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?
- Anonymous1 decade agoFavorite Answer
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.
- kirchweyLv 71 decade ago
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.
- JohnLv 41 decade ago