$($a$)$ A trapezoidal channel, with a bottom width of $B=4m$ and side siopes of $11$ in $0$ls$,$ carries a fiom of $15\frac{m^3}{s}.$ The channel's slope and Manning's a are $0\mathrm{.}001$ and $0\mathrm{.}012\frac{s}{m^{\frac{2}{3}}}$ respectivel$-$

i$)$ Determine the normal and critical depths.

$(625]$

ii$)$ Classify the type of the bottom and the state of the flow $(=$umiform? Not umifemen Sub$/$supercritical$?$ Drawdown$/$backwater$?)$ when the water depth is $1\mathrm{.}2$ m $.$

$1425$

$($b$)$ Sketch the water profiles in two prismatic channels below and point out profile types of gradually varied flows or hydraulic jumps.

i$)$ Flow from a steep slope to a mild slope; supercritical upstream.

$7a3$

ii$)$ On a steep slope, flow goes through a sluice gate. The surface at the back of the gate is above the critical depth and the surface at the opening of the gate is below the normal depth.