New approximate analytical solutions for creeping flow past axisymmetric rigid bodies

摘要

We describe a new approximate method to discuss uniform flow past rigid bodies of two different shapes using a complete general solution (Palaniappan et al., 1992; Padmavathi et al., 1998) of Stokes equations in an incompressible, viscous fluid. We also sketch the streamlines in both the cases. However, the solution, although approximate, has an added advantage that it is known at all the points in the domain since it is given in an analytical form, unlike the numerical methods like finite difference methods or finite element methods which use meshes, where the solution is known only at certain predetermined points. This method hence enables us to obtain in a simple way, more accurate values of physical quantities like the drag experienced by a rigid body, even though the solution may be approximate. We also note that the method can easily be extended to other arbitrary axisymmetric Stokes flows also.