MAE305_practice1s

# MAE305_practice1s - M&AE 3050 Solution This exam is for...

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M&AE 3050 Practice Exam 1 Fa 2009 Solution This exam is for your practice only. 1. On a summer day, the temperature in the stratosphere above Edwards Air Force Base in southern California is constant, and equal to T 1 = 236 . 65 K for altitudes in the range 11 , 000 m h 25 , 000 m. A test pilot flying there wants to make some performance measurements of her aircraft at a density altitude h d = 20 , 000 m. (a) What must be the local (ambient) density at the altitude of her test? (b) At what pressure altitude h p should she fly for the test? Note: the distribution of temperature T in the Standard Atmosphere , up to 32,000 meters, is given by 0 h 11 , 000 m: T = 288 . 15 K - ( . 0065 K/m) h 11 , 000 m h 20 , 000 m: T = 216 . 65 K 20 , 000 m h 32 , 000 m: T = 216 . 65 K + ( . 0010 K/m) h Solution If the density altitude is given by h d = 20, 000 m, then from Appendix A in Anderson we have that the density is ρ = 8 . 8909 × 10 - 2 kg/m 3 . The temperature is T 1 = 236.65 K (a) From above ρ = 8 . 8909 × 10 - 2 kg/m 3 (b) From the ideal gas law p = ρRT = (8 . 8909 × 10 - 2 )(287 . 05)(236 . 65) = 6039 . 6 Pa From Appendix A we have p 1 = 6074.4 Pa at h G 1 = 19, 400 m, p 2 = 5979.9 Pa at h G 2 = 19, 500 m. If we perform a linear interpolation between these two points we have p = p 1 + ( p 2 - p 1 ) (

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