Chapter 11.4 1a2 1b2 1c2 FL1.6 1b21.8 dimensionless; yes1.10 dimensionless; yes1.12 yes1.14 1a2 1b2 70.2 kg; 1c2 13.4 N;

1d2 1e21.16 1a2 1b2

1c2 1d21e2 289 K

1.20 1a2 1b21c2

1.22 30.6 kg; 37.3 N1.241.261.28

*1.30

1.32 58.0 kPa1.34 oxygen1.361.401.42 31.0%1.441.461.48 15,000 1water2; 752 1air2

*1.50*1.52

1.541.561.58 acting to left on plate

*1.60 1a21b2

1.62*1.641.681.70 104 psi1.721.741.76 1.061.78 4.74 psia1.80 70.1 kPa 1abs2; 10.2 psia1.82 97.9 Pa1.84 1a21.86 0.0614 in.1.88 water column

Chapter 22.2 1a2 16.0 kPa; 9.31 kPa; 1b2 no2.6 50.5 M Pa; 7320 psi2.8 No2.102.12 36,000 lb2.16 �7.7 psi

p � K h2�2 � g0h

24.5°

En 1water2 � En 1air2 � 1.52 � 1041.52 kg�m3

3.00 � 105 psi2.45 lb � s�ft20.944 ft � lb; 17.8 ft � lb�slb�ft2 1y � 0.05 ft2

5.72 � 10�5 lb�ft2 1y � 02; 6.94 � 10�5C1 � 153 s�1; C2 � 4350 ft�2s�1

0.552 U�d N�m27.22°ratio � 1103 K; 5.76 � 10�4 N � s�m2

D � 1.767 � 10�6 N � s�m2; B � 1.870 �C � 1.43 � 10�6 kg� 1m � s � K1�22;

0.116 lb � s�ft2; larger5 � 10�5 N � s�m2; 10.4 � 10�7 lb � s�ft2

1.5 � 10�3 N � s�m2; 3.1 � 10�5 lb � s�ft26.44 � 10�3 slugs�ft3; 0.622 lb

991.5 kg�m3r � 1001 � 0.05333 T � 0.004095 T 2;16.0 kN�m3; 1.63 � 103 kg�m3; 1.630.0186 ft3; no2.65 slugs�ft3; 1.37

2.67 ft3�s4,540 liters�min;7.57 � 10�2 m3�s;

5.90 � 104 W;3.86 � 105 m;7.83 � 105 J;6.47 � 105 m2;

1.12 N � s�m222.3 m�s2;4.32 mm�s;

FL�3;FL�2;

ANS-1

Answers to SelectedEven-Numbered

Homework Problems

7708d_Ans_01-06 8/25/01 6:17 PM Page ANS-1 mac76 Mac 76:1st shift:

*Problems marked with an á* are intended to be solved with the aid of a programmable calculator or computer.

2.18 1a2 0.759 m; 0.759 m 1without vaporpressure2; 1b2 10.1 m; 10.3 m 1without vaporpressure2; 1c2 12.3 m; 13.0 m 1without vaporpressure2

2.20 1a2 1b21c2

2.222.24 4.67 psi2.262.28 78.4 lb2.32 0.224 psi2.342.36 0.040 m2.38 94.9 kPa2.402.42 4.06 ft2.442.46 0.304 ft 1down22.48 665 lb2.502.52 1350 lb2.54 33,900 lb; 2.49 ft above base of triangle2.56 2660 lb2.58 436 kN2.62 1a2 1060 kN 1rectangle2; 1010 kN 1semicircle2;

1b22.64 1.88 ft

*2.66 426 kN; 2.46 m below fluid surface2.68 0.1462.702.72 acting 406 ft up from base of

dam2.74 3360 psi2.76 60.8 kN; 0.100 m below center of tank end

wall2.78 203 kN2.80 585 lb acting vertically downward along

vertical axis of bottle2.82 1.22 ft; no change2.84 54,600 lb2.882.90 1a2 18.9 kPa; 1b22.922.942.962.982.100

Chapter 33.2 1a2 1b2 41.2 psi3.4

3.63.8 1⁄2 1⁄23.10 12.0 kPa; 3.12 1a2 1b23.143.163.18 43.0 psi3.20 10.7 s3.223.24 1a2 1b23.263.28 1.40 mph3.303.323.34 45.7 ft3.363.383.40 30 deg3.42 0.188 in.3.44 19.63 psi3.46 2.50 in.3.48 1.31 ft3.503.52 2.343.54 From 3.58 15.4 m3.60 1.98 ft3.62 5.18 psi3.643.66 0.37 m3.68 7.53 ft3.703.723.743.763.82 7.98 psi; 3.84 53.4 psi; 48.1 psi3.863.883.903.92 0.630 ft; 4.48 ft3.943.96 6.51 m; 25.4 m; 6.51 m;

Chapter 44.4 12,224.64.104.124.144.18 �8 m�s2; �2.0 m�s2; �0.08 m�s2

2c2x3; 2c2y3; x � y � 0x � �h1u0�v02 ln 31 � 1y�h2 4xy � Cwhen x � � y; x � y � 0

�9.59 m0.174 m3�s

Q � CH23000 ft3�s; 2000 ft3�s; 2120 ft3�s�7.14 � 10�5 psi

3.97 ft3�s29.0 ft�s;R � 0.998z1�48.68 � 10�3 m3�s0.351 ft3�s7.38 m3�s

0.303 ft3�s; 499 lb�ft2; 312 lb�ft2; �187 lb�ft2

0.229 d10 to 1.00 d10

�8.11 psi

2.54 � 10�4 m3�sD � D1� 31 � 1p2gD1

4 z�8Q22 4 1�4

0.0156 m3�sQ � 1.56 D2, where Q � m3�s, D � m

2.45 � 105 kN�m2; 5.50 � 10�6 m3�s4.10 lb�ft2�5.12 lb�ft2;

10.8 lb�ft2; 124 lb�ft2

8.93 lb�ft234.2 ft�s; none

0.681 lb�ft34.97 lb�ft3;�20.1 kPa

rcz2 � constantrV2 � rg0z �p ��0.838 psi�ft; 0.0292 psi�ft

�30.0 kPa�m�19411 � x2 � 62.4 lb�ft3;

6.04 rad�s10.5 rad�s158 lb�ft24.91 m�s2dz�dy � 0.502

0.208 m320.9 ft3

7.77 � 109 lbFH � 882 kN; FV � 983 kN; yes

1.37 � 106 N � m

�4.51 kPa

27.8°

1930 kg�m3

h � 1p1 � p22 � 1g2 � g12

7,100 N�m3

12.1 kPa; 0.195 kg�m31270 lb�ft2 1abs2

1040 lb�ft2 1abs2;1240 lb�ft2 1abs2;

ANS-2 � Answers to Selected Even-Numbered Homework Problems

7708d_Ans_01-06 8/30/01 7:23 AM Page ANS-2 mac45 Mac 45:1st Shift:

4.244.26 1a2 1b2 1c2 0.25 s4.324.344.36 2

4.384.44 1a2 1b2 1c2

at from streamline4.464.484.504.524.60

Chapter 55.2 1a2 1b25.45.6 19.5 ft5.8 3.18 ft5.105.12 0.064 m5.145.16 1a2 0.711; 1b2 0.791; 1c2 0.837; 1d2 0.8665.185.205.22 32.7 hr5.24 1a2 1b25.30 352 lb to left5.32 to left;

to left; 5.345.365.38 9.27 N to left5.405.44 2.1%5.46 117 lb; 89.2 lb5.48 213 lb to left5.50 0.108 kg5.52 1.82 kPa5.54 at 5.56 05.58 motion to right 1a2, 1b2, 1c2; motion to left 1d25.60 3.97 m5.62 2.96 lb5.66 1a2 181 lb; 1b2 146 lb5.68 1a2 1b2 1c2 920 rpm5.74 1a2 1b25.76 1b25.80 71%5.82 84.2%

5.84 86%5.86 778 ft5.88 1a2 56%; 1b2 11.7 lb5.905.925.96 1a2 392 kPa; 1b2 422 kPa5.102 1a2 1.65 psi; 1b2 1c2 77.2 lb5.106 1a2 1b25.108 2.22 MW5.110 301 hp5.112 actual, ideal, 88%5.114 1a2 1b2 1c25.116 2.02 hp5.118 1a2 4.08 hp; 1b2 9.94 ft5.120 31.3 hp5.1225.124 1a2 1.11; 1b2 1.08; 1c2 1.06; 1d2 1.05; 1e2 1.04;

1f2 1.03

Chapter 66.2

6.4 1a2 0; 1b2No

6.6 No; None 1except both equal to zero26.8 1a2 0; 1b2 1c2

1d26.106.12 1a2 1b2 no stagnation points6.14 No6.16 1a2 1b2

6.18 1a2 Yes; 1b2 Only for 1c2

6.20 1a2 1b26.22 1b26.26 1a2 1b26.286.306.32 60.5 psi6.34 1a2 Yes; 1b2 Yes, 1c2 06.36 80.1 kPa6.38 1a2 1b2 No6.40 1a2

1b2 184 kPa6.42 Yes6.446.466.48 0.0185 at from x-axis36.4°m�s

≠ � v¢u 1b2 � a22C � 0.500 m

0p�0r � 11.60 � 1032 r�3 kPa�m;c � �Kr2�2 � C;

f � 21x � y2 � C;

u � p, r � A�Bf � A ln r � Br cos u � C;c � 5x2y � 15�32y3 � C

pB � p0pA � p0;�1 m3�s 1per unit width2

1.41 ft�sv � �2y;1B�A2x2 � C

y2 �A � B;�Vx � C, c � �Vr cos u � C

c �vr � V sin u, vu � V cos u;

76.0°;x � y � 0;v � 4yz2 � 6y2zg#

� U�bz � �1U�b2k;v � �1U�2b2k;

1y�22k;v � �1y�2 � z2 i � 15z�22j �

0a 0 � 407 ft�s2V � �24j; 0V 0 � 24 ft�s; a � 288i � 288j;ay 1local2 � 0; ay 1conv2 � 181x2 y � y32;ax 1local2 � 0; ax 1conv2 � 181x3 � xy22;

14,500 1ft � lb2�s

0.705 m3�s0.928 m3�s;1.20 m3�s;267°R303°R

558 1N � m2�s4.29 m�s, 17.2°;203 1ft � lb2�slug;

4.58 � 10�3 m3�s0.042 m3�s

166 1ft � lb2�slug;

9800 1ft � lb2�slug;3130 1ft � lb2�slug

53.4 1ft � lb2�s43°;1.35 ft � lb;2.96 ft � lb;

45°7.07 ft�s

17.1 lb�ft

3.94 ft3�s7.01 ft3�s; 674 lb down

Ry � 0FA,y � 0; Rx � 1890 lbFA, x � 1890 lb

62.4 gal�min15.6 gal�min;

17�82 U/d0.0114 slug�s

2.00 m3�s

2.23 ft�s

314 m�s20.4 ft�s45.8 ft�s;

3000 kg�s; 3.00 m3�sr0V�0be�bt3.75 m3�s�25,600 ft�s2; �25.0 ft�s23.13 � 10�5 m�s2; 2.00 � 10�3 m�s2

63.4°22.4 ft�s220 ft�s2;10 ft�s2, 20 ft�s2;

0, K�r 3

32.2 ft�s0; 100 N�m2 � s�18.9 °C�s; �16.8 °C�s

�0.5 s;�0.3 e�0.5t;�x�t2; x�t2

Answers to Selected Even-Numbered Homework Problems � ANS-3

7708d_Ans_01-06 8/30/01 7:23 AM Page ANS-3 mac45 Mac 45:1st Shift:

6.50 1a2 1b26.526.546.60 1a2

1b2*6.626.66 1b2 1c2

6.68 1b26.70 falls in range

of6.72 1a2 1b2 1c2

6.74 1a2 1b2 1acting indirection of flow2;1c2

6.766.786.806.82 1⁄36.846.90 1a2 1b2 180 kPa; 1c2 60.0

6.92 1b2 1.20 Pa6.946.98 0.165 ft

Chapter 77.4 1a2 103 m�s; 1b2 444 m�s7.67.87.107.127.14 1a2 1b2

7.167.18 1for a given velocity2

7.207.22

*7.24

7.26 1a2 correct; 1b2*7.28 1a2

1b27.307.327.34 129 m�s�7.367.38

7.40 187 mph7.427.44 1a2 1b27.46 50.2 kPa 1abs27.48 1a2

no 1b27.50 1a2 1b27.527.54 1a2

1b2 no7.56 100 to 450 mph; no7.58 0.0647 to 0.09717.607.627.64 0.129 psf

Chapter 88.4 2.27 ft8.6 laminar8.8 1a2 1b2 1c2 55.0

8.108.12 0.102 ft8.168.188.208.22 18.5 m8.24 08.26 1a2 0.707 R; 1b2 0.750 R8.288.30 0.03008.348.36 25.1 psi8.388.44 yes8.46 9.008.52 21.08.54 48.0 psi8.56 1a2 1b2

1c28.58 0.188 m8.60 0.285 m8.62 127 hp pump8.64 24.4 hp8.66 disagree8.688.708.728.74 84.0 ft8.76 0.750 psi

0.710 ft3�s22.5 ft�s; 17.0 ft�s0.899 lb�ft2

4.95 m, 6.58 � 105 N�m2N�m2;9.09 m, 8.91 � 10450.2 m, 602 N�m2;

0.211 psi�ft

1.02 � 10�4 ft

0.266 psi, 1.13 psi, �0.601 psi

h � 0.509 m2.01 ft�s0.00376 ft � lb�s

Downhill; 0.596 lb�ft2; 0.238 lb�ft2; 0lb�ft3

�69.8 lb�ft3;�7.40 lb�ft3;

1.31 m�s; 1.25 � 1050.440 ft; 2.80 ft3�s

1r � rs2�r;Vm

2 �gm Dm � V2�g D, 1r � rs2m �rm �Vm

�Um � V�U, Vm Dm �vsm � VD�vs,11.6 ft3�s; 0.500 psi

31.11bd�rV2D2 � f1d�D2;0.410 gpm; 2.46 in.

V/2�Q � f1/i�/, Q2�/5g, rQ�/m2;

170 N400 km�hr;4.62 � 10�9 m2�s; no

1170 km�hrsm�s � 4.44 � 10�3

6.52 � 10�2 ft�sQ�2gH5 � f1b�H2

H�b � 0.0833 1h�b2�1.00H�b � f 1h�b, /�b2;

t � 1.36m�0.0103; 6.26 lb�ft2¢p�rV2 � �1.101A1�A22

2 � 1.07 1A1�A22h�D � f1s�gD22v � CD2g�m 1C � constant2; decrease

¢p 1�D2d�rV2/1

2 � f1V�c, /i�/1222�b�prdD2

V �VD 2r�� � f1b�d, d�D2;Q�A5�4 2g � f1�2A, S02

d�d12 V2 r � f1d2�d1, rVd1�m2

q�b3�2 2g � f1H�b, m�rb3�2 2g2v2/�g � f1h�/2

vu � R2 v�r

N�m2Re � 640 6 2100;

0.355 N � my�b �u � 3 1U1 � U22�b 4y � U2

q � �2rgh3�3mq � 1rgh3 sin a2�3m

0.105 m�s

40 N�m22.81 � 10�4 m2�s;2m � 2rx3

0p�0x �a � 2x3i;0v�0y � �2x;�90°

0ps�0u � 4rU2 sin u cos u; um � 4pAL2

p0 � 1rm2�2p22 3y� 1/2 � y22 4 2pwall �Vwall � 1m�p2 3y� 1/2 � y22 4 ;

y�a � 1012r�3a2 11 � a2�r22sin u � 1

pmin � p0 � 3rU2�2 1at u � p�22;pmax � p0 � rU2�2 1at u � 0 and p2;

8.49 � 10�4 m�s7.50 m2�s

0p�0r � r≠2�4p2 r30p�0u � 0;

ANS-4 � Answers to Selected Even-Numbered Homework Problems

7708d_Ans_01-06 8/30/01 7:23 AM Page ANS-4 mac45 Mac 45:1st Shift:

8.78 1a2 135 ft; 1b2 137 ft8.80 98.82 0.476 ft8.84 78.1 psi8.86 16.5 ft8.888.90 0.442 ft8.92 379 kW8.94 0.491 ft

*8.96 0.0445 m*8.98 0.0746 cfs; 0.339 cfs8.1008.1028.104 24.9 psi8.106 32.4 kPa8.1088.1108.112 5.77 ft8.114

Chapter 99.29.4 1.919.6 Yes9.10 4.70 mm; 14.8 mm; 47.0 mm9.129.16

9.22 0.171 ft; 0.134 ft9.24 1⁄2

9.26 1⁄2

9.28 29.309.34 0.0296 N9.369.40 No9.429.449.46 2.829.489.50 2,200 lb9.52 43.2%9.54 greater9.56 58.4 hp9.62 counterclockwise9.68 859 lb9.70 4.31 MN; 4.17 MN9.72 1a2 0.91, 0.840; 1b2 rise9.78 53.5 kW; 4.46 kW9.809.84 0.0187 U

9.86 65.9 hp9.88 22.5%9.90 1.80 U9.96 19.19.98 0.480, 0.409, 0.451, 0.482

Chapter 1010.2 1a2 supercritical; 1b2 supercritical;

1c2 subcritical10.6 5.66 ft10.810.1010.14 4.14 ft or 1.42 ft10.16 0.528 ft; 0.728 ft10.22 No10.24 2 ft, 3.51 ft; 2 ft, 1.38 ft10.28 3.44 m10.3010.32 1a2 1b2 0.0469; 1c2 0.63610.3410.36 greater10.38 7.42 min10.40 0.00066410.42 0.00026910.44 Yes10.4810.50 2.23 ft; 0.75610.52 Same10.54 0.856 h10.5610.58 0.861 m10.60 10.7 m10.6410.70 0.0075710.72 Decreases10.7410.7610.7810.80 1a2 0.228 ft; 1b2 8.10, 0.223; 1c2 5.15 ft10.82 1.51 m, 12,500 kW10.84 0.0577; 0.00024010.8610.8810.90 53 deg10.9210.94 Yes10.96 3⁄2 5⁄2

Chapter 1111.611.8 351 K

�1890 J� 1kg � K2

�152 4�32 � 18HQ � CW12g 3 12bH

0.470 m3�s

5.85 ft3�s4.36 ft�s

0.00759 ft3�s13.7 ft�s�7.07 � 10�5

18.2 m3�s

244 yd3

33.0 ft3�s

35.0 m3�s1.80 lb�ft2;

0.0468 lb�ft2

8.30 ft�s3.60 m�s

2.47 � 103 kW

7,080 N � m

16.8 ft�s1.06 m�s

0.0438 N � m

2.83d; 0.354d

d�x � 5.03�Rex

d � 5.48 1vx�U2

N�m20.0130 m; 0.0716 N�m2; 0.0183 m; 0.05060.00718 m�s; 0.00229 m�s

0.06 1rU2�22; 2.40

0.0936 ft3�s

0.115 ft3�s0.0221 m3�s

0.0284 m3�s; 0.0143 m3�s; 0.0141 m3�s0.0180 m3�s

5.73 ft�s

Answers to Selected Even-Numbered Homework Problems � ANS-5

7708d_Ans_01-06 8/30/01 7:23 AM Page ANS-5 mac45 Mac 45:1st Shift:

11.10 1a2 constant

1b2 constant

1c2 constant slug; varying

11.1211.16 1a2 1b2 1c211.20 1a2 1b211.22 1a2 1b2 1c211.2411.30 1a2

1b21c21d21e21f21g2

11.32 1a2 1b211.34 1a2 1b2

1c211.3611.44 1a2 1b2 1c211.46 1a2 1b2

11.48 1a2 1b2 1c21d2

11.5411.56 1a2 1b211.58 1a2 1b2

11.60 1a2 1b211.62

11.64 404 kPa 1abs2; 81.19 K;

11.66 1a2 56 kPa; 1b2 47.6 kPa11.68 1a2

1b2

11.7011.72 1a2 0.94; 4 kPa; 1b2 0.8; 17 kPa; 1c2 0.47;

50 kPa11.74 1a2

1b211.76

Chapter 1212.412.6 1b2 fan; 1c212.8 0.08 kW12.10 1b212.12 1.84 hp12.14 11.5 m12.18 No12.22 365 gpm12.24 255 gpm; no12.2612.30 1000 gpm; 800 ft12.32 Yes12.34 centrifugal pump12.36 mixed-flow pump12.44 0.0826 ft; 19.8 hp; less12.46 1a2 1b212.50 26,600 N; 37.6 m�s; 707 kg�s

17.4 m2�s2; 0.84316.6 m2�s2; 0.849;

0.0529 m3�s; 13% open

918 ft � lb; 0 rpm

7160 ft2�s21.02 1ft � lb2�lbm

ft�sT0,2 � 657 °R; p0,2 � 9.8 psia; V2 � 1140Vy � 784 ft�s; T2 � 549 °R; p2 � 5.31 psia;7.5 psia; T0,y � 598 °R; p0,y � 10.2 psia;11 psia; Vx � 1490 ft�s; Ty � 533 °R; py �410 °R; px � 3 psia; T0,x � 598 °R; p0,x �°R; p0,1 � 14.7 psia; V1 � 1660 ft�s; Tx �T1 � 291 °R; p1 � 1.91 psia; T0,1 � 519

p2 �p0,1 � 0.16; Ma2 � 0.89p2 �p0,1 � 0.213; Ma2 � 0.62;

1240 ft�s; 1.25330 psia; Vy � 3500 ft�s2390 °R; Ty � 2190 °R; p0,y � 409 psia; py �

May � 0.521; T0,y �Vy � 937 ft�s;°R; p0,y � 360 psia; py � 309 psia;

May � 0.475; T0,y � 1690 °R; Ty � 1620

31 m�sp02 � 84.9 kPa 1abs2; V2 � 520 m�s674K; p2 � 45 kPa 1abs2; T02 � 786K;p01 � 101 kPa 1abs2; V1 � 104 m�s; T2 �T1 � 282K; p1 � 95 kPa 1abs2; T01 � 288K;

2550 lb�ft22830 lb�ft2;1abs2; 593 m�s; 0.39

18.4 kPa34.7 kPa 1abs2; 314 m�s; 0.8;1.52 kg�s1.7 kg�s;

11 psia�0.0163%

�0.445%;1.43%;0.0483%;m2; 24.8 kPa 1abs2; 82.6 K

0.2570.36 m2; 23 kPa 1abs2; 113 K;0.0308 ft20.00994 ft2;0.012 ft2;

269 m�s; 0.9001070 m�s; 0.884

231 m�s; 0.913;283 m�s; 0.89;0.03 slug�s0.0277 slug�s;

p*�p0 � 0.5283; T *�T0 � 0.8333p*�p0 � 0.5283; T*�T0 � 0.8333;p*�p0 � 0.5439; T *�T0 � 0.8658;p*�p0 � 0.5266; T *�T0 � 0.8299;p*�p0 � 0.4881; T *�T0 � 0.7519;p*�p0 � 0.5457; T *�T0 � 0.8696;p*�p0 � 0.5283; T *�T0 � 0.8333;

0.6251636 mph2400 ft�s;732 m�s;

1280 ft�s; 390 m�s335 ft�s; 102 m�s;893 m�s2930 ft�s;2000 mph;

944 ft�sh2 � h1 � 2.19 � 107 1ft � lb2�slug

cp,� h1 � 1.47 � 107 1ft � lb2�cp, h26.29 � 106 1ft � lb2�slug;

106 1ft � lb2�slug; varying cp, h2 � h1 �cp, h2 � h1 � 4.9 �lb2�slug;

lb2�slug; varying cp, h2 � h1 � 51,000 1ft �cp, h2 � h1 � 49,000 1ft �

ANS-6 � Answers to Selected Even-Numbered Homework Problems

7708d_Ans_01-06 8/30/01 7:23 AM Page ANS-6 mac45 Mac 45:1st Shift: