Question $1$: Open Channel Flow $-$ Channel Expansion and the Energy Equation

Water flows in a rectangular open channel without energy loss. The channel width $($B$)$ contracts between two adjacent Sections $1$ and $2,$ resulting in some differences in the flow parameters between the two sections.

$($i$)$ Write the energy equation between the two sections.

$($ii$)$ Draw a typical Specific Energy vs Depth diagram.

Fill in the blank spaces in the following Table $1$ by computing the downstream flow values $($i$.$e$.,$ at Section $2)$ based on the upstream conditions. Show all working.

Table $1$

$[$Hint: $(1)$ The change in depth is less than $5$ cm ; $(2)$ Use the energy equation to solve for $\backslash ($ d $\backslash ),$ using a trial$-$and$-$error solution to a cubic equation in $\backslash ($ d $\backslash )]$

Question $2$: Open Channel Flow $-$ Specific Energy Principles

$($a$)$ A rectangular channel $4$ m wide is conveying water at a depth $\backslash (\backslash$mathrm$\{$d$\}\_\{1\}=1\mathrm{.}55\backslash$mathrm$\{$~m$\}\backslash )$ and at a velocity $\backslash (\backslash$mathrm$\{$V$\}\_\{1\}=\backslash )\backslash (2\mathrm{.}1\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The flow enters a transition region as shown in the figure below, in which the channel bed is raised $0\mathrm{.}2$ m $.$

i$.$ Is the flow at Section $1$ supercritical?

ii$.$ What is the Specific Energy above the raised bed $($i$.$e$.$ at Section $2)?$

iii. What is the Critical Depth?