An analytical method for the drag force of a thin flat plate in a flow of viscous fluid

Abstract

In the problem of classical hydrodynamics about a thin finite-length flat plate in a uniform flow of viscous incompressible fluid we propose a new analytical method to develop an explicit representation for the drag force. The approach proposed is based on a certain integral equation of the first kind which is valid in the case of small Reynolds numbers (strong viscosity, or slow stream). The constructed asymptotic solution coincides with the classical Harrison–Filon formula, developed by absolutely different technique, as a particular case of the Oseen slow flow around an elliptical cylinder.