QUESTION $\backslash (4[30]\backslash )$

$4\mathrm{.}1$ The normal depth of flow in trapezoidal concrete lined channel is $2$ m $.$ The channel base width is $5$ m and it has side slopes of $1$:$2.$ Manning's n is $0\mathrm{.}015$ and the bed slope is $0\mathrm{.}001.$ Determine:

i$.$ Discharge

ii$.$ Mean velocity

iii. Reynolds number

$4\mathrm{.}2$ A long rectangular channel of width $5$ m has a slope of $1$:$5000$ and a Manning's roughness coefficient $\backslash ($ n $\backslash )$ of $0\mathrm{.}02.$ The total discharge is $\backslash (10\backslash$mathrm$\{$~m$\}^\{3\}\backslash$mathrm$\{$~s$\}^\{-1\}\backslash ).$ The channel narrows to a width of $1\mathrm{.}2$ m over a short length.

$($i$)$ Determine the normal depth at this flow rate in the $5$ m $-$wide channels.

$($ii$)$ Show that critical conditions occur at the narrow section.

$($iii$)$ Determine the depth just upstream of the narrowed section, where the width is $5$ m

$4\mathrm{.}3$ A long channel $1\mathrm{.}5$ m wide terminates in a full$-$width rectangular weir whose crest height is $300$ mm above the stream bed. If the measuring station is recording a depth of $400$ mm above the weir crest, estimate the discharge.

$($i$)$ Assuming a flow with a negligible velocity of approach $($take $\backslash ($ C$\_\{$d$\}\backslash )$ as $0\mathrm{.}7)$

$($ii$)$ Including velocity of approach $($taking the Coriolis coefficient, $\backslash (\backslash$alpha $\backslash ),$ as $1\mathrm{.}1$ and $\backslash ($ C$\_\{$d$\}\backslash )$ as $0\mathrm{.}7)$