$(40$ p$)$ The isochrone, run$-$off coefficients, and partial areas for a basin are shown in

the below figure.

a$)$ Calculate the volume $($liter$)$ of direct run$-$off per time $($second$)$ at point $A(Q_A)$ using

the Rational Method for the $25$ th minute $(t=25$min$)$ that will be produced by a rainfall

with a duration of $15$ minutes $(td=15$min$)?$

b$)$ Derive rising and recession curves $($S$-$Curves$)$ and prove your previous result $(Q_A)$

by showing on the outlet hydrograph.

$($Hint: $i_{15}=36m\frac{m}{h}r).$