Float height of a rectangular plate in planar stagnation flow

Numerical integrations of the self-similar equations for steady planar fluid motion between infinite stationary parallel plates are reported for the case where the upper plate is impermeable and the lower plate has uniform transpiration. Such a reduction characterized by a single Reynolds number represents a new exact solution of the Navier-Stokes equations. High-Reynolds number asymptotics greatly facilitate numerical integration by a standard shooting technique. The results are applied to model the float height a rectangular plate under gravity when the plate separation distance is small. We use the results to compare the float heights of disks of fixed mass and surface area supported by axisymmetric and planar stagnation flows.