Question

For a flow with Mach number 4, P1 = 2.65 × 10^4 Pa what is the pressure behind the oblique shock wave having shock angle as 30 degrees?

(a) 8.525 × 10^4 Pa

(b) 11.925 × 10^4 Pa

(c) 4.502 × 10^4 Pa

(d) 15.278 × 10^4 Pa

The question was posed to me in an interview for job.

My doubt stems from Mach Number Independence in chapter Transonic and Hypersonic Flows of Aerodynamics

Answer 1

The correct option is (b) 11.925 × 10^4 Pa

Easy explanation: Given, P1 = 2.65 × 10^4 Pa, M1 = 4, β = 30°

The normal component of the Mach number upstream of the shockwave is given by:

Mn1 = M1sinβ = 4sin⁡(30) = 2

Using the normal shock table, for Mn1 = 2 we get the relation between the pressure upstream and downstream

\(\frac {P_2}{P_1}\) = 4.5

Since P1 = 2.65 × 10^4, we get P2 = 4.5 × 2.65 × 10^4 = 11.925 × 10^4 Pa.