Two sets of exact isentropic-flow equations are developed, corresponding respectively to the Tait-Kirkwood equation (P + B) v kT = constant and to the Laplace-Poisson equation Pv kL = constant. The exact real-fluid equations have the form of conventional perfect-gas equations, with additional correction terms which are usually small. Similarity principles for each set of equations are given, the Laplace-Poisson form being new. Various simplified forms of the exact equations, of the kind used in practice, are tested for accuracy in an example.

The steady isentropic flow of a fluid which satisfies an arbitrary equation of state is treated, with emphasis on the prediction of pressure, density, velocity, and massflow at the sonic state. The isentrope P(v) is described by a limited number of thermodynamic parameters, the most important ones being the soundspeed c and fundamental derivative Γ. Using this description, an application of the Bernoulli equation and appropriate thermodynamic relations yields simple closed-form predictions for the sonic state. These predictions are recognizable as generalizations of well-known ideal gas formulas, but are applicable to fluids very far removed from the ideal gas state, even including liquids. Comparisons in several cases for which precise independent solutions are available suggest that the methods found here are accurate. A derived similarity principle allows the accurate prediction of sonic properties from any single given sonic property.

Transonic flow in a curved two-dimensional throat is considered. The approximate calculation is based on the full nonlinear inviscid equations and an integral continuity condition. Numerical results are presented in the form of curves which permit the determination of the flow in a nozzle of specified geometry. Analytical results reduce after linearization to those of Sauer for the limiting case of a symmetric channel.