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olem $3$: $(25$ Points$)$

ater is flowing in a rectangular channel shown below. The discharge in the channel is $11\mathrm{.}2\frac{m^3}{sec}$ and the width of the channel is $5$ m $.$ The sluice gate is placed between section $2$ and section $3.$ Determine the flow depth at section $1$ and section $2.($Hint: Check the states of the flow at each section$)$

$($:$y_2,1(\sqrt[\phantom{2}]{1+3f_{e_1^2}^2})-1\}$