| Bernoulli's equation is one of the cornerstones of classical fluid
mechanics. The equation describes the relationship between kinetic
energy, pressure and potential energy in an inviscid fluid (ideal fluid). This
requires an fluid in which there is no internal friction, and thus no
conversion of mechanical energy to heat.
The equation was derived by Daniel Bernoulli, who investigated the
forces present in a moving fluid:
P + ½ ρ v2 + ρ g h = constant
where P is pressure, ρ is the fluid density, v is the
velocity, h is elevation, and g is the gravitational acceleration.
The equation is only valid under the following conditions:
Despite these seemingly severe restrictions, Bernoulli's equation is
used very commonly, since it gives a good insight in the interconversion
between pressure (P), kinetic energy (½ρv2), and
potential energy (ρgh). For many applications, the equation gives
a good quantitative estimate, or a qualitative argument for its
behavior.
It is easy to see that the Bernoulli effect (an increase in fluid velocity results in a
drop in total pressure) follows directly from Bernoulli's Equation.
Another effect is directly related to this is the Magnus effect (as
described nicely by bigmouth_strikes).
Some other applications:
- Airfoil calculations: The aerodynamic forces on wings (lift and
drag) can be described using Bernoulli's equation.
- Pitot tube: This device measures the difference between static
and dynamic pressure in a fluid. It can be used to calculate fluid
velocities; e.g.airplanes are fitted with these devices to
measure air speed.
- General flow phenomena: pressure drop of flow through
orifices, free falling liquid flow (explains why the flow
from a tap contracts and accelerates as it falls), flow from open or
pressurized containers.
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