Compressible flow through nozzles and constrictions

Pressure profiles for compressible flow through a convergent nozzle 

This is illustrated by conditions (a) to (c). In each case the pressure PE at the exit plane is equal to the back pressure PB. Flow is subsonic throughout the nozzle. This type of behaviour in which the flow rate increases as the back pressure is reduced (P0 held constant) continues until a critical value of the pressure ratio P/P0 is reached at the throat of the nozzle, condition (d). At the critical pressure ratio PJPo, the gas reaches the speed of sound at the throat. It will be shown that PJPo is a function of y only. 

If the back pressure is reduced below P, there is no increase in the flow rate through the nozzle, ie the flow is choked. In a convergent nozzle it is impossible for the gas speed to exceed the speed of sound. This case is 

The shock wave occurs in such a position as to allow the exit pressure to equal the imposed back pressure. The back pressure being lower for condition (d) than for condition (c), the shock wave for condition (d) is closer to the exit plane. 

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