Flow About a Stationary Sphere in a Slowly Rotating, Viscous Fluid

Analytical solutions are presented for the flow about a nonrotating sphere immersed in a slowly rotating fluid by the singular perturbation technique valid for small Reynolds numbers. Streamlines are plotted and the torque necessary to hold the sphere stationary is calculated. It is found that the transition from inflow near the equator to outflow near the poles takes place at an angle of 54.50 deg measured from the poles. Flow velocities and the stream function are also calculated for the problem when the sphere rotates with an angular velocity different from that of the fluid.