$7\mathrm{.}27.$ Water is released from under a vertical gate into a $2-m-$ wide lined rectangular channel. The gate opening is $50cm,$ and the flow rate into the channel is $10\frac{m^3}{s}.$ The channel is lined with reinforced concrete and has a Manning roughness coefficient of $0\mathrm{.}015,$ a horizontal slope, and merges with a river where the depth of flow is $3\mathrm{.}5m.$ Does a hydraulic jump occur in the lined channel? If so$,$ how far downstream of the gate does the jump occur, and what could be done to ensure that a hydraulic jump does not occur?