Question

Problem 2 (20 points) Consider a subsonic compressible flow in cartesian coordinates (x and y in meters), with velocity potential: 70 -211-My °(x, y) = Vox+ sin 27 x VI - M For an altitude of 10 km and velocity of 240 m/s, Calculate M, P, and T for the location (0.10 m, 0.15 m).

Answer 1

0-21 Solution : 21 (70) 2K 51-mily) cos zax Voot ſi-M2 do - 25 JT-Moby :( 20 VI-me le 1-M2 V-May. sincha = -140 Te 70 dy Sinzax 21 V NOW, VORT For h = 10 km - loooom standard atmosphen I= -50°C: 223 K P. 26045 kPa 2001.) (2812 (223) a = 299.33 m/s Mos 240 299-33 = 0.801 Thus at (0.100.15) 25 (70) ezt fr-to-007) Tois eos above 2 40+ Us 577.32 mts

-2x ti-(0.80152 10.15) Sin [27(0.1) V:-140 e 146.86 m/s Now, v 14² + v2 577.32 + 146.862 595.70 m/8 Now, For Moo o. 801, Table A 1 To 1.128 Too To = 1.128 Too T11287223) = 252 K :.90 = V TRT. 1.4 (287)(252) 318 m 9o + (v2) 2 2 1.4-1 2 a? = (318) + ($95.70) 2 a 172044.90 m/s - a 414.78 m/s. 595.70 414.78 11:43 Ans a

Also, For M = 0.801 , Po Poo 1.524, TE TA = 1.122 For, M= 1.43 Po P. = 3.32, I To Т. =1.40 :-P Chalet - (1524) (26.43) 3.32 P I 2013 Кра Ans & T: G To Too = + 140 (7.128 128)(223) T 179:67 K Ans