Question

If the wave velocity is 900 m/s and the density ratio across the shock wave is 0.6, then what is the value of velocity of induced mass motion behind the wave?

(a) 400 m/s

(b) 360 m/s

(c) 180 m/s

(d) 980 m/s

This question was posed to me in a national level competition.

I want to ask this question from Moving Normal Shock Waves topic in division Unsteady Wave Motion of Aerodynamics

Answer 1

Right choice is (b) 360 m/s

The explanation is: Given, W = 900 \( \frac {m}{s}\), \( \frac {\rho _2}{\rho _1}\) = 0.6

For a moving shock wave that propagates into a stagnant gas, it induces a mas motion of velocity up.

This velocity is given by the relation:

up = W\(\big (\)1 – \( \frac {\rho _2}{\rho _1} \big ) \)

Substituting the values:

up = 900(1 – 0.6) = 360 m/s