Experimental and analytical study of the motion of a sphere falling along an inclined plane in still water.

MARTINO, ROMÁN GUSTAVO; PATERSON, AGNES; PIVA, MARCELO FABIÁN

POWDER TECHNOLOGY

ELSEVIER SCIENCE SA

Lugar: Amsterdam; Año: 2015 vol. 283 p. 227 - 233

0032-5910

In this work, the transient regime of motion of a sphere, that falls along aninclined smooth plane, submerged in still water, is studied experimental andanalytically. Several experiments were performed, with spheres of differentdiameters and densities, and two slope angles. The measurements show thatthe motion of the sphere presents two well dened stages: a transitionalregime, where the sphere rapidly accelerates from rest, and an asymptoticregime, where the sphere moves with constant velocity. Closed expressions,for the position and velocity of the sphere as functions of time, are obtainedby direct integration of the motion equations. This theoretical analysis isbased on the empirical correlation for the drag coefficient as a function ofthe Reynolds number of the sphere, that was proposed by Chhabra andFerreira [2] for the experimental data set of Jan and Chen [1]. The analyticalsolution shows good agreement with experimental results, for a wide rangeof experimental conditions.