9769

Torricelli's Law for Tank Draining

A liquid flows out of the bottom of a funnel. By Torricelli's law, the velocity of the liquid at the outlet is , where is the acceleration due to gravity and is the depth of the liquid. The flow is then , where is the volume and is the radius of the drain.

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The differential equation for , the depth of the water (in feet), is , where the empirical constant can be set to compensate for viscosity and turbulence, is the drain radius (inches), is the initial height of the water, and is the radius of the top of the cone.
The final time is .
The volume of the cone is , where is the height of the cone, and = for this Demonstration.
The volume of the tank is , where is the radius of the tank and is its height.
At any time the height of the water in the drain tank can be found by: .
The volume of the drain tank is exactly the same as the cone when it is filled to the top.
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