Hostname: page-component-7bb8b95d7b-nptnm Total loading time: 0 Render date: 2024-09-05T10:44:15.944Z Has data issue: false hasContentIssue false
  • English
  • Français

Efflux from a slit in a vertical wall

Published online by Cambridge University Press:  21 April 2006

E. O. Tuck
E. O. Tuck
Affiliation:
Department of Applied Mathematics, University of Adelaide, GPO Box 498, Adelaide, SA 5001, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

A numerical solution is provided for flow of a stream of water falling under gravity after emerging from a simple slit orifice in a vertical wall. The classical free-streamline flow with contraction coefficient 0.611 applies in the absence of gravity, or as F → ∞, where F is the Froude number based on the net volume flux and the slit width. We assume here that F is finite, but find that the flow exists only for F [ges ] 0.496, with initial backflow at the upper stream surface for 0.496 [les ] F [les ] 0.578. The limiting flow at F = 0.496 has a stagnation point at the upper edge.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 176 , March 1987 , pp. 253 - 264
Copyright
© 1987 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics, Cambridge University Press.
Budden, P. J. & Norbury, J. 1977 Sluice-grate problems with gravity. Math. Proc. Camb. Phil. Soc. 81, 157–175.Google Scholar
Conway, W. E. 1967 The two-dimensional vertical jet under gravity. J. Math. Anal. Appl. 19, 282–290.Google Scholar
Geer, J. & Keller, J. B. 1979 Slender streams. J. Fluid Mech. 93, 97–115.Google Scholar
Goh, M. K. 1986 Numerical solution of quadratically nonlinear boundary-value problems using integral equation techniques, with application to jets and nozzle flows. Ph.D. thesis. University of Adelaide.
Goh, M. K. & Tuck, E. O. 1985 Thick waterfalls from horizontal slots. J. Engng Maths 19, 341–349.Google Scholar
Grant, M. A. 1973 The singularity at the crest of a finite-amplitude progressive Stokes wave. J. Fluid Mech. 59, 257–262.Google Scholar
Kandaswamy, P. K. & Rouse, H. 1957 Characteristics of flow over terminal weirs and sills. J. Hydraulics Div. ASCE 4, 1–13.Google Scholar
Keady, G. & Norbury, J. 1975 The jet from a horizontal slot under gravity. Proc. R. Soc. Lond. A 344, 471–487.Google Scholar
Vanden-Broeck, J.-M. 1986a Pointed bubbles rising in a two-dimensional tube. Phys. Fluids 29, 1343–1344.Google Scholar
Vanden-Broeck, J.-M. 1986b Flow under a gate. Phys. Fluids 29, 3148–3151.Google Scholar
Vanden-Broeck, J.-M. & Keller, J. B. 1986 Pouring flows. Phys. Fluids 29, 3958–3961.Google Scholar