All problems will be based on the figure seen below, along with supplemental information to be provided in each problem statement. Please show all work neatly on separate paper, including any preparatory work for inputs to be used in software$-$based polonintione no moutiol neadit move ha menntad

Question $4(4$ points$)$

If the channel in Question #$2$ is a spillway from the top of a reservoir, determine the depth of water at its entrance for the flow from Question $1,$ as well as $3$ other flows.

All problems will be based on the figure seen below, along with supplemental information to be provided in each problem statement. Please show all work neatly on separate paper, including any preparatory work for inputs to be used in software$-$based calculations as nartial credit mav he oranted

Question $1(5$ points$)$

Assuming the conduit in the figure is a $42"$ wrought iron pipe flowing full, and if we move the outlet to point $A$ :

a$)$ calculate the head loss in the flow by the time it reaches point $A.$

b$)$ calculate the velocity and flow in the pipe at point $A,$ considering friction.

Question $2(8$ points$)$

Assuming the conduit in the figure is a trapezoidal good concrete$-$lined excavated rock open channel with bottom width of $9\text{'}$ and side slopes of $3\mathrm{.}25\text{'}$ horizontal to $2\text{'}$ vertical, and that the flow carried must be the same as in Question $1$:

a$)$ Determine the critical depth of the flow.

b$)$ Determine the normal depth of flow based on Manning's equation.

c$)$ If we place a $50V-$notch weir at the right side of the reservoir, with the bottom of the notch ${26\mathrm{.}5}^{\text{'}}$ above the invert, what will be the discharge over the weir?

d$)$ Determine the size and character of the hydraulic jump occurring at the entrance to the conduit. $($Assume the initial depth is the depth emerging from the reservoir.$)$

Question $3(7$ points$)$

For the reservoir at the top of the figure $($assuming it is $125$ feet long by $35$ feet wide$)$:

a$)$ Determine, via the Rational Method, whether the reservoir, if empty, will reach the elevation shown during a $50-$year storm in Louisville, KY$,$ based on the following characteristics of a drainage area flowing into it:

a$.$ Cover based on Belmill soil, of which:

i$.7$ acres are open space with $80\%$ grass cover

ii$.10$ acres are untreated cultivated land

iii. $3$ acres are paved

iv$.2$ acres consists of dirt road

b$.$ Time of concentration based on:

i$.$ Overland flow for $100$ feet from Elev. ${628}^{\text{'}}$ to Elev. ${624}^{\text{'}},$ with dense grass cover

ii$.$ Shallow concentrated flow for $1000$ feet $($unpaved$)$ to Elev. $554\text{'}$

iii. Stream flow via the channel in Question #$2$ carrying to a depth of $3\mathrm{.}5$ feet for $2200$ feet to the top of the reservoir

Question $4(4$ points$)$

If the channel in Question #$2$ is a spillway from the top of a reservoir, determine the depth of water at its entrance for the flow from Question $1,$ as well as $3$ other flows.