Consider a $12$m long, $0\mathrm{.}5$m wide rectangular channel with a longitudinal slope of $0\mathrm{.}028.$ There are two gates in the channel, one at $7$m$($x$=7$m$)$from the inlet and the other at $12$m$($x$=12$m$)$from the inlet. The gate openings are $0\mathrm{.}04$m and $0\mathrm{.}04$m$,$ respectively. The flow depth just upstream of the gates are $0\mathrm{.}21$m and $0\mathrm{.}225$m$,$ respectively. The flow depths at x$=0$m and x$=7\mathrm{.}01$m are $0\mathrm{.}04$m and $0\mathrm{.}03$m$,$ respectively. For a flowrate of $30$ lit$/$sec and Manning's n$=0\mathrm{.}008,$

$($i$)$ identify the number of flow regimes in the channel

$($ii$)$ calculate flow depths along the channel,$$

$($iii$)$ plot the flow profiles in the channel and$$

$($iv$)$ find the location of hydraulic jumps$$

$($v$)$ on the same graph, plot the experimental measurements provided in the measurements.txt file below and provide your observations on the comparison with your calculated flow depths.$$

$[$Hint: Identify the flow regimes in the channel and their control sections. Once you identify the control sections, calculate the GVF and plot it with x on the x$-$axis and depth on the y$-$axis. This graph should have x ranging from x$=0$m to $12$m$.$ For reference, you may watch the video below.$]$