a$)$ Given below are observed flows from a storm of $6-$hour duration on a stream with a catchment area of $500$ km $2.$

$\backslash$table$[[$Time $(hr),0,6,12,18,24,30,36,42,48,54,60,66,72],[$Flow $(\frac{m^3}{s}),20,120,270,220,170,120,90,70,55,45,35,25,20]]$

Assuming a constant base flow of $20\frac{m^3}{s},$ derive the ordinates of a $6-$hour unit hydrograph.

b$)$ The ordinates of a $3-$hour unit hydrograph of a basin at a $6-$hour interval are given below $0,3,5,9,11,7,5,4,2,1,0$ cumees. Derive the storm hydrograph due to a $3-$hour storm with a total rainfall of $15$ cm $.$ Assume an initial loss of $0\mathrm{.}5$ cm and $-$ index of $1c\frac{m}{h}r.$ Take base flow $=4$ cumecs.