Slow Viscous Flow Past a Lattice of Equal Flat Plates

Abstract

Two-dimensional slow viscous uniform flow past a lattice of equal parallel and equidistant flat plates is investigated based on the Stokes' approximation. The plates are at rest and the flow is generated by a pressure difference between two sides of the lattice at infinity. By solving a three-part Wiener-Hopf equation, analytic expression for the stream function is obtained for a parameter a, where a is the length of the plate. Drag force exerted on the plate is calculated and pressure and shear stress distributions are shown. The asymptotic form of the drag for a→ 0 is obtained by considering a pair of dual integral equations. Local analysis for the flow near the edge of the plate is also included.