Accelerated Motion of a Sphere in a Viscous Fluid

An investigation was made of the free fall of a sphere from rest in a viscous fluid in order to gain a better understanding of this fundamental form of accelerated motion. For spheres within the Stokes range, an analytical solution to the equation of motion was obtained. At present (1963), no experimental evidence is available to verify the solution for spheres with a Reynolds number less than 0.9. For spheres above the Stokes range, the approximate equation of motion was evaluated by numerical methods. The numerical solutions agree closely with the experimental data obtained, by Moorman, for a wide range of Reynolds numbers. It is hoped that the approach developed as a result of this study may be applied to other types of accelerated particle motion, such as that frequently encountered in natural environments involving sediment transportation and deposition.