Problem $1$:

Route the inflow hydrograph given below through a reservoir up to $5\mathrm{.}7$ hours. The pool level is at $68\mathrm{.}9$ ft initially. The elevation of the crest of the spillway is $68\mathrm{.}7$ ft $.$ The flow over the spillway $($cfs$)$ is given by $\backslash (4\mathrm{.}8$ L$^\{3/2\}\backslash ).$ The length of the spillway is $98$ ft $.$ 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 $\backslash (($E$)\backslash ),$ i$.$e$.,\backslash ($ H$=$E $\backslash )-$Spillway Crest elevation. Storage versus elevation and $\backslash ($ E $\backslash )$ versus $\backslash (2$ S $/\backslash$Delta t$+$O $\backslash )$ equations must be determined based on the data given and outflow equation, where $\backslash (\backslash$Delta t $\backslash )$ 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.