Nonsteady motion of solid sphere in compressible viscous fluid

The problem of nonsteady motion of a solid body in a fluid medium is solved for a solid sphere in a compressible viscous fluid. An approximate solution is sought through linearization of the corresponding equations of motion. A perfectly rigid sphere is assumed to move in a quiescent boundless Stokes fluid with mechanical properties characterized by density and acoustic velocity. The motion of the sphere is described in two systems of coordinates, a Cartesian one and a spherical one with common origin. Its translational motion along one of the Cartesian axes is characterized by a velocity V(t) that varies in time. The vector equation of motion is reduced to two partial differential equations for the scalar potential and the vector potential in the fluid. The solution is obtained with the aid of a Laplace transformation, assuming zero initial conditions. The drag force of the fluid is calculated with the aid of asymptotic expansion for the special case of constant acceleration.