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GATE 2022 ME (ME1) – Question 30

Fluid Mechanics · One-dimensional compressible flow, nozzles · 1 mark · Multiple select

The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant thermophysical properties operating under choked condition. The exit plane shown in the figure is located within the nozzle. If the inlet pressure ($P_0$) is increased while keeping the back pressure ($P_{back}$) unchanged, which of the following statements is/are true?

a convergent nozzle from the inlet pressure $P_0$ to an exit plane at the narrowest section, with the back pressure $P_{back}$ outside.
  1. Mass flow rate through the nozzle will remain unchanged.
  2. Mach number at the exit plane of the nozzle will remain unchanged at unity.
  3. Mass flow rate through the nozzle will increase.
  4. Mach number at the exit plane of the nozzle will become more than unity.

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Show answer and explanation

Correct answer: (B) Mach number at the exit plane of the nozzle will remain unchanged at unity.; (C) Mass flow rate through the nozzle will increase.

Explanation

A convergent nozzle that is choked has $M = 1$ at the exit, and it cannot go beyond this (B true, D false). The choked mass flow is proportional to the stagnation pressure, $\dot{m} \propto P_0$, so it increases when $P_0$ is raised (C true, A false).