An analytical study of the motion of a sphere rolling down a smooth inclined plane in an incompressible Newtonian fluid

The accelerated motion of a sphere rolling down a smooth inclined plane imm ersed in a quiescent Newtonian fluid has been investigated theoretically us ing Jan and Chen's drag and added mass coefficient data [C.D. Jan, J.C. Che n, J. Hydraulic Res. 35 (1997) 689]. A modified expression for the drag coe fficient was used to obtain an analytical solution to the equations of moti on in the inclined plane. Closed form solutions for the instantaneous accel eration, time and distance required by the sphere to reach a given velocity are presented, and the sphere's settling velocity is determined. The relat ionship between the plane's angle of inclination and the time and distance required by the sphere to reach 99% of its terminal velocity is also invest igated. The analysis reported herein is, however, restricted to dense spher es immersed in light liquids where additional effects arising from the Bass et forces can be neglected. (C) 1999 Elsevier Science S.A. All rights reser ved.