Problem $1$:

Route the inflow hydrograph given below through a reservoir up to $6\mathrm{.}6$ hours. The pool level is at $69\mathrm{.}7ft$ initially. The elevation of the crest of the spillway is $69\mathrm{.}5ft.$ The flow over the spillway $($cfs$)$ is given by $4\mathrm{.}5L{H}^{\frac{3}{2}}.$ The length of the spillway is $95ft.$ The storage versus elevation data for the reservoir is given below. $[10]$

Hint: The outflow equation is given as flow over spillway. The $H$ in the equation must be converted to water surface level $(E),$ i$.$e$.,H=E-$Spillway Crest elevation. Storage versus elevation and $E$ versus $2\frac{S}{}t+O$ equations must be determined based on the data given and outflow equation, where $t$ is the time interval of the inflow hydrograph, as discussed in the lecture. The next time is to perform routing following the procedure outlined in the class problem.

$\backslash$table$[[$Time $($Hours$),$Q $($cfs$)],[0\mathrm{.}0,120],[0\mathrm{.}3,350],[0\mathrm{.}6,470],[0\mathrm{.}9,690],[1\mathrm{.}2,950],[1\mathrm{.}5,1320],[1\mathrm{.}8,1900],[2\mathrm{.}1,1780],[2\mathrm{.}4,1530],[2\mathrm{.}7,1220],[3\mathrm{.}0,950],[3\mathrm{.}3,640],[3\mathrm{.}6,305],[3\mathrm{.}9,210],[4\mathrm{.}2,130],[4\mathrm{.}5,100]]$

$\backslash$table$[[$Elevation $($ft$),$Storage $($acre$-$ft$)],[68,296\mathrm{.}00],[69,335\mathrm{.}88],[70,381\mathrm{.}32],[71,423\mathrm{.}69],[72,470\mathrm{.}07],[73,522\mathrm{.}23],[,],[,],[,],[,],[,],[,],[,],[,]]$