Suppose that a tank containing a certain liquid has an outlet near the bottom. Let $h(t)$ be the height of the liquid surface above the outlet at time $t$. Torricelli's principle states that the outflow velocity $v$ at the outlet is equal to the velocity of a particle falling freely (with no drag) from the height $h$.
Consider a water tank in the form of a right circular cylinder that is $3 \mathrm{~m}$ high above the outlet. The radius of the tank is $1 \mathrm{~m}$ and the radius of the circular outlet is $0.1 \mathrm{~m}$. If the tank is initially full of water, determine how long it takes to drain the tank down to the level of the outlet.
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