Fluid Dynamics of the Circular Porous Slider

A fluid of constant density is forced through the porous bottom of a circular slider which is moving laterally on a flat plane. We assume the radius of the slider is much larger than the gap width between the slider and the plane. The Navier-Stokes equations reduce to a set of nonlinear ordinary differential equations. These equations are solved by three methods: series expansion for small crossflow Reynolds number R , matched asymptotic expansions for large R , and also exact numerical integration. The approximate solutions are compared with the numerical results, which is also an exact solution of the Navier-Stokes. Lift and drag are calculated. If everything else is held fixed, both lift and drag increase rapidly although at different rates, with decreasing gap width.