Water flows in a rectangular channel $($width $3$ m$)$ at $8$ m$^3/$s$.$

$($a$)$ For each of the following depths, calculate the Froude number and determine whether the flow is subcritical or supercritical: y $=0\mathrm{.}3$ m$,1$ m$,$ and $2$ m$.$

$($b$)$ Calculate the critical depth, yc$.$

$($c$)$ Create the E$-$y diagram for this flow in this channel.$$ Create your graph for y $=0\mathrm{.}3$ to $4.$ Show yc on the graph.