Question

The properties of a flow with subscript * denotes M=1. Which of these is the correct ratio for a flow with gamma= 1.4?

(a) \(\frac {T^*}{T_0}\)=0.528

(b) \(\frac {P^*}{P_0}\)=0.833

(c) \(\frac {\rho ^*}{\rho_0}\)=0.634

(d) Data inadequate

I had been asked this question during an internship interview.

Origin of the question is The Basic Normal Shock Equations topic in section Normal Shock Waves of Aerodynamics

Answer 1

The correct answer is (c) \(\frac {\rho ^*}{\rho_0}\)=0.634

Best explanation: The defined flow properties are related to each other with relations involving only Mach number and gamma. Hence, when these two values are given, the ratios can be calculated. These are important ratios and for M=1 and gamma=1.4 the values are \(\frac {T^*}{T_0}\)=0.833, \(\frac {P^*}{P_0}\)=0.528, \(\frac {\rho ^*}{\rho_0}\)=0.634