Shear and pressure force partition in cylinder lubrication ($F_w^s=2\mu U{J}_1,F_c^s=-2\mu W{J}_1,F_c^p=2\mu (W-U)J_1$)

In the translating-cylinder frame, a wall moves at $-U$ and the nearby cylinder surface at $W$. With gap $d+x^2/(2a)$ and equal outer pressures, lubrication theory gives the displayed forces with $J_1=\pi \sqrt{2a/d}$. Wall and cylinder shear forces alone do not balance because the sloping cylinder's pressure force is of the same order. Their complete sum is zero. Pressure exerts no moment about the circular cylinder center, while shear supplies the leading singular rotational resistance.