Question

If the Mach number of the moving shock wave relative to the laboratory Ms = 1.25 then what is the Mach number of the reflected shock wave in a calorically perfect gas?

(a) 1.2331

(b) 1.4821

(c) 1.5671

(d) 1.1102

This question was posed to me in an online interview.

This key question is from Reflected Shock Wave in section Unsteady Wave Motion of Aerodynamics

Answer 1

Correct choice is (a) 1.2331

Easy explanation: Given, Ms = 1.25

The relation between Ms and MR is:

\(\frac {M_R}{M_R ^2 – 1} = \frac {M_s}{M_s ^2 – 1} \sqrt {1 + \frac {2(γ – 1)}{(γ + 1)^2}(M_s^2 – 1)\big (γ + \frac {1}{M_s ^2} \big )}\)

Substituting the values we get

\(\frac {M_R}{M_R ^2 – 1} = \frac {1.25}{1.25^2 – 1}\sqrt {1 + \frac {2(1.4 – 1)}{(1.4 + 1)^2}  (1.25^2 – 1)\big (1.4 + \frac {1}{1.25^2} \big )} \)

\(\frac {M_R}{M_R ^2 – 1} = \frac {1.25}{1.25^2 – 1}\sqrt {1 + \frac {2(1.4 – 1)}{(1.4 + 1)^2}  (1.25^2 – 1)\big (1.4 + \frac {1}{1.25^2} \big )} \)

\(\frac {M_R}{M_R ^2 – 1}\) = 2.20\(\sqrt {1 + \frac {0.8}{5.76}  (0.5625)(2.04)}\) = 2.3689

MR = 2.3689 MR^2 – 2.3689MR

On solving the quadratic equation we get two results:

MR = 1.2331, – 0.81

Negative values of Mach number is not possible, hence MR = 1.2331