A polytropic analytical equation system for the internal e ow of nozzles and ducts has been developed by a solution to the combined friction/area change compressible e ow equations. Validation of the system is sought through comparison with experimental data and numerical simulations using FLUENT in the prediction of the performances of two conventional axisymmetric nozzles. Analytical performance coefe cient equations have been developed from the polytropic equation system for this purpose. The predictions with consideration of nozzle divergence angle and roughness are presented for the e rst time. 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 and performance factors, and analytical performance modeling. In aircraft nozzle simulations, where empirical data may not be available, this model provides more precise simulation capability especially applicable to modern thrust-vectoring nozzles.