#$4)$ The velocity in a $2\mathrm{.}5-ft$ wide rectangular open channel is defined by the equation: $v=y^{1\mathrm{.}7}$

where $v$ is the velocity in $f\frac{t}{s}$ and $y$ is the depth $($in $ft)$ measured from the bottom of the channel

a$.$ The depth of water in the channel is $3\mathrm{.}0ft.$ Plot the velocity profile over the depth $($depth

on the y$-$axis$).$ Remember that plots are not sketches, and need to be plotted to scale,

with axes properly labeled. If you use Excel, remember to print a copy of your plot, but

also submit your spreadsheet to Moodle. Don't forget to name your files correctly.

b$.$ Draw a cross$-$section of the rectangular channel showing width and depth. To integrate

the area, you need to create an incremental small area, $dA,$ to integrate. If you are going

to integrate over the depth axis, draw an appropriate $\text{'}$dA$\text{'}$ section on the cross$-$section and

label it$.$ Based on this figure, write an equation to define the area of the $\text{'}dA\text{'}$ term.

c$.$ Based on the given velocity equation and your $dA$ term, integrate the flow equation to

determine the flow rate.

$Q={\displaystyle \underset{A}{\overset{\phantom{}}{}}}v*dA$

d$.$ What is the mean velocity for the cross$-$section? What depth has this velocity?