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Sluice-gate problems with gravity

  • P. J. Budden (a1) and J. Norbury (a1)

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.

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(1)Budden, P. J. and Norbury, J. Uniqueness and asymptotics for the sluice-gate problem. (To appear.)
(2)Keady, G. and Norbury, J.The jet from a horizontal slot under gravity. Proc. Roy. Soc. Ser. A344 (1975), 471487.
(3)Kellogg, O. D.Foundations of Potential Theory (Springer-Verlag, 1967).
(4)Protter, M. H. and Weinberger, H. F.Maximum principles in differential equations (Prentice-Hall, 1967).
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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