Open AccessThe rotation of two circular cylinders in a viscous fluid
Author(s) -
G. B. Jeffery
Publication year - 1922
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1922.0035
Subject(s) - rotation (mathematics) , analogy , concentric , bounded function , mathematics , motion (physics) , mathematical analysis , function (biology) , stream function , boundary (topology) , viscous liquid , physics , mechanics , geometry , classical mechanics , vorticity , philosophy , linguistics , evolutionary biology , vortex , biology
In a previous communication we employed the solution of the equation ∇4 ψ = 0 in bipolar co-ordinates defined byα +iβ = logx +i (y +a )/x +i (y -a ) (1) to discuss the problem of the elastic equilibrium of a plate bounded by any two non-concentric circles. There is a well-known analogy between plain elastic stress and two-dimensional steady motion of a viscous fluid, for which the stream-function satisfies ∇4 ψ = 0. The boundary conditions are, however, different in the two cases, and the hydrodynamical problem has its own special difficulties.