The ANZIAM Journal

Research Article

Unsteady flow induced by a withdrawal point beneath a free surface

T. E. Stokesa1, G. C. Hockinga2 and L. K. Forbesa3

a1 Department of Mathematics, University of Waikato, Hamilton, New Zealand.

a2 School of Engineering Science, Murdoch University, Murdoch, WA 6150, Australia; e-mail:

a3 School of Mathematics and Physics, Universiy of Tasmania, GPO Box 252-37, Hobart, TAS 7001, Australia.


The unsteady axisymmetric withdrawal from a fluid with a free surface through a point sink is considered. Results both with and without surface tension are included and placed in context with previous work. The results indicate that there are two critical values of withdrawal rate at which the surface is drawn directly into the outlet, one after flow initiation and the other after the flow has been established. It is shown that the larger of these values corresponds to the point at which steady solutions no longer exist.

(Received July 30 2004)

(Revised July 22 2005)