Models & Qualitative Behavior · Hard problem

A conical funnel, vertex down, drains through a small hole at the vertex. By Torricelli's law its water depth $h$ (in cm) satisfies $h' = -\dfrac{k}{h^{3/2}}$ for a constant $k > 0$. The depth is $4$ cm at $t = 0$ and $1$ cm at $t = 31$ seconds. At what time (in seconds) is the funnel empty?