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Unformatted text preview: M&AE 3050 Practice Exam 2 Fa 2009 This is for practice only. You do NOT need to submit. 1. We wish to consider the effect of altitude on the difference between true airspeed and calibrated airspeed, making the following comparisons. (a) Determine the i. true airspeed; the ii. equivalent airspeed; and the iii. calibrated airspeed for flight at an altitude of h = 12 , 000 m in the standard atmosphere when the flight Mach number is M ∞ = 0 . 80. (b) Repeat the calculation of true, equivalent, and calibrated airspeed for flight at the same Mach number, but at standard sea level conditions. Solution (a) At a height of h = 12 , 000 m in standard atmosphere, the density is ρ = 0 . 31194 kg/m 3 , the pressure is P = 1 . 9399 × 10 4 Pa and the temperature is T = 216 . 66 K. At standard sea level, air density is ρ s = 1 . 225 kg/m 3 , pressure is P s = 101 , 325 Pa and temperature is T s = 288 . 16 K. For flight at M ∞ = 0 . 8, i. The true airspeed can be found by relating the speed of sound to the Mach number V t = M ∞ a = M ∞ radicalbig γRT V t = M ∞ radicalbig (1 . 4)(287)(216 . 66) = 236 . 04 m/s ii. We calculate the equivalent airspeed as follows V e = V t radicalbigg ρ ρ s V e = (236 . 04) radicalBigg (0 . 31194) (1 . 225) = 119 . 11 m/s iii. The calibrated airspeed is given by V 2 cal = 2 a 2 s γ − 1 bracketleftBigg parenleftbigg P − P P s + 1 parenrightbigg γ 1 γ − 1 bracketrightBigg Where a s is the speed of sound at standard sea level a s = radicalbig γRT s = radicalbig (1 . 4)(287)(288 . 16) = 340 . 27 m/s To find the pressure drop P − P we employ the isentropic relation for pressure P P = bracketleftbigg 1 + parenleftbigg γ − 1 2 parenrightbigg M 2 bracketrightbigg γ γ 1 P P = bracketleftbigg 1 + parenleftbigg 1 . 4 − 1 2 parenrightbigg (0 . 8) 2 bracketrightbigg 1 . 4 1 . 4 1 = 1 . 5243 P P − 1 = 0 . 5243 P − P = 0 . 5243 P = 0 . 5243(1 . 9399 × 10 4 ) = 10 , 172 Pa We then calculate the calibrated airspeed V 2 cal = 2(340 . 27) 2 1 . 4 − 1 bracketleftBigg parenleftbigg (10172) (101 , 325) + 1 parenrightbigg 1 . 4 1 1 . 4 − 1 bracketrightBigg V cal = 126 . 66 m/s (b) Repeating the approach from 1a using standard sea level conditions we obtain i. V t = 272 . 21 m/s ii. V e = 272 . 21 m/s iii. V cal = 272 . 21 m/s 2. The North American Mustang P51 was one of the first aircraft designed to incorporate a “laminar flow” wing. For the purpose of estimating skinfriction drag on this aircraft, we will approximate the wing as a flat plate having a rectangular planform of span b = 37 ft and mean chord ¯ c = 6 . 3 ft. We wish to estimate the skin friction drag on the wing at a speed of V = 440 mph at h = 25 , 000 ft in the standard atmosphere for several different scenarios, as described below....
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 Fall '08
 CAUGHEY
 Fluid Dynamics, Mach number, test section, skin friction drag, standard sea level, γ γ

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