On the flow of a viscous incompressible fluid between two parallel flat plates one in uniform motion and the other at rest, with unsteady pressure gradient

Abstract

In the present paper an attempt is made to find the solution of the Navier-Stokes equations for the unsteady flow of a viscous incompressible fluid through a channel bounded by two parallel flat plates, the upper one in uniform motion and the other at rest, under the influence of pressure gradient (i) varying linearly with time, and (ii) decreasing exponentially with time. In the first case it is seen that the velocity of any point above the axis of the channel is more than the velocity of the point symmetrical to this below the axis of the channel.