A disk hovers on a cushion of air above an air-table - a fine porous plate through which a constant flux of air is pumped. Let the disk have a radius $R$ and a weight $M g$ and hover at a low height $h \ll R$ above the air-table. Let the volume flux of air, which has density $\rho$ and viscosity $\mu$, be $w$ per unit surface area. The conditions are such that $\rho w h^{2} / \mu R \ll 1$. Explain the significance of this restriction.

Find the pressure distribution in the air under the disk. Show that this pressure balances the weight of the disk if

$$h=R\left(\frac{3 \pi \mu R w}{2 M g}\right)^{1 / 3}$$