In fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs
simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. Bernoulli's principle is named
after the Dutch–Swiss mathematician Daniel Bernoulli who published his principle in his book Hydrodynamica in 1738.
It is most commonly associates with how an airplane can fly. As the engine of the airplane (jet or prop) generates thrust,
the airplane begins to move forward. As it moves air begins to move fast over the top of the wings surface. Bernoulli's
principle states the faster a fluid (air in this case) moves over the wing, the lower the pressure on that surface. So as air
moves faster over the wings, the pressure on the tops of the wings is decreased. At the same time air is not moving as
fast on the underside or bottom of the wing as on the top. Air in the atmosphere is also not moving as fast. This means
the air pressure under and outside the wing is greater or more than the pressure of the fast moving air on top of the
wing. Air pressure is about 15 pounds per square inch normally. So the faster moving air on the wing-top is less than the
surrounding air pressure of 15 pounds per square inch. As a result lift is created and the airplane is pushed up by the air
with more pressure.
Bernoulli's principle can be applied to various types of fluid flow, resulting in what is loosely denoted as Bernoulli's
equation. In fact, there are different forms of the Bernoulli equation for different types of flow. The simple form of
Bernoulli's principle is valid for incompressible flows (e.g. most liquid flows) and also for compressible flows (e.g.
gases) moving at low Mach numbers. More advanced forms may in some cases be applied to compressible flows at
higher Mach numbers (see the derivations of the Bernoulli equation).
Bernoulli's principle is equivalent to the principle of conservation of energy. This states that in a steady flow the sum of all
forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that
the sum of kinetic energy and potential energy remain constant. If the fluid is flowing out of a reservoir the sum of all
forms of energy is the same on all streamlines because in a reservoir the energy per unit mass (the sum of pressure
and gravitational potential ρgh) is the same everywhere.
Fluid particles are subject only to pressure and their own weight. If a fluid is flowing horizontally and along a section of a
streamline, where the speed increases it can only be because the fluid on that section has moved from a region of
higher pressure to a region of lower pressure; and if its speed decreases, it can only be because it has moved from a
region of lower pressure to a region of higher pressure. Consequently, within a fluid flowing horizontally, the highest
speed occurs where the pressure is lowest, and the lowest speed occurs where the pressure is highest.
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