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The Quarterly Journal of Mechanics and Applied Mathematics 1949 2(2):129-135; doi:10.1093/qjmam/2.2.129
© 1949 by Oxford University Press
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ON A FAMILY OF ROTATIONAL SPATIAL GAS FLOWS

R. PRIM and P. NEMÉNYI

( Naval Ordnance Laboratory White Oak, Maryland, U.S.A. )

An investigation is made of steady flows of an ideal gas in the absence of body forces for which the three velocity components in a cylindrical coordinate system based on a plane isometric net depend on only one isometric coordinate. It is shown that such flows exist only if the basic isometric net consists of logarithmic spirals or their limiting cases (concentric circles, radial straight lines, and parallel straight lines). Several large classes of rotational and spatial gas-flow solutions are obtained, some in explicit forms involving an arbitrary function, and others as solutions to ordinary differential equations involving several arbitrary parameters.


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