Fluid Drag on a Sphere Rolling in a Tube

Abstract

The incompressible fluid drag force on a sphere rolling at constant speed in a closed-end tube has been analyzed for the case where the tube inside diameter is only slightly larger than the sphere diameter. One drag law is found for Reynolds numbers much less than 75π/4λ1/2 , where λ is a parameter defined by the sphere and tube diameters. A second drag law is found for Reynolds numbers much larger than 75π/4λ1/2 . Experimental results show good agreement with these drag laws. The first law is almost identical with the results of Christopherson and Dowson, and of McNown, et al., for a sphere falling in a vertical tube.