Engineering Fluid Mechanics

692 Pages·2012·86.47 MB·English

by  Clayton T. Crowe, Barbara C. Williams, John A. Roberson

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ENGINEERING
FLUID MECHANICS
lOth Edition
DONALD F. ELGER
BARBARA C. WILLIAMS
CLAYTON T. CROWE
JoHN A. RoBERSON
TABLE F. 1 Formulas for Unit Conversions*
Name, Symbol, Dimensions Conversion Formula
I
Length L L I m = 3.281 ft = 1.094 yd = 39.37 in = km/1000 = 106 J..Lm
I ft = 0.3048 m = 12 in = mile/5280 = km/3281
I mm = m/1000 = in/25.4 = 39.37 mil = 1000 11-m = 107 A
Speed v LIT I m/s = 3.600 km/hr = 3.281 ft/s = 2.237 mph = 1.944 knots
I ft/s = 0.3048 m/s = 0.6818 mph = 1.097 km/hr = 0.5925 knots
Mass m M I kg= 2.205lbm = 1000 g = slug/14.59 = (metric ton or tonne or Mg)/1000
I ibm= lbf · s2/(32. 17 ft) = kg/2.205 = slug/32.17 = 453.6 g
= 16 oz = 7000 grains = short ton/2000 = metric ton (tonne)/2205
Density p M/U 1000 kglm3 = 62.43 lbm/ft3 = 1.940 slug/ft3 = 8.345 Ibm/gal (US)
Force F ML/P Ilbf = 4.448 N = 32.17lbm · ft/s 2
IN= kg· m/s2 = 0.2248lbf = 105 dyne
Pressure, Shear p, T M/LT2 I Pa = N/m2 = kg/m · s2 = 10- 5 bar = 1.450 X 10- 4 lbf/in2 = inch Hp/249.1
Stress = 0.007501 torr= 10.00 dyne/cm2
I atm = 101.3 kPa = 2116 psf = 1.013 bar= 14.70 lbf/in2 = 33.90 ft of water
= 29.92 in of mercury= 10.33 m of water= 760 mm of mercury= 760 torr
I psi= atm/14.70 = 6.895 kPa = 27.68 in H20 = 51.71 torr
Volume ¥ p I m3 = 35.31 ft3 = 1000 L = 264.2 U.S. gal
I ft3 = 0.02832 m3 = 28.32 L = 7.481 U.S. gal= acre-ft/43,560
I U.S. gal = 231 in3 = barrel (petroleum)/42 = 4 U.S. quarts = 8 U.S. pints
= 3.785 L = 0.003785 m3
Volume Flow Q PIT I m'/s = 35.31 ft3/s = 2119 cfm = 264.2 gal (US)/s = 15850 gal (US)/m
Rate (Discharge) I cfs = 1 ft3/s = 28.32 Lis = 7.481 gal (US)/s = 448.8 gal (US)/m
Mass Flow Rate m MIT I kg/s = 2.205lbm/s = 0.06852 slug/s
Energy and E,W MV/P I J =kg· m2/s2 = N · m = W · s = volt• coulomb = 0.7376 ft ·lbf
Work = 9.478 X 10- 4 Btu = 0.2388 cal = 0.0002388 Cal= 107 erg= kWh/3.600 X 106
Power P,E, W MV!T' I W = J/s = N · m/s = kg · m2/s3 = 1.341 X 10- 3 hp
= 0.7376 ft ·lbf/s = 1.0 volt-ampere= 0.2388 calls = 9.478 X 10- 4 Btu/s
I hp = 0.7457 kW = 550ft ·lbf/s = 33,000 ft · lbf/min = 2544 Btu/h
Angular Speed w T - l 1.0 rad/s = 9.549 rpm = 0.1591 rev/s
Viscosity J..L MILT I Pa · s = kg/m · s = N · s/m2 = 10 poise = 0.02089lbf · s/ft2 = 0.6720 lbm/ft · s
Kinematic v V/T I m2/s = 10.76 ft2/s = 106 eSt
Viscosity
Temperature T 0 K = °C + 273.15 = 0 R/1.8
°C = (°F - 32)/1.8
0
R = °F + 459.67 = 1.8 K
°F = 1.8°C + 32
*A useful online reference is www.onlineconversion.com
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TABLE F.2 Commonly Used Equations
Ideal gas law Mass flow rate equation
p = pRT (Eq. 1.10, p. 14)
m=pAV=pQ= IpVdA= IpV·dA (Eq.5.ll,p.174)
Specific weight A A
"Y = pg (Eq. 2.3, p. 31) Continuity equation
Specific gravity
:J pdV + f p V · dA = 0 (Eq. 5.28, p. 183)
S= _ _:_P_ _ (Eq. 2.5, p. 32) cv cs
PH,O at 4°C "YH,O at 4·c
(Eq. 5.29, p. 183)
Kinematic viscosity
v = J..L/p (Eq. 2.15, p. 38) (Eq. 5.33, p. 189)
Definition of viscosity Momentum equation
dV
T=J..L
dy- (Eq. 2.16, p. 39) L F = :Jc v vp dV + Jcs vpV · dA (Eq. 6.7, p. 213)
Pressure equations
Pgage = Pabs - Patm (Eq. 3.3a; p. 62) (Eq. 6.10, p. 213)
Pvacuum = Patm - Pabs (Eq. 3.3b, p. 62)
Hydrostatic equation
p, P2
- + z1 = - + z2 = constant (Eq. 3.10a, p. 66)
"Y "Y
Pz = p, + -yz, = p2 + -yzz = constant (Eq. 3.10b, p. 66) (Eq. 7.29; p. 262)
t.p = --yt.z (Eq. 3.10c, p. 66) The power equation
Manometer equations P = FV = Tw (Eq. 7.3, p. 255)
P = mgh = -vQh (Eq. 7.31; p. 265)
Pz = p, + L -y,h, - L -y,h, (Eq. 3.21, p. 74)
down up Efficiency of a machine
(Eq. 3.22, p. 75) Poutput
11 =-- (Eq. 7.32; p. 267)
Hydrostatic force equations (flat panels) Pinput
Fp = pA (Eq. 3.28, p. 80) Reynolds number (pipe)
VD pVD 4Q 4m
(Eq. 3.33, p. 81) Re 0 = -= --= --= -- (Eq. 10.1, p. 361)
v J..L TIDY TIDJ..L
Buoyant force (Archimedes equation) Combined head loss equation
FB = -yVo (Eq. 3.41a, p. 87) L V 2 V 2
hL= 2:J--+ L K- (Eq. 10.45, p. 382)
The Bernoulli equation pipes D 2g components 2g
( -p:y, + V2gT + z, ) = (P-:yz + V2~g + z2 ) (Eq.4.21b,p.l33) Fricti6o4n factor f (Resistance coefficient)
f = - Re :s 2000 (Eq. 10.34, p. 370)
Rev
(Eq. 4.21a, p.133) 0.25
f = [ ( k, 5.74 )] 2 (Re :=::: 3000) (Eq.10.39, p. 375)
Coefficient of pressure log10 3.7D + Re~9
Pz- Pzo h - ho
c
p = pVJ/2 =v;t-(2-g) (Eq. 4.47, p. 147) Drag force equation
Volume flow rate equation Fo = C0A(p~~) (Eq. 11.5, p. 409)
Q = vA = m = I vdA =I v · dA (Eq. 5.10, p. 17 4) Lift force equation
p A A
FL = CLA (-p2V~-) (Eq.11.17,p.424)
TABLE F.3 Useful Constants
IN ame of Constant Value
Acceleration of gravity ______ ,_+~ = 9.81 m/s2 = 32.:?. ftN __ _ __
Universal gas constant R. = 8.314 kj/kmol· K = 1545 ft · lbf/lbmol · 0 R
--+--
Standard atmospheric pressure P• • m = 1.0 atm = 101.3 kPa = 14.70 p£I = 2116 psf = 33.90 li of .,.-ater
P.,m = 10.33 m of water= 760 mm of Hg = 29.92 in ofHg = 160 torr= 1.013 bar
TABLE F.4 Properties of Air [T = 20°C (68°F), p = 1 atm]
Property SI Units
Specific gas constant R,,. = 287.0 j/kg · K
Density p = 1.20 kg/m·'
Specific weight -y = 11.8 N/m'
------- ---- ---~----
Viscosity 1.1.= 1.81 X 10 'N ·s/m: 1-l = 3.8 L X 10"7 lbf · s/ft1
- ----~----.. -r-
Kinematic viscosity l v=!.51Xl0-sm2/s v = 1.63 X 10-~ ft1/s
Specific heat ratio k = c /c = 1.40 k = c,tc, = 1.40
-1-~- --
Specific heat r> = 1~0~ Jlkg. K cP-:: 0.241 Btu/lbm · oR
Speed of sound I c =343m/~
1 c = 1130 ft/s
TABLE F.S Properties of Water [T = l5°C (59°F),p = I atm]
SJ Units
p - 999kg/m' p = 62.4lbm/ft3 = 1.94 slug/ft'
---
Specific weight 'Y = 9800 N/m' 1 -y - 62.4lbf/ft'
-=~::, ~"~~~=-=--- J___-:: : : ::::: :,:'~' - ~- - _t' : : ::: : ::_: ::~ ,,.,
Surface tension (water-air) 1 u = 0.073 N/m CJ = 0.0050 lbflft
-- -- ----- - ~
Hulk modulus of elasticity li. :- 2.14 X 109 Pa I E, = 3.10 X 10' p~ri
TABLE F.6 Properties of Water [T = 4°C (39°F),p = 1 alml
<::-·.•;
Propertr • SI Units ::::
:~-
Density _i p = 1000 kglm' p = 62.4 lbm/ftJ = 1.94 slug/ft'
Specific wc1ght !:;= 9Sl0 N/m1 '1 = 62.4 lbf/ft3 - -- --------
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ENGINEERING
FLUID MECHANICS
.L
u
TENTH EDITION
Donald F. Elger
University of Idaho, Moscow
gues, Barbara C. Williams
1nd live University of Idaho, Moscow
es
ct.com
Clayton T. Crowe
Washington State University, Pullman
john A . Roberson
Washington State University, Pullman
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Library of Congress Cataloging-in-Publication Data
Roberson, John A.
Engineering fluid mechanics I Donald F. Elger, University of Idaho, Moscow, Barbara C. Williams, UniversitY o-
Idaho, Moscow, Clayton T. Crowe, Washington State University, Pullman, John A. Roberson, Washington State
University, Pullman.-- Tenth edition.
pages em
Original edition: Engineering fluid mechanics I John A. Roberson and Clayton T. Crowe. 1975.
Includes bibliographical references and index.
ISBN978-1-118-16429-7(cloth: alk.paper) 1. Fluid mechanics. I. Elger,D.F. II. Williams,BarbaraC.,l -
III. Crowe, C. T. (Clayton T.) IV. Title.
TA357.R6 2012
620.1'06--dc23
2012020571
ISBN 978-1-118-16429-7 (Main Book)
ISBN 978-1-1-118-37220-3 (Binder-Ready Version)
Printed in the United States of America
10987654321
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This 1Oth Edition is dedicated to our friend
and colleague Clayton T. Crowe (1933-2012)
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