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A note on the motion of a closely fitting plug along a fluid‐filled tube
Author(s) -
Hocking L. M.
Publication year - 1977
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300008925
Subject(s) - spark plug , tube (container) , mechanics , radius , mathematics , allowance (engineering) , leakage (economics) , plug flow , flow (mathematics) , geometry , materials science , physics , thermodynamics , composite material , mechanical engineering , engineering , computer security , macroeconomics , computer science , economics
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.