On the Slow Broadside Motion of a Flat Plate along the Center-Line of a Fluid-Filled Two-Dimensional Channel

Abstract

Two-dimensional slow viscous flow due to the broadside translation of a flat plate along the center-line between two parallel walls is investigated on the basis of the Stokes approximation. An iterative solution is obtained by reducing the problem to a Fredholm integral equation of the second kind. Series expressions in power of ratio of widths of plate to channel are obtained for the drag on the plate and additional pressure difference between the ends of the channel due to the presence of the plate. Limiting values of the drag and the additional pressure drop are estimated from the series expression, when the plate nearly blocks the channel.