Viscous Flows past a Spheroid

Abstract

A solution of the Stokes equations of motion of a viscous fluid is given in a form suitable for dealing with the flows past an ellipsoid. When the ellipsoid has rotational symmetry, the solution is expressed in infinite triple integrals.
By utilizing these results, two kinds of steady flows of a viscous fluid past a spheroid are studied when the direction of the main stream is parallel to the axis of symmetry of the spheroid. The first is the flow past a spheroid between two parallel plane walls and the second is the flow past a spheroid in a cylindrical pipe with its axis of revolution along the axis of the pipe.
In particular, the drag and the moment acting on the spheroid as well as the pressure drop in the pipe are discussed in detail. It is worth noticing that the moment of force acting on a spheroid moving uniformly between two parallel walls changes its sign when the rate of roundness of the spheroid exceeds a certain definite value.