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solhw3 - MAE135 SOLUTIONS TO HW 3 Spring 2010 PROBLEM 1(5...

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Unformatted text preview: MAE135 SOLUTIONS TO HW 3 Spring 2010 PROBLEM 1 (5 points) (a) Given M = 4, and that the flow is isentropic, the area-Mach number relation (Table A.1) gives A/A * =10.72. (b) We need to figure out the test section static pressure p and temperature T . We are given M , u , and ρ . The first two are related by u = M radicalbig γRT → T = u 2 M 2 γR = 224 ◦ K Using the equation of state, p = ρRT = 6 , 429 Pa For M = 4, Table A.1 gives the total-to-static pressure ratio p /p = 151 . 8. The reservoir pressure is therefore p = 976 , 148 Pa = 9.634 atm. (c) For M = 4, Table A.1 gives the total-to-static temperature ratio T /T = 4 . 2. The reservoir temperature is therefore T = 940 . 8 ◦ K. PROBLEM 2 (5 points) We note immediately that it is impossible for flow in region 1 to be supersonic, since it doesn’t pass through a sonic throat. Therefore, only the subsonic solution applies there. Given that M 2 > 1, them we must have M 3 > 1 because there is no sonic throat between stations 2 and 3. So flow in station 3 must be supersonic. Using the isentropic tables, we obtain: Region 1: subsonic A 1 A * = 4 . → M 1 = 0 . 14 → p 1 = 19 . 72 atm ,T 1 = 298 . 8 K Region 2: supersonic A 2 A * = 4...
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solhw3 - MAE135 SOLUTIONS TO HW 3 Spring 2010 PROBLEM 1(5...

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