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Engineering Fluid Mechanics 10th Elger

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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\u2022 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

-------· --

TABLE F.2 Commonly Used Equations

Ideal gas law
p = pRT

Specific weight
&quot;Y = pg

Specific gravity
S= _ _:_P __

PH,O at 4°C &quot;YH,O at 4·c

Kinematic viscosity
v = J..L/p

Definition of viscosity
dV

T=J..L-
dy

Pressure equations
Pgage = Pabs - Patm

Pvacuum = Patm - Pabs

Hydrostatic equation
p, P2
- + z1 = - + z2 = constant
&quot;Y &quot;Y
Pz = p, + -yz, = p2 + -yzz = constant
t.p = --yt.z

Manometer equations

Pz = p, + L -y,h, - L -y,h,
down up

Hydrostatic force equations (flat panels)
Fp = pA

Buoyant force (Archimedes equation)
FB = -yVo

The Bernoulli equation

( p, VT ) (Pz V~ ) -:y + 2g + z, = -:y + 2g + z2

Coefficient of pressure
Pz- Pzo h - ho c = =--

p pVJ/2 v;t(2g)
Volume flow rate equation

Q = vA = m = I vdA =I v · dA
p A A

(Eq. 1.10, p. 14)

(Eq. 2.3, p. 31)

(Eq. 2.5, p. 32)

(Eq. 2.15, p. 38)

(Eq. 2.16, p. 39)

(Eq. 3.3a; p. 62)
(Eq. 3.3b, p. 62)

(Eq. 3.10a, p. 66)
(Eq. 3.10b, p. 66)
(Eq. 3.10c, p. 66)

(Eq. 3.21, p. 74)

(Eq. 3.22, p. 75)

(Eq. 3.28, p. 80)

(Eq. 3.33, p. 81)

(Eq. 3.41a, p. 87)

(Eq.4.21b,p.l33)

(Eq. 4.21a, p.133)

(Eq. 4.47, p. 147)

(Eq. 5.10, p. 17 4)

Mass flow rate equation

m=pAV=pQ= IpVdA= IpV·dA (Eq.5.ll,p.174)
A A

Continuity equation

:J pdV + f p V · dA = 0 (Eq. 5.28, p. 183)
cv cs

Momentum equation

L F = :J vp dV + J vpV · dA
cv cs

The power equation
P = FV = Tw
P = mgh = -vQh
Efficiency of a machine

Poutput
11 =--

Pinput

Reynolds number (pipe)
VD pVD 4Q 4m

Re 0 = -= --= --= --
v J..L TIDY TIDJ..L

L V 2 V 2

hL= 2:J--+ L K-
pipes D 2g components 2g

(Eq. 5.29, p. 183)

(Eq. 5.33, p. 189)

(Eq. 6.7, p. 213)

(Eq. 6.10, p. 213)

(Eq. 7.29; p. 262)

(Eq. 7.3, p. 255)
(Eq. 7.31; p. 265)

(Eq. 7.32; p. 267)

(Eq. 10.1, p. 361)

(Eq. 10.45, p. 382)

Friction factor f (Resistance coefficient)
64 f = - Re :s 2000 (Eq. 10.34, p. 370)

Rev
0.25

f = [ ( k, 5.74 )] 2 (Re :=::: 3000) (Eq.10.39, p. 375)
log10 3.7D + Re~9

Drag force equation

Fo = C0A(p~~) (Eq. 11.5, p. 409)
Lift force equation

( pV~) FL = CLA -2- (Eq.11.17,p.424)

TABLE F.3 Useful Constants

I Name of Constant Value
Acceleration of gravity

Universal gas constant

Standard atmospheric pressure

______ ,_+~ = 9.81 m/s2 = 32.:?. ftN __ _ __
R. = 8.314 kj/kmol· K = 1545 ft · lbf/lbmol · 0 R

--+--
P \u2022\u2022 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

Specific gas constant

Density

Specific weight

Viscosity

Kinematic viscosity

Specific heat ratio

Specific heat

Speed of sound

SI Units

R,,. = 287.0 j/kg · K
p = 1.20 kg/m·'

-y = 11.8 N/m'

1.1.= 1.81 X 10 'N ·s/m:
- ----~----.. -r-l v=!.51Xl0-sm2/s

k = c /c = 1.40

r> = 1~0~ Jlkg. K
I c =343m/~

TABLE F.S Properties of Water [T = l5°C (59°F),p = I atm]

Specific weight

SJ Units

p - 999kg/m'

'Y = 9800 N/m'

------- ---- ---~----

1-l = 3.8 L X 10&quot;7 lbf · s/ft1

v = 1.63 X 10-~ ft1/s

k = c,tc, = 1.40
-1-~- --

1

cP-:: 0.241 Btu/lbm · oR
c = 1130 ft/s

p = 62.4lbm/ft3 = 1.94 slug/ft'
---

1 -y - 62.4lbf/ft'

-=~::, ~&quot;~~~=-=--- 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

Density

Specific wc1ght

\u2022 SI Units
:~-

_i p = 1000 kglm'
!:; = 9Sl0 N/m1

<::-·.\u2022;
::::

p = 62.4 lbm/ftJ = 1.94 slug/ft'
- -- --------

'1 = 62.4 lbf/ft3

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ENGINEERING
FLUID MECHANICS

TENTH EDITION

Donald F.