GATE 2022 AE – Question 44
A convergent nozzle fed from a constant pressure, constant temperature reservoir, is discharging air to atmosphere at 1 bar (absolute) with choked flow at the exit (marked as Q). Flow through the nozzle can be assumed to be isentropic. If the exit area of the nozzle is increased while all the reservoir parameters and ambient conditions remain the same, then at steady state
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Correct answer: (A) the nozzle will remain choked; (C) the Mach number at section P will increase
Explanation
**Choked flow in a convergent nozzle.** The exit is choked ($M=1$) as long as the reservoir pressure is high enough compared with the back pressure (here the ratio of the reservoir pressure to 1 bar exceeds about 1.893 for air). The reservoir conditions and the ambient pressure do not change, so the condition for choking is still satisfied.
- **A. The nozzle remains choked.** True. Changing the exit area does not change the pressure ratio. ✓
- **B. The nozzle becomes un-choked.** False.
- **C. The Mach number at section P increases.** With choking, the mass flow rate is $\dot m\propto A_{exit}$. A larger exit area passes more mass flow, so at the upstream section P (area fixed) the flow must be faster. In terms of the area ratio $A_P/A^*$: the throat area $A^*=A_{exit}$ increased, so $A_P/A^*$ decreases, and the subsonic Mach number at P corresponding to this smaller ratio is higher. ✓
- **D. The Mach number at P decreases.** False.
Answer **A and C**.