Q$3(7$ marks$)$: There is a step in a rectangular channel. The channel is $2\mathrm{.}0$ m wide and carries a flow of $2\mathrm{.}4\frac{m^3}{s}.$ The water depth before the step is $1\mathrm{.}0$ m $.$ Neglect head losses in this question.

$($a$)(3$ marks$)$ Determine the maximum upward step such that hydraulic choke does not occur.

$($b$)(3$ marks$)$ When the step is an upward step and its height is $0\mathrm{.}20$ m $,$ mathematically we have two possible water depths after the upward step. These two water depths are $0\mathrm{.}39$ m and $0\mathrm{.}74$ m $.$ Which water depth is the right answer? Clearly provide your rationale and$/$or calculations to justify your answer.

$($c$)(1$ mark$)$ Determine the maximum downward step such that hydraulic choke does not occur.