An open channel is designed based on a precast concrete pipe.

The pipe diameter is$,d=2\mathrm{.}4m$ and the flow rate is$,Q=3\mathrm{.}5\frac{m^3}{s}.$

a$-$ Find the wetted area, wetted perimeter and hydraulic radius for the following values of water depth:

$D=\frac{d}{4},D=\frac{d}{2},D=3\frac{d}{4},D=d$

$[70$ marks$]$

b$-$ Calculate the velocity and Froude number for each water depth and indicate the depths for which the flow is subcritical.

$[30$ marks$]$