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Sluice-gate problems with gravity

Published online by Cambridge University Press:  24 October 2008

P. J. Budden  and
J. Norbury
P. J. Budden
Affiliation:
Department of Mathematics, University College London
J. Norbury
Affiliation:
Department of Mathematics, University College London
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Abstract

In this paper, a free-boundary problem of the steady plane flow of an ideal fluid through a slot is solved. The fluid flows under the effect of gravity between rigid boundaries, and then out of a slot as a jet which becomes horizontal at infinity downstream. A constructive proof of the existence of solutions to a non-linear integral equation is given for a parameter range 0 < ε < ε* ≃ 1·02 (where ε, the inverse Froude number, measures the effect of gravity). Approximations to the solution are then found for ε → 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 1 , January 1977 , pp. 157 - 175
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

REFERENCES

(1)Budden, P. J. and Norbury, J. Uniqueness and asymptotics for the sluice-gate problem. (To appear.)Google Scholar
(2)Keady, G. and Norbury, J.The jet from a horizontal slot under gravity. Proc. Roy. Soc. Ser. A344 (1975), 471–487.Google Scholar
(3)Kellogg, O. D.Foundations of Potential Theory (Springer-Verlag, 1967).CrossRefGoogle Scholar
(4)Protter, M. H. and Weinberger, H. F.Maximum principles in differential equations (Prentice-Hall, 1967).Google Scholar