Laminar throughflow between closely spaced rotating disks

Abstract

Laminar throughflow between finite parallel disks, one stationary and the other rotating, can be characterized by four dimensionless parameters in the general case. But, if the ratio of disk spacing to disk radius is small, an approximate definition of the flow may be made with reference to a single parameter, the Ekman number. The equations of motion and the equation of continuity in this ‘thin-film’ approximation are reduced here to an initial-value problem for nonlinear ordinary differential equations, by a Galerkin-type procedure. Hamming's modified predictor-corrector method is employed subsequently to solve for the stream functions. Radial pressure profiles of this solution are compared with published experimental data. The calculated results may be applied to the design of hydrostatic bearings and face seals.