For a $2$ hour, $8\frac{mm}{h}$ intensity rainfall, the hydrograph given in Table is observed. The area of watershed is $500k{m}^2$

Table: Propeller readings

$\backslash$table$[[$Time$,0,2,4,6,8,10,12,14,16,18,20,22,24],[\backslash$table$[[$flow rate$(m^3/$s$),8+$y$,14+$y$,18+$y$,30+$y$,45+$y$,38+$y$,28+$y$,24+$y$,18+$y$,14+$y$,10+$y$,8+$y$,8+$y$]]$

y$=7$

a$)$Obtain $2$ hour unit$-$hydrograph for the considered flow section.

b$)$Obtain $4$hour unit$-$hydrograph for the considered flow section.

c$)$Obtain the hydrograph of a rainfall with $4$ hour duration and $10\frac{mm}{h}.$