examf_coverplustables

examf_coverplustables - EGN3353C Fluid Mechanics Spring...

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Unformatted text preview: EGN3353C Fluid Mechanics Spring 2011! Final Exam LAST NAME:___________________________ FIRST NAME:________________ SECTION:______ INSTRUCTIONS: Closed book, closed notes, calculator allowed. FORMULAS • Conservation of energy in control-volume form, assuming zero shear and other work: ￿ ￿ ￿ ￿ p V2 ˙ − Wshaft = d ˙ ￿ Q ρe d ∀ + ρ u+ + + gz Vrel · ￿ dA n dt CV ρ 2 CS EGN 3353C - Fluid Mechanics • Compressible flow: Spring Semester 2011 Exam 3: Formula Sheet Notation A a k M m ˙ p R T u ρ area speed of sound Ratio of specific heats Mach number mass flow pressure gas constant temperature velocity density Isentropic Flow Subscript 0 and superscript ∗ denote stagnation (total) and sonic conditions, respectively. T0 k−1 2 =1+ M T 2 k ￿ ￿ k −1 ￿ ￿k p0 T0 k − 1 2 k −1 = = 1+ M p T 2 1 ￿ ￿ k −1 ￿ ￿1 ρ0 T0 k − 1 2 k −1 = = 1+ M ρ T 2 ￿￿ k+1 ￿ ￿ A 1 2 k − 1 2 2(k−1) = 1+ M A∗ M k+1 2 ￿ ￿ 2(kk+11) √ − 2 pk∗ ∗∗ ∗ √0 m = ρuA = ρ a A = ˙ A k+1 RT0 (1) (2) (3) (4) (5) Normal Shock Waves Subscripts 1 and 2 denote conditions ahead of and behind the shock wave, respectively. 2 ρ2 u1 (k + 1)M1 = = 2 ρ1 u2 2 + (k − 1)M1 ￿ p2 2k ￿ 2 =1+ M1 − 1 p1 k+1 ￿ 2 2 + (k − 1)M1 M2 = 2 2kM1 − (k − 1) (6) (7) (8) EGN3353C Fluid Mechanics Spring 2011! Final Exam Appendix B Isenlropic F Iow T obles Isentropic Flow Table (γ=1.4) F TABLE .1 l sentropic low T able( y : 1 .4) 8 M TITO 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.1,4 0.1.6 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 1 .0000 0 .9999 0 .9997 0 .9993 0 .9987 0 .9980 0 .9971. 0 .9961. 0 .9949 0 .9936 0 .9927 0 .9904 0 .9886 0 .9867 0 .9846 0 .9823 0 .9799 0 .9774 0 .9147 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 0 .9013 0 .8964 0 .8915 0 .8865 0 .8815 0 .8763 0 .8711 0 .8659 0 .8606 0 .8552 plpo 1.0000 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 0.77t6 0.759t 0.7465 0.7338 0.7209 0.7080 0.6951 0.68?1 0.6691 0.6560 0.6430 0.6300 0.6170 0.6041 0.5913 0.5785 p lpo 1 .0000 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 .79L6 0 .78L4 0 .7712 0 .7609 0 .7505 0 .7400 0 .7295 0 .7189 0 .7083 0 .6977 0 .6870 0 .6764 A IA* oo 28.9421. 1 .4.4815 9 .66s9 7 .261.6 5 .8218 4 .8643 4 .1824 3 .6727 3 .2779 2 .9635 2 .7076 2 .4956 2 .3173 2 .1656 2 .0351. t .92I9 t .8229 1 ..7358 1 .6587 1 .5901 r .5289 r .4740 r ,4246 1 .3801 1 .3398 1 ..3034 7 .2703 1 ..2403 t .2t30 1 .1882 r .1656 1 _.t451 1 .1265 t .I097 r .0944 1 .0806 1 .0681 1 .0s70 1 .0471, 1 .0382 1 .0305 L 0237 I .0r79 r .0129 1 .0089 1 .0056 M 0.94 0.96 0.98 1.00 t.02 1..04 1.06 1.08 1.10 1..\2 1..1.4 1..16 1.18 t.20 1..22 t.24 r.26 1.28 1.30 L.32 1.34 1,.36 1.38 1.40 1..42 1..44 1.46 1.48 1.50 1,.52 1..54 1.56 1.58 1.60 1.62 r.64 r.66 1.68 r.70 r.7z r.74 r.76 r.78 1.80 1..82 1.84 1.86 T ITO 0 .8498 0 .8444 0 .8389 0 .8.333 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 .741,6 0 .7358 0 .7300 0 .7242 0 .tt84 0 .7126 0 .7069 0 .7011 0 .6954 0 .6897 0 .6840 0 .6783 0 .6726 0 .6670 0 .661.4 0 .6558 0 .6502 0 .6447 0 .6392 0 .6337 0 .6283 0 .6229 0 .6775 0 .612r 0 .6068 0 .6015 0 .5963 0 .5910 plpo 0.5658 0.5532 0.5407 05283 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 03t42 0.3055 0.2969 0.2886 0.2804 0.2724 0.2646 0.2570 0.2496 0.2423 0.2353 0.2284 0.22t7 0.21.51 0.2088 0.2026 0.1.966 0.1907 0.1850 0.1794 0.1740 o.ioss 0.1637 0.1587 p lpo 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 .41t6 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 .31.29 0 .3062 0 .2996 0 .2931 0 .2868 0 .2806 0 .2745 0 .2686 A rA* 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 7 .0366 1 .0432 1 .0504 1 .0581 r .0663 1 .0750 1 ,.0842 1 .0940 1 .1042 L .II49 1 .1262 I .I379 1 .1501 I .t629 1 .fi62 1 .1899 1 ..2042 1 .2790 t .2344 r .2502 7 .2666 r .2836 1 .3010 1 .3190 1 ..3376 7 .3567 I .3764 I .3967 r .4175 r .$9A 1 ..4610 1 ..4836 1 .5069 I TABLE8 .1 ( Continued) M T IT" 1.88 1.90 t.92 1.94 r.96 1.98 2.00 2.02 2.04 2.06 2.08 2.r0 2.12 2.14 2.16 2.r8 2.20 2.22 2.24 2.26 2.28 2.30 2.32 2.34 2.36 2.38 2.40 2.42 2.44 2.46 2.48 2.50 2.52 2.s4 2.56 2.58 2.60 2.62 2.64 2.66 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 3.00 0 .5859 0 .5807 0 .5756 0 .5705 0 .5655 0 .560s 0 .5556 0 .5506 0 .5458 0 .5409 0 .5361 0 .s313 0 .5266 0 .52t9 0 .5t73 0 .5127 0 .5081 0 .5036 0 .4991 0 .4947 0 .4903 0 .4859 0 .4816 0 .4773 0 .473r 0 .4688 0 .4647 0 .4606 0 .4565 0 .4524 0 .4484 0 .4444 0 .4405 0 .4366 0 .4328 0 .4289 0 .4252 0 .4214 0 .4t77 0 .4141 0 .4t04 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 .366s 0 .3633 0 .3602 0 .3s7r plpo 0.1 539 0.t492 0.t447 0.1403 0.1360 0.1318 1 Q. 278) 0fT59 0.1201 0.1164 0.1128 0.1094 0.1060 0. 1027 0.0996 0.0965 0.0935 0.0906 0.0878 0.08s 1 0.0825 0.0800 0.0175 0.0751 0.0728 0.0706 0.0684 0.0663 0.0643 0.0623 0.0604 0.0585 o.osoz 0.0550 0.0533 0.0517 0.0s0r 0.0486 0.0471 0.0457 0.0443 0.0430 0.0417 0.0464 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 p lPo 0 .2627 0 .2570 0 .25t4 0 .2459 0 .2405 0 .2352 0 .2300 0 .22s0 0 .2200 0 .2152 0 .2104 0 .2058 0 .2013 0 .l 9 68 0 .1925 0 .1882 r 0 .184 0 .1800 0 .1760 0 .t72t 0 .1683 0 .1646 0 .1609 0 .1s74 0 .1539 0 .1505 0 .1472 0 .t439 0 .1408 0 .1377 0 .1346 0 .l 3 l 7 0 .1288 0 .1260 0 .1232 0 .120s 0 .I r 79 1 0 .1 53 0 .l128 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 A IA* r . 5308 1 .5553 1 .5804 1 .6062 1 .6326 1 .6s97 | . 687 s r .7160 1 .t45r 1 .7750 1 .8056 1 .8369 1 .8690 I . 901 8 1 .93s4 1 .9698 2 .0050 2 .0409 2 .0777 2 .rr53 2 .1s38 2 .1931 2 .2333 2 .2744 2 .3164 2 3s93 2 .403r 2 .4479 2 .4936 2 .5403 2 .5880 2 .6367 2 .686s 2 .7372 2 .789r 2 .8420 2 .8960 2 .95rr 3 .0073 3 .0647 3 .1233 3 .1830 3 .2440. 3 .3061 3 369s 3 .4342 3 .5001 3 .s674 3 .63s9 3 .7058 3 .777 | 3 .8498 3 .9238 3 .9993 4 .0763 4 .1s47 4 .2346 M T ITO plpo 3.02 3.04 3.06 3.08 3.10 3.12 3.14 3.16 3.18 3.20 3.22 3.24 3.26 3.28 3.30 3.32 3.34 3.36 3.38 3.40 3.42 3.44 3.46 3.48 3.s0 3.52 3.54 3.56 3.58 3.60 3.62 3.64 3.66 3.68 3.70 3.72 3.74 3.76 3.78 3.80 3.82 3.84 3.86 3.88 3.90 3.92 3.94 3.96 3.98 4.00 4.02 4.04 4.06 4.08 4.I0 4.12 4.1.4 0 .3541 0 .3511 0 .3481 0 .3452 0 .3422 0 .3393 0 .3365 0 .3337 0 .3309 0 .328'1. 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 .18ee 0 .287s 0 .2852 0 .2829 0 .2806 0 .2784 0 .2762 0 .2740 0 .27t8 0 .2697 0 .2ff75 0 .2654 0 .2633 0 .2613 0 .2592 0 .2572 0 .2552 0 .2532 0 .251,3 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 0.0264 0.02s6 0.0249 0.0242 0.0234 0.0228 0.0221 0.02t5 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 0.0727 0.0124 0.0120 0.0117 0.0114 0.0111 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 p lpo 0 .0746 0 .0730 0 .0715 0 .0700 0 .0685 0 .067t 0 .0657 0 .0643 0 .0630 0 .06t7 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 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 .026t 0 .0256 0 .0252 0 .0247 0 .0242 A IA* 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 .420r 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 .047r 7 .t79r 7 .3135 7 .450t 7 .5891 7 .7305 7 .8742 8 .0204 8 .1691 8 .3202 8 .4739 8 .6302 8 .7891 8 .9506 9 .1148 9 .28t7 9 .4513 9 .6237 9 .7990 9 .9771 1 0.1581 1 ,0.3420 1 0.5289 1 0.7188 1 0.9177 1 r.7077 1 1.3068 1 1.5091 1 1..71,47 1 ,L9234 1 2.1354 Appendix C Normql-Shock T obles Normal Shock Table (γ=1.4) TABLE .l C Mr 1.00 r.02 1.04 1.06 1.08 1.10 r.Lz r.r4 L16 1.18 r.20 t.22 t.24 r.26 r.28 1.30 r.32 r.34 t.36 1.38 1.40 1..42 1..44 1.46 t.48 1.50 r.52 r.54 1.56 1.58 1.60 t.62 r.64 t.66 1.68 r.70 t.72 L74 r.76 1.78 1.80 r.82 1.84 1.86 1.88 1.90 N ormal-Shock able( y = 1 .4) T M2 1 .0000 0 .9805 0 .9620 0 .9444 0 .9277 0.9118 0 .8966 0 .8829 0 .8682 0 .8549. 0 .8422 0 .8300 0 .8183 0 .8071 0 .7963 0 .7860 0 .7760 . 0.7664 0 .7572 0 .7483 0 .7397 0 .731.4 0 .7235 0 .7157 0 .7083 0 .7071 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 .62t0 0 .6165 0 .6t21. 0 .6078 0 .6036 0 .5996 0 .5956 p zlpt 1.0000 1..0471 7.0952 7.1442 t.1947 1.2450 1.2968 t.3495 1.,4032 1.4578 1.5133 1.5698 t.6272 1.6855 1.7448 1.8050 1.8661 r.92821 r.9972 2.055! 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.t261 3.2050 3.2848 3.3655 3.4472 3.5298 3.6133 3.6978 3.7832 3.8695 3.9568 4.0450 T zlTl p zlh p ozlpor p ozlpr 1.0000 t.0r32 r.0263 1.0393 t.0522 1.0649 t.0776 1.0903 1.1029 1..1.154 1.1280 1.1405 1.1531 1.t657 r.1783 1.1909 1..2035 t.2t62 1.2290 L2478 1.2547 r.2676 r.2807 t.2938 1.3069 1.3202 r.3336 r.3470 1..3606 r.3742 1.3880 1.4018 1.4158 1..4299 1.4440 1.4583 t.4721 1.4873 1.5019 t.5767 t.53r6 r.5466 r.5617 r.5770 1.5924 r.6079 1 .0000 1 ..0334 r .0671. 1 .1009 1 ..1349 L .L69L r .2034 r .2378 7 .2123 1 .3069 1 3416 r .3764 t .4r12 1 ..4460 1 .4808 t .5r57 1 .5505 1 .5854 t .6202 1 ..6549 1 ..6897 1 .7243 t .7589 r .7934 r .8278 r .862r 1 .8963 1 .9303 t .9643 1 .9981 2 .0317 2 .0653 2 .0986 2 .1.318 2 .',1.649 2 .1977 2 .2304 2 .2629 2 .2952 2 .3273 2 .3592 2 .3909 2 .4224 2 .4537 2 .4848 2 5157 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 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 0.91.66 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 r .8929 1 ..9379 1 ..9844 2 .0325 2 .0819 2 .1328 2 .185r 2 .2388 2 .2937 2 .3500 2 .4075 2 .4663 2 .5263 2 .5875 2 .6500 2 .7t36 2 .7784 2 .8444 2 .91.t5 2 .9798 3 .0492 3 .1198 3 .1915 3 .2643 3 .3382 3 .4133 3 .4894 3 .5667 3 .6450 3 .7244 3 .8050 3 .8866 3 .9693 4 .0531 4 .1.379 4 .2238 4 .3108 4 .3989 4 .4880 4 .5782 4 .6695 4 .7618 4 .8552 4 .9497 5 .0452 5 .1418 A ppendixC T N ormal-Shockables TABLEC .1 ( Continued) M1 1..92 1..94 1..96 1.98 2.00 2.02 2.04 2.06 2.08 2.I0 2.I2 2.14 2.1,6 2.r8 2.20 2,22 ' 2.24 2,26 2.28 2.30 2.32 234 2.36 238 2.40 2.42 2.44 2.46 2.48 2.50 2.52 2.54 2.56 2.58 2.60 2.62 2.64 2.66 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 3.00 3.02 3.04 Mz 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 .532r 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 .s022 0 .5005 0 .4988 0 .4972 4 .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 p zlpt 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 6.1728 6.2215 6.33t2 6.4418 6.5533 6.6658 6.7792 6.8935 7.0088 7.1.250 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.rrr1. 9.2432 9,3162 9.5101 9.6450 9.7808 9.9n5 10.0552 10.1938 10.3333 10.473806152 T 2lTr p zlh p ozlpot r .6236 1 ,.6394 1 .6553 1 .671.3 7 .6875 1 .7038 r .7203 t .7369 t .7536 t .7705 r .7875 1 .8046 r .82I9 1 .8393 1 .8569 1 .8746 1 .8924 1 .9104 1 _.9285 1 _.9468 r .9652 1 .9838 2 .0025 2 .0213 2 .0403 2 .0595 2 .0788 2 .0982 2 .rr78 2 .t375 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 .5n9 2 .5405 2 .5632 2 .586r 2 .609r 2 .6322 2 .6555 2 .6790 2 .7026 2 .7264 2.5463 2.5767 2.6069 2.6369 2.6667 2.6962 2.7255 2.7545 2.7833 2.8t19 2.8402 2.8683 2.8962 2.9238 2.9512 2.9784 3.0053 3.0319 3.0584 3.0845 3.1105 3.1362 3.1617 3.1869 3.2tr9 3.2367 3.2612 3.2855 3.3095 3.3333 3.3569 3.3803 3.4034 3.4263 3.4490 3.47t4 3.4937 3.5157 3.5314 3.5590 3.5803 3.6015 3.6224 3.6431 3.6636 3.6838 3.7039 3.7238 3.7434 3.7629 3.7821 3.8012 3.8200 3.8387 3.8571, 3.8754 3.8935 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 .0rqr 0 .6100 0 .6011 0 .5921 0 .5833 0 .5745 0 .s658 0 .5s72 0 .5486 0 .5401 0 5317 0 .5234 0 .5752 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 .3t72 p ozlpt 5 .2394 5 .3381 5 .4378 5 .5386 5 .6404 5 .7433 5 .8473 5 .9523 6 .0583 6 .1654 6 .2735 6 .3827 6 .4929 6 .6042 6 .7165 6 .8298 6 .9442 7 .0597 7 .1762 7 .2937 7 .4722 7 .531.9 7 .6525 7 .7742 7 .8969 8 .0207 8 .1455 8 .2773 8 .3982 8 .526r 8 .6551 8 .7851 8 .9161 9 .0482 9 .1813 9 .3155 9 .4506 9 .5869 9 .7241 9 .8624 1 0.0017 r 0.r421 1 0.2835 1 0.4259 1 0.5694 1 0.7139 1 0.8594 1 1.0060 7 r.1536 r r.3022 r r.45r9 1 7.6026 1 .r.7544 1 r.9072 1 2.0610 1 2.2158 1 2.3717 .%:L'erE 1 ca;.ra; ' eJaqtunu q ctl4tr u rrerlsdn s norrrBl r o; e lEur u orlcagap.$,og q ll,rr e l8ur o ^",td-{coqs J o u oltrurL-'T,.tuYtrC s aar 6ap'g'a16uo u or13al l a6 f a t @ nrO w v6 oz i ol I 9 I 9" o tD o f e_ J! o? 8'g 9'g te n^ lo v> a -<b CL ID (D lll zE 0e 8',2 gz og z'e gE o'b ^ 9t -o 8-ai @.'14/ sc IJ,nY NOUo y U O.{ S UIIU{WOC zn T U OS IAC Y I Y N OTJY N - 98I I , r U O dS U 8? p apnlcuoc-'z r uYHc u s a a J 6 a pg ' a 1 6 u o o r 1 3 a l l a O ' U' ! o 1oo ,€ I o (D o 5 tO p F _cL 9o |c! o a ,^ id.oT.{ t rTalsssudnoc u od S .LuvHc c Nv ' sgTgl/.l, ' sttol.lvnbg AppendixE P randtl-MeyerFunctions Prandtl-Meyer Function Table (γ=1.4) ( TABLE .1 P randtl-Meyer unctions 7 = 1 .4; E F 1.00 r.02 1.04 1.06 1.08 1.10 t.r2 T.T4 1.16 1.18 r.20 1,.22 t.24 1.26 1.28 1.30 t.32 r.34 r.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 r.52 r.54 r.56 1.58 1.60 r.62 r.64 r.66 1.68 r.70 r.72 t.74 r.76 1..78 1.80 1_.82 1.84 1.86 1.88 1.90 0.0000 0.t257 0.3510 0.6367 0.9680 1.3362 1..7350 2.1.600 2.6073 3.0743 3.5582 4.0572 4.5694 5.0931 5.6272 6.1703 6.72t3 7.2794 7.8435 8.4130 8.9870 9.5650 10.1.464 10.7305 17.3169 11.9052 12.4949 13.0856 13.6770 14.2686 14.8604 15.4518 16.0427 16.6328 17.2220 17.8099 78.3964 18.9814 19.5646 20.1.458 20.7251 2r.302r 21..8768 22.4492 23.0190 23.5867 9 0.0000 78.6351, 7 4.0576 7 0.6300 6 7.8084 6 5.3800 6 3.2345 6 1.3056 5 9.5497 5 7.9362 5 6.4427 5 5.0520 5 3.7507 5 2.5280 5 1..3752 5 0.2849 4 9.2509 48.2682 4 7.332r 4 6.4387 4 5.5847 4 4.7670 43.9830 4 3.2302 42.5066 4 1.8103 4L1395 4 0.4927 3 9.8683 3 9.26s2 38.6822 3 8.1181 3 7.5719 3 7.0427 3 6.5296 3 6.0319 35.5487 3 5.0795 34.6235 34.1802 3 3.7490 3 3.3293 3 2.9207 3 2.5227 3 2.1349 3 r.7569 7.92 1..94 1.96 1.98 2.00 2.02 2.04 2.06 2.08 2.t0 2.r2 2.14 2.16 2.1.8 2.20 2.22 2.24 2.26 2.28 2.30 2.32 2.34 2.36 2.38 2.40 2.42 2.44 2.46 2.48 2.50 2.52 2.54 2.56 2.58 2.60 2.62 2,64 2.66 2.68 2.70 2.72 2.74 2.76 2.78 2.80 2.82 24.1506 24.7123 25.27tL 25.8269 263798 26.929s 27.4762 28.0t97 28.5600 29.0971. 29.6308 30.1613 30.6884 31..2r2r 31.7325 32.2494 32.7629 33.2730 33.7796 34.2828 34.7825 35:2787 35.77t5 36.2607 36.7465 37.2289 37.7077 38.18.31 38.6551 39.1236 39.5886 40.0503 40.5085 40.9633 41.4747 41:8628 42.3074 42.7488 43.1868 43.62t5 44.0529 44.48t0 44.9059 45.3275 45.7459 46.1611 31.3882 3 1.0285 3 0.6774 30.3347 3 0.0000 29.6730 2 9.3535 29.041r 2 8.7357 2 8.4369 28.1446 2 7.8585 2 7.5785 2 7.3043 2 7.0357 2 6.7726 2 6.51.48 2 6.2621. 2 6.0L44 2 5.771.5 25.5332 25.2995 2 5.0702 24.8452 2 4.6243 2 4.4075 2 4.1945 2 3.9854 2 3.7800 2 3.5782 2 3.3799 2 3.1850 2 2.9934 22.8051. 2 2.6199 2 2.4377 2 2.2586 2 2.0824 2 t.9090 2 1..7385 2 r.5706 2 r.4053 2 1..2427 2 1_.0825 20.9248 20.7695 A ppendix E P randtl-MeyerF unctions TABLEE .1 ( Continued) M 2.84 2.86 2.88 2.90 2.92 2.94 2.96 2.98 3.00 3.02 3.04 3.06 3.08 3.10 3.r2 3.1.4 3.t6 3.18 3.20 3.22 3.24 3.26 3.28 3.30 3.32 3.34 3.36 3.38 3.40 3.42 3.44 3.46 3.48 3.50 3.52 3.54 3.56 3.58 3.60 3.62', 3.64 3.66 3.68 3.70 3.72 3.74 3.76 3.78 3.80 3.82 3.84 3.86 3.88 3.90 3.92 v 46.5731 46.9820 47.3877 47.7903 48.1898 48.5863 48.9796 49.3700 49.7573 50.1417 50.5231 50.9016 51.2777 5r.6497 52.0195 52.3864 52.7505 53.1118 53.4703 53.8261. 54.1791 54.5294 54.8770 55.2220 55.5643 55.9040 56.247r 56.5756 56.9075 57.2369 57.5639 57.8883 58.2t02 58.5298 58.8469 59.1.616 59.4739 59.7838 60.0915 60.3968 60.6998 61.0005 61.2990 61.5953 61.8893 62.1812 62.4709 62.7584 63.0438 63.3271 63.6083 63.8874 64.1645 64.4395 64.7125 lL 20.6166 20.4659 2 0.3175 2 0.t7r3 2 0.0272 1 9.8852 1 9.7452 1 9.6072 1 9.4712 1 9.3371 19.2049 1 9.0745 1 8.9459 1 8.8191 1 8.6939 1 8.5705 18.4487 1 8.3285 1 8.2100 18.0929 1 7.9774 1 7.8634 t 7.7508 1 7.6397 1 7.5300 \ 7.4216 r 7.3r47 7 7.2090 1 7.1046 1 7.0016 1 6.8997 1 6.7991 1 6.6997 1 6.6015 1 6.5045 1 6.4086 t 6.3t39 1 6.2202 7 6.t276 1 6.0361 7 5.9456 7 5.8562 1 5.7678 1 5.6804 1 5.5939 1 5.5084 1 5.4239 1 5.3402 1 5.2575 r 5.t757 1 5.0948 r 5.0r47 1 4.9355 1 4.8572 1 4.7796 M 3.94 3.96 3.98 4.00 4.02 4.04 4.06 4.08 4.10 4.r2 4.74 4.76 4.18 4.20 4.22 4.24 4.26 4.28 4.30 4.32 4.34 4.36 4.38 4.40 4.42 4.44 4.46 4.48 4.50 4.52 4.54 4.56 4.58 4.60 4.62 4.64 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 4.92 4.94 4.96 4.98 5.00 v 64.9836 65.2526 65.5797 65.7848 66.0480 66.3093 66.s688 66.8263 67.0820 67.3359 67.5879 67.8381 68.0866 68.3332 685782 68.8213 69.0628 69.3026 69.5406 69.7770 70.0118 70.2449 70.4763 70.7062 70.9344 7L.r6n 7r.3862 77.6097 7t.8377 72.0522 72.2712 72.4887 72.7046 72.9792 73.1322 73.3438 73.5540 73.7628 73.9701. 74.1761 74.3801 74.s839 74.7858 74.9863 75.1855 75.3833 75.5799 75.7752 75.9691 76.1619 76.3533 76.5435 76.7325 76.9202 It 1 4.7029 1 4.6270 1 4.5519 1 4.4775 t 4.4039 t4.33rl t 4.2590 14.1876 1 4.1170 1 4.0470 1 3.9778 13.9092 1 3.84t4 t 3.7741 1 3.7076 13.6417 13.5764 1 3.5118 7 3.4477 t3.3843 7 3.3275 13,2593 7 3.1976 1 3.1366 7 3.0761 1 3.0161 1 2.9567 1 2.8979 1 2.8396 1 2.7818 t 2.7246 1 2.6678 t 2.6rI6 t 2.5559 1 2.5006 1 2.4459 t 239t6 1 2.3378 1 2.2845 7 2.23t6 7 2.1792 t 2.1273 1 2.0758 1 2.0247 r r.9747 7r.9239 r t.8741 1 1.8247 r r.7757 1 1.7272 r r.6790 1 1.6313 1 1.5839 t t.5370 6 47 ...
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This note was uploaded on 09/05/2011 for the course EGN 3353C taught by Professor Lear during the Spring '07 term at University of Florida.

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