VISCOUS IMPULSIVE ROTATION OF AN ANNULAR DISK

The problem of viscous impulsive agitation due to slow unsteady rotation about the axis of symmetry of an annular disk with arbitrary angular velocity OMEGA(T) in a large expanse of otherwise quiescent fluid is studied. Secondary flows are neglected. The solution of this mixed boundary value problem reduces to solving triple integral equations. Using Cooke's technique, the equations are solved. Analytical expression in integral form is given for the physically important quantity - the torque on the disk. Adopting a suitable numerical Laplace inversion formula, the torque is computed. It is observed that the instantaneous torque on the annular disk decreases as the ratio of annular radii increases, showing thereby that the liquid in the inner core of the disk acts like an accelerator. The corresponding steady-state results are also obtained.