A closed-form solution is presented for internal compressible flows with an arbitrary combination of area change, heat addition, friction and non-uniform flow. The approach assumes steady flow of a calorically perfect ideal gas using the integral form of the governing equations. It is shown that the equations reduce to a simple, bi-quadratic equation in exit Mach number. This solution is compared to previously known solutions for Rayleigh flow, Fanno flow, isentropic flow and normal shock

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... ons. Theoretical solutions for sudden expansion, sudden contraction, and supersonic–supersonic two-stream constant area mixing are also presented. These solutions were found to be in agreement with data available in the literature.