An oblique shock is inclined 35° to upstream velocity 517.56 m/s. Flow deflection is 5.75° and downstream temperature is 182.46 K. R = 287 J/(kg K), γ = 1.4, cp = 1005 J/(kg K). Find upstream Mach number to 1 decimal place.
Tangential velocity is unchanged across the shock: $V_2\cos(35^\circ-5.75^\circ)=V_1\cos35^\circ$. Thus V₂ ≈ 486.0 m/s. Energy conservation gives $T_1=T_2-(V_1^2-V_2^2)/(2c_p)\approx166.7$ K. Then $M_1=V_1/\sqrt{\gamma RT_1}\approx2.0$. The shock angle and the downstream flow angle must be distinguished.
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