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GATE 2024 AE – Question 43

Aerodynamics · Compressible flows: isentropic flow, normal and oblique shocks, Prandtl-Meyer flow, nozzles and diffusers · 2 marks · Multiple choice

Shock structures for flow at three different Mach numbers over a given wedge are shown in the figure below. Assuming that only the weak shock solutions are possible for the attached oblique shocks, which one of the following options is TRUE?

Three panels with the same wedge. At $M_1$ an attached oblique shock lies at a moderate angle. At $M_2$ the attached shock lies close to the wedge surface (a small angle). At $M_3$ the shock is detached from the tip and curved (a bow shock).
  1. $M_1 < M_2 < M_3$
  2. $M_1 > M_2 > M_3$
  3. $M_1 < M_3 < M_2$
  4. $M_3 < M_1 < M_2$

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Correct answer: (D) $M_3 < M_1 < M_2$

Explanation

For a fixed wedge, the shock angle decreases as the Mach number rises (weak solution). The detached bow shock occurs when the Mach number is too low for an attached shock, so $M_3$ is the lowest. Of the two attached shocks, the one lying closer to the wedge (the smaller angle) has the higher Mach number, so $M_2 > M_1$. So $M_3 < M_1 < M_2$.