Annular lubrication drag on a settling cylinder
= Annular lubrication drag on a settling cylinder
For a cylinder of radius $a$ in a coaxial container with gap $h\ll a$, global displacement forces reverse flow through the gap and creates
$$
\Delta p\simeq\frac{6\mu aLU}{h^3}.
$$
The pressure drag exceeds side shear by order $a/h$. Balancing it with excess weight gives $U\simeq\Delta\rho,gh^3/(6\mu a)$.