Question

What is the density behind the shock in hypersonic flow?

(a) Zero

(b) Infinite

(c) \( \frac {γ + 1}{γ – 1}\)

(d) \( \frac {γ – 1}{γ + 1}\)

The question was asked during an internship interview.

The query is from Newtonian Theory topic in portion Numerical Techniques for Nonlinear Supersonic Flow, Elements of Hypersonic Flow, Couette and Poiseuille Flow of Aerodynamics

Answer 1

The correct choice is (b) Infinite

The explanation: The oblique shock relation is given by:

\( \frac {ρ_2}{ρ_∞} = \frac {(γ + 1)M_∞^2 sin^2 β}{(γ – 1) M_∞^2 sin^2 β + 2}\)

Applying the limit M∞ → 1

\( \frac {ρ_2}{ρ_∞} = \frac {γ + 1}{γ – 1}\)

Applying the limit γ → 1

\( \frac {ρ_2}{ρ_∞}\) → ∞

Thus, the density behind the shock wave in a hypersonic flow is infinitely large.