$($b$)$ Along the irrigation network, it is planned to construct a gate for better management of the water. If the gate is $7$ m $,$ the flow in the channel is $9\mathrm{.}5m\frac{3}{s}$ and the slope of the channel is $0\mathrm{.}002.$ Estimate the horizontal distance from the gate, where the backwater effect induced by the gate will be recorded.

$[15$marks$]$