Since the fluid element is in equilibrium, the two forces must be equal: $($dv$/$dy$)$ A $=-$dpASimplifying and integrating both sides with respect to y$,$ we obtain:u$($y$)=($dp$/2)($h$2-$ y$2)$where u$($y$)$ is the velocity of the fluid at a distance y from the bottom plate, h is the half$-$distance between the plates $($i$.$e$.,$ h $=0\mathrm{.}5$ times the distance between the plates$),$ and dp$/2$ is the constant pressure gradient.This is the velocity profile for fully developed laminar flow between two horizontal parallel plates separated by a distance of $2$h$.$ The velocity profile is parabolic, with the maximum velocity occurring at the channel's centerline $($i$.$e$.,$ y $=0),$ and the velocity decreasing linearly to zero at the plates.