# Basic aerodynamics problem. What is Pf/Pi?

The air is moving at Mach 2 and it hits a wedge at an angle of 15 deg. What is the ratio of Pf/Pi after the shockwave and what is the angle of the shock relative to the upstream air?

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• Anonymous

2-D compressible flow...

(Pf-Pi)/Pi = [2k/(k+1)]*(M^2sin^2 (beta) -1)

ex Hughes & Brighton

beta = 45 degrees for the oblique shock

off a 15 degree wedge (although 80 degrees is also possible...because 15 degrees < max angle for M=2 which is about 23 degrees... although not as likely) for M=2. k=cp/cv = 1.4 for air

Thie yields a pressure ratio of 2.17

The shock angle relative to the upstream air is 30 degrees since the upstream velocity vector is parallel to the wedge.

-Fred

p-ratio = 2.196

shock angle = 45.314 deg

See the calculator at the ref. page. The shock angle solution is a real bear, because the (known) wedge angle is defined as a complicated function of shock angle, not vice versa. The few analytical solutions I've found don't agree, and many sources prefer to use converging-approximation techniques to arrive at the value.

• John
Lv 4