Question

What is the relation between mach number and pressure ratio?

(a) \(\frac{p1}{p2}=\Big\{1+\frac{\gamma-1}{2}(M)^2\Big\}^\frac{\gamma}{\gamma-1}\)

(b) \(\frac{p2}{p1}=\Big\{1+\frac{\gamma-1}{2}(M)^2\Big\}^\frac{\gamma}{\gamma-1}\)

(c) \(\frac{p1}{p2}=\Big\{1+\frac{\gamma+1}{2}(M)^2\Big\}^\frac{\gamma}{\gamma-1}\)

(d) \(\frac{p1}{p2}=\Big\{1-\frac{\gamma+1}{2}(M)^2\Big\}^\frac{\gamma}{\gamma-1}\)

I got this question during an interview for a job.

Question is taken from Measurement of Mach Number topic in section Atmosphere and Air Data Measurement of Aircraft Performance

Answer 1

Right choice is (a) \(\frac{p1}{p2}=\Big\{1+\frac{\gamma-1}{2}(M)^2\Big\}^\frac{\gamma}{\gamma-1}\)

Easy explanation: The relation between mach number and pressure is \(\frac{p1}{p2}=\Big\{1+\frac{\gamma-1}{2}(M)^2\Big\}^\frac{\gamma}{\gamma-1}\) where p1, p2 are pressures at two points, M=mach number and γ is the ratio of specific heat at constant pressure to that of specific heat at constant volume.