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Slow motion of viscous liquid in a semi-infinite channel

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 slow two-dimensional steady motion of liquid caused by a pressure gradient in a semi-infinite channel is considered. The medium is bounded by two parallel semi-infinite planes represented in Fig. 1 by the straight lines AB, DE. The stream-function ψ is a biharmonic function of x, y which exactly satisfies the condition that AB, DE must be stream-lines, but the condition that there must be no velocity of slip on these boundaries is satisfied only approximately, and the calculated velocity of slip gives a measure of the accuracy of the solution.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 1 , January 1951 , pp. 127 - 141
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

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