$($b$)$ Further down the watercourse, an engineer is commissioned to manage flooding. They propose a simple compound channel, in place of the existing floodplain and channels, see sketch Figure Q$1$b$.$ This channel section slopes at a $1\mathrm{.}5$ m elevation drop every $1$ km $.$ Channel side slope ratios are shown y:x$.$

$($iii$)$ Determine the maximum flow rate that could be conveyed in this compound channel.

$($iv$)$ Discuss the accuracy of the discharge estimate from Q$1$b$($i$).$ Where else within the engineer's design calculations could there be uncertainty; why does this arise, and what could be done to improve the accuracy of these calculations?