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What is critical pressure ratio for compressible flow in nozzle? Explain its significance
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Consider a Converging Diverging (CD) Nozzle with pressure $P_1$ at the throat and pressure $P_o$ at the inlet.

Now, it can be observed that reducing $P_1$ promotes the flow of fluid from inlet to throat to outlet, at a rate which increases with pressure drop

The flow rate continues to increase till the velocity at the throat reaches the local sonic velocity.

Further reduction in downstream pressure has no effect on the conditions upstream i.e. no further increase in flow rate,thus leading to choked conditions

The pressure at the throat at which the flow chokes is called the critical pressure $P_c$ and the ratio of the critical pressure $P_c$ at the choked plane (throat) to the inlet pressure $P_o$ is known as the Critical Pressure Ratio$P_c/P_o$.

The Critical pressure ratio indicates the pressure ratio after which mass flow rate cannot be increased further even if exit pressure is reduced. This occurs when Mach number equals 1 at the minimum cross section.

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