Slow Viscous Flow Due to Sliding of a Semi-Infinite Plate over a Plane

Abstract

Two-dimensional slow viscous flow in a region bounded by a plane wall and an inclined semi-infinite flat plate at a distance is investigated on the basis of Stokes' approximation. The motion is caused by the translation of the plane wall parallel to itself. A formal expression for the flow is obtained by solving a pair of simultaneous Wiener-Hopf equations. Streamlines and stress distributions on the plate are determined by evaluating the formal expression. The case in which the flow is caused by a pressure difference between up- and down-stream infinity with the plane wall at rest is also considered. When the plate is not perpendicular to the plane, it is found that separation occurs at the leading edge of the plate for both cases and that for the flow due to pressure difference a viscous eddy of which size diminishes as the inclination angle approaches 90° appears adjacent to the broader side of the plate.