GATE ME 2024 Set 1 — Question 40
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Fluid Mechanics → Compressible Flow → Normal Shock
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Question
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 and denote the flow conditions just upstream and downstream of the normal shock, respectively, which of the following statement(s) is/are TRUE?
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
Solution
Across a stationary normal shock wave in a steady, adiabatic flow:
1.Static Pressure (): The pressure increases across the shock, so . Statement (A) is TRUE.
2.Density (): The density increases across the shock, so . Statement (B) is TRUE.
3.Mach Number (): The flow is supersonic upstream () and becomes subsonic downstream (). Thus, . Statement (C) is FALSE.
4.Specific Entropy (): A shock wave is an irreversible process, leading to an increase in entropy. Thus, . Statement (D) is TRUE.
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