A $6-$m$-$wide roctangular channel has a velocity of $4\frac{m}{s}$ and flow depth of $4$ m $.20$ points

$($a$)$ Determine the maximum value of $z$ that would not affect the upstream flow condition i$.$e$.,$

the incipient condition for choking.

$($b$)$ Determine $y_i^{\text{'}}$ i$.$e$.$ water depth upstream of the transition id $z=0\mathrm{.}54m.$

$($c$)$ Plot the specific energy diagram and show $y_1$ and $y_i$ on the specific energy diagram. Use

spreadsheet for plotting.