
9
II
I
I
1 2 3 4 5 6 7 8 9
4.0
4.1
4.2
4.3
4.4
6021
6128
6232
6335
6435
6031
6138
6243
6345
6444
6042
6149
6253
6355
6454
6053
6160
6263
6365
6464
6064
6170
6274
6375
6474
6075
6180
6284
6385
6484
6085
6191
6294
6395
6493
6096
6201
6304
6405
6503
6107
6212
6314
6415
6513
6117
6222
6325
6425
6522
2
2
2
2
2
3
3
3
3
3
4
4
4
4
4
5
5
5
5
5
6
6
6
6
6
8
7
7
7
7
9 10
8 9
8 9
8 9
8 9
4.5
4.6
4.7
4.8
4.9
6532
6628
6721
6812
6902
6542
6637
6730
6821
6911
6551
6646
6739
6830
6920
6561
6656
6749
6839
6928
6571
6665
6758
6848
6937
6580
6675
6767
6857
6946
6590
6684
6776
6866
6955
6599
6693
6785
6875
6964
6609
6702
6794
6884
6972
6618
6712
6803
6893
6981
1 2 3
1 2 3
1 2 3
1 2 3
1 2 3
4
4
4
4
4
5
5
5
4
4
6
6
5
5
5
7
7
6
6
6
8
7
7
7
7
9
8
8
8
8
5.1
5.2
5.3
5.4
5.0
6990
7076
7160
7243
7324
6998
7084
7168
7251
7332
7007
7093
7177
7259
7340
7016
7101
7185
7267
7348
7024
7110
7193
7275
7356
7033
7118
7202
7284
7364
7042
7126
7210
7292
7372
7050
7135
7218
7300
7380
7059
7143
7226
7308
7388
7067
7152
7235
7316
7396
1
1
1
1
1
2
2
2
2
2
3
3
2
2
2
3
3
3
3
3
4
4
4
4
4
5
5
5
5
5
6
6
6
6
6
7
7
7
6
6
8
8
7
7
7
5.5
5.6
5.7
5.8
5.9
7404
7482
7559
7634
7709
7412
7490
7566
7642
7716
7419
7497
7574
7649
7723
7427
7505
7582
7657
7731
7435
7513
7589
7664
773"
7443
7520
7597
7672
7745
7451
7528
7604
7679
7752
7459
7536
7612
7686
7760
7466
7543
7619
7694
7767
7474
7551
7627
7701
7774
1
1
1
1
1
2
2
2
1
1
2
2
2
2
2
3
3
3
3
3
4
4
4
4
4
5
5
5
4
4
5
5
5
5
5
6
6
6
6
6
7
7
7
7
7
6.1
6.2
6.3
6.4
6.0
7782
7853
7924
7993
8062
7789
7860
7931
8000
8069
7796
7868
7938
8007
8075
7803
7875
7945
8014
8082
7810
7882
7952
8021
8089
7818
7889
7959
8028
8096
7825
7896
7966
8035
8102
7832
7903
7973
8041
8109
7839
7910
7980
8048
8116
7846
7917
7987
8055
8122
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
3
3
3
3
3
4
4
3
3
3
4
4
4
4
4
5
5
5
5
5
6
6
6
5
5
6
6
6
6
6
6.5
6.6
6.7
6.8
6.9
8129
8195
8261
8325
8388
8136
8202
8267
8331
8a95
8142
8209
8274
8338
8401
8149
8215
8280
8344
8407
8156
8222
8287
8351
8414
8162
8228
8293
8357
8420
8169
8235
8299
8363
8426
8176
8241
8306
8370
8432
8182
8248
8312
8376
8439
8189
8254
8319
8382
8445
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
3
3
3
3
2
3
3
3
3
3
4
4
4
4
4
5
5
5
4
4
5
5
5
5
5
6
6
6
6
6
7.0
7.1
7.2
7.3
7.4
8451
8513
8573
8633
8692
8457
8519
8579
8639
8698
8463
8525
8585
8645
8704
8470
8531
8591
8651
8710
8476
8537
8597
8657
8716
8482
8543
8603
8663
8722
8488
8549
8609
8669
8727
8494
8555
8615
8675
8733
8500
8561
8621
8681
8739
8506
8567
8627
8686
8745
1
1
1
1
1
1 2 2 3
1 2 2 3
1 2 2 3
1 2 2 3
1 2 2 3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
6
5
5
5
5
7.5
7.6
7.7
7.8
7.9
8751
8808
8865
8921
8976
8756
8814
8871
8927
8982
8762
8820
8876
8932
8987
8768
8825
8882
8938
8993
8774
8831
8887
8943
8998
8779
8837
8893
8949
9004
8785
8842
8899
8954
9009
8791
8848
8904
8960
9015
8797
8854
8910
8965
9020
8802
8859
8915
8971
9025
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
5
5
4
4
4
5
5
5
5
5
8.0
8.1
8.2
8.3
8.4
9031
9085
9138
9191
9243
9036
9090
9143
9196
9248
9042
9096
9149
9201
9253
9047
9101
9154
9206
9258
9053
9106
9159
9212
9263
9058
9112
9165
9217
9269
9063
9117
9170
9222
9274
9069
9122
9175
9227
9279
9074
9128
9180
9232
9284
9079
9133
9186
9238
9289
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
8.5
8.6
8.7
8.8
8.9
9294
9345
9395
9445
9494
9299
9350
9400
9450
9499
9304
9355
9405
9455
9504
9309
9360
9410
9460
9509
9315
9365
9415
9465
9513
9320
9370
9420
9469
9518
9325
9375
9425
9474
9523
9330
9380
9430
9479
9528
9335
9385
9435
9484
9533
9340
9390
9440
9489
9538
1
1
0
0
0
1 2 2 3
1 2 2 3
1 1 2 2
1 1 2 2
1 1 2 2
3
3
3
3
3
4
4
3
3
3
4
4
4
4
4
5
5
4
4
4
9.0
9.1
9.2
9.3
9.4
9542
9590
9638
9685
9731
9547
9595
9643
9689
9736
9552
9600
9647
9694
9741
9557
9605
9652
9699
9745
9562
9609
9657
9703
9750
9566
9614
9661
9708
9754
9571
9619
9666
9713
9759
9576
9624
9671
9717
I 9763
9581
9628
9675
9722
9768
9586
9633
9680
9727
9773
9.5
9.6
9.7
9.8
9.9
9777
9823
9782
9827
9786
9832
9877
9921
9965
9791
9836
I 9881
9926
9969
9795
9841
9886
9930
9974
9800
9805
9845
9850
9890 I 9894
9934
9939
9978
9983
9809
9854
9899
9943
9987
2
I
6
7
9912 i "
9917
....
"
9956
9961
N
I
0
I
0 1 1 2 2 3 3 4 4
Ii 00 11 11 22 22 33 33 44 44
0 1 1 2 2 3 3 4 4
0 1 1 2 2 3 3 4 4
9818 Ii
9814
9859
9863
9903
9908
9948 iI 9952
9991 I 9996
I
I
I
i
II
0
0
0
0
0
1
1
1
1
1
2
2
2
2
1 2
1
1
1
1
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
3
4
4
4
4
4
i
1
3
4
5
8
9
1 2 3 4 5 6 7 8 9
CRANE
APPENDIX B - ENGINEERING DATA
Flow of Water Through Schedule 40 Steel Pipe
Pressure Drop per 100 feet and Velocity in Schedule 40 Pipe for Water at 60 F.
Discharge
Veloc- Press. Veloc- Press.
hy
Drop
ity
Drop
Veloc- Press,
ity
Drop
Feet
Feet
Lbs.
Gallons
per
Cubic Ft.
per
per
Minute
Second
Second
0.000446
0.000668
0.000891
0.00111
0.00134
0.00178
1..13
1.69
2.26
.2
.3
.4
.5
.6
.8
I
2
3
4
5
Feet
Lbs.
per
a
o
1.86
4.22
6.98
10.5
14.7
25,0
2.82
3.39
4.52
0.359
0.903 0.504
1.61 , 0.672
2.39 I' 0.840
3.29
1.01
5.44 11.34
I
I
I
2
per
per
. per
Second Sq. In
per
64.1
111.2
8J~~1 8~gl
2"
a 574
25
30
35
40
45
0.05570
0.06684
0.07798
0.08911
0.1003
2.39
2.87
3.35
3.8J
4.30
0.234
0.327
0.436
0.556,
0.668
50
60
70
80
90
0.1114
0.1337
0.1560
0.1782
0.2005
4
lao
0.2228
0.2785
0.3342
0.3899
0.4456
840
110 .08
51. 9
!3 .44
91. 1
0.046 1
3"
0.094,
0.158, 0.868
0.056
15.8
27,7
42.4
J.61
4.81
6.02
9.03
12.OJ
3 1/2"
ity
Lbs
per
per
Second Sq. In.
0.429
0.044
0.858
3.84
6.60
9.99
21.6
37.8
2.23
2.97
3.71
'j ,57
7.43
1.073
0.044
O. 090, 0.473
0. 150 18ng
0.043
0.071
0.104
I. 29
1.72
2.15
J .22
4.29
0.946
0.518, 1.26
0.774, 1.58
1.63 ' 2.37
2.78 3.16
0.145
0.241
0.361
0.755
1.28
4.22
5.92
7.90
10.24
12.80
3.94
4.73
5.52
6.30
7.09
1.93
2.72
3.64
4.65
5.85
15.66
22.2
7.88
9.47
11.05
12 .62
1420
13.71
~: ~::I
0.083 0
0.114 0
0.151 I
0.192 I
0.239 1
4"
9.28
0.041
0.056
11.14
0.07) a 882
0.04112.99
0.05214.85
0.095 I 01
0.117 1.13
0.064
7
8
0.839,1 2 17
1.18 ' 2.60
1.59 3.04
2.03 3.47
2.53 3.91
0.288
0.406
0.540
0.687
0.801
0.142
0,204
0.261
0.334
0.416
0.076
0.107
0.143
0.180
0.224
.12
.2il
.44
0.047
0.060
0.074
9 56
11.97
14.30
16.75
19.14
3.09
4.71
6.09
S.97
11.68
4.34
5.43
6.51
7.60
8.68
1.05
I. 61
2.24
3.00
3.87
.52
0.509
15
0.769
1.08 3.78
1.44 4.4 I
5.04
1. 85
0.272
0.415
0.580
0.774
0.985
1.60
2.01
2.41
2.81
3.21
0.090 1.11
0.135 1.39
0.190 l.b7
0.253 1.94
0.323 2.22
O. 036 I 5 . 78
0.0551972
0.077
14.63
9
77
4.83
5.93
7.14
8.36
9.89
2.32
2.S4
3.40
4.02
4.09
1.23
1.46
1. 79
2.11
2.47
J.61
401
4.41
4.81
5.21
0.401 2
0.495' 2
0.583 3
0.683, J
0.797' J
0.162 1.44
0.195 1.,,0
0.234 1.70
0.275, 1.92
0.320' 2.08
0.043
0.051
0.061
0.071
0.083
5.41
6.18
7.03
7.89
8.80
2.84
3.25
3.68
4.12
4.60
0.91913
0.367[2.24
0,416,2.40
0,471,2.56
0.529' 2. 7J
0.590 2.89
0.095
0.108
0.121
0.136
0.151
3.04
J .21
3.53
385
4.17
0.166
0.182
0.219
0.258
0.301
5
6
.09
.30
.52
.74
.95
J
4
4
5
6
16.7
23.8
32.2
41.5
5"
6"
8: 19~
3~5
0.5013
0.557
0.6127
0.6684
0.7241
350
375
400
425
450
0.7798
0.8355
0.8912
0.9469
1.003
475
500
550
1.059
1.114
1.225
1.93
2.03
2.24
2~1
g:g~~1
700
750
800
850
900
1.560
1.671
1.782
1.894
2.005
2.85
3.05
325
346
3.b6
0.112,2.01
0.12712.15
0.143,2.29
0.160,2.44
0.179'1' 2.58
0,047
0.054
0.061
0,068
0.075
9 50
1 00 0
1100
1 200
1300
2.117
2.228
2.451
2.674
2.896
3.86
407
4.48
4 81\
'5.29
0,198 2
0.218· 2
0,260 3
0.306, J
0.35513
0.083 2.25
0.091 2.37
0.11012.61
0.128 2.85
0.150 3.08
0.052
0.057 1
0.0681
0.080 2
0.093.2
1400
1500
1600
1800
2000
3.119
3.342
3.565
4.010
4.456
15.70
,6.10
, 6 51
1'732
8.14
0,4091
0.4661
0.5271
0.663
0 .. 808
0.171 ' 3.32
0.195 3.56
0.219 3.7')
1
0.276,427
0.339 4.74
0.10712
0.122 2
0.138 2
0.172 3
0.209 J
0.0551
0.063
0.071
0.088
0.107
2500
3000
3500
4000
4500
5.570
".684
7.798
8.912
10.03
10.17
il2.20
'14.24
'16.27
11831
1.24! 717
1.76, 8.M
2.38 ,10m
3.08 ;I1.47
3.87112.90
0.515 5.~l3
0.731 7.11
0.98218.30
1.27 948
1.60 10.67
0.321: 4.54
0.4511545
0.607" 35
0,787 7.26
0.990i 8.17
0.1631359
0.232 4.30
0.312 5 02
0.401 5.74
0.503, b 4t'
g:?i~ 3.46
0.173 4.04
0.222,4.b2
0,280,5.20
I 03
0.0751
24"
0.101
,22.44
0.129: .19
0.052'25.65
0.162,3.59
0.06528.87
5000
6000
7000
8000
9000
11.14
13.37
15.60
17.82
20.05
120.35
24.41
28.40
4.71 14.33
6.741720
9.11 20.07
1.95,11.85
2,77 14.21
3.74,16.,,0
4.841'18.96
6.09 21.34
1.21
1.71
2.31
2.99
3.76
0,617' 7.17
0.877' 8.61
1.18110.04
1.51 11.47
1.90 12.91
0.340 ' 5.77
0,483 6.93
0.652 R.OI<
0.839,1 'J.n
1.05,1039
0.1991 J
0.280 4
0.376,5
0.488,
0.6081
11.94
1300
14 12
10"
U~~
l~ggg iU~
Ii ~g 5
20 000
10.85
5>115:
40
44.56
i,
0.054
0.059
0.07L
2193
25.79
I,·~ .
5.12
5.65
6.79
12"
8.04
14"
.02
13
0.042
0.047
16"
1
U~ 11
26.9
41.4
4
5
7.62
8.02
R.B2
16~~
1.64
1.81
2.17
2.55
2.98
6
6
11.23
12.03
.12.83
13.64
14.44
3.43
3.92
4.43
5.00
5.581
1.35 4.49
1.55 4.81
1.75
5.13
1.96 ' 5 45
2.18
5.77
0.343
0.392
0.443
0,497
0.554
115.24
6.21 10.
6.84 II
8.23.12
1'1143
2.42 C
2.68
3.22 1
3
4 .'4851 1
0.613
0.675
0.807
0.948
1.11
5.13 8.98
5.85 9.62
6.61 10.20
8.3711.54
10.3112.82
1.28
1.46
1.65
2.08
2.55
1~24
3.94
5.59
7.56
9.80
12.2
1604
0.042
0.0481
O~
17.59
22.0
1.33
1,48
17.6>
9
10./i9
12.71
14.52
16.34
7.15
10.21
8"
225
250
275
300
~g
Drop
Feet
11;4"
0.6001 0.60£
2.10
1.20
4.33
1.81
7.42 2.41
11.2
J.OI
2%"
0.765
0.956
1.43
1.91
Iff
0.408, 0.481
5.04
6."'
Veloc- Press.
3,4"
0.0611
0.086
3~:i8 i ~j~
0.00223
0.00446
0.00668
0.00891
0.01114
0.01337
0.01782
0.02228
0.03342
0.04456
125
150
175
200
Lbs.
Sp.cnnd Sq. In. Second
8
10
15
20
I)
Veloc- Press. Veloc- Press. Veloc- Press.
ity
Drop
ity
Drop
ity
Drop
Feet
Lbs.
Feet
Lbs.
Feet
Lbs.
Veloc- Press.
ity
Drop
Feet
Lbs
7
15.55
16.66
1777
19.99
[22.21
18"
0.050
0.060
5
5
20"
0.653
0.720
0.861
1.02
LIS
0.079
0.111
0.150
0.192
0.242
1~:j6 li~~} t~~ l'iU~ Uj I'liii U~ 11U~ ?:~~9[ ~:~~ g:~i:
1
:.•• '.133. '.1.9
8.89
.,~3025.0641
n
36. J I
~:~j ~~g~
7.31 ,2582
9.032" 69
U~ iltl~
4.0320.77
4.93 m OR
U~ [i U~
2.32 14.36
2.86 15.06
g:~~~
0.907
1"'. .::.12"---_'-'-_"'""7-'-----:.
For pipe lengths other than 100 feet. the-pressurcdropispr:;portionarto-t.:;h-e----"-'-----':.:.;\=.re~1i'-o'---c7it-YIsa-fGnci:Tor;-;fthe cro~s sectional
flow area; thus, it is constant for a given
length. Thus, for 50 feet of pipe, the pressure drop is approximately
the value given in the table.
for 300 feet, three times the given
flow rate and is independent of pipe length.
Fo, calcula,ions for pipe o,her ,han Schedule 40, see explanation on nex' page.
8-15
APPENDIX 8- ENGINEERING DATA
CRANE
Flow of Air Through Schedule 40 Steel Pipe
- - - , - - ,....
For lengths of pipe other than
100 feet, the pressure drop is
proportional to the length.
Thus, for 50 feet of pipe, the
pressure drop is approximately
one-half the value gi ven in the
table ... for 300 feet, three
times the given value, etc.
The pressure drop is also inversely proportional to the
absolute pressure and directly
proportional to the absolute
temperature.
Therefore, to determine the
pressure drop for inlet or average pressures other than 100
psi and at temperatures other
than 60 F, multiply the va4les
given in the table by the ratio:
,.----.
t)
100 + 147 )(460 +
( P + 14.7
520
where:
"P" is Lhe inlet or average
gauge pressure in pounds per
square inch, and,
.. (. is the temperature in
degrees Fahrenheit under
consideration.
The cubic feet per minute of
compressed air at any pressure is inversely proportional
to the absolute pressure and
directly proportional to the
absolute temperature.
·T0 determine the cubic feet
per minute of compressed air
at any temperature and pressure other than standard conditions, multiply the value of
cubic feet per minute of free
air by the ratio:
t)
147 )(460 +
( 14.7 + P "'520
Calclliation" for Pipe
Other than Schedllie 40
To determine the velocity of
water, or the pressure drop
of water or air, through pipe
other than Schedule 40, use
the following formulas:
Va = V40
C~o
r
r
APa = AP•• ( ~o
Subscript "a" refers to the
Schedule of pipe through
which velocity or pressure
drop is desired.
Subscript "40" refers to the
velocity or pressure drop
through Schedule 40 pipe, as
given in the tables on these
facing pages.
Free Air
q'm
Compressed Air
Pressure Drop of Air
In Pounds per Square Inch
Per 100 Feet of Schedule 40 Pipe
For Air at 100 Pounds per Square Inch
Gauge Pressure and 60 F Temperature
Cubic Feet Cubic Feet
Per Minute Per Minute
at 60 F and at bOF and
100 psig
14.7 psia
IfsN
1/4"
3,4"
1/2 "
1
2
3
4
5
0.128
0.256
0.384
0.513
0.641
0.361
1.31
3.06
4.83
7.45
0,083
0.285
0.605
1.04
1.58
0.018
0.064
0.133
0.226
0.343
0.020
3,4"
0.042
0.071 i
0.106 : 0.027
6
8
10
15
20
0.769
1.025
1.282
1.922
2.563
10.6
18.6
28.7
2.23
3.89
5.96
13.0
22.8
0.408
0.848
1.26
2.73
4.76
0.148
0.255
0.356
0.S34
1.43
0.037
0.062
0.094
0.201
0.345
0.019
0.029
0.062
0.102
25
30
35
40
45
3.204
3.845
4.486
5.126
5.767
35.6
7.34
10.5
14.2
18.4
23.1
2.21
3.15
4.24
5.49
6.90
0.526
0.748
1.00
1.30
1.62
0.156
0.219
0.293
0.379
0.474
...
...
...
...
...
...
...
..,
...
. ..
. ..
0.067
0.094
0.126
0.162
0.203
33.2
7.69
11.9
17.0
23.1
30.0
2.21
3.39
4.87
6.60
8.54
0.534
0.825
1.17
1.58
2.05
0.247
0.380
0.537
0.727
0.937
0.070
0.107
0.151
0.205
0.264
37.9
10.8
13.3
16.0
19.0
22.3
2.59
3.18
3.83
4.56
5.32
1.19
1.45
1.75
2.07
2.42
0.331
0.404
0.484
0.573
0.673
..
25.8
29.6
33.6
37.9
6.17
7.05
8.02
9.01
10.2
2.80
3.20
3.64
4.09
4.59
0.776
0.887
1.00
1.13
1.26
..
...
11.3
12.5
15.1
IS.0
11.1
5.09
5.61
6.79
8.04
9.43
1.40
1.55
1.87
2.21
1.60
0.032
0.036
0.041
0.046
0.051
6"
24.3
17.9
31.8
35.9
40.2
1'0.9
12.6
14.2
16.0
18.0
3.00
3.44
3.90
4.40
4.91
0.178
0.197
0.236
0.279
0.327
0.057
0.063
0.075
0.089
0.103
0.023
O.(}M
0.030
0.035
0.041
...
20.0
22.1
26.7
31.8
37.3
5.47
6.06
7.29
8.63
10.1
0.718
0.824
0.931
1.18
1.45
0.377
0.431
0.490
0.616
0.757
0.119
0.136
0.154
0.193
0.237
0.047
0.054
0.061
0.075
0.094
0.023
4.76
6.82
9.23
12.1
15.3
2.25
3.20
4.33
5.66
7.16
1.17
1.67
2.26
2.94
3.69
0.366
0.514
0.709
0.919
1.16
0,143
0.204
0.276
0.358
0.450
0.035
0.051
0.068
0.088
O.lll
0.016
0.022
0.028
0.035
12"
18.8
27.1
36.9
8.85
1l.7
17.2
22.5
28.5
4.56
6.57
8.94
11.7
14.9
1.42
2.76
3.59
4.54
0.552
0.794
1.07
1.39
1.76
0,136
0.195
0.262
0.339
0.427
0.043
0.061
0.082
0.107
0.134
0.018
0.025
0.034
0.044
0.055
·.....
35.2
. ..
. ..
18.4
22.2
26.4
31.0
36.0
5.60
6.78
8.07
9.47
1I.0
2.16
2.62
3.09
3.63
4.21
0.526
0.633
0.753
0.884
1.02
0.164
0.197
0.234
0.273
0.316
0.067
0.081
0.0%
0.112
0.129
..
12.6
14.3
18.2
22.4
27.1
4.64
5,50
6.96
8.60
10.4
1.17
1.33
1.68
2.01
2.50
0.364
0.411
0.520
0.642
0.771
0.148
0.167
0.213
0.260
0.314
32.3
37.9
12.4
14.5
16.9
19.3
2.97
3.49
4.04
4.64
0.918
0.371
0.435
0.505
0.520
12.82
16.02
19.22
22.43
25.63
0.029
0.044
0.062
0.083
0.107
0.021
0.028
0.036
3%"
225
250
275
300
325
28.84
32.04
35.24
38.45
41.65
0.134 : 0.045
0.164
0.055
0.066
0.191
0.232
0.078
0.090
0.270
0.022
0.027
0.032
0.037
0.043
350
375
400
425
450
44.87
48.06
51.26
54.47
57.67
0.313
0.356
0.402
0.452
0.507
0.104
0.119
0.134
0.151
0.168
0.050
0.057
0.064
0.072
0.081
0.030
0.034
0.038
0.042
475
500
550
600
650
60.88
64.08
70.49
76.90
83.30
0.562
0.623
0.749
0.887
1.04
0.187
0.206
0.248
0.293
0.342
0.089
0.099
0.118
0.139
0.163
0.047
0.052
0.062
0.073
0.086
5"
700
750
800
850
900
89.71
96.11
102.5
108.9
115.3
1.19
1.36
1.55
1.74
1.95
0.395
0.451
0.513
0.576
0.642
0.188
0.214
0.244
0.274
0.305
0.099
0.113
0.127
0.144
0.160
950
1000
1100
1200
1300
121.8
128.2
141.0
153.8
166.6
2.18
2.40
2.89
3.44
4.01
0.715
0.788
0.948
1.13
1.32
0.340
0.375
0.451
0.533
0.626
1400
1500
1600
1800
2000
179.4
192.2
205.1
230.7
256.3
4.65
5.31
6.04
7.65
9.44
1.52
1.74
1.97
2.50
3.06
2500
3000
3500
4000
4500
320.4
384.5
448.6
512.6
576.7
14.7
21.1
28.8
37.6
47.6
5000
6000
7000
8000
9000
640.8
769.0
897.1
1025
lI53
10000
11 000
12 000
13000
14000
1182
1410
1538
1666
1794
...
...
...
..
...
...
...
...
...
15000
16000
18000
20000
22000
1922
2051
2307
2563
2820
ift!
...
...
...
...
2"
0.149
0.200
0.270
0.350
0.437
100
125
150
175
200
24000
26000
28000
30000
0.019
0.026
0.035
0.044
0.055
0.578
0.819
1.10
1.43
1.80
...
...
...
0.019
0.023
...
0.039
0.055
0.073
0.095
0.116
1.99
2.85
3.&3
4.96
6.25
2%"
...
1112"
0.026
8.49
12.2
16.5
21.4
27.0
28.5
40.7
6.40S
7.690
8.971
10.25
11.53
...
1111"
0.019
0.027
0.036
0.046
0.058
50
60
70
80
90
'"
1"
3"
·....
. ..
...
...
. ..
...
...
· ..
...
.. .
. ..
...
...
..
...
. ..
" .
...
. ..
. ..
. ..
...
. ..
. ..
. ..
4"
.
. ..
. ..
...
...
. ..
...
...
..
...
..
...
..
..
..
2.03
. ..
."
...
...
..
...
...
...
...
8"
10"
1.12
1.25
1.42
1l.8
13.5
15.3
19.3
23.9
37.3
8-16
APPENDIX 8
ENGINEERING DATA
CRANE
PIPE DATA
Carbon and Alloy Steel -
Stainless Steel
(also see next three pages)
:'>Iominal
Pipe
Size
Out.side
Diam.
Inches
Inches
Inside
Diameter
Area
of
Metal
(d)
Inches
Square
Inches
Transverse • Moment Weight Weight External Section
Pipe
Water Surface Modulus
Internal Area
of
Inertia
(n)
!
(A)
(I)
Pounds Pounds Sq. Ft.
Square Square
per
per foot per foot
Inches'
foot
of pipe of pipe
Inches
Feel
I
~~==~==~===~===
lOS
.049
.307
.0548
.0740 i00051~
.00088
.19
.032
.106
.00437
0.405
STD
40
40S
.068
.269
.0720
.0568
.00040 .00106
.24
.025
.106
,00523
80
XS
.215
.0925
.0364
.00025 .00122
.31
.016
,106
.00602
80S
.095
----~--.~.~.-+·--.~.~.~--1~0~·:·········~~~,O~6-5~+--.4~1-0-4--.0~9~70-~--.1-32-~0~
7~9~--.~3·3--+--,057·--~,~1~41--r-.0~1~0~32~
0.540
40
SID
40S
.088
,364
.1250
.1041
31.42
.043
.141
.01227
XS
80
.119
.302
.1574
.0716
.00050 .00377
,54
.031
,141
,01395
80S
118
1/4
-~--t-
3{8
0.675
112
0.840
SID
XS
lOS
40S
80S
40
80
.545
.493
.423
.1246
,1670
.2173
.2333
.1910
.1405
.00162· .00586
.00133 .00729
.00098 i .00862
.42
.57
.74
.101
,083
.061
.178
.178
.178
.01736
.02160
,02554
,065
.083
.109
.147
.187
.294
.710
.674
.622
.546
.466
.252
.1583
.1974
.2503
.3200
.3836
.5043
.3959
.00275 •. 01197
.3568
.00248 .01431
.3040
.00211 .01709
.2340
.00163 .02008
.1706 1.00118 .02212
.050
• .00035 .02424
.54
.67
.85
1.09
1.31
l. 71
.172
.155
.132
.102
.074
.022
.220
.220
.220
.220
.220
.220
.02849
.03407
.04069
.04780
.05267
.0.1772
5S
lOS
40S
80S
.065
.083
.113
.154
.219
.308
.920
.884
.824
.742
.612
.434
.2011
.2521
.3326
.4335
.5698
.7180
.6611.8
.6138
.5330
.4330
.2961
.148
.00462
.00426
.00371
.00300
.00206
.00103
.02450
.02969
.03704
.04479
.05269
.05792
.69
.86
1.13
1.47
1.94
2.44
.288
.266
.231
.188
.128
.064
.275
.275
.275
.275
.275
.04667
.05655
.07055
.0853]
.100.36
.11032
5S
lOS
40S
80S
.065
.109
.133
.179
.250
.358
1.185
1.097
. 1.049
.957
.815
.599
.2553
.4130
.4939
.6388
.8:-165
1.0760
1.l029
.9452
.8640
.7190
.5217
.282
.00766
.00656
.00600
.00499
.00362
.00196
.04999
.07569
.08734
.1056
.1251
.1405
.87
1.40
1.68
2.17
2.84
3.66
.478
.409
.375
.:H2
.230
.122
.344
.344
.344
.344
.:344
.344
.07603
.1l512
.1328
.1606
.1903
.2136
5S
lOS
40S
80S
.065
.109
.140
.191
,250
.382
1.530
1.442
1.380
1.278
1.160
.896
.3257
.4717
.6685
.8815
1.1070
1.5:34
1.839
1.633
1.495
1.283
1.057
.630
.01277
.01134
.01040
.00891
.007.34
.00438
.1038
.1605
.1947
.2418
.2839
.3411
.797
.708
.649
.555
.458
.273
.435
.435
.435
.435
.435
.435
'.1250
.1934
.2346
.2913
.3421
.4110
5S
105
40S
80S
.065
.109
,145
.200
.281
.400
1.770
1.682
1.610
1.500
1.338
1.100
.3747
.6133
.7995
1.068
1.429
1.885
2.461
2.222
2.036
1.767
1.406
.950
1.066
.963
.882
.765
,608
.42
.497
.497
.497
.497
.497
.497
.1662
.2598
.3262
.4U8
.5078
.5977
SID
XS
XXS
1.050
SID
XS
XXS
1.315
SID
XS
XXS
-
....- - - 0 - - - -
80
160
...
--+-"'-'-1~--
1.660
1%
:40 I
: SID
XS
40
80
160
...
1.900
SID
XS
40
80
160
XXS
,
I
·--+-----+---~-+----~T----__T·····-----,~----·~········--+_--+_-···~
~--~~
.~--~--~.-.~~~~
1
-1-- -1---+--····-·, -'-'-"'-"j-...- ...-.-.+..~. -1---+- ..--"----...+~--~~.~--
XXS
Ph
---+--.---+.----+ .... - - -
.065
.091
126
-+---+......
1.11
1.81
2,27
3.00
3,76
5.21
--+-~-+--.. 1.01709 .1579
1.28
,01543 .2468
2.09
: .01414 .3099
2.72
.01225 .3912
3.63
j.00976 .4824
4.86
.00660 .5678
6.41
/ - - - - i - . - - - + - ...... - - -
5S
lOS
40S
80S
.065
2.245
.4717 3.9.58
: ,02749 .3149
1.61
1.72
.622
.26,52
.109
2.157
.7760 3.654
.02538 .4992
2.64
1.58
.622
.4204
SID
40
.1,54
2.067
1.075
3.355
i .02330 .6657
3,65
1.45
.622
.5606
2.375
2
XS
.218
1.939
1.477
2.9.53
.02050 .8679
5.02
1.28
,622
.7309
80
...
160
344
1.687 :2.190
2.241
.01556 1.162
7.46
.97
.622
.979
XXS
...
...
i :436 1.503 :2.656 1.774
.01232 1.311
9.03
.77
.622
1.l04
--·--T----+-...-+-~.~
..--~--5S:.,--r-.0~83-~2.7~09--.-.~7-28-0~-5-.7··64···-~~.~0~400-2+-~.7~10~0~+-2~.~48-+-2-.5~0---r-.--{5-3--+--.4-9-39---
2.875
SID
XS
40
80
160
lOS
405
80S
.120
.203
.276
.375
.552
2.635
2.469
2.323
2.125
1.771
1.039
1.704
2.254
2.945
4.028
5S
lOS
40S
80S
. 083
.120
.216
.300
3.334
3.260
3.068
2.900
2.624
2.300
.8910 8.730
.0606311.301
! 3.03
3.78
.916
.7435
1.274
8.347
.05796 1.822
4.33
3.62
.916
1.041
2.228
7.393
.05130 3.017
7.58
3.20
.916
1.724
3.016
6.605
.04587 3.894
110.25
2.86
.~16
2.225
4.205
5.408
.03755 5.032
14.32
2.35
.916
2.876
5. 466 L'1~.~15~5_-,-'0~2_8..8_5-L5_.9_9_3_-,-1~8_.58 -.Ll.....~80_~1_._9_16_...L3.....4.. : 2:. .4__~
XXS
40
80
160
0438
._ _ _ _ ~...L.._ _.__--L_X_X_S___'L.....~._. __.L...._.'_'_...L..~6oo__
3
SID
XS
5.453
4.788
4.238
3.546
2.464
.03787
.03322
.02942
.02463
.01710
.
.9873
1.530
1.924
2.353
2.871
3.53
5.79
7.66
10,01
.13.69
2.36
2.07
1.87
1.54
1.07
.753
.753
.753
.753
.753
I------+-~ +-----_t_--.-+--~--+-
Identillcallon, .elllhickne•• end .eIVhl. are extracted from ANSI 836.10 and 836.19. The notations
STD, X8, and XXS indIcate Standard. Extra Strong, and Double Extra Strong plP~ respectively.
.6868
1.064
1.339
1.638
1.997
~ f - - - -.
Tran.verl. Internal .r•• values listed in "square feet" also
represent \lolume in cubic feet per foot 0' pipe length.
CRANE
APPENDIX B
B·17
ENGINEERING DATA
PIPE DATA - cont.
---1--- Id""""'i';~-ri", 1000.
Nom-
Oul,id"
inal
Pipe
Size
Diam.
Inche,
:Wz
Inche~
4.000
Stain-
Steel
Iron
Pipe
Size
STD
XS
Schoo.
No.
11:':--:-'
nt'~!-
f'ler
Sleel
Sched.
No.
(I)
(d)
Area
Transverse
of
Melal
Internal Area
(a)
Square
Inche,;
,
1
Mo:en
'w~~, ~:~: ~;:~I ,::-'~-:-,
Inertia
(A)
Square
(1)
I)
Inche>
Inche,
.120
.226
.318
3.834
3.760
3.548
3.364
1.021
1.463
2.680
3.678
11.543
I J.l04
9.886
8.888
.07711
.06870
.06170
2.755
4.788
6.280
4.97
9.11
12.50·
.083
.120
.237
.337
.438
.531
.674
4.334
4.260
4.026
3.826
3.624
3.438
3.152
1.152
3.174
4.407
5..;95
6.621
8.101
14.75
14.25
12.73
11.50
10.31
9.28
7.80
.10245
.09898
.08840
.07986
.0716
.0645
.0542
2.810
3.963
7.233
9.610
11.6:;
13.27
15.28
.109
.134
.258
.375
.500
.625
.750
5.345
5.295
5.047
4.813
4.563
4.313
4.063
1.868
2.285
4.300
6.112
7.953
9.696
11.340
22.44
22.02
20.01
18.19
16.35
14.61
12.97
.1558
.1529
1. 1390
.1263
.1136
.0901
6.947
8.425
15.16
20.67
25.73
30.03
33.63
5S
lOS
40S
80S
.109
.134
.280,
.432
.562
.719
.864
6.407
6.357
6.065
5.761
5.501
5.187
4.897
2.231
2.733
5.S81
8.405
10.70
13.32
15.64
32.24
31. 74
28.89
26.07
23.77
21.15
18.84
.2239
.22M
.2006
.1810
.1650
.1469
11.85
14.40
28.14
40.49
49.61
58.97
5S
lOS
.109
.148
.250
.277
.322
.406
.500
.594
.719
.812
.875
.906
8.407
8.329
8.125
8.071
7.981
7.813
7.625
7.437
7.187
7.001
6.875
6.813
2.916
3.941
6.57
7.26
8.40
10.48
12.76
14.96
17.84
19.93
21.30
21.97
55.51
54.48
51.85
51.16
50.03
47.94
45.66
43.46
40.59
38.50
37.12
36.46
.38:;5
.3784
.3601
.3553
.3474
.3329
.3171
.3018
.2819
.2673
.2578
.2532
26.44
. 35.41
57.72
63.35
72.49
88.73
105.7
1 12 1.3
140.5
153.7
162.0
165.9
.134
.165
.250
.307
.365
.500
.594
.719
1.000
'1. 125
10.482
10.420
10.250
10.136
10.020
9.750
9.562
9.312
9.062
8.750
8.500
4.36
.,).49
8.24
10.07
11.90
16.10
18.92
22.63
26.24
30.63
34.02
86.29
8S.28
82.52
80.69
78.86
74.66
71.84
68. 13
64.5:i
60.13
56.75
.5992
.5922
, .5731
.5603
.5475
.5185
.4989
.4732
.4481
.4176
.3941
156
.180
.250
.330
.375
.406
.500
.562
.688
.844
1.000
1.125
1.312
12.438
12.390
12.250
12.090
12.000
11.938
I J. 750
11.626
11.374
11.062
10.750
10.500
10.126
6.17
7.11
9.82
12.87
14.58
15.77
19.24
21.52
26.03
31.53
36.91
41.08
47.14
121.50
120.57
117.86
114.80
In. 10
11 1.93
108.43
106.16
101.64
96.14
90.76
86.59
80.S3
; .8438
.8373
.8185
.7972
.7854
.7773
.7528
.7372
.7058
.6677
.6303
.6013
.5592
.
3S
lOS
40S
80S
- - --
..... --
--- - --_..
.~::~ I~~~J~=:O::·~1~~=f~5P=.~=pe:=;:=O=f=p=IP=e:::;::====
.9799
1.047
4.81
4.29
3.84
LM7
1.047
I.M7
1.378
2.394
3.140
3.92
5.61
I 0.79
14.98
I 9.00
22.51
2 7.54
6.39
6.18
5.50
4.98
4.47
4.02
3.38
1.178
1.178
1.178
1.178
!.l78
1.249
I. 761
3.214
4.271
5.178
5.898
6.791
6.36
20.78
9.72
9.54
8.67
7.88
2 7.04
3 2.96
38.55
.~~~-
4
4.500
STD
\S
40
80
120
160
5S
lOS
40S
80S
XXS
/"
5
5.563
STD
XS
40
80
120
160
5S
lOS
40S
80S
XXS
6
6.625
STD
XS
40
80
120
160
XXS
/"'.
STD
8
8.625
XS
20
30
40
60
80
100
120
140
40S
80S
XXS
160
5S
lOS
10
10.750
STD
XS
\\S
20
30
40
60
80
100
120
140
160
40S
80S
.844
5S
lOS
20
30
STD
40S
40
/".
XS
/".
12
12.75
~
\\S
80S
60
80
100
120
140
160
1.6.~ I
Identlfica1ion, wall thickness and weights are extracted trom ANSI B36.10 and 836.19. The notat1ors
STD, XS, and XXS IndIcate Standard. Extra St~ong, and DOiJb:e Extra Strong pIpe respectively
_.
Pounds Pounds Sq. Fl. '(
per
per fOOl per foot; 2 O.D.
Square
Inches
..
40
80
Thick- 1 !)jam-
. lOIS
_
....
_
..
i
l.l ~8
I.li8
I 1.456
I
6.33
5.61
1.456
1.456
1.456
1.456
1.456
1.456
2.498
3.029
5.451
7.431
9.250
10.796
12.090
7.60
9.29
I 8.97
28.57
36.39
4 5.35
53.16
13.97
13.75
12.51
11.29
10.30
9.16
8.16
1. 734
1.734
1.73,t
1.734
I. 734
1.734
1.734
3.576
4.346
8.496
12.22
14.98
17.81
20.02
9.93
2 2.36
24.70
28.55
35.64
43.39
5 0.95
60.71
6 7.76
72.42
74 .69
24.06
23.61
22.47
22.17
21.70
20.7-7
19.78
18.83
17.59
16.68
16.10
15.80
2.258
2.258
2.258
2.258
2.258
2.258
2.258
2.258
2.258
2.258
2.258
2.258
6.131
8.212
13.39
14.69
16.81
20.58
24.51
28.14
32.58
35.65
37.56
38.48
63.0
76.9
113.7
137.4
160.7
212.0
244.8
286.1
324.2
367.8
399.3
15.19
18.65
28.04
34.24
4 OAll
5 4.74
6 4.43
7 7.03
89 .29
10't13
II 5.64
37.39
36.9535.76
34.96
34.20
32.35
31.13
29.53
27.96
26.06
24.59
2.814
2.814
2.814
2.814
2.814
2.814
2.814
2.814
2.814
2.814
2.814
11.71
14.30
21.15
25.57
29.90
39.43
45.54
53.22
60.32
68.43
74.29
122.4
140.4
191.8
248.4
279.3
300.3
361.5
400.4
475.1
561.6
641.6
700.5
78U
52.65
2 0.98
52.25
24 .17
51.07
33 .38
49.74
43 #ii
49 .56
49.00
48.50
53 .52
65 ..12
46.92
46.00
73 .15
88 .63
'l4.M
, 1.32 I 41.66
1
125.49
39.33
1139 .67
jJ;52
34.89
160. 2~1
_ ...
'!!~~E.3~
..,1 ... -
i.i'
) 4.62
7.09
) 3.40
_.
.~.
I
1O~
i
_... - -..-
f----- i--
3.338
3.338
3.338
3.338
3.338
3.338
3.338
3.338
3.338
3.338
3.338
3.338
3.338
19.2
22.0
30.2
39.0
43.8
47.1
56.7
62.8
74.6
88.1
100.7
109.9
122.6
Transverse internal area values listed in 'square feet" also
represent volurre in cubic feet pe( foot of pipe length,
CRANE
APPENDIX B - ENGINEERING DATA
PIPE DATA-cont.
- - -.....
Nominal
Pipe
Size
Outside - -.....
Identification
Oiam.
StainSteel
less
Iron
Sched.
Steel
Pipe
No.
Sched.
Inches
Size
No.
Inches
...
. ..
...
· ..
10
20
.30
40
.. .
...
STO
...
14
14.00
XS
.. .
...
60
80
100
120
140
160
...
.. .
.. .
.. .
...
...
...
16
16.00
STO
XS
...
...
...
·.." .
.. .
...
...
...
...
STO
...
18
18.00
XS
· ..
.. .
.. .
...
.. .
20.00
...
'"
...
'"
10
20
30
40
60
80
100
120
140
160
...
...
...
...
.. .
...
.165
.188
.250
.312
.375
.438
.500
.562
.750
.938
1.156
1.375
1.562
1.781
17.670
17.624
17.500
17.376
17.250
17.124
17.000
16.876
16.500
16.124
15.688
15.250
14.876
14.438
.188
.218
,250
.375
.500
,594
.812
1.031
1.281
1.500
1.750
1.969
19.624
19.564
19.500
19.250
19.000
18.812
18.376
17.938
17.438
17.000
16.500
16.062
5S
lOS
.188
.218
.250
.375
.500
...
. ..
r
21.624
21.564
21.500
21.250
21.000
20.250
19.75
19.25
18.75
18.25
17.75
...
...
. ..
SS
105
...
. ..
...
...
20
8.21
9.34
12.37
15.38
18.41
24.35
31.62
40.14
48.48
56.56
65.78
72.10
...
...
· ..
...
...
10
20
...
STO
X5
.16S 15.670
.188 15.624
.2S0 15.500
.312 IS . .376
.375 15.250
.500 15.000
.656 14.688
.844 14.312
1.031
13.938
1.219 ,13.562
1.438 • 13.124
1.594 12.812
. ..
. ..
...
5S
lOS
40
60
80
100
120
140
160
...
........
...
...
...
(1_1 )
I 6.78
...
...
30
· ..
...
...
...
. ..
...
...
...
. ..
· ..
., .
...
...
...
. ..
...
...
'"
55
lOS
...
...
...
. ..
. ..
. ..
...
· ..
...
...
.156
.188
.250
.312
.375
.438
.500
.594
.750
.938
1.094
1.250
1.406
•
I
...
.. ,
STO
XS
22
22.00
..
...
,
...
· ..
_ .....
i
...
.. .
...
10
20
30
60
80
100
120
140
160
I
13.688
13.624
13.500
13.376
13.250
13.124
13.000
12.812
12.500
12.124
11.812
11.500
11.188
5S
lOS
10
20
30
40
60
80
100
120
140
160
...
I
Wall
Transverse
Moment Weight Weight External Section
i~side Area
of
Thick- • Oiam- i
of
Internal Area
PIpe i Water Surface Modulus
Metal
Inertia
ness
eter
(A)
(a.)
(t)
(d)
Pounds Pounds Sq. Ft.
(I)
per
per foot per foot -O.D.
Square i Square Square
of pipe i of pipe
Inches Inches Inches Inches
Feet
Inches'
foot
.........
· ..
· ..
...
...
1.125
1.375
1.625
...
. ..
... ......... ~:~~~
-
----~
~--
1.0219
162.6
1.0124
194.6
255.3
.9940
.9758
314.4
.9575
372.8
.9394
429.1
483.8
.9217
.8956
562.3
.8522
678.3
.8020
824.4
.7612
929.6
.7213 1027.0
.6827 • 11l7.0
23.07
27.73
36.71
45.61
54.57
63.44
72.09
85.05
106.13
130.85
150.79
170.28
189.11
63.77
63.17
62.03
60.89
59.75
58.64
57.46
55.86
53.18
50.04
47.45
4S.01
42.60
3.665
3.665
3.665
3.665
3.665
3.665
3.665
.3.665
3.665
3.665
3.665
3.66S
3.66S
23.2
27.8
36.6
45.0
53.2
61.3
69.1
80.3
98.2
117.8
132.8
146.8
159.6
192.85 11.3393
191.72 ,1.3314
188.69 1.3103
185.69 1.2895
182.65 1.2684
176.72 1.2272
169.44 1.1766
160.92 1.1175
1 152.58 1.0596
144.50 1.0035
135.28
.9394
.8956
i 128.96
2S7.3
291.9
383.7
473.2
562.1
731.9
932.4
1155.8
1364.5
1555.8
1760.3
1893.5
27.90
31.75
42.05
52.27
62.58
82.77
107.50
136.61
164.82
192.43
223.64
245.25
83.S7
83.08
81.74
80.50
79.12
76.58
73.42
69.73
66.12
62.62
58.64
55.83
4.189 i
4.189
4.189
4.189
4.189
4.189
4.189
4.189
4.189
4.189
4.189
4.189
32.2
36.5
48.0
59.2
70.3
91.5
116.6
144.5
170.5
194.5
220.0
236.7
9.25
10.52
13.94
17.34
20.76
24.17
27.49
30.79
40.64
SO.23
61.17
71.81
80.66
90.75
'245.22 1.7029
243.95 1.6941
240.53 1.6703
237.13 1.6467
i 233.71 1.6230
230.30 1.5990
226.98 1.5763
223.68 1.5533
213.83 1.4849
204.24 1.4183
193.30 , 1.3423
182.66 • 1.2684
173.80 1.2070
163.72 i 1.1369
367.6
417.3
549.1
678.2
806.7
930.3
1053.2
1171.5
1514.7
1833.0
2180.0
2498.1
2749.0
3020.0
31.43
35.76
47.39
58.94
70.59
82.15
93.45
104.67
138.17
170.92
207.96
244.14
274.22
308.50
106.26
105.71
104.21
102.77
lOLl8
99.84
98.27
96.93
92.57
88.50
83.76
79.07
75.32
70.88
4.712
4.712
4.712
4.712
4.712
4.712
4.712
4.712
4.712
4.712
4.712
4.712
4.712
4.712
40.8
46.4
61.1
75.5
89.6
103.4
117.0
130.1
168.3
203.8
242.3
277.6
305.5
335.6
11.70
13,55
15.51
23.12
30.63
36.15
48.95
61.44
75.33
87.18
100.33
111.49
302.46
300,61
298.65
290.04
283.53
278.00
265.21
252.72
238.83
226.98
213.82
.202.67
2.1004
2.0876
2,0740
2,0142
1.9690
1.9305
1.8417
1.7550
1.6585
1.5762
1.4849
1.4074
574.2
662.8
765.4
1113.0
1457.0
1703.0
2257.0
2772.0
3315.2
3754.0
4216.0
4585.5
39.78
46.06
52.73
78,60
104.13
123.11
166.40
208.87
256.10
296.37
341.09
379.17
131.06
130.27
129.42
125.67
122.87
120.46
114.92
109.51
103.39
98.35
92.66
87.74
5.236
5.236
5.236
5.236
5.236
5.236
5.236
5.236
5.236
5.236
5.236
5.236
57.4
66.3
75.6
1l1.3
145.7
170.4
225.7
277.1
331.5
375.5
421.7
458.5
12.88
14.92
17.08
25.48
33.77
58.07
73.78
89.09
104.02
1367.25
365.21
363.05
354.66
346 36
.
322.06
2.5503
2.5362
2.5212
i 2.4629
2.4053
2.2365
2.1275
2.0211
1.9175
1.8166
1. 7184
766.2
884.8
1010.3
1489.7
1952.5
3244.9
4030.4
4758.5
5432.0
6053.7
43.80
50.71
58.07
86.61
114.81
197.41
250.81
302.88
353.61
403.00
451.06
159.14
158.26
157.32
153.68
150.09
139.56
132.76
126.12
119.65
113.36
107.23
5.760
5.760
5.760
5.760
5.760
5.760
5.760
5.760
5.760
5.760
5.760
69.7
80.4
91.8
135.4
1l7.5
295.0
366.4
432.6
493.8
550.3
602.4
147.15
145.78
8.16
143.14
10.80
13.42
140.52
16.05
137.88
18.66
135.28
21.21
132.73
24.98
128.96
31.22
122.72
38.45
115.49
44.32
109.62
50.07 1103.87
SS.63
98.31
_
......
~32.68
1
1306.35
291.04
12
I
1.45
Identification, wall thick" ••• and weight, are extracted from ANSI 836.10 and 836_19. The notations
STD, XS, and XXS indicate Standard, Extra Strong, and Double Extra Strong pipe respectively_
6626A
I
Transverse Internal area valUes listed in "square feet" also
represent volume in cubic feet per foot of pipe length
CRANE
APPENDIX II
8-19
ENGINEERING DATA
PIPE DATA-cont.
Nominal
Pipe
Size
Inches
Inches
Steel
Iron
Pipe
Size
Sched.
No.
...
...
., .
10
20
STD
X5
24.00
...
...
80
...
...
...
...
26.00
10
...
5TD
XS
...
28
28.00
30.00
32
32.00
96.0
109.6
161.9
212.5
237.0
285.1
387.7
472.8
570.8
652.1
718.9
787.9
436.10
433.74
424.56
415.48
411.00
402.07
382.35
365.22
34l.32
326.08
310.28
292.98
.312
.375
.500
25.376
25.250
25.000
25.18
30.19
40.06
505.75 i 3.5122 i 2077.2
500.74 i 3.4774 2478.4
490.87 ! 3.4088 3257.0
85.60
102.63
136.17
219.16
216.99
212.71
6.806
6.806
6.806
159.8
190.6
250.5
I
92.26
110.64
146.85
182.73
255.07
252.73
248.11
243.53
7.330
7.330
7.330
7.330
185.8
221.8
291.8
359.8
55
105
.250
.312
.375
.500
.625
29.500
29.376
29.250
29.000
28.750
23.37 683.49
29.10 677.76
34.90 671.96
46.34 660.52
57.68 i649.18
4.7465
4.7067
4.6664
4.5869
4.5082
2585.2
3206.3
3829.4
5042.2
6224.0
79.43
98.93
118.65
157.53
196.08
296.18
293.70
291.18
286.22
281.31
7.854
7.854
7.854
7.854
7.854
172.3
213.8
255.3
336.1
414.9
. ..
. ..
.312
.375
.500
.625
.688
31.376
31.250
31.000
30.750
30.624
31.06
37.26
49.48
61.60
67.68
773.19
766.99
754.77
742.64
736.57
5.3694
5.3263
5.2414
5.1572
5.1151
3898.9
4658.5
6138.6
7583.4
8298.3
105.59
126.66
168.21
209.43
230.08
335.05
332.36
327.06
321.81
319.18
8.378
8.378
8.378
8.378
8.378
243.7
291.2
3&3.7
474.0
518.6
.34l
.375
.500
.625
36.37
39.61
52.62
65.53
72.00
871.55
868.31
855.30
842.39
835.92
6.0524
6.0299
5.9396
5.8499
5.8050
5150.5
5599.3
7383.5
9127.6
9991.6
123.65
134.67
178.89
222.78
24l.77
377.67
376.27
370.63
365.03
362.23
8.901
8.901
8.901
8.901
8.901
303.0
329.4
434.3
536.9
587.7
34.98
41.97
55.76
69.46
83.06
982.90
975.91
962.11
948.42
934.82
6.8257
6.7771
6.6813
5569.5
6658.9
8786.2
118.92 425.92
142.68 422.89
189.57 416.91
236.13 1417.22
282.35 405.09
9.425
9.425
9.425
9.425
9.425
309.4
369.9
488.1
603.8
717.0
...
...
. ..
...
. ..
10
...
. ..
20
30
40
...
. ..
.,.
.688
33.312
33.250
33.000
32.750
32.624
. ..
. ..
.312
.375
.500
.625
.750
35.376
35.250
35.000
34.750
34.500
...
...
. ..
34.00
..
..
10
...
I
6.283
6.283
6.283
6.283
6.283
6.283
6.283
6.283
6.283
6.283
6.283
6.283
16.29
18:65
27.83
36.91
41.39
50.31
70.04
87.17
108.07
126.31
142.11
159.41
2601.0
3105.1
4084.8
5037.7
...
36
188.98
187.95
183.95
179.87
178.09
174.23
165.52
158.26
149.06
141.17
134.45
126.84
23.564
23.500
23.250
23.000
22.876
22.624
22.062
21.562
20.938
20.376
19.876
19.312
4.0501
3.9761
3.9028
20
30
...
1151.6
55.37
1315.4
63.41
1942.0 • 94.62
2549.5 i 125.49
2843.0 140.68
3421.3 171.29
4652.8 238.35
5672.0 296.58
6849.9 367.39
7825.0 429.39
8625.0 483.12
9455.9 542.13
.218
.250
.375
.500
.562
.688
.969
1.219
1.531
1.812
2.062
2.34l
i 4.0876
...
STD
3.0285
3.0121
2.9483
2.8853
2.8542
2.7921
2.6552
2.5362
2.3911
2.2645
2.1547
2.0346
Inches
588.61
583.21
572.56
562.00
..
34
(20.~)J
Inches
27.14
32.54
43.20
53.75
10
'"
Pounds 5q. Ft.
per foot per foot
of pipe of pipe
Square
Inches
27.376
27.250
27.000
26.750
...
...
(a)
(d)
.312
.375
.500
.625
...
...
Weight External Section
Water Surface Modulus
Square
Inches
Moment Weight
Pipe
of
Inertia
(A)
Pounds
(I)
per
Square
Inches' foot
Feet
. ..
. ..
20
30
STD
XS
Transverse
Internal Area
10
...
...
eter
Area
of
Metal
...
...
STD
XS
Inside
Diam-
20
STD
X5
...
30
..
. ..
...
. ..
...
...
...
...
...
...
. ..
. ..
100
120
140
160
...
26
55
lOS
30
40
60
...
Wall
Thickness
(t)
Stainless
Steel
Sched.
No.
...
...
24
:c:
T,
Outside
Diam.
20
30
40
I
I
Identification. wall thickness and welghta ara axlraCled from ANSI 636.10 and 636.19. The notalions
•
•
STD, XS, and
XXS indicate
Standard, Extra Strong, and Double Extra Strong pipe respectively
6.5~4
6.49
.1
Ttana"e,.. lnternal area values listed in "square feet" also
represent volume in cubic teet per foot of pipe length.
;...B_-_2_0_ _ _ _ _ _ _ _ _ _ _ _ _~A.:.:..P:...:PE:.:...N.:.:..D::..:IX:...:B:_.:E:.:...N:.::G:.:..IN:..:.E=_ER::..:IN.:.:G:......:.:DA.:.:T.:..:.A_ _ _ _ _ _ _ _ _ _ _ _...::C:.,:R A N E
TEMPERATURE CONVERSION
.. ....
_--
.......
c
IAI
F
--':273 .-460
c
I~I
300 0 to 890 G
61° to 290"
10 to 60°
-460° to 0°
F
c
I~I
F
c
l:~:~
i~~
~t~
-420
-16.1
-15.6
-15.0
1
2
3
4
5
37.4
39.2
41.0
16.1
16.7
17.2
17.8
18.3
61
62
63
64
65
145.4
147.2
149.0
-410
-400
-390
-380
-370
-14.4
-13.9
-13.3
-12.8
-12.2
6
7
8
9
10
42.8
44.6
46.4
48.2
50.0
18.9
19.4
20.0
20.6
21.1
66
67
68
69
70
-11.7
--11.1
-10.6
-10.0
-9.4
11
12
-196
-360
-350
-340
-330
-320
13
14
15
51.8
53.6
55.4
57.2
59.0
21.7
22.2
22.8
23.3
23.9
-190
--184
---179
--173
-169
-310
-300
-290
-280
-273
-460
8.9
8.3
7.8
7.2
6.7
16
17
18
19
20
60.8
62.6
64.4
66.2
68.0
--16~
-162
·-157
--151
--146
-270
-260
-250
240
-230
-454
-436
418
-400
-382
- 6.1
- 5.6
- 5.0
4.4
3.9
22
23
24
25
21
--140
134
-129
-123
--118
-220
-210
-200
-190
-180
-364
-346
-328
-310
-292
3.3
2.8
- 2.2
-- 1.7
- 1.1
--112
-107
-101
96
90
-170
160
-150
-140
-130
1--
-274
-256
--238
-220
-202
84
79
73
68
- 62
-120
-110
--100
90
80
-- 57
51
46
40
- 34
l~
F
C
160
166
17l
300
310
320
330
340
~~~
608
626
644
482
488
493
499
504
150.8
152.6
154.4
156.2
158.0
177
182
188
193
199
350
360
370
380
390
662
680
698
716
734
7l
72
73
74
75
159.8
161.6
163.4
165.2
167.0
204
210
216
221
227
400
410
420
430
440
24.4 •
25.0
25.6
26.1
26.7
76
77
78
79
80
168.8
170.6
172.4
174.2
176.0
232
238
243
249
254
69.8
71.6
73.4
75.2
77.0
27.2
27.8
28.3
28.9
29.4
81
82
83
84
85
177.8
179.6
181.4
183.2
185.0
26
27
28
29
30
78.8
80.6
82.4
84.2
86.0
30.0
30.6
31.1
31.7
32.2
86
87
88
89
90
- 0.6
0.0
0.6
1.1
1.7
31
32
33
34
35
87.8
89.6
91.4
93.2
95.0
32.8
33.3
33.9
34.4
35.0
-184
-166
--148
--130
-112
2.2
2.8
3.3
3.9
4.4
36
37
38
39
40
96.8
98.6
100.4
102.2
104.0
70
- 60
..... 50
- 40
-- 30
- 94
- 76
58
- 40
22
5.0
5.6
6.1
6.7
7.2
41
42
43
44
45
- 20
-- 29
- 23
10
._. 17.8
0
4
14
32
7.8
8.3
8.9
9.4
10.0
-268
---262
--257
--251
-450
-440
-246
240
~234
~229
-223
-218
-212
-207
~201
I~
F
i~n-
900
910
920
930
940
1688
1706
1724
510
516
521
527
532
950
960
970
980
990
1742
1760
1778
1796
1814
752
770
788
806
824
538
549
560
57l
582
1000
1020
1040
1060
1080
1832
1868
1904
1940
1976
450
460
470
480
490
842
860
878
896
914
593
604
616
627
638
1100
1120
1140
1160
1180
2012
2048
2084
2120
2156
260
266
27l
277
282
500
510
520
530
540
932
950
968
986
1004
649
660
67l
6!h
693
1200
1220
1240
1260
1280
2192
2228
2264
2300
2336
186.8
188.6
190.4
192.2
194.0
288
293
299
304
310
550
560
570
580
590
1022
1040
1058
1076
1094
704
732
760
788
816
1300
1350
1400
1450
15()0
2372
2462
2552
2642
2732
91
92
93
94
95
195.8
197.6
199.4
201.2
203.0
316
321
327
332
338
600
610
620
630
640
1112
1130
1148
1166
1184
843
87l
899
927
954
1550
1600
1650
1700
1750
2822
2912
3002
3092
3182
35.6
36.1
36.7
37.2
37.8
96
97
98
99
100
204.8
206.6
208.4
210.2
212.0
343'
349
354
360
366
650
660
670
680
690
1202
1220
1238
1256
1274
982
1010
1038
1066
1093
1800
1850
1900
1950
2000
3272
3362
3452
3542
3632
105.8
107.6
109.4
111.2
113.0
43
49
54
60
66
110
120
130
140
150
230
248
266
284
302
371
377
382
388
393
700
710
720
730
740
1292
1310
1328
1346
1364
1121
1149
1177
1204
1232
2050
2100
2150
2200
2250
3722
3812
3902
3992
4082
46
47
48
49
50
114.8
116.6
118.4
120.2
122.0
71
77
82
88
93
160
170
180
190
200
320
338
356
374
392
399
404
410
416
421
750
760
770
780
790
1382
1400
1418
1436
1454
1260
1288
1316
1343
1371
2300
2350
2400
2450
2500
4172
4262
4352
4442
4532
10.6
11.1
11.7
12.2
12.8
51
52
53
54
55
123.8
125.6
127.4
129.2
131.0
99
100
104
110
116
210
212
220
230
240
410
413.6
428
446
464
427
432
438
443
449
800
810
820
830
840
1472
1490
1508
1526
1544
1399
1427
1454
1482
1510
2550
2600
2650
2700
2750
4622
4712
4802
4892
4982
13.3
13.9
14.4
15.0
15.6
56
57
58
59
60
132.8
134.6
136.4
138.2
140.0
121
127
132
138
143
250
260
270
280
290
482
500
518
536
554
454
460
466
471
477
850
860
870
880
890
1562
1580
1598
1616
1634
1538
1566
1593
1621
1649
2800
2850
2900
2950
3000
5072
5162
5252
5342
5432
j~:~
~430
_-_ .
900" to 3000°
!
Locate temperature in middle column. If in degrees CelSius, read Fahrenheit equivalent
in right hand column; if in degrees Fahrenheit, read Celsius equivalent in left hand column.
J( I 'If) I+-
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
III
II
II
1
l 1
l 1
l 1
l 1
l 1
l 1
l
1
l
1
l
1
l
1
l
1
l
1
l
1
l
1
l
1
l
1
l
1
l
1
l
1
l