Movements of a sphere rolling down an inclined plane

Abstract

Released from rest on an inclined smooth plane in a stationary fluid, a sphere accelerates along the plane under the influence of gravity and eventually reaches a terminal velocity. The variations of velocity with time and distance, the terminal velocity, the terminal distance (the practical distance required for a sphere from rest to its terminal velocity), are investigated through laboratory experiments and a theoretical analysis. The relationship of the drag coefficient and the Reynolds number for the moving sphere with its terminal velocity is obtained and compared with that in the free fall. The effect of proximity of sidewalls of the flume on the fluid drag acting on the steady movement of the sphere is evaluated. The terminal velocity and the terminal distance against the sediment number are presented in dimensionless graphs. Given bed inclination as well as the properties of the fluid and the sphere, the terminal velocity and the terminal distance can be determined directly from the graphs. The experiments of the steady movement for a sphere rolling down a rough inclined boundary are also presented.