An Asymptotic Solution for Laminar Flow of an Incompressible Fluid Between Rotating Disks

Laminar flow is considered between parallel rotating disks having a circular exhaust hole at an inner radius and supplied with fluid at the outer radius with pressure higher than the available sink pressure. The problem statement for asymptotic (fully developed) flow is formulated. A procedure for perturbing a creeping flow solution and an iteration scheme are developed to produce a solution for higher Reynolds numbers. The solution depends on two parameters, a Reynolds number and a mass flow parameter, and is asymptotic in the sense that a third parameter would be necessary for a solution with an arbitrary tangential velocity component specified at the outer radius of the disks and/or an arbitrary distribution of the radial velocity component between the disks. From computations conducted by digital computer, the region having uninflected radial velocity profiles is delineated. Typical results are presented for the velocity components as functions of Reynolds number, the average radial component of velocity at the entrance, and the inner radius of the disks.