# Math Help - Find the time required for an inverted conical tank...?

1. ## Find the time required for an inverted conical tank...?

Find the time required for an inverted conical tank of radius $R$ and height $H$ to empty through a round hole of cross sectional area $a$ at the bottom. Given that the water flows according to the formula $V(t) = k\sqrt{2gh(t)}$ where $V(t)$ and $h(t)$ are respectively the velocity of flow through the hole and the height of water level above the hole at time $t$ and $g$ is the acceleration due to gravity.

2. The solution is:

$t = \frac{6 B_0}{5a V_0}$

where $B_0$ is the initial volume and $V_0$ is the initial velocity. I can't be bothered going through all the working as it would take too long to Late $\chi$!