$($b$)$ Water is impounded behind a vertical sluice gate to a depth of $4\mathrm{.}1m.$ An opening

below the sluice gate allows water to flow at a depth of $0\mathrm{.}6m$ into a wide

rectangular channel. The longitudinal bed slope of the channel is $0\mathrm{.}005$ and the

downstream flow depth is controlled to $2m.$ The Manning's roughness coefficient

for the channel may be taken as $0\mathrm{.}015.$

$($i$)$ Verify that a hydraulic jump will occur in these circumstances.

$($ii$)$ Estimate the jump location relative to the sluice gate.

$(35\%)$

$($iii$)$ Sketch the water surface profile in the channel with consideration being given

to the classification of gradually varied flow profiles.

$(15\%)$

Note: You may assume that energy losses at the sluice gate are negligible.