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GATE 2024 ME – Question 40

Fluid Mechanics · One-dimensional compressible flow, nozzles · 2 marks · Multiple select

Steady, compressible flow of air takes place through an adiabatic converging-diverging nozzle, as shown in the figure. For a particular value of pressure difference across the nozzle, a stationary normal shock wave forms in the diverging section of the nozzle. If $E$ and $F$ denote the flow conditions just upstream and downstream of the normal shock, respectively, which of the following statement(s) is/are TRUE?

A converging-diverging nozzle with the flow from left to right and a vertical normal shock in the diverging part. E is just upstream of the shock and F is just downstream.
  1. Static pressure at $E$ is lower than the static pressure at $F$
  2. Density at $E$ is lower than the density at $F$
  3. Mach number at $E$ is lower than the Mach number at $F$
  4. Specific entropy at $E$ is lower than the specific entropy at $F$

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Show answer and explanation

Correct answer: (A) Static pressure at $E$ is lower than the static pressure at $F$; (B) Density at $E$ is lower than the density at $F$; (D) Specific entropy at $E$ is lower than the specific entropy at $F$

Explanation

The flow is supersonic upstream of a normal shock and subsonic downstream of it. Across the shock the static pressure, the density, the temperature and the specific entropy all increase, and the Mach number falls. So the pressure at E is lower than at F (A), the density at E is lower (B) and the entropy at E is lower (D), which is the second law at work. The Mach number at E is higher than at F, so C is false.