Torque on a Finite Disk Executing Damped Harmonic Oscillations in a Viscous Fluid Near a Rigid Boundary

Abstract

Expressions are derived for the torque exerted on a finite cylindrical disk that executes torsional oscillations about its cylindrical axis while immersed in a viscous fluid parallel to a rigid plane boundary. The relations for the total torque of the fluid on the oscillating disk are given in terms of the period and decrement of the disk's oscillation for small, large, and intermediate separation distances between the disk and the rigid plane boundary. Theoretical relations for the torque of the fluid on the disk are found, assuming that the disk oscillates slowly and that the force per unit area on the plane and cylindrical surfaces of the disk is equal to that for an infinite disk and cylinder, respectively. An empirical correction is used to account for the torque which is due to the effects of the sharp corners of the disk. The effects of the bounding plane on the reactive and dissipative components of the torque are given in terms of the depth of penetration of a decaying transverse wave propagated into the fluid.