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The Quarterly Journal of Mechanics and Applied Mathematics 1950 3(4):446-451; doi:10.1093/qjmam/3.4.446
© 1950 by Oxford University Press
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FLUID MOTIONS WHOSE KINEMATICS ARE INDEPENDENT OF THE COMPRESSIBILITY OF THE FLUID

D. H. PARSONS

( Exeter College Oxford )

The following question is studied: What steady motions of a compressible fluid may be reproduced exactly by the motion of an incompressible fluid ? More precisely, what vector functions of position exist, representing simultaneously the velocity in a possible motion of a compressible fluid, and the velocity in a possible motion of an incompressible fluid ? A general account is given of the theory of motions of this type. Two-dimensional motion is then studied in detail, and it is shown that in order that a two-dimensional fluid motion may be of the required type, it is necessary and sufficient that the streamlines be either concentric circles or parallel straight lines. A very special case of three-dimensional motion, in which the streamlines are parallel straight lines, is then mentioned. Finally a general discussion is given of the type of results obtained, and it is shown how the restrictions encountered are interpreted by means of the theory of partial differential equations.


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