Qill: A very wide horizontal rectangular channel carrying a flow passes through a smooth gradual transition into a triangular concrete channel with Manning's roughness $n=0\mathrm{.}015.$ The side slopes of the triangular channel are $1\mathrm{.}5$ horizontal to $1\mathrm{.}0$ vertical and the bed slope is steep. The invert of the triangular channel is $0\mathrm{.}5$ m above the downstream invert of the rectangular channel.

Q$"1($a$)$: Determine the critical depth $(y_c)$ at the start of the triangular channel section as a flow of $1\mathrm{.}5\frac{m^3}{s}$ completes its gradual transition from the wide rectangular channel upstream.

$0\mathrm{.}615$ m

$0\mathrm{.}727$ m

$0\mathrm{.}573$ m

$0\mathrm{.}0\mathrm{.}369$ m

$0\mathrm{.}448$ m

Q#$1($b$)$: If the critical depth $(y_c)$ in the triangular channel in part $($a$)$ is $0\mathrm{.}96$ m when the flow is $3\mathrm{.}0\frac{m^3}{s},$ calculate its corresponding critical specific energy.

$0\mathrm{.}96$ m

$0\mathrm{.}27$ m

$0\mathrm{.}33$ m

$1\mathrm{.}20$ m

$0\mathrm{.}41$ m

Q#$1($c$)$: Assuming the same conditions in $1($b$),$ determine the minimum slope of the triangular channel to ensure critical flow at the entrance to the triangular section

$0\mathrm{.}0051$

$0\mathrm{.}0036$

$0\mathrm{.}0014$

$0\mathrm{.}0029$

$0\mathrm{.}0042$

Q#$1($d$)$: Assuming the same conditions in $1($b$),$ determine the total energy level in the rectangular channel

$1\mathrm{.}70$ m

$1\mathrm{.}83$ m

$1\mathrm{.}61$ m

$2\mathrm{.}41$ m

$1\mathrm{.}96$ m

Q$"1($e$)$: If the total energy from $1($d$)$ is $1\mathrm{.}85$ m $,$ and assuming the same flow and critical depth in $1($b$),$ determine the normal flow depth in the rectangular channel for a channel width of $2$ m under subcritical flow regime

$1\mathrm{.}572$ m

$1\mathrm{.}471$ m

$1\mathrm{.}762$ m

$1\mathrm{.}631$ m

$1\mathrm{.}815$ m