Problem $3(15$ pts$.)$: A constant$-$thickness film of viscous liquid flows in laminar motion down a plate inclined at angle $,$ as shown in the figure. The velocity profile is

$u=Cy(2h-y),v=w=0$

a$)$ Find the constant $C$ in terms of the specific weight and viscosity and the angle $.$

b$)$ Find the volume flux $Q$ per unit width in terms of these parameters.

$1$