Problem $2$:

Given the inflow and outflow hydrographs at the upstream and downstream ends of a river reach, determine the Muskingum routing constants. $[10]$

Hint: This problem can be easily solved in excel. Assume $x$ value and determine $\frac{?}{xI}+(1-x)O$ and cumulative $S$ values as shown in class. Plot cumulative $S$ versus $\frac{?}{xI}+(1-x)O$ for different values of $x$ till you get a straight line. Fit a straight$-$line equation to find the slope of the line.

$\backslash$table$[[\backslash$table$[[$Time$],[($Hours$)]],\backslash$table$[[$Inflow$],[($cfs$)]],\backslash$table$[[$outflow$],[($cfs$)]]],[6\mathrm{.}00,0\mathrm{.}00,0\mathrm{.}00],[12\mathrm{.}00,75\mathrm{.}50,32\mathrm{.}80],[18\mathrm{.}00,174\mathrm{.}00,69\mathrm{.}30],[24\mathrm{.}00,128\mathrm{.}00,111\mathrm{.}80],[6\mathrm{.}00,100\mathrm{.}50,114\mathrm{.}30],[12\mathrm{.}00,79\mathrm{.}50,106\mathrm{.}30],[18\mathrm{.}00,55\mathrm{.}50,89\mathrm{.}20],[24\mathrm{.}00,25\mathrm{.}00,68\mathrm{.}30],[6\mathrm{.}00,25\mathrm{.}00,47\mathrm{.}50],[12\mathrm{.}00,25\mathrm{.}00,38\mathrm{.}70],[18\mathrm{.}00,25\mathrm{.}00,30\mathrm{.}80],[24\mathrm{.}00,25\mathrm{.}00,25\mathrm{.}70]]$