A conical funnel is full of liquid. The diameter of the top (mouth) is $D_{1}$, and that of the bottom (spout) is $D_{2}$ (where $D_{2} \ll D_{1}$ ), and the depth of the fluid above the bottom is $H_{o}$. Derive an expression for the time required for the fluid to drain by gravity to a level of $H_{o} / 2$, assuming frictionless flow.