Past exam of the mathematics course of the University of Cambridge / 2016 / ib / Paper 2 / 7C / c / Solution

The bottom-wall shear stress vanishes exactly when $u^{\prime }(0)=0$. Differentiating the velocity profile givesWith this value the velocity profile becomes $u(y)=-G{y}^2/(2\mu )$, so the volume flux per unit transverse width isFor $G>0$, the plate must move against the pressure-driven direction, and the resulting signed volume flux is negative. Zero bottom-wall shear does not mean zero flow.