Accelerated Motion of a Spheroid in Viscous Fluid

The exact solution of the equation of motion of a spheroid accelerated along its axis of symmetry to an arbitrarily applied force in a viscous fluid of infinite extent is obtained. The solutions are presented in terms of tabulated functions. The unsteady drag predicted by the Stokes-flow solution is adopted in the analysis. Both prolate and oblate spheroids are considered. The results are reduced to those of accelerated sphere case, in which the spheroid becomes a sphere. The prolate spheroid with the ratio of major axis to minor axis equal to 1.96 is found to have the greatest terminal settling velocity due to gravity and to travel longest distance due to an impulsive force among the spheroids of equal volume. The variations of velocity and displacement with time for some spheroids falling from rest are presented in graphs.