PROBLEM $1$

Given the following $6-$hr unit hydrograph $(1-cm$ of rainfall excess$)$ for a catchment

$($a$)$ calculate the ordinates of the direct unit hydrograph due to a rainfall excess of $4$ cm occurring in $6$ hrs

$($b$)$ calculate the runoff hydrograph for two storms of $6-$hr duration each that occur successively, having rainfall excess values of $3\mathrm{.}0$ and $1\mathrm{.}5$ cm $,$ respectively.

$[[$Time $($hr$),0,3,6,9,12,15,18,21,24,27,30,33,36],[$Unit hydrograph $(\frac{m^3}{s}),0,7,22,30,45,48,36,30,20,8,6,2,0]]$