A stream passes through a $200-$ac Land parcel with three rain guages

The following inflow hydrograph is given for a reservoir that has a weir$-$spillway outflow

structure.

The flow through the spillway is governed by the equation

$Q=3\mathrm{.}75L{y}^{\frac{3}{2}}(cfs)$

where $L$ is the length of the weir and $y$ is the height of the water above the spillway

crest. The storage in the reservoir is governed by the equation

$S=3600y(cfs-hr)$

$($a$)$ Using $t=12hr,L=15ft,$ and $y_0=0,$ route the inflow hydrograph through

the reservoir using the level$-$pool method. Continue the routing procedure until

$t=228hr$ to capture the recession limb$.$ Plot the inflow and outflow hydrographs

on the same graph for comparison.

$($b$)$ Determine the percent reduction in peak discharge due to the reservoir.