The Steady Flow of Viscous Fluid past a Fixed Spheroidal Obstacle at Small Reynolds Numbers

Abstract

By making use of an exact solution of Oseen's equations of motion detailed theoretical discussion is made on the steady flow of an incompressible viscous fluid past a prolate or oblate spheroid, including a circular disc as a special case. The analytical exact solution of Oseen's equations are first obtained by the use of spheroidal functions, mathematical properties of which are also investigated separately in the writer's subsequent paper. The drag experienced by a spheroid is then computed and the general formula for the drag is obtained. Approximate formulae for the drags on a prolate and oblate spheroid and on a circular disc are also derived and some numerical results are obtained. Discussions on the pressure drag and the frictional drag experienced by a spheroid are made and it is thus found that these two drags contribute to the total drag in a definite ratio which is independent of the Reynolds number. Detailed analytical calculations are given only for the case of a prolate spheroid and the essential parts of the analysis for the case of an oblate spheroid are given in Appendix.