Talk:Bernoulli's principle

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The equation v^2/2 +gz + p/row = constant
is in terms of energy per kgm, i.e. it has been divided-through by M - but the text refers to the term gz as quote "force potential". This has no meaning, and serves only to confuse. It is really the potential energy in earth's gravity - per kg.

The term p/row, is same as (N/m^2 /kg) x m^3, which cancels to N-m/kg, so it is in fact, energy/kgm.
Since we were considering only INcompressible flow, row is constant and so dissappears to join the constant on the other side, to give

V^2/2 + gh + p = K
where p= pressure (N/m^2), g= 9.8 m/s/s, h = relative height, V = velocity m/s

It is clearer to not divide by mass, so that the equation is directly in terms of energy, i.e.
0.5.M.V^2 + M.g.h + P.Volume = k
i.e. Volume = M/row

What Bernoulli did was yet another example of the Conservation of Energy Principle.
He added k.e. (M.V^2/2) to Potential enerergy, (m.g.h) to P.Volume and states that the total will remain constant - in an isentropic, or streamlined, flow.

However, what does not so far seem to have been pointed-out, is one hideously "obvious" fact, which is - disastrously - often over looked. i.e. that in a duct of varying csa, the speed at any plane, z, along the the duct, is entirely determined by the csa at that plane. (INcompressible fluid)
An example of this is the guy who went to great effort to try to make a litre of water fall onto a fan on a vertical axis, to turn an alternator. He directed the water - or attempted-to! - with a parallel pipe, and, as I explained to him, the water cannot accelerate AND keep the same diameter - that is mathematically impossible. But I had no reply.
What happened was that air was drawn into the lower end of the pipe to effectively - but randomly - decrease its csa. This caused a drenching drowning kind of splatter onto the fan, rather than a streamlined flow, "wasting" most of the energy in oxygenating the water!

Also, it is for this reason that a turbine which works very efficiently in its designed direction of flow, Cannot - In Principle - work efficiently with the flow reversed.
It will, however - in Principle - work as a compressor - or pump - if energy is supplied to the rotor, (reverse rotation), and a suitable exit nozzle fitted to slow the flow back to the inlet speed.
Bert Vaughan — Preceding unsigned comment added by Bert Vaughan (talk • contribs)

Possible error in reference [15]

Hi everyone, I think that I noticed an error in reference [15] about the use of incompressible flow bernouilli's equation. It gives the reference to page 602 of the book but it rather seems to be at page 610 as you can see here. This is the first time I suggest something on wikipedia so I don't know if I have to modify it by myself or signal it first. — Preceding unsigned comment added by 86.208.16.31 (talk) 19:04, 14 August 2020 (UTC)

Reference 15 quotes p.602 in the 6th edition of White’s book. Are you quoting from the 6th, or some other, edition? I haven’t been able to download the .pdf file you supplied. Dolphin (t) 03:40, 15 August 2020 (UTC)

Seems they linked the 7th edition so I think we can put this to rest. 35drake (talk) 16:45, 1 February 2023 (UTC)

Adjustment to the lead

Currently the second paragraph speaks about some fairly high-level concepts such as isentropic flows, irreversible processes, non-adiabatic processes, incompressible flows and compressible flows. In contrast, the third paragraph is confined to simpler concepts such as conservation of energy, kinetic energy, potential energy and internal energy. In the interests of WP:Make technical articles understandable, I feel these two paragraphs should be reversed - the third should become the second, and the second should become the third. I will make the change. Dolphin (t) 12:21, 11 May 2023 (UTC)

It appears this suggested edit has already been done. I would go further and move the current third paragraph (isentropic flows, irreversible processes, non-adiabatic processes, incompressible flows and compressible flows) to the end of the lead, moving current paragraphs four and five up to three and four. Mr. Swordfish (talk) 01:06, 28 May 2023 (UTC)

Good idea. I have no objection to the change you are proposing for the third paragraph. Dolphin (t) 07:50, 28 May 2023 (UTC)

Not how but why?

There is no explanation here of why an increase in flow velocity should decrease the dynamic pressure, as described by Euler's equation. That is to say, why does the conservation of energy manifest as a drop in dynamic pressure and not in, say, a change in temperature (as it does in some other circumstances, such as gas expansion), or simple flow disruption and back-pressure, similar to transonic choking? Bernoulli observed the effect, Euler figured out the equation, but has anybody explained why it happens this way in the first place? — Cheers, Steelpillow (Talk) 16:45, 12 June 2023 (UTC)

The third paragraph contains the following two sentences:

If a small volume of fluid is flowing horizontally from a region of high pressure to a region of low pressure, then there is more pressure behind than in front. This gives a net force on the volume, accelerating it along the streamline.

Newton's second law says F=ma, and humans tend to think that the force comes first and causes the acceleration, not the other way around. It's possible to get way into the weeds arguing over whether the laws of physics describe causes and effects or whether they just quantify relationships between things like force and acceleration, but intuitively most of us think of acceleration as being caused by a force. For instance when you kick a football you apply a force on the ball and that "causes" the ball to accelerate; the ball accelerating does not somehow magically cause your foot to kick it.

This (in my opinion) is why so many people have trouble understanding Bernoulli's principle: it is often explained that the speed change happens "first" and this somehow "causes" the pressure to change. This reverses our usual intuitive notion of forces causing acceleration. But if you think about BP as the pressure differences exerting a force, and that force "causing" an acceleration it's much easier to understand.

Perhaps the article could be more clear about this. Mr. Swordfish (talk) 15:15, 13 June 2023 (UTC)

Your question is entirely valid. I doubt I have the skill to answer it to the satisfaction of a physicist, but I can think about it and record my thoughts.

Firstly, an important technicality: an increase in flow velocity is accompanied by a decrease in static pressure, not a decrease in dynamic pressure. (Dynamic pressure is defined to be one half rho times the square of the flow speed, so there is no mystery as to why an increase in velocity is accompanied by an increase in dynamic pressure - it is a consequence of the definition of dynamic pressure.)

Early scientists observed that providing the various forms of energy were defined consistently, energy always seemed to be conserved. They used these observations to formulate the law of conservation of energy. Those observations included Bernoulli’s principle which was the inescapable conclusion that in the flow of an incompressible fluid the sum of the static pressure and dynamic pressure is the same along a streamline, and in many situations, it is the same throughout the flowfield. So rather than say a fluid flow is constrained to conform to the law of conservation of energy, it is more accurate to say that the observations made by Bernoulli contributed to the formulation of the law we now know as conservation of energy.

Another example that might have helped formulate the law of conservation of energy is the motion of a pendulum - as the speed of the bob of the pendulum increases, so the gravitational potential energy of the bob decreases. Your question regarding fluid flow is analogous to asking “why does the potential energy of a pendulum bob decrease when the speed of the bob increases?”

The bob of a pendulum is incompressible so as its kinetic energy changes its temperature does not. Similarly Bernoulli’s principle talks about incompressible fluids so any change in kinetic energy won’t be accompanied by a change in temperature.

Energy can be identified in an incompressible fluid in two ways - its kinetic energy per unit of volume, and its potential energy per unit of volume. The kinetic energy per unit of volume is what is called the dynamic pressure. (The pressure unit pascal is equivalent to joules per cubic metre where the joule is the unit of energy.) The potential energy per unit of volume is the sum of the static pressure and the height above the datum multiplied by density. Along the datum the gravitational potential energy is arbitrarily zero.

The universe behaves in a manner that, in many ways, is uniform. We describe this uniformity using the law of conservation of energy. Fluid flow is included in this. The law of conservation of energy predicts that kinetic energy plus potential energy will always remain constant throughout a flowfield. Bernoulli’s observations confirmed that it had always been so. Dolphin (t) 15:24, 13 June 2023 (UTC)

Thank you both for your thoughts. However they pretty much address the problem rather than the solution, the how and not the why. The question remains; why is the flow incompressible, with both the total pressure and the temperature remaining constant? Why does it accelerate and squeeze down into a venturi and not slow down and bunch up, increasing the total pressure under its kinetic impact, like a crowd queueing to get out the door? For example it is easy to see that if a pressure gradient develops then the speed will increase, but not why the gradient develops in the first place, when there is no compressive or thermal buildup at the mouth (arguing that it is caused by, or inseparable from, the acceleration is just begging the original question as to why this circular cause-and-effect spirals up out of nothing). I should add that I am not alone in this concern; see for example Ed Regis; "No One Can Explain Why Planes Stay in the Air," Space & Physics, Scientific American website, 1 February 2020. — Cheers, Steelpillow (Talk) 16:18, 13 June 2023 (UTC)

why is the flow incompressible, with both the total pressure and the temperature remaining constant?

It isn't, and those two quantities don't remain constant. But these are useful simplifying assumptions that make the math easier, so they are commonly assumed. A more thorough model deals with compressibility and temperature variations etc.

Why does it accelerate and squeeze down into a venturi and not slow down and bunch up...

The narrow part of a venture tube acts as an obstruction which does cause the fluid to "slow down and bunch up" behind the obstruction, with an associated increase in pressure. Once the fluid moves past the obstruction, the higher pressure behind it pushes on the fluid and accelerates the fluid.

it is easy to see that if a pressure gradient develops then the speed will increase, but not why the gradient develops in the first place

For an airfoil, it's easy to see why the gradient develops: the streamline curvature theorem says that any time a fluid follows a path that is curved there is a pressure gradient perpendicular to the fluid flow. Lowered pressure on the top, higher pressure on the bottom. As the air flows from ambient pressure to the region along the "top" of the foil the pressure decreases. As BP predicts, the air speeds up, but this is more of an interesting factoid than a reason why airfoils do what they do.

To understand the streamline curvature theorem, think of a tornado or a hurricane or simply a low pressure system in the atmosphere. Lower pressure on the inside of the curve. And if you want to derive it, just take the kinematics of circular motion and apply Newton's second law at the differental level and it pops out in one step, two or three if you want to be pedantic.

As for Regis's article, it's pure horseshit. The best advice I can give is to ignore it. Mr. Swordfish (talk) 17:51, 13 June 2023 (UTC)

Well, thank you, the editors of Scientific American, curator of aerodynamics at the National Air and Space Museum John Anderson, our sometime resident expert Doug McLean, and the other verifiable experts whom Regis gives voice to, will be glad to know they have wasted their careers. For the benefit of any subsequent readers, I should mention that your other points are no better placed. — Cheers, Steelpillow (Talk) 19:05, 13 June 2023 (UTC)

My reading of Doug McLean is that he shares my opinion of the Regis article. Perhaps not in the stark language that I would use, but his book is a hundreds pages long explanation of why Regis is off base.

Don't know about how Anderson feels about it, but my reading of his works is not that he thinks "nobody can explain" why planes stay in the air.

It very settled, well understood engineering and physics. Saying "nobody understands it" is sensationalist crap. I'm sure it gets lots of clicks, but... Mr. Swordfish (talk) 00:44, 14 June 2023 (UTC)

Steelpillow To the best of my knowledge, the current thread is the third time this theme has been aired on Wikipedia. The previous two were:

Talk:Lift (force)/Archive 8#Limits of current human knowledge

Talk:Lift (force)/Archive 12#Humility in the face of the unknown. (User:Steelpillow contributed to this thread in three edits - 2 May, 3 May and (again) 3 May, all in 2020.)

Several Users made the point that the Scientific American article is technically sound and has high-quality artwork, but nothing therein supports the sensational title given to the article. I have challenged supporters of the SA article to identify some element of the article that supports, or is directly related to, the title but no-one has accepted my challenge. It looks like the person(s) who came up with the title was not the same person who wrote the body of the SA article. It is conceivable that the title is due to an editor or sales manager who wanted a sensational title to catch the eye of potential customers. Dolphin (t) 14:01, 14 June 2023 (UTC)

Yes. It is very common for magazine and newspaper articles to have their title written by the editor, not the author. It's even more common in the internet age where an article will be given several different titles to see which one gets the most engagement. The SA article's title is effective clickbait, but as you observe it is at odds with the body of the article.

I re-read it last night, and it's not as bad as I recall, other than the title that is.

It's like the following hypothetical article:

We asked several famous chefs how to make tomato sauce, and their recipes varied widely. One of them said directly, "There is no one singular way to make tomato sauce." We then asked a chemist, and he said that while the chefs make tasty sauces, their recipes present an incomplete understanding since they don't reflect all the chemical reactions that occur when preparing the sauce.

And then some idiot editor comes along and gives it the title "Nobody knows how to make tomato sauce."

Anyway, the purpose of the talk page is to discuss how to improve the article, not navel gaze about epistemology.

There are two common ways to derive BP - apply conservation of energy or apply Newton's second law. The former is easier and only involves algebra so it is tractable for students at the grade school level. But it somewhat obscures the physics - the latter approach makes the physics clearer by starting with forces and acceleration, then applying a bit of calculus to compute the speed changes that occur because of the forces. Many people are confused as to why the air should have reduced pressure just because it has sped up, but when presented with an analysis of the forces due to pressure and the ensuing acceleration due to those forces it becomes much easier to see why the relationship between speed and pressure happens.

We present the conservation of energy approach first, I think because that's the order it is usually presented to students, but it tends to confuse people. Historically, the law of conservation of energy was not discovered for many decades after Bernoulli and Euler did their work, so perhaps that should come first? Mr. Swordfish (talk) 14:39, 14 June 2023 (UTC)

@Dolphin51: Thank you for the reminder. My understanding has moved on a bit since then. I still dislike the "Woo!" aspect, such as Regis's headline, which is why I only mentioned it here in passing. What a dangerous thing to do on Wikipedia! The problem I have with the conservation-of-energy argument as an "explanation" is that it does not rule out other energy-conserving phenomena, such as flow stalling or temperature change: it is as incomplete as the model it is trying to explain. But what does come out of this thread is that there is evidently still no clear answer available. — Cheers, Steelpillow (Talk) 15:41, 14 June 2023 (UTC)

You refer to “no clear answer available”. Are you suggesting that there is, or should be, one truly correct explanation for the Bernoulli effect or fluid dynamic lift? My view is that there is no “one true explanation of lift” (and similarly no “one true explanation of the Bernoulli effect”.) I believe these things can be explained satisfactorily in two or more ways. Unfortunately this is sometimes interpreted incorrectly as disharmony within the scientific community and therefore evidence that “No-one really knows why ... ...” Dolphin (t) 15:55, 14 June 2023 (UTC)

It is out of place to speculate here, but I do think that this is the billion-dollar question. The maths works, no question. But is the reason why that is the right math something waiting to be understood, or is the reason an irreducible complexity? It would be nice to be able to cite an answer to that. — Cheers, Steelpillow (Talk) 17:22, 14 June 2023 (UTC)

There is definitely a philosophical question there, worthy of a philosophical discussion. The answer and the discussion won’t be unique to Bernoulli’s principle. They will be equally applicable to conservation of energy, conservation of linear momentum, conservation of angular momentum; in fact all the conservation laws. These discussions have likely already taken place somewhere like Philosophy of science. Dolphin (t) 14:42, 15 June 2023 (UTC)

That is not quite the point being considered. There is the narrower question as to why, in the particular case of Bernoulli/Venturi, the conservation laws manifest as a reduction in pressure, and not as a change of say temperature and/or density. — Cheers, Steelpillow (Talk) 16:11, 15 June 2023 (UTC)

The simple reason is that when deriving the BP, temperature and density are assumed to be constant. If the model includes temperature and density changes then a more complex formula that relates speed, pressure, temperature, and density will be produced, i.e. the Euler equations.

Of course, this begs the question of why ignoring temperature and density changes is a good approximation for many scenarios. I don't have a simple answer to that, and even if I did we couldn't put it in the article unless we could find a source for it. Mr. Swordfish (talk) 23:26, 15 June 2023 (UTC)

Indeed. This is exactly the question I asked at the beginning: is there any such source? — Cheers, Steelpillow (Talk) 06:51, 16 June 2023 (UTC)

If your question can be presented as “when a gas is compressed its volume decreases pressure increases a little and its temperature increases a little. Why is the temperature change not more, or less? Why is there any change at all, in the temperature?” This type of question puzzled many scientists in the 19th century and it was eventually solved by formulation of the Second law of thermodynamics which, among other things, says entropy can increase or remain zero, but it never decreases. It may be that what you are questioning is why, in a Venturi or other example of the Bernoulli principle, does entropy not decrease? The Second law tells us that a reduction in entropy has never been observed so we assume it never will.

I acknowledge that Bernoulli’s principle is confined to incompressible liquids but my point is still valid. In a Venturi or other example of the Bernoulli principle the resulting pressure, temperature and velocity are always the same. What determines these resultant parameters? The answer is that these parameters are those that involve no change in entropy. Why does entropy remain unchanging in the absence of irreversibilities? See the second law of thermodynamics. Dolphin (t) 03:03, 17 June 2023 (UTC)

Of course, the second law of thermodynamics applies only to closed systems, while a body moving relative to a fluid is an open system, but something like that and/or the principle of least action may be at work here. If it is, then it is surprising that none of the smart people who have studied this question have ever figured it out. As Wikipedians, it is the sourcing that matters to us, not the explanation per se. — Cheers, Steelpillow (Talk) 08:05, 17 June 2023 (UTC)

Explanation on the molecular level

There is a lot of misinformation on Bernoulli, allowing many people to get an incorrect understanding of how it works. And the correct explanations typically use abstract terms like internal energy and dynamic pressure. While correct, these explanations are unintelligible to most people.

If we were able to explain it on the molecular level, as balls bouncing around, I would think that readers would have an easier time understanding the concept. There are few articles and videos explaining how it works on the molecular level. And the one’s I’ve seen are not as clear as I would like.

So my question - what does the community think about having a section in the article explaining what is going on at the molecular level, in a way that is fairly easy for average readers to understand? Showing that the molecules can only have so much velocity, and if that velocity is in the direction of flow, less velocity is available to make pressure. I’m happy to write it and make illustrations. But I’m also wary that there may be significant resistance from some editors… I’m not interested in an edit war. Thoughts? Thanks! --Zojj tc 21:04, 30 July 2023 (UTC)

Bernoulli's Hydrodynamica was the seminal work in Statistical Mechanics, and that's probably worth mentioning in the article, but I'm skeptical that a statistical approach to the topic will provide much in the way of an intuitive understanding of the BP. Of course, I'd be willing to look at a draft. That's what our sandboxes are for.

I'd be careful with the molecules can only have so much velocity, and if that velocity is in the direction of flow, less velocity is available to make pressure. argument - it's been somewhat refuted in this article: [[1]]

The reason so many people get an incorrect understanding of BP is that so many presentations get it backwards - they say the fluid speeds up for some reason (call it reason X) and this causes the pressure to drop. The problem with all these reason X explanations is that they are always wrong. If you start with pressure differences, it is easy to see that more pressure behind will exert a force that accelerates the fluid (and more pressure in front will decelerate it). The pressure differences cause the speed changes, not the other way around.

Granted, the equations don't talk about cause and effect, but for any intuitive understanding of force and acceleration, we humans are predisposed to think of forces causing acceleration, not the other way around. When you try to present the phenomena as "acceleration causes the force to appear" it's counter-intuitive. Mr. Swordfish (talk) 14:06, 31 July 2023 (UTC)

Good call on the sandbox. And thank you for link and your thoughts on how to better help people understand. At first glance the paper makes a leap on the perpendicular speed concept... I’ll look into it more. --Zojj tc 12:24, 2 August 2023 (UTC)