Porous-plate lubrication cushion
= Porous-plate lubrication cushion
Uniform normal injection of speed $V$ through the lower plate of a stationary axisymmetric gap of thickness $h$ and radius $R$ produces
$$
w=V\left[1-3(z/h)^2+2(z/h)^3\right],
\qquad
u_r=\frac{3Vr}{h}(z/h)(1-z/h).
$$
With 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 $3\pi\mu VR^4/(2h^3)$.