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The conditions relative to the throat of a convergent nozzles for isentropic flow of an ideal gas

Stated as follows: a.       The maximum velocity at the throat equals sonic velocity. b.       The maximum pressure at the throat is the critical pressure. c.        Maximum mass flow rate occurs when the throat pressure is maximum. d.       Decreasing the back pressure below the critical pressure does not change the velocity or pressure at the throat or mass flow rate. e.       When the back pressure is lowered below critical value the gas     expands in the divergent part of the nozzle and velocity becomes supersonic.