Question

For a given Prandtl-Meyer expansion, the upstream Mach number is 3.8 and the pressure ratio across the wave is p2/p1 = 0.5. Calculate the turning angle, θ, in degrees (°) relative to the free-stream direction. 

          For a given Prandtl-Meyer expansion, the upstream Mach number is 3.8 and the pressure ratio across the wave is p2/p1 = 0.5. Calculate the turning angle, θ, in degrees (°) relative to the free-stream direction.

Added by Clayton S.

University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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For a given Prandtl-Meyer expansion, the upstream Mach number is 3.8 and the pressure ratio across the wave is p2/p1 = 0.5. Calculate the turning angle, θ, in degrees (°) relative to the free-stream direction.
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Transcript

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00:01 In this question, solution here is m1 is equals to 3, p2 divided by p1 is equals to 0 .4.
00:09 Now from table, we get here m1 is equals to 3.
00:14 So here p0 divided by p1 is equals to 36 .73.
00:21 Now since p02 is equals to p0, then p02 divided by p2 is equals to p01 divided by p2 multiply by p1 divided by p1 which is equals to p01 divided by p1 multiply by p1 divided by p2.
00:53 So here we get p02 divided by p2 is equals to 36 .73 multiply by 1 divided by 0 .4 which is equals to 91 .83.
01:13 Now again from table, a .1 for p02 divided by p2 is equals to 91 .83.
01:28 Here m2 is equals to 3 .63...
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