Sonic flow for an isentropic expansion

The most important case of sonic flow is that where the expansion is isentropic no heat is exchanged with the surroundings and frictional effects may be neglected. For an ideal gas undergoing an isentropic expansion, n = y. Substituting into (5.51) gives 

The ratio of critical specific volume to inlet specific volume follows from equation (5.52)  

For the special case where the upstream temperature is constant, we may usefully progress equation (5.59) further by the use of the characteristic gas equation  

If the upstream temperature is constant, and if the gas is either an ideal (Z = 1) or semi-ideal gas (Z = Z(T)), then the term 

IV a Pi, is often convenient in simulating the interface of a toiler plant to a turbine, where sonic conditions are frequently designed for in the first stage. 

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