$(40$ Points$)$ Incompressible steady flow in the inlet between parallel plates is uniform, $u=U_0=5\frac{(m)}{(s)},$

while downstream the flow develops into the parabolic laminar profile $u=\frac{4u_{\text{m}\text{a}\text{x}}}{z_0^2}z(z_0-z).$

What is the volumetric rate $($flux$)$ of the upstream flow?

If the flux is conserved from upstream to downstream and given $z_0$ is $2$ m $,$ what is the value of

$u_{\text{m}\text{a}\text{x}}$ in $\frac{m}{s}?$