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The first compressible flow solution based solely on the locally analytical method is developed. This is accomplished by developing the flow model and locally analytical solution for inviscid subsonic compressible flow. The stream function for irrotational, compressible flow without body forces was chosen as the governing differential equation. To demonstrate the modelling and locally analytical solution, this analysis is then applied to predict the flow in convergent nozzles, both planar and axially symmetric,for different back pressures. Results are presented which demonstrate the effectiveness of this technique.

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