Porous-plate lubrication cushion

Uniform normal injection of speed $V$ through the lower plate of a stationary axisymmetric gap of thickness $h$ and radius $R$ producesWith ambient pressure at the rim, the lubrication pressure is $p-p_0=3\mu V(R^2-r^2)/h^3$, and its integral supports the load $3\pi \mu V{R}^4/(2h^3)$.