Fluid Friction on the Circular Disc Rotating in the Cylindrical Vessel

Abstract

The fluid friction on the rotating disc in the fluid enclosed within the cylindrical vessel, which has flat ends and the cylindrical shell, was analytically treated and compared with the experimental results obtained by others. For laminar flow, the approximate solution was derived, on the basis of Navier-Stokes'equations, especially taking into consideration the existence of the cylindrical shell, which has been ignored in all treatments hitherto shown. For turbulent flow, the momentum equation has been adopted, in the assumption that (1) the flow in the boundary layer along the disc is forced radially outwards and circulates along the cylindrical surface and afterwards along the flat end surface, (2) the flow outside the boundary layer rotates in a fixed angular velocity, and (3) the parabolic and the seventh-root law holds for the velocity distribution in the laminar and the turbulent boundary layer.