Torricelli's theorem
Torricelli's law, also known as Torricelli's theorem, is a theorem in fluid dynamics relating the speed of fluid flowing from a hole to the height of fluid above the hole.
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Commentary
Torricelli's theorem
Torricelli's law, also known as Torricelli's theorem, is a theorem in fluid dynamics relating the speed of fluid flowing from a hole to the height of fluid above the hole.
Why does Torricelli's theorem matter?
This principle is one of the building blocks physicists use to explain the world. Without it, a whole class of phenomena would have no mathematical description. Engineers, chemists, and astronomers all rely on it.
v
=
2
g
h
{\displaystyle v={\sqrt {2gh}}}
Background: Torricelli's theorem
Torricelli's law, also known as Torricelli's theorem, is a theorem in fluid dynamics relating the speed of fluid flowing from a hole to the height of fluid above the hole. The law states that the speed
v
{\displaystyle v}
of efflux of a fluid through a sharp-edged hole in the wall of the tank filled to a height
h
{\displaystyle h}
above the hole is the same as the speed that a body would acquire in falling freely from a height
h
{\displaystyle h}
,
v
=
2
g
h
{\displaystyle v={\sqrt {2gh}}}
where
g
{\displaystyle g}
is the acceleration due to gravity. This expression comes from equating the kinetic energy gained,
1
2
m
v
2
{\displaystyle {\tfrac {1}{2}}mv^{2}}
, with the potential energy lost,
m
g
h
{\displaystyle mgh}
, and solving for
v
.
{\displaystyle v.}
The law was discovered (though not in this form) by the Italian scientist Evangelista Torricelli, in 1643. It was later shown to be a particular case of Bernoulli's principle.
Sources: Wikipedia
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