$1.$

Water flows in the triangular steel channel shown in the figure below. Find the depth of flow if the channel slope is $0\mathrm{.}0015$ and the discharge is $0\mathrm{.}22$ m$3/$s$.($n$=0\mathrm{.}014)$

$2.$

A trapezoidal channel has Manning$$s n $=0\mathrm{.}020$ and bed slope So $=0\mathrm{.}0004,$ which is made in the shape of a half$-$hexagon for maximum efficiency. For what length of L will the channel carry $7\mathrm{.}1$ m$3/$s of water at its full capacity.

$3.$

Water flow in a wide channel approaches a $10$ cm high bump at $1\mathrm{.}5$ m$/$s and a depth of $1$ m$.$ Estimate

$($a$)$ the water depth y$2$ over the bump, and

$($b$)$ the bump height which will cause the crest flow to be critical