Develop a Simulink computer program to simulate food routing through a reservoir described by equations $(1)$ through

$(5)$ The storage capacity of the reservoir above the spllway crest is shown in Figure $1.$ The highest recorded $12-$hour

inflow hydrograph into the reservoir for a $50-$year recurrence interval is shown in Figure $2.$ Assume that the spillway

structure has the articulated design with the following parameters

Orop box inlet has an $90$ foot effective edge $(b=90h)$

$"$ Box inlet has an unobstructed approach $(\{$:$c=3\mathrm{.}0\frac{f^{17}}{sec})$

"The outlet pipe is a $125$ foot long. $30$ inch, circular, concrele pipe $(L=1\mathrm{.}25ft,A=4\mathrm{.}91ft,K=\frac{0\mathrm{.}0107}{f}t$

$"$ The pipe has a square inlet $(K_q=0\mathrm{.}5)$ and a fully exposed outlet $(K_6=1\mathrm{.}0)6\mathrm{.}5$ foot below the spillway crest

$(d=6\mathrm{.}5ft)$

Use your program to compute the discharge and the stage of the reservoir in response to the inflow hydrograph of

Figure $2$ assuming that the pond was just full when the water inflow started. Use your program to examine the following

variations in the design parameters $($assume that the original design will be maintained except for the variation$)$:

A $24$ inch outlet pipe $(A=3\mathrm{.}14f{t}^2,K=0\mathrm{.}0144)$

A $36$ inch outlet pipe $(A=707f{t}^2,K=000839)$

$3$ Pipe outlet is $5$ foot below crest.

Pipe outlet is $8$ foot below crest

Discuss your program and your results.

Pipe size, inches

$24$

$30$

$36$

Include in your report:

A title page.

This handout.

Simulink block diagram.

Report the integration method and time interval $($if fixed$)$ that you used in your simulation.

The output of your program equivalent to Figures $1$&$2$

Include a table showing the gains on blocks that must be varied for each of the five cases in part $7b.$

At least the following three graphs:

a$.$ for $d=6\mathrm{.}5ft,$ diameter $={30}^{**}$; inflow $i,$ stage $h,$ and discharge $q$ as a function of time $($hrs$)(1$ graph$)$

b$.$ inflow hydrograph and discharge vs time for the variations $(6$ lines, $1$ graph$)$:

$d=6\mathrm{.}5ft$;$24$ and ${36}^{\text{'}\text{'}}$ pipes

$30$ pipe; $d=5\mathrm{.}0,6\mathrm{.}5$ and $8ft$

c$.$ stage vs time for variations in $($b$)(5$ lines, $1$ graph$)$

Discussion of results of the simulation as reported in #$7$

Describe how the time base was changed from seconds to hours in your program including the calculation with units

List the assumptions which led to equation $1($discussion requested in first paragraph on page $1)$

Include the discussion requested at the bottom of page $1.$