hw8 - (b) Use the exact (shock-expansion) theory to nd the...

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MAE135 Homework No. 8 Spring 2010 Date assigned: Tuesday May 25, 2008 Due date: 5 pm Thursday June 3, 2010 PROBLEM 1 (6 points) Α θ=0 θ=? 1 2 2 1 o Α=1.7Α 1 A planar supersonic nozzle with area ratio A/A * = 1 . 7 is connected to a reservoir with p 0 = 150 psia. The exit fow is uniForm and in the direction θ 1 = 0 . Outside the nozzle, the ambient pressure is p a =14.7 psia and the velocity is zero. (a) Characterize the wave phenomenon that occurs at the nozzle exit (expansion or compression?) (b) ±ind the direction oF the slipstream, θ 2 , immediately downstream oF the exit. PROBLEM 2 (12 points) M 1 = 3 p 1 = 1 atm θ 1 = 0 o p a = 3 atm 2 3 4 1 Plane of symmetry ±or the overexpanded jet shown, ²nd the Mach number M , static pressure p , and fow angle θ in regions 2,3, and 4. PROBLEM 3 (12 points) 5 o 5 o 5 o M 1 = 3 1 2 3 4 A supersonic airFoil has equilateral triangular shape with tip angles oF 5 . It is placed at an angle oF attack oF 5 against an airstream with M 1 = 3. (a) Sketch the wave pattern around the airFoil.
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Unformatted text preview: (b) Use the exact (shock-expansion) theory to nd the static pressure ratio p/p 1 in regions 2, 3, and 4. (c) Using linear theory, nd an approximate value For static pressure ratio p/p 1 in regions 2, 3, and 4. TURN PAGE 1 (d) To compute the lift and drag of the airfoil, we Frst calculate the force (per unit span) acting on each airfoil surface (since these are pressure forces, they act normal to the surface). Summing the force components normal to ow direction gives the lift L . Summing the force components parallel to ow direction gives the drag D . The non-dimensional lift and drag coecients are C l = L 1 2 1 U 2 1 c = L 1 2 p 1 M 2 1 c C d = D 1 2 1 U 2 1 c = D 1 2 p 1 M 2 1 c where c is the chord length. Compute C l and C d based on (i) the exact theory and (ii) on the linear theory. 2...
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This note was uploaded on 08/31/2010 for the course ENGRMAE 135 taught by Professor Staff during the Spring '08 term at UC Irvine.

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hw8 - (b) Use the exact (shock-expansion) theory to nd the...

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