By making a momentum balance over the same slab of thickness $y,$ one arrives at a differential equation for the velocity distribution

$\frac{d^2{v}_z}{d{y}^2}=\frac{dp}{dz}+pg$

Here the viscosity has been assumed constant $($see Problem $10$B$\mathrm{.}11$ for a solution with temperature$-$dependent viscosity$).$

Develop this eqution