# Time to Drain a Tank Using Torricelli's Law

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Liquid flows out of a tank at a rate given by Toricelli's law, , where * *is the volume and the height of the water in the tank (both functions of time), is the radius of the tank, * *is the radius of the hole in the bottom of the tank, = 9.81 , the acceleration due to gravity, and is the time. The volume is given by and the solution of the differential equation gives . Thus the length of time required to drain the tank, so that , is given by seconds.

Contributed by: Ed O'Grady (November 2010)

Based on a program by: Ernest Lee

Open content licensed under CC BY-NC-SA

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In the graphic, the radius of the spigot is increased tenfold.

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