Journal of Engineering Mathematics

, Volume 61, Issue 1, pp 55–68 | Cite as

On starting conditions for a submerged sink in a fluid

  • Lawrence K. ForbesEmail author
  • Graeme C. Hocking
  • Tim E. Stokes


Withdrawal of a fluid through an isolated line sink (for planar flow) or a point sink (for axi-symmetric flow in three dimensions) is considered. A linearized solution is presented in both cases, under the assumption that the sink strength is small and the sink is turned on gradually. The results show that the behaviour for small times is as if an image source were present above the surface. Asymptotic results indicate that, in both cases, the flow rapidly develops an effective image sink above the free surface.


Asymptotic behaviour Heuristic derivation Linearized solution Method of stationary phase Withdrawal flows 


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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  • Lawrence K. Forbes
    • 1
    Email author
  • Graeme C. Hocking
    • 2
  • Tim E. Stokes
    • 3
  1. 1.School of Mathematics and PhysicsUniversity of TasmaniaHobartAustralia
  2. 2.Division of Science, School of Mathematics and StatisticsMurdoch UniversityMurdochAustralia
  3. 3.University of WaikatoHamiltonNew Zealand

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