Models & Qualitative Behavior · Challenge problem

A hemispherical bowl of radius $1$ m is full of water, which drains through a small hole at the bottom. At depth $h$ the water surface is a disc of area $\pi(2h - h^2)$, and Torricelli's law gives $\pi(2h - h^2)\,h' = -\dfrac{\pi}{15}\sqrt{h}$ ($t$ in minutes). How many minutes does the bowl take to empty?