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The Stokes flow problem for a class of axially symmetric bodies

Published online by Cambridge University Press:  28 March 2006

L. E. Payne  and
W. H. Pell
L. E. Payne
Affiliation:
Institute for Fluid Dynamics and Applied Mathematics, University of Maryland
W. H. Pell
Affiliation:
National Bureau of Standards, Washington 25, D.C.
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Abstract

The Stokes flow problem is concerned with fluid motion about an obstacle when the motion is such that inertial effects can be neglected. This problem is considered here for the case in which the obstacle (or configuration of obstacles) has an axis of symmetry, and the flow at distant points is uniform and parallel to this axis. The differential equation for the stream function ψ then assumes the form L2−1ψ = 0, where L−1 is the operator which occurs in axiallysymmetric flows of the incompressible ideal fluid. This is a particular case of the fundamental operator of A. Weinstein's generalized axially symmetric potential theory. Using the results of this theory and theorems regarding representations of the solutions of repeated operator equations, the authors (1) give a general expression for the drag of an axially symmetric configuration in Stokes flow, and (2) indicate a procedure for the determination of the stream function. The stream function is found for the particular case of the lens-shaped body.

Explicit calculation of the drag is difficult for the general lens, without recourse to numerical procedures, but is relatively easy in the case of the hemispherical cup. As examples illustrative of their procedures, the authors briefly consider three Stokes flow problems whose solutions have been given previously.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 7 , Issue 4 , April 1960 , pp. 529 - 549
Copyright
© 1960 Cambridge University Press

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