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A note on the motion of a closely fitting plug along a fluid-filled tube

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  26 February 2010

L. M. Hocking
L. M. Hocking
Affiliation:
Department of Mathematics, University College London, London, WC1E 6BT.
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Abstract

In finding the resistance to the motion of a closely fitting plug along a tube filled with fluid, allowance must be made for the leakage of fluid through the gap between the plug and the tube. If there is no leakage, theoresistance is theoretically infinite. For a plug of length d in a tube of radius a and with a gap b between the plug and tube, the dominant term in the resistance comes from the flow in the gap, and is proportional to da/b. If, however, the plug is very short, so that it may be considered as a disk, the calculation of the flow near the disk shows that the resistance is now proportional to aln (a/b) and the presence of the disk increases the force on the tube by an amount equivalent to an increase in length of the tube by only a few radii.

MSC classification

Secondary: 76D99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 24 , Issue 1 , June 1977 , pp. 63 - 70
Copyright
Copyright © University College London 1977

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References

1.Wagner, M. H.. “Developing flow in circular conduits: transition from plug flow to tube flow”, J. Fluid Mech., 72 (1975), 257–268.CrossRefGoogle Scholar
1.Batchelor, G. K.. An introduction to fluid dynamics (1967, Cambridge University Press).Google Scholar
3.Hocking, L. M.. “A moving fluid interface. Part II. The removal of the force singularity by a slip flow”, J . Fluid Mech., 79 (1977), 209–229.CrossRefGoogle Scholar