Isentropic steady-state flow

A very important special case of the polytropic flow equation (5.25) is that describing a reversible, adiabatic expansion, where no heat is exchanged with the surroundings, i.e. an isentropic expansion. In this case, the ratio of specific heats, y, is substituted for n in the mass-flow equation  

As was discussed in Section 3.3.1, the theoretical value of the index, y, is 1.67 for a monatomic gas such as helium or argon. 1.4 for diatomic gases such as hydrogen, oxygen and nitrogen and 1.33 for a polyatomic gas such as carbon dioxide or superheated steam. The true indices will deviate somewhat from these values in practice for instance the value of 1.3 is normally used as a better approximation for superheated steam. 

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If one can assume (1) the flow is one-dimensional and steady-state, (2) the flow is isentropic, and (3) the combustion gas is an ideal gas and the specific heat ratio is constant, the diagrams of p - v and h - s are uniquely determined.16-91 The enthalpy change due to the propellant combustion is given by... 

Moving on to compressible flow, it is first of all necessary to explain the physics of flow through an ideal, frictionless nozzle. Chapter S shows how the behaviour of such a nozzle may be derived from the differential form of the equation for energy conservation under a variety of constraint conditions constant specific volume, isothermal, isentropic and polytropic. The conditions for sonic flow are introduced, and the various flow formulae are compared. Chapter 6 uses the results of the previous chapter in deriving the equations for frictionally resisted, steady-state, compressible flow through a pipe under adiabatic conditions, physically the most likely case on... 

The sizing coefficient for steady-state conditions of an ideal gas through the nozzle without friction and heat exchange with the wall is written as (isentropic flow of an ideal gas)... 

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