Bernoulli's equation is one of the cornerstones of classical fluid
. The equation describes the relationship between kinetic
and potential energy
in an inviscid fluid
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
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