In a rectangular channel, b $=3$ m$,$ n $=0\mathrm{.}014,$ S$0=0\mathrm{.}0004,$ and Q $=4\mathrm{.}5$ m$3/$s$.$ At the entrance to the channel, flow issues from a sluice gate at a depth of $0\mathrm{.}15$ m$.$ The channel is sufficiently long that uniform flow conditions are established away from the entrance region. Find the nature of the water surface profile $($mild$,$ steep, or critical$)$ in the vicinity of the entrance. You require to obtain y$1,$ y$0$ and yc and plot the water profile.

Hint: Identify if a hydraulic jump occurs or not, if yes, find the water depth, y$1,$ before the

jump. To obtain y$0,$ you can use $1\mathrm{.}25$ m as an initial guess and a step between $0\mathrm{.}01$m and $0\mathrm{.}05$m$.$

The error should be smaller than $5\%.$