A polytropic analytical equation system for the internal flow of nozzles, inlets, and ducts has been developed through an analysis of the compressible flow equations including the friction and area change driving potentials. These equations are verified through comparison with experimental data and numerical simulations using FLUENT 5.0. The nozzle performance predictions include consideration of the nozzle divergence and surface roughness. It is demonstrated that the analytical model well matches the experimental data after the throat is fully choked. The numerical and analytical results are compared and discussed. Such an analytical model is extremely useful in bridging the gap between accepted empirical parameters such as the friction factor, performance coefficients, and analytical performance modeling. Furthermore, it provides the first analytical model for thrust-vectoring nozzle performance predictions. In aircraft nozzle simulations where empirical data may not be available, this model provides good simulation capability.