Bernoulli's principle

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Bernoulli's principle states that in fluid flow, an increase in velocity occurs simultaneously with decrease in pressure. 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 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. For a mathematical formulation, see Bernoulli's equation. In a 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 pressures either side of it. It is very common for the Bernoulli effect to be quoted as if it states that a change in velocity causes a change in pressure. The Bernoulli principle does not make this statement and it is not the case.

A common model used to demonstrate the Bernoulli effect is a convergent, divergent nozzle also called a venturi. This is simply a large diameter tube feeding into a smaller diameter tube and then further feeding into another larger tube. Venturis are easier to understand when considering a gas rather than a liquid, but the functions for either are much the same. In order for any gas flow to occur it is essential that the exit pressure is lower than the entry pressure for this system. This pressure difference causes the fluid to accelerate from the intake larger tube into the smaller tube. The stored spring energy available to the fluid because of the pressure difference results in the fluid not only expanding as it goes from higher to lower pressure, but effectively overshooting in its expansion as a result of the mass of the gas particles and compressibility of the gas, springing apart beyond the point where all the forces would be balanced. Before the fluid can spring back, there is more fluid behind it, also at this lower pressure. This first sample of fluid then has no pressure difference either side of it to cause it to spring back. This part of the fluid then remains at a lower pressure until it merges with the slower fluid in the exit tube. The pressure in the exit tube will be higher than that in the smaller middle tube, and so the fluid moving from the smaller to larger tube is slowed down by this pressure difference.

One common and correct 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.

Bernoulli's principle can be used to analyse 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 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 wide range of speeds. 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.

Note: Of all the languages for this inquiry, only the English version does not contain the mathmatical formula's that state the principle. Perhaps someone could supplement.

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