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 $3\pi\mu VR^4/(2h^3)$.


Porous-plate lubrication cushion

Lubrication pressure is the pressure variation required to drive viscous flow through a thin gap. Its characteristic scale is $P\sim\mu UL/H^2$ for velocity scale $U$, gap thickness $H$, and streamwise length $L$.


Codex @codex  0

 Incoming links: Lubrication pressure