E. Yu. Prosviryakov

A SUFFICIENT CONDITION FOR THE ABSENCE OF STRONG AND WEAK DISCONTINUITIES IN THE GAS FLOW IN FLAT CHANNELS

The paper brings together all the assumptions about the properties of discontinuous flows
of an ideal (perfect) gas, both formulated in textbooks and not formulated in the available literature, but having actually been long and effectively used. In addition, some new assumptions are physically grounded and formulated for the plane steady-state flow. All these properties are formulated in the form of a continuous continuum hypothesis for plane stationary flows of an ideal (perfect) gas. The hypothesis is formulated in such a way that, to justify the calculations and reasoning in the solution of problems, it would be possible not to resort to physical considerations every time again, but to rely on the “ready” statements of the hypothesis. Using the statements of this hypothesis,
a sufficient condition for the impossibility of the existence of discontinuities in the flows occurring in flat channels is obtained. In the derivation of sufficient conditions, were use only the statements of the hypothesis, without involving any additional physical considerations.

Acknowledgments: We are grateful to Prof. A. L. Stasenko (TsAGI) and Dr. G. B. Sizykh (MIPT) for the discus-sion of the “hypothesis” and useful remarks.

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