I've been trying to reconcile two theories, but I think I'm missing something fundamental.

My problem is that the Bernoulli principle states that faster moving fluid has a lower pressure. Special relativity states that there is no preferred inertial reference frame, and by implication no absolute velocity.

Now let's imagine that there is an experimental setup where a pressure difference is created by differential flow rates. If I imagine sitting on the 'faster' (ie. low pressure) stream of fluid then I see 'my fluid' as stationary and the other fluid as moving. But this means I should measure the other fluid stream as having a lower pressure. So I can't be sat on the low pressure stream after all.

Where is my thinking going wrong?

Any help will be much appreciated. It's been driving me mad thinking about it.

Maybe special relativistic length contraction resolves the issue. Let the fluids be flowing through pipes. When sitting on the 'faster' (ie. low pressure) stream of fluid, you should measure the other pipe to be length-contracted. Then the same amount of fluid is flowing through a smaller region, hence more pressure as you measure. Just a guess.

On second thought that's probably not it, since presumably the Bernoulli principle is noticable at everyday speeds, where special relativistic length contraction is negligible.

It's an interesting problem.

James_R says here (http://www2b.abc.net.au/science/k2/stn/archives/archive53/newposts/432/topic432876.shtm): "Bernoulli's formula is used to compare the fluid flow at two points along a streamline. If you go to a relatively moving frame of reference, the speeds at both points change."

Don't know if that's right. Also google for "Bernoulli relativity".

Hi CheshireCat,

As I hope to explain, the key idea is that the zero of energy is relative. Consider first an ordinary particle in a uniform gravitational field. You know this system has a conserved energy given by E = mgz + \frac{1}{2} m v^2 . To find E you simply have to look once at the particle and measure its position and velocity. The important thing is that you do this measurement in a particular reference frame. Provided you continue to measure things with respect to this frame, you will find that the velocity and position of your particle are related by the energy conservation equation.

Now, suppose your friend is moving with respect to you. Because Newton's laws are invariant under galilean transformations your friend can use energy conservation just as well as you can. However, and this is critical, your friend will calculate a different value for E than you! Specifically, suppose you both measure the particles position and velocity at a time t = 0 when the origins of you and your friend's coordinate systems coincide. You will both find the same value for the potential energy, but your friend will measure a different velocity because he is in motion relative to you. Consequently, he will say the energy of the particle is E' which differs from your E (but in a perfectly definite way). You both agree energy is conserved, but you disagree about what the value of the conserved energy is.

Notice in particular that while you disagree with your friend about the initial and final velocities of the particle along some part of its trajectory, you both agree on the change in velocity. This is where James R's statement connects.

The case of the fluid is very similar. The pressure you and your friend measure is the same, after all pressure just comes from the random bouncing around of atoms in your fluid. On the other hand, you both measure different values for the averaged velocity of the flow. However, as we saw above, this simply changes the value of the conserved constant in Bernoulli's equation. You will both still agree on the change in velocity due to pressure gradients, say.

Cheshirecat,
CheshireCat
Registered User (1 posts)
02-22-07, 08:42 AM #1

I've been trying to reconcile two theories, but I think I'm missing something fundamental.

My problem is that the Bernoulli principle states that faster moving fluid has a lower pressure. Special relativity states that there is no preferred inertial reference frame, and by implication no absolute velocity.

Now let's imagine that there is an experimental setup where a pressure difference is created by differential flow rates. If I imagine sitting on the 'faster' (ie. low pressure) stream of fluid then I see 'my fluid' as stationary and the other fluid as moving. But this means I should measure the other fluid stream as having a lower pressure. So I can't be sat on the low pressure stream after all.

Where is my thinking going wrong?

Any help will be much appreciated. It's been driving me mad thinking about it.

Very interesting question/problem!
I will study it deeper since it could be important for me.
I'm proposing a new theory in Physics and Relativity is shown wrong. I present them at the site: http://www.geocities.com/anewlightinphysics
In the first chapter is presented some inconsistencies found in Relativity Theory, particularly it is shown that non-invariant laws actually exist in Physics and the De Broglie law is presented as one.
It is possible that the Bernoully law could be other meaningfull one.

Can you cite me a site where the Bernoully law is well presented?

Amusing...

I've been trying to reconcile two theories, but I think I'm missing something fundamental. You are not missing anything, both events are not mutualy exclusive.

My problem is that the Bernoulli principle states that faster moving fluid has a lower pressure. Special relativity states that there is no preferred inertial reference frame, and by implication no absolute velocity. My guess is pressure decreases to allow large space for velocity. Though this still has nothing to do with SR.

Now let's imagine that there is an experimental setup where a pressure difference is created by differential flow rates. If I imagine sitting on the 'faster' (ie. low pressure) stream of fluid then I see 'my fluid' as stationary and the other fluid as moving. But this means I should measure the other fluid stream as having a lower pressure. So I can't be sat on the low pressure stream after all.No, you don't see yourself as stationary, you see other moving objects as stationary. You only see yourself as stationary if you have no reference frame, that is, if you are not aware you are on a moving fluid.

Where is my thinking going wrong?

Any help will be much appreciated. It's been driving me mad thinking about it....If I knew what you are driving at. I may help.

Chesirecat,
Now I know what is the problem on your reasoning:
Now let's imagine that there is an experimental setup where a pressure difference is created by differential flow rates. If I imagine sitting on the 'faster' (ie. low pressure) stream of fluid then I see 'my fluid' as stationary and the other fluid as moving. But this means I should measure the other fluid stream as having a lower pressure. So I can't be sat on the low pressure stream after all.

Where is my thinking going wrong?

The problem is that Bernoully equation considers the velocity of the fluid relative to the streamline which is the same independently of the considered frame of observation.
I mean the velocity to be considerd is V = V(fluid) - V(streamline) which is the same in any referential.