II. Flow with circulation

This is a sequel to an earlier paper (Cherry 1947) in which was found a family of exact solutions for compressible flow past a cylinder. In the present paper the solution is extended to the case where the circulation round the cylinder is not zero. The formulae are developed for the case where the c...

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Bibliographic Details
Published in:Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences Mathematical and physical sciences, 1949-02, Vol.196 (1044), p.1-31
Main Author: Cherry, Thomas Macfarland
Format: Article
Language:English
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Summary:This is a sequel to an earlier paper (Cherry 1947) in which was found a family of exact solutions for compressible flow past a cylinder. In the present paper the solution is extended to the case where the circulation round the cylinder is not zero. The formulae are developed for the case where the circulation is sufficiently small for the existence of a pair of stagnation points on the surface of the cylinder, under the condition that the speed at infinity is subsonic. One substantial point which arises in the present investigation is that the most direct generalization of the formulae for incompressible flow yield multiple-valued formulae for compressible flow. To get a single-valued solution it is necessary to add another multiple-valued solution, involving a set of constants which are to be determined from an infinite set of linear equations. The explicit solution of these equations is found, and hence the flow around a profile which is a slightly distorted circular cylinder.
ISSN:0080-4630
2053-9169
DOI:10.1098/rspa.1949.0009