Munson B.R. Fundamentals of Fluid Mechanics

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Chapter 1

1.2 1a2L

; 1b2LT

⫺2

; 1c2FL

⫺1

; L

; ML

⫺2

1.6 1a2L

⫺2

; 1b2M

⫺3

; 1c2M

1.8 LT

⫺1

, F

, LT

⫺1

1.10 Yes

1.12 1 2, ⫺12

1.14 No, no

1.16 1a24.66 ⫻ 10

ft; 1b25.18 ⫻ 10

⫺2

lb ft

;

1c23.12 ⫻ 10

⫺3

slugs ft

; 1d22.36 ⫻ 10

⫺2

ft ⭈ lb s;

1e25.17 ⫻ 10

⫺6

ft s

1.20 1a27.57 ⫻ 10

⫺2

s; 1b24540 liters min;

1c22.67 ft

1.24 1a20.240 mi

; 1b24.41 ⫻ 10

1.26 30.6 kg; 37.3 N

1.28 1150 kg m

; 11.3 kN m

1.32 9770 N m

; 996 kg m

; 0.996

1.34 0.335; 3290 N m

1.36 4.76 kg

1.38 1a20.0214 kg m

; 1b2␳

Mars

␳

earth

⫽ 1.75%

1.40 1.26 m

1.42 668 lb

1.46 0.6 N ⭈ sm

, 1.3 ⫻ 10

⫺2

lb ⭈ s ft

1.48 31.0%

1.50 5 ⫻ 10

⫺5

N ⭈ sm

; 10.4 ⫻ 10

⫺7

lb ⭈ s ft

1.52 0.116 lb ⭈ s ft

; larger

1.54 15,000 1water2; 752 1air2

1.56 C ⫽ 1.43 ⫻ 10

⫺6

kg 1m ⭈ s ⭈ K

2; S ⫽ 107 K

1.58 D ⫽ 1.767 ⫻ 10

⫺6

N ⭈ sm

; B ⫽ 1.870 ⫻ 10

5.76 ⫻ 10

⫺4

N ⭈ sm

1.60 V

V ⫽ 2c 11 ⫹ c2

1.62 11.7 ⫻ 10

⫺4

1.64 0.0883 m s

1.66 1a2C

⫽ 153 s

⫺1

; C

⫽ 4350 ft

⫺2

⫺1

1b25.72 ⫻

⫺5

lb ft

1y ⫽ 02; 6.94 ⫻ 10

⫺5

lb ft

1y ⫽ 0.05 ft2

1.68 0.944 ft ⭈ lb; 17.8 ft ⭈ lb s

1.70

1.76 4.14 ⫻ 10

psi

1.78 1a2343 m s; 1b21010 m s; 1c2446 m s

1.80 170 psi

1.82 4.25 ⫻ 10

⫺3

slugs ft

; 305 ⬚F

1.88 3000 m

1.90 13 kPa 1abs2

Ⲑ

ⲐⲐⲐ

᐀ ⫽ 2pR

/mw1R

⫺ R

Ⲑ

ⲐⲐ

Ⲑ

ⲐⲐ

Ⲑ

ⲐⲐ

Ⲑ

ⲐⲐ

Ⲑ

ⲐⲐ

Ⲑ

ⲐⲐ

Ⲑ

ⲐⲐ

1.92 5.81 kPa 1abs2; 0.842 psi 1abs2

1.94 0.0600 N m

1.96 12.2 Pa

1.98 1a20.126 D; 0.126 in.

1.100 3.00 mm

1.102 0.186 in.; 4.65 in.

Chapter 2

2.2 59.2 kPa

2.4 1a216.0 kPa; 9.31 kPa; 1b2no

2.6 50.5 M Pa; 7320 psi

2.8 0.0797 psi

2.12 10.2 psia

2.14 1a258.8 kPa; 1b2442 mm Hg

2.16 1a21240 lb ft

1abs2; 1b21040 lb ft

1abs2;

1c21270 lb ft

1abs2

2.18 12.1 kPa; 0.195 kg m

2.20 29.43 in. Hg

2.22 60 kPa

2.24 ⫺187 lb ft

2.26 1a20.759 m; 0.759 m 1without vapor pressure2;

1b210.1 m; 10.3 m 1without vapor pressure2;

1c212.3 m; 13.0 m 1without vapor pressure2

2.28 4.67 psi

2.30 ⫺3.32 kPa

2.32 0.224 psi

2.34 h ⫽ 1p

⫺ p

21␥

⫺ ␥

2.36 0.040 m

2.38 94.9 kPa

2.40 0.449 m

2.42 3.99 psi

2.44 27.8 deg

2.46 0.304 ft 1down2

2.48

2.50 p1psi2⫽ 0.416

2.52 889 N

2.54 92.4 kN; 0.0723 m along gate below centroid

2.56 639 kN; 0.990 m above bottom

2.58 107 kPa

2.64 33,900 lb

2.66 1a216.2 m; 1b2No

2.68 5.24 ft

/ ⫽ 3d ⫹ 11.31 ⫺ 1d

⫹ 18.61 d ⫹ 1282

Ⲑ

ⲐⲐ

Ⲑ

nswers to

Selected Even-Numbered

Homework Problems

ANS-1

JWCL068_ans_01-06.qxd 9/12/08 2:06 PM Page ANS-1

2.70 3.55 m

2.72 1a22.11 m; 1b2941 kN

2.74 78.5 kN; 2.03 m below free surface

2.76 102 ft ⭈ lb

2.78 48.2 ft; 61.1 ft; 71.8 ft; 81.1 ft; 89.1 ft

2.84 20,200 lb

2.86 7.77 ⫻ 10

lb acting 406 ft up from base of dam

2.88 64.4 kN

2.90 60.8 kN; 0.100 m below center of tank end wall

2.92 337 lb, 882 lb

2.94 485 kN

2.98 1a2786,000 lb; 1b2315,000 lb

2.100 54,600 lb

2.104 2480 kg

2.106 681 lb up; 6.22 ft to right of A

2.108 89.5

2.110 ⫺8.63 ft s

2.112 1a268.9 lb ft

; 1b257.4 lb

2.114 37.4 deg

2.116

2.118 5.76 ft

2.120 28.8 kPa

Chapter 3

3.2 13.7 m s

3.4 1a2⫺19411 ⫹ x2⫹ 62.4 lb ft

; 1b241.2 psi

3.6 ⫺30.0 kPa m

3.8 ⫺0.838 psi ft; 0.0292 psi ft

3.10 1a2⫺2 a

[1 ⫺ 1ax2

] x

1b2p

⫹ V

[1ax2

⫺ 1ax2

3.14 12.0 kPa; ⫺20.1 kPa

3.16 1a24.97 lb ft

; 1b20.681 lb ft

3.22 3.21 N m

3.24 4.50 kPa

3.26 30 deg

3.28 0.14 in.

3.30 194 mph

3.32 3.26 m

3.36 Tank 1a2

3.38 1248 lb ft

3.40 h ⫽ 0

3.44 43.0 psi

3.46 10.7 s

3.48 1a20.223 ft; 1b29.22 lb ft

3.50 3.19 ft

3.52 0.0156 D

[10.12

⫺ D

s when D m

3.54 2.35 m; 11.9 m

3.56 2.54 ⫻ 10

⫺4

3.58 hH⫽ 1 [1 ⫹ 1dD2

]

3.60 1a23.98 ft; 1b236.0 ft s, ⫺510 lb ft

3.62 86.3 Pa

3.64 1.31 ft

3.66 ⫺8.11 psi

3.68 1a20.0696 m

s; 1b20.574 m

3.70 HH

⫽ 1 11 ⫹ cx L2

, where

c ⫽ 2g

max

Ⲑ

ⲐⲐⲐ

Ⲑ

ⲐⲐ

ⲐⲐⲐ

Ⲑ

⬃

Ⲑ

ⲐⲐ

ⲐⲐⲐ

ⲐⲐ

Ⲑ

h ⫽ a/

Ⲑ

ANS-2 Answers to Selected Even-Numbered Homework Problems

3.72 0.0132 m

3.74 0.346 ft

s, 7.89 ⫻ 10

⫺4

slugs s; 0.0254 lb s

3.76 4

3.78 0.141 ft

s, ⫺499 lb ft

, ⫺312 lb ft

3.80 0.37 m

3.82 7.53 ft

3.84 1.38 ft

3.86 0.351 ft

3.88 36.5 s

3.92 404.5 kPa

3.94 9.10 ⫻ 10

⫺3

s; 57.9 kPa

3.96 2.00 ⫻ 10

⫺4

s; 0.129 m

3.98 155 N m

3.102 0.174 m

3.106 6.10 ⫻ 10

⫺3

3.108 1.016 in.

3.110 3.46 Q

3.112 145 ft

Chapter 4

4.6 5 ft s; 1x

⫹ 8x ⫹ 252

ft s

4.8 20 ft s for any x, y; ⫺90 deg, ⫺45 deg, 0 deg

4.10 y

⫽ x ⫹ c

4.12

4.14 1a20.712, ⫺8.50; 1b21.69 ft s

4.18 xh⫽ 1u

2ln1h 1h ⫺ y2⫺ yh

4.20 10 ft s, 9 ft s, 6 ft s, 4 ft s

4.22 ;

4.24 a

⫽ x; a

⫽ 8x

14x

y ⫺ 12; a

⫽⫺1x ⫹ 4x

4.26 1a24 ft s

, 2 ft s

; 1b2negative

4.28 10 ft s; 10 ft s

4.30 ⫺1.65 ⫻ 10

ft s

; ⫺5.12 ⫻ 10

4.32

4.34 ⫺33.8 ft s

; 1.05

4.36 1225x ⫹ 1502ms

; 0; 1225x ⫹ 1502ms

;

150 m s

; 375 m s

4.42 0, Kr

4.44 19V

4a2sin ␪ cos ␪; 19V

4a2sin

␪; 0 deg; 90 deg

4.46 14V

a2sin ␪ cos ␪; 14V

a2sin

␪

4.48 1a20.4 ft s

, 0; 1b21.28 ft s

, 2.88 ft s

;

1c21.34 ft s

, 2.88 ft s

4.50 3.13 ⫻ 10

⫺5

; 2.00 ⫻ 10

⫺3

4.52 25,600 ft s

; 25.0 ft s

4.54 40 mi hr

4.56 1a22.5 ⬚F hr; 1b21.25 ⬚F hr; 1c2⫺10 ⬚F hr

4.60 5.0 m

4.62 132 ft

4.66 2V

hb 3

4.72 7.14 slug ⭈ ft s

Chapter 5

5.6 3.66 slugs s

5.8 1.70 ft s

5.10 decrease

Ⲑ

ⲐⲐⲐ

Ⲑ

ⲐⲐ

ⲐⲐⲐ

ⲐⲐ

Ⲑ

ⲐⲐ

Ⲑ

c ⫽ 0.490 s

⫺1

11 ⫺ x

Ⲑ

/23ce

⫺ct

⫺ 1V

Ⲑ

/211 ⫺ e

⫺ct

Ⲑ

ⲐⲐ

⫽ 1V

Ⲑ

⫽ 1V

Ⲑ

ⲐⲐⲐⲐ

ⲐⲐ

Ⲑ

y ⫽ e

Ⲑ

2⫺x2

⫺ 1

Ⲑ

ⲐⲐⲐⲐ

ⲐⲐⲐ

Ⲑ

JWCL068_ans_01-06.qxd 9/12/08 2:06 PM Page ANS-2

5.12 3.18 ft

5.14 0.0125 lbm ft

5.16 229 s

5.18 3.63 ft s

5.20 1a20.711; 1b20.791; 1c20.837; 1d20.866

5.22 485 slugs s

5.24

5.26 12.2 min

5.30 0.51 ft day

5.32 3.52 gal flush 1gpf2

5.38 2.66 10

4

5.40 0; 7420 N

5.42 motion to right 1a2, 1b2, 1c2; motion to left 1d2

5.44 70.1 m s; 30,800 N

5.46 72,000 N; 67,400 N

5.48 6650 lb

5.50 28.7 ft

5.52 1a2W

 9.8 lb; 1b2W

 14.7 lb

5.54 185 kN; 45.8 kN

5.56 3580 lb

5.58 43 lb

5.60 13.3 lb

5.62 34

5.64 1a2181 lb; 1b2146 lb

5.66 3.94 ft

5.68 2.52 ft

s; 61.2 ft s

5.70 8220 lb

5.76 1a2231 N  m; 185 rad s; 1b2200 N  m;

160 rad s; 1c2116 N  m; 92.5 rad s

5.78 12.8 MW

5.80 348 kW

5.82 turbine; 36.8 1ft  lb2slug or 1.14 1ft  lb2lbm

5.90 No

5.92 right to left; 0.32 ft

5.94 2.17 ft

5.96 right to left; 0.5 m

5.100 0.830 ft

5.102 30.4 ft

s; 36.3 ft

5.104 9261ft  lb2slug; 2001ft  lb2slug

5.108 2.22 MW

5.110 1.21  10

5.112 930 kW

5.114 303 R; 267 R; 0.88

5.116 1.67 ft

5.118 16101ft  lb2slug; 2.02 hp

5.120 31.1 hp

5.122 1.78 kW

5.124 1a256%; 1b211.7 lb

5.126 32,200 lb; 8,190 lb

5.128 2.36 ft

5.130 1a24.29 m s; 17.2 1b2558 N  ms

5.132 1a21.11; 1b21.08; 1c21.06; 1d21.05; 1e21.04;

1f21.03

5.134 305 1ft  lb2lbm; 71%

5.136 84.2%

5.138 5.16 1ft  lb2lbm; 86%























82 U/d



Answers to Selected Even-Numbered Homework Problems ANS-3

Chapter 6

6.2 2x,4xt

; 2y,4yt

; V  0; a  4  4 ft s

;

a  5.66 ft s

6.4 1a20; 1b2

6.6

6.8

6.10

6.16 No

6.18

6.22

6.24

6.26 1a2 ; 1b2 A ln r  C

6.28 1a2  2xy; 1b2q  2x

6.32 1a2p

 p

; 1b2p

 p

6.34  1532x

 5xy

 C

6.36  A ln r  Br cos ␪  C; ␪  ␲, r  AB

6.38 60.5 psi

6.40 1a2Yes; 1b2Yes,  21x  y2 C; 1c20

6.42 1a2  U10.866x  0.500y2;  U10.866y 

0.500x2; 1b2

6.46 1a2 ; 1b2␪  1.33 rad

6.50 0

6.52 1.80 ft

6.54 , H  0.0250 ft

6.58 80 mph; 53.3 mph; 40 mph

6.60

6.62 1b2V

 0, V

 68.2 mph

6.64 u

 U  1 H2␲

6.68 F

 978 lb ft

6.70 1a20; 1b24␲Ua

6.72 1a2F

 34,900 lb; 1b2F

 105,000 lb

6.76 sin ␪ cos ␪; ␪ falls in range

6.80 ␴

5.98 kPa, ␴

6.02 kPa, ␶

 45.0 Pa

6.82 1a21b21c2

6.84

6.86

6.88 4.98 gal min

6.90

6.92

6.94

⁄3

6.96 0.355 N  m

6.100 1a2Re  640  2100; 1b2180 kPa; 1c260.0 N m



b 

u  31U

 U



b4y  U

q  1rgh

sin a2





3mV

 rg



/  2.3  10

5



s, t  2.25 N



2m  2rx



0x a  2x

;0v



0y 2x;

90°



0u  4rU







2pA

y 

2pU

c  m a



g



cc 

Ar

 C

4ru  9r

cos u  f 1r2

v 

y

 f1x2

c  Au  Br

1

sin u  C



r

 r

u 



 f1y2

z  3xy

k; No



22k

;v 1y



2  z2i

 15z



22j





JWCL068_ans_01-06.qxd 9/12/08 2:06 PM Page ANS-3

6.102

6.104 V  1.10  10

2

6.106

6.108 lb ft

per ft

6.110 1a242.6%; 1b221.7%

Chapter 7

7.6 1a2103 m s; 1b2444 m s

7.8 k  r  3 pi terms

7.10 1a2p is halved; 1b2p is doubled

7.12 pD

1V2 1D

, D

V 2

7.14 p 1D



2 1QD

2

7.16 p 1D



2 1QD

2

7.18

7.20 hD 1D

7.22 p  1 D

1for a given velocity2

7.24 dD 1VD , V

7.26 1a2

1b2

7.30 p 1V

2 0.505 1Dd2

3.99

7.32 1a2

1b2

7.34 1a2n 1 2; 1b2Yes

7.38 Colder

7.40 0.963 ft s

7.42 9.49 m s

7.44

7.46 1170 km hr

7.48 187 mph

7.50

7.52 1a2400 km hr; 1b2170 N

7.54 26.4 lb

7.56 1a2d

 dD, 



 

, g











, V

D   



; 1b2V



0.707

7.58 1a21b2

7.60 1a212 m s; 1b2900 N

7.62 0.0647 to 0.0971

7.68 1a2400 N; 1b27222 W

7.70 1a2 ; no

1b20.410 gpm; 2.46 in.

7.72 1a2nD V  1VD 2; 1b2Yes; 1c27.54 ft s

7.74 1a2

1b2no

7.76 1a2 ; 1b20.333 ft; 1c2p  1VV

, No

7.78

7.80

Chapter 8

8.2 1.0 ft

8.4 blue and yellow streams; green



r*2 0v



0r*



0t*  p



m2 0



0r*



1rvh



m2 0u*



0t*  0



0y*



 f1/



1r  r



 V



g D, 1r  r







 V



U, V



 VD







Q  f1/



/, Q



g, rQ



/m2



31.1 lbd



 f1d



D2;







d  f1H



d, g



, m



s  4.44  10

3



b  0.0833 1h



1.00



b  f1h



b, /



b2;



22ᐃb



prdD

V VD 2r



ᐃ  f1b



d, d



D2;









/  f1s



gr2









¢p

 33.1



11  r



c1 



 R



ANS-4 Answers to Selected Even-Numbered Homework Problems

8.6 17.7 ft

8.8 0.0883 m

8.10 1a28.93  10

; 1b28.93  10

8

8.12 V

max

 2 m s, V  1 m s, Q  1.3 

3

8.14 0.15 lb ft

, 0.06 lb ft

, 0 lb ft

8.16 from 1b2to 1a2

8.18 0.354 D

8.20 3.43 m, 166 kPa

8.22 1a212.42 kPa; 1b215.85 kPa

8.24 2.01 ft s

8.26 D

8.28 18.5 m

8.30 8.88  10

8

8.32 26,300, turbulent

8.38 0.00243 ft

8.42 0.65 Pa m

8.44 0.02 ft ft

8.46 water out if air in if

8.48 1b2

8.50 smaller pipe

8.52 1a21a2

8.54 21.0

8.58 8.15 ft

8.60 1a2

8.62 39.7 kPa from losses and 93.0 kPa from

change in kinetic energy

8.64 13.0

8.66 0.223 lb ft

8.68 9

8.70 disagree

8.72 aspect ratio equal to 4

8.74 0.188 m

8.76

8.78 1a2 ; 1b2

8.80 No

8.82 50.0 m

8.84 0.325 psi

8.86 16.5 ft

8.90 379 kW

8.94

8.98

8.100 0.442 ft

8.102 0.535 ft

8.104 0.031 m by 0.053 m

8.108 0.0746 cfs; 0.339 cfs

8.110 0.662 ft

8.112

8.116 24.9 psi

8.118 64.8 kPa

8.120

8.122

8.124

Chapter 9

9.2 1.1

9.4 3.45 kN, 0.560 kN; 3.47 kN, 0.427 kN

0.0936 ft



0.115 ft



0.528 ft



0.0284 m



s; 0.0143 m



s; 0.0141 m



5.73 ft



0.06 ft



137 ft135 ft

0.899 lb



133 kPa;

23.8 ft

908 lb



34.5 lb



;

V  0.5 m



sV  5 m









JWCL068_ans_01-06.qxd 10/14/08 8:06 PM Page ANS-4

9.6 Fig. 9.6c

9.12 1.12 m, 7.92  10

3

9.14

9.16 7.54  10

3

ft s; 0.471 ft s; 2.62  10

5

ft s

9.22 1a227.6 ft s; 1b220.5 mph

9.30 , 

 4U 132

9.36 Larger by a factor of 4

9.38 48.8 lb

9.40 10,300 lb

9.42 1.4, upright

9.44 85.4 kW

9.46 2

9.48 0.0296 N

9.50 12.9 hp

9.52 1.06 m s

9.54 16.8 ft s

9.58 1.10  10

7

m s, 1.20  10

7

9.60 162 ft ⴢ lb

9.62 8,950 N ⴢ m

9.64 0.350 hp

9.66 greater

9.68 58.4 hp

9.72 180 N

9.76 7220 m s

9.78 9.65 lb ft

9.80 0.841 ft s

9.86 41.6 ft s

9.90 1a20.0166 hp; 1b232.4 hp

9.92 11.2 ft

9.94 0.288

9.96 405 lb

9.98 1.72 U

sea level

9.104 19.1

9.106 5.72% increase

9.110 28.4%

Chapter 10

10.2

10.4 1a2supercritical; 1b2supercritical;

1c2subcritical

10.8 5.66 ft

10.12

10.14

10.16 2.45 m; 0.388 m

10.18 1.13 ft; 5.82 ft

10.20 1.77 ft; 1.97 ft

10.24 1.83 ft

10.26 0.694 ft

10.30 0.429 ft

10.34

10.36 0.0126

10.38

10.40 0.0169

10.42

10.44 Yes

10.46 Yes

10.48 40.9 m



9.25 ft



5.14 N



7.07  10

5

616 km



8.30 ft



25 m







d  4.121nx





6.65  10

6



Answers to Selected Even-Numbered Homework Problems ANS-5

10.50

10.54

10.56

10.58

10.60 1.19 m

10.62 0.840 m

10.64 2.31 ft

10.66 Same

10.68 2.53 ft; Not possible

10.70 8.77 m

10.72 0.368 ft

10.74 2.21 m

10.76 1.64 ft

10.78 0.000816

10.80 0.000664

10.82 0.000269

10.84 0.00757

10.88

10.90

10.92 1a20.228 ft; 1b28.09, 0.223; 1c25.15 ft

10.94 1.51 m, 12,500 kW

10.96 upstream

10.98

10.100 Yes

10.102

10.104 4.70 ft

10.106 0.324 ft hr; 5.53 hr

10.110

Chapter 11

11.4 1a271,700 J kg; 1b2100,000 J kg;

1c21.58 kg m

; 1d2396 J kg ⴢ K

11.10 351 K

11.12 1a21520 1ft ⴢ lb2lbm; 1580 1ft ⴢ lb2lbm;

1b21.52  10

1ft ⴢ lb2lbm; 1.95  10

1ft ⴢ lb2lbm;

1c24.56  10

1ft ⴢ lb2lbm; 6.80  10

1ft ⴢ lb2lbm

11.16 ,c

water

 1470 m s,

air

 340 m s

11.24 0.625

11.28 1a22000 mph; 1b22930 ft s; 1c2893 m s

11.36 1a22.34 lbm s; 1b22.51 lbm s

11.38 283 m s; 0.89

11.40 269 m s; 0.90

11.46 A

 0.36 m

, p

 23 kPa 1abs2,T

 113 K

11.48 1a20.483%; 1b21.43%; 1c20.445%; 1d20.0163%

11.54 increase

11.56 11 psia

11.58 2830 lb ft

11.60

11.62 404 kPa 1abs2; 81.19 K; 31 m s

11.66 2.29

11.68 1.9; 648 m s

11.70 394 K; 82 kPa 1abs2

11.72 1160 R; 132 psia; 26.1 lbm s



 84.9 kPa 1abs2; V

 520 m



674 K; p

 45 kPa 1abs2; T

 786 K;

 101 kPa 1abs2; V

 104 m



s; T



 282 K; p

 95 kPa 1abs2; T

 288 K;







steel

 2.19  10





 1.294 ft; H

 4.39 ft; triangular



0.116 m



4.36 ft



0.00759 ft



13.7 ft



119 m



17.3 m



18.2 m



6.22 ft



JWCL068_ans_01-06.qxd 10/14/08 8:06 PM Page ANS-5

11.74 1.35 m

11.76 at duct entrance T  130 K; p  6.0 kPa 1abs2;

 293 K; p

 101 kPa 1abs2; V  571 m s;

just upstream of shock T  296 K; p  17

kPa 1abs2; T

 396 K; p

 47.7 kPa 1abs2;

V  448 m s; just downstream of shock

T  354 K; p  30.8 kPa 1abs2; T

 396 K;

 46.4 kPa 1abs2; V  299 m s; at duct exit

T  351 K; p  26.6 kPa 1abs2; T

 407 K;

 45.9 kPa 1abs2; V  337 m s

Chapter 12

12.4 pump

12.8 BG, 1ft ⴢ lb2slug; hp; SI, 1N ⴢ m2kg or J kg; J s

or watt 1W2; EE, 1ft ⴢ lb2lbm; hp

12.10 10.8 lb ft

; turbine

12.16 turbine and pump

12.18 379 1ft ⴢ lb2lbm







ANS-6 Answers to Selected Even-Numbered Homework Problems

12.20 1b2891 ft ⴢ lb; 0 rpm

12.22 1.84 hp

12.24 11.5 m

12.28 increase to 8.43 ft

12.30 1a22.07 kW; 1b212.6 m

12.34 365 gpm

12.36 255 gpm; no

12.38 1a20.0529 m

s; 1b213%

12.42 0.0328 m

s; 8 m

12.44 Yes

12.46 1000 gpm; 800 ft

12.48 671 at maximum efficiency

12.54 mixed-flow

12.56 6.4 hp; 163 ft

12.62 0.0109 ft

s; 0.150 ft ⴢ lb; 0.0409 hp

12.66 23,200 kW

12.68 41,000 hp

12.70 Francis; 378 ft



JWCL068_ans_01-06.qxd 9/12/08 2:06 PM Page ANS-6

I-1

Absolute pressure, 13, 48

Absolute temperature, 7, 13

Absolute velocity, 176, 196, 218, 647

Absolute viscosity, 15

of air, 717, 718

of common gases, 14, 714

of common liquids, 12, 714

of U.S. Standard Atmosphere, 719, 720

of water, 716

Acceleration, 95, 156, 265

centrifugal, 164, video V3.4

convective, 160, 164

field, 156, 265

gravitational, 8, 719, 720

local, 159

normal, 95, 164, video V3.1, video V3.4

particle, 156

streamwise, 95, 164, video V3.1, video V5.3

Accessibility of flow, 544

Acoustic velocity, 22, 585

of air, 717, 718

of water, 716

Adiabatic flow, 224, 584

with friction, see Fanno line flow

reversible, see Isentropic flow

Adverse pressure gradient, 300, 490

Aerodynamics, 28

Air, table of properties of, 717, 718

Airfoil, 514, video V9.15, video V9.17, video V9.18

Alternate depths, 543

Analogy, compressible and open channel flow, 634

Andrade’s equation, 18

Aneroid barometer, 55

Angle:

of attack, 492, 515

of contact, 25

of Mach cone, 590

Angular deformation, 264, 267, 269, video V6.3

ndex

Angular momentum, see Moment of momentum

Angular momentum flow, 216, video V5.10

Annulus, flow in, 316

Apparent viscosity, 16

Archimedes, 27, 28, 69

Archimedes’ principle, 68, video V2.7

Area:

centroid, 59, 60

moment of inertia, 59, 60

product of inertia, 59, 60

Area ratio, critical, isentropic flow, 602

Aspect ratio:

airfoil, 515

plate, 341

Atmosphere, standard, 47

properties of, 47, 719, 720

Atmospheric pressure, 13, 47

Available energy, 230

Average velocity, 190

Axial-flow machine, 647

Axial-flow pump, 671

Axisymmetric flow, 463

Backward curved blades, 657

Backward difference, 703

Barometer:

aneroid, 55

mercury, 49

Basic differential equations of fluid motion, 279

Basic dimensions, 4, 334

Bellows meter, 447

Bends, 421

Bernoulli, D., 27, 28, 99

Bernoulli equation:

cautions on use of, 99, 281

derivation from , 99, 279, video V3.1

derivation from first law of thermodynamics, 229

extended, 232

F ⫽ ma

JWCL068_ind_001-014.qxd 11/12/08 10:51 AM Page I-1

I-2 Index

Bernoulli equation: (cont.)

irrotational flow, 130, 283

outside boundary layer, 473

physical interpretation, 102

restrictions on use of, 126, 281, video V3.12

unsteady flow, 128

use of, 110, video V3.2

Best efficiency point, 660

Best hydraulic cross section, 554

BG units, see British gravitational system of units

Bingham plastic, 17

Blade velocity, 647

Blasius, H., 29, 353, 475

Blasius formula, 353, 415

Blasius solution, 476, 477

Blower, 645, 673

Blunt bodies, 463, video V9.2

Body force, 40, 201, 276

Boiling, 23, 116

Booster, 673

Bottom slope, 541

Boundary conditions:

inviscid flow, 295

no-slip, 15, 297, 309, video V1.4, video V6.11,

video V6.12

numerical methods, 705

pipe exit, 110

Boundary element method, 701

Boundary layer:

concept of, 27, 282, 468, video V1.4, video

V6.11, video V9.8

displacement thickness, 472

effect of pressure gradient on, 488

effect of wall roughness, 504

equations, 475

flat plate, 470, 472

laminar:

approximate solution, 482

Blasius solution, 476, 477

momentum integral equation for, 479, 482

momentum thickness, 474

pipe, 388

pressure gradient, 488

separation, 468, 490, video V6.8

thickness, 472, video V9.3

transition, 471, 483, video V9.5

turbulent, 471, 485

velocity profiles, 484, 491, video V9.3

vorticity, 471

Bound vortex, 519, video V4.6

Bourdon pressure gage, 55, video V2.3

Boussinesq, J., 405

Brake horsepower, 659

British gravitational system of units, 8

Broad-crested weir, 564, video V10.14

Buckingham, E., 29, 335

Buckingham pi theorem, 335

Bulk modulus, 20, 587, video V1.7

of common liquids, 12

of elasticity, 20

Buoyant force, 68, video V2.6, video V2.7,

video V11.4

Canal, 551

Capillary action, 25, video V1.10

Capillary tube viscometer, 33, video V1.5

Casing, 653

Cauchy, A., 28, 349

Cauchy number, 347, 349

Cavitation, 24, 116

number, 349, 363, 372

Center of buoyancy, 69, video V2.10

Center of pressure, 58, 60

Central difference, 703

Centrifugal pump, 653

Centroid, 59

of common areas, 60

CFD, 318, 701, video V2.9, video V6.2,

video V6.15, video V11.5, video VA.1

Chaos, 409

Chezy, A., 28, 548

Chezy coefficient, 549

Chezy equation, 547, 548

Choked flow, 597, 613

Chord length, 514

Circulation, 292

about an airfoil, 518

origin of, 519

Colebrook formula, 414

Completely turbulent flow, 412

Composite body drag, 507

Compressibility criterion, 127

Compressibility of fluids, 20

Compressible flow, 126, 580, video V11.4

with area change, 593, video V11.5, video V11.6

categories, 588

graphs of, 721–724

with friction, 609

with heat transfer, 620

turbomachines, 685

two-dimensional, 635

Compression wave, 635, video V11.7

Compressor, 645, 673, 686, video V12.5

corrected speed, 689

multi stage, 686

stall, 688

surge, 688

Computational fluid dynamics (CFD), 318, 701,

video V2.9, video V6.2, video V6.15, video V11.5

Conservation:

of energy, see First law of thermodynamics

of linear momentum, 200, 275, video V5.4,

video V5.5, video V5.6

of mass, 112, 188, 269

Contact angle, 25

Continuity equation:

cylindrical coordinates, 272

differential equation, 270

finite control volume, 112, 188

compressible flow, 593

incompressible flow, 195, video V5.1, video V5.2

unsteady flow, 189, 271

rectangular coordinates, 270

Continuum hypothesis, 4

Contraction coefficient, 111, 121, 566

Control surface, 165

Control volume, 165

accelerating, 201

deforming, 166, 198

fixed, 165, 188

JWCL068_ind_001-014.qxd 11/12/08 10:51 AM Page I-2

Index I-3

guidelines for selection, 177, 200

infinitesimal, 263

moving, 176, 196, 212

velocity, 196

Convective acceleration, 160, 164

Convective derivative, 159

Converging–diverging diffuser, 595

Converging–diverging duct flow, 595, video V11.5,

video V11.6

Converging–diverging nozzle, 595, video V11.5,

video V11.6

Conversion factors, 9

Core flow, 282

Couette flow, 311

Creeping flow, 318, 348

Critical depth, 543

Critical flow, open channel, 536, 540, 634

Critical pressure ratio, 597

Critical Reynolds number, 471, 483

Critical state, compressible flow, 597, 615

Curl operator, 268

Curved surface, forces on, 66

Cylinder:

drag coefficient for, 501

inviscid flow around, 301, video V6.6

large Reynolds number flow around, 468,

video V6.8

low Reynolds number flow around, 468,

video V6.15

pressure distribution on surface of, 301

rotating, 303, 520

Cylindrical coordinates, 75, 272

D’Alembert, J., 28, 302

D’Alembert’s paradox, 302, 489

Darcy, H., 28

Darcy friction factor, 396

Darcy–Weisbach equation, 412

DaVinci, L., 27, 28

Deepwater wave, 538

Deformation:

angular, 264, 267, video V6.3

linear, 264, 266

rate of, 266

Deforming control volume, 166, 198

Del (gradient) operator:

cylindrical coordinates, 284

rectangular coordinates, 41

Density, 11

of air, 717, 718

of common gases, 14

of common liquids, 12

of U.S. Standard Atmosphere, 719, 720

of water, 716

Derivative:

convective, 159

local, 159

material, 157

substantial, 157

Detached shock, 636

Differential analysis, 263

Diffuser, 420, 595

Diffuser pump, 654, video V8.11

Dimensional analysis, 5, 333, 335

Dimensional homogeneity, 4, 333

Dimensionless groups, 334

list of, 347

Dimensionless products, 334, 335

Dimensions:

basic, 4, 334

of common physical quantities, 5

reference, 335, 342

Discharge coefficient:

nozzle, 443

orifice, 442

sluice gate, 566

Venturi meter, 444

weir, 563, 565

Discretization, 701

Displacement thickness, 472

Distorted model, 359, video V7.8, video V7.12,

video V7.11, video V7.17, video V7.18

Doppler effect, 590

Doublet, 293

strength of, 294

Drag, 302, 463, 493

form, 495, video V7.2, video V9.7

friction, 482, 494

in potential flow, 305

pressure, 495

Drag coefficient, 350, 466, 494

airfoil, 519

automobile, 508

composite body, 507

cylinder, 501

effect of compressibility on, 503, 588

effect of Froude number on, 506, video V9.12

effect of Mach number on, 503, 588

effect of Reynolds number on, 498, 588

effect of shape on, 497, 502, video V9.7,

video V9.13

effect of surface roughness on, 366, 504

ellipse, 497

flat plate normal to flow, 497, 502, video V7.2

flat plate parallel to flow, 487, 497, 502

form, 495

friction, 487

from model studies, 363

pressure, 495

selected three-dimensional objects, 511

selected two-dimensional objects, 510

sphere, 366, 499, 501, 504, 505, 521, 588

streamlined body, 498

vehicle, 508

Duct, 383, 425, 609

Dynamic pressure, 105

Dynamic similarity, 356

Dynamic viscosity, 15

of air, 717, 718

of common gases, 14, 714

of common liquids, 12, 714

of U.S. Standard Atmosphere, 719, 720

of water, 716

Eddies, 403

Eddy viscosity, 405, video V8.7

EE units, see English engineering system of units

Efficiency, 239, 659, 683

hydraulic, 659

isentropic, 688

JWCL068_ind_001-014.qxd 11/12/08 10:51 AM Page I-3

I-4 Index

Efficiency, (cont.)

mechanical, 659

overall, 659

polytropic, 688

volumetric, 659

Elbows, losses in, 422

Elevation head, 103, 124

Energy:

available, 230

internal, 223, 580

kinetic, 103, 223

per unit mass, 223

per unit volume, 233

per unit weight, see Head

potential, 103, 223

specific, 542

stored, 223

useful, 230

Energy equation, see First law of thermodynamics

Energy line, 123, 430, 541

English engineering system of units, 8

Enthalpy, 226, 581

Entrance length, 388, video V8.10

Entrance loss, 417

Entrance region, 283, 388, 417

Entropy, 240, 583

Equations:

general homogeneous, 5

of motion, 279

restricted homogeneous, 5

Equation of state, 12, 580

Equipotential line, 287

Equivalent length, 416

Euler, L., 27, 28, 279, 349

Eulerian description of motion, 150, video V6.2

Euler number, 347, 349, 372

Euler turbomachine equation, 652

Euler’s equations, 94, 279

Exhauster, 673

Exit pipe loss, 419, video V8.10

Expansion wave, 608, 635, video V11.5,

video V11.8

Extensive property, 166

External flow, 461

Eye, 653

Falling head curve, 659

Fan, 645, 673

Fanning friction factor, 396

Fanno line flow, 609

basic equations of, 609

choking length for, 613

normal shock in, 613

graph for computations of, 722

T–s diagram, 610, 613

Favorable pressure gradient, 490

Field representation, 148, video V4.2

Finite control volume analysis, 187

Finite difference:

grid, 702, 703

method, 701

Finite element:

mesh, 702

method, 701

Finite volume, 701

First law of thermodynamics, 223, 225, video

V5.13, video V5.14

First moment of area, 59

Fittings, losses in, 422

Flap, airfoil, 516, video V9.17, video V9.18

Flat plate:

Blasius solution, 476, 477

momentum integral equation, 478

laminar flow, 480

turbulent flow, 485

roughness effect, 487

Floating body, 69, video V2.7

Flow coefficient, 667, 683

FlowLab, 712

Flow measurement:

external flow

Pitot-static tube, 106, video V3.8

Pitot tube, 124, 632, video V3.8

internal flow:

bellows meter, 447

nozzle meter, 119, 442

nutating disk meter, 446, video V8.14

orifice meter, 119, 442

rotameter, 445, video V8.13

turbine meter, 446

Venturi meter, 119, 443, video V3.10

open channel flow:

sluice gate, 120, 566

weir, 120, 561, video V10.13

Flow meters, see Flow measurement

Flow net, 287

Flowrate:

mass, 112, 189

volume, 112, 190

Flow separation, 468, 492, video V9.6,

video V9.13

Flow visualization, 151, video V4.1, video V4.6,

video V4.9, video V7.16, video V9.13,

video V11.4

Fluid:

definition, 3

ideal, 281

inviscid, 279

Newtonian, 15

non-Newtonian, 16, video V1.6

Fluid dynamics, 11

Fluid machines, 646, videos V12.1–V12.4

Fluid mechanics, history of, 27

Fluid particle, 94

Fluid properties:

graphs of, 714

tables of, 12, 14, 714

Fluid statics, 11

equilibrium in, 40

forces in, 57

pressure height relation, 42, 46, 48

Force:

anchoring, 202, 206

body, 40, 201, 276

buoyant, 68, video V2.6, video V2.7

compressibility, 347

drag, 302, 463, 493

gravity, 347

JWCL068_ind_001-014.qxd 11/12/08 10:51 AM Page I-4