Problem#$3$:

Collecting rainwater is emerging as a source of freshwater at different regions worldwide. For this problem an area in the shape of a wedge of a circle is considered. All of rainwater goes to the outlet where an underground tank is installed.

Derive an expression for $h(t)=\frac{dA}{dt}$ where $A$ is the area of wedge $($here you may consider it as the watershed's area$),t$ is time. Since basin is small, it is acceptable to assume that $t_c=\frac{R}{v}$ where $v$ is the velocity of water between the upper boundary and basin and outlet. Similarly, you may assume time $t=\frac{r}{v}$ where $0rR$ is the travel time from any location to the outlet. To solve this, estimate first the time of concentration $t_c.$ Then, determine the cumulative area $($as a function of time$)A(t),$ that is being drained. Once you determine $A(t),$ find $h(t).$ Hint: Area of the wedge $=\frac{R^{2}45}{360}$