Question: Depth$-$averaged velocity observations from a Red River cross$-$section are given

below. Here, x is the distance from the left bank $($m$),$ U is the depth$-$averaged velocity $($m$/$s$),$

and H is the flow depth $($m$).$

x $=[0,5,10,15,20,25,30,35,40]$

U $=[0,0\mathrm{.}10,0\mathrm{.}14,0\mathrm{.}20,0\mathrm{.}18,0\mathrm{.}14,0\mathrm{.}11,0\mathrm{.}07,0]$

H $=[0,-1\mathrm{.}1,-1\mathrm{.}9,-3\mathrm{.}5,-3\mathrm{.}3,-2\mathrm{.}5,-2,-1\mathrm{.}5,0]$;

Step $1$: Plot the shape of the measured cross$-$section.

Step $2$: Interpolate $($spline$)$ the measured data for a

smoother cross$-$section using $0\mathrm{.}01$ increment.

Step $3$: Include the interpolated cross$-$section in the

plot.

Step $4$: Follow the same steps for the lateral velocity

distribution. Please note that you need to label your

figures as follows if you need to publish multiple figures

from the same script:

figure$(1)$

plot$(....$

figure$(2)$

plot$(....$

Step $5$: Perform a basic fit analysis to find the best equation of the interpolated velocity curve.

Use only linear, cubic, and quadratic options. After you make the choice based on R$2$

$,$ please

plot that equation versus the interpolated velocity curve as the third plot.

Step $6$: Calculate the average velocity $($V$)$ for the cross$-$section. Please use interpolated U to

calculate the mean value.

Step $7$: Write an interactive section for the parameters V in your script to calculate the

Gauckler$-$Manning coefficient $($n$)$ using the following equation.

$=$

$1$

$$

$$

$2312$

Here:

V : cross$-$sectional averaged velocity $($m$/$s$)$

n : Gauckler$-$Manning coefficient

Rh : hydraulic radius $($Rh $=2$m$)$

S : channel bed slope $($S $=0\mathrm{.}00004)$

Step $8$: First, use the calculated V as the input and compute n$.$ Then double the V and re$-$

compute n$.$ Finally, make a short comment based on the difference. The most important

outcome of this test is to understand how n changes based on V$.$

Show Matlab script of solution.