On the flow of a compressible fluid by the hodography method I : unification and extension of present-day results
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Kaplan, Carl↗
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On the flow of a compressible fluid by the hodography method II : fundamental set of particular flow solutions of the Chaplygin differential equation
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Kaplan, Carl↗
On two-dimensional flows of compressible fluids
This report is devoted to the study of two-dimensional steady motion of a compressible fluid. It is shown that the complete flow pattern around a closed obstacle cannot be obtained by the method of Chaplygin. In order to overcome this difficulty, a formula for the stream-function of a two-dimensional subsonic flow is derived. The formula involves an arbitrary function of a complex variable and yields all possible subsonic flow patterns of certain types. Conditions are given so that the flow pattern in the physical plane will represent a flow around a closed curve. The formula obtained can be employed for the approximate determination of a subsonic flow around an obstacle. The method can be extended to partially supersonic flows.
HODOGRAPHY METHOD↗