Problem $4$ Water flows in a rectangular channel with channel width $B=4\mathrm{.}0(m).$ The specific energy diagram $($SED$)$ of this flow is given in the figure below. $)=(0\mathrm{.}2(m)$

$(1)$ Estimate the channel discharge $Q$ from the given SED.

$(2)$ If the water depth in the channel at a cross section is $y_1=0\mathrm{.}45($m$).$ The channel bottom is raised smoothly by $z=0\mathrm{.}2(m).$ Determine if the flow will be "choked" by the raised step. If yes, estimate the "backed up$"$ depth upstream, $y_1^{\text{'}}.$ If not, what is the water depth $y_2$ above the step?