## bernoulli.101

Discussions on classical and modern physics, quantum mechanics, particle physics, thermodynamics, general and special relativity, etc.

### bernoulli.101

bernoulli (def):
1) air flowing faster over a surface causes lower pressure and vice versa.

ron

annex
air is matter in a gaseous state
flow is measure of velocity by volume
faster means greater velocity
over means above or on top
surface means boundary or layer
causes refers to the reaction as matter is acted upon by inertial differentia
lower means decreasing
pressure refers to static pressure as measured at right angle to flow
vice versa means opposite holds equally true
rwjefferson
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### Re: bernoulli.101

That's true in a manner of speaking. What Bernoulli's principle actually states is that, for an inviscid flow, whenever the velocity of the fluid increases the potential energy decreases (and this lowered potential energy causes a lower pressure.) It is essentially a statement of conservation of energy. Note that it can be violated for systems in which there is viscous friction (i.e. what you've been terming "viscosity" elsewhere). I am therefore not sure how you're going to claim that this is related to your other posts elsewhere on the forum.

I should note that Bernoulli's Principle actually makes a very precise statement. It doesn't simply say that the velocity goes up and the potential energy goes down; it says that in a mathematically precise way which can usefully make quantitative experimental predictions. Explicitly, it says this:

"Given a conservative external force corresponding to the potential $\Phi$, along a streamline in an inviscid flow, the following quantity is constant:

$v^2/2+\Phi+p/\rho$

where v is the local value of the velocity field along the streamline, p is the pressure, and $\rho$ is the density."

linford86
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### Re: bernoulli.101

This is beginner forum stuff?

Lincoln
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### Re: bernoulli.101

Not sure, maybe this belongs in the physics or anything science forums.
It should also be pointed out that
linford86 wrote:"Given a conservative external force corresponding to the potential $\Phi$, along a streamline in an inviscid flow, the following quantity is constant:

$v^2/2+\Phi+p/\rho$

where v is the local value of the velocity field along the streamline, p is the pressure, and $\rho$ is the density."

only holds for low mach numbers where flow is incompressible as well.

Heron
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### Re: bernoulli.101

Ah, thanks for the input Heron. It's been a while since I took undergraduate fluid dynamics.

linford86
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### Re: bernoulli.101

eh, I found it relative since the op mentioned air as the fluid in question.

Seems I remember the assumptions went this way.
Navier stokes (nasty stuff)
> inviscid flow > eulers (less scary but still has teeth)
> inviscid and noncompressible flow > Bernoulli (down right sweet)

Heron
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### Re: bernoulli.101

Hehe. Ah, yes, I remember Euler's equation. That's a fun equation to solve (and I'm not being sarcastic.) In my mind, the break down is more like this:

Navier Stokes (good freaking luck with that one)
>inviscid flow > euler's equation (FUN!)
> Inviscid and incompressible flow > Bernoulli (boring -- too easy)
> incompressible and irrotational > conformal mapping (yay!!!!!)

It's been a while since I've done this -- like I said before -- and I didn't really remember any of this before we started talking about it. But of course the mathematics is the same as for any classical field theory, and in fact one can show that any classical field theory that conserves momentum must have a material derivative involved (so the Navier-Stokes equation is actually a special case of a momentum conserving classical field.) The case where the vorticity is zero and the fluid is incompressible gives you that the curl and the divergence of the velocity field is zero. This condition is isomorphic to electrostatics with zero charge density (you're solving the same PDE.) In my own research, I recently derived that in a particular limit my system is well described by 6 non-linear fully coupled PDEs which are related to hydrodynamic equations. It's good times....

Incidentally, I am going to recommend that this be moved to the Physics section by the appropriate mods.

linford86
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### Re: bernoulli.101

Yeah....words like "Navier-Stokes" and PDEs probably shouldn't be in a forum called "Beginner"

Lincoln
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### back to real physics

mentoring moderators and good teachers:
As always; it is as you wish. I mean only to keep physics simple and basic so insulting moderators and innocent children of all ages might someday see beyond symbols and advanced degrees. Force is inertial differential; geometry is not quite the same as force.

linford86 wrote: …That's true in a manner of speaking... Note that it can be violated for systems in which there is viscous friction…

It is only in the manner of unclear thinking and speaking that systems are warped to violate the rule of real physics. Viscosity and friction are newton.101; not bernoulli. Overruled by greater is not quite the same as violated.

The last time I checked, the National Air and Space Museum still taught that it is the geometry (i.e. shape, i.e. warp) of a wing causes the air (i.e. wind) to flow faster over and that this creates the lower pressure over that lifts the wing. Is this true? Does a wing lift because air flows faster over the top surface?

k.i.s.s. :
This is bernoulli.101. Support your answer with either newton.101 – inertial differential; or bernoulli.101 – in verse pressure differential

ItS
peace
r~

bernoulli.102 - bernoulli is newton’s delicate partner in the dance of vortex
rwjefferson
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### Re: bernoulli.101

Look, rw, I'm not sure what you wish to accomplish here. If you want to keep on blathering about your alternative theory concerning the motion of spacecraft -- and I can see that that is where this thread is going -- then we are unfortunately going to have to take moderator action.

If, however, you want me to explain to you the proper statement of Bernoulli's principle, then I can do that. However, you have already attempted to fight my more technical definition. I cannot -- and probably should not -- instruct students who are unruly and argumentative. And let me make this very clear to you; the only role that I am willing to take towards you is as a teacher which means that I expect you to respond as a student, which means that you will stop arguing with me and you will make some attempt to understand what I am saying. You can ask as many questions as you would like, but if I feel that it is a battle to convince you of some point, then its not worth my time. That is to say, I really don't feel like going to war with you; life would be simpler for both of us if you regarded me as someone from whom you could learn, instead of regarding me as an adversary. The only other action that I am willing to make towards you is to kick you straight off here and never speak to you ever again. So either you will accept instruction or you will say good bye to this forum.

First, I need to say that what you originally quoted as Bernoulli's Principle is simply not Bernoulli's Priciple. It is an application of Bernoulli's Principle, which often mistakenly gets called "Bernoulli's Principle". The true statement of Bernoulli's Principle is the one I already gave. However, since you gave your K.I.S.S. request, I'll provide you with something simple. The simplest statement of Bernoulli's Principle that I know how to give is that under certain very precise (in fact, mathematically precise) conditions, as the velocity of a fluid increases, the pressure decreases and vice versa.

It is true that it is often taught that airplane flight is due to the shape of the wing. And, in fact, I would be willing to bet that the museum you mentioned teaches it that way. I've been there, but it's definitely been many years since my last visit. However, as with most things, the real story behind airplane flight is far more complicated and involves more than Bernoulli's principle. Therefore, strictly speaking, it is simply false that the geometry alone is responsible for flight. If that were true, then, for example, aircraft would not be able to fly upside down. There are fighter jets which can and routinely do fly upside down. You might have seen some examples of this stunt work portrayed in the Tom Cruise film Top Gun.

Now, it is also false that Bernoulli's Principle is somehow disconnected from Newton's Laws. You seem to think that they are somehow disconnected. You wrote:

"It is only in the manner of unclear thinking and speaking that systems are warped to violate the rule of real physics."

Yet, Bernoulli's Principle is not real physics, in the sense that it does not apply universally and it is not believed to be a law. In fact, it cannot be a fundamental law because it is derivable from deeper laws under very precise conditions and is known to hold only under those precise conditions. It is known, and accepted, that there are conditions under which Bernoulli's Principle fails to be true. Perhaps this is why we call it a principle, though I should note, in passing, that there are many other principles in physics which are not called "laws" but probably should be (in the sense that they are truly deep and fundamental. Noether's Theorem or Einstein's Field Equations are a couple of examples.)

I also dislike your present terminology. The statement that force is "inertial differential" is unclear, and -- in fact, if taken literally -- simply false. In physics, the word "differential" means an infinitely small change, and mass is taken to be the measure of linear inertia. Thus, literally speaking, "inertial differential" would mean an infinitely small change in mass. The more proper statement is that force is the rate of change of the momentum with respect to time. In the case that mass is constant and quantum and relativistic effects are negligible, then force is linearly proportional to the acceleration with the mass being the proportionality constant (that is to say, F=ma, or force equals mass times acceleration). This is precisely what we call "Newton's second law".

Furthermore, the simplest statement of Bernoulli's Principle that I can give you is that under certain very specific conditions, as the velocity of a fluid goes up, the pressure goes down, and vice versa. I don't know what "inverse pressure differential" means to you, but again, in physics, that would be an abuse of terminology.

linford86
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### Re: back to real physics

rwjefferson wrote:
The last time I checked, the National Air and Space Museum still taught that it is the geometry (i.e. shape, i.e. warp) of a wing causes the air (i.e. wind) to flow faster over and that this creates the lower pressure over that lifts the wing. Is this true? Does a wing lift because air flows faster over the top surface?

Actually(as linford pointed out) you need to understand lift a bit better.

Bernoulli's principle is perfectly fine for a back of the envelope calculation of the maximum theoretical head in a pumping system but not so much for airfoil design.

Heron
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### wormhole.101

L.O.L. Wow. Wrong around again. Oh yes in deed Alice, there is such a thing as a relative headwind. Take another pill and try again.

Go easy, guys – maybe there's a teachable moment here.
Or maybe not.
RiP
good teachers and mentors are always greatly appreciated; at least by me

I am not the disruptive student that insults fellow students.
great hostility is released even as dogma is most gently kissed
copernicus.bruno.galileo.newton.darwin.occam.et.al

rwjefferson wrote: I understand all of the posts.

Telling me what I already know does not make me change my mind. That I know how the insulting moderator's thinking is confused does not mean I do not understand. I am just a messenger. The insulting moderator's war against real physics is not just with me.

Higher Authority wrote: Science Chat Forum (SCF) and Philosophy Chat Forum (PCF) are discussion and debate forums, and our primary purpose is the discussion of science or philosophy and related matters. Our goal is to foster a friendly environment in which ideas can be freely exchanged and discussed, where questions can be asked and answered.
Amen

bernoulli.101
1) as fluid velocity over a boundary increases; static pressure over decreases and vice versa
2) as static pressure over a boundary decreases, fluid velocity over increases in verse vice versa

lift.101
A wing attacks a relative headwind with inertial differential. As air crosses the highest point of attack, relative inertia forces the air to separate from the trailing upper wing. Inertia forces lower pressure over the wing. Lower pressure over the wing in turn forces acceleration (i.e. air flows faster) over and down. Action in verse reaction.
a wing forces air downward ~ in turn air forces the wing back in verse up

newton.101
1) inertial differential accelerates air and wing
2) pressure differential accelerates air and wing
3) warp (i.e. shape of wing) does not

Challenge: Name a shape (i.e. geometry) that cannot be forced to lift.

peace
rwj~

that you do not know what I mean does not mean I do not understand your tongue well enough
rwjefferson
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### Re: bernoulli.101

Okay, you're done.

linford86
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