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hw04_solutions - AA311 Atmospheric Flight Mechanics Autumn...

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AA311 - Atmospheric Flight Mechanics Autumn 2010 University of Washington Homework 4 Solutions Problem 1 We can find pressure at free stream as using Appendix A with h G = 3000 m p = 7.0121 ä 10 4 N ë m 2 pinfty = 7.0121 10 4 ; Because the flow is assumed isentropic, the relationship between freestream pressure and total pressure is found using Eq.4.74 p o = p J 1 + g- 1 2 M 2 N g g- 1 Minfty = 0.5; γ = 1.4; po = pinfty 1 + γ − 1 2 Minfty 2 γ γ− 1 83 178.4 We can apply Eq.4.74 to the point on the wing p o p w = J 1 + g- 1 2 M w 2 N g g- 1 p w = p o J 1 + g- 1 2 M w 2 N g g- 1 where M w = 0.9 Mw = 0.9; pw = po I 1 + γ− 1 2 Mw 2 M γ γ− 1 49 180.1 So we have p w = 49 180.1 N ë m 2 Clear @ pw, Mw, po, γ , Minfty, pinfty D AA311 - Atmospheric Flight Mechanics Christopher Lum Printed by Mathematica for Students
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Problem 2 We can obtain conditions at 25,000 ft from Appendix B r = 1.0663 ä 10 - 3 slug ë ft 3 ρ infty = 1.0663 10 3 ; The problem states that the aircraft is flying with a velocity of 800 ft/s, this is assumed to be the true velocity. So the dynamic pressure experienced by the aircraft is q = Å 1 2 r V true 2 Vtrue = 800; qinfty = 1 2 ρ infty Vtrue 2 341.216 At sea level, the density is r s = 2.3769 ä 10 - 3 slug ë ft 3 . So to experience the same dynamic pressure, the equivalent airspeed is obtained by solving q = Å 1 2 r s V e 2 V e = J 2 q r s N 1 ê 2 ρ s = 2.3769 10 3 ; Ve = 2 qinfty ρ s 1 ê 2 535.827 So we see that V e = 535.8 ft ê s Clear @ Ve, ρ s, qinfty, Vtrue, ρ infty D 2 hw04_solutions.nb Printed by Mathematica for Students
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Problem 3 Part a. Assuming laminar flow, the drag force over one side of the plate is given by D è f , l = C f q S recall: C f = 1.328 Re L = 1.328 Re L q S recall: Re L = r V c m = 1.328 J r V c m N 1 ë 2 q S recall: q = Å 1 2 r V 2 = 1.328 J r V c m N 1 ë 2 I Å 1 2 r V 2 M S = 1.328 J r c m N 1 ë 2 V 1 ë 2 I Å 1 2 r V 2 M S D è f , l = 1.328 2 r S J r c m N 1 ë 2 V 3 ê 2 Multiplying by two to obtain the drag over the entire plate we obtain D f , l = 1.328 r S J r c m N 1 ë 2 V 3 ê 2 So we see that laminar skin friction drag is proportional to V 3 ê 2 Part b.
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