Find the time required for a cylindrical tank of radius $r$ and height $H$ to empty through a round hole of area $a$ at the bottom. The flow through the hole is according to the law $v\left(t\right)=k\sqrt{2gh\left(t\right)}$ , where $v\left(t\right)$ and $h\left(t\right)$ , are respectively, the velocity of flow through the hole and the height of the water level above the hole at time $t,$ and $g$ is the acceleration due to gravity.

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