The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant thermophysical properties operating under choked condition. The exit plane shown in the figure is located within the nozzle. If the inlet pressure (P0) is increased while keeping the back pressure (Pback) unchanged, which of the following statements is/are true?
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In choked flow conditions in a convergent nozzle, the Mach number at the exit remains at unity regardless of changes in the inlet pressure, and the mass flow rate increases when the inlet pressure increases.
Mass flow rate through the nozzle will remain unchanged.
Mach number at the exit plane of the nozzle will remain unchanged at unity.
Mass flow rate through the nozzle will increase.
Mach number at the exit plane of the nozzle will become more than unity.
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The Correct Option isB, C
Solution and Explanation
- (A) Mass flow rate through the nozzle will remain unchanged: This statement is FALSE. When the inlet pressure (P0) increases, it provides a higher pressure differential for the flow, which leads to an increase in mass flow rate. In a choked nozzle, the mass flow rate is dependent on the pressure difference between the inlet and the exit. As P0 increases, the mass flow rate through the nozzle increases as well.
- (B) Mach number at the exit plane of the nozzle will remain unchanged at unity: This statement is TRUE. In a convergent nozzle operating under choked flow conditions, the Mach number at the exit plane remains at unity (M = 1), irrespective of changes in the inlet pressure, as long as the back pressure remains unchanged. This is a characteristic of choked flow.
- (C) Mass flow rate through the nozzle will increase: This statement is TRUE. As mentioned earlier, increasing the inlet pressure (P0) will result in an increased pressure difference, which will cause the mass flow rate through the nozzle to increase. The choked flow condition ensures that the flow rate is limited by the upstream conditions.
- (D) Mach number at the exit plane of the nozzle will become more than unity: This statement is FALSE. The Mach number at the exit plane remains at unity under choked conditions. Increasing the inlet pressure does not cause the Mach number to exceed unity; the nozzle remains at the critical flow condition where M = 1.
Hence, the correct options are (B) and (C).
