ON THE EFFECTS OF UNIFORM SUCTION ON THE STEADY FLOW DUE TO A ROTATING DISK

Abstract

The exact ordinary differential equations of von Kármán for the flow due to a rotating disk of infinite radius are integrated for the case of uniform suction through the disk. In the analysis a suction parameter a is introduced, where a√νω is the velocity of suction, v being the kinematic viscosity and w the Angular velocity of the disk. For a = 1 the equations are integrated numerically, but for higher valuesof a a series solution in descending powers of a is obtained. The magnitude of the radial component of flow is found to decrease rapidly as the suction increases, while at the disk the derivative of the tangential component—with respect to distance from the disk—increases. If the ratio of distance from disk to displacement thickness is used as the dimensionlees independent variable, the change of the radial component with suction is seen to occur mainly in the velocity scale, with little change of shape, while the tangential component of flow changes very little.