Drag on spheres in rolling motion in inclined smooth tubes filled with incompressible liquids

The fluid-dynamic resistance to spheres rolling down inclined smooth wall tubes filled with Newtonian liquids has been investigated experimentally. Numerous spheres made of glass and steel have been used in conjunction with four smooth walled glass tubes of different diameters. In order to cover a wide range of sphere Reynolds number, numerous aqueous solutions of glycerol and glucose syrup were used to obtain liquids of different viscosities. Altogether, the present work encompasses angles of inclination from 3° to 30°, sphere-to-tube diameter ratios from 0.114 to 0.58, and the sphere Reynolds number from 10−6 to 3000. The drag on a sphere in rolling motion is always greater than that on a freely falling sphere under all kinematic conditions, although as the value of Reynolds number increases the divergence between the two values diminishes.