Problem $3$: $($Chapter $9)$: A partial inflow hydrograph to a reservoir is given below. Route this hydrograph through the reservoir to a time of $8$ hours using a time step of $1$ hr $.$ At $t=0,$ the storage in the reservoir is $40-cfs-hr,$ and the reservoir has the following storage$-$outflow characteristics:

$Q=\{\begin{array}{c}0\mathrm{.}25(\frac{2S}{t}+Q-100)cdots\frac{2S}{t}+Q>100\\ 0\text{c}\text{d}\text{o}\text{t}\text{s}& \frac{2S}{t}+Q100\end{array}$

where S is in cfs$-$hr$,t$ is in hours, and Q is in cfs$.$

a$)$ Determine the initial outflow $(3\text{'})$:

b$)$ Fill the table below to determine the outflow hydrograph. Please provide the computation for $t=1$ and $2(32\text{'})$

$\backslash$table$[[\backslash$table$[[$Time$],[($hour$)]],\backslash$table$[[$Inflow$],[(cfs)$