$8\mathrm{.}5\mathrm{.}2$ Using the one$-$hour unit hydrograph given in problem $8\mathrm{.}3\mathrm{.}3,$ develop the $3-$hr unit hydrograph using the S$-$curve method.

$8\mathrm{.}5\mathrm{.}3$ Suppose the $4-$hr unit hydrograph for a watershed is

$\backslash$table$[[$Time $(hr),0,2,4,6,8,10,12,14],[UH(\frac{m^3}{s}\frac{?}{10(mm)}),0,15,45,65,50,25,10,0]]$

$($a$)$ Determine the $2-$hr unit hydrograph.

$($b$)$ From the frequency analysis, the $10-$year $4-$hr storm has a total depth of $3$ cm with an effective rainfall intensity of $1c\frac{m}{h}r$ in the first $2$ hr and $0\mathrm{.}5c\frac{m}{h}r$ in the second $2$ hr $.$ Assuming the baseflow is $10\frac{m^3}{s},$ calc ulate the total runoff hydrograph from the $10-$year $4-$hr storm.