Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 1 / 16C / a / ii / Solution

The pressure force in the $x$-direction on a rectangle of dimensions $\delta x\times \delta y$ isThe shear stress is ${\tau }_{xy}=\mu u_y$, so the net viscous force isThere is no convective acceleration. Dividing the momentum balance by the area and taking the limit givesThe $y$-momentum balance gives $p_y=0$, so the pressure depends only on $x$.