13. A hemispherical tank of radius 2 metres is initially full of water and has an outlet of 12 cm 2 cross sectional are at the bottom. The outlet is opened at some instant. The flow through the outlet is according to the law $\mathrm { v } ( \mathrm { t } ) = 0.6 \sqrt { } ( 2 \mathrm { gh } ( \mathrm { t } ) )$, where $\mathrm { v } ( \mathrm { t } )$ and $\mathrm { h } ( \mathrm { t } )$ are respectively the velocity of the flow through the outlet and the height of water level above the outlet at time $t$, and $g$ is the acceleration due to gravity. Find the time it takes to empty the tank. (Hint : Form a differential equation by relating the decrease of water level to the outflow).
13. A hemispherical tank of radius 2 metres is initially full of water and has an outlet of 12 cm 2 cross sectional are at the bottom. The outlet is opened at some instant.
The flow through the outlet is according to the law $\mathrm { v } ( \mathrm { t } ) = 0.6 \sqrt { } ( 2 \mathrm { gh } ( \mathrm { t } ) )$, where $\mathrm { v } ( \mathrm { t } )$ and $\mathrm { h } ( \mathrm { t } )$ are respectively the velocity of the flow through the outlet and the height of water level above the outlet at time $t$, and $g$ is the acceleration due to gravity. Find the time it takes to empty the tank.\\
(Hint : Form a differential equation by relating the decrease of water level to the outflow).\\