A simple approach
My log in does not support clever symbols. Any treatise will do but pp65-88 of Philip G Hill & R Peterson ISBN 0-201-14569-2, Dewey classification 629.1328 published by Addison Wesley does the job.
Caveats are:- the assumption that flow can be assumed as one-dimensional through the control volume is tosh; but on this basis pressure, shear and body forces satisfy a simple momentum equation provided that the fluid is a perfect gas and gravitational potential energy can be neglected; therefore stagnation enthalpy contains only two terms; therefore stagnation temperature is a function solely of cp, dT and therefore the ratio of specific heats; for an infinitesimally thin slice of control volume it is customary to neglect shear force [but what about body forces?] so that for an isentropic flow -dp = rho a du; thus du can be eliminated by simultaneous equations and a*a = kRT.
That is as far as Hill and Peterson go in the quoted first four pages leaving the difficult stuff to the rest of the chapter, sadly glossing over choking flow but non-isentropic flow and shocks are handled.
Boundary layer and the limitation of simple control volume theory are expounded in Chapter Four.
Last edited by mathy; 5th Jul 2012 at 15:32.
Reason: typing