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Note on the slow motion of fluid

Published online by Cambridge University Press:  24 October 2008

W. R. Dean
W. R. Dean
Affiliation:
Trinity College
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Extract

In this paper we consider the slow two-dimensional motion of viscous liquid past a sharp edge projecting into and normal to the undisturbed direction of the stream. The liquid is supposed bounded by rigid planes represented by ABCDE in Fig. 1, and, apart from the disturbance caused by the projection, is assumed to be in uniform shearing motion. The stream function is then a bi-harmonic function that must vanish together with its normal derivative at all points of the boundary, and must be proportional to y2 at a great distance from the projection.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 32 , Issue 4 , December 1936 , pp. 598 - 613
Copyright
Copyright © Cambridge Philosophical Society 1936

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References

* The writer is indebted to Dr A. Weinstein for suggesting the second transformation. Although the functions in § 5 are practically the same as those the writer has used in a recent paper, Phil. Mag. 21 (1936), 727Google Scholar, they are much more simply expressed in terms of w than in terms of ζ.

* Aeronautical Research Committee, F.M. 101 (1933), 506.Google Scholar

* Phil. Mag. 15 (1933), 929.Google Scholar