A full channel width undershot sluice gate is partially lowered across a rectangular channel $2m$

wide conveying $18\frac{m^3}{s}$ of water. The water backs up upstream of the sluice and a hydraulic

jump forms a short distance downstream of the sluice. The depth after the jump is observed to

be $4m.$ Assuming negligible velocity head upstream of the sluice, no loss of energy at the sluice

or in the channel flow and no change of momentum at the jump, determine the depths upstream

and downstream of the sluice $(C).$

$(6\mathrm{.}55m,0\mathrm{.}851m)$