Can someone give me a proof for Bernoulli's Principle?

Question

I know what it states, I want to know why that happens thought.

Answer 1

It follows from the momentum equation, equation of state, and continuity equation of fluid dynamics. Wiki has a derivation.

Answer 2

I'm assuming you're talking about the part of Bernoulli's Principle that states that a fluid's pressure decreases as its speed increases.

This is not a proof, but it may give you more of an intuitive understanding.

Say you have some fluid flowing from left to right in region "A". Then at some point along its path (in region "B"), its speed increases (maybe because it got constricted through a narrower channel).

Bernoulli reasoned thus (so I'm told): Since the fluid sped up as it passed from "A" to "B", some force must have accelerated it. That force must be a difference in pressure between "A" and "B". So region "A" must be at a higher pressure than region "B".

I've also tried to understand this on a microscopic scale (Bernoulli didn't make any assumptions about the fluids being composed of atoms; but for some reason the microscopic picture is sometimes easier for me to grasp intuitively). The best I've come up with is this: Say region "A" is a wide pipe and region "B" is a narrow pipe connected to it. The molecules in "A" are bouncing around at random; some against the walls, perpendicular to the fluid flow; and some parallel to the fluid flow. The "parallel" moving atoms are the ones that are most likely to make it through the pipe into region "B". But now "B" is "enriched" with molecules whose velocity vectors are biased in the rightward-moving direction, with relatively fewer of the atoms which bounce around in other directions and manifest themselves as high pressure.

I'm not completely satisfied with that, but it's the best I can think of.

Answer 3

Bernoulli's Principle is based on the principle of conservation of energy.

If there is some gain energy then there will be an equal amount of loss of energy and the total of all energy remains constant.

The principle of conservation of energy is law of nature and it cannot be proved.

But we can give or show the principle of energy in every day life.

Thus we can show that the Bernoulli’s’ principle is applied well in some physical phenomenon and we cannot prove that.

Answer 4

Flight is a common example for Bernoulli's principle but its actually wrong.

It happens because of the conservation of mass, energy and momentum.

A better example is of a garden hose. If you set the nozzle on spray you'll find that the droplets travel quickly because of the high pressure differential. If you set it on water, you'll find that the water travels at pretty much the same pace it does while it was inside the hose because there is little pressure drop at the nozzle.

Bottom line is, you have to have the same mass flow of water, but because of the difference in pressure in each case, the velocities are different. It balances out.

Answer 5

You mean it is not the engineers that make planes fly, but your god? It is not the kerosene and the engines and wings, but the hand of god? Then why don't priests build planes but engineers? Why don't we just sit on a carpet and pray it to fly us anywhere we want? I tell you why. Your god does not exists. Sitting on a chair and pray for it to fly you somewhere does not and will never work. The process of humans finding out how they could build airplanes gave us (this does not include you) to a good understanding of how aerodynamics and flight mechanics work. If our knowledge about this were really wrong we would not be able to build reliable airplanes. Even the pope uses real airplanes and does not pray to god to fly him through the world. Also evolution is a fact.

Answer 6

An airplane flying! the bernoulli's principle makes it go up! just think about it!

Answer 7

an airfoil, thats the shape of an airplane wing