Torricelli's Law for Tank Draining
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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.
Contributed by: Stephen Wilkerson and Mark Evans (Towson University) (March 2009)
Open content licensed under CC BY-NC-SA
Snapshots
Details
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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