$($a$)$ Convert the direct runoff hydrograph shown in Figure into a $2$hr UH$.$ Note the duration of net rainfall is $2$ hrs$.$ The total rainfall hyetograph is given in figure and the $-$index for the storm was $0\mathrm{.}5$ in$/$hr$.$ The base flow in the channel was $100$ cfs $($constant$).$ What are Tp and Tb for the storm.

$($b$)$ From the above $2$HR UH$,$ Derive $3$HR UH by first identifying S$-$

Hydrograph.

$($c$)$ From the above S$-$Hydrograph, Derive $5$HR UH$.$

$($d$)$ From the above $3$HR UH and $5$HR UH derive S$-$Hydrograph and check if they are the same as earlier S$-$Hydrograph.

$($e$)$ From the above $2$HR UH$,$ Derive $7$ HR UH and $9$HR UH

$($f$)$ Derive S$-$Hydrographs from K Hr UH $($where K $=2,3,5,7,9).$ Multiply each S$-$Hydrograph with correspoding K$.$ What do you notice? Explain in simple words.It has $2$ one hour Rainfall excess. So the

$UH$ is UH for $2$ hour duration. Total RFE depth is $2$ inches. So

divide the Rainfall

excess is