Please explain Bernoulli's Principle

[scienceisfun]

Why is the velocity of a fluid high where the pressure it exerts is low, and why is the velocity of a fluid low when the pressure it exerts is high?

 

Please explain.

 

Thank you.

[Flashman]

A way to think of it is, that when the bulk velocity of a fluid is zero, it's molecules in random motion are causing pressure on a surface by pounding on it randomly, according to the amount of thermal energy in the fluid. When in motion across a surface, the fluid is more organised, the molecules have more velocity in the direction of travel, and less molecules pound on the surface. The more velocity the fluid has, the less component of velocity the molecules have in a perpendicular direction to it, so they pound on it less.

[scienceisfun]

Ok. Thank you. That definitely helps.

 

Let's say you have a narrow tube that connects to a wide tube with water flowing through it. I still don't get how the velocity just suddenly drops once the water goes into the wider tube (and vice versa - why does the velocity increase when it goes from a wide tube to narrow tube?)

[Sisyphus]

Ok. Thank you. That definitely helps.

 

Let's say you have a narrow tube that connects to a wide tube with water flowing through it. I still don't get how the velocity just suddenly drops once the water goes into the wider tube (and vice versa - why does the velocity increase when it goes from a wide tube to narrow tube?)

 

Basically because you have the same amount of water passing through through the wide tube and the narrow tube per unit time. Thus if that water has to go through a narrower cross-section, it is forced to move faster, because water is incompressible. A somewhat analogous situation (with cause and effect reversed) occurs with falling water. If you turn on a faucet, the flow of water is constant, so the same amount of water per unit time passes all points in the "waterfall." However, as it falls, it accelerates, so the water near the bottom of the stream is moving faster, and the stream becomes narrower.

[Severian]

You see the same effect in rivers. Where rivers are wide they flow very slowly while where they are narrow they flow very fast. Simple conservation of water (as Sisyphus said already).

[Norman Albers]

Conservation of mass is thus clear, but further sciencefisfun asks about pressure tradeoffs in changing flows. These are what happens in situations of changing diameters of pipe. If you analyze energy content of what goes in and then comes out, acknowledging that velocity manifests energy, as does pressure, they trade off, given no other inputs or losses.

[gcol]

If I were to see it as simply friction, ( and drag) between moving water and fixed containment vessel, why would I be wrong?

 

Oh, wait, a little reading indicates that friction plays little or no part in bernoulli's scheme. Hmmm.... Does it apply to only a narrow set of conditions?

Edited November 17, 2008 by gcol
Afterthought

[Norman Albers]

When you set up equations for conservation of energy and conservation of momentum for the incompressible case, you get that pressure is potential energy and velocity is kinetic energy. When a flow diameter is reduced, an exchange between the two forms is created. Friction is a certain rate of loss of these energies.