# Bernoulli’s principle

The Bernoulli principle , equation Bernoulli or Trinomio Bernoulli as it is also known can be regarded as a statement on the principle of conservation of energy for fluid flow. The qualitative behavior often labeled with the term “Bernoulli effect” is the decrease of the pressure of the fluid in the regions where the velocity of the flow increases. This decrease in pressure consists of a narrowing of the trajectoryof flow that may seem contradictory, but not so much when pressure is considered as energy density .

## What is the Bernoulli principle?

The Bernoulli principle is an equation that describes how to behave having a fluid that moves along a power line and tells us that in an ideal fluid the energy remains constant in its path .

• What is Bernoulli’s principle?
• Who proposed it
• History
• Statement
• Characteristics of Bernoulli’s principle
• Formula
• Explanation
• Applications of Bernoulli’s principle
• Experiments
• Examples
• Conclution

## What is Bernoulli’s principle?

The Bernoulli principle is the direct application of the principle that talks about the energy conservation which tells us that if the fluid does not exchange energy with the outside , then must remain constant . Take into account the only three types of energy that a fluid has and that can change from one point to another at the time of conduction . These types are kinetic energy , gravitational potential energy, and hydrostatic energy .

## Who proposed it

Bernoulli’s principle was proposed by Daniel Bernoulli in 1726 in his work called Hydrodynamics .

## History

The history of the principle of Bernoulli originates in the year 1598 when Benedetto Castelli refuted the way of measuring the flow in rivers by Giovanni Fontana , because according to the speed one had to take into account. In 1625, Castelli established the equation that bears his name (Q = AV). Galileo Galilei proposed that bodies experience a uniform acceleration when falling into a vacuum. Isaac Newton said that water has an effective fall inside a tank and finally Daniel Bernoulli was in charge of explaining and clarifying the enigma of the double column, giving rise to its principle.

## Statement

Bernoulli’s principle establishes the following: “within a horizontal flow of fluid, the points of higher velocity of the fluid will have lower pressure than those of lower velocity “ .

## Characteristics of Bernoulli’s principle

The main characteristics of Bernoulli’s principle are the following:

• Each of the terms in the equation of this principle have units of length and represent different forms of energy.
• It can be seen as a form of the law of conservation of energy.
• It allows to explain phenomena related to the acceleration of fluids .
• The equation is applied in fluid dynamics .
• One of its direct consequences is known as the Bernoulli effect .

## Formula

The formula for Bernoulli’s principle is as follows:

1 + (1/2) ρv 2 + ρgh 1 = P 2 + (1/2) ρv 2 + ρgh 2

Formula in which the variables P 1 , v 1 , h 1 , refer to the pressure , the velocity and the height of the fluid respectively. The variables P 2 , v 2 h 2 refer to the pressure, the speed and the height of the point w.  To apply the equation, the following assumptions must be made:

• Viscosity (internal friction) = 0 That is, the current line on which it is applied is considered to be located in a non-viscous place in the fluid.
• Constant flow
• Incompressible fluid – ρ is constant

## Explanation

Bernoulli’s principle tells us that for an ideal fluid along a conduit that is closed, the energy remains constant . Describe then, the way to behave that can have a liquid that is at rest and that moves along a stream of water. The principle explains that in a regime of circulation of a fluid in a closed conduit , the energy that this fluid has remains constantly throughout its path.

## Applications of Bernoulli’s principle

Some of the applications of this principle are as follows:

• The chimneys are built high to take advantage of the fact that the wind speed is more constant and higher at higher altitudes. The higher the speed of the wind over the mouth of a chimney, the lower the pressure will be and the difference in pressure will be greater between the base and the mouth of the chimney, so the combustion gases will be better extracted.
• When we decrease the cross – sectional area of a pipe to increase the velocity of the fluid passing through it, the pressure will decrease.
• When the hands of the swimmer cut water generating a lower pressure and higher propulsion .
• In a carburetor of car , the air pressure in the body decreases when the carburetor passes through a throttle . When the pressure decreases then the gasoline flows , vaporizes and mixes with the air stream.
• In oxygen therapy , most delivery systems use Venturi devices , which are based on Bernoulli’s principle.

## Experiments

There are several experiments that can be performed to prove Bernoulli’s principle, some of them are as follows:

• When a stream of air passes through a curved surface , that stream tries to follow the curve over the object with which it makes contact.
• The air passing between the two soda cans , the two sheets of paper or the two balloons , generates an attraction in the objects. What you might expect is that these objects will be pushed aside or repelled.
• Another experiment can be done by making holes at different heights in a plastic bottle , temporarily covered with electrical tape and the bottle is filled with water and the bottle is not covered. When the tape is removed, the water is seen to flow perpendicular to the surface of the bottle.

## Examples

Some examples of where we can observe the principle are:

• Chimneys and Pipes
• Car carburettors
• In swimming
• Venturi devices and in aviation

## Conclution

As a conclusion, we can make a description of the fluids that move along a line of current and also that in a closed conduit, the energy that a certain fluid has will always remain constant while it travels.