Effect of fluid compressibility on the flow caused by a sudden impulse applied to a sphere immersed in a viscous fluid

The flow of a viscous compressible fluid about a sphere suddenly set in motion by an applied impulse is studied on the basis of linearized hydrodynamic equations. Mixed slip-stick boundary conditions are assumed to hold at the surface of the sphere. An analytic expression for the flow pattern is presented for an idealized fluid in which the damping of sound waves is neglected. The time dependence of the pressure part and the viscous part of the fluid momentum is investigated. It is shown that at long times, one-third of the imparted momentum resides in the pressure part.