GATE ME 2023 Set 1 — Question 20
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Fluid Mechanics → Compressible Flow → Isentropic Flow & Stagnation
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Question
Consider an isentropic flow of air (ratio of specific heats = ) through a duct as shown in the figure. The variations in the flow across the cross-section are negligible. The flow conditions at Location 1 are given as follows: , , The duct cross-sectional area at Location 2 is given by , where denotes the duct cross-sectional area at Location 1. Which one of the given statements about the velocity and pressure at Location 2 is TRUE?
Correct answer
(C) u₂ u₁, P₂ < P₁
Solution
First, determine the Mach number at Location 1. The speed of sound is .
The Mach number . Since , the flow is supersonic.
For supersonic flow in a diverging duct (), the area-velocity relation implies that , so .
From the isentropic relation or Bernoulli's equation for compressible flow, an increase in velocity leads to a decrease in pressure, so .
The Mach number . Since , the flow is supersonic.
For supersonic flow in a diverging duct (), the area-velocity relation implies that , so .
From the isentropic relation or Bernoulli's equation for compressible flow, an increase in velocity leads to a decrease in pressure, so .
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