Sonic flow during an isothermal expansion

Achieving sonic flow during an isothermal expansion is a highly improbable eventuality because the rapid heat transfer needed would take a great effort to contrive. Nevertheless, it is a theoretical possibility and has an interest as the limiting case of a reversible polytropic expansion. Accordingly a brief treatment will be provided here for completeness. 

To estimate the critical pressure ratio, we equate the sonic velocity to the outlet velocity calculated via equation (5.34). Substituting p = p, = p2 gives  

The value of the critical pressure ratio clearly depends on the value of y when y= 1.4, then Pc/pi = 0.4966, while when the value of y appropriate for steam is taken, namely y — 1.3, then p/fpi == 0.5220. 

The critical velocity can be found in terms of the upstream parameters by substituting from (5.65) back into equation (5.34) or directly by substituting from (5.63) into equation (5.47)  

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