The flow of viscous fluid in a two-dimensional rectangular cavity has been studied. It is assumed that the cavity is bounded by three rigid plane walls, on which the fluid velocity is zero, and by a flat plate moving in its own plane. For the ratio of the lengths of sides of rectangular cross section, three cases have been chosen: 2:1, 1:1, 1:2. The Reynolds number of the flow is varied as 0, 1, 2, 4, 8, 16, 32, 64, 128. For these cases, the Navier-Stokes equations have been numerically integrated with the aid of high-speed electronic digital computers. Stream-lines, equi-vorticity lines, and isobaric lines for some typical cases are shown in figures. Velocity distributions along the centre line and pressure distributions over the both side walls are also shown.
Mitutosi Kawaguti (1961) studied this question.