Question $1$: $(50$ marks$)$

Water is flowing in a rectangular channel with a width $b=4\mathrm{.}5m,$ a channel bottom slope $S_0=$

$0\mathrm{.}00045,$ and a Manning coefficient $n=0\mathrm{.}012.$ A sluice gate is placed in the channel and the

water depth immediately downstream of the sluice gate is measured to be $0\mathrm{.}3m$ with a flow

velocity of $6\mathrm{.}0\frac{m}{s}.$

a$)$ Calculate the critical and uniform flow depths for the channel.

b$)$ Calculate the flow depth immediately upstream of the sluice gate, assuming there are no

losses across the sluice gate.

c$)$ Calculate the flow depth immediately upstream of the hydraulic jump that forms downstream

of the sluice gate to return the flow to subcritical flow conditions.

d$)$ Classify the water surface profiles upstream of the sluice gate, and between the sluice gate

and the hydraulic jump that forms downstream of the sluice gate.

e$)$ Using the standard step method and a single intermediate flow depth calculate how far

downstream of the sluice gate the hydraulic jump forms, summarizing your calculations in

the attached table.