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Water flows from a lake into a steep rectangular channel $2\mathrm{.}3m$ wide. The lake level is $4\mathrm{.}0m$ above the channel bed at the outfall, where the water level is equal to the critical depth.

Assuming that the head losses between the lake and the outfall are negligible, calculate the discharge into the channel.

The head at the outfall m

The flow rate per unit width m$2/$s

The flow rate in the channel m$3/$s