GATE 2023 AE – Question 44

Aerodynamics · Compressible flows: isentropic flow, normal and oblique shocks, Prandtl-Meyer flow, nozzles and diffusers · 2 marks · Multiple select

Consider a one-dimensional inviscid supersonic flow in a diverging duct with heat addition (Qin) as shown. Which of the following statement(s) is/are always TRUE?

source diagram and its labels are reproduced in the attached image.

$M_2>M_1$
$P_{01}>P_{02}$
$P_2>P_1$
$T_{01}<T_{02}$

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Correct answer: (B) $P_{01}>P_{02}$; (D) $T_{01}<T_{02}$

Explanation

In the duct the supersonic flow is inviscid, one-dimensional, with **heat addition** ($Q_{in}>0$) and an increasing area.

**B. $P_{01}>P_{02}$.** True. Heat addition is an irreversible process (Rayleigh flow) that increases entropy and so **reduces the stagnation pressure**. ✓
**D. $T_{01}<T_{02}$.** True. Heat added to the flow raises the stagnation temperature. ✓
**A. $M_2>M_1$.** Not always. In a supersonic stream, heating tends to **lower** the Mach number toward 1, while area increase tends to raise it. The result depends on the relative sizes of the two effects. ✗
**C. $P_2>P_1$.** Not always. In supersonic flow area increase lowers the static pressure, but heat addition raises it, so the result can go either way. ✗

Answer **B and D**.