Drainage of a Hemispherical Tank

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A full hemispherical tank of radius drains under the influence of gravity from a circular hole of radius
at the bottom of the tank. The velocity of fluid flowing from the hole is
(Torricelli's law), where
is the gravitational acceleration and
is the height of water at time
, which is shown in the tank and plotted below.
Contributed by: Enrique Zeleny (December 2012)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The differential equation for the depth of fluid at time
is
.
Integrating and finding the constant yields
.
The time that it takes for the tank to empty is
.
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