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Bernoulli's Principle in Fluid Dynamics

Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure. The principle is named after Daniel Bernoulli who published it in 1738. It can be applied to different types of fluid flow and is derived from the principle of conservation of energy, which states that the total mechanical energy in a fluid remains constant along a streamline. Bernoulli's principle can also be derived from Newton's second law, where a difference in pressure across a small volume of fluid results in a net force accelerating it along the streamline from high to low pressure.

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49 views2 pages

Bernoulli's Principle in Fluid Dynamics

Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure. The principle is named after Daniel Bernoulli who published it in 1738. It can be applied to different types of fluid flow and is derived from the principle of conservation of energy, which states that the total mechanical energy in a fluid remains constant along a streamline. Bernoulli's principle can also be derived from Newton's second law, where a difference in pressure across a small volume of fluid results in a net force accelerating it along the streamline from high to low pressure.

Uploaded by

Raxy Kumar
Copyright
© © All Rights Reserved
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Bernoulli's principle

From Wikipedia, the free encyclopedia

This article is about Bernoulli's principle and Bernoulli's equation in fluid dynamics. For Bernoulli's Theorem
(probability), see Law of large numbers. For an unrelated topic in ordinary differential equations, see Bernoulli
differential equation.

A flow of air into a venturi meter. The kinetic energy increases at the expense of the fluid pressure, as shown by the
difference in height of the two columns of water.

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.[1][2] Bernoulli's
principle is named after the Dutch-Swiss mathematician Daniel Bernoulli who published his principle in his
book Hydrodynamica in 1738.[3]
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 can be derived from 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. Thus an increase
in the speed of the fluid occurs proportionately with an increase in both its dynamic pressure and kinetic
energy, and a decrease in its static pressure and potential energy. 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 volume (the
sum of pressure and gravitational potential g h) is the same everywhere.[4]

Bernoulli's principle can also be derived directly from Newton's 2nd law. If a small volume of fluid is flowing
horizontally from a region of high pressure to a region of low pressure, then there is more pressure behind than
in front. This gives a net force on the volume, accelerating it along the streamline. [5][6]
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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