10.5 Applications in Hydrodynamics 181
With the help of the multipoles in D dimensions, expressions analogous to
the Stokes force and the torque acting on a rotating body can be computed for the
D-dimensional case [38]. This is of particular interest for the caseD=2, cf. [39].
10.3 Exercise: Compute the Torque on a Rotating Sphere
A sphere rotating with the angular velocityΩexperiences a friction torque
Tμ=− 8 πηR^3 Ωμ.Derive this result from the creeping flow equation by considerations similar to those
used for the Stokes force.