# Bernoulli's law

## Main Question or Discussion Point

According to Bernoulli's law pressure and velocity along a stream line are related to each other.
What is the most correct way to describe it ?
A. First the pressure change and then the flow velocity change.
the change in the flow velocity is caused by the pressure change (F=Ma> PA=Ma).
B. First the velocity change and then it cause change in pressure (for example: flow throw a nozzle).

I'm not sure about B., because if the velocity change there must be some force who causes it - F=Ma , and if this force is not related to pressure, what other force can it be?
And I'm not sure about A., because what causes the change in pressure if not the velocity change?

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Hi there:

Check out eFunda.com at: http://ww.efunda.com -- Fluid Mechanics section.

Thanks,

Gordan

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Which came first, the chicken or the egg?
Basically, that is your question here. ;)

I think that the correct answer is that neither "A" nor "B" are correct and, in the same time, both of them are.

Hi there:

Velocity can change if the cross sectional area changes in order to have the continuity equation be satisfied at all conditions.

There are all kinds of different scenarios.

Again, my suggestion is to take a look at the governing equations, plug in a few values for different examples and plot the results.

Data analysis will bring some light into what has the impact on the output values.

Therefore, I would like to suggest that it might be worthwhile to checkout eFunda.com section on fluid mechanics and take advantage of the free online calculators.

Thanks,

Gordan

Which came first, the chicken or the egg?
Basically, that is your question here. ;)

I think that the correct answer is that neither "A" nor "B" are correct and, in the same time, both of them are.
To change the velocity of an object you need a force, if they are both correct then
they it is like saying that change in the velocity causes force, but some force is needed at the first place in order to the change the velocity.

Hi there:

Velocity can change if the cross sectional area changes in order to have the continuity equation be satisfied at all conditions.
The continuity equation is conserved, but it doesn't say if the velocity change causes pressure change or is it the other way around.

I found this interesting http://user.uni-frankfurt.de/~weltner/Mis6/mis6.html" [Broken].

"Acceleration of air is caused by pressure gradients. Air is accelerated in direction of the velocity if the pressure goes down. Thus the decrease of pressure is the cause of a higher velocity. It is wrong to say that a lower pressure is caused by a higher velocity."
"Bernoulli's law is insufficient to explain the generation of low pressure. A faster streaming velocity never produces or causes lower pressure. The physical cause of low or high pressure is the forced normal acceleration of streaming air caused by obstacles or curved planes in combination with the Coanda-effect."

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To change the velocity of an object you need a force, if they are both correct then they it is like saying that change in the velocity causes force, but some force is needed at the first place in order to the change the velocity.
That sounds correct, considering the limits of what we are talking about.

I found this interesting article.
..."Bernoulli's law is insufficient to explain the generation of low pressure."."
And that's where the limits are.
Bernoulli's law is valid for incompressible fluids only. It doesn't give you any clue about the cause-effect relation between pressure and velocity because incompressible fluids don't allow the concept of "speed of sound". The sound (which is - pressure waves) have an infinite speed in an incompressible flow field. That means that any pressure (and therefore velocity) disturbances act instantly through the whole flow field.

The physical cause of low or high pressure is the forced normal acceleration of streaming air caused by obstacles or curved planes in combination with the Coanda-effect."
Mmmmh... :uhh: So do they also say what is the Coanda-effect and how is it produced?

Since the egg can't evolve, then the chicken obviously came first.

If you suddenly drop the pressure in a room with a window open to the outside, then air will rush in to fill the void created by the decrease in space between atoms of air. Likewise if a sudden gust of wind enters the room from outside, that too will change the pressure. I'm not entirely sure what you are asking, but it works both ways...q+pgh+p=q+pgh+p=constant. If this means nothing else other than one side equals the other, than it works both ways.

Also, who cares which came first. I never understood that. According to evolution, something had to produce the egg, and egg layers are a consequence of evolution from a single cell. Therefore, obviously the chicken came first. I know I'm taking it literally but if someone can explain the philosophy behind it that would be really great.

Astronuc
Staff Emeritus
According to Bernoulli's law pressure and velocity along a stream line are related to each other.
What is the most correct way to describe it ?
A. First the pressure change and then the flow velocity change.
the change in the flow velocity is caused by the pressure change (F=Ma> PA=Ma).
B. First the velocity change and then it cause change in pressure (for example: flow throw a nozzle).

I'm not sure about B., because if the velocity change there must be some force who causes it - F=Ma , and if this force is not related to pressure, what other force can it be?
And I'm not sure about A., because what causes the change in pressure if not the velocity change?
Bernoulli's law is simply a statement about conservation of energy. Looking at the terms,

$$P\,+\,\frac{1}{2}\rho{v^2}\,+\,\rho g h$$,

the static pressure P represents a potential (mechanical) energy, since afterall, the pressure is due to momentum (product of mass and velocity) of the atoms/molecules. 1/2 rho v2 is simply kinetic energy, and mgh is the gravitational potential energy.

The continuity equation is conservation of mass, i.e. the difference between rates mass in and out gives the rate of mass accumulation or loss depending on which is greater.

The momentum equation relates forces and changes in momentum. Forces due to pressure get a gas or liquid moving, and then moving fluids encounter shear forces either on contact surfaces or against slower moving fluides.

Altogether, these three relationships (equations) are known as the Navier Stokes equations:

http://www.grc.nasa.gov/WWW/K-12/airplane/nseqs.html

http://www.efunda.com/formulae/fluids/navier_stokes.cfm

Remember Newton's laws of motion, specifically anything that is a rest will remain at rest - until a force is applied. A force is required to get things moving. The world/universe is a dynamic system.

http://csep10.phys.utk.edu/astr161/lect/history/newton3laws.html

http://scienceworld.wolfram.com/physics/BernoullisLaw.html

http://user.uni-frankfurt.de/~weltner/Mis6/mis6.html [Broken] - misinterpretations of Bernoulli's law

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