Two-Dimensional Slow Viscous Flow Due to the Motion of Flat Plate over a Plane Wall

Abstract

Two-dimensional slow viscous flow due to sliding of a semiinfinite flat plate over a perpendicular plane wall at a distance is investigated on the basis of Stokes' approximation. Streamlines and pressure distributions are determined from exact formal expressions of the stream function and the pressure field obtained by use of the Wiener-Hopf technique. It is also found that the force on the plate increases logarithmically as the clearance diminishes. The case in which the flow is caused by a pressure difference between up- and down-stream infinity with the planes at rest is also considered.