Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-19T16:35:07.276Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on withdrawal from a fluid of finite depth through a point sink

Published online by Cambridge University Press:  17 February 2009

G. C. Hocking ,
J.-M. Vanden-Broeck  and
L. K. Forbes
G. C. Hocking
Affiliation:
Mathematics and Statistics, DSE, Murdoch University, Murdoch, WA, 6150, Australia.
J.-M. Vanden-Broeck
Affiliation:
Department of Mathematics, University of East Anglia, Norwich, UK.
L. K. Forbes
Affiliation:
School of Mathematics and Physics, The University of Tasmania, Hobart, TAS 7001, Australia.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The problem of withdrawal through a point sink of water from a fluid of finite depth with a free surface is considered. Assuming the flow to be axisymmetric, it is found that there is a maximum Froude number at which such flows can exist. This maximum corresponds to the formation of a secondary stagnation ring on the free surface. This result extends earlier work on this problem. Comparison is made with a small Froude number solution and past experimental results.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 2 , October 2002 , pp. 181 - 191
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Abramowitz, M. and Stegun, I. A. (eds.). Handbook of Mathematical Functions (Dover, New York, 1970).Google Scholar
[2]Baek, J. H. and Chung, H. Y., “Numerical analysis on axisymmetric draining from a cylindrical tank with a free surface”, J. Comp. Fluid Dynamics 6 (1998) 413–425.Google Scholar
[3]Craya, A., ‘Theoretical research on the flow of nonhomogeneous fluids”, La Houille Blanche 4 (1949) 44–55.CrossRefGoogle Scholar
[4]Forbes, L. K. and Hocking, G. C., “Flow caused by a point sink in a fluid having a free surface”, J. Austral. Math. Soc. Ser B 32 (1990) 231–249.CrossRefGoogle Scholar
[5]Forbes, L. K. and Hocking, G. C., “The bath-plug vortex”, J. Fluid Mech. 284 (1995) 43–62.CrossRefGoogle Scholar
[6]Forbes, L. K., Hocking, G. C. and Chandler, G. A., “A note on withdrawal through a point sink in fluid of finite depth”, J. Austral. Math. Soc. Ser. B 37 (1996) 406–416.CrossRefGoogle Scholar
[7]Gariel, P., “Experimental research on the flow of nonhomogeneous fluids”, La Houille Blanche 4 (1949) 56–65.Google Scholar
[8]Harleman, D. R. F., Morgan, R. L. and Purple, R. A., “Selective withdrawal from a vertically stratified fluid”, in Proc. Int. Assoc. Hyd. Res., 8th Congress, Montreal (1959).Google Scholar
[9]Hocking, G. C., “Supercritical withdrawal from a two-layer fluid through a line sink”, J. Fluid Mech. 297(1995) 37–47.CrossRefGoogle Scholar
[10]Imberger, J. and Hamblin, P. F., “Dynamics of lakes, reservoirs and cooling ponds”, Ann. Rev. Fluid Mech. 14 (1982)153–187.CrossRefGoogle Scholar
[11]Jirka, G. H. and Katavola, D. S., “Supercritical withdrawal from two-layered fluid systems. Part 2—Three dimensional flow into a round intake”, J. Hyd. Res. 17 (1979) 53–62.CrossRefGoogle Scholar
[12]Lawrence, G. A. and Imberger, J., “Selective withdrawal through a point sink in a continuously stratified fluid with a pycnocline”, Technical Report ED–79–002, Dept of Civil Eng., University of Western Australia, Australia, 1979.Google Scholar
[13]Lubin, B. T. and Springer, G. S., “The formation of a dip on the surface of a liquid draining from a tank”, J. Fluid Mech. 29 (1967) 385–390.CrossRefGoogle Scholar
[14]Sautreaux, C., “Mouvement d'un Iiquide parfait soumis à la pesanteur. De termination des lignes de Courant”, J. Math. Pures Appl. 7 (1901) 125–159.Google Scholar
[15]Tuck, E. O. and Vanden-Broeck, J.-M., “A cusp-like free-surface flow due to a submerged source or sink”, J. Aust. Math Soc. Sen B 25 (1984) 443–450.CrossRefGoogle Scholar
[16]Vanden-Broeck, J.-M. and Keller, J. B., “Free surface flow due to a sink”, J. Fluid Mech. 175 (1987) 109–117.CrossRefGoogle Scholar
[17]Vanden-Broeck, J.-M. and Keller, J. B., “An axisymmetric free surface with a 120° along a circle”, J. Fluid Mech. 342 (1997) 403–409.CrossRefGoogle Scholar
[18]Wood, I. R., “Selective withdrawal from two-layer fluid”, J. Hyd. Div. (ASCE) HY12 (1978) 1647–1659.CrossRefGoogle Scholar
[19]Zhou, Q. and Graebel, W. P., “Axisymmetric draining of a cylindrical tank with a free surface”, J. Fluid Mech. 221 (1990) 511–532.Google Scholar