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GATE 2023 AE – Question 37

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

A supersonic aircraft has an air intake ramp that can be rotated about the leading edge O such that the shock from the leading edge meets the cowl lip as shown in the figure. Select all the correct statement(s) as per oblique shock theory when the flight Mach number M is increased.

source diagram and its labels are reproduced in the attached image.
  1. One can always choose $\theta_{RAMP}$ so $\beta_{SHOCK}$ remains fixed.
  2. At fixed $\theta_{RAMP}$, $\beta_{SHOCK}$ increases.
  3. Above a critical M no ramp setting retains the same $\beta_{SHOCK}$.
  4. $\beta_{SHOCK}<\sin^{-1}(1/M)$

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Show answer and explanation

Correct answer: (A) One can always choose $\theta_{RAMP}$ so $\beta_{SHOCK}$ remains fixed.

Explanation

At fixed shock angle β above the Mach angle, the θ–β–M relation yields a ramp angle for larger M. For fixed ramp deflection the weak-shock angle decreases; a shock cannot lie below the Mach angle.

Official GATE 2023 answer key: https://gate2026.iitg.ac.in/doc/download/Answer_keys2023/AE_ANS_GATE2023.pdf