The GATE Grind

GATE 2024 AE – Question 22

Aerodynamics · Compressible flows: isentropic flow, normal and oblique shocks, Prandtl-Meyer flow, nozzles and diffusers · 1 mark · Multiple choice

On Day 1, an aircraft flies with a speed of $V_1$ m/s at an altitude where the temperature is $T_1$ K. On Day 2, the same aircraft flies with a speed of $\sqrt{1.2}\,V_1$ m/s at an altitude where the temperature is $1.2\,T_1$ K. How does the Mach number $M_2$ on Day 2 compare with the Mach number $M_1$ on Day 1?

Assume ideal gas behavior for air. Also assume the ratio of specific heats and molecular weight of air to be the same on both the days.

  1. $M_2 = 0.6M_1$
  2. $M_2 = M_1$
  3. $M_2 = \frac{1}{\sqrt{1.2}}M_1$
  4. $M_2 = \sqrt{1.2}\,M_1$

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Show answer and explanation

Correct answer: (B) $M_2 = M_1$

Explanation

The speed of sound is $a = \sqrt{\gamma R T}$. On Day 2 it is $\sqrt{1.2}\,a_1$, so $M_2 = \frac{\sqrt{1.2}V_1}{\sqrt{1.2}a_1} = M_1$.