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Unformatted text preview: Appendix A Physical Properties of Fluids 0.5 0.4 0.3 0.2 Castor oil SAE 10 oil 0.1 0.06 Glycerin 0.04 0.03 SAE 30 oil Crude oil (SG 0.86) 0.02 Absolute viscosity µ, N ⋅ s / m2 0.01 6 4 3 Kerosine Aniline 2 Mercury Carb on t 1 × 10 – 3 etra chlo ride 6 Ethyl alcohol 4 3 Benzene Water Gasoline (SG 0.68) 2 1 × 10 – 4 6 4 3 Helium 2 Carbon dioxide 1× | v v Fig. A.1 Absolute viscosity of common fluids at 1 atm. | Air 10 – 5 Hydrogen 5 – 20 e-Text Main Menu | 0 20 40 60 Temperature, °C Textbook Table of Contents 80 100 120 769 | Study Guide 770 Appendix A 1 × 10 – 3 8 6 4 3 2 Glycerin Helium SAE 10 oil Hydrogen Kinematic viscosity ν, m2 / s 1 × 10 – 4 8 6 SAE 30 oil 4 3 Air and oxygen 2 Carbon dioxide 1 × 10 – 5 8 6 Crude oil (SG 0.86) 4 3 2 1 × 10 – 6 8 6 Kerosine Benzene Ethyl alcohol Water 4 3 Gasoline (SG 0.68) 2 Carbon tetrachloride Mercury 1 × 10 – 7 –20 | v v Fig. A.2 Kinematic viscosity of common fluids at 1 atm. | 0 e-Text Main Menu 20 | 40 60 Temperature, °C 80 Textbook Table of Contents 100 | 120 Study Guide Physical Properties of Fluids 771 Table A.1 Viscosity and Density of Water at 1 atm T, °C , kg/m3 0 10 20 30 40 50 60 70 80 90 100 1000 1000 998 996 992 988 983 978 972 965 958 , N s/m2 1.788 1.307 1.003 0.799 0.657 0.548 0.467 0.405 0.355 0.316 0.283 , m2/s E-3 E-3 E-3 E-3 E-3 E-3 E-3 E-3 E-3 E-3 E-3 1.788 1.307 1.005 0.802 0.662 0.555 0.475 0.414 0.365 0.327 0.295 T, °F , slug/ft3 32 50 68 86 104 122 140 158 176 194 212 1.940 1.940 1.937 1.932 1.925 1.917 1.908 1.897 1.886 1.873 1.859 E-6 E-6 E-6 E-6 E-6 E-6 E-6 E-6 E-6 E-6 E-6 Suggested curve fits for water in the range 0 3 (kg/m ) T ln 1.704 3.73 2.73 2.09 1.67 1.37 1.14 0.975 0.846 0.741 0.660 0.591 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 , ft2/s 1.925 E-5 1.407 E-5 1.082 E-5 0.864 E-5 0.713 E-5 0.597 E-5 0.511 E-5 0.446 E-5 0.393 E-5 0.352 E-5 0.318 E-5 100°C: 0.0178T °C 1000 , lb s/ft2 4°C1.7 5.306z 0.2% 7.003z2 0 273 K TK z Table A.2 Viscosity and Density of Air at 1 atm T, °C , kg/m3 , N s/m2 1.520 1.290 1.200 1.090 0.946 0.835 0.746 0.675 0.616 0.525 0.457 1.51 1.71 1.80 1.95 2.17 2.38 2.57 2.75 2.93 3.25 3.55 40 0 20 50 100 150 200 250 300 400 500 1.788 E-3 kg/(m s) 0 , m2/s E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 0.99 1.33 1.50 1.79 2.30 2.85 3.45 4.08 4.75 6.20 7.77 , slug/ft3 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 40 32 68 122 212 302 392 482 572 752 932 , lb s/ft2 2.94 2.51 2.34 2.12 1.84 1.62 1.45 1.31 1.20 1.02 0.89 T, °F 3.16 E-7 3.58 E-7 3.76 E-7 4.08 E-7 4.54 E-7 4.97 E-7 5.37 E-7 5.75 E-7 6.11 E-7 6.79 E-7 7.41 E-7 E-3 E-3 E-3 E-3 E-3 E-3 E-3 E-3 E-3 E-3 E-3 Suggested curve fits for air: p RT Power law: 0 Sutherland law: 0 | v v with T0 | e-Text Main Menu 273 K, | 0 T T0 T T0 Rair 287 J/(kg K) 0.7 3/2 T0 T S S Sair 110.4 K 1.71 E-5 kg/(m s), and T in kelvins. Textbook Table of Contents | Study Guide , ft2/s 1.07 1.43 1.61 1.93 2.47 3.07 3.71 4.39 5.12 6.67 8.37 E-4 E-4 E-4 E-4 E-4 E-4 E-4 E-4 E-4 E-4 E-4 772 Appendix A Table A.3 Properties of Common Liquids at 1 atm and 20°C (68°F) Liquid , kg/m3 , kg/(m s) Ammonia Benzene Carbon tetrachloride Ethanol Ethylene glycol Freon 12 Gasoline Glycerin Kerosine Mercury Methanol SAE 10W oil SAE 10W30 oil SAE 30W oil SAE 50W oil Water Seawater (30%) 13,608 13,881 31,590 13,789 31,117 31,327 13,680 31,260 13,804 13,550 13,791 13,870 13,876 13,891 13,902 13,998 31,025 2.20 E-4 6.51 E-4 9.67 E-4 1.20 E-3 2.14 E-2 2.62 E-4 2.92 E-4 1.49 1.92 E-3 1.56 E-3 5.98 E-4 1.04 E-1‡ 1.7 E-1‡ 2.9 E-1‡ 8.6 E-1‡ 1.00 E-3 1.07 E-3 2.13 E-2 2.88 E-2 2.70 E-2 2.28 E-2 4.84 E-2 — 2.16 E-2 6.33 E-2 2.83 E-2 4.84 E-1 2.25 E-2 3.63 E-2 — 3.53 E-2 — 7.28 E-2 7.28 E-2 Bulk modulus, N/m2 Viscosity parameter C† — 1.43 E 9 9.65 E 8 9.03 E 8 — — 9.58 E 80 4.34 E 90 1.63 E 90 2.55 E 10 8.33 E 80 1.31 E 90 — 1.38 E 90 — 2.19 E 90 2.33 E 90 p , N/m2 , N/m* 1.05 4.34 4.45 5.72 11.7 1.76 3.68 28.0 5.56 1.07 4.63 15.7 14.0 18.3 20.2 Table A.1 7.28 9.10 1.01 1.20 5.73 1.23 E5 E4 E4 E3 E1 — 5.51 E 4 1.43 E-2 3.11 E 3 1.13 E-3 1.34 E 4 — — — — 2.34 E 3 2.34 E 3 * In contact with air. The viscosity-temperature variation of these liquids may be fitted to the empirical expression † exp C 20°C 293 K TK 1 with accuracy of 6 percent in the range 0 T 100°C. ‡ Representative values. The SAE oil classifications allow a viscosity variation of up to temperatures. Table A.4 Properties of Common Gases at 1 atm and 20°C (68°F) Gas Molecular weight R, m2/(s2 K) g, N/m3 , N s/m2 H2 He H2O Ar Dry air CO2 CO N2 O2 NO N2O Cl2 CH4 2.016 4.003 18.020 39.944 28.960 44.010 28.010 28.020 32.000 30.010 44.020 70.910 16.040 4124 2077 0461 0208 0287 0189 0297 0297 0260 0277 0189 0117 0518 00.822 01.630 07.350 16.300 11.800 17.900 11.400 11.400 13.100 12.100 17.900 28.900 06.540 9.05 1.97 1.02 2.24 1.80 1.48 1.82 1.76 2.00 1.90 1.45 1.03 1.34 † | v v The power-law curve fit, Eq. (1.27), / 293K 1000 K. The temperature must be in kelvins. | e-Text Main Menu | Specific-heat ratio (T/293)n, fits these gases to within | Power-law exponent n† 1.41 1.66 1.33 1.67 1.40 1.30 1.40 1.40 1.40 1.40 1.31 1.34 1.32 E-6 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 E-5 Textbook Table of Contents 50 percent, especially at lower 0.68 0.67 1.15 0.72 0.67 0.79 0.71 0.67 0.69 0.78 0.89 1.00 0.87 4 percent in the range 250 Study Guide T Physical Properties of Fluids 773 Table A.5 Surface T, °C Tension, Vapor 0 Pressure, and Sound 10 Speed of Water , N/m 20 30 40 50 60 70 80 90 100 0.0756 0.0742 0.0728 0.0712 0.0696 0.0679 0.0662 0.0644 0.0626 0.0608 0.0589 120 140 160 180 200 220 240 260 280 300 320 340 360 374* 0.0550 0.0509 0.0466 0.0422 0.0377 0.0331 0.0284 0.0237 0.0190 0.0144 0.0099 0.0056 0.0019 0.0*19 p , kPa a, m/s 0.611 1.227 2.337 4.242 7.375 12.34 19.92 31.16 47.35 70.11 101.3 1402 1447 1482 1509 1529 1542 1551 1553 1554 1550 1543 198.5 361.3 617.8 1,002 1,554 2,318 3,344 4,688 6,412 8,581 11,274 14,586 18,651 22,090* 1518 1483 1440 1389 1334 1268 1192 1110 1022 920 800 630 370 0* | v v *Critical point. | e-Text Main Menu | Table A.6 Propz, m erties of the 0 500 Standard 0,0000 Atmosphere T, K Textbook Table of Contents | , kg/m3 a, m/s 291.41 288.16 284.91 281.66 278.41 275.16 271.91 268.66 265.41 262.16 258.91 255.66 252.41 249.16 245.91 242.66 239.41 236.16 232.91 229.66 226.41 223.16 219.91 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 216.66 218.60 220.60 222.50 224.50 226.50 250.40 270.70 255.70 219.70 0,0500 01,000 01,500 02,000 02,500 03,000 03,500 04,000 04,500 05,000 05,500 06,000 06,500 07,000 07,500 08,000 08,500 09,000 09,500 10,000 10,500 11,000 11,500 12,000 12,500 13,000 13,500 14,000 14,500 15,000 15,500 16,000 16,500 17,000 17,500 18,000 18,500 19,000 19,500 20,000 22,000 24,000 26,000 28,000 30,000 40,000 50,000 60,000 70,000 p, Pa 107,508 101,350 095,480 089,889 084,565 079,500 074,684 070,107 065,759 061,633 057,718 054,008 050,493 047,166 044,018 041,043 038,233 035,581 033,080 030,723 028,504 026,416 024,455 022,612 020,897 019,312 017,847 016,494 015,243 014,087 013,018 012,031 011,118 010,275 009,496 008,775 008,110 007,495 006,926 006,401 005,915 005,467 004,048 002,972 002,189 001,616 001,197 000,287 000,080 000,022 000,006 1.2854 1.2255 1.1677 1.1120 1.0583 1.0067 0.9570 0.9092 0.8633 0.8191 0.7768 0.7361 0.6970 0.6596 0.6237 0.5893 0.5564 0.5250 0.4949 0.4661 0.4387 0.4125 0.3875 0.3637 0.3361 0.3106 0.2870 0.2652 0.2451 0.2265 0.2094 0.1935 0.1788 0.1652 0.1527 0.1411 0.1304 0.1205 0.1114 0.1029 0.0951 0.0879 0.0645 0.0469 0.0343 0.0251 0.0184 0.0040 0.0010 0.0003 0.0001 342.2 340.3 338.4 336.5 334.5 332.6 330.6 328.6 326.6 324.6 322.6 320.6 318.5 316.5 314.4 312.3 310.2 308.1 306.0 303.8 301.7 299.5 297.3 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 296.4 297.8 299.1 300.4 301.7 317.2 329.9 320.6 297.2 Study Guide Appendix B Compressible-Flow Tables Table B.1 Isentropic Flow of a Perfect Gas, k 1.4 Ma p/p0 / 0.0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7 0.72 1.0 0.9997 0.9989 0.9975 0.9955 0.9930 0.9900 0.9864 0.9823 0.9776 0.9725 0.9668 0.9607 0.9541 0.9470 0.9395 0.9315 0.9231 0.9143 0.9052 0.8956 0.8857 0.8755 0.8650 0.8541 0.8430 0.8317 0.8201 0.8082 0.7962 0.7840 0.7716 0.7591 0.7465 0.7338 0.7209 0.7080 1.0 0.9998 0.9992 0.9982 0.9968 0.9950 0.9928 0.9903 0.9873 0.9840 0.9803 0.9762 0.9718 0.9670 0.9619 0.9564 0.9506 0.9445 0.9380 0.9313 0.9243 0.9170 0.9094 0.9016 0.8935 0.8852 0.8766 0.8679 0.8589 0.8498 0.8405 0.8310 0.8213 0.8115 0.8016 0.7916 0.7814 0 T/T0 A/A* Ma p/p0 / 1.0 0.9999 0.9997 0.9993 0.9987 0.9980 0.9971 0.9961 0.9949 0.9936 0.9921 0.9904 0.9886 0.9867 0.9846 0.9823 0.9799 0.9774 0.9747 0.9719 0.9690 0.9659 0.9627 0.9594 0.9559 0.9524 0.9487 0.9449 0.9410 0.9370 0.9328 0.9286 0.9243 0.9199 0.9153 0.9107 0.9061 28.9421 14.4815 9.6659 7.2616 5.8218 4.8643 4.1824 3.6727 3.2779 2.9635 2.7076 2.4956 2.3173 2.1656 2.0351 1.9219 1.8229 1.7358 1.6587 1.5901 1.5289 1.4740 1.4246 1.3801 1.3398 1.3034 1.2703 1.2403 1.2130 1.1882 1.1656 1.1451 1.1265 1.1097 1.0944 1.0806 0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1.0 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.2 1.22 1.24 1.26 1.28 1.3 1.32 1.34 1.36 1.38 1.4 1.42 1.44 1.46 0.6951 0.6821 0.6690 0.6560 0.6430 0.6300 0.6170 0.6041 0.5913 0.5785 0.5658 0.5532 0.5407 0.5283 0.5160 0.5039 0.4919 0.4800 0.4684 0.4568 0.4455 0.4343 0.4232 0.4124 0.4017 0.3912 0.3809 0.3708 0.3609 0.3512 0.3417 0.3323 0.3232 0.3142 0.3055 0.2969 0.2886 0.7712 0.7609 0.7505 0.7400 0.7295 0.7189 0.7083 0.6977 0.6870 0.6764 0.6658 0.6551 0.6445 0.6339 0.6234 0.6129 0.6024 0.5920 0.5817 0.5714 0.5612 0.5511 0.5411 0.5311 0.5213 0.5115 0.5019 0.4923 0.4829 0.4736 0.4644 0.4553 0.4463 0.4374 0.4287 0.4201 0.4116 0 T/T0 A/A* 0.9013 0.8964 0.8915 0.8865 0.8815 0.8763 0.8711 0.8659 0.8606 0.8552 0.8498 0.8444 0.8389 0.8333 0.8278 0.8222 0.8165 0.8108 0.8052 0.7994 0.7937 0.7879 0.7822 0.7764 0.7706 0.7648 0.7590 0.7532 0.7474 0.7416 0.7358 0.7300 0.7242 0.7184 0.7126 0.7069 0.7011 1.0681 1.0570 1.0471 1.0382 1.0305 1.0237 1.0179 1.0129 1.0089 1.0056 1.0031 1.0014 1.0003 1.0000 1.0003 1.0013 1.0029 1.0051 1.0079 1.0113 1.0153 1.0198 1.0248 1.0304 1.0366 1.0432 1.0504 1.0581 1.0663 1.0750 1.0842 1.0940 1.1042 1.1149 1.1262 1.1379 1.1501 | v v 774 | e-Text Main Menu | Textbook Table of Contents | Study Guide Compressible-Flow Tables 775 | Ma p/p0 / 1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64 1.66 1.68 1.7 1.72 1.74 1.76 1.78 1.8 1.82 1.84 1.86 1.88 1.9 1.92 1.94 1.96 1.98 2.0 2.02 2.04 2.06 2.08 2.1 2.12 2.14 2.16 2.18 2.2 2.22 2.24 2.26 2.28 2.3 2.32 2.34 2.36 2.38 2.4 2.42 2.44 2.46 2.48 2.5 2.52 2.54 0.2804 0.2724 0.2646 0.2570 0.2496 0.2423 0.2353 0.2284 0.2217 0.2151 0.2088 0.2026 0.1966 0.1907 0.1850 0.1794 0.1740 0.1688 0.1637 0.1587 0.1539 0.1492 0.1447 0.1403 0.1360 0.1318 0.1278 0.1239 0.1201 0.1164 0.1128 0.1094 0.1060 0.1027 0.0996 0.0965 0.0935 0.0906 0.0878 0.0851 0.0825 0.0800 0.0775 0.0751 0.0728 0.0706 0.0684 0.0663 0.0643 0.0623 0.0604 0.0585 0.0567 0.0550 0.4032 0.3950 0.3869 0.3789 0.3710 0.3633 0.3557 0.3483 0.3409 0.3337 0.3266 0.3197 0.3129 0.3062 0.2996 0.2931 0.2868 0.2806 0.2745 0.2686 0.2627 0.2570 0.2514 0.2459 0.2405 0.2352 0.2300 0.2250 0.2200 0.2152 0.2104 0.2058 0.2013 0.1968 0.1925 0.1882 0.1841 0.1800 0.1760 0.1721 0.1683 0.1646 0.1609 0.1574 0.1539 0.1505 0.1472 0.1439 0.1408 0.1377 0.1346 0.1317 0.1288 0.1260 v v Table B.1 (Cont.) Isentropic Flow of a Perfect Gas, k 1.4 | 0 e-Text Main Menu T/T0 A/A* Ma p/p0 / 0.6954 0.6897 0.6840 0.6783 0.6726 0.6670 0.6614 0.6558 0.6502 0.6447 0.6392 0.6337 0.6283 0.6229 0.6175 0.6121 0.6068 0.6015 0.5963 0.5910 0.5859 0.5807 0.5756 0.5705 0.5655 0.5605 0.5556 0.5506 0.5458 0.5409 0.5361 0.5313 0.5266 0.5219 0.5173 0.5127 0.5081 0.5036 0.4991 0.4947 0.4903 0.4859 0.4816 0.4773 0.4731 0.4688 0.4647 0.4606 0.4565 0.4524 0.4484 0.4444 0.4405 0.4366 1.1629 1.1762 1.1899 1.2042 1.2190 1.2344 1.2502 1.2666 1.2836 1.3010 1.3190 1.3376 1.3567 1.3764 1.3967 1.4175 1.4390 1.4610 1.4836 1.5069 1.5308 1.5553 1.5804 1.6062 1.6326 1.6597 1.6875 1.7160 1.7451 1.7750 1.8056 1.8369 1.8690 1.9018 1.9354 1.9698 2.0050 2.0409 2.0777 2.1153 2.1538 2.1931 2.2333 2.2744 2.3164 2.3593 2.4031 2.4479 2.4936 2.5403 2.5880 2.6367 2.6865 2.7372 2.56 2.58 2.6 2.62 2.64 2.66 2.68 2.7 2.72 2.74 2.76 2.78 2.8 2.82 2.84 2.86 2.88 2.9 2.92 2.94 2.96 2.98 3.0 3.02 3.04 3.06 3.08 3.1 3.12 3.14 3.16 3.18 3.2 3.22 3.24 3.26 3.28 3.3 3.32 3.34 3.36 3.38 3.4 3.42 3.44 3.46 3.48 3.5 3.52 3.54 3.56 3.58 3.6 3.62 0.0533 0.0517 0.0501 0.0486 0.0471 0.0457 0.0443 0.0430 0.0417 0.0404 0.0392 0.0380 0.0368 0.0357 0.0347 0.0336 0.0326 0.0317 0.0307 0.0298 0.0289 0.0281 0.0272 0.0264 0.0256 0.0249 0.0242 0.0234 0.0228 0.0221 0.0215 0.0208 0.0202 0.0196 0.0191 0.0185 0.0180 0.0175 0.0170 0.0165 0.0160 0.0156 0.0151 0.0147 0.0143 0.0139 0.0135 0.0131 0.0127 0.0124 0.0120 0.0117 0.0114 0.0111 0.1232 0.1205 0.1179 0.1153 0.1128 0.1103 0.1079 0.1056 0.1033 0.1010 0.0989 0.0967 0.0946 0.0926 0.0906 0.0886 0.0867 0.0849 0.0831 0.0813 0.0796 0.0779 0.0762 0.0746 0.0730 0.0715 0.0700 0.0685 0.0671 0.0657 0.0643 0.0630 0.0617 0.0604 0.0591 0.0579 0.0567 0.0555 0.0544 0.0533 0.0522 0.0511 0.0501 0.0491 0.0481 0.0471 0.0462 0.0452 0.0443 0.0434 0.0426 0.0417 0.0409 0.0401 | Textbook Table of Contents | Study Guide 0 T/T0 A/A* 0.4328 0.4289 0.4252 0.4214 0.4177 0.4141 0.4104 0.4068 0.4033 0.3998 0.3963 0.3928 0.3894 0.3860 0.3827 0.3794 0.3761 0.3729 0.3696 0.3665 0.3633 0.3602 0.3571 0.3541 0.3511 0.3481 0.3452 0.3422 0.3393 0.3365 0.3337 0.3309 0.3281 0.3253 0.3226 0.3199 0.3173 0.3147 0.3121 0.3095 0.3069 0.3044 0.3019 0.2995 0.2970 0.2946 0.2922 0.2899 0.2875 0.2852 0.2829 0.2806 0.2784 0.2762 2.7891 2.8420 2.8960 2.9511 3.0073 3.0647 3.1233 3.1830 3.2440 3.3061 3.3695 3.4342 3.5001 3.5674 3.6359 3.7058 3.7771 3.8498 3.9238 3.9993 4.0763 4.1547 4.2346 4.3160 4.3990 4.4835 4.5696 4.6573 4.7467 4.8377 4.9304 5.0248 5.1210 5.2189 5.3186 5.4201 5.5234 5.6286 5.7358 5.8448 5.9558 6.0687 6.1837 6.3007 6.4198 6.5409 6.6642 6.7896 6.9172 7.0471 7.1791 7.3135 7.4501 7.5891 776 Appendix B Table B.1 (Cont.) Isentropic Flow of a Perfect Gas, k 1.4 Ma p/p0 / 3.64 3.66 3.68 3.7 3.72 3.74 3.76 3.78 3.8 3.82 3.84 3.86 3.88 3.9 3.92 3.94 3.96 3.98 4.0 4.02 4.04 4.06 4.08 4.1 4.12 4.14 4.16 4.18 4.2 4.22 4.24 4.26 4.28 4.3 4.32 0.0108 0.0105 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0086 0.0084 0.0082 0.0080 0.0077 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 0.0062 0.0061 0.0059 0.0058 0.0056 0.0055 0.0053 0.0052 0.0051 0.0049 0.0048 0.0047 0.0046 0.0044 0.0043 0.0393 0.0385 0.0378 0.0370 0.0363 0.0356 0.0349 0.0342 0.0335 0.0329 0.0323 0.0316 0.0310 0.0304 0.0299 0.0293 0.0287 0.0282 0.0277 0.0271 0.0266 0.0261 0.0256 0.0252 0.0247 0.0242 0.0238 0.0234 0.0229 0.0225 0.0221 0.0217 0.0213 0.0209 0.0205 Table B.2 Normal-Shock Relations for a Perfect Gas, k 1.4 0 T/T0 A/A* Ma p/p0 / 0.2740 0.2718 0.2697 0.2675 0.2654 0.2633 0.2613 0.2592 0.2572 0.2552 0.2532 0.2513 0.2493 0.2474 0.2455 0.2436 0.2418 0.2399 0.2381 0.2363 0.2345 0.2327 0.2310 0.2293 0.2275 0.2258 0.2242 0.2225 0.2208 0.2192 0.2176 0.2160 0.2144 0.2129 0.2113 7.7305 7.8742 8.0204 8.1691 8.3202 8.4739 8.6302 8.7891 8.9506 9.1148 9.2817 9.4513 9.6237 9.7990 9.9771 10.1581 10.3420 10.5289 10.7188 10.9117 11.1077 11.3068 11.5091 11.7147 11.9234 12.1354 12.3508 12.5695 12.7916 13.0172 13.2463 13.4789 13.7151 13.9549 14.1984 4.34 4.36 4.38 4.4 4.42 4.44 4.46 4.48 4.5 4.52 4.54 4.56 4.58 4.6 4.62 4.64 4.66 4.68 4.7 4.72 4.74 4.76 4.78 4.8 4.82 4.84 4.86 4.88 4.9 4.92 4.94 4.96 4.98 5.0 0.0042 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 0.0035 0.0035 0.0034 0.0033 0.0032 0.0031 0.0031 0.0030 0.0029 0.0028 0.0028 0.0027 0.0026 0.0026 0.0025 0.0025 0.0024 0.0023 0.0023 0.0022 0.0022 0.0021 0.0021 0.0020 0.0020 0.0019 0.0019 0.0202 0.0198 0.0194 0.0191 0.0187 0.0184 0.0181 0.0178 0.0174 0.0171 0.0168 0.0165 0.0163 0.0160 0.0157 0.0154 0.0152 0.0149 0.0146 0.0144 0.0141 0.0139 0.0137 0.0134 0.0132 0.0130 0.0128 0.0125 0.0123 0.0121 0.0119 0.0117 0.0115 0.0113 v v | Man2 p2/p1 1.0 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.2 1.22 1.24 | Man1 1.0000 0.9805 0.9620 0.9444 0.9277 0.9118 0.8966 0.8820 0.8682 0.8549 0.8422 0.8300 0.8183 1.0000 1.0471 1.0952 1.1442 1.1941 1.2450 1.2968 1.3495 1.4032 1.4578 1.5133 1.5698 1.6272 e-Text Main Menu | V1/V2 2/ 1 1.0000 1.0334 1.0671 1.1009 1.1349 1.1691 1.2034 1.2378 1.2723 1.3069 1.3416 1.3764 1.4112 0 T/T0 A/A* 0.2098 0.2083 0.2067 0.2053 0.2038 0.2023 0.2009 0.1994 0.1980 0.1966 0.1952 0.1938 0.1925 0.1911 0.1898 0.1885 0.1872 0.1859 0.1846 0.1833 0.1820 0.1808 0.1795 0.1783 0.1771 0.1759 0.1747 0.1735 0.1724 0.1712 0.1700 0.1689 0.1678 0.1667 14.4456 14.6965 14.9513 15.2099 15.4724 15.7388 16.0092 16.2837 16.5622 16.8449 17.1317 17.4228 17.7181 18.0178 18.3218 18.6303 18.9433 19.2608 19.5828 19.9095 20.2409 20.5770 20.9179 21.2637 21.6144 21.9700 22.3306 22.6963 23.0671 23.4431 23.8243 24.2109 24.6027 25.0000 T2/T1 p02/p01 A*/A* 2 1 1.0000 1.0132 1.0263 1.0393 1.0522 1.0649 1.0776 1.0903 1.1029 1.1154 1.1280 1.1405 1.1531 1.0000 1.0000 0.9999 0.9998 0.9994 0.9989 0.9982 0.9973 0.9961 0.9946 0.9928 0.9907 0.9884 1.0000 1.0000 1.0001 1.0002 1.0006 1.0011 1.0018 1.0027 1.0040 1.0055 1.0073 1.0094 1.0118 Textbook Table of Contents | Study Guide Compressible-Flow Tables 777 Table B.2 (Cont.) Normal-Shock Relations for a Perfect Gas, k 1.4 v v | Man2 p2/p1 1.26 1.28 1.3 1.32 1.34 1.36 1.38 1.4 1.42 1.44 1.46 1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64 1.66 1.68 1.7 1.72 1.74 1.76 1.78 1.8 1.82 1.84 1.86 1.88 1.9 1.92 1.94 1.96 1.98 2.0 2.02 2.04 2.06 2.08 2.1 2.12 2.14 2.16 2.18 2.2 2.22 2.24 2.26 2.28 2.3 2.32 | Man1 0.8071 0.7963 0.7860 0.7760 0.7664 0.7572 0.7483 0.7397 0.7314 0.7235 0.7157 0.7083 0.7011 0.6941 0.6874 0.6809 0.6746 0.6684 0.6625 0.6568 0.6512 0.6458 0.6405 0.6355 0.6305 0.6257 0.6210 0.6165 0.6121 0.6078 0.6036 0.5996 0.5956 0.5918 0.5880 0.5844 0.5808 0.5774 0.5740 0.5707 0.5675 0.5643 0.5613 0.5583 0.5554 0.5525 0.5498 0.5471 0.5444 0.5418 0.5393 0.5368 0.5344 0.5321 1.6855 1.7448 1.8050 1.8661 1.9282 1.9912 2.0551 2.1200 2.1858 2.2525 2.3202 2.3888 2.4583 2.5288 2.6002 2.6725 2.7458 2.8200 2.8951 2.9712 3.0482 3.1261 3.2050 3.2848 3.3655 3.4472 3.5298 3.6133 3.6978 3.7832 3.8695 3.9568 4.0450 4.1341 4.2242 4.3152 4.4071 4.5000 4.5938 4.6885 4.7842 4.8808 4.9783 5.0768 5.1762 5.2765 5.3778 5.4800 5.5831 5.6872 5.7922 5.8981 6.0050 6.1128 e-Text Main Menu | V1/V2 1.4460 1.4808 1.5157 1.5505 1.5854 1.6202 1.6549 1.6897 1.7243 1.7589 1.7934 1.8278 1.8621 1.8963 1.9303 1.9643 1.9981 2.0317 2.0653 2.0986 2.1318 2.1649 2.1977 2.2304 2.2629 2.2952 2.3273 2.3592 2.3909 2.4224 2.4537 2.4848 2.5157 2.5463 2.5767 2.6069 2.6369 2.6667 2.6962 2.7255 2.7545 2.7833 2.8119 2.8402 2.8683 2.8962 2.9238 2.9512 2.9784 3.0053 3.0319 3.0584 3.0845 3.1105 Textbook Table of Contents | T2/T1 p02/p01 A*/A* 2 1 1.1657 1.1783 1.1909 1.2035 1.2162 1.2290 1.2418 1.2547 1.2676 1.2807 1.2938 1.3069 1.3202 1.3336 1.3470 1.3606 1.3742 1.3880 1.4018 1.4158 1.4299 1.4440 1.4583 1.4727 1.4873 1.5019 1.5167 1.5316 1.5466 1.5617 1.5770 1.5924 1.6079 1.6236 1.6394 1.6553 1.6713 1.6875 1.7038 1.7203 1.7369 1.7536 1.7705 1.7875 1.8046 1.8219 1.8393 1.8569 1.8746 1.8924 1.9104 1.9285 1.9468 1.9652 2/ 1 0.9857 0.9827 0.9794 0.9758 0.9718 0.9676 0.9630 0.9582 0.9531 0.9476 0.9420 0.9360 0.9298 0.9233 0.9166 0.9097 0.9026 0.8952 0.8877 0.8799 0.8720 0.8639 0.8557 0.8474 0.8389 0.8302 0.8215 0.8127 0.8038 0.7948 0.7857 0.7765 0.7674 0.7581 0.7488 0.7395 0.7302 0.7209 0.7115 0.7022 0.6928 0.6835 0.6742 0.6649 0.6557 0.6464 0.6373 0.6281 0.6191 0.6100 0.6011 0.5921 0.5833 0.5745 1.0145 1.0176 1.0211 1.0249 1.0290 1.0335 1.0384 1.0436 1.0492 1.0552 1.0616 1.0684 1.0755 1.0830 1.0910 1.0993 1.1080 1.1171 1.1266 1.1365 1.1468 1.1575 1.1686 1.1801 1.1921 1.2045 1.2173 1.2305 1.2441 1.2582 1.2728 1.2877 1.3032 1.3191 1.3354 1.3522 1.3695 1.3872 1.4054 1.4241 1.4433 1.4630 1.4832 1.5039 1.5252 1.5469 1.5692 1.5920 1.6154 1.6393 1.6638 1.6888 1.7144 1.7406 Study Guide 778 Appendix B Table B.2 (Cont.) Normal-Shock Relations for a Perfect Gas, k 1.4 v v | Man2 p2/p1 2.34 2.36 2.38 2.4 2.42 2.44 2.46 2.48 2.5 2.52 2.54 2.56 2.58 2.6 2.62 2.64 2.66 2.68 2.7 2.72 2.74 2.76 2.78 2.8 2.82 2.84 2.86 2.88 2.9 2.92 2.94 2.96 2.98 3.0 3.02 3.04 3.06 3.08 3.1 3.12 3.14 3.16 3.18 3.2 3.22 3.24 3.26 3.28 3.3 3.32 3.34 3.36 3.38 3.4 | Man1 0.5297 0.5275 0.5253 0.5231 0.5210 0.5189 0.5169 0.5149 0.5130 0.5111 0.5092 0.5074 0.5056 0.5039 0.5022 0.5005 0.4988 0.4972 0.4956 0.4941 0.4926 0.4911 0.4896 0.4882 0.4868 0.4854 0.4840 0.4827 0.4814 0.4801 0.4788 0.4776 0.4764 0.4752 0.4740 0.4729 0.4717 0.4706 0.4695 0.4685 0.4674 0.4664 0.4654 0.4643 0.4634 0.4624 0.4614 0.4605 0.4596 0.4587 0.4578 0.4569 0.4560 0.4552 6.2215 6.3312 6.4418 6.5533 6.6658 6.7792 6.8935 7.0088 7.1250 7.2421 7.3602 7.4792 7.5991 7.7200 7.8418 7.9645 8.0882 8.2128 8.3383 8.4648 8.5922 8.7205 8.8498 8.9800 9.1111 9.2432 9.3762 9.5101 9.6450 9.7808 9.9175 10.0552 10.1938 10.3333 10.4738 10.6152 10.7575 10.9008 11.0450 11.1901 11.3362 11.4832 11.6311 11.7800 11.9298 12.0805 12.2322 12.3848 12.5383 12.6928 12.8482 13.0045 13.1618 13.3200 e-Text Main Menu | V1/V2 T2/T1 p02/p01 A*/A* 2 1 1.9838 2.0025 2.0213 2.0403 2.0595 2.0788 2.0982 2.1178 2.1375 2.1574 2.1774 2.1976 2.2179 2.2383 2.2590 2.2797 2.3006 2.3217 2.3429 2.3642 2.3858 2.4074 2.4292 2.4512 2.4733 2.4955 2.5179 2.5405 2.5632 2.5861 2.6091 2.6322 2.6555 2.6790 2.7026 2.7264 2.7503 2.7744 2.7986 2.8230 2.8475 2.8722 2.8970 2.9220 2.9471 2.9724 2.9979 3.0234 3.0492 3.0751 3.1011 3.1273 3.1537 3.1802 0.5658 0.5572 0.5486 0.5401 0.5317 0.5234 0.5152 0.5071 0.4990 0.4911 0.4832 0.4754 0.4677 0.4601 0.4526 0.4452 0.4379 0.4307 0.4236 0.4166 0.4097 0.4028 0.3961 0.3895 0.3829 0.3765 0.3701 0.3639 0.3577 0.3517 0.3457 0.3398 0.3340 0.3283 0.3227 0.3172 0.3118 0.3065 0.3012 0.2960 0.2910 0.2860 0.2811 0.2762 0.2715 0.2668 0.2622 0.2577 0.2533 0.2489 0.2446 0.2404 0.2363 0.2322 1.7674 1.7948 1.8228 1.8514 1.8806 1.9105 1.9410 1.9721 2.0039 2.0364 2.0696 2.1035 2.1381 2.1733 2.2093 2.2461 2.2835 2.3218 2.3608 2.4005 2.4411 2.4825 2.5246 2.5676 2.6115 2.6561 2.7017 2.7481 2.7954 2.8436 2.8927 2.9427 2.9937 3.0456 3.0985 3.1523 3.2072 3.2630 3.3199 3.3778 3.4368 3.4969 3.5580 3.6202 3.6835 3.7480 3.8136 3.8803 3.9483 4.0174 4.0877 4.1593 4.2321 4.3062 2/ 1 3.1362 3.1617 3.1869 3.2119 3.2367 3.2612 3.2855 3.3095 3.3333 3.3569 3.3803 3.4034 3.4263 3.4490 3.4714 3.4937 3.5157 3.5374 3.5590 3.5803 3.6015 3.6224 3.6431 2.6636 3.6838 3.7039 3.7238 3.7434 3.7629 3.7821 3.8012 3.8200 3.8387 3.8571 3.8754 3.8935 3.9114 3.9291 3.9466 3.9639 3.9811 3.9981 4.0149 4.0315 4.0479 4.0642 4.0803 4.0963 4.1120 4.1276 4.1431 4.1583 4.1734 4.1884 Textbook Table of Contents | Study Guide Compressible-Flow Tables 779 Table B.2 (Cont.) Normal-Shock Relations for a Perfect Gas, k 1.4 v v | Man2 p2/p1 3.42 3.44 3.46 3.48 3.5 3.52 3.54 3.56 3.58 3.6 3.62 3.64 3.66 3.68 3.7 3.72 3.74 3.76 3.78 3.8 3.82 3.84 3.86 3.88 3.9 3.92 3.94 3.96 3.98 4.0 4.02 4.04 4.06 4.08 4.1 4.12 4.14 4.16 4.18 4.2 4.22 4.24 4.26 4.28 4.3 4.32 4.34 4.36 4.38 4.4 4.42 4.44 4.46 4.48 | Man1 0.4544 0.4535 0.4527 0.4519 0.4512 0.4504 0.4496 0.4489 0.4481 0.4474 0.4467 0.4460 0.4453 0.4446 0.4439 0.4433 0.4426 0.4420 0.4414 0.4407 0.4401 0.4395 0.4389 0.4383 0.4377 0.4372 0.4366 0.4360 0.4355 0.4350 0.4344 0.4339 0.4334 0.4329 0.4324 0.4319 0.4314 0.4309 0.4304 0.4299 0.4295 0.4290 0.4286 0.4281 0.4277 0.4272 0.4268 0.4264 0.4260 0.4255 0.4251 0.4247 0.4243 0.4239 13.4791 13.6392 13.8002 13.9621 14.1250 14.2888 14.4535 14.6192 14.7858 14.9533 15.1218 15.2912 15.4615 15.6328 15.8050 15.9781 16.1522 16.3272 16.5031 16.6800 16.8578 17.0365 17.2162 17.3968 17.5783 17.7608 17.9442 18.1285 18.3138 18.5000 18.6871 18.8752 19.0642 19.2541 19.4450 19.6368 19.8295 20.0232 20.2178 20.4133 20.6098 20.8072 21.0055 21.2048 21.4050 21.6061 21.8082 22.0112 22.2151 22.4200 22.6258 22.8325 23.0402 23.2488 e-Text Main Menu | V1/V2 4.2032 4.2178 4.2323 4.2467 4.2609 4.2749 4.2888 4.3026 4.3162 4.3296 4.3429 4.3561 4.3692 4.3821 4.3949 4.4075 4.4200 4.4324 4.4447 4.4568 4.4688 4.4807 4.4924 4.5041 4.4156 4.5270 4.5383 4.5494 4.5605 4.5714 4.5823 4.5930 4.6036 4.6141 4.6245 4.6348 4.6450 4.6550 4.6650 4.6749 4.6847 4.6944 4.7040 4.7135 4.7229 4.7322 4.7414 4.7505 4.7595 4.7685 4.7773 4.7861 4.7948 4.8034 Textbook Table of Contents | T2/T1 p02/p01 A*/A* 2 1 3.2069 3.2337 3.2607 3.2878 3.3151 3.3425 3.3701 3.3978 3.4257 3.4537 3.4819 3.5103 3.5388 3.5674 3.5962 3.6252 3.6543 3.6836 3.7130 3.7426 3.7723 3.8022 3.8323 3.8625 3.8928 3.9233 3.9540 3.9848 4.0158 4.0469 4.0781 4.1096 4.1412 4.1729 4.2048 4.2368 4.2690 4.3014 4.3339 4.3666 4.3994 4.4324 4.4655 4.4988 4.5322 4.5658 4.5995 4.6334 4.6675 4.7017 4.7361 4.7706 4.8053 4.8401 2/ 1 0.2282 0.2243 0.2205 0.2167 0.2129 0.2093 0.2057 0.2022 0.1987 0.1953 0.1920 0.1887 0.1855 0.1823 0.1792 0.1761 0.1731 0.1702 0.1673 0.1645 0.1617 0.1589 0.1563 0.1536 0.1510 0.1485 0.1460 0.1435 0.1411 0.1388 0.1364 0.1342 0.1319 0.1297 0.1276 0.1254 0.1234 0.1213 0.1193 0.1173 0.1154 0.1135 0.1116 0.1098 0.1080 0.1062 0.1045 0.1028 0.1011 0.0995 0.0979 0.0963 0.0947 0.0932 4.3815 4.4581 4.5361 4.6154 4.6960 4.7780 4.8614 4.9461 5.0324 5.1200 5.2091 5.2997 5.3918 5.4854 5.5806 5.6773 5.7756 5.8755 5.9770 6.0801 6.1849 6.2915 6.3997 6.5096 6.6213 6.7348 6.8501 6.9672 7.0861 7.2069 7.3296 7.4542 7.5807 7.7092 7.8397 7.9722 8.1067 8.2433 8.3819 8.5227 8.6656 8.8107 8.9579 9.1074 9.2591 9.4131 9.5694 9.7280 9.8889 10.0522 10.2179 10.3861 10.5567 10.7298 Study Guide 780 Appendix B Table B.2 (Cont.) Normal-Shock Relations for a Perfect Gas, k 1.4 Man1 v v | p2/p1 4.5 4.52 4.54 4.56 4.58 4.6 4.62 4.64 4.66 4.68 4.7 4.72 4.74 4.76 4.78 4.8 4.82 4.84 4.86 4.88 4.9 4.92 4.94 4.96 4.98 5.0 Table B.3 Adiabatic Frictional Flow in a Constant-Area Duct for k 1.4 Man2 0.4236 0.4232 0.4228 0.4224 0.4220 0.4217 0.4213 0.4210 0.4206 0.4203 0.4199 0.4196 0.4192 0.4189 0.4186 0.4183 0.4179 0.4176 0.4173 0.4170 0.4167 0.4164 0.4161 0.4158 0.4155 0.4152 V1/V2 23.4583 23.6688 23.8802 24.0925 24.3058 24.5200 24.7351 24.9512 25.1682 25.3861 25.6050 25.8248 26.0455 26.2672 26.4898 26.7133 26.9378 27.1632 27.3895 27.6168 27.8450 28.0741 28.3042 28.5352 28.7671 29.0000 4.8119 4.8203 4.8287 4.8369 4.8451 4.8532 4.8612 4.8692 4.8771 4.8849 4.8926 4.9002 4.9078 4.9153 4.9227 4.9301 4.9374 4.9446 4.9518 4.9589 4.9659 4.9728 4.9797 4.9865 4.9933 5.0000 Ma p/p* 1778.4500 440.3520 193.0310 106.7180 66.9216 45.4080 32.5113 24.1978 18.5427 14.5333 11.5961 9.3865 7.6876 6.3572 5.2993 4.4467 3.7520 3.1801 2.7054 2.3085 1.9744 54.7701 27.3817 18.2508 13.6843 10.9435 9.1156 7.8093 6.8291 6.0662 5.4554 4.9554 4.5383 4.1851 3.8820 3.6191 3.3887 3.1853 3.0042 2.8420 2.6958 2.5634 p02/p01 A*/A* 2 1 0.0917 0.0902 0.0888 0.0874 0.0860 0.0846 0.0832 0.0819 0.0806 0.0793 0.0781 0.0769 0.0756 0.0745 0.0733 0.0721 0.0710 0.0699 0.0688 0.0677 0.0667 0.0657 0.0647 0.0637 0.0627 0.0617 10.9054 11.0835 11.2643 11.4476 11.6336 11.8222 12.0136 12.2076 12.4044 12.6040 12.8065 13.0117 13.2199 13.4310 13.6450 13.8620 14.0820 14.3050 14.5312 14.7604 14.9928 15.2284 15.4672 15.7902 15.9545 16.2032 T/T* 0.0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 | f L*/D T2/T1 4.8751 4.9102 4.9455 4.9810 5.0166 5.0523 5.0882 5.1243 5.1605 5.1969 5.2334 5.2701 5.3070 5.3440 5.3811 5.4184 5.4559 5.4935 5.5313 5.5692 5.6073 5.6455 5.6839 5.7224 5.7611 5.8000 2/ 1 1.2000 1.1999 1.1996 1.1991 1.1985 1.1976 1.1966 1.1953 1.1939 1.1923 1.1905 1.1885 1.1863 1.1840 1.1815 1.1788 1.1759 1.1729 1.1697 1.1663 1.1628 1.1591 e-Text Main Menu | Textbook Table of Contents */ V/V* 0.0 0.0219 0.0438 0.0657 0.0876 0.1094 0.1313 0.1531 0.1748 0.1965 0.2182 0.2398 0.2614 0.2829 0.3043 0.3257 0.3470 0.3682 0.3893 0.4104 0.4313 0.4522 | Study Guide p0/p* 0 28.9421 14.4815 9.6659 7.2616 5.8218 4.8643 4.1824 3.6727 3.2779 2.9635 2.7076 2.4956 2.3173 2.1656 2.0351 1.9219 1.8229 1.7358 1.6587 1.5901 1.5289 Compressible-Flow Tables 781 | v v Table B.3 (Cont.) Adiabatic Frictional Flow in a Constant-Area Duct for k 1.4 | Ma f L*/D p/p* T/T* 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1.0 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.2 1.22 1.24 1.26 1.28 1.3 1.32 1.34 1.36 1.38 1.4 1.42 1.44 1.46 1.48 1.5 1.6915 1.4509 1.2453 1.0691 0.9174 0.7866 0.6736 0.5757 0.4908 0.4172 0.3533 0.2979 0.2498 0.2081 0.1721 0.1411 0.1145 0.0917 0.0723 0.0559 0.0423 0.0310 0.0218 0.0145 0.0089 0.0048 0.0021 0.0005 0.0000 0.0005 0.0018 0.0038 0.0066 0.0099 0.0138 0.0182 0.0230 0.0281 0.0336 0.0394 0.0455 0.0517 0.0582 0.0648 0.0716 0.0785 0.0855 0.0926 0.0997 0.1069 0.1142 0.1215 0.1288 0.1361 2.4428 2.3326 2.2313 2.1381 2.0519 1.9719 1.8975 1.8282 1.7634 1.7026 1.6456 1.5919 1.5413 1.4935 1.4482 1.4054 1.3647 1.3261 1.2893 1.2542 1.2208 1.1889 1.1583 1.1291 1.1011 1.0743 1.0485 1.0238 1.0000 0.9771 0.9551 0.9338 0.9133 0.8936 0.8745 0.8561 0.8383 0.8210 0.8044 0.7882 0.7726 0.7574 0.7427 0.7285 0.7147 0.7012 0.6882 0.6755 0.6632 0.6512 0.6396 0.6282 0.6172 0.6065 1.1553 1.1513 1.1471 1.1429 1.1384 1.1339 1.1292 1.1244 1.1194 1.1143 1.1091 1.1038 1.0984 1.0929 1.0873 1.0815 1.0757 1.0698 1.0638 1.0578 1.0516 1.0454 1.0391 1.0327 1.0263 1.0198 1.0132 1.0066 1.0000 0.9933 0.9866 0.9798 0.9730 0.9662 0.9593 0.9524 0.9455 0.9386 0.9317 0.9247 0.9178 0.9108 0.9038 0.8969 0.8899 0.8829 0.8760 0.8690 0.8621 0.8551 0.8482 0.8413 0.8344 0.8276 e-Text Main Menu | Textbook Table of Contents | */ V/V* 0.4729 0.4936 0.5141 0.5345 0.5548 0.5750 0.5951 0.6150 0.6348 0.6545 0.6740 0.6934 0.7127 0.7318 0.7508 0.7696 0.7883 0.8068 0.8251 0.8433 0.8614 0.8793 0.8970 0.9146 0.9320 0.9493 0.9663 0.9833 1.0000 1.0166 1.0330 1.0492 1.0653 1.0812 1.0970 1.1126 1.1280 1.1432 1.1583 1.1732 1.1879 1.2025 1.2169 1.2311 1.2452 1.2591 1.2729 1.2864 1.2999 1.3131 1.3262 1.3392 1.3520 1.3646 Study Guide p0/p* 0 1.4740 1.4246 1.3801 1.3398 1.3034 1.2703 1.2403 1.2130 1.1882 1.1656 1.1451 1.1265 1.1097 1.0944 1.0806 1.0681 1.0570 1.0471 1.0382 1.0305 1.0237 1.0179 1.0129 1.0089 1.0056 1.0031 1.0014 1.0003 1.0000 1.0003 1.0013 1.0029 1.0051 1.0079 1.0113 1.0153 1.0198 1.0248 1.0304 1.0366 1.0432 1.0504 1.0581 1.0663 1.0750 1.0842 1.0940 1.1042 1.1149 1.1262 1.1379 1.1501 1.1629 1.1762 782 Appendix B | v v Table B.3 (Cont.) Adiabatic Frictional Flow in a Constant-Area Duct for k 1.4 Ma p/p* T/T* 1.52 1.54 1.56 1.58 1.6 1.62 1.64 1.66 1.68 1.7 1.72 1.74 1.76 1.78 1.8 1.82 1.84 1.86 1.88 1.9 1.92 1.94 1.96 1.98 2.0 2.02 2.04 2.06 2.08 2.1 2.12 2.14 2.16 2.18 2.2 2.22 2.24 2.26 2.28 2.3 2.32 2.34 2.36 2.38 2.4 2.42 2.44 2.46 2.48 2.5 2.52 2.54 2.56 2.58 | f L*/D 0.1433 0.1506 0.1579 0.1651 0.1724 0.1795 0.1867 0.1938 0.2008 0.2078 0.2147 0.2216 0.2284 0.2352 0.2419 0.2485 0.2551 0.2616 0.2680 0.2743 0.2806 0.2868 0.2929 0.2990 0.3050 0.3109 0.3168 0.3225 0.3282 0.3339 0.3394 0.3449 0.3503 0.3556 0.3609 0.3661 0.3712 0.3763 0.3813 0.3862 0.3911 0.3959 0.4006 0.4053 0.4099 0.4144 0.4189 0.4233 0.4277 0.4320 0.4362 0.4404 0.4445 0.4486 0.5960 0.5858 0.5759 0.5662 0.5568 0.5476 0.5386 0.5299 0.5213 0.5130 0.5048 0.4969 0.4891 0.4815 0.4741 0.4668 0.4597 0.4528 0.4460 0.4394 0.4329 0.4265 0.4203 0.4142 0.4082 0.4024 0.3967 0.3911 0.3856 0.3802 0.3750 0.3698 0.3648 0.3598 0.3549 0.3502 0.3455 0.3409 0.3364 0.3320 0.3277 0.3234 0.3193 0.3152 0.3111 0.3072 0.3033 0.2995 0.2958 0.2921 0.2885 0.2850 0.2815 0.2781 0.8207 0.8139 0.8071 0.8004 0.7937 0.7869 0.7803 0.7736 0.7670 0.7605 0.7539 0.7474 0.7410 0.7345 0.7282 0.7218 0.7155 0.7093 0.7030 0.6969 0.6907 0.6847 0.6786 0.6726 0.6667 0.6608 0.6549 0.6491 0.6433 0.6376 0.6320 0.6263 0.6208 0.6152 0.6098 0.6043 0.5989 0.5936 0.5883 0.5831 0.5779 0.5728 0.5677 0.5626 0.5576 0.5527 0.5478 0.5429 0.5381 0.5333 0.5286 0.5239 0.5193 0.5147 e-Text Main Menu | Textbook Table of Contents */ V/V* 1.3770 1.3894 1.4015 1.4135 1.4254 1.4371 1.4487 1.4601 1.4713 1.4825 1.4935 1.5043 1.5150 1.5256 1.5360 1.5463 1.5564 1.5664 1.5763 1.5861 1.5957 1.6052 1.6146 1.6239 1.6330 1.6420 1.6509 1.6597 1.6683 1.6769 1.6853 1.6936 1.7018 1.7099 1.7179 1.7258 1.7336 1.7412 1.7488 1.7563 1.7637 1.7709 1.7781 1.7852 1.7922 1.7991 1.8059 1.8126 1.8192 1.8257 1.8322 1.8386 1.8448 1.8510 | Study Guide p0/p* 0 1.1899 1.2042 1.2190 1.2344 1.2502 1.2666 1.2836 1.3010 1.3190 1.3376 1.3567 1.3764 1.3967 1.4175 1.4390 1.4610 1.4836 1.5069 1.5308 1.5553 1.5804 1.6062 1.6326 1.6597 1.6875 1.7160 1.7451 1.7750 1.8056 1.8369 1.8690 1.9018 1.9354 1.9698 2.0050 2.0409 2.0777 2.1153 2.1538 2.1931 2.2333 2.2744 2.3164 2.3593 2.4031 2.4479 2.4936 2.5403 2.5880 2.6367 2.6865 2.7372 2.7891 2.8420 Compressible-Flow Tables 783 | v v Table B.3 (Cont.) Adiabatic Frictional Flow in a Constant-Area Duct for k 1.4 | Ma f L*/D p/p* T/T* 2.6 2.62 2.64 2.66 2.68 2.7 2.72 2.74 2.76 2.78 2.8 2.82 2.84 2.86 2.88 2.9 2.92 2.94 2.96 2.98 3.0 3.02 3.04 3.06 3.08 3.1 3.12 3.14 3.16 3.18 3.2 3.22 3.24 3.26 3.28 3.3 3.32 3.34 3.36 3.38 3.4 3.42 3.44 3.46 3.48 3.5 3.52 3.54 3.56 3.58 3.6 3.62 3.64 3.66 0.4526 0.4565 0.4604 0.4643 0.4681 0.4718 0.4755 0.4791 0.4827 0.4863 0.4898 0.4932 0.4966 0.5000 0.5033 0.5065 0.5097 0.5129 0.5160 0.5191 0.5222 0.5252 0.5281 0.5310 0.5339 0.5368 0.5396 0.5424 0.5451 0.5478 0.5504 0.5531 0.5557 0.5582 0.5607 0.5632 0.5657 0.5681 0.5705 0.5729 0.5752 0.5775 0.5798 0.5820 0.5842 0.5864 0.5886 0.5907 0.5928 0.5949 0.5970 0.5990 0.6010 0.6030 0.2747 0.2714 0.2682 0.2650 0.2619 0.2588 0.2558 0.2528 0.2498 0.2470 0.2441 0.2414 0.2386 0.2359 0.2333 0.2307 0.2281 0.2256 0.2231 0.2206 0.2182 0.2158 0.2135 0.2112 0.2090 0.2067 0.2045 0.2024 0.2002 0.1981 0.1961 0.1940 0.1920 0.1901 0.1881 0.1862 0.1843 0.1825 0.1806 0.1788 0.1770 0.1753 0.1736 0.1718 0.1702 0.1685 0.1669 0.1653 0.1637 0.1621 0.1616 0.1590 0.1575 0.1560 0.5102 0.5057 0.5013 0.4969 0.4925 0.4882 0.4839 0.4797 0.4755 0.4714 0.4673 0.4632 0.4592 0.4552 0.4513 0.4474 0.4436 0.4398 0.4360 0.4323 0.4286 0.4249 0.4213 0.4177 0.4142 0.4107 0.4072 0.4038 0.4004 0.3970 0.3937 0.3904 0.3872 0.3839 0.3807 0.3776 0.3745 0.3714 0.3683 0.3653 0.3623 0.3594 0.3564 0.3535 0.3507 0.3478 0.3450 0.3422 0.3395 0.3368 0.3341 0.3314 0.3288 0.3262 e-Text Main Menu | Textbook Table of Contents | */ V/V* 1.8571 1.8632 1.8691 1.8750 1.8808 1.8865 1.8922 1.8978 1.9033 1.9087 1.9140 1.9193 1.9246 1.9297 1.9348 1.9398 1.9448 1.9497 1.9545 1.9593 1.9640 1.9686 1.9732 1.9777 1.9822 1.9866 1.9910 1.9953 1.9995 2.0037 2.0079 2.0120 2.0160 2.0200 2.0239 2.0278 2.0317 2.0355 2.0392 2.0429 2.0466 2.0502 2.0537 2.0573 2.0607 2.0642 2.0676 2.0709 2.0743 2.0775 2.0808 2.0840 2.0871 2.0903 Study Guide p0/p* 0 2.8960 2.9511 3.0073 3.0647 3.1233 3.1830 3.2440 3.3061 3.3695 3.4342 3.5001 3.5674 3.6359 3.7058 3.7771 3.8498 3.9238 3.9993 4.0763 4.1547 4.2346 4.3160 4.3989 4.4835 4.5696 4.6573 4.7467 4.8377 4.9304 5.0248 5.1210 5.2189 5.3186 5.4201 5.5234 5.6286 5.7358 5.8448 5.9558 6.0687 6.1837 6.3007 6.4198 6.5409 6.6642 6.7896 6.9172 7.0471 7.1791 7.3135 7.4501 7.5891 7.7305 7.8742 784 Appendix B Ma f L*/D p/p* T/T* 3.68 3.7 3.72 3.74 3.76 3.78 3.8 3.82 3.84 3.86 3.88 3.9 3.92 3.94 3.96 3.98 4.0 0.6049 0.6068 0.6087 0.6106 0.6125 0.6143 0.6161 0.6179 0.6197 0.6214 0.6231 0.6248 0.6265 0.6282 0.6298 0.6315 0.6331 0.1546 0.1531 0.1517 0.1503 0.1489 0.1475 0.1462 0.1449 0.1436 0.1423 0.1410 0.1397 0.1385 0.1372 0.1360 0.1348 0.1336 0.3236 0.3210 0.3185 0.3160 0.3135 0.3111 0.3086 0.3062 0.3039 0.3015 0.2992 0.2969 0.2946 0.2923 0.2901 0.2879 0.2857 Table B.4 Frictionless Duct Flow with Heat Transfer for k 1.4 Ma T0/T* 0 p/p* T/T* 0.0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6 0.0 0.0019 0.0076 0.0171 0.0302 0.0468 0.0666 0.0895 0.1151 0.1432 0.1736 0.2057 0.2395 0.2745 0.3104 0.3469 0.3837 0.4206 0.4572 0.4935 0.5290 0.5638 0.5975 0.6301 0.6614 0.6914 0.7199 0.7470 0.7725 0.7965 0.8189 2.4000 2.3987 2.3946 2.3800 2.3787 2.3669 2.3526 2.3359 2.3170 2.2959 2.2727 2.2477 2.2209 2.1925 2.1626 2.1314 2.0991 2.0657 2.0314 1.9964 1.9608 1.9247 1.8882 1.8515 1.8147 1.7778 1.7409 1.7043 1.6678 1.6316 1.5957 0.0 0.0023 0.0092 0.0205 0.0362 0.0560 0.0797 0.1069 0.1374 0.1708 0.2066 0.2445 0.2841 0.3250 0.3667 0.4089 0.4512 0.4933 0.5348 0.5755 0.6151 0.6535 0.6903 0.7254 0.7587 0.7901 0.8196 0.8469 0.8723 0.8955 0.9167 | v v Table B.3 (Cont.) Adiabatic Frictional Flow in a Constant-Area Duct for k 1.4 | e-Text Main Menu | Textbook Table of Contents */ V/V* 2.0933 2.0964 2.0994 2.1024 2.1053 2.1082 2.1111 2.1140 2.1168 2.1195 2.1223 2.1250 2.1277 2.1303 2.1329 2.1355 2.1381 */ V/V* 0.0 0.0010 0.0038 0.0086 0.0152 0.0237 0.0339 0.0458 0.0593 0.0744 0.0909 0.1088 0.1279 0.1482 0.1696 0.1918 0.2149 0.2388 0.2633 0.2883 0.3137 0.3395 0.3656 0.3918 0.4181 0.4444 0.4708 0.4970 0.5230 0.5489 0.5745 | Study Guide p0/p* 0 8.0204 8.1691 8.3202 8.4739 8.6302 8.7891 8.9506 9.1148 9.2817 9.4513 9.6237 9.7990 9.9771 10.1581 10.3420 10.5289 10.7188 p0/p* 0 1.2679 1.2675 1.2665 1.2647 1.2623 1.2591 1.2554 1.2510 1.2461 1.2406 1.2346 1.2281 1.2213 1.2140 1.2064 1.1985 1.1904 1.1822 1.1737 1.1652 1.1566 1.1480 1.1394 1.1308 1.1224 1.1141 1.1059 1.0979 1.0901 1.0826 1.0753 Compressible-Flow Tables 785 | v v Table B.4 (Cont.) Frictionless Duct Flow with Heat Transfer for k 1.4 | Ma T0/T* 0 p/p* T/T* 0.62 0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1.0 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.2 1.22 1.24 1.26 1.28 1.3 1.32 1.34 1.36 1.38 1.4 1.42 1.44 1.46 1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64 1.66 1.68 0.8398 0.8592 0.8771 0.8935 0.9085 0.9221 0.9344 0.9455 0.9553 0.9639 0.9715 0.9781 0.9836 0.9883 0.9921 0.9951 0.9973 0.9988 0.9997 1.0000 0.9997 0.9989 0.9977 0.9960 0.9939 0.9915 0.9887 0.9856 0.9823 0.9787 0.9749 0.9709 0.9668 0.9624 0.9580 0.9534 0.9487 0.9440 0.9391 0.9343 0.9293 0.9243 0.9193 0.9143 0.9093 0.9042 0.8992 0.8942 0.8892 0.8842 0.8792 0.8743 0.8694 0.8645 1.5603 1.5253 1.4908 1.4569 1.4235 1.3907 1.3585 1.3270 1.2961 1.2658 1.2362 1.2073 1.1791 1.1515 1.1246 1.0984 1.0728 1.0479 1.0236 1.0000 0.9770 0.9546 0.9327 0.9115 0.8909 0.8708 0.8512 0.8322 0.8137 0.7958 0.7783 0.7613 0.7447 0.7287 0.7130 0.6978 0.6830 0.6686 0.6546 0.6410 0.6278 0.6149 0.6024 0.5902 0.5783 0.5668 0.5555 0.5446 0.5339 0.5236 0.5135 0.5036 0.4940 0.4847 0.9358 0.9530 0.9682 0.9814 0.9929 1.0026 1.0106 1.0171 1.0220 1.0255 1.0276 1.0285 1.0283 1.0269 1.0245 1.0212 1.0170 1.0121 1.0064 1.0000 0.9930 0.9855 0.9776 0.9691 0.9603 0.9512 0.9417 0.9320 0.9220 0.9118 0.9015 0.8911 0.8805 0.8699 0.8592 0.8484 0.8377 0.8269 0.8161 0.8054 0.7947 0.7840 0.7735 0.7629 0.7525 0.7422 0.7319 0.7217 0.7117 0.7017 0.6919 0.6822 0.6726 0.6631 e-Text Main Menu | Textbook Table of Contents | */ V/V* 0.5998 0.6248 0.6494 0.6737 0.6975 0.7209 0.7439 0.7665 0.7885 0.8101 0.8313 0.8519 0.8721 0.8918 0.9110 0.9297 0.9480 0.9658 0.9831 1.0000 1.0164 1.0325 1.0480 1.0632 1.0780 1.0923 1.1063 1.1198 1.1330 1.1459 1.1584 1.1705 1.1823 1.1938 1.2050 1.2159 1.2264 1.2367 1.2467 1.2564 1.2659 1.2751 1.2840 1.2927 1.3012 1.3095 1.3175 1.3253 1.3329 1.3403 1.3475 1.3546 1.3614 1.3681 Study Guide p0/p* 0 1.0682 1.0615 1.0550 1.0489 1.0431 1.0376 1.0325 1.0278 1.0234 1.0193 1.0157 1.0124 1.0095 1.0070 1.0049 1.0031 1.0017 1.0008 1.0002 1.0000 1.0002 1.0008 1.0017 1.0031 1.0049 1.0070 1.0095 1.0124 1.0157 1.0194 1.0235 1.0279 1.0328 1.0380 1.0437 1.0497 1.0561 1.0629 1.0701 1.0777 1.0856 1.0940 1.1028 1.1120 1.1215 1.1315 1.1419 1.1527 1.1640 1.1756 1.1877 1.2002 1.2131 1.2264 786 Appendix B | v v Table B.4 (Cont.) Frictionless Duct Flow with Heat Transfer for k 1.4 Ma p/p* T/T* 1.7 1.72 1.74 1.76 1.78 1.8 1.82 1.84 1.86 1.88 1.9 1.92 1.94 1.96 1.98 2.0 2.02 2.04 2.06 2.08 2.1 2.12 2.14 2.16 2.18 2.2 2.22 2.24 2.26 2.28 2.3 2.32 2.34 2.36 2.38 2.4 2.42 2.44 2.46 2.48 2.5 2.52 2.54 2.56 2.58 2.6 2.62 2.64 2.66 2.68 2.7 2.72 2.74 2.76 | T0/T* 0 0.8597 0.8549 0.8502 0.8455 0.8409 0.8363 0.8317 0.8273 0.8228 0.8185 0.8141 0.8099 0.8057 0.8015 0.7974 0.7934 0.7894 0.7855 0.7816 0.7778 0.7741 0.7704 0.7667 0.7631 0.7596 0.7561 0.7527 0.7493 0.7460 0.7428 0.7395 0.7364 0.7333 0.7302 0.7272 0.7242 0.7213 0.7184 0.7156 0.7128 0.7101 0.7074 0.7047 0.7021 0.6995 0.6970 0.6945 0.6921 0.6896 0.6873 0.6849 0.6826 0.6804 0.6781 0.4756 0.4668 0.4581 0.4497 0.4415 0.4335 0.4257 0.4181 0.4107 0.4035 0.3964 0.3895 0.3828 0.3763 0.3699 0.3636 0.3575 0.3516 0.3458 0.3401 0.3345 0.3291 0.3238 0.3186 0.3136 0.3086 0.3038 0.2991 0.2945 0.2899 0.2855 0.2812 0.2769 0.2728 0.2688 0.2648 0.2609 0.2571 0.2534 0.2497 0.2462 0.2427 0.2392 0.2359 0.2326 0.2294 0.2262 0.2231 0.2201 0.2171 0.2142 0.2113 0.2085 0.2058 0.6538 0.6445 0.6355 0.6265 0.6176 0.6089 0.6004 0.5919 0.5836 0.5754 0.5673 0.5594 0.5516 0.5439 0.5364 0.5289 0.5216 0.5144 0.5074 0.5004 0.4936 0.4868 0.4802 0.4737 0.4673 0.4611 0.4549 0.4488 0.4428 0.4370 0.4312 0.4256 0.4200 0.4145 0.4091 0.4038 0.3986 0.3935 0.3885 0.3836 0.3787 0.3739 0.3692 0.3646 0.3601 0.3556 0.3512 0.3469 0.3427 0.3385 0.3344 0.3304 0.3264 0.3225 e-Text Main Menu | Textbook Table of Contents */ V/V* 1.3746 1.3809 1.3870 1.3931 1.3989 1.4046 1.4102 1.4156 1.4209 1.4261 1.4311 1.4360 1.4408 1.4455 1.4501 1.4545 1.4589 1.4632 1.4673 1.4714 1.4753 1.4792 1.4830 1.4867 1.4903 1.4938 1.4973 1.5007 1.5040 1.5072 1.5104 1.5134 1.5165 1.5194 1.5223 1.5252 1.5279 1.5306 1.5333 1.5359 1.5385 1.5410 1.5434 1.5458 1.5482 1.5505 1.5527 1.5549 1.5571 1.5592 1.5613 1.5634 1.5654 1.5673 | Study Guide p0/p* 0 1.2402 1.2545 1.2692 1.2843 1.2999 1.3159 1.3324 1.3494 1.3669 1.3849 1.4033 1.4222 1.4417 1.4616 1.4821 1.5031 1.5246 1.5467 1.5693 1.5924 1.6162 1.6404 1.6653 1.6908 1.7168 1.7434 1.7707 1.7986 1.8271 1.8562 1.8860 1.9165 1.9476 1.9794 2.0119 2.0451 2.0789 2.1136 2.1489 2.1850 2.2218 2.2594 2.2978 2.3370 2.3770 2.4177 2.4593 2.5018 2.5451 2.5892 2.6343 2.6802 2.7270 2.7748 Compressible-Flow Tables 787 | v v Table B.4 (Cont.) Frictionless Duct Flow with Heat Transfer for k 1.4 | Ma T0/T* 0 p/p* T/T* 2.78 2.8 2.82 2.84 2.86 2.88 2.9 2.92 2.94 2.96 2.98 3.0 3.02 3.04 3.06 3.08 3.1 3.12 3.14 3.16 3.18 3.2 3.22 3.24 3.26 3.28 3.3 3.32 3.34 3.36 3.38 3.4 3.42 3.44 3.46 3.48 3.5 3.52 3.54 3.56 3.58 3.6 3.62 3.64 3.66 3.68 3.7 3.72 3.74 3.76 3.78 3.8 3.82 3.84 0.6761 0.6738 0.6717 0.6696 0.6675 0.6655 0.6635 0.6615 0.6596 0.6577 0.6558 0.6540 0.6522 0.6504 0.6486 0.6469 0.6452 0.6435 0.6418 0.6402 0.6386 0.6370 0.6354 0.6339 0.6324 0.6309 0.6294 0.6280 0.6265 0.6251 0.6237 0.6224 0.6210 0.6197 0.6184 0.6171 0.6158 0.6145 0.6133 0.6121 0.6109 0.6097 0.6085 0.6074 0.6062 0.6051 0.6040 0.6029 0.6018 0.6008 0.5997 0.5987 0.5977 0.5967 0.2030 0.2004 0.1978 0.1953 0.1927 0.1903 0.1879 0.1855 0.1832 0.1809 0.1787 0.1765 0.1743 0.1722 0.1701 0.1681 0.1660 0.1641 0.1621 0.1602 0.1583 0.1565 0.1547 0.1529 0.1511 0.1494 0.1477 0.1461 0.1444 0.1428 0.1412 0.1397 0.1381 0.1366 0.1351 0.1337 0.1322 0.1308 0.1294 0.1280 0.1267 0.1254 0.1241 0.1228 0.1215 0.1202 0.1190 0.1178 0.1166 0.1154 0.1143 0.1131 0.1120 0.1109 0.3186 0.3149 0.3111 0.3075 0.3039 0.3004 0.2969 0.2934 0.2901 0.2868 0.2835 0.2803 0.2771 0.2740 0.2709 0.2679 0.2650 0.2620 0.2592 0.2563 0.2535 0.2508 0.2481 0.2454 0.2428 0.2402 0.2377 0.2352 0.2327 0.2303 0.2279 0.2255 0.2232 0.2209 0.2186 0.2164 0.2142 0.2120 0.2099 0.2078 0.2057 0.2037 0.2017 0.1997 0.1977 0.1958 0.1939 0.1920 0.1902 0.1884 0.1866 0.1848 0.1830 0.1813 e-Text Main Menu | Textbook Table of Contents | */ V/V* 1.5693 1.5711 1.5730 1.5748 1.5766 1.5784 1.5801 1.5818 1.5834 1.5851 1.5867 1.5882 1.5898 1.5913 1.5928 1.5942 1.5957 1.5971 1.5985 1.5998 1.6012 1.6025 1.6038 1.6051 1.6063 1.6076 1.6088 1.6100 1.6111 1.6123 1.6134 1.6145 1.6156 1.6167 1.6178 1.6188 1.6198 1.6208 1.6218 1.6228 1.6238 1.6247 1.6257 1.6266 1.6275 1.6284 1.6293 1.6301 1.6310 1.6318 1.6327 1.6335 1.6343 1.6351 Study Guide p0/p* 0 2.8235 2.8731 2.9237 2.9752 3.0278 3.0813 3.1359 3.1914 3.2481 3.3058 3.3646 3.4245 3.4854 3.5476 3.6108 3.6752 3.7408 3.8076 3.8756 3.9449 4.0154 4.0871 4.1602 4.2345 4.3101 4.3871 4.4655 4.5452 4.6263 4.7089 4.7929 4.8783 4.9652 5.0536 5.1435 5.2350 5.3280 5.4226 5.5188 5.6167 5.7162 5.8173 5.9201 6.0247 6.1310 6.2390 6.3488 6.4605 6.5739 6.6893 6.8065 6.9256 7.0466 7.1696 788 Appendix B Ma T0/T* 0 p/p* T/T* 3.86 3.88 3.9 3.92 3.94 3.96 3.98 4.0 0.5957 0.5947 0.5937 0.5928 0.5918 0.5909 0.5900 0.5891 0.1098 0.1087 0.1077 0.1066 0.1056 0.1046 0.1036 0.1026 0.1796 0.1779 0.1763 0.1746 0.1730 0.1714 0.1699 0.1683 Table B.5 Prandtl-Meyer Supersonic Expansion Function for k 1.4 Ma | v v Table B.4 (Cont.) Frictionless Duct Flow with Heat Transfer for k 1.4 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 | , deg 0.0 0.49 1.34 2.38 3.56 4.83 6.17 7.56 8.99 10.44 11.91 13.38 14.86 16.34 17.81 19.27 20.73 22.16 23.59 24.99 26.38 27.75 29.10 30.43 31.73 33.02 34.28 35.53 36.75 37.95 39.12 40.28 41.41 42.53 43.62 44.69 45.75 46.78 47.79 48.78 49.76 e-Text Main Menu Ma 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 4.05 4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45 4.50 4.55 4.60 4.65 4.70 4.75 4.80 4.85 4.90 4.95 5.00 | , deg 50.71 51.65 52.57 53.47 54.35 55.22 56.07 56.91 57.73 58.53 59.32 60.09 60.85 61.60 62.33 63.04 63.75 64.44 65.12 65.78 66.44 67.08 67.71 68.33 68.94 69.54 70.13 70.71 71.27 71.83 72.38 72.92 73.45 73.97 74.48 74.99 75.48 75.97 76.45 76.92 Ma 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80 5.85 5.90 5.95 6.00 6.05 6.10 6.15 6.20 6.25 6.30 6.35 6.40 6.45 6.50 6.55 6.60 6.65 6.70 6.75 6.80 6.85 6.90 6.95 7.00 Textbook Table of Contents */ V/V* 1.6359 1.6366 1.6374 1.6381 1.6389 1.6396 1.6403 1.6410 , deg 77.38 77.84 78.29 78.73 79.17 79.60 80.02 80.43 80.84 81.24 81.64 82.03 82.42 82.80 83.17 83.54 83.90 84.26 84.61 84.96 85.30 85.63 85.97 86.29 86.62 86.94 87.25 87.56 87.87 88.17 88.47 88.76 89.05 89.33 89.62 89.90 90.17 90.44 90.71 90.97 | p0/p* 0 7.2945 7.4215 7.5505 7.6816 7.8147 7.9499 8.0873 8.2269 Ma 7.05 7.10 7.15 7.20 7.25 7.30 7.35 7.40 7.45 7.50 7.55 7.60 7.65 7.70 7.75 7.80 7.85 7.90 7.95 8.00 8.05 8.10 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.55 8.60 8.65 8.70 8.75 8.80 8.85 8.90 8.95 9.00 Study Guide , deg 91.23 91.49 91.75 92.00 92.24 92.49 92.73 92.97 93.21 93.44 93.67 93.90 94.12 94.34 94.56 94.78 95.00 95.21 95.42 95.62 95.83 96.03 96.23 96.43 96.63 96.82 97.01 97.20 97.39 97.57 97.76 97.94 98.12 98.29 98.47 98.64 98.81 98.98 99.15 99.32 Compressible-Flow Tables 789 4.0 Ma 2 β Ma1 β= 20° θ θ 25 3.0 Weak 30 shock Mach line 10 Ma 2 θ = 0° 5 2.0 35 15 40 20 45 25 50 30 35 55 60 65 70 Strong 75 shock 80 90 85 1.0 Normal shock 0 | v v Fig. B.1 Mach number downstream of an oblique shock for k 1.4. | 1.0 e-Text Main Menu 2.0 3.0 4.0 Ma1 | Textbook Table of Contents | Study Guide 790 Appendix B 80° 70 β = 90 75 65 60 55 50 45 10.0 β p2 Ma1, p 1 9.0 θ θ = 30° θ 40 8.0 Normal shock 7.0 35 Strong shock 6.0 25 p2 p1 30 5.0 20 4.0 25 15 3.0 5 1.0 | v v Fig. B.2 Pressure ratio downstream of an oblique shock for k 1.4. 20 10 2.0 1.0 2.0 Weak shock 3.0 4.0 Ma1 | e-Text Main Menu | Textbook Table of Contents | Study Guide Appendix C Conversion Factors During this period of transition there is a constant need for conversions between BG and SI units (see Table 1.2). Some additional conversions are given here. Conversion factors are given inside the front cover. Length 1 1 1 1 1 ft 12 in 0.3048 m mi 5280 ft 1609.344 m nautical mile (nmi) 6076 ft yd 3 ft 0.9144 m angstrom (Å) 1.0 E-10 m Volume 1852 m 1 1 1 1 1 3 3 2 2 ft 0.028317 m U.S. gal 231 in3 0.0037854 m3 L 0.001 m3 0.035315 ft3 U.S. fluid ounce 2.9574 E-5 m3 U.S. quart (qt) 9.4635 E-4 m3 Mass 1 1 1 1 slug 32.174 lbm 14.594 kg lbm 0.4536 kg short ton 2000 lbm 907.185 kg tonne 1000 kg Area 1 1 1 1 ft 0.092903 m mi2 2.78784 E7 ft2 2.59 E6 m2 acre 43,560 ft2 4046.9 m2 hectare (ha) 10,000 m2 Velocity 1 ft/s 0.3048 m/s 1 mi/h 1.466666 ft/s 0.44704 m/s 1 kn 1 nmi/h 1.6878 ft/s 0.5144 m/s Acceleration 2 1 ft/s Mass flow 1 slug/s 1 lbm/s 14.594 kg/s 0.4536 kg/s Volume flow 1 gal/min 0.002228 ft3/s 0.06309 L/s 1 106 gal/day 1.5472 ft3/s 0.04381 m3/s Pressure 2 1 lbf/ft 47.88 Pa 1 lbf/in2 144 lbf/ft2 6895 Pa 1 atm 2116.2 lbf/ft2 14.696 lbf/in2 101,325 Pa 1 inHg (at 20°C) 3375 Pa 1 bar 1.0 E5 Pa 0.3048 m/s2 Force 1 1 1 1 1 lbf 4.448222 N 16 oz kgf 2.2046 lbf 9.80665 N U.S. (short) ton 2000 lbf dyne 1.0 E-5 N ounce (avoirdupois) (oz) 0.27801 N | v v 791 | e-Text Main Menu | Textbook Table of Contents | Study Guide Appendix C Energy Power 1 ft lbf 1.35582 J 1 Btu 252 cal 1055.056 J 778.17 ft lbf 1 kilowatt hour (kWh) 3.6 E6 J 1 hp 550 ft lbf/s 745.7 W 1 ft lbf/s 1.3558 W Specific weight 3 1 lbf/ft Density 3 3 1 slug/ft 515.38 kg/m3 1 lbm/ft3 16.0185 kg/m3 1 g/cm3 1000 kg/m3 157.09 N/m Viscosity Kinematic viscosity 1 slug/(ft s) 47.88 kg/(m s) 1 poise (P) 1 g/(cm s) 0.1 kg/(m s) 2 1 ft /h 0.000025806 m2/s 1 stokes (St) 1 cm2/s 0.0001 m2/s Temperature scale readings TF 9 TC 32 TC 5 (TF 32) TR TF 459.69 TK TC 273.16 5 9 where subscripts F, C, R, and K refer to readings on the Fahrenheit, Celsius, Kelvin, and Rankine scales, respectively Specific heat or gas constant* 1 ft lbf/(slug °R) 0.16723 N m/(kg K) 1 Btu/(lb °R) 4186.8 J/(kg K) Thermal conductivity* 1 Btu/(h ft °R) 1.7307 W/(m K) *Although the absolute (Kelvin) and Celsius temperature scales have different starting points, the intervals are the same size: 1 kelvin 1 Celsius degree. The same holds true for the nonmetric absolute (Rankine) and Fahrenheit scales: 1 Rankine degree 1 Fahrenheit degree. It is customary to express temperature differences in absolute-temperature units. | v v 792 | e-Text Main Menu | Textbook Table of Contents | Study Guide Appendix D Equations of Motion in Cylindrical Coordinates The equations of motion of an incompressible newtonian fluid with constant , k, and cp are given here in cylindrical coordinates (r, , z), which are related to cartesian coordinates (x, y, z) as in Fig. 4.2: x r cos The velocity components are r, y , and r sin z. z z (D.1) The equations are: Continuity: 1 (r ) rr r 1 r () z ( z) 0 (D.2) Convective time derivative: V r r 1 r z (D.3) z Laplacian operator: 1 r rr r 2 1 r2 2 2 2 (D.4) z2 The r-momentum equation: r t (V ) 1 r r 1p r 2 r 2 gr r r2 2 r2 (D.5) The -momentum equation: (V t 1 r ) 1p r r 2 g r2 2 r2 r (D.6) The z-momentum equation: z t (V ) z 1p z gz 2 z (D.7) | v v 793 | e-Text Main Menu | Textbook Table of Contents | Study Guide Appendix D The energy equation: cp T t (V )T rr k 2 T [2( z 2 rr r zz where 2 zz) r r 2 rz z 2 r (D.8) (D.9) z 1 r z r 2 z r 1 r z z rz 2 1 r r z r r Viscous stress components: rr r 2 2 rr r z 2 zz z rz zz (D.10) rz Angular-velocity components: r 1 r z z r z v | | e-Text Main Menu | z z v 794 r 1 (r ) rr (D.11) 1 r r Textbook Table of Contents | Study Guide Appendix E Introduction to EES Overview EES (pronounced “ease”) is an acronym for Engineering Equation Solver. The basic function provided by EES is the numerical solution of nonlinear algebraic and differential equations. In addition, EES provides built-in thermodynamic and transport property functions for many fluids, including water, dry and moist air, refrigerants, and combustion gases. Additional property data can be added by the user. The combination of equation solving capability and engineering property data makes EES a very powerful tool. A license for EES is provided to departments of educational institutions which adopt this text by WCB/McGraw-Hill. If you need more information, contact your local WCB/McGraw-Hill representative, call 1-800-338-3987, or visit our website at www.mhhe.com. A commercial version of EES can be obtained from: F-Chart Software 4406 Fox Bluff Rd Middleton, WI 53562 Phone: (608)836-8531 Fax: (608)836-8536 Background Information The EES program is probably installed on your departmental computer. In addition, the license agreement for EES allows students and faculty in a participating educational department to copy the program for educational use on their personal computer systems. Ask your instructor for details. To start EES from the Windows File Manager or Explorer, double-click on the EES program icon or on any file created by EES. You can also start EES from the Windows Run command in the Start menu. EES begins by displaying a dialog window which shows registration information, the version number, and other information. Click the OK button to dismiss the dialog window. Detailed help is available at any point in EES. Pressing the F1 key will bring up a Help window relating to the foremost window. (See Fig. E.1.) Clicking the Contents | v v 795 | e-Text Main Menu | Textbook Table of Contents | Study Guide 796 Appendix E Fig. E.1 EES Help index. button will present the Help index shown below. Clicking on an underlined word (shown in green on color monitors) will provide help relating to that subject. EES commands are distributed among nine pull-down menus as shown below. Many of the commands are accessible with the speed button palette that appears below the menu bar. A brief summary of their functions follows. (A tenth pull-down menu, which is made visible with the Load Textbook command described below, provides access to problems from this text.) | v v The System menu appears above the File menu. The System menu is not part of EES but rather is a feature of the Windows operating system. It holds commands which allow window moving, resizing, and switching to other applications. | e-Text Main Menu | Textbook Table of Contents | Study Guide Introduction to EES 797 The File menu provides commands for loading, merging, and saving work files; libraries; and printing. The Load Textbook command in this menu reads the problem disk developed for this text and creates a new menu to the right of the Help menu for easy access to EES problems accompanying this text. The Edit menu provides the editing commands to cut, copy, and paste information. The Search menu provides Find and Replace commands for use in the Equations window. The Options menu provides commands for setting the guess values and bounds of variables, the unit system, default information, and program preferences. A command is also provided for displaying information on built-in and usersupplied functions. The Calculate menu contains the commands to check, format, and solve the equation set. The Tables menu contains commands to set up and alter the contents of the parametric and lookup tables and to do linear regression on the data in these tables. The parametric table, which is similar to a spreadsheet, allows the equation set to be solved repeatedly while varying the values of one or more variables. The lookup table holds user-supplied data which can be interpolated and used in the solution of the equation set. The Plot menu provides commands to modify an existing plot or prepare a new plot of data in the parametric, lookup, or array tables. Curve-fitting capability is also provided. The Windows menu provides a convenient method of bringing any of the EES windows to the front or to organize the windows. The Help menu provides commands for accessing the on-line help documentation. A basic capability provided by EES is the solution of a set of nonlinear algebraic equations. To demonstrate this capability, start EES and enter this simple example problem in the Equations window. Text is entered in the same manner as for any word processor. Formatting rules are as follows: 1. Uppercase and lowercase letters are not distinguished. EES will (optionally) change the case of all variables to match the manner in which they first appear. | v v 2. Blank lines and spaces may be entered as desired since they are ignored. | e-Text Main Menu | Textbook Table of Contents | Study Guide Appendix E 3. Comments must be enclosed within braces { } or within quotation marks “ ”. Comments may span as many lines as needed. Comments within braces may be nested, in which case only the outermost set of braces is recognized. Comments within quotes will also be displayed in the Formatted Equations window. 4. Variable names must start with a letter and consist of any keyboard characters except ( ) ‘*/ ^ { } : " or ;. Array variables are identified with square braces around the array index or indices, e.g., X[5,3]. The maximum variable length is 30 characters. 5. Multiple equations may be entered on one line if they are separated by a semicolon (;). The maximum line length is 255 characters. 6. The caret symbol (^) or ** is used to indicate raising to a power. 7. The order in which the equations are entered does not matter. 8. The position of knowns and unknowns in the equation does not matter. If you wish, you may view the equations in mathematical notation by selecting the Formatted Equations command from the Windows menu. Select the Solve command from the Calculate menu. A Dialog window will appear indicating the progress of the solution. When the calculations are completed, the button will change from Abort to Continue. Click the Continue button. The solution to this equation set will then be displayed. | v v 798 | e-Text Main Menu | Textbook Table of Contents | Study Guide Introduction to EES A Pipe Friction Example Problem 799 Let us now solve Prob. 6.55 from the text, for a cast-iron pipe, to illustrate the capabilities of the EES program. This problem, without EES, would require iteration for Reynolds number, velocity, and friction factor, a daunting task. State the problem: 6.55 Reservoirs 1 and 2 contain water at 20°C. The pipe is cast iron, with L 4500 m and D 4 cm. What will be the flow rate in m3/h if z 100 m? This is a representative problem in pipe flow (see Fig. E.2), and, being water in a reasonably large (noncapillary) pipe, it will probably be turbulent (Re 4000). The steadyflow energy equation (3.71) may be written between the surfaces of reservoirs 1 and 2: 2 V1 2g p1 g Since p1 p2 z1 p2 g patm and V1 2 V2 2g V2 z2 hf where hf f 2 L Vpipe D 2g 0, this relation simplifies to z f L V2 D 2g (1) where V Q/A is the velocity in the pipe. The friction factor f is a function of Reynolds number and pipe roughness ratio, if the flow is turbulent, from Eq. (6.64): 1 f 1/2 2.0 log10 /D 3.7 2.51 Re f 1/2 if Re 4000 (2) Finally, we need the definitions of Reynolds number and volume flow rate: Re and Q where and VD (3) V D2 4 (4) are the fluid density and viscosity, respectively. z 1 L, D, 2 | v v Fig. E.2 Sketch of the flow system. | e-Text Main Menu | Textbook Table of Contents | Study Guide 800 Appendix E There are a total of 11 variables involved in this problem: (L, D, z, , g, , , V, Re, f, Q). Of these, seven can be specified at the start (L, D, z, , g, , ), while four (V, Re, f, Q) must be calculated from relations (1) to (4) above. These four equations in four unknowns are well posed and solvable but only by laborious iteration, exactly what EES is designed to do. Start EES or select the New command from the File menu if you have already been using the program. A blank Equations window will appear. Our recommendation is to always set the unit system immediately: Select Unit System from the Options menu (Fig. E.3). We select SI and Mass units and trig Degrees, although we do not actually have trigonometric functions this time. We select kPa for pressure and Celsius for temperature, which will be handy for using the EES built-in physical properties of water. Fig. E.3 Unit Selection dialog window. Now, onto the blank screen, enter the equations for this problem (Fig. E.4), of which five are known input values, two are property evaluations, and four are the relations (1) to (4) from above. | v v Fig. E.4 Equations window. | e-Text Main Menu | Textbook Table of Contents | Study Guide Introduction to EES 801 There are several things to notice in Fig. E.4. First, quantities in quotes, such as “m,” are for the user ’s benefit and ignored by EES. Second, we changed Eps and D to meters right away, to keep the SI units consistent. Third, we called on EES to input the viscosity and density of water at 20°C and 1 atm, a procedure well explained in the Help menu. For example, viscosity(water,T 20,P 101) meets the EES requirement that temperature (T) and pressure (P) should be input in °C and kPa — EES will then evaluate in kg/(m s). Finally, note that EES recognizes pi to be 3.141593. In Fig. E.4 we used only one built-in function, log10. There are many such functions, found by scrolling down the Function Information command in the Options menu. Having entered the equations, check the syntax by using the Check/Format command in the Calculate menu. If you did well, EES will report that the 11 equations in 11 unknowns look OK. If not, EES will guess at what might be wrong. If OK, why not go for it? Hit the Solve command in the Options menu. EES reports “logarithm of a negative number—try setting limits on the variables”. We might have known. Go to the Variable Information command in the Options menu. A box, listing the 11 variables, will appear (Fig. E.5). All default EES “guesses” are unity; all default limits are to , which is too broad a range. Enter (as already shown in Fig. E.5) guesses for f 0.02 and Re 10,000, while V 1 and Q 1 seem adequate, and other variables are fixed. Make sure that f, Re, V, and Q cannot be negative. The “display” columns normally say “A”, automatic, satisfactory for most variables. We have changed “A” to “F” (fixed decimal) for Q and V to make sure they are displayed to four decimal places. The “units” column is normally blank—type in the correct units and they will be displayed in the solution. Our guesses and limits are excellent, and the Solve command now iterates and reports success: “max residual 2E-10”, a negligible error. (The default runs for 100 | v v Fig. E.5 Variable Information window with units and guess values entered. | e-Text Main Menu | Textbook Table of Contents | Study Guide 802 Appendix E iterations, which can be modified by the Stop Criteria command in the Options menu.) Hit Continue, and the complete solution is displayed for all variables (Fig. E.6). Fig. E.6 The Solutions window for Prob. 6.55. This is the correct solution to Prob. 6.55: this cast-iron pipe, when subjected to a 100-m elevation difference, will deliver Q 3.17 m3/h of water. EES did all the iteration. Parametric Studies with Tabular Input One of the most useful features of EES is its ability to provide parametric studies. For example, suppose we wished to know how varying z changed the flow rate Q. First comment out the equation that reads DELTAZ 100 by enclosing it within braces. (If you select the equation and press the right mouse button, EES will automatically enter the braces.) Select the New Parametric Table command in the Options menu. A dialog will be displayed (Fig. E.7) listing all the variables in the problem. Highlight what you wish to vary: z. Also highlight variables to be calculated and tabulated: V, Q, Re, and f. | v v Fig. E.7 New Parametric Table window showing selected variables (V is not shown). | e-Text Main Menu | Textbook Table of Contents | Study Guide Introduction to EES 803 Click the OK button and the new table will be displays (Fig. E.8). Enter 10 values of z that cover the range of interest — we have selected the linear range 10 z 500 m. Fig. E.8 Parametric Table window. Clearly the parametric table operates much like a spreadsheet. Select Solve Table from the Calculate menu, and the Solve Table dialog window will appear (Fig. E.9). These are satisfactory default values; the author has changed nothing. Hit the OK button and the calculations will be made and the entire parametric table filled out, as in Fig. E.10. Fig. E.9 Solve Table Dialog. | v v The flow rates can be seen in Fig. E.10, but as always, in the author’s experience, a plot is more illuminating. Select New Plot window from the Plot menu. The New Plot window dialog (Fig. E.11) will appear. Choose z as the x-axis and Q as the y-axis. We added grid lines. Click the OK button, and the desired plot will appear in the Plot window (Fig. E.12). We see a nonlinear relationship, roughly a square-root type, and learn that flow rate Q is not linearly proportional to head difference z. The plot appearance in Fig. E.12 can be modified in several ways. Double-click the mouse in the plot rectangle to see some of these options. | e-Text Main Menu | Textbook Table of Contents | Study Guide Appendix E Fig. E.10 Parametric Table window after calculations are completed. Fig. E.11 New Plot Setup dialog window. | v v 804 | e-Text Main Menu | Textbook Table of Contents | Study Guide Introduction to EES 805 Fig. E.12 Plot window for flow rate versus elevation difference. | v v Loading a Textbook File | A problems disk developed for EES has been included with this textbook. Place the disk in the disk drive, and then select the Load Textbook command in the File menu. Use the Windows Open File command to open the textbook problem index file which, for this book, is named WHITE.TXB. A new menu called Fluid Mechanics will appear to the right of the Help menu. This menu will provide access to all the EES problem solutions developed for this book organized by chapter. As an example, select Chap. 6 from the Fluid Mechanics menu. A dialog window will appear listing the problems in Chap. 6. Select Problem 6.55 — Flow Between Reservoirs. This problem is a modification (smooth instead of cast-iron pipe) of the problem you just entered. It provides a diagram window in which you can enter z. Enter other values, and then select the Solve command in the Calculate menu to see their effect on the flow rate. At this point, you should explore. Try whatever you wish. You can’t hurt anything. The on-line help (invoked by pressing F1) will provide details for the EES commands. EES is a powerful tool that you will find very useful in your studies. e-Text Main Menu | Textbook Table of Contents | Study Guide Answers to Selected Problems | v v Chapter 1 1.2 1.3 E44 molecules 1.4 1.63 slug/ft3, 839 kg/m3 1.6 (a) {L2/T 2}; (b) {M/T} 1.8 1.00 My/I 1.10 Yes, all terms are {ML/T 2} 1.12 {B} {L 1} 1.14 Q Const B g1/2H3/2 1.16 All terms are {ML 2T 2} 1.18 V V0e mt/K 1.20 zmax 64.2 m at t 3.36 s 1.22 (a) 0.372U 2 /R; (b) x 1.291 R 1.24 e 221,000 J/kg 1.26 Wair 0.71 lbf 1.28 1.10 kg/m3, dry 1.13 kg/m3 wet 1.30 W1-2 21 ft lbf 1.32 (a) 76 kN; (b) 501 kN 1.34 1300 atm 1.36 (a) BN2O 1.33 E5 Pa; (b) Bwater 2.13 E9 Pa 1.38 1380 Pa, ReL 28 1.40 A 0.0016 kg/(m s), B 1903 K 1.42 / 200K (T K/200 K)0.68 1.44 Data 50 percent higher; Andrade fit varies 50 percent 1.46 V 15 m/s 1.48 F ( 1/h1 2/h2)AV 3 1.50 M(ro ri)/(2 ri L) 1.52 P 73 W 1.54 M R4/h 1.56 3M sin /(2 R3) 1.58 0.040 kg/(m s), last 2 points are turbulent flow 1.60 0.88 0.023 kg/(m s) 1.62 28,500 Pa 1.64 (a) 0.023 m; (b) 0.069 m 1.66 F 0.014 N 806 | e-Text Main Menu 1.68 1.70 1.72 1.74 1.76 1.78 1.80 1.82 1.84 h ( / g)1/2 cot h 2 cos /( gW) z 4800 m Cavitation occurs for both (a) and (b) z 7500 m (a) 25°C; (b) 4°C x2y y3/ 3 constant y x tan constant x x0{ln (y/y0) ln2 (y/y0)} Chapter 2 289 lb/ft2, AA 577 lb/ft2 2.2 xy 2Cz/B 2.4 x Const e 2.6 (a) 30.3 ft; (b) 30.0 in; (c) 10.35 m; (d ) 13,100 mm 2.8 DALR 9.77°C/km 2.10 10,500 Pa 2.12 8.0 cm 2.14 74,450 Pa with air; 75,420 Pa without air 2.16 (a) 21,526 cm3; (b) 137 kPa 2.18 1.56 2.20 14 lbf 2.22 0.94 cm 2.24 psealevel 117 kPa, mexact 5.3 E18 kg 2.26 (a) 2580 m; (b) 5410 m 2.28 4400 400 ft 2.30 101,100 Pa 2.32 22.6 cm 2.34 p h[ water(1 d 2/D2) d 2/D2)] oil(1 2.36 25° 2.38 (a) p1,gage ( m (t a)gh a)gH 2.40 21.3 cm 2.42 pA pB ( 2 1)gh 2.44 (a) 171 lb/ft2; (b) 392 lb/ft2; manometer reads friction loss | Textbook Table of Contents | Study Guide Answers to Selected Problems 807 2.68 2.70 2.72 2.74 2.76 2.78 2.80 2.82 2.84 2.86 2.88 2.90 2.92 2.94 2.96 2.98 2.100 2.102 2.104 2.106 2.108 2.110 2.112 2.114 2.116 2.118 2.120 2.122 2.124 2.126 2.128 2.130 2.132 2.134 2.136 2.138 2.140 1.45 F 39700 N (a) 524 kN; (b) 350 kN; (c) 100 kN 0.96 879 kg/m3 16.08 ft 0.40 m Fnet 23,940 N at 1.07 m above B 10.6 ft 1.35 m F 1.18 E9 N, MC 3.13 E9 N m counterclockwise, no tipping 18,040 N 4490 lbf at 1.44 ft to right and 1.67 ft up from point B 33,500 N F ba2 0{(a2/g)[exp(gh/a2) 1] h} P ( /24)h2b(3 csc2 ) P R3/4 (a) 58,800 Pa; (b) 0.44 m FH 97.9 MN, FV 153.8 MN FH 4895 N, FV 7343 N FH 0, FV 6800 lbf FH 176 kN, FV 31.9 kN, yes 467 lbf Fone bolt 11,300 N Cx 2996 lb, Cz 313 lbf (a) 940 kN; (b) 1074 kN; (c) 1427 kN FH 7987 lbf, FV 2280 lbf FH 0, FV 297 kN 124 kN 5.0 N 4310 N/m3 12.6 N h (a) 7.05 mm; (b) 7.00 mm (a) 39 N; (b) 0.64 0.636 19100 N/m3 (a) draft 7.24 in; (b) 25 lbf 34.3° a/b 0.834 6850 m h/H Z (Z2 1 )1/2, d/H, Z (2 )/2, pa/( gH ) Yes, stable if S 0.789 Slightly unstable, MG 0.007 m Stable if R/h 3.31 (a) unstable; (b) stable MG L2/(3 R) 4R/(3 ) 0 if L 2R 2.77 in deep; volume 10.8 fluid ounces ax (a) 1.96 m/s2 (deceleration); (b) 5.69 m/s2 (deceleration) | v v 2.46 2.48 2.50 2.52 2.54 2.56 2.58 2.60 2.62 2.64 2.66 | e-Text Main Menu | 2.142 2.144 2.146 2.148 2.150 2.152 2.154 2.157 2.158 (a) 16.3 cm; (b) 15.7 N (a) ax 319 m/s2; (b) no effect, pA pB Leans to the right at 27° Leans to the left at 27° 5.5 cm; linear scale OK (a) 224 r/min; (b) 275 r/min (a) both are paraboloids; (b) pB 2550 Pa (gage) 77 r/min, minimum pressure halfway between B and C 10.57 r/min Chapter 3 3.2 r position vector from point O 3.6 Q (2b/3)(2g)1/2[(h L)3/2 (h L)3/2] 3.8 Q K per unit depth 3.10 ( /3)R2 U0cpTw 3.12 (a) 44 m3/h; (b) 9.6 m/s 3.14 dh/dt (Q1 Q2 Q3)/( d2/4) 3.16 Qtop 3U0b /8 3.18 (b) Q 16bhumax /9 3.20 (a) 7.97 mL/s; (b) 1.27 cm/s 3.22 (a) 0.06 kg/s; (b) 1060 m/s; (c) 3.4 3.24 h [3Kt2d2/(8 tan2 )]1/3 3.26 Q 2U0bh/3 3.28 t (1 1/ 3)h01/2/(2CA 2g) 3.30 (a) dh/dt Q/(2hb cot 20°) 3.32 Vhole 6.1 m/s 3.34 V2 4660 ft/s 3.36 U3 6.33 m/s 3.38 V V0r/(2h) 3.40 500 N to the left 2 2 3.42 F (p1 pa)A1 1] 1A1V 1 [(D1/D2) 2 3.44 F U Lb/3 3.46 (1 cos )/2 3.48 V0 2.27 m/s 3.50 102 kN 2 3.52 F WhV 1[1/(1 sin ) 1] to the left 3.54 163 N 3.56 2.45 N/m 3.58 40 N 3.60 2100 N 3.62 3100 N 3.64 980 N 3.66 8800 N 3.70 91 lbf 3.72 Drag 4260 N 3.74 Fx 0, Fy 17 N, Fz 126 N 3.76 77 m/s 2 2 2 3.80 F ( /2)gb(h 1 h 2) h1bV 1(h1/h2 1) 3.82 25 m/s 3.84 23 N 3.86 274 kPa Textbook Table of Contents | Study Guide 808 3.88 3.90 3.92 3.94 3.96 3.100 3.102 3.104 3.106 3.108 3.110 3.112 3.114 3.116 3.118 3.120 3.122 3.124 3.126 3.128 3.130 3.134 3.136 3.138 3.140 3.142 3.144 3.146 3.148 3.152 3.154 3.156 3.158 3.160 3.162 3.164 3.166 3.168 3.170 3.172 3.174 3.176 3.178 3.180 3.182 Answers to Selected Problems V [ 2 2Vj]1/2, Q/2k dV/dt g dV/dt gh /(L h) h 0 at t 70 s d 2Z/dt2 2gZ/L 0 (a) 507 m/s and 1393 m; (b) 14.5 km 1 1 2 h2/h1 8V 1/(gh1)]1/2 2 2 [1 ( Ve /R) ln (1 m t/M0) ˙ 75 rad/s final (a) V V0 /(1 CV0t/M), C bh(1 cos ) (a) 0.113 ft lbf; (b) 250 r/min T mR 0 ˙2 (a) 414 r/min; (b) 317 r/min P Qr2 [r2 Q cot 2/(2 r2b2)] P QuVn(cot 1 cot 2) (a) 22 ft/s; (b) 110 ft/s; (c) 710 hp L h1 (cot )/2 41 r/min 15.5 kW (work done on the fluid) 1.07 m3/s 34 kW 4500 hp 5.6 m3/h gd4(H L)/(128LQ) 2 Q/(16 L) 1640 hp (a) 1150 gal/min; (b) 67 hp 26 kW h 3.6 ft hf 0.21 m (a) 85.9°; (b) 55.4° h 0.133 m (a) 102 kPa; (b) 88 mi/h (a) 169.4 kPa; (b) 209 m3/h (a) 31 m3/s; (b) 54 kW Q 166 ft3/min, p 0.0204 lbf/in2 (a) 5.25 kg/s; (b) 2.9 cm (a) 60 mi/h; (b) 1 atm h 1.08 ft h 1.76 m D 0.132 ft (a) 5.61 ft/s; (b) further constriction reduces V2 (a) 9.3 m/s; (b) 68 kN/m h2 2.03 ft (subcritical) or 0.74 ft (supercritical) V Vf tanh (Vf t/2L), Vf (2gh)1/2 kp/[(k 1) ] V 2/2 gz constant 4.8 4.12 4.14 4.16 4.18 4.20 4.22 4.28 4.30 4.32 4.34 4.36 4.38 4.42 4.48 4.50 4.52 4.54 4.60 4.62 4.66 4.68 4.70 4.72 4.74 4.76 4.78 4.80 4.82 4.84 4.86 4.88 4.90 Chapter 5 5.2 1.21 m 5.4 V 1.55 m/s, F 1.3 N 5.6 F 450 N 5.10 (a) {ML 2T 2}; (b) {MLT 2} 5.14 /x fcn ( Ux/ ) 5.16 Stanton number h/( Vcp) 5.18 Q /[( p/L)b4] const 5.20 P/( 3D5) fcn[Q/( D3), D2/ ] 5.22 D/V fcn(N, H/L) 5.24 F/( V2L2) fcn( , VL/ , L/D, V/a) 5.26 (a) indeterminate; (b) T 2.75 s 5.28 /L fcn[L/D, VD/ , E/( V2)] 5.30 hL/k fcn( UL / , cp/k) 5.32 Q/(bg1/2H3/2) const 5.34 khydrogen 0.182 W/(m K) v v Chapter 4 2 4.2 (a) du/dt (2V 0/L)(1 2x/L) 4.4 At (2, 1), dT/dt 125 units 2 4.6 (a) 6V 0/L; (b) L ln 3/(2V0) | | e-Text Main Menu (a) 0.0196 V 2/L; (b) at t 1.05 L /U If 0, r r 2 fcn ( , ) fcn(r) only y2 3x2y fcn(x, z) Vt) 0L0/(L0 const, {K} {L/T}, {a} {L 1} 0 1.82 kg/m3 xL Exact solution for any a or b p const ( K2/2)(x2 y2) f1 C1r; f2 C2/r p p(0) 4 umaxz/R2 C g sin /(2 ) Cz yx xy Tmean (∫uT dy)/(∫u dy) Kxy const Inviscid flow around a 180° turn 4Q /( b) Q ULb 22 Irrotational, z0 H R /(2g) 2 Vy /(2h) const K sin /r m tan 1[2xy/(x2 y2 a2)] cos /r 2, 2am (a) 8.8m; (b) 55 m Uy K ln r (a) 0.106 m from A; (b) 0.333 m above the wall (a) Vwall,max m/L; (b) pmin at x L (a) w ( g/2 )(2 x x2) Obsessive result: R2/r ( gb2/2 ) ln (r/a) ( g/4 )(r2 a2) z Q 0.0031 m3/(s m) U ln (r/b)/[ln (a/b)] z F 3.34 N | Textbook Table of Contents | Study Guide Answers to Selected Problems 809 5.36 5.38 5.40 5.44 5.48 5.50 5.52 5.54 5.56 5.58 5.60 5.62 5.64 5.66 5.68 5.70 5.72 5.74 5.76 5.78 5.80 5.82 (a) Qloss R/(A ) constant d/D fcn( UD/ , U2D/Y) h/L fcn( gL2/Y, , ) (a) { } {L2} F 0.17 N; (doubling U quadruples F) (a) F/( UL) constant U 5 ft/s, F 0.003 lbf/ft Power 7 hp V 128 ft/s 87 mi/h V 2.8 m/s Prototype power 157 hp 26.5 r/s; p 22,300 Pa max 0.77 Hz aluminum (a) V 27 m/s; (b) z 27 m (a) F/( U ) constant; (b) No, not plausible F 87 lbf V 25 ft/s Prototype moment 88 kN m Drag 107,000 lbf Weber no. 100 if Lm/Lp 0.0090 (a) 1.86 m/s; (b) 42,900; (c) 254,000 Speeds: 19.6, 30.2, and 40.8 ft/s; Drags: 14,600; 31,800; and 54,600 lbf 5.84 Vm 39 cm/s; Tm 3.1 s; Hm 0.20 m 5.88 At 340 W, D 0.109 m 5.90 pD/( V2L) 0.155( VD/ ) 1/4 | v v Chapter 6 6.2 (a) x 2.1 m; (b) x 0.14 m 6.4 (a) 39 m3/h; (b) 1.3 m3/h 6.6 (a) laminar; (b) laminar 6.8 (a) 3600 Pa/m; (b) 13,400 Pa/m 6.10 (a) from A to B; (b) hf 7.8 m 6.18 (a) 0.054 m3/s; (b) 8.5 m/s; (c) 122 Pa; (d) 542 kPa 6.20 (a) 0.204 m; (b) 19,800 Pa/m; (c) 9980 Pa/m 6.22 (a) 39 kg/s; (b) 1430 6.24 Head loss 25 m 6.26 4 mm 6.28 Q 0.31 m3/h 6.30 F 4N 6.32 (a) 127 MPa; (b) 127 kW 6.34 0.000823 kg/(m s) 6.36 p 65 Pa 6.38 (a) 19.3 m3/h; (b) flow is up 6.40 (a) flow is up; (b) 1.86 m3/h 6.44 hf 10.5 m, p 1.4 MPa 6.46 Input power 11.2 MW 6.48 r/R 1 e 3/2 6.50 (a) 4000 Pa/m; (b) 50 Pa; (c) 46 percent | e-Text Main Menu | 6.52 6.54 6.56 6.58 6.64 6.66 6.68 6.70 6.72 6.74 6.76 6.78 6.80 6.82 6.84 6.86 6.90 6.92 6.94 6.96 6.98 6.102 6.104 6.106 6.108 6.110 6.112 6.114 6.116 6.118 6.120 6.122 6.124 6.126 6.128 6.130 6.132 6.134 6.136 6.138 6.140 6.142 6.144 6.146 6.148 6.150 6.152 6.154 p1 2.38 MPa D 0.118 m (a) 188 km; (b) 27 MW Power 870 kW Q 19.6 m3/h (laminar, Re 1450) (a) 56 kPa; (b) 85 m3/h; (c) u 3.3 m/s at r 1 cm Power 204 hp Q 2.21 ft3/s Optimum 90° (0.7 m rise) D 0.52 in Q 15 m3/h Q 25 m3/h (to the left) Q 0.905 m3/s D 0.394 m D 0.104 m (a) 3.0 m/s; (b) 0.325 m/m; (c) 2770 Pa/m Q 19.6 ft3/s (a) 1530 m3/h; (b) 6.5 Pa (vacuum) 260 Pa/m Cross section 0.106 m by 0.531 m Approximately 128 squares (a) 5.55 hp; (b) 5.31 hp with 6° cone p 0.0305 lbf/in2 Q 0.0296 ft3/s Q 0.22 ft3/s 840 W Q 0.0151 ft3/s (a) Q1 0.0167 m3/s, Q2 0.0193 m3/s, p 774 kPa Q 0.027 m3/s p 131 lbf/in2 Q1 0.0109 m3/s, Q2 0.0264 m3/s, Q3 0.0183 m3/s Increased /d and L/d are the causes Q1 2.09 ft3/s, Q2 1.61 ft3/s, Q3 0.49 ft3/s 35° opening QAB 3.47, QBC 2.90, QBD 0.58, QCD 5.28, QAC 2.38 ft3/s (all) QAB 0.95, QBC 0.24, QBD 0.19, QCD 0.31, QAC 1.05 ft3/s (all) 2 6°, De 2.0 m, pe 224 kPa 2 10°, We 8.4 ft, pe 2180 lbf/ft2 (a) 25.5 m/s, (b) 0.109 m3/s, (c) 1.23 Pa 46.7 m/s p 273 kPa Q 18.6 gal/min, dreducer 0.84 cm Q 54 m3/h (a) 0.00653 m3/s; (b) 100 kPa (a) 1.58 m; (b) 1.7 m p 27 kPa D 4.12 cm h 59 cm Textbook Table of Contents | Study Guide 810 Answers to Selected Problems 6.156 Q 0.924 ft3/s 6.158 (a) 49 m3/h; (b) 6200 Pa 7.108 7.110 7.114 7.116 7.118 7.120 7.122 7.124 | v v Chapter 7 7.2 Rec 1.5 E7 7.4 d 8 mm lies in the transition region 7.6 H 2.5 (versus 2.59 for Blasius) 7.8 Approximately 0.08 N 7.12 Does not satisfy ∂2u/∂y2 0 at y 0 7.14 C const 0 (wall suction) 0/ 7.16 (a) F 181 N; (b) 256 N 7.18 0.16°; Fdrag 0.024 N 7.20 x 0.91 m 7.22 ( xU)1/2 f( ) 7.24 h1 9.2 mm; h2 5.5 mm 7.26 Fa 2.83 F1, Fb 2.0 F1 7.28 (a) Fdrag 2.66 N2( L)1/2U3/2a 7.30 (a) F 72 N; (b) 79 N 7.32 F 0.0245 1/7 L6/7 U013/7 7.34 F 725 N 7.36 7.2 m/s 14 kn 7.38 (a) 7.6 m/s; (b) 6.2 m/s 7.40 L 3.53 m, b 1.13 m 7.42 P4 blades 0.032 1/7( C)6/7 20/7 R27/7 7.44 Accurate to about 6 percent 7.46 9 mm, U 11.2 m/s 22 kn 7.48 Separation at x/L 0.158 (1 percent error) 7.50 Separation at x/R 1.80 rad 103.1° 7.52 CD (Re L )1/2 2.67 (by numerical integration) 7.54 Moment 200,000 N m 7.56 (a) 10 N; (b) 80 N 7.58 (a) 3200 N/m; (b) 2300 N/m 7.60 Tow power 140 hp 7.62 Square side length 0.83 m 7.64 t1000–2000m 202 s 7.68 (a) 34 m/s; (b) no, only 67 percent of terminal velocity at impact 7.70 (a) 642 ft; (b) 425 ft 7.72 (a) L 6.3 m; (b) 120 m 7.78 p 100 Pa 7.80 72° 7.82 Vmin 138 ft/s; (b) Vmax 377 ft/s 7.84 V 9 m/s 7.86 Approximately 3.05 m by 6.1 m 7.88 (a) 62 hp; (b) 86 hp 7.90 Voverturn 145 ft/s 99 mi/h 7.94 Torque (CD/4) 2DR4, max 85 r/min 7.96 0.21 U/D avg 7.98 (b) h 0.18 m 7.100 (b) Dmax 78 m 7.106 (a) 300 m; (b) 380 m | e-Text Main Menu xball 13 m y 1.9 ft Vfinal 18.3 m/s 66 km/h (a) 87 mi/h; (b) 680 hp (a) 21 m/s; (b) 360 m (L /D)max 21; 4.8° (a) 6.7 m/s; (b) 13.5 m/s 26 kn 340 r/s crude theory Chapter 8 2 2 8.2 (R2 R1) 8.4 No, 1/r is not a proper two-dimensional potential 8.6 B(y2 x 2) 8.8 4B 8.12 0 8.14 Irrotational outer, rotational inner; minimum 22 pp R at r 0 8.18 From afar: a single source 4m 8.20 Vortex near a wall (see Fig. 8.17b) 8.22 Same as Fig. 8.6 except upside down 8.24 Cp {2(x/a)/[1 (x/a)2]}2, Cp,min 1.0 at x a 8.26 Vresultant 9.4 m/s at 47° 8.28 Creates a source in a square corner 8.34 Two stagnation points, at x a/ 3 8.36 U 12.9 m/s, 2L 53 cm, Vmax 22.5 m/s 8.42 K/(U a) 0.396, h/a 1.124 8.44 K 4.6 m2/s; (a) 218 kPa; (b) 214 kPa at upper shoulder, 6 kPa at lower shoulder (cavitation) 8.46 F1-bolt 5000 N 8.50 h 3a/2, Umax 5U/4 8.52 Vboat 10.2 ft/s with wind at 44° 8.54 Fparallel 6700 lbf, Fnormal 2700 lbf, power 560 hp (very approximate) 8.56 CD 2.67 (too high, incorrect prear) 8.60 This is Fig. 8.15a, flow in a 60° corner 8.62 Stagnation flow near a “bump” 8.64 All favorable gradients: no separation 8.66 0.45m/(5m 1) if U Cx m 8.68 Flow past a Rankine oval 8.70 Applied to wind-tunnel “blockage” 8.72 Adverse gradient for x a 8.74 VB,total (8Ki 4Kj)/(15a) 8.78 Need an infinite array of images 8.82 (a) 4.5 m/s; (b) 1.13; (c) 1.26 hp 8.84 (a) 0.21; (b) 1.9° 8.86 (a) 26 m; (b) 8.7; (c) 1600 N 8.88 Thrust1-engine 2900 lbf 8.90 (a) 4.0; (b) 4.8° 8.92 (a) 0.77 m; (b) V 4.5 m/s at (r, ) (1.81, 51°) and (1.11, 88°) 8.94 Yes, they are orthogonal | Textbook Table of Contents | Study Guide Answers to Selected Problems 811 8.98 Yes, a closed teardrop shape appears 8.100 V 14.1 m/s, pA 115 kPa 8.102 (a) 1250 ft; (b) 1570 ft (crudely) | v v Chapter 9 9.2 (a) V2 450 m/s, s 515 J/(kg K); (b) V2 453 m/s, s 512 J/(kg K) 9.4 About 50 m/s 9.6 Exit at about T2 54°C and V2 1445 m/s 9.8 410 K 9.10 Ma 0.78 9.12 (a) 2.13 E9 Pa and 1460 m/s; (b) 2.91 E9 Pa and 1670 m/s; (c) 2645 m/s 9.18 (a) 930 ft/s; (b) 878 ft/s 9.20 (a) air: 144 kPa and 995 m/s; (b) helium: 128 kPa and 2230 m/s 9.22 (a) 267 m/s; (b) 286 m/s 9.24 (b) at Ma 0.576 9.28 (a) 0.17 kg/s; (b) 0.90 9.30 (a) 262 m/s; (b) 0.563; (c) 0.905 kg/m3 9.32 (a) 141 kPa; (b) 101 kPa; (c) 0.706 9.34 (a) 0.00424 slug/s; (b) 0.00427 slug/s 9.40 (a) 2.50; (b) 7.6 cm2; (c) 1.27 kg/s; (d) Ma2 1.50 9.42 (a) Ma 0.90, T 260 K, V 291 m/s 9.44 Ve 5680 ft/s, pe 15.7 psia, Te 1587°R, thrust 4000 lbf 9.46 Rx 8 N (to the left) 9.48 (a) 313 m/s; (b) 0.124 m/s; (c) 0.00331 kg/s 9.50 (a) Dexit 5.8 cm 9.52 (a) 5.9 cm2; (b) 773 kPa 9.54 Ma2 0.648, V2 279 m/s, T2 461°K, p2 458 kPa, p02 607 kPa 9.56 At about A1 24.7 cm2 9.58 (a) 306 m/s; (b) 599 kPa; (c) 498 kPa 9.60 Upstream: Ma 1.92, V 585 m/s 9.62 C 19,100 ft/s, Vinside 15,900 ft/s 9.64 (a) 0.150 kg/s; (b, c) 0.157 kg/s 9.66 h 1.09 m 9.68 patm 92.6 kPa; max flow 0.140 kg/s 9.70 (a) 388 kPa; (b) 19 kPa 9.72 Mass flow 0.5 kg/s, pe 185 kPa, Mae 0.407 9.74 (a) 1.096 MPa; (b) 2.24 kg/s 9.76 tshocks 23 s; tchoking-stops 39 s 9.78 Case A: 0.0071 kg/s; B: 0.0068 kg/s 9.80 A* 2.4 E-6 ft2 or Dhole 0.021 in 9.82 Ve 110 m/s, Mae 0.67 (yes) 9.84 (a) 0.96 kg/s; (b) 0.27; (c) 435 kPa 9.86 V2 107 m/s, p2 371 kPa, T2 330 K, p02 394 kPa 9.88 L 2 m, yes, a shock at Ma2 2.14 9.90 (a) 0.764 kg/s; (b) 0.590 kg/s; (c) 0.314 kg/s 9.92 (a) 0.45; (b) 2.04 kg/s | e-Text Main Menu | 9.98 9.100 9.102 9.104 9.106 9.108 9.112 9.116 9.118 9.120 9.122 9.126 9.128 9.130 9.132 9.134 9.136 9.138 9.140 9.142 9.146 9.148 9.150 9.152 (a) 430; (b) 0.12; (c) 0.00243 kg/h Lpipe 69 m Flow is choked at 0.69 kg/s ptank 99 kPa (a) 0.031 m; (b) 0.53 m; (c) 26 m Mass flow drops by about 32 percent (a) 105 m/s; (b) 215 kPa Vplane 2640 ft/s V 204 m/s, Ma 0.6 P is 3 m ahead of the small circle, Ma 2.0, Tstag 518 K 23.13°, Ma2 2.75, p2 145 kPa (a) 25.9°; (b) 26.1° 15.5° wedge (a) 57.87°; (b) 21.82° (a) pA 18.0 psia; (b) pB 121 psia Ma3 1.02, p3 727 kPa, 42.8° (a) h 0.40 m; (b) Ma3 2.43 pr 21.7 kPa Ma2 2.75, p2 145 kPa (a) Ma2 2.641, p2 60.3 kPa; (b) Ma2 2.299, p2 24.1 kPa 9.47° (helium) CL 0.184 (approximately linear), CD 0.0193 (approximately parabolic) (a) 4.10°; (b) drag 2150 N/m Parabolic shape has 33 percent more drag Chapter 10 10.2 (a) C 3.31 m/s; (b) V 0.030 m/s 10.4 These are piezometer tubes (no flow) 10.6 (a) Fr 3.8; (b) Vcurrent 7.7 m/s 10.8 ttravel 6.3 h 10.10 2 ( / g)1/2 crit 10.14 Flow must be fully rough turbulent (high Re) for Chézy to be valid 10.16 20 percent less flow, independent of n 10.18 yn 0.993 m 10.20 Q 74 ft3/s 10.22 S0 0.00038 (or 0.38 m/km) 10.24 yn 0.56 m 10.26 (a) 17.8 m3/s; (b) 1.79 m 10.30 t 32 min 10.32 74,000 gal/min 10.34 If b 4 ft, y 9.31 ft, P 22.62 ft; if b 8 ft, y 4.07 ft, P 16.14 ft 10.36 y2 3.6 m 10.38 Dsemicircle 2.67 m (16 percent less perimeter) 10.42 P 41.3 ft (71 percent more than Prob. 10.39) 10.44 Hexagon side length b 2.12 ft 10.46 Best h0/b 0.53 0.03 Textbook Table of Contents | Study Guide 812 Answers to Selected Problems 10.48 10.50 10.52 10.54 10.56 10.58 10.60 10.64 10.66 10.70 10.72 10.76 10.78 10.80 10.82 10.84 10.86 10.88 10.90 10.92 10.94 10.98 10.106 10.108 10.110 10.112 10.114 10.116 10.120 10.122 10.124 10.126 10.128 (a) 0.00634; (b) 0.00637 (a) 2.37; (b) 0.62 m; (c) 0.0026 W 2.06 m (a) 1.98 m; (b) 3.11 m/s; (c) 0.00405 (a) 1.02 m3/s; (b) 0.0205 Fr 0.628R1/6, R in meters (a) 0.052 m3/(m s); (b) 0.0765 m hmax 0.35 m (a) 1.47; (b) y2 1.19 m (a) 0.15 m; (b) 3.2; (c) 0.59 m3/(s m) (a) 0.046 m; (b) 4.33 m/s; (c) 6.43 H 0.011 m t 8.6 s (crude analysis) (a) 3.83 m; (b) 4.83 m3/(s m) (a) 0.88 m; (b) 17.6 m/s; (c) 2.89 m y2 0.82 ft; y3 5.11 ft; 47 percent (a) 6.07 m/s; (b) V 2.03 m/s (a) downstream; (b) 5.7 percent 0.0207 (or 1.19°) (a) 3370 ft3/s; (b) 7000 hp (a) 0.61 m; (b) 3.74 m/s; (c) 0.89 m (a) steep S-3; (b) S-2; (c) S-1 No entry depth leads to critical flow (a, b) Both curves reach y yn 0.5 m at x (a) ycrest 0.782 m; (b) y(L) 0.909 m M-1 curve, with y 2 m at L 214 m Vexing! Flow chokes at Q 17 m3/s Q 9.51 m3/s Y 0.64 m, 34° 5500 gal/min M-1 curve, y 10 ft at x 3040 ft At x 100 m, y 2.81 m At 300 m upstream, y 2.37 m | v v Chapter 11 11.6 This is a diaphragm pump 11.8 (a) H 112 ft and p 49 lb/in2; (b) H gasoline); P 15 hp 11.10 (a) 1300 r/min; (b) 2080 lbf/in2 11.12 (a) 11.3 m; (b) 1520 W 11.14 1870 W | 11.16 11.18 11.20 (a) 1450 W; (b) 1030 r/min Vvane (1/3)Vjet for max power (a) 2 roots: Q 7.5 and 38.3 ft3/s; (b) 2 roots; H 180 ft and 35 ft 11.22 (a) BEP 92 percent at Q 0.22 m3/s 11.26 Correlation is “fair,” not geometrically similar 11.28 BEP at about 6 ft3/s; Ns 1430, Qmax 12 ft3/s 11.30 (a) 1700 r/min; (b) 8.9 ft3/s; (c) 330 ft 11.32 Correlation “fair,” not geometrically similar 11.34 (a) 11.5 in; (b) 28 hp; (c) 100 ft; (d) 78 percent 11.36 D 9.8 in, n 2100 r/min 11.38 (a) 18.5 hp; (b) 7.64 in; (c) 415 gal/min; (d) 81 percent 11.40 (a) Ds D(gH*)1/4/Q*1/2 11.42 NPSHproto 23 ft 11.44 No cavitation, required depth is only 5 ft 11.46 Ds C/Ns, C 7800 7 percent 11.52 (a) 7.97 m3/s; (b) 14.6 kW; (c) 28.3° 11.54 Centrifugal pumps, D 7.2 ft 11.56 (a) D 5.67 ft, n 255 r/min, P 700 hp; (b) D 1.76 ft, n 1770 r/min, P 740 hp 11.58 Centrifugal pump, 67 percent, D 0.32 ft 11.60 (a) 623; (b) 762 gal/min; (c) 1.77 ft 11.62 D 18.7 ft, p 1160 Pa 11.64 No speed is able to get to BEP 11.66 Q 1240 ft3/min 11.68 Qnew 15,300 gal/min 11.70 (a) 212 ft; (b) 5.8 ft3/s 11.72 (a) 10 gal/min; (b) 1.3 in 11.74 (a) 14.9; (b) 15.9; (c) 20.7 kgal/min 11.76 Dpipe 1.70 ft 11.78 Dpipe 1.67 ft, P 2000 hp 11.80 Q32 22,900 gal/min; Q28 8400 gal/min, H 343 ft for both 11.84 Two turbines: (a) D 9.6 ft; (b) D 3.3 ft 11.86 Nsp 70, hence Francis turbines 11.88 Q 52 ft3/s, D 10.5 ft 11.90 P 800 kW 11.92 Pelton and Francis wheels both OK 11.94 (a) 71 percent; (b) Nsp 19 11.96 (a) 1.68 ft; (b) 0.78 ft 11.100 (a) 190 kW; (b) 24 r/min; (c) 9.3 ft/s 11.102 Q 29 gal/min 250 m 112 ft (of e-Text Main Menu | Textbook Table of Contents | Study Guide Index A | v v Acceleration of a particle, 15, 90, 216 centripetal, 90, 157 convective, 216 Coriolis, 157 local, 216 Ackeret airfoil theory, 635–636 Acoustics, 573 Actuator disk theory, 752–753 Added mass, 539–540 Adiabatic flow, 578–579 atmospheric lapse rate, 102, 105 with friction, 604–606, 776–780 Adverse pressure gradient, 430, 445–448, 501 Aerodynamic forces and moments, 452–453 NACA designs, 471, 528–530, 565 Air-cushion vehicle, 206 Airfoil description, 468, 529 Airfoil theory, 523–534 finite-span, 530–534 supersonic flow, 632–637 thick-cambered, 528–530 thin-plate, 524–528 Andrade’s equation, 49 Anemometer cup, 387, 485 hot-wire and film, 387, 389 Angle of attack definition, 468 in inviscid flow, 499, 517 | e-Text Main Menu | Angular momentum theorem, 130, 158–159, 230 Angular velocity of a fluid, 246–247 Annulus flow in, 362–364 laminar friction factors, 364 Answers to selected problems, 806–812 Archimedes’ laws of buoyancy, 44, 84 Area, body reference, 453 Area change in a duct, 583–587 Aspect ratio of a diffuser, 384 of a wing, 472, 473, 530 Atmosphere isothermal, 68 U. S. standard, 69, 773 Automobile drag forces, 461–463 Average velocity, 143, 26 in pipe flow, 144, 341, 344, 346 Avogadro’s number, 46 Axial-flow pumps, 730–734 Axisymmetric potential flow, 534–540 B Backwater curve, 693–695 Barometer, 66–67 Basic equations (see Differential equations of flow) Basic laws of fluid motion, 35, 129–131 Bend losses, 371 813 Textbook Table of Contents | Study Guide Index Bernoulli, Daniel, 10, 174 Bernoulli constant, 176, 248 Bernoulli obstruction meters, 397–404 Bernoulli’s equation, 10, 174–177, 230, 248–249 outside a boundary layer, 435 compared to the energy equation, 176, 580 for irrotational flow, 230, 249, 496 for isentropic flow, 580–581 limitations and assumptions, 176, 177 in rotating coordinates, 717 for unsteady flow, 175, 248, 249, 496 Betz number, 753 BG units, 8 Bingham-plastic fluid, 28 Blasius flat-plate solution, 437–439, 478 Blasius pipe friction formula, 345 Blowdown analysis, 598, 643 Blower, 711 Blunt-body flows, 429 Body forces, 61, 224 Bore in a channel, 702 Boundary conditions, 34, 234–236 for a boundary layer, 436 free surface or interface, 234–236, 497 at an inlet or outlet, 234, 496 for inviscid flow, 496, 497 kinematic, 235 no-slip, 24, 34, 234 Boundary-element method, 546–548 Boundary layer, 23, 45, 250, 431, 496, 578 displacement thickness, 433, 438, 443 equations of, 434–436 on a flat plate, 153–155, 266 momentum thickness, 431, 438 with pressure gradient, 445–450 with rough walls, 443–444 separation, 435, 447, 447–449 shape factor, 438, 443, 448 thickness, 428, 442 transition, 298, 432, 439 Bourdon tube gage, 99–100 Brinkman number, 268 Broad-crested weir, 689, 690 Buckingham pi theorem, 280, 286–288 Bulk modulus, 49, 102, 577 of various liquids, 772 | v v 814 | e-Text Main Menu | Bump, channel flow over, 675–676 Butterfly valve, 370 Buoyancy, 84–86 Buoyant force, 85 C Cambered airfoil, 468, 471, 528–530 Capillary effect, 31, 299–300 Cauchy-Riemann equations, 249 Cavitation, 32–33, 552 of a pump, 720, 721 of a turbine, 765 Cavitation erosion, 33 Cavitation number, 32, 294, 297 Center of buoyancy, 85, 88 Center of mass, 80 Center of pressure, 75–76 of an airfoil, 527, 636 Centrifugal pump, 161–162, 200, 714–718 dimensionless coefficients, 724–726 performance curves, 720–723, 758, 759 similarity rules, 727–729 Centripetal acceleration, 90, 157 Centroid, 75 of various cross-sections, 76 Channel flow (see Open channel flow) Chézy coefficient, 665 Chézy formulas, 664–666 Choked flow, 586, 598, 740 due to friction, 608–609 due to heat transfer, 617 in an open channel, 676 Chord line, 452, 468 Circular section open channel, 668–669 pipe flow, 338–357 Circulation, 499 at airfoil trailing edge, 524 on a cylinder, 509, 511 Classification of flow, 36–37 Colebrook pipe-friction formula, 348 Complex-variable potential theory, 516–521 Textbook Table of Contents | Study Guide Index | v v Composite channel flows, 687–688 Compressibility criterion, 35, 221, 571 Compressible flow, 220, 315, 571 with area change, 583–587, 774–776 with friction, 603–613, 780–784 with heat transfer, 613–618, 784–788 tables, 774–788 Compressor, 711, 740–741 Computational fluid dynamics, 3, 434, 465, 540–555, 735–736 commercial codes, 552–553 Concentric cylinder flows, 261–263 Cone flow, supersonic, 638 Conformal mapping, 516, 562 Conical diffuser, 373, 386 Conjugate depths, 699 Conservation laws, 35, 130–131 for angular momentum, 130, 158–159 for energy, 131, 163–165, 231 for linear momentum, 130, 146 for mass, 130, 141–146 for salt or species, 35, 315 Consistent units, 11–13 Contact angle, 30–31 Continuity, equation of, 218 cylindrical polar form, 219–220, 793 incompressible flow, 220 spherical polar form, 265 turbulent flow, 334 Continuum, 6–7 Contraction losses, 372, 374 Control section of a channel, 687, 693 Control surface, 136 Control volume, 36, 133 arbitrary but fixed, 135–136 deformable, 137–138, 140 differential-sized, 218 guidelines for selection, 183 moving, 133, 137, 152 one-dimensional, 134–135 Convective acceleration, 15–16 Converging-diverging nozzle, 600–603 Converging nozzle, 598–600 Conversion factors, 8–9, 791–792 Coriolis acceleration, 156, 157, 250 Corner flow, inviscid, 242, 518–519 Correlations, turbulent, 334 | e-Text Main Menu | 815 Corresponding states, law of, 24 Couette flow between cylinders, 261–263 instability of, 262–263 between plates, 25–26, 258–259 nonnewtonian, 272 Couple, concentrated, 268 Creeping motion, 25, 298, 315, 317, 328, 483 past a sphere, 47, 457, 483 Critical channel flow, 671–674 Critical depth, 664, 672 Critical Reynolds number, 329–330 Critical slope of a channel, 674 Critical sonic-point properties, 581, 605 Critical state, 6, 24 Crossflow turbine, 764 Crump weir, 705 Cup anemometer, 387, 485 Cup-mixing temperature, 268 Curl of a vector, 247 Current meter, 387, 389 Curved surface, force on, 79–82 Curvilinear coordinate system, 267 Cylinder array of, 515 in inviscid flow, 245, 508–510 rotating, 512 in viscous flow, 261–263, 295–296, 298, 455 Cylindrical coordinates, 219 equations of motion, 793–794 D da Vinci, Leonardo, 44, 143 d’Alembert paradox, 45, 510 Darcy friction factor, 340, 342, 344, 604 Darcy’s law of porous flow, 420 Darcy-Weisbach equation, 340, 664 Decimal prefixes, 13 Deformable control volume, 133, 137 Deformation of a fluid element, 245–247 Del operator, 216, 219 Textbook Table of Contents | Study Guide Index Density definition of, 6, 17 of various fluids, 771–772 Detached shock wave, 624 Diaphragm transducer, 101 Differential equations of flow, 36, 215, 682, 793 angular momentum, 230 continuity or mass, 217–221 cylindrical coordinates, 793–794 energy, 231–233 incompressible, 220, 228, 236–237 linear momentum, 62, 223–227 Diffuser flows, 313, 381–385, 447 head loss, 373 performance maps, 385, 386 separation and stall, 383, 447–448 stability map, 382 subsonic versus supersonic, 584 Digital computer (see Computational fluid dynamics) Dilatant fluid, 28 Dimensional analysis, 7, 12, 277 of the basic equations, 292–294 of the boundary conditions, 293–294 of pipe flow, 307–309 pitfalls of, 305–307 of turbomachines, 724–726, 744 Dimensional homogeneity, 11–12, 280 nonhomogeneity, 285–286 Dimensional matrix, 313 Dimensionless groups, list of, 297 Dimensions, 7–13, 278 list of, 8–9, 287 Discharge coefficient, 12, 179, 181, 398 flow nozzle, 401 orifice plate, 399–400 sluice gate, 677 venturi, 401, 402 weir, 690–692 Displacement thickness, 433 for a flat plate, 433, 438, 443 Dissipation function, 233 of a hydraulic jump, 680 Divergence of a vector, 220, 226 Dot product, 133 | v v 816 | e-Text Main Menu | Doublet line, 270, 505–506 point, 536 Downwash on a wing, 531, 532 Draft tube, 765 Drag, 452–467 biological adaptation, 467–468 induced, 472, 533 Drag coefficient, 195, 297, 453, 468, 632 of airfoils, 457, 468, 471–473 of a cylinder, 298, 455, 457 rotating, 511–512 on a flat plate, 438, 442–443 at high Mach numbers, 465–466 of road vehicles, 461–463 of a sphere, 298, 456, 457 spinning, 487, 488 of surface ships, 464–465 of three-dimensional bodies, 457, 460 of two-dimensional bodies, 457–458 Drag reduction, 456, 462, 464 Drowned channel flow, 678, 701 Duct flow, 325, 603 compressible, with friction, 603–613, 780 with heat transfer, 613–618, 784 Dynamic similarity, 304–305 E Eckert number, 297 Eddy viscosity, 406 Effective duct diameter, 360 Efficiency, 47, 715 of an open channel, 669–671 of a turbomachine, 715, 734 volumetric, 716, 757 of wind turbines, 753 Elbows, losses in, 368, 369 Elliptical wing, 533 Energy, 18, 131, 163 Energy equation, 163–165, 231–233 steady flow, 167–168 Energy flux, 165, 231 Energy grade line, 177–178, 339 672 Textbook Table of Contents | Study Guide Index Engineering Equation Solver (EES), 41 Enthalpy, 19, 165, 574 Entrance length, 331 Entrance losses, 331, 371, 372 Entrance region, 330–331 Entropy, of an ideal gas, 574 Entropy change, 574 across a normal shock, 591 across a weak oblique shock, 627 Equations of motion (see Differential equations of flow) Equilibrium of forces, 61–62 Equivalent length, minor losses, 367 Erosion of particles, 313, 698 Euler, Leonhard, 45, 174, 294 Euler number, 294, 297 Euler turbine equations, 161–162, 717 Eulerian description, 14, 216 Euler’s equation, 227, 237, 247 Exit pipe loss, 371, 372 Expansion losses, 372–373 Explicit numerical model, 549 External flow, 333, 427, 451–467 F | v v Falling-body problem, 12 dimensional analysis of, 282–285, 289 Fanno line, 648 Favorable pressure gradient, 430, 445–447, 495, 502 Film of fluid draining down an inclined plane, 268 down a vertical cylinder, 272 down a vertical plate, 271 Finite-difference method, 541–543 Finite-element method, 541 Finite-span wings, 472–473, 530–534 First law of thermodynamics, 131, 163 Fittings, losses in, 368 Flap, airfoil, 471, 472, 474 Flat-plate flow,153–155, 428, 431–433 Blasius solution, 437–439, 478 | e-Text Main Menu | 817 integral theory, laminar, 432 turbulent, 441–444 normal to the stream, 457–459, 519–521 with rough walls, 443–444 Flettner rotorship, 511–512, 559 Floating element shear measurement, 480 Flooding of channels, 698 Flow between plates, 25–27, 258–260, 359– 360 Flow coefficient of a meter, 398 Flow meters (see Fluid meters) Flow net, 497 Flow nozzle, 399, 400–401 Flow straighteners, 479 Flow visualization, 40, 426, 470, 515, 554 Fluctuation, turbulent, 326, 333–334 Fluid, definition of, 4 Fluid meters, 385–404 Coriolis type, 395, 396 electromagnetic, 389 flow nozzle, 399, 400–401 head losses, 402 hot-wire, hot-film, 387, 389 laminar-flow element, 396–397 laser-doppler, 387, 389–390 obstruction type, 397–404 orifice plate, 398–400 pitot-static tube, 387, 388–389 rotameter, 395 Savonius rotor, 387, 486 turbine type, 392–393 ultrasonic, 394–395 venturi meter, 399, 401–402 volume flow type, 391 vortex type, 393–394 Fluid properties, 769–773 Force coefficient, 278, 310 Forces hydrostatic, 74 –84 on a turning vane, 150–151 Fourier’s law of conduction, 27, 231 Francis turbine, 742 Free-body concept, 77, 133 Free overfall, 687, 688 Free-streamline theory, 520–521 Free-surface flows, 4–5, 236, 326, 497, 659 Textbook Table of Contents | Study Guide Index Free vortex, 253 Friction drag, 154, 453 Friction losses, 168 Friction factor, 42, 340, 342, 604 compressible flow, 606 Friction factor— Cont. laminar pipe-flow, 342 noncircular ducts, 364, 365 rocky channels, 665 turbulent pipe-flow, 345, 348 Friction velocity, 336 Frictionless flow, 227, 495, 613 Frontal area, 453, 462 Froude, William, 45, 294 Froude number, 294, 297, 465–466, 662, 679, 683 Froude scaling laws, 303–304 Fully developed flow, 258, 330–331 Fully rough flow in channels, 665 on a flat plate, 443–444 in pipes, 347, 348 Fundamentals of Engineering (FE) Exam, 43 G Gage pressure, 63, 77, 148 Gages, pressure, 97–101 Gas constant, 19, 573 of various gases, 772 Gas dynamics (see Compressible flow) Geometric similarity, 301–303 violation of, 302, 303, 307 Glide angle, 489 Gradient operator, 61, 216, 219 Gradual contraction loss, 374 Gradual expansion loss, 373 Gradually varied flow, 662, 682–687 classification, 683–685 effect of width changes, 704 Grashof number, 297 Gravity acceleration of, 9, 64 variation with radius, 65 | v v 818 | e-Text Main Menu | Gravity force on an element, 61, 224 Grid, numerical, 542, 549, 553, 564 H Hagen, G. L. H., 329 Hagen-Poiseuille flow, 341 Half-body, plane, 256–258, 501–502 axisymmetric, 537–538 Halocline, 120 Hazen-Williams formula, 47, 285 Head loss, 168, 340, 661 of a hydraulic jump, 680 minor, 367–375 in pipe flow, 340 Heat addition, flow with, 613–618, 784–788 Heat conduction equation, 233 Heat flux through an element, 232 Heat transfer coefficient, 312 Hele-Shaw flow, 513–514 Herschel-type venturi, 401 High-lift devices, 474 History of fluid mechanics, 44–46, 280 Hodograph for an oblique shock, 623, 624 Homologous points, 302, 727 Honeycomb flow straightener, 408 Horseshoe vortex, 555 Hot-wire or hot-film anemometer, 387, 389 Hydraulic diameter, 358, 363, 661 Hydraulic efficiency, 716 Hydraulic grade line, 177–178, 339, 659 Hydraulic jump, 198–199, 664, 678–681, 702 classification, 679 sloping, 702 Hydraulic model, 307 Hydraulic radius, 13, 358, 661 Hydraulically smooth wall, 347 Hydrodynamic mass, 539–540 Hydrogen bubble technique, 34 Hydrometer, 118 Hydrostatic condition, 4, 59, 62, 63 in gases, 67–69 in liquids, 65–66 Textbook Table of Contents | Study Guide Index Hydrostatic forces on curved surfaces, 79–83 in layered fluids, 82–84 laboratory apparatus, 127 on plane surfaces, 74–79 Hydrostatic pressure distribution, 63–65 Hypersonic flow, 572, 639 I Icebergs, 89–90 Ideal gas (see Perfect-gas law) Images, 521–522 Implicit numerical model, 550 Impulse turbines, 745–749 Incompressible flow, 17, 142–143, 220, 236, 572 Induced drag, 533 Inertial coordinate system, 156 Initial conditions, 234 Integral equations (see Control volume) Intensity of turbulence, 334, 405 Interface, 29 Internal energy, 18, 574 Internal flow, 330 Inviscid flow, 36, 496 Irrotational flow, 230, 247–249, 496 frictionless, 247, 579–582 Isentropic flow, 579–582, 529 with area change, 583–587, 774 compared to Bernoulli’s equation, 580–581 tables, 774–776 Isentropic process, 574 Isothermal duct flow, 610–611 Isovelocity contours, 660 J | v v Jet exit pressure condition, 149 Jet flow, laminar and turbulent, 326–327 Jet pump, 189, 712 | e-Text Main Menu | 819 Jet-turning vane, 150–151 Joukowski transformation, 562 K Kaplan turbine, 742, 746, 749 Kármán momentum-integral relation, 154, 431 Kármán vortex street, 295–296 Kelvin oval, 513–514 Kinematic properties, 15 Kinematic similarity, 303–304, 498 Kinematic viscosity, 24 of various fluids, 24, 770–772 Kinetic energy, 18, 164 correction factor, 170–171 Kline-Fogleman airfoil, 473, 474 Kutta condition, 523–524 Kutta-Joukowski lift theorem, 510–511 L Lagrangian description, 14 Laminar flow, 34, 326, 327, 551 in a concentric annulus, 346–364 between parallel plates, 25–27, 258–260, 359–360 in a pipe, 341–344 between rotating cylinders, 261–263 Laplace’s equation, 239, 251, 496, 497, 516, 793 numerical simulation, 541–543 in polar coordinates, 498, 564, 793 Lapse rate, 68 Large-eddy simulation, 554 Laser-Doppler anemometer, 387, 389 Law-of-the-wall, 336 Lawn sprinkler analysis, 163 Layered fluids, 70, 82–84 Lift definition of, 452, 468 in flow past a cylinder, 510–511 Textbook Table of Contents | Study Guide Index Lift coefficient of airfoils, 470–474, 527, 529–530, 533 supersonic, 632–637 definition, 297, 468, 632 maximum, 473, 528 of a rotating cylinder, 511–512 of a rotating sphere, 488 Lift-drag polar plot, 472 Lifting line theory, 532 Lifting vane, 150–151, 469 Linear momentum, 130, 146–158, 223–227 Liquids versus gases, 4–6 Local acceleration, 216 Local mass-flow function, 586–587 Logarithmic velocity profile, 336, 344 Loss minor, 367–375 in pumps, 723 Lubricating oil properties, 769, 770, 772 Lubrication theory, 271 M Mach angle, 619 Mach cone, 619 Mach number, 35, 221, 295, 297, 306, 572, 579, 592 effect on body drag, 467 Mach waves, 594, 618–621, 628 analogy to water waves, 663, 673, 681 Magnus effect, 510 Manifold flow, 422–423 Manning, Robert, 13, 665 Manning roughness factor, 13, 285, 665 for various channels, 667 Manometer, 70–73, 97, 99 two-fluid differential, 72, 108 Mass, units of, 8 Mass flow, 133, 142, 586, 599, 611 in choked flow, 586 MATLAB contouring, 506 Mean free path of a gas, 7, 46 Meniscus, 74 Metacenter, 87 | v v 820 | e-Text Main Menu | Metacentric height, 87, 88 Meter (see Fluid meters) Minor losses in pipe flow, 367–375 Mixing-length theory, 406 Model-testing principles, 278, 301–307 pitfalls and discrepancies, 296–297 Mohr’s circle, 4–5, 59 Molecular weight, 19, 573 of various gases, 772 Moment of inertia, 76, 88, 131 for various areas, 76 Momentum angular, 130, 158, 230 linear, 130, 146–148, 223–227 Momentum flux, 147, 224 correction factor, 155–156 Momentum integral theory, 155, 431–433, 448 Momentum thickness, 431 for a flat plate, 438, 442 Thwaites’ parameter, 448 Moody chart, 349, 443, 606, 665 Moody pump-size formula, 728 Moving shock wave, 595–596 Multiple-pipe systems, 375–381 N NACA airfoils, 470–471, 528, 567 Nappe, 687, 689 Natural convection, 312, 315, 573 Navier-Stokes equations, 45, 228, 789 nonuniqueness of, 263 Net positive suction head, 721–722 Network, piping, 380–381 Neutral buoyancy, 86, 386 Newton, Sir Isaac, 23, 45, 577 Newtonian fluid, 23, 227–228 Newton’s second law, 8, 130, 146 for a fluid element, 62, 216, 224 in noninertial coordinates, 156–158 No-slip condition, 24, 34, 234, 259, 262, 340 No-temperature-jump condition, 34, 234 Noncircular duct flow, 357–366 Textbook Table of Contents | Study Guide Index Nondimensionalization (see Dimensional analysis) Noninertial coordinate system, 156–158 Nonnewtonian fluids, 28, 272 Nonwetting liquid, 30, 31 Normal channel depth, 662, 667 Normal shock wave, 590–595, 618 tables, 776–780 Normal stresses, 225 Nozzle flow, 598–601 analogy with a sluice gate, 664, 677 choked, 586, 600 converging-diverging, 600–603 design conditions, 600–601 Nozzle flow— Cont. subsonic versus supersonic, 584 Numerical analysis, 3, 434, 540–555 instability, 549 of inviscid flow, 540–548 of open-channel flow, 685–687 of pumps, 735–736 of viscous flow, 548–555 O | v v Oblique shock wave, 620, 621–628, 789–790 reflection of, 651 One-dimensional approximation, 134–135, 138, 147, 165, 583, 660–661 One-seventh power-law, 439, 442, 479 Open channel flow, 236, 659 analogy with gas dynamics, 663, 664, 673, 677, 681 classification of, 662–664 critical flow, 671–674 gradually varied flow, 682–687 most efficient section, 669–671 over weirs, 687–693 Orifice plate, 398–400 Orthogonality conditions, 249, 497–498, 516 Outer layer, turbulent, 335–336 Overlap layer, 335–336, 441 Overrelaxation, 543 | e-Text Main Menu | 821 P Parallel plates, 26, 258–259, 359–360 Pascal unit, 9, 11 Pascal’s law, 71 Pathline, 37–38 Pelton wheel turbine, 745, 747 Perfect-gas law, 19, 35, 67, 573, 585 Permeability of porous media, 315, 420 Physical properties of fluids, 769–773 Pi theorem, 286–288 Piezometer, 103 Pipe flow, 328, 338–357 bend loss, 371 compressible, 604–613, 780–788 flow rate determination, 352–355 head loss or pressure drop, 307, 339, 351 laminar, 341–344 minor losses, 367–375 in a network, 380–381 noncircular, 357–366 in parallel, 376–378 with rough walls, 346–349 in series, 375–376 sizing problem, 355–357 turbulent, 344–348 Pipe standard sizes, 357 Pipelines, 168, 610 Pitching moment, 452, 527 Pitot-static tube, 387, 388, 642 Planform area, 299, 453, 468 Pode’s angle, 487 Poiseuille, J. L. M., 10, 341 Poiseuille flow, 260, 341–342 Poisson’s ratio, 577 Polar coordinates, 220, 243, 498, 499 Polar drag plot, 472 Positive-displacement pump, 711–714, 757 Potential energy, 18, 164 Potential flow, 252–257, 497 analog methods, 513–515 axisymmetric, 534–540 complex variable, 516–521 numerical analysis, 540–548 Potential lines, 248, 498 Potential vortex, 253, 498 Textbook Table of Contents | Study Guide Index Power coefficient, 724, 753, 761 Power-law correlation, for pipe flow, 309, 345 for velocity profile, 155, 439, 442, 479 for viscosity, 27, 772 Power product method, 286 Power specific speed, 744 Prandtl, Ludwig, 2, 45, 434, 629 flat-plate formulas, 479 lifting line theory, 532 Prandtl-Meyer angle, 630, 788 Prandtl-Meyer expansion waves, 628–631, 788 Prandtl number, 297, 579 Prefixes for units, 13 Pressure, 17, 59–61 absolute versus gage, 63 at a point, 60 stagnation, 312, 580 vacuum, 63 vapor, 31–32, 772, 773 Pressure coefficient, 297, 454, 526, 546 Pressure condition at a jet exit, 149 Pressure distribution, 62, 89 hydrostatic, 63–65 in irrotational flow, 249 in a nozzle, 599, 601 in rigid-body translation, 91–93 in rotating rigid-body motion, 93–97 Pressure drop in pipes, 339, 345 Pressure drag, 453 Pressure force on a control volume, 147–148 on a curved surface, 79–82 on an element, 60–61 on a plane surface, 74–79 Pressure gradient, 61, 96, 259, 341 adverse and favorable, 430, 445–448, 501 Pressure head, 65, 102, 168 Pressure measurement, 97–101 Pressure recovery of a diffuser, 373, 382, 385, 386 Pressure transducers, 99–101 Primary dimensions, 8, 278 Principle of corresponding sates, 24–25 Principle of dimensional homogeneity, 10–11, 280 Problem-solving techniques, 44 Product of inertia, 76 | v v 822 | e-Text Main Menu | Propeller turbine, 742, 746, 749 Properties of fluids, 769–773 Propulsion, rocket, 158 Prototype, 36, 278 Pseudoplastic fluid, 28 Pump-system matching, 735–740 Pump-turbine system, 203, 746 Pumps, 47, 711 axial-flow, 729–733 centrifugal, 161–162, 714–718 dimensionless, 724 effect of blade angle, 719 effect of viscosity, 729, 730 multistage, 740 net positive-suction head, 721–722 in parallel, 738–739 performance curves, 204, 212, 714, 720– 722, 733–735, 758, 759 positive-displacement, 711–714 in series, 739–740 similarity rules, 727–728 size effects, 728 R Radius of curvature, 29, 235 Rankine half-body, plane, 256–258, 501–502 axisymmetric, 537–538 Rankine oval, plane, 507–508 axisymmetric, 563 Rankine-Hugoniot relations, 590 Rapidly varied channel flow, 662, 687 Rarefaction shock, 593, 624 Rayleigh line, 649 Reaction turbines, 742 Rectangular duct flow, 365, 366 Relative roughness, 349 Relative velocity, 137–138, 152 Reversible adiabatic flow (see Isentropic flow) Reynolds, Osborne, 45, 294, 330 Reynolds number, 24, 278, 294, 297, 325, 427 for an airfoil, 469 local, 429 Reynolds pipe-flow experiment, 330 Reynolds time-averaging concept, 333–334 Textbook Table of Contents | Study Guide Index Reynolds transport theorem, 133–141 Rheology, 5, 28 Rheopectic fluid, 28 Rigid-body fluid motion, plane, 89–97 Rocket motion, 158 Rolling moment, 452 Rotameter, 395 Rotating cylinder, 512 sphere, 488 Rotationality, generation of, 249–250 Rough-wall effects on channels, 665–667 on cylinder drag, 298 on a flat plate, 443–444 on pipe flow, 346–348 on pumps, 726 sand-grain tests, 347 on sphere drag, 321, 456 Roughness of commercial pipes, 349 of open channels, 667 S | v v Salinity, 22 Sandgrain roughness, 347 Savonius rotor, 387, 486 Saybolt viscosity, 286 Scaling laws, 278–279, 304, 306 Scaling parameters, 282 Schedule-40 pipe sizes, 357 Seawater properties, 22, 772 Second law of thermodynamics, 131, 233, 606, 624, 679, 680 Secondary dimensions, 8–9 Secondary flow, 365–366 Separated flow, 429, 455, 456, 502 Separation bubble, 469 Separation point on an airfoil, 525 on a cylinder, 455 definition of, 447 in a diffuser, 447 in a laminar boundary layer, 449, 501–502 on a sphere, 456 | e-Text Main Menu | 823 Shaft work, 164 Shape factor, 438, 443, 448 Sharp-crested weir, 689–690 Shear stresses, 4–5, 23, 225 turbulent, 334 Shear work, 164 Shock-expansion theory, 632–637 Shock polar, 623, 624 Shock-tube wind tunnel, 598 Shock wave, 250, 591, 521 detached, 624 linearized, 626 moving, 595–596 normal, 590–595, 776–780 oblique, 621–628, 789–790 rarefaction, 593, 624 strong versus weak, 624–626 Shut-off head of a pump. 719–720 SI units, 7–8 Silicon resonance transducer, 67, 101 Similarity, 279, 301 dynamic, 304–305 geometric, 301–303 violations, 302, 303, 307 kinematic, 303–304, 498 for pumps, 727–728 Sink line, 253, 498, 563 point, 536 Siphon, 208, 406 Skin friction coefficient, 432, 438, 441, 442, 449 Slip conditions in inviscid flow, 237 Sluice gate, 664, 677–678 drowned, 678, 701 Smoke-flow visualization, 40, 470 Soap bubble, 29 Sonic boom, 620, 621 Sonic point, 581, 605 Source line, 253, 498, 517 point, 536 Spar buoy, 119 Specific diameter, 760–761 Specific energy, 671–672 Specific gravity, 12, 18 Specific heat, 19–20, 573 Textbook Table of Contents | Study Guide Index Specific-heat ratio, 19, 295, 297, 572 of common gases, 21, 772 Specific speed, 730–731, 734, 735 Specific weight, 17 of common fluids, 65, 772 Speed of sound, 35, 221, 575–577 in the atmosphere, 773 of a perfect gas, 35, 577 of various materials, 577 of water, 577, 769 Sphere inviscid flow, 265, 538–539 viscous flow, 298, 321, 456, 457, 483, 488 Spherical droplet, 29 Spherical polar coordinates, 265, 535–536 Stability of floating bodies, 86–89 Stability of a pump, 720, 763 Stability map of a diffuser, 382 Stagnation density, 580 Stagnation enthalpy, 167, 578, 614 Stagnation point, 38, 249, 252, 256, 519 plane flow near, 39–40, 265 Stagnation pressure, 312, 580 Stagnation properties, 578–580 Stagnation speed of sound, 579 Stagnation temperature, 579 Stall angle of attack, 528 Stall speed, 473 Stalled airfoil, 470 Standard atmosphere, 69, 773 Stanton number, 312 Starting vortex, 469 State, equation of, 16, 18, 67, 131, 234, 573 for gases, 18–20, 573–574 for liquids, 21–22 van der Waals, 642 Static-pressure measurement, 97 Steady-flow energy equation, 167–168, 578, 661 Stokes flow past a sphere, 47, 457, 483, 487 Stokes’ stream function, 269, 535 Stopping vortex, 469 Strain rate, 23, 247 Stratified flow, 221, 250 Streakline, 37–38 Stream function, 238–244, 497 axisymmetric flow, 243–244, 535 | v v 824 | e-Text Main Menu | compressible flow, 243 geometric interpretation, 240–241 irrotational flow, 239, 497 polar coordinates, 243 of Stokes, 269, 535 Streamline, 37–40, 240, 498 Streamline coordinates, 267 Streamlining of bodies, 456 Streamtube, 38, 143, 174 Stress gradients, 225 Stress tensor, 225, 227, 794 symmetry condition, 231 Strouhal number, 295, 296, 297 Subcritical channel flow, 663, 672 Subsonic flow, 572 Substantial derivative, 216 Suction specific speed, 731 Sudden expansion or contraction, 192–193, 371–372 Supercritical channel flow, 663, 672–673 Superposition of potential flows, 254–257, 500–501 Supersonic airfoil theory, 632–637 Supersonic flow, 149, 572, 618 Surface forces, 61, 225 Surface tension, 29–31, 235, 693 of air-water, 30, 773 of various interfaces, 29, 772 Sutherland-law viscosity formula, 27, 771 Swallow float, 86 System, 16, 130 System-matching of pumps, 735–740 Systems of units, 7 T Tainter gate, 115 Takeoff analysis for aircraft, 475 Taylor number, 262 Taylor vortices, 263 Tee-junction losses, 368 Temperature definition, 17 rise due to dissipation, 238 Terminal velocity, 309, 483 Textbook Table of Contents | Study Guide Index | v v Thermal conductivity, 27, 231 Thermodynamic properties, 16, 131, 771–772 Thickness drag, supersonic, 635 Thin-airfoil theory, 524–527, 635 Thixotropic fluid, 28 Three-dimensional flow, 535–540, 637 compressible, 637–640 Three-reservoir pipe junction, 376, 379 Throat in a duct, 585 Thwaites’ integral method, 448–450 Time-averaging of turbulence, 333–334 Timeline, 37 Tornado flow model, 255, 501, 556 Torricelli’s formula, 179 Total head, 168, 177 Trailing vortex, 469, 531–532 Transition to turbulence, 326–330 in a boundary layer, 299, 432, 439 on a flat plate, 405, 439 in a jet exit stream, 327 in pipe flow, 326, 328 in sphere flow, 310, 405 Transitional roughness, 347 Transonic flow, 572 Transport properties, 16 Trapezoidal channel, 668, 670–671 Triangular duct flow, 365, 366 Tri-diagonal matrix, 550 Trip wire, 405 Troposphere, 68 Tube bundle, 412 Turbines, 742–749 efficiency, 744, 748–749 impulse, 745–749 reaction, 742 windmills, 750–754 Turbomachine classification, 711–714 Turbulent flow, 3, 34, 376 on a flat plate, 441–444 fluctuations 326, 333–334 historical details, 328–330 intensity, 405 intermittency, 326 numerical models, 552–553 in a pipe, 328, 344–348 Turbulent puff, 328 | e-Text Main Menu | 825 Turbulent shear flow, 333–337 logarithmic overlap layer, 335–337 wall and outer layers, 335–336 Turbulent stresses, 334 Two-phase flow, 6, 219 U Ultrasonic flowmeter, 394 Uncertainty of data, 42–43 Uncoupling of velocity and temperature, 236–237 Uniform channel flow, 662, 664–667 Uniform stream, 252–253, 498, 517, 536 Unit normal vector, 132, 136 U. S. Standard Atmosphere, 69, 773 Units, 7–10 Universal gas constant, 19, 573 Unsteady Bernoulli equation, 175, 248, 249, 496 Unsteady flow, 36, 40, 549 Upwind differencing, 552 V V-notch weir, 692–693, 705 Vacuum pressure, 63 Valve flows, 12, 367–370 Van der Waals’ equation, 642 Vane flow, 150–151 Vapor pressure, 31–32 of various fluids, 772 of water, 32, 773 Varied flow, 662, 682–687 Vector differentiation, 215–217 Velocity-defect law, 336 Velocity diagrams, 717, 732, 743 Velocity field, 14–15, 215 Velocity gradient, 23, 246 Velocity head, 168, 367 Velocity measurement, 385–390 Velocity of approach factor, 398 Velocity potential, 248, 496, 535 Textbook Table of Contents | Study Guide Index Velocity profile, 23, 34, 439, 449, 535 for the Blasius solution, 437, 439 Vena contracta, 391, 392, 397, 398, 678 VentureStar spacecraft, 639–640 Venturi flume, 704 Venturi meter, 180–181, 207, 399, 401–402 Virtual mass, 539–540 Viscometer, 50, 51, 203 Viscosity, 22–24 formula for liquids, 27 generalized chart, 25 Sutherland and power-law, 27, 772 of various fluids, 24, 769, 771–772 Viscous dissipation, 233 Viscous flow analysis, 258–263 Viscous force on an element, 226 Viscous stresses, 23, 225, 228 symmetry condition, 231 Viscous sublayer, 337–347 Viscous work, 164 Visualization of flow, 40 Volume expansion rate, 15 Volume flow, 132, 142 measurement of, 391–404 Von Kármán, Theodore, 45, 154, 406, 431, 567 Vortex, line, 253–254, 498, 503, 518 infinite row, 503–504 potential, 253, 498 starting and stopping, 469 trailing, 531–532 Vortex flowmeter, 393–394 Vortex shedding, 295–296 Vortex sheet, 504–505 for a thin airfoil, 524–527 Vorticity, 247 W v | | e-Text Main Menu Waterline area, 88 Wave drag of ships, 464–466 of supersonic bodies, 635 Wave motion, 494, 576, 663–664, 672 periodic, 696 Weber number, 294, 297, 693 Weirs, 47, 687–693 broad-crested, 689, 690 Crump type, 705 drowned, 196, 705 inviscid flow model, 560 sharp-crested, 689–690 Wetted area, 453, 465 Wetted perimeter, 358, 661 Wind turbines, 750–754 performance of, 753 typical designs, 751 world energy distribution, 754 Wing theory, two-dimensional, 523–534 finite span, 472, 530–534 Work, 164 due to viscous stresses, 232 X X-33 spacecraft, 639–640 Y Yawing moment, 452 Young’s modulus, 577 Z Wake flow, 190, 195, 250, 426, 429, 455 Wall roughness, 339–340 Wall shear stress, 341, 342, 438, 442 v 826 | Zero-lift airfoil angle, 530 Zones of action and silence, 620, 672 Textbook Table of Contents | Study Guide ...
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