Cylinder translating parallel to a wall in a thin gap ($F=2\pi \mu V\sqrt{2a/b}$)

For a nonrotating cylinder of radius $a$ translating parallel to a stationary wall at minimum gap $b\ll a$, the leading gap is $h=b+x^2/(2a)$. In the cylinder frame, the constant flux is $-2Vb/3$ and the pressure gradient is $2\mu V(4b-3h)/h^3$. The pressure is $2\mu Vx/h^2$. Integrating the wall shear $4\mu V(1/h-b/h^2)$ gives the displayed leading force per unit axial length. Full wetting and negligible inertia are assumed; cavitation would change the pressure boundary conditions.