When rain flows down a roof, it forms a layer whose velocity $u$ and volume flow rate $\frac{Q}{W}.$

The velocity distribution $u(y)$ is given by:

$u=\frac{gsin}{v}(hy-\frac{y^2}{2})$

The volume flow rate per unit width $\frac{Q}{W}$ is:

$\frac{Q}{W}=\frac{g{h}^{3}sin}{3}$

$u$

As illustrated in figure, consider the case of an upward wind flow that exerts a shear stress $$ on the upper surface