A Viscous Source Flow Between Curved Circular Plates

Abstract

A viscous source flow between a curved circular plate and a flat one is studied theoretically and experimentally. Assuming the ratio of the gap between two plates to the radius of the curved plate to be small, an approximate solution is found with the accuracy of the second order of that ratio. The stream function, the pressure and the flow rate are found as a function of the profile of the curved plate. In a case of the curved disk with a cross-sectional profile consisting of the several straight lines, the theoretical pre5sure distribution is found to fairly agree with the experimental one obtained by using air. The conditions under which the pressure gradient in the radial direction becoTnes positive are found in the space of the Reynolds number and the depth of the hollow on the curved disk. When the force acting on the curved disk is represented as a function of the depth of the hollow, it is found to take a maximum value.