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# hw8 - (b Use the exact(shock-expansion theory to ²nd 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 flow 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) Find 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 For the overexpanded jet shown, find the Mach number M , static pressure p , and flow 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 ²nd the static pressure ratio p/p 1 in regions 2, 3, and 4. (c) Using linear theory, ²nd 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 coe²cients are C l = L 1 2 ρ 1 U 2 1 c = L 1 2 γp 1 M 2 1 c C d = D 1 2 ρ 1 U 2 1 c = D 1 2 γp 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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hw8 - (b Use the exact(shock-expansion theory to ²nd the...

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