Symmetric Sink Flow Between Parallel Plates

Abstract

Steady, laminar, incompressible flow converging radially between two stationary disks is investigated numerically as a continuously developing flow problem under the internal boundary layer approximations. At dimensionless radii much greater than one the velocity profile becomes parabolic and invariant, but at radii less than one a typical external boundary layer evolves close to the wall with an approximately uniform core region; and the boundary layer thickness decreases from one-half the disk spacing to values proportional to the local radii as the flow accelerates. At large radii the friction factor approaches the classic value obtained for fully developed flow between infinite plates, 6ν/Vt, but at small radii it approaches the constant 2.17/R0, where R0 is an overall Reynolds number based on the volumetric flow rate and the disk spacing and is independent of radius. Tabular and graphical results are provided for the intermediate range of radii, where both viscous and inertial effects are important and exact analyses are not available.