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Note on the shearing motion of fluid past a projection

Published online by Cambridge University Press:  24 October 2008

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

1. A method has lately been developed by N. Muschelišvili (1) for the solution of problems of the slow two-dimensional motion of viscous liquid and of the corresponding problems of plane stress and plane strain, in cases in which the area in the x, y-plane that is concerned can be represented conformally on the interior of the circle |ζ| = 1 in the ζ-plane by a relation of the form z = x + iy = r(ζ), where r(ζ) is a rational function of ζ. In most problems in which the method has been used the function r(ζ) has been a simple one, but it is of importance to consider a rational function of as general a form as possible since, given any relation z = f(ζ), it will usually be possible to find a rational function that approximates to f(ζ) throughout the circle |ζ| = 1 and for a close approximation a complicated function r(ζ) will in general be required.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 40 , Issue 3 , November 1944 , pp. 214 - 222
Copyright
Copyright © Cambridge Philosophical Society 1944

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References

REFERENCES

(1)Muschelišvili, N.Z. angew. Math. Mech. 13 (1933), 264–82.CrossRefGoogle Scholar
(2)Dean, W. R.Proc. Cambridge Phil. Soc. 36 (1940), 300–13; 40 (1944), 19–36.CrossRefGoogle Scholar