A conical funnel of half-angle \(\theta=30^{\circ}\) drains through a small hole of diameter \(d=6.25 \mathrm{~mm}\). at the vertex. The speed of the liquid leaving the funnel is \(V=\sqrt{2 g y}\), where \(y\) is the height of the liquid free surface above the hole. The funnel initially is filled to height \(y_{0}=300 \mathrm{~mm}\). Obtain an expression for the time, \(t\), for the funnel to completely drain, and evaluate. Find the time to drain from \(300 \mathrm{~mm}\) to \(150 \mathrm{~mm}\) (a change in depth of \(150 \mathrm{~mm}\) ), and from \(150 \mathrm{~mm}\) to completely empty (also a change in depth of \(150 \mathrm{~mm}\) ). Can you explain the discrepancy in these times? Plot the drain time \(t\) as a function diameter \(d\) for \(d\) ranging from \(6.25 \mathrm{~mm}\) to \(12.5 \mathrm{~mm}\).