Question

Which of these is the governing parameters for change across shock wave when it is moving?

(a) Mach number

(b) Density

(c) Pressure ratio

(d) Velocity ratio

This question was addressed to me in semester exam.

My enquiry is from Moving Normal Shock Waves topic in chapter Unsteady Wave Motion of Aerodynamics

Answer 1

Correct choice is (c) Pressure ratio

The best I can explain: In a stationary wave, changes across the shock wave is governed by the Mach number. But, in a moving shock wave it is dependent majorly on the pressure ratio as seen in the formula below which shows the equation for density and pressure ratio across a moving shock wave.

\( \frac {T_2}{T_1} = \frac {p_2}{p_1} \Bigg ( \frac {\frac {γ + 1}{γ – 1} + \frac {p_2}{p_1}}{1 + \frac {γ + 1}{γ – 1} \frac {p_2}{p_1}} \Bigg )\)

\( \frac {\rho _2}{\rho _1} = \frac {1 + \frac {γ + 1}{γ – 1} \frac {p_2}{p_1}}{\frac {γ + 1}{γ – 1} + \frac {p_2}{p_1}}\)