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final-sample[1] - MAE 103 FINAL EXAM (Closed Book, Closed...

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Unformatted text preview: MAE 103 FINAL EXAM (Closed Book, Closed Lecture Notes, 3~page notes allowed) Please note: 0 There are 6 problems all together. CHOOSE 5 OUT OF 6. If you solve all of them, I will grade first 5 only. a Show your work and your thought process even if you cannot complete a problem so that I can give you partial credit for your effort. However, scratch out those parts that you do not want me to read. Otherwise, some points may be taken off for wrong statements. Also, you will get no credit if your writing is illegible! 0 You may need the following information: — Reynolds Transport Theorem: d 8 #33327 MW 32 . dA, dt 3’ art/cup +fcsp W n Where W represents the absolute velocity for a fixed control volume or the relative velocity for a moving control volume. 7 The absolute temperature: K = 00 + 273 in Kelvin or 0R = 9F + 460 in Rankine. — 1 horse power (hp) = 550 ft—lb/s. e Attached figure of the Moody chart. — Attached table for isentropic flow of a perfect gas with k=1.4. * Attached table for normal shock relations for a perfect gas with 1921.4. Name: 1 (20) 2 (20) 3 (20) 4 (20) 5 (20) 6 (20) Total: 1. (20pt) The specific gravity of seawater and ice is 1.025 and 0.917, respectively. Compute the “tip of an iceberg,” i.e., the fraction of an iceberg that is visible above the water surface. 2. (4 pt each) Please respond with T for true or F for false and a short sentence -— I mean a short sentence and that’s all I will read 7 for your reasoning. (a) Swimming in seawater is easier than swimming in a freshwater pool. (b) In steady flows, acceleration of a fluid particle, which is the time rate of change of the fluid velocity, is always zero. (c) Surface roughness inside a pipe increases as the pipe surface corrodes over the years. If the flow remains laminar, the pump power required to maintain the same flow rate needs to be increased. (d) Divergence of velocity, V - u, is zero for isentropic compressible flows. (e) For an isentropic compressible flow inside a converging—diverging duct, if you know the area ratio, A/A*, where A* is the area of the throat, you can tell the flow Mach number. 3. (20 pt) Water of density ,0 issues smoothly from a spigot of circular cross—section into the atmosphere, as shown below. At the flange, the velocity is V. The diameter decreases from D at the flange to D/4 at the exit. Ignore losses and the weight of water contained in the spigot. (a) Find the gauge pressure at the flange in terms of p and V. (b) Find the magnitude and direction of the force exerted by the water on the spigot in terms of p, D, and V. Spigot Flange D I 4 4. (20 pt) A pipe is attached to a large water reservoir. The head loss in the pipe is equal to kfl/pg/Zg), where V1; is the velocity in the pipe and k is a given constant. A nozzle is attached to the pipe and water issues from that nozzle into the atmosphere. The top of the reservoir is exposed to the atmosphere. The water level in the reservoir is maintained at a height ft above the nozzle. The cross—sectional area of the pipe is AP, and the ratio of the area of the jet to that of the pipe is r (Aj/Ap = r). Neglect nozzle losses and other losses. (a) Determine an expression for the jet velocity in terms of h, k, r, and 9. Is your result consistent with the “thumb eifect” discussed in the class? (b) Develop an expression for the power of the jet. (0) The area of the pipe, AP, is given, but the jet can be changed by adjusting the nozzle. The ratio r is, therefore, variable. Find 7', which maximizes the power in the get. 5. (20 pt) Water (7:62.11 1b/ft3, p=1.94 slugs /ft3, p, x 2.34 X 10—51b—S/ft2) is circulated from a large tank, through a filter, and back to the tank as shown below. The power added to the water by the pump is 0.36 hp. Determine the flow rate through the fiiter. You can use the attached Moody chart and /or the foilowing Haaiand formula: 1.11 m —1.810g + 1 (1) i x/f \ 200 ft. of G.1—ft-dia. pipe with e/D m 0101 - -~;|JJJlI__l|; Fiiter g E E 6. (20 pt) A blow—down supersonic wind tunnel is supplied with air from a large reservoir as shown below. The Mach number in the test section is M2 2: 2, and the pressure is below atmospheric so that a shock wave is formed just at the exit. The temperature at Point 0 in the reservoir is 30°C and the pressure at Point 3 immediately behind the shock is 14.7 psi. Reservoir Shock Wave Tes t Sec tion Pitot Tube (a) 10033913392: and M3- 00) A Pitot tube is placed in the exit jet as shown. What is the pressure p4? Why is p4 < 100'? (c) Find T3 and V3. E .53 m2 E E E . m m w scum w m q scam m m w Amocm m m w rosm w w v Amocm . Eoooomiilf . , . h . m L m . . g H m 382 _ . . . , ., "mom: 8.0 880.0, 88.9 88.0,. . . N H MS.“ 38.0 >3; t n 88.0 . 5553 wooed . M H006 “No.0 mood “.39 «8.2 mod 80.? 80.3 8.0 .m .. 3o Bod N mo 0 mod 28 . moo 5.0 . mad 80 mod 26: “5.393 .3655 mod Comprssible Flw Tables Table 13.1 Isentropic Flow M3 . .. .. .. .... ‘ . . . ._ _. . . .. .. Mil pip" pip“ TIT" 714* Of a Perfect Gas, 0.00 1.0000 1.0000 1.0000 00 1.75 0.1878 0.3029 0.6202 1.3365 k z 0.05 0.9983 0.9933 0.9995 11.5914 1.30 0.1740 0.2868 0.6063 1.4390 0.10 0.9930 0.9950 0.9930 5.8218 1.85 0.1612 0.2715 0.5936 1.4952 0.15 0.9844 0.9388 0.9955 3.9103 1.90 0.1492 0.2570 0.5807 1.5553 0.20 0.9725 0.9303 0.9921 2.9635 1.95 0.1381 0.2432 0.5680 1.6193 0.25 0.9575 0.9694 0.9877 2.4027 2.00 0.1273 0.2300 0.5556 1.6875 0.30 0.9395 0.9564 0.9823 2.0351 2.05 0.1132 0.2176 0.5433 1.7600 0.35 0.9188 0.9413 0.9761 1.7730 2.10 0.1094 0.2058 0.5313 1.3369 0.40 0.3956 0.9243 0.9690 1.5901 2.15 0.1011 0.1946 0.5196 1.9185 0.45 0.8703 0.9055 0.9611 1.4437 2.20 0.0935 0.1841 0.5081 2.0050 0.50 0.3430 0.8352 0.9524 1.3398 2.25 0.0865 0.1740 0.4969 2.0964 0.55 0.3142 0.8634 0.9430 1.2549 2.30 0.0800 0.1646 0.4859 2.1931 0.60 0.7840 0.8405 0.9328 1.1832 2.35 0.0740 0.1556 0.4752 2.2953 0.65 0.7528 0.3164 0.9221 1.1356 2.40 0.0684 0.1472 0.4647 2.4031 0.70 0.7209 0.7916 0.9107 1.0944 2.45 0.0633 0.1392 0.4544 2.5168 0.75 0.6336 0.7660 0.8989 1.0624 2.50 0.0585 0.1317 0.4444 2.6367 0.30 0.6560 0.7400 0.8865 1.0382 2.55 0.0542 0.1246 0.4347 2.7630 0.35 0.6235 0.7136 0.8737 1.0207 2.60 0.0501 0.1179 0.4252 2.8960 0.90 0.5913 0.6870 0.8606 1.0039 2.65 0.0464 0.1115 0.4159 3.0359 0.95 0.5595 0.6604 0.8471 1.0021 2.70 0.0430 0.1056 0.4068 3.1830 1.00 0.5233 0.6339 0.8333 1.0000 2.75 0.0398 0.0999 0.3980 3.3377 1.05 0.4979 0.6077 0.8193 1.0020 2.80 0.0368 0.0946 0.3394 3.5001 1.10 0.4634 0.5817 0.8052 1.0079 2.35 0.0341 0.0896 0.3810 3.6707 1.15 0.4398 0.5562 0.7908 1.0175 2.90 0.0317 0.0849 0.3729 3.8493 1.20 0.4124 0.5311 0.7764 1.0304 2.95 0.0293 0.0804 0.3649 4.0376 1.25 0.3861 0.5067 0.7619 1.0468 3.00 0.0272 0.0762 0.3571 4.2346 1.30 0.3609 0.4829 0.7474 1.0663 3.05 0.0253 0.0723 0.3496 4.4410 1.35 0.3370 0.4598 0.7329 1.0890 3.10 0.0234 0.0685 0.3422 4.6573 1.40 0.3142 0.4374 0.7184 1.1149 3.15 0.0218 0.0650 0.3351 4.8833 1.45 0.2927 0.4158 0.7040 1.1440 3.20 0.0202 0.0617 0.3281 5.1210 1.50 0.2724 0.3950 0.6397 1.1762 3.25 0.0188 0.0585 0.3213 5.3691 1.55 0.2533 0.3750 0.6754 1.2116 3.30 0.0175 0.0555 0.3147 5.6286 1.60 0.2353 0.3557 0.6614 1.2502 3.35 0.0163 0.0527 0.3082 5.9000 1.65 0.2184 0.3373 0.6475 1.2922 3.40 0.0151 0.0501 0.3019 6.1337 1.70 0.2026 0.3197 0.6337 1.3376 3.45 0.0141 0.0476 0.2953 6.4301 819 830 Appendix B ?§:;:lfé:d) Mn pip“ pI'Pu 771']; .4/A* Isentropic Now of 3.45 0.0141 0.0476 0.2958 6.4801 3 Perfect Gas, 3.50 0.0131 0.0452 0.2899 6.7896 k = 1.4 3.55 0.0122 0.0430 0.2341 7.1128 3.60 0.0114 0.0409 0.2784 7.4501 3.65 0.0106 0.0389 0.2729 7.8020 3.70 0.0099 0.0370 0.2675 8.1691 Table 13.2 Normal Shock Relations for a Perfect Gas, k = 1.4 1.0000 1.1196 1.2450 1.3763 1.5133 1.6563 1.8050 1.9596 2.1200 2.2863 2.4583 2.6363 2.8200 3.0096 3.2050 3.4063 3.6133 3.8263 4.0450 4.2696 4.5000 4.7363 4.9783 5.2263 5.4800 5.7396 6.0050 6.2763 6.5533 6.8363 7.1250 7.4196 7.7200 8.0262 8.3383 8.6562 8.9800 9.3096 9.6450 9.9862 10.3333 Ma 19/74 3.75 3.80 3.85 3.90 3.95 4.00 1.0000 1.0840 1.1691 1.2550 1.3416 1.4286 1.5157 1.6028 1.6897 1.7761 1.8621 1.9473 2.0317 2.1152 2.1977 2.2791 2.3592 2.4381 2.5157 2.5919 2.6667 2.7400 2.8119 2.8823 2.9512 3.0186 3.0845 3.1490 3.2119 3.2733 3.3333 3.3919 3.4490 3.5047 3.5590 3.6119 3.6636 3.7139 3.7629 3.8106 3.8571 0.0092 0.0086 0.0081 0.0075 0.0070 0.0066 1.0000 0.0352 0.0335 0.0320 0.0304 0.0290 0.0277 1.0328 1.0649 1.0966 1.1280 1.1594 1.1909 1.2226 1.2547 1.2872 1.3202 1.3538 1.3880 1.4228 1.4583 1.4946 1.5316 1.5693 1.6079 1.6473 1.6875 1.7285 1.7705 1.8132 1.8569 1.9014 1.9468 1.9931 2.0403 2.0885 2.1375 2.1875 2.2383 2.2902 2.3429 2.3966 2.4512 2.5067 2.5632 2.6206 2.6790 PIP" 0.2623 0.2572 0.2522 0.2474 0.2427 0.23 81 1.0000 0.9999 0.9989 0.9967 0.9928 0.9871 0.9794 0.9697 0.9582 0.9448 0.9298 0.9132 0.8952 0.8760 0.8557 0.8346 0.8127 0.7902 0.7674 0.7442 0.7209 0.6975 0.6742 0.6511 0.6281 0.6055 0.5833 0.5615 0.5401 0.5193 0.4990 0.4793 0.4601 0.4416 0.4236 0.4062 0.3895 0.3733 0.3577 0.3428 0.3283 772'" AJ'.4.* 8.5517 8.9506 9.3661 9.7990 10.2496 10.7188 1.0000 1.0001 1.0011 1.0033 1.0073 1.0131 1.0211 1.0312 1.0436 1.0584 1.0755 1.0951 1.1171 1.1416 1.1686 1.1982 1.2305 1.2655 1.3032 1.3437 1.3872 1.4337 1.4832 1.5360 1.5920 1.6514 1.7144 1.7810 1.8514 1.9256 2.0039 2.0865 2.1733 2.2647 2.3608 2.4617 2.5676 2.6788 2.7954 2.9176 3.0456 E i 2 g E : € : Compressible Flow Tables 32}. Table B.2 (Concluded) Normal .4314"; Shock Relations for a Perfect Gas, ma“ MR"; ‘0 2 [P1 V“sz : 92,91 , " pulp"! k = 3.00 0.4752 10.3333 3.8571 . 0.3283 3.0456 3.05 0.4723 10.6363 3.9025 . 0.3145 3.1796 3.10 0.4695 11.0450 3.9466 . 0.3012 3.3199 1 3.15 0.4669 11.4096 3.9896 . 0.2835 3.4667 3.20 0.4643 11.7800 4.0315 . 0.2762 3.6202 3.25 0.4619 12.1563 I 4.0723 . 0.2645 3.7306 3.30 0.4596 12.5383 4.1120 . 0.2533 3.9483 3.35 0.4573 12.9263 4.1507 . 0.2425 4.1234 3.40 0.4552 13.3200 4.1884 . 0.2322 4.3062 3.45 0.4531 13.7196 4.2251 . 0.2224 4.4969 ‘ 3.50 0.4512 14.1250 4.2609 . 0.2129 4.6960 3.55 0.4492 14.5363 4.2957 . 0.2039 4.9036 3.60 0.4474 14.9533 4.3296 . 0.1953 5.1200 3.65 0.4456 15.3763 4.3627 . 0.1871 5.3456 3.70 0.4439 15.8050 4.3949 . 0.1792 5.5306 3.75 0.4423 16.2396 4.4262 . 0.1717 5.3253 3.80 0.4407 16.6300 4.4563 . 0.1645 6.0301 3.35 0.4392 17.1263 4.4866 . 0.1576 6.3454 3.90 0.4377 17.5783 4.5156 . 0.1510 6.6213 3.95 0.4363 18.0363 4.5439 . 0.1443 6.9034 4.00 0.4350 18.5000 4.5714 . 0.1338 7.2069 4.05 0.4336 13.9696 4.5983 . 0.1330 7.5172 4.10 0.4324 19.4450 4.6245 . 0.1276 7.8397 4.15 0.4311 19.9263 4.6500 . 0.1223 3.1747 4.20 0.4299 20.4133 4.6749 . 0.1173 3.5227 4.25 0.4233 20.9063 4.6992 . 0.1126 3.8840 4.30 0.4277 21.4050 4.7229 . 0.1080 9.2591 4.35 0.4266 21.9096 4.7460 . 0.1036 9.6484 4.40 0.4255 22.4200 4.7685 . 0.0995 10.0522 4.45 0.4245 22.9362 4.7904 . 0.0955 10.4711 3 4.50 0.4236 23 .4533 4.3119 . 0.0917 10.9054 4.55 0.4226 23.9862 4.8323 . 0.0381 11.3556 4.60 0.4217 24.5200 4.8532 . 0.0346 11.3222 4.65 0.4203 25.0596 4.8731 . 0.0313 12.3057 4.70 0.4199 25.6050 4.3926 . 0.0781 12.8065 '- 4.75 0.4191 26.1562 4.9116 . 0.0750 13.3251 ; 4.80 0.4133 26.7133 4.9301 . 0.0721 13.3620 4.35 0.4175 27.2762 4.9432 . 0.0694 14.41771 4.90 0.4167 27.8450 4.9659 . 0.0667 14.9928 4.95 0.4160 23.4196 4.9831 . 0.0642 15.5873 5.00 0.4152 29.0000 5.0000 . 0.0617 16.2032 ...
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This test prep was uploaded on 04/03/2008 for the course MAE 103 taught by Professor Kim during the Winter '08 term at UCLA.

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final-sample[1] - MAE 103 FINAL EXAM (Closed Book, Closed...

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