what is the principal of bernoulli theoram?

Answer 1

Bernoulli's principle states that in an ideal fluid (low speed air is a good approximation), with no work being performed on the fluid, an increase in velocity occurs simultaneously with decrease in pressure or gravitational energy.

This principle is a simplification of Bernoulli's equation, which states that the sum of all forms of energy in a fluid flowing along an enclosed path (a streamline) is the same at any two points in that path. It is named after the Dutch/Swiss mathematician/scientist Daniel Bernoulli, though it was previously understood by Leonhard Euler and others. In fluid flow with no viscosity, and, therefore, one in which a pressure difference is the only accelerating force, it is equivalent to Newton's laws of motion. It is important to note that the only cause of the change in fluid velocity is the difference in pressure on either side of it. It may be misunderstood to be that a change in velocity simply causes a change in pressure; the Bernoulli principle does not make any such statement.

Examples used to demonstrate the effect

[edit] Lift

One common way of understanding how an airfoil develops lift relies upon the pressure differential above and below a wing. In this model the pressures can be calculated by finding the velocities around the wing and using Bernoulli's equation. However, this explanation often uses false information, such as the incorrect assumption that the two parcels of air which separate at the leading edge of a wing must meet again at the trailing edge, and the assumption that it is the difference in air speed that causes the changes in pressure.

A common model to demonstrate the law of Bernoulli is a convergent / divergent nozzle, the Venturi Tube usually just called a venturi. This is a large diameter tube, gradually feeding into a smaller diameter tube and then again gradually into another larger tube.

As a gas or fluid medium flows through the venturi, the total pressure is constant across the entire cross section and the entire length of the tube, save for some friction losses. From the same total pressure on both ends of the convergent section and different cross sectional areas at the inflow and outflow end of this section follows a net force that accelerates the medium in the general direction of flow.

In addition to this acceleration, the medium is also forced to change the direction of flow as it enters the convergent section and again as it leaves the convergent section and enters the smaller diameter tube. The changes in direction imply additional acceleration normal (orthogonal) to the direction of flow. The necessary forces are provided by the wall of the tube and result in a change of static pressure. Upon entering the convergent section the direction of acceleration is such that the pressure increases. Upon leaving it, the direction of curvature is reversed, resulting in a pressure decrease. Since the medium is flowing faster at the latter point, the amount of pressure decrease is larger than the initial increase. This mechanism for pressure change establishes a direct link between flow velocity and change in static pressure. Thus the net difference in static pressure between the large diameter tube and the small diameter tube is directly related to the change in velocity between these two sections, which is expressed mathematically with Bernoulli's equation.

The divergent section at the outflow of the small diameter tube presents a reversed situation regarding the cross section areas. Therefore here exists a net force working against the flowing medium, forcing it to slow down and to gradually assume the static pressure in the larger diameter tube.

It is important to stress that the mechanisms described here only exist in the Venturi Tube and therefore represent a special case for the application of the Bernoulli's law. Acceleration in a free stream (not bounded by walls) can only happen due to differences in pressure and will follow Bernoulli's law.

Static pressure = pressure in a medium e.g. atmospheric air pressure (also referred to as head)
Dynamic pressure = pressure due to motion.
Total pressure = sum of static and dynamic pressure

[edit] Venturi effect and carburetors

Bernoulli's principle can be used to analyze the venturi effect that is used in carburetors and elsewhere. In a carburetor, air is passed through a Venturi tube to increase its speed and by the mechanisms explained above, decrease its pressure. The low pressure air is routed over a tube leading to a fuel bowl. The low pressure sucks the fuel into the airflow so that the combined fuel and air can be sent to the engine. The pressure reduction is somewhat proportional to the rate of air flow squared, so that more fuel is sucked in as the air flow increases, and the fuel:air mixture remains roughly the same proportion over a moderate range of speeds, however as the flow increases beyond a set point, the signal strength (in auto terms) rises less linearly, and more exponentially. Proper carburettor sizing selection must take into account the airflow demands, via engine size, typical operational rpm range, and expected or potential volumetric efficiency, so that the venturi effect and the resultant fuel metering is more optimal for those conditions. The eventual mixture enrichment can still get beyond acceptable limits at the upper rpm/flow ranges and so to address this, high speed air bleeds (or air correctors as named in certain brands of carburettor particularly webers) are integrated into the design, which will allow air to be drawn into the main fuel metering circuit at higher flows, working progressively more as flow increases (and specifically because as the signal increases, it will be proportionally easier to get more air (relative to its potential flow through an orifice, obviously not compared to a liquid), than solely additional fuel thereby leveling off the fuel curve to a more desirable result.

The pressure reduction effect can be observed by blowing over the top end of a straw with the bottom of the straw in a container of water; the water level will rise in the straw as the flow over the top of the straw increases in speed.

Answer 2

A body spray bottle with a rubber bulb dispenser demonstrates Bernoulli's theory. You squeeze the rubber bulb increasing the rigidity and skill means of the air interior. The air passes via a skinny hollow metal tube. the aptitude means of rigidity is switched over to kinetic means of speed. because countless the aptitude means of rigidity develop into switched over the rigidity interior the tube is decreased starting to be a partial vacuum used to siphon up the body spray to be atomized at discharge.

Answer 3

to say simply, bernoulli's theorem states that that the sum of all the energies of a liquid at a point is constant provided the flow of the liquid is streamlined.the energies possessed by a flowing liquid are 1.potential energy 2.kinetic energy 3.pressure energy.

Answer 4

Here is the definition --

It's a law in physics whereby the sum of the pressure and the product of one half of the density times the velocity squared is constant along a streamline for steady flow in an incompressible nonviscous fluid at constant height

Answer 5

simply it is based on conservation of energy per unit volume

Answer 6

here you go:

http://bernoulliequation.com