Question

What is the temperature ratio across a moving shock wave in ambient air if the pressure ratio is 8.5?

(a) 1.43

(b) 2.37

(c) 4.21

(d) 3.82

I had been asked this question in a job interview.

Question is from Moving Normal Shock Waves in chapter Unsteady Wave Motion of Aerodynamics

Answer 1

The correct answer is (b) 2.37

The explanation: Given, \(\frac {p_2}{p_1}\) = 8.5, γ = 1.4 (ambient air)

The temperature ratio across a moving shock wave is given by:

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

Substituting the values, we get:

\( \frac {T_2}{T_1}\) = 8.5\( \Bigg ( \frac {\frac {1.4 + 1}{1.4 – 1} + 8.5}{1 + \frac {1.4 + 1}{1.4 – 1} \times 8.5} \Bigg )\) = 8.5\( \Bigg ( \frac {\frac {2.4}{0.4} + 8.5}{1 + \frac {2.4}{0.4} \times 8.5} \Bigg ) \)

\( \frac {T_2}{T_1}\) = 8.5\(\big ( \frac {14.5}{52} \big ) \) = 2.37