# Talk:Bernoulli's principle

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## Invert the redirect

Since at least since Feynman, 1962 (cited) who titles par. 40-3 as Bernoulli's theorem, Bernoulli's logical proposition has ceased to be considered as a principle but rather is explained as a theorem (also Lamb, Hydrodynamics, Cambridge 1895, derive it from Euler equations) I would kindly ask to invert the redirect with Bernoulli's theorem. Thank you for your kind answers. --87.10.61.143 (talk) 17:45, 28 December 2014 (UTC)

Do you have a reliable source verifying that "Bernoulli's logical proposition has ceased to be considered as a principle but rather is explained as a theorem"? Mr. Swordfish (talk) 21:01, 30 December 2014 (UTC)
1. Feynman, paragraph cited in the text. Never called a "principle".
2. Enciclopedia Britannica http://www.britannica.com/EBchecked/topic/62615/Bernoullis-theorem
3. Wolfram demonstration project http://demonstrations.wolfram.com/BernoullisTheorem/
John Hunter in [1] even call it Bernoulli's law. — Preceding unsigned comment added by 87.10.61.143 (talk) 13:25, 1 January 2015 (UTC)
There is a wide chasm between citing three examples of usage of "Bernoulli's theorem" and verifying that "Bernoulli's logical proposition has ceased to be considered as a principle but rather is explained as a theorem"
If you peruse the cited sources for this article you'll find that the terms principle, equation, law, theorem, and effect are used more or less interchangeably by the various sources to refer to Bernoulli's _______. Which to use as the main title for this article? I don't have a strong opinion but I'd need to see a much stronger argument than the one given before changing it. Mr. Swordfish (talk) 22:08, 2 January 2015 (UTC)

Of course you are right, you need a stronger argument. Excuse me, but in the actual wikipedia article is the Bernoulli stuff threated as a physical principle] (for which a derivation is at least contradictory) or as a theorem (for which a derivation is suitable but is more appropriately called a demonstration)? Come on! --87.10.61.143 (talk) 09:06, 3 January 2015 (UTC)

Out of curiosity I went to the library and took a look at some college physics textbooks to see who called it what. Here's what I found:

Bernoulli's Principle is used by the following authors:

• Howe
• Little
• Robeson
• Rusk
• Saunders
• Taylor (who also refers to it as Bernoulli's effect)
• Buckman
• Hudson

Bernoulli's equation is used by the following authors:

• Halliday & Resnick
• Sears
• Kungsburg
• Landau et. al.
• Borowitz
• Bueche
• Jones
• Ohanian
• Tilley
• Arfken et. al.

Bernoulli's Theorem is used by the following authors:

• Hausman & Slack
• Heil
• Randall
• Semat
• Smith
• Weber

In addition one text refers to it as Bernoulli's Law.

I don't claim that this count is dispositive. It's only Physics textbooks aimed at an introductory college physics course - different disciplines may prefer a different terminology. It's also only a sample of what my particular library had on it's shelves. And it would be a mistake to place equal emphasis on all these books since some are widely used and others are rather obscure.

I think it does demonstrate that we are on solid ground using the term "Bernoulli's Principle" and that there is no standardization of terminology across texts. "Bernoulli's equation" is the term most often used, but these are college physics texts after all so one would expect that equations would be emphasized.

At this point I am not seeing any compelling reason to rename the article. Mr. Swordfish (talk) 20:31, 8 January 2015 (UTC)

## Recent major changes by ip users

There have been a large number of substantive changes by two ip users (who may or may not be the same person). I've found that the best way to make major revisions to an article is to first propose a draft in the user's sandbox and ask for comment, as oposed to simply making them in-place. To that end, I'm reverting the changes. Ideally, the user(s) who proposed he changes will create an account and provide a draft in his/her sandbox. Then we can discuss here on the talk page to see if there's consensus to make the changes to the actual article.

At this point I haven't formed an opinion on whether the changes are an improvement or not - there are too many to digest all at once. Let's slow down and proceed deliberately. Mr. Swordfish (talk) 21:21, 28 December 2014 (UTC)

Ok, I accept your (deliberate) decision. Anyway please discuss the criticism I made above on the actual "derivation" and compare with classical text. In the paragraphs I added I also precisely referred to some traditional threatments made by Lamb, Feynman and other accessible sources: it's definitely not an original research or work of mine. Surely I am not glad to see that the author of the deliberate revert seems also to ignore this well-stablished threatment of the subject (Mr Swordfish said explicitly in the above paragraph "Derived from Euler equation?" he did not know the rigorous derivation, so I suppose he had not read at least the paragraphs in the books I cited). Moreover, there are few and at the same time minor sources that support the actual "derivation" from Newton's second law (I am sure it is not a formal derivation, it seems more to an explanation for freshmen who know the Newton's principles of dynamics and something on ordinary derivatives), at least at the present time. The first question I ask to Mr. Swordfish is: "Which are the sources calling this threatment "derivation"? Are they reliable?"

The sources that are currently cited (Feynman for example, largely cited) adopt the derivation from Euler equations and are somehow violated as appearing in support of another argumentation. To be clear: if Feynman says Euler-->Bernoulli of course I can cite him to say "Feynman says something on Bernoulli" and of course I cannot cite him to say: Newton-->Bernoulli. But I think that if I say Newton-->Bernoulli and I say "Feynman says something on Bernoulli" I should also honestly write at least also "but he has another point of view than us". This would be honest and transparent, while the actual reference system of the page is obscure and misleading. The freshman reading this article is brought to have 2 wrong ideas:

1. Well, I'll find similar and maybe deeper explanation on these books, while it is quite different 2. If he checks he could think somehow like Mr. Swordfish: "Why this particular derivation from Euler if one can derive it from Newton law?"

And then the second question I ask to Mr. Sworfish: "Why do you think Feynman (and others like Lamb) did not even cite the derivation from Newton law, provided he was talking both to experts and to freshmen?" Honestly, my opinion is: "Because it is misleading and do not provide any notable insight". Mr. Swordfish, I look forward to hearing from you, 87.10.61.143 (talk) 12:46, 29 December 2014 (UTC)

I have placed the proposed changes in my user space at User:Mr_swordfish/Bernoulli_principle. The current version of the article is the previous version in my user space so one can observe the diff at https://en.wikipedia.org/w/index.php?title=User%3AMr_swordfish%2FBernoulli_principle&diff=640150896&oldid=640150430
I invite the other editors to read the proposed changes and comment. Please make comments here rather than at my user space. It would be helpful for the editor proposing the changes to provide concise edit summary of the main changes and the reasoning behind them. Then we can try to arrive at consensus on whether these proposed changes are an improvement. Mr. Swordfish (talk) 22:17, 29 December 2014 (UTC)
@Mr Swordfish: Thank you for making your user space available to display the proposed new version of this article so those of us with an interest in the subject can attempt to reach consensus. That is very generous.
I have had a quick look at the proposed new version. My first impression is that it has taken a backward step with respect to the principle of WP:Make technical articles understandable. For example, the traditional version has, as its first sub-heading, "Incompressible flow equation" and progressively builds up the level of math, supported by appropriate explanation. In contrast, the proposed new version has, as its first sub-heading, "Formal derivation" and proceeds immediately with a lot of higher-level math. That is not the way Wikipedia articles should be built because Wikipedia is not an encyclopedia for people with PhD degrees.
Another change I noticed is that the sub-heading "Compressible flow in thermodynamics" and its entire content appear to have been erased. I don't see any explanation on the Talk page about why this sub-heading and its content have been erased. This article has reached a high level of maturity so major changes of the kind now being proposed should not be made without an explanation of why they are being made. I agree that, in the absence of an attempt to explain why each of these changes will improve the quality of the article, the changes should be reverted. Dolphin (t) 05:10, 30 December 2014 (UTC)

Dear Mr. Sworfish, I also thank you for the opportunity. Could you please also answer to my two questions? As you requested I summarise the main changes (the reasoning are essentially the ones I put above):

• Change from a newtonian (from Newton's second lawof dynamics) derivation (it is actually only an explanation "a fortiori") to a formal derivation from Euler equations (fluid dynamics) according to the authors I and other former editors cited
• Flow velocity u is distinguished from the misleading velocity v, since the first is not the time derivative of position (see material derivative!)
• Mathematical formalisation from the intuitive language one should avoid in an equation especially if with little effort one can explain the notation (like H = constant along a streamline was explained to be the way one should read in common language the equation:
${\displaystyle \mathbf {u} \cdot \nabla H=0}$

I think these points are right, maybe I made some mistakes in realising them into my edit. Could the community please improve my edit? Or if there is someone thinking it should be ignored or it is just rubbish, could you please say it explicitly here?

Dear Dolphin, I think there are a little straw man in your revision. For example, the math in the paragraph "Formal derivation" is not of PhD level but rather undergraduate (Feynman course of physics was thought for freshmen with introductory courses in diff calculus, and I can provide if you want many examples of undergraduate texts and wikipedia articles using the mathematics the paragraph required). Please believe me when I say that I am not a PhD in physics but a simple graduate in mechanical engineering. I think the article in its acual form is useless also from a computational point of view, while the formalisation makes it useful for checking the validity of an approximation in an hydraulic code. On the other hand I agree with the idea of a simple begin with progressive formalisation. But instead of the misleading newtonian explanation, why don't we put as in many wikipedia articles first the statements and simple paragraphs and then the "eulerian" paragraph "Formal derivation"? I mean, in comparison with the actual "newtonian" correspondant paragraph the eulerian one used also tools nearly of the same-level (divergence, gradients, in the eulerian ecc. against total derivatives and finite differences in the newtonian): I think it's also stupid to pretend freshmen to use nablas since introductory courses in electromagnetic theory and to suppose they don't know in fluid dynamics courses. Does someone disagree with Feynman's opinion (at the Vol. II, paragraph 40-2 The equations of motion, that was already cited in wikipedia article!):

"(The hydrodynamic equations are often closely analogous to the electrodynamics equations; that's why we studied electrodynamics first. Some people argue the other way; they think that one should study hydrodynamics first so that it will be easier to understand electricity afterwards. But electrodynamics is really much easier than hydrodynamics.)

I agree. I also think one does violate a source when he just pick up things and change the fundamental message, even if I know it's much more comfortable to pretend the source was just saying the same thing.

So I suggest: could some experts in theoretical fluid dynamics and/or transport theory please give a feedback on the "newtonian" derivation? Euler equations are formally derived from averaging in Chapman-Enskog approximation for some transport equations, for example from Boltzmann equation. Transport eq. can in turn be derived from Liouville equation for example by cutting the BBGKY hierarchy. On one hand, Liouville equation is much more general than newtonian dynamics. On the other hand, these procedures introduce cuts and approximations clearly informing at each step of the assumptions made, while this article boasts of a simple newtonian derivation and does not show the assumptions made. I repeat: in that paragraph the reader is brought to think that Bernoulli's principle is valid for any system for which Newton's second law is valid, and only for that newtonian system. And it is called formal derivation. This is no good!

Finally, why don't we edit according to influential references this paragraph I made, put it n the text in the order the community desire, and connect it with the former article? Could also someone please discuss the inversion of redirect to Bernoulli's theorem? Luckily, we are no more in the XXIIIth century, so we can change the name from the original one.

--87.10.61.143 (talk) 15:12, 30 December 2014 (UTC)

1) "Which are the sources calling this threatment "derivation"? Are they reliable?"
The derivation of Bernoulli's Principle (BP) directly from Newton's laws as in the current version of the article is fairly standard freshman physics that you should be able to find in the usual texts, eg Sears and Zemanski, Hocking and Young Young and Freedman, Halliday and Resnick etc. I can give you editions and page numbers once I get back to school from vacation if you'd like. A readily available version, although not exactly the same as in the article, can be found in the appendix to Babinsky's paper http://iopscience.iop.org/0031-9120/38/6/001/pdf/pe3_6_001.pdf . Yes, these are reliable sources.
2) Why do you think Feynman (and others like Lamb) did not even cite the derivation from Newton law, provided he was talking both to experts and to freshmen?
I have no idea why Fenyman did many of the things he did. Likewise, I have no idea why he didn't do some of the things he didn't.
Mr. Swordfish (talk) 22:20, 30 December 2014 (UTC)
First of all, thank you Mr Swordfish for your answer to the first question. I see the whole "derivation" (I see so it is called also in Babinsky's short article) is contained in the Appendix and is substantially the same of Wikipedia's article. But please note that "How do wings work" is a divulgative article on lift, that laterally (in the Appendix) talks about BT (Bernoulli's theorem, I insist). At least one should include also the other deeper and formal derivation. To go deeper in the second question, Feynman added after the formal derivation another one based on a mass balance on a control volume (same paragraph, 40-3). To introduce it, he said:
"Bernoulli's theorem is so important and so simple that we would like to show you how it can be derived in a way that is different the formal calculations we have just used. [...] The conservation of mass requires ..."
This is sustantially also why I agree with Dolphin when he suggests to go step by step. But I am still convinced that for now the article is partial and deficient. Note also I did not erase the Newtonian "derivation", but simply added another paragraph. So I recognise I was wrong when I put it as first paragraph: Dolphin, did I put it in the wrong place? Why don't you just check the punctual references I put and then move the paragraph where do you want? I think it could require some 10 minutes, and it should be worth the effort. --87.10.61.143 (talk) 15:13, 31 December 2014 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── @87.10.61.143: In the current version of this article, the first appearance of math is:

A common form of Bernoulli's equation, valid at any arbitrary point along a streamline, is:

${\displaystyle {v^{2} \over 2}+gz+{p \over \rho }={\text{constant}}}$

(A)

In contrast, in your proposed version, the first appearance of math is:

For an ideal fluid, the Euler equations hold: the momentum equation among them put in lagrangian form is:
${\displaystyle {\frac {D{\boldsymbol {u}}}{Dt}}+{\frac {\nabla p}{\rho }}-{\boldsymbol {g}}={\boldsymbol {0}}}$
or explicitly:
${\displaystyle {\frac {\partial {\boldsymbol {u}}}{\partial t}}+\mathbf {u} \cdot \nabla \mathbf {u} +\nabla \left({\frac {p}{\rho }}\right)-{\boldsymbol {g}}={\boldsymbol {0}}}$

This is too high a level of math for the first use of math, in any article. Also you are trying to suggest that some understanding of lagrangian mechanics is necessary for an understanding of Bernoulli’s principle!

A little further down, you propose:

The following tensor calculus identity holds for the covariant derivative of a sufficiently regular vector field:
${\displaystyle \mathbf {a} \cdot \nabla \mathbf {a} =(\nabla \times \mathbf {a} )\times \mathbf {a} +\nabla \left({\frac {1}{2}}a^{2}\right)}$

You are trying to suggest that an understanding of tensor calculus, covariant derivative and regular vector field are necessary for an understanding of Bernoulli’s principle! You are implying that these things come before Bernoulli’s principle!

You have defended this level of presentation by saying it isn’t PhD level but only undergraduate level. Wikipedia is not an encyclopedia for college undergraduates and above. Our article on Bernoulli’s principle is intended for anyone with an interest in Bernoulli, starting with young people and people with no formal education in math. That is why the lead section of this article, and most scientific and engineering articles, contain no math at all. After that, perhaps the simplest level of math might be introduced, working up eventually to the highest level of math available in reliable published sources. This is the important principle described at WP:Make technical articles understandable. Your proposed changes are not consistent with this most important principle, and therefore your proposed changes appear to be unacceptable to me. Remember, people are likely to hear about Bernoulli’s principle for the first time when they are 12 or 13 years of age and so the first section in our article must be understandable by 12 and 13 year olds. Wikipedia is not an encyclopedia for freshmen and above.

If you are serious about working on Wikipedia and making extensive, constructive changes, these things can only be done satisfactorily by registered users. Please give serious consideration to registering as a user, like Mr Swordfish and I have done. That way you will have a Talk page that we can use to communicate with you; you can have a Watchlist to monitor changes made to articles in which you have an interest, and you can initiate new articles; none of these things are available to unregistered users. Most unregistered users make edits from two or more IP addresses so they have no recognisable identity and it is therefore difficult to have a conversation with them. I have written all the above in an attempt to have a conversation with you, but I may choose not to do so again while you remain an unregistered user. Dolphin (t) 06:36, 1 January 2015 (UTC)

Thank you Dolphin, I appreciate your invitation but i do not want to register for Bernoulli's theorem. I think "If you are serious about working on Wikipedia and making extensive, constructive changes, these things can only be done satisfactorily by registered users." is wrong. If I am allowed to modify and answer to your questions "Dolphin51"contains the same information on the user as 87.10.61.143. If you tell me you are confident with this topic and I told you I am too, these informations are equally both not verifiable. For what concerns: "@87.10.61.143: In the current version of this article, the first appearance of math is: [...] In contrast, in your proposed version, the first appearance of math is: [...] This is too high a level of math for the first use of math, in any article. Also you are trying to suggest that some understanding of lagrangian mechanics is necessary for an understanding of Bernoulli’s principle!". Now:

1. Have you ever read my sentences: "Finally, why don't we edit according to influential references this paragraph I made, put it n the text in the order the community desire, and connect it with the former article?" and ":::This is sustantially also why I agree with Dolphin when he suggests to go step by step. But I am still convinced that for now the article is partial and deficient. Note also I did not erase the Newtonian "derivation", but simply added another paragraph. So I recognise I was wrong when I put it as first paragraph: Dolphin, did I put it in the wrong place? Why don't you just check the punctual references I put and then move the paragraph where do you want? I think it could require some 10 minutes, and it should be worth the effort"?

2. Do you know lagrangian mechanics has nothing to do with material derivative except for the author, Lagrange? In which equations I put do you find some lagrangian mechanics?

I am a little astonished... --87.10.61.143 (talk) 13:41, 1 January 2015 (UTC)

In your proposed version, at the first appearance of a math expression, you say: "For an ideal fluid, the Euler equations hold: the momentum equation among them put in lagrangian form is:"
This may not be lagrangian mechanics but it implies that to understand the introductory math associated with Bernoulli the reader must first understand the expression "lagrangian form". Dolphin (t) 05:53, 2 January 2015 (UTC)

Well Dolphin, whether you are precise you are right, so the problem apperas to me very easy to solve:

"For an ideal fluid, the Euler equations hold: the momentum equation among them, expressed with the material derivative, is:"

Are there other issues? I will be glad to explain and improve the obscure points... I am sure such obscure language terms are not compromising the whole paragraph. Have you ever checked the consinstency with the sources I cited? I insist given also their online versions are open-access and the paragraphs required are very short. --87.10.61.143 (talk) 15:14, 2 January 2015 (UTC)

If the expression "Lagrangian form" is erased and replaced by "material derivative", nothing changes. When "Lagrangian form" is used it implies readers must comprehend this expression before they can comprehend the first appearance of math in an explanation of Bernoulli. When "material derivative" is used it implies readers must comprehend this expression before they can comprehend the first appearance of math in an explanation of Bernoulli.
Bernoulli is a relatively simple physical concept. Even the math associated with the Bernoulli equation begins with a relatively simple algebraic equation. It can all be comprehended long before people reach the stage in their math where they are conversant with Lagrangian form and material derivative. We are expected to maintain this article in conformance with WP:Make technical articles understandable. Dolphin (t) 07:10, 4 January 2015 (UTC)

Dolphin, I say it for the last time since you seem not to get what I say: of course I agree with "Bernoulli equation begins with a relatively simple algebraic equation. It can all be comprehended long before people reach the stage in their math where they are conversant with Lagrangian form and material derivative. We are expected to maintain this article in conformance with WP:Make technical articles understandable." So I simple would like to add the paragraph I wrote after all that introductory stuffs you care about so much. Nothing more. "When "Lagrangian form" is used it implies readers must comprehend this expression before they can comprehend the first appearance of math in an explanation of Bernoulli": it is clearly a straw man argument. Please do not repeat another time that it is important to introduce step by step poor common readers to the argument and so on. I do agree with you, so this part of the discussion is finished. We are now talking about adding another paragraph, as I said several times before. Dolphin, if you want to really answer me, you should just say whether, and why, you think the paragraph I'm adding at the end, and not substituting the old simple ones, is violating the principle WP:Make technical articles understandable. I carefully read but I could not find any violation.

Moreover, without this part this article is suitable for a childpedia, not for wikipedia. See for example Special relativity or Quantum mechanics - simplified: one should simplify as possible but not omit and delete some aspects and connections with other arguments of the topic (like material derivative). To explain QM to common people clearly another page was created and the technical and fundamental page was not contaminated. Two very differnt targets --> two articles. Bernoulli's theorem as well as these articles have really in their original, formal and more useful sense the contents not suitable for everybody. "Bernoulli equation begins with a relatively simple algebraic equation. It can all be comprehended long before people reach the stage in their math where they are conversant with Lagrangian form and material derivative". Of course if "it" stand for "the relatively simple algebraic equation". If you had said "Bernoulli's theorem can all be comprehended long before people reach the stage in their math where they are conversant with Lagrangian form and material derivative", you would have been wrong. You can't vulgate Bernoulli to such a ground level and then think to have been exhaustive. I repeat this point for example: try to write a CFD program with these equations. They are just toys: useful for learning, not for working. If you want to introduce children or people with unknown basis in math and physics, basing on experience on the QM page we should put all these very discursive and introductory things (like the awful combination of math and common languange "= constant on a streamline") on a page like Bernoulli's theorem - simplified.

Another question: hey, I think there should be anyone else interested in this edit beside Dophin, Mr Swordfish and me. Is the decision of one or three people democratic for Wikipedia? Who gives Mr Swordfish ort Dolphin the authority to revert my edit? I think it should come from the decision of a larger community... --87.10.61.143 (talk) 23:46, 7 January 2015 (UTC)

87.10.61.143,
I would suggest that you familiarize yourself with the standard wikipedia policies and procedures at the help page. In particular, you may find WP:CONSENSUS, WP:POLICY, WP:CIVIL, WP:DISPUTE, WP:ACCOUNT, WP:TALK, WP:INDENT, WP:EQ and WP:WALLS to be informative. This is not an exhaustive list.
I can't speak for other editors, but I can say that I have well over a hundred articles on my watch list and tend to remain silent about 99% of the time if I think the involved editors are sorting things out acceptably. I can't say for sure, but I'd surmise that this is what's going on here.
Other editors,
Is there support for any of these proposed changes? If so, I will be happy to continue discussing them. Mr. Swordfish (talk) 15:19, 8 January 2015 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── @87.10.61.143: I will summarize my understanding of what has happened with this article, and with your proposed changes.

• Beginning on 25 July 2002 and progressing through to 28 December 2014, many editors worked on this article and raised it to an accurate and mature document on the subject of Bernoulli’s principle. Since June 2009 one of the major contributors to the article has been Mr Swordfish.
• From 15 December 2014 until 28 December 2014 a number of anonymous editors made a large number of significant changes to the article. Up until that date, none of these anonymous editors explained what they were trying to achieve, or what problems they were trying to solve.
• On 28 December 2014 Mr Swordfish returned the article to its status at 15 December. As anonymous editors cannot create personal sandbox pages, he copied the proposed alternative version of the article, as at 28 December, into one of his own sandbox pages so the anonymous authors of these changes could work on the new version. See User:Mr_swordfish/Bernoulli_principle. This is a very generous gesture by Mr Swordfish. The associated Talk page is available to these anonymous editors and others to discuss problems with the existing version, and to discuss the proposed changes - see User talk:Mr_swordfish/Bernoulli_principle. On Wikipedia, the only way to make substantial changes to a mature article is to consult with others who have an interest in the article, persuade them of the need to make changes, and seek agreement on what the changes should say. See WP:Consensus. If substantial changes are made to a mature article without first offering to engage in discussion, those changes will inevitably be reverted and the author will be asked to withhold his changes until he has first explained why substantial changes are needed, and why his proposed changes will improve the quality of the article. This will always be more difficult for users who edit anonymously from a number of different IP addresses than for a registered user.
• You have asked me to help improve your proposed version of the article. In the absence of some explanation of what problems exist with the current version, I remain satisfied with that current version. I don’t see a need for substantial changes so I am not inclined to help you develop your proposed version. If you agree that your version requires further work I think you will have to do it yourself. I suggest you begin by using the Talk page to explain what problems you see with the current version of this article, and why you see a need for substantial changes. Mr Swordfish has kindly provided a Talk page for you to do all of these things - User talk:Mr_swordfish/Bernoulli_principle. Once people have been persuaded of the need to make substantial changes, we can all move on to discuss why your proposed changes are the remedy for the problems. Dolphin (t) 06:09, 9 January 2015 (UTC)

## Removed GF content in March

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 (talkcontribs)

"In fluid dynamics, Bernoulli's principle states that for an inviscid flow of a non-conducting fluid, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.[1][2] The principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738.[3]"

This is not really clear for someone who doesn't already know something about fluid dynamics. And that just an example of the style of the whole article. While we don't want to dumb things down, the article would benefit from some additional context for non-experts. In particular, the introduction should be accessible to a wide audience. 96.50.110.69 (talk) 15:50, 17 February 2016 (UTC)

I have simplified the statement to agree with the definitions in Britannica and Merriam-Webster. The previous statement was incorrect: Bernoulli’s principle is a consequence of the law of conservation of energy and is not limited to inviscid non-conducting fluids. The contributor was perhaps describing Bernoulli’s equation, which is also covered by the article. However, the principle is of wider application than the equation.
If a contributor still wishes to include inviscid and non-conducting, this can be done in the next section, which is about the equation. Nevertheless, other authorities ( for example Princeton University) do not apply that constraint. Apuldram (talk) 12:30, 22 February 2016 (UTC)
The revised text continues to cite Aerodynamics by L.J. Clancy, but the revised text isn't consistent with what is stated by Clancy. Consider a garden hose: the speed of flow through the hose is constant and yet the pressure falls progressively along the length of the hose so that the pressure at the outlet is equal to atmospheric pressure. The pressure gradient along the hose is caused by the viscous shear stresses that act on the water moving along the hose. Dolphin (t) 14:00, 22 February 2016 (UTC)
Agreed. I have modified the text to remove any implication that an increase in speed is the only cause of a pressure reduction. Apuldram (talk) 17:15, 22 February 2016 (UTC)
I have reverted these recent ""simplification" edits. The wording is too close to the lazy and misleading presentation of Bernoulli's principle you see in elementary texts: "Faster moving air has lower pressure". We need to be careful to not reinforce this common misconception. That said, I have no problem with simplification per se. Let's just make sure that the language does not imply that the oft-repeated but incorrect presentation. I would prefer to come to consensus here on the talk page before making further edits. Mr. Swordfish (talk) 20:54, 22 February 2016 (UTC)

The words inviscid and non-conducting in the first sentence of the lead are misleading and should be removed. How did those contributions arise? Possibly through a confusion of Bernoulli's principle with the pressure calculations in the various versions of Bernoulli's equation. Possibly through unsound logic. The pressure at a point in a fluid system is independently affected by several factors, including: Bernoulli's principle; a change in potential, for example, gravitational potential; loss of energy through friction. That does not mean that Bernoulli's principle is dependent on the absence of friction, on the fluid being inviscid.

• inviscid. Bernoulli's principle applies also to viscous fluids, and is used, for example in the oil industry, in flow measurement for petroleum, a far from inviscid fluid. See Orifice plate.
• non-conducting. Bernoulli's principle is valid for brine, which is definitely not non-conducting, and for several other conducting fluids used in the chemical industry.

The lead sentence is correct - the principle does apply to inviscid non-conducting fluids - but misleading, as the principle also applies to viscous conducting fluids. In addition to being misleading it confuses non-technical readers, see the section above. We should try to make (at least the lead section) as understandable to as many readers as possible, see the advice here. Apuldram (talk) 11:02, 24 February 2016 (UTC)

I have no issue with removing the words inviscid and non-conducting in the first sentence of the lead as long as these provisos are adequately explained later. My issue is with language that implies a cause-and-effect relationship where a change is speed causes a change in pressure. Consider the recently reverted language:
In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid is accompanied by a decrease in pressure or a decrease in the fluid's potential energy.[1][2][3]
contrasted with the current language:
...an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.
This may seem like hair-splitting, but there's a large body of incorrect and misleading material out there saying an increase in speed causes a decrease in pressure and we need to avoid that. Looking forward to seeing other editors' opinions on this. Mr. Swordfish (talk) 21:26, 25 February 2016 (UTC)
I am content with the wording: "... an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy". My concern is that the words inviscid and non-conducting should be removed, as they falsely imply that Bernoulli's principle only applies to inviscid non-conducting fluids. Apuldram (talk) 10:47, 26 February 2016 (UTC)

I have now removed the misleading adjectives in the first sentence of the lead. A later section, Incompressible flow equation, indicates that the more specific equation assumes negligable friction. Apuldram (talk) 15:41, 2 March 2016 (UTC)

I reinstated inviscid and non-conducting. These words just indicate the conditions under which Bernoulli's principle/equation is valid: negligible effects of viscosity and conduction. The words inviscid and non-conducting, as well as the word fluid itself, refer to the concepts as used in certain models applied in fluid dynamics (which is the framework of the article). With inviscid and non-conducting is not meant that real fluids exist having these properties: it just refers to (part of the) flow in which their effects can be neglected and thus Bernoulli's principle can be applied. Acclaimed textbooks on fluid dynamics, like those by Batchelor and Landau & Lifshitz, clearly state the conditions under which Bernoulli's principle is a useful approximation. -- Crowsnest (talk) 21:35, 5 March 2016 (UTC)
Please distinguish between Bernoulli's principle and the several forms of Bernoulli's equation. The principle is valid for viscous and conducting fluids, as evidenced by the examples I gave above. It is misleading to imply otherwise. We cannot deny that, in applications of fluid dynamics, in viscous flow of a conducting fluid, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. The principle applies over a wide range of compressibilities, viscosities and conductivities.
The second and third paragraphs of the lead section help to explain the derivation and wide applicability of the principle.
However, some of the various equations are indeed approximations, and it is right that they should carry caveats, such as incompressible, frictionless or adiabatic, to indicate the conditions under which they are reliable approximations. Apuldram (talk) 22:38, 5 March 2016 (UTC)
The orifice plate is indeed a very good example, since it clearly shows that Bernoulli's principle is not a general principle, but only applicable when the flow can be treated as inviscid. As the description section of the article says, Bernoulli's principle is applicable upstream of the vena contracta – the cross section where the flow contraction is largest. In the flow expansion downstream of the vena contracta, Bernoulli's principle is not valid (but the empirical Borda–Carnot equation) because there is viscous dissipation. For a strong constriction of the flow by the orifice plate (with loss coefficient ξ equal to one) the velocity drops in the flow expansion downstream of the vena contracta, while the pressure stays constant (at the same value as at the vena contracta).
Ultimately, examples don't count in Wikipedia. What counts are reliable sources of due weight, like Batchelor and Landau & Lifshitz. And they clearly state that Bernoulli's principle is only valid under certain conditions, which is also important to mention in the lead of the article, see WP:LEDE: ... "The lead should stand on its own as a concise overview of the article's topic. It should identify the topic, establish context, explain why the topic is notable, and summarize the most important points, including any prominent controversies."
I cannot find reliable references which support the distinction you make between "Bernoulli's principle" and "Bernoulli's equation". Note that also "Bernoulli's theorem" is often used:
Bernoulli's principle 86,000 1,420 6,060
Bernoulli's theorem 42,300 1,700 9,740
Bernoulli's equation 155,000 8,200 25,200
Bernoulli's law 21,000 1,300 3,200
"Bernoulli's equation" is most often used. The scientific community – in this case the science of fluid dynamics, see the columns for "Google Scholar" and "Google Books" – also frequently utilizes "Bernoulli's theorem", e.g. Batchelor, Milne-Thomson, Feynman, Leighton & Sands. While Landau & Lifshitz and Tritton use "Bernoulli's equation" in these authoritative fluid-dynamics textbooks. -- Crowsnest (talk) 20:23, 11 March 2016 (UTC)
The above contribution makes the statement: "As the description section of the [Orifice plate] article says ..." and then follows it immediately with opinions which are not in the description section, nor anywhere else in that article.
The description section of the Orifice plate article says that the velocity reaches its maximum and the pressure reaches its minimum a little downstream of the orifice, at the vena contracta.
This is in accordance with Bernoull's principle that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure. As the fluid whose flow is being measured is often petroleum or a viscous chemical, this is a demonstration that Bernoulli's principle applies to viscous fluids as well as inviscid ones. Apuldram (talk) 10:17, 13 March 2016 (UTC)
This means we agree that – for the case of the orifice plate – Bernoulli's principle is only valid up to the vena contracta, and not in the flow expansion where viscous effects are important. Since the references I gave before (e.g. Batchelor and Landau & Lifshitz) clearly state the conditions under which Bernoulli's principle is applicable, I will adapt the lede accordingly. – Crowsnest (talk) 21:48, 16 March 2016 (UTC)
No. We do not agree. Nowhere in the orifice plate article, or in my contribution, is any implication that "Bernoulli's principle is only valid up to the vena contracta, and not in the flow expansion where viscous effects are important." In fact, the opposite is stated in the article: "Beyond that [the vena contracta], the flow expands, the velocity falls and the pressure increases." That is in accordance with Bernoulli's principle and demonstrates that Bernoulli's principle applies to viscous fluids as well as to inviscid ones. Once again, Crowsnest has made a statement which, when checked, is shown to be untrue. Apuldram (talk) 22:48, 17 March 2016 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── Well, it is (besides all references mentioned before) also in accordance with for instance "Orifice Plates and Venturi Tubes" by Michael Reader-Harris, 2015, ISBN: 978-3-319-16879-1, page 7: "In the case of an orifice plate ... the flow continues to converge downstream of the plate with the location of maximum convergence called the vena contracta. The fluid then expands and re-attaches to the pipe wall; however there is a relatively large net pressure loss across the plate which is not recovered. Bernoulli's Theorem can be applied between an upstream plane and the vena contracta..." and pp. 62–65 showing how a momentum balance (see Borda–Carnot equation) instead of Bernoulli's principle has to be used in the flow expansion downstream of the vena contracta.

Further, you have not provided reliable secondary sources supporting your point of view. -- Crowsnest (talk) 11:00, 18 March 2016 (UTC)

My take is that the words inviscid and non-conducting in the first sentence of the article are a distraction for most readers and are not necessary. There are many assumptions underpinning Bernoulli's principle and these are just two of them. Strictly speaking, Bernoulli's principle (and almost everything else in fluid dynamics) only applies to continuous fluids, not the discrete collection of molecules that comprise any real fluid. But for most real fluids we can neglect the molecular nature of the fluid and treat it as a continuum. So, the first sentence of this article is not the place to go into a digression on the continuum assumption. It's also not the place to bring up viscosity and conduction.

I do think that these assumptions should be covered, but at a later point in the article so that the lay-reader isn't confronted with distracting jargon in the first sentence. For most real-world fluids, including the two most common ones, water and air, the effects of conduction, viscosity, and molecule-ness are negligible and Bernoulli's principle applies to them, at least in most situations. So, the simply worded current lead ("Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.") is not misleading. Agree that it's not as complete as it might be, but sometimes as editors we need to make the trade off between readability and complete precision.

I would have no objections to making the assumptions explicit in the article, and noting that Bernoulli's principle is not a general principle but only applies when certain assumptions are met. If worded carefully, this material can be incorporated into the lead section. But I don't think cramming a couple adjectives into the first sentence serves the readers. Mr. Swordfish (talk) 15:59, 18 March 2016 (UTC)

I agree with Mr Swordfish's summary of the situation, and I support his proposed trade-off.
A relevant consideration is Wikipedia:Make technical articles understandable. The beginning of all technical articles should be understandable to young people and others who are new to the field. Complexity should be added progressively so that, by the end of the article, even the most knowledgeable reader feels satisfied that the article is complete. Dolphin (t) 11:01, 19 March 2016 (UTC)
@Mr swordfish: There are just 3 assumptions made in the derivation Bernoulli's equation, all mentioned by you: the continuum hypothesis, inviscid flow and a non-conducting fluid. See Landau & Lifshitz pp. 1 & 3, Batchelor pp. 4 & 159 ("We shall suppose, throughout this book, that the macroscopic behaviour of fluids is the same as if they were perfectly continuous in structure ..." and "The particular fluid properties found to be sufficient for validity of Bernoull's theorem—zero values of the viscosity and heat conductivity ...").
@Mr swordfish and Dolphin51: I agree fully with you about needing to find a wording which is understandable. From MOS:LEAD: "The lead should stand on its own as a concise overview of the article's topic. It should identify the topic, establish context, explain why the topic is notable, and summarize the most important points, including any prominent controversies." Besides the omission of a clear description in the article of the conditions under which Bernoulli's equation has been derived, to my opinion it is important to mention something about this context of its derivation/validity/applicability in the first or second paragraph of the lead.
-- Crowsnest (talk) 22:32, 20 March 2016 (UTC)
I’d support the inclusion in the lead section of a paragraph that makes it clear that Bernoulli’s equation is subject to the caveats we’ve discussed. Landau & Lifshitz clearly state (chapter 1 section 5 page 10) that Bernoulli’s equation is subject to the constraints of an ideal fluid, i.e. one in which thermal conductivity and viscosity are minimal (c1 s2 p4). For the reasons I’ve already given I’d oppose any implication that the caveats apply to Bernoulli’s principle. Orifice plates demonstrate that Bernoulli’s principle is valid for viscous or conducting fluids.
Reliable accessible sources that provide a definition can be found here, here and here. The first of these is the best, as it shows the reversible nature of the principle, but is too long (IMO) for inclusion in the lead. Apuldram (talk) 11:51, 19 March 2016 (UTC)
I have provided enough references, and you have provided none, to show that Bernoulli's principle only applies in the flow upstream of the vena contracta [for the case of the orifice plate]. Further for your information: counter-examples are: 1. for a pipe of constant cross-section and viscous flow, the velocity is the same in each cross section while the pressure drops in the downstream direction; 2. for a pipe exit into a large vessel all kinetic energy (dynamic pressure) in the Bernoulli constant is ultimately lost [dissipated] by viscous friction, the velocity drops to zero while the pressure in the pipe exit and the vessel are the same (instead of rising according to Bernoulli's principle).
The terms Bernoulli's principle/equation/theorem/law are all used interchangeably in the literature. Since you like to cite encyclopediae and dictionaries, see e.g. [2]. You do not provide reliable sources supporting the distinction you make. On the contrary, the first link provided by you derives Bernoulli's equation from the conservation of kinetic energy (for the case without friction/viscosity), and calls the equation "Bernoulli's principle".
On further comments by you in which you do not provide reliable secondary sources, I may feel free not to react. -- Crowsnest (talk) 22:32, 20 March 2016 (UTC)

We had a discussion about a year ago (Dec 2014) regarding the title of the article, whether it should be called Bernoulli's Principle, equation, law, theorem etc. I did a little research and posted the following: --begin quote--

If you peruse the cited sources for this article you'll find that the terms principle, equation, law, theorem, and effect are used more or less interchangeably by the various sources to refer to Bernoulli's _______...

...I went to the library and took a look at some college physics textbooks to see who called it what. Here's what I found:

Bernoulli's Principle is used by the following authors:

• Howe
• Little
• Robeson
• Rusk
• Saunders
• Taylor (who also refers to it as Bernoulli's effect)
• Buckman
• Hudson

Bernoulli's equation is used by the following authors:

• Halliday & Resnick
• Sears
• Kungsburg
• Landau et. al.
• Borowitz
• Bueche
• Jones
• Ohanian
• Tilley
• Arfken et. al.

Bernoulli's Theorem is used by the following authors:

• Hausman & Slack
• Heil
• Randall
• Semat
• Smith
• Weber

In addition one text refers to it as Bernoulli's Law.

I don't claim that this count is dispositive. It's only Physics textbooks aimed at an introductory college physics course - different disciplines may prefer a different terminology. It's also only a sample of what my particular library had on it's shelves. And it would be a mistake to place equal emphasis on all these books since some are widely used and others are rather obscure.

I think it does demonstrate that we are on solid ground using the term "Bernoulli's Principle" and that there is no standardization of terminology across texts. "Bernoulli's equation" is the term most often used, but these are college physics texts after all so one would expect that equations would be emphasized. --end quote--

In terms of the present discussion, my reading of this material is that they make no distinction between Bernoulli's equation and Bernoulli's principle (or law or theorem or effect) - some authors call it one thing, others call it something else, but it's all the same idea. The distinction between principle and equation is a false one that is not supported by the relevant literature and further discussion along those lines does not help to improve the article. Mr. Swordfish (talk) 18:57, 21 March 2016 (UTC)

Thanks for the quote. That is an impressive inquiry, which I missed out on previously! -- Crowsnest (talk) 14:45, 22 March 2016 (UTC)

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