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The Coaxial Circular Disc Problem
Author(s) -
Cooke J. C.
Publication year - 1958
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19580380904
Subject(s) - coaxial , cylinder , rotation (mathematics) , condenser (optics) , physics , mechanics , circular motion , constant angular velocity , angular velocity , classical mechanics , simple (philosophy) , mathematics , optics , geometry , mechanical engineering , engineering , light source , philosophy , epistemology
Two problems involving equal coaxial circular discs are discussed (i) the discs charged to equal, or equal and opposite, potentials, and (ii) the discs rotating slowly with equal, or equal and opposite, angular velocities in a viscous fluid. In this paper some improved values are given for the cases of most interest, namely the “condenser problem” and the “viscometer problem”, that is to say, the cases of opposite potentials or directions of rotation. When the discs are close together the numerical work is very laborious and a semi‐empirical method is given whereby important constants can be obtained as a correction to an approximation originally due to Maxwell, which is simple numerically. An attempt is also made to assess the effect of placing the disc system inside a coaxial cylinder.