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Can Bernoulli's principle be applied to bird flight?

I am a biologist and I have always believed that Bernoulli's principle could be used to explain aspects of bird flight due to the aerofoil shape of their wings. Is this true? I have looked at this page and several others on flight and birds, but none seem to make the connection. If it is true, it could make a useful addition to this article on Bernoulli's principle.__DrChrissy (talk) 20:52, 11 February 2013 (UTC)

I am not a biologist, but my understanding is that the motion of a bird's wing in flight is far more complicated than a simple airfoil (e.g. a wing of a fixed-wing aircraft) making rigorous mathematical analysis very difficult. Many books on birds do use the Bernoulli principle to explain bird flight, unfortunately they tend to rely on the erroneous equal-transit-time fallacy to do so. You can see some examples at http://en.wiki.x.io/wiki/User:Mr_swordfish/List_of_works_with_the_equal_transit-time_fallacy I am unaware of any sources that correctly utilize Bernoulli's prinicple to explain bird flight; I think it's possible, but unless we can find reliable sources to cite we can't put it in the article. Mr. Swordfish (talk) 21:47, 11 February 2013 (UTC)

Thanks very much for the informative and speedy answer. I wonder if Bernoulli's prinicple might be used for specific cases such as soaring birds (e.g. vultures) which tend not to flap their wings, however, I concede that they do make small adjustments to maintain balance. Another possibility is the penguin which 'glides' underwater. It just strikes me that a physics principle which explains why a plane stays in the air should help explain why a bird with a similar wing shape also stays in the air. ...but perhaps I am on the wrong flight path  ;-) __DrChrissy (talk) 22:04, 11 February 2013 (UTC)

You are on the right track. These are all examples of aerodynamic lift, and the physical principle is the same whether it's a plane, a helicopter, or a bird. There are multiple ways to explain lift, some of which utilize Bernoulli's principle, however simple explanations using Bernoulli's principle are usually incorrect. See the lift article for details. Mr. Swordfish (talk) 22:34, 11 February 2013 (UTC)

I agree with Mr Swordfish. Man's first attempts to construct functional airfoils were based on the thin cross-sections of birds' wings. For that reason, early triplanes and biplanes had wings with very thin cross-sections. It was only towards the end of World War I that aircraft designers departed from the thin cross-sections of birds' wings and tried thicker airfoil sections, and ultimately moved on to monoplanes with relatively thick airfoil sections. Presumably birds did not evolve thick wings because such wings can't be folded readily, and wouldn't articulate well for flapping flight.

Bernoulli's principle is just as applicable to the flight of birds as to the flight of aircraft. However, Bernoulli's principle can only ever be half of the explanation. The other half needs to explain why the air moves faster across the top surface of the wing than across the bottom surface. To explain this other half, I use the Kutta condition. This not only establishes that the air moves faster across the top surface, it also explains why all airfoil sections, including birds' wings, have sharp trailing edges. Dolphin (t) 04:57, 12 February 2013 (UTC)

Thanks again for the extremely useful information. Your comment on birds having thin wings started me thinking. One exception to this is possibly the penguin wing (flipper) where the leading edge is actually relatively thick. I wonder if this is due to differences between aerodynamics and hydrodynamics, although my very basic knowledge of physics is that the two are very similar. Thanks again __DrChrissy (talk) 17:20, 13 February 2013 (UTC)

I don't think it has to do with any hydrodyanmic/aerodynamic difference. A simple explanation is that birds that fly need to be light weight, so thicker wings would be a disadvantage. Since penguins don't fly they can be heavy, and this is exhibited in more ways than just "thick flippers". Another factor is that they live in cold temperatures which favors thicker rounder body shapes to minimize heat loss. Of course, this is just speculation on my part and we're getting away from discussing the article. Mr. Swordfish (talk) 18:44, 13 February 2013 (UTC)

Yes, we are getting off the subject of this article - thanks again for your help.__DrChrissy (talk) 19:11, 13 February 2013 (UTC)

DrChrissy mentioned that penguins' flippers have relatively thick leading edges. My comment was not about thin leading edges but about sharp (thin?) trailing edges. All subsonic airfoils have rounded (thick?) leading edges with a generous radius. It may be that the thick leading edges on penguins' flippers are perfect examples of low-speed foils. Dolphin (t) 00:12, 14 February 2013 (UTC)

All? Sailboats and early airplanes are obvious counter-examples. Mr. Swordfish (talk) 01:19, 14 February 2013 (UTC)

Good point. Flat plates, thin plates and flexible plates can be used to generate lift because they all have sharp trailing edges. (However, they can only generate a low wing loading.) The sails on a sailboat are a good example of a thin, flexible structure that is employed solely for the purpose of generating lift. In aerodynamics, it is customary to use the term airfoil to refer to a rigid structure employed to generate lift. The precise shape of an airfoil is usually defined by x and y co-ordinates that establish the shape to within one or two hundredths of an inch at every point on the perimeter. (See NACA airfoil.) The keel on a sailboat is a good example from hydrodynamics of a rigid foil shape. Dolphin (t) 01:50, 14 February 2013 (UTC)

all airfoil sections, including birds' wings, have sharp trailing edges. Dolphin (t) 04:57, 12 February 2013 (UTC)

The lifting body space re-entry vehicle prototytpes, Northrop_M2-F2 and Northrop_M2-F3, have fairly thick trailing edges (for the M3-F3, that's where the rocket engines nozzles were located). A wedge with the sharp end at the front and thick end at the back will generate lift. The problem with a thick trailing edge is the large amount of drag produced. Rcgldr (talk) 08:37, 29 March 2013 (UTC)

Recent edits removing quotes from references

Recent edits have removed relevant quotes from some references. Is there a reason behind this? I find that a short quotation in-line within a cite is very helpful in establishing verifiability since it saves the reader from having to click through to the source and try to find the relevant material. I haven't found any wiki policy addressing this specifically though; it's my own preference and I understand that it may not be universally shared.

So I'm curious, why the removal? Mr. Swordfish (talk) 14:29, 3 June 2013 (UTC)

I agree that a quotation from the cited source can be very helpful where I don't have access to the source document. Even if the in-line citation directs to a web site, a quotation is often sufficient and I find I don't need to access the web site.

Your question will be more easily answered if you post some of the diffs showing erasure of quotations. Dolphin (t) 09:34, 6 June 2013 (UTC)

The following quotations have been removed from the footnotes:

• Babinsky: "If the particle is in a region of varying pressure (a non-vanishing pressure gradient in the x-direction) and if the particle has a finite size l, then the front of the particle will be ‘seeing’ a different pressure from the rear. More precisely, if the pressure drops in the x-direction (dp/dx < 0) the pressure at the rear is higher than at the front and the particle experiences a (positive) net force. According to Newton’s second law, this force causes an acceleration and the particle’s velocity increases as it moves along the streamline... Bernoulli’s equation describes this mathematically (see the complete derivation in the appendix)."

• Denker: " The idea is that as the parcel moves along, following a streamline, as it moves into an area of higher pressure there will be higher pressure ahead (higher than the pressure behind) and this will exert a force on the parcel, slowing it down. Conversely if the parcel is moving into a region of lower pressure, there will be an higher pressure behind it (higher than the pressure ahead), speeding it up. As always, any unbalanced force will cause a change in momentum (and velocity), as required by Newton’s laws of motion."

• Babinsky: "In fact, the pressure in the air blown out of the lungs is equal to that of the surrounding air..."

• Eastwell: "...air does not have a reduced lateral pressure (or static pressure...) simply because it is caused to move, the static pressure of free air does not decrease as the speed of the air increases, it misunderstanding Bernoulli's principle to suggest that this is what it tells us, and the behavior of the curved paper is explained by other reasoning than Bernoulli's principle."

• Babinsky: "Blowing over a piece of paper does not demonstrate Bernoulli’s equation. While it is true that a curved paper lifts when flow is applied on one side, this is not because air is moving at different speeds on the two sides... It is false to make a connection between the flow on the two sides of the paper using Bernoulli’s equation."

• Eastwell: ""An explanation based on Bernoulli’s principle is not applicable to this situation, because this principle has nothing to say about the interaction of air masses having different speeds... Also, while Bernoulli’s principle allows us to compare fluid speeds and pressures along a single streamline and... along two different streamlines that originate under identical fluid conditions, using Bernoulli’s principle to compare the air above and below the curved paper in Figure 1 is nonsensical; in this case, there aren’t any streamlines at all below the paper!"

• Denker: "Bernoulli’s principle is very easy to understand provided the principle is correctly stated. However, we must be careful, because seemingly-small changes in the wording can lead to completely wrong conclusions."

• Babinsky: "...if a streamline is curved, there must be a pressure gradient across the streamline, with the pressure increasing in the direction away from the centre of curvature."

It is unclear whether this removal was intentional or merely an artifact of re-formatting and consolidating the citations. If it was unintentional, then we should restore them. If it was intentional, I'd like to hear the reasoning behind it. Mr. Swordfish (talk) 14:48, 6 June 2013 (UTC)

Regardless of whether the erasures were intentional or inadvertent, I'm in favor of them all being restored. If someone objects to the restorations, someone can then join this discussion and explain why the quotations should be erased again. So far, no-one has responded to this thread and argued that the article is better without the quotations. Dolphin (t) 11:55, 7 June 2013 (UTC)

I have restored the inline quotations by reverting the citation cleanup. I welcome a future citation cleanup to format the cites in a more consistent manner, but please do not remove useful content when doing so. Mr. Swordfish (talk) 02:30, 24 June 2013 (UTC)

Intro

I'm a science and technical advisor at one of the 40+ Challenger Learning Centers. For a project related to lift, I wanted a correct understanding of Bernoulli's Principle and have read several of the cited papers and watched Babinski's video (have his equivalent paper) and McLean's video, but also see the inumerable bad explanations on the net. If, as cited, it applies only along a streamline, or in a constant energy system, why is that not made explicit in the intro. Most folks going to Wiki will read what is now there, stop at the first paragraph as validation of their previously poor understanding, and come to the billionth wrong conclusion. Shouldn't the intro have the qualification at least in the first paragraph, if not the first sentence? So far I got one self-proclaimed 'professor' to pull his bumb Bernoulli explanation of lift video off a Teacher site. -- Steve -- (talk) 04:06, 22 July 2014 (UTC)

On Wikipedia, we understand the Intro to be everything before the commencement of the list of Contents. The Intro to Bernoulli's principle consists of five paragraphs. The third paragraph contains the following sentence: the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. So it is in the Intro although not in the first paragraph.

We try to provide a gradient of complexity in the Intro, and indeed throughout the whole of any article. The beginning is intended to be a simple explanation of the subject, and as the article proceeds, the explanation becomes increasingly complex in order to eventually capture all the information that can be found in reliable published sources.

In the case of Bernoulli's equation, I think the concept of total mechanical energy being constant along a streamline is not a simple concept so I would not be in favor of it being moved to the first sentence in the Intro. In the case of Bernoulli's principle, I think the principle is simply that where the flow accelerates the pressure decreases, and where the flow decelerates the pressure increases, without any need for trying to confine it to a streamline. Readers who have no knowledge of streamlines would not be able to comprehend Bernoulli's equation, but should be able to comprehend Bernoulli's principle.

I think where it is at present is about right. Dolphin (t) 12:54, 22 July 2014 (UTC)

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Life prevented getting back here sooner...

I understand. Referring to changes in speed are better than talking about streamlines because the implication of a streamline is implicit in the changing speed of a "particle' of air.

..

Now, I will admit that I am on a bit of a personal quest to get at least some of the more notable places that Bernoulli is explained improperly to either remove or correct their information. Perhaps this is quixotic, but, so far, I got one lecture video on TeacherTube removed that showed all the classical errors; ... but retained a copy for myself...(;-). I also got the attention of two others and time will tell how successful I am.

So, Because Wiki is the go-to place, for many, to find understanding, I'm also hoping that, at least, wiki does not contribute to the misunderstanding. This one statement leaves me uneasy:

.. RE:

"an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy."

..

While this is certainly true as stated, it is not apparent that there is a cause and effect. If we accept that pressure gradients cause fluid accelerations, then I believe this one sentence doesn't help to enforce that idea. So, I'd like to see that sentence reworded to reduce the wrong interpretation. This is in view of the fact (assumption) that some, if not many readers will come into the article with the preconceived notion that speed causes a pressure decrease.

If it is simply reversed, I'd feel better:

..

"a decrease in pressure of the fluid occurs simultaneously with an increase in the speed or a decrease in the fluid's potential energy."

..

Though I think the 'decrease in potential energy' part could be left off for later in the article for more sophisticated readers. I see, and have had at times, a desire to include every possible aspect of the phenomenon right at the top in order to be "completely correct", but too much detail can confuse the beginner.

..

That said, in my discussions with a noted expert, he has said something to the effect that "it works both ways", but I haven’t been able to get back to him and have him clarify that. Each time I try to construct a situation where a speed change causes a pressure difference, I always come to the conclusion that pressure change/gradient comes first... this is not necessarily trivial.

..

Other comments above in the School Demo section...Regards, -- Steve -- (talk) 01:19, 23 November 2014 (UTC)

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Misapplications of Bernoulli's principle in common classroom demonstrations (Incorrect)

It doesn't create a lower air pressure on bottom because gravity is moving the paper toward the flow of the current but the lower pressure does exist on top. Who wrote this section? some idiot student? — Preceding unsigned comment added by 212.7.192.139 (talk) 22:24, 21 December 2012 (UTC)

Yes you are correct. That's wrong and should be deleted or changed. In a better demonstration setup the paper hangs vertically to create a symmetric situation. Then it works on both sides (of course). Not necessary to call anyone an idiot, though.Echohunter (talk) 21:41, 22 June 2013 (UTC)

The entry as currently written is very well sourced from peer-reviewed published papers. Yes, there are many unreliable sources that incorrectly explain the phenomenon (elementary-school level materials, self-published blogs, poorly edited popular magazines, etc) but the academic world is basically unanimous on the subject. The misconception is unfortunately quite common, but it is as false as the equal transit time fallacy. Please follow the cites and read the academic papers that treat it.

Agree that a vertically hung paper might be a better demonstration, but there are two problems with it:

1)The paper doesn't deflect in that situation

2)It is still false to apply Bernoulli's principle to compare the pressures in the different airstreams. See Babinsky's paper for more details. http://iopscience.iop.org/0031-9120/38/6/001/

Mr. Swordfish (talk) 12:19, 23 June 2013 (UTC)

OK, guilty for not reading the papers. But I cannot quite agree with (1). It does work with a piece of paper. Otherwise I would not have written the comment. I now used a piece of stiff cardboard hanging down the edge of a table. And I changed sides to make sure its not a residual curvature in the cardboard. Working. But - now thinking about it, I remember that the setup I saw or read about first were TWO pieces of paper held vertically in a small distance and blowing into the created channel. That works extremely well too. Anyways, I am certainly not going to change anything before reading the papers. Echohunter (talk) 20:56, 23 June 2013 (UTC)

Well, when I try it, the paper doesn't move in any noticable direction, it just flutters a bit. I suspect that there may be some confirmation bias here - those who expect the paper to deflect blow in a manner that makes it deflect and those who don't expect it to deflect blow in a manner so that it doesn't deflect. In any event, we can say two things: 1) our original research doesn't belong in the wikipedia article and 2) if it does deflect it is a much much more subtle effect as compared to when the paper is curved. A straightforward (mis)application of the Bernoulli principle would predict equally dramatic results regardless of whether the paper is curved or not. And what happens when you blow on the bottom? It moves in the wrong direction from what the common (mis)application predicts.

I'd also add that if you can somehow get the paper to deflect without some corresponding deflection of the air in the opposite direction, you should document that experiment carefully and publish it - this would no doubt win a Nobel prize since it would be the first experimental evidence of the the law of conservation of momentum being violated. Mr. Swordfish (talk) 23:44, 23 June 2013 (UTC)

well duh! that's why they called it a misapplication. meaning, it is not right.

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I'd like to suggest a better explanation in this one area. I believe it is a misinterpretation of good sources. It is the word 'speed':

.. RE:

"Bernoulli's principle predicts that the decrease in pressure is associated with an increase in speed, i.e. that as the air passes over the paper it speeds up and moves faster than it was moving when it left the demonstrator's mouth. But this is not apparent from the demonstration."

..

While Max Feil's quote seems to say the same, I am unable to see the part of his article where that quote is from (Google only provides one page), however, he is discussing lift not simple Bernoulli. I am also not aware of Mr. Feil's credentials.

The on-line paper by Anderson & Eberhardt does explain using acceleration as does Babinsky.

Mr. Geurts' quote is correct in using the word 'acceleration', but he is also discussing lift and, unfortunately, his example of the "super wing" is a rather poor argument which weakens his credibility as a good source for understanding fluid dynamics rather than someone repeating others as best he can.

..

I submit the following. Recall that velocity has both speed and direction. Air following the convex curved surface moves in a curve which is caused by a cross-flow pressure gradient. This is radial acceleration just like that of an orbiting satellite. Therefore, acceleration can be a direction change with no speed change. Yes, the air over an airfoil experiences a speed increase as well, but the topic here is under the definition of Coanda, not airfoil airflow and the conditions are not identical.

I believe the following is a better representation.

"Bernoulli's principle predicts that the decrease in pressure is associated with an acceleration, i.e. that as the air passes over the paper it experiences a radial acceleration and flows in a different direction than it was moving when it left the demonstrator's mouth. The pressure gradient causes the "lift", not the inherent 'speed'. This change in direction is missed in the explanation that leads to the wrong conclusion."

..

Other comments below in the Intro section...Regards, -- Steve -- (talk) 01:19, 23 November 2014 (UTC)

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Bernoulli's principle is a scalar equation, not a vector equation. It deals with speed (a scalar quantity), not velocity (which is a vector quantity). Bernoulli's equation does not account for directional changes, only speed variations. In particular, it does not make any predictions about radial acceleration. The first sentence of your proposed text, which talks about directional changes, misrepresents Bernoulli's principle.

In the demonstration, there is a region of low pressure above the paper. You are correct in ascribing that low pressure as being a result of radial acceleration. Bernoulli's principle predicts that as the air flows through that region of low pressure it speeds up and moves faster than it was moving when it left the demonstrator's mouth. This speed change is not easily observable, and that's why it's a poor demonstration of Bernoulli's principle.

I don't think we are at odds as to why the paper rises in the demonstration. But the article needs to be clear about what Bernoulli's principle actually states, and apply it carefully to the demonstration. When applied carefully, Bernoulli's principle does not predict the main result of the demonstration (i.e. the paper rises) It predicts something else, which is not at all obvious. Mr. Swordfish (talk) 16:04, 24 November 2014 (UTC)

................................................... EngineerSteve responds :

If this is too much for a Talk page, we can move to our private pages, email or phone if you wish.

Yes, we agree the demo is incorrect. I understand your comment about vector vs. scalar. However, I subscribe to the view that Newton prevails and that a force is required to accelerate a mass. Therefore, the Pressure Difference (force) is required to cause a velocity change of a mass (of fluid) and that velocity is vector because the streamline can and does curve.

However, your explanation appears to be incorrectly stating your argument/conclusion. Bernoulli applies along a streamline. The pressure difference in the case of the convex curve is not along a streamline but perpendicular to it -- therefore, it is a misapplication of Bernoulli to say that the speed increases due to the lower pressure along the convex curve. The lower pressure is close to the surface and the higher pressure (atmospheric) as away from the surface, yet the streamline is not traveling *toward* the surface. This is why I bring in the claim that we must now consider the radial acceleration.

I see you are on a similar quest as I. I must admit that I have not deeply studied the whole Babinsky paper, but did watch the YouTube video of the related lecture, found the "missing" notes with his graphics that were so shortsightedly not shown in the video, but did some comparisons in areas I felt as critical. https://www.youtube.com/watch?v=XWdNEGr53Gw

I do, however take issue with his calling the upper airfoil phenomenon "Coanda" based on discussions with Doug McLean the Boeing Aerodynamics Fellow.

From your wording here (as well as a scan of your sandbox article), it appears you may ascribe to a speed change being the *cause of* a pressure difference/gradient -- or -- at least you seem to switch back and forth between the two cause-and-effect camps.

Every time I attempt to set up conditions where a speed change occurs that is not due to a pressure difference I fail. I do acknowledge, however, that it can be difficult to explain just why the convex curve causes a pressure decrease, but the "lack of entrainment" at the surface of the curve does seems to fit physics for me.

I assure you that it is not my intent to argue, but discuss the merits of the various views and make sure that everything fits within and compliments the current body of physics as it is understood. I have also communicated with a couple of authorities in the area, but I am not finished discussing this with them.

I share your frustration with the body of what I call "Bad Bernoulli" information in many thousands of places. There seems to be a strong force in the universe to use the rather eye catching demonstrations to explain *something* and poor Bernoulli is sadly the victim of misunderstanding. ...OR... there is a strong force to use Bernoulli for *something* eye catching with a goal of generating enthusiasm in Science.

Many years ago when I first heard the "bad lift" story, it was unsatisfying for me, but life prevented me from looking deeper. It may not have done any good at that time anyway with all the repeated misinformation... (;-(

I have contacted both Matt Carlson and Steve Spangler (see below). Mr. Carlson responded that he will consider my input, but hasn't responded after a few weeks. Mr. Spangler's team was only recently contacted.

I would be interested in your analysis for the Spangler Soda-Can-Jump demo below. (my measurements confirmed my analysis to-the-letter...)

You may have these, but I also did not see them in your Wiki-list of references:

Weltner in PDF - "Misinterpretations of Bernoulli's Law":

http://user.uni-frankfurt.de/~weltner/Misinterpretations%20of%20Bernoullis%20Law%202011%20internet.pdf

Weltner as a web page:

http://www-stud.rbi.informatik.uni-frankfurt.de/~plass/MIS/mis6.html

...

Anderson & Eberhardt AAPT paper: The Newtonian Description of Lift of a Wing-Revised 2009:

http://home.comcast.net/~clipper-108/Lift_AAPT.pdf

A couple of "Bad Bernoulli" videos. "Dr." Carlson's appears to use all the wrong demos in the book (except the ball-in-tube which I have not analyzed).

Dr. Matt Carlson: https://www.youtube.com/watch?v=olVJzVadiFs

Steve Spangler:

https://www.youtube.com/watch?v=BARzS0Mqpa0 House TP video

https://www.youtube.com/watch?v=5dgCZgtS3ig Ellen - with other demos.

EDIT:

Soda-Can Jump with the "due to Bernoulli explanation": http://www.stevespanglerscience.com/lab/experiments/soda-can-jump

This is a YouTube video with no explanation: https://www.youtube.com/watch?v=kgJSuo_6O-A

This fella' responded to my ping, but has yet to respond.

https://www.youtube.com/watch?v=xcBRhKD1SRo

I just ran across this one from Harvard-Westlake "Prep school" (joyful pursuit of educational excellence). It starts out looking good then quickly falls apart and continues on to do the same "equal constants" math as the previous video):

. http://www.teachertube.com/video/podcast-53-bernoulli039s-equation-141754

.......... Cheers, Steve -- Steve -- (talk) 02:07, 25 November 2014 (UTC)

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<outdent>The pressure difference in the case of the convex curve is not along a streamline but perpendicular to it -- therefore, it is a misapplication of Bernoulli to say that the speed increases due to the lower pressure along the convex curve.

Along the top of an airfoil (or the curved drooping piece of paper in the demo) there are pressure differences both perpendicular and parallel to the air flow. I agree that the perpendicular pressure differences have a lot more to do with the lifting force than the parallell pressure differences, but these pressure differences parallel to the direction of the airflow are definitely present. Bernoulli's equation quantifies the relationship between speed and pressure, or more precisely between speed changes and pressure changes along the streamline.

Agree that "radial acceleration" is key to understanding why the paper rises, and the current version of the article says as much although using a less technical wording. Since this article is about Bernoulli's principle, going into lengthy technical explanations that are not based on Bernoulli's principle is not appropriate for the article. I think the two sentences devoted to the "correct explanation" is sufficient. The wording could probably be improved, and I'm open to suggestions there.

Regarding cause and effect, Bernoulli's equation itself doesn't speak to cause and effect - it merely expresses a relationship between the speed and the pressure. Personally, I'm in the Weltner camp in that it is easier to intuitively grasp Bernoulli's equation by thinking of the speed change as a result of the pressure differences: i.e. if a small volume of air has a higher pressure behind than in front it will experience a net force causing it to speed up. It is not intuitive at all to think of the speed change causing a pressure change, but it is sometimes presented this way and this is responsible for a lot of students having difficulty understanding Bernoulli's principle.

Of course, this wikipedia page is not a venue for me to express my personal views, and since the bulk of what has been written in reliable sources does not address cause and effect the article is mostly neutral in this regard; where cause and effect are addressed it is carefully worded and cited.

I appreciate your efforts to correct the common misconceptions about Bernoulli's principle, and it's important that this article gets it right. Thanks for the links - I was aware of most of them, but I haven't reviewed the list of references in some time. I'll take a look and add as warranted. Mr. Swordfish (talk) 19:04, 25 November 2014 (UTC)

Applications - calculating lift force on a wing

From the first paragraph in the applications section: Whenever the distribution of speed past the top and bottom surfaces of a wing is known, the lift forces can be calculated (to a good approximation) using Bernoulli's equations. This statement is true, but how would someone determine or calculate this distribution of speed without simultaneously determining or calculating distribution of pressures, since these essentially co-exist rather than having a cause and effect relationship? That statement could be reversed, whenever the distribution of pressure is known, then the distribution of speed can be calculated. Is there any actual practical application where distribution of speed can be indpendently determined or calculated, and then afterwards distribution of pressure calculated based on that distribution of speed?

My issue is with the way the statement is worded. In my opinion, a statement along the line that Bernoulli's equations define a relationship between distibution of speeds and pressures, and this relationship is part of the process for calculating how an airfoil will perform.. Rcgldr (talk) 08:23, 29 March 2013 (UTC)

At the risk of gross oversimplification, the "classic" way to calculate lift is to:

1) Apply conservation of mass, momentum, and energy an a few other considerations to derive the differential equations expressing how the fluid moves. This results in the Navier-Stokes equations or Euler equations depending on whether you model viscosity.

2) Solve the equations, either through numerical methods (Computational fluid Dynamics), or by making simplifying assumptions (eg potential flow). The result is a vector field representing the velocity of the fluid at every point in space.

3) Using the vector field obtained above, calculate the pressure at each point on the surface of the foil using Bernoulli's formula.

4) Integrate the pressure to obtain the total net force and resolve the force into two components, lift and drag.

In this method, the speed is calculated first, and the pressure obtained form the speed, so yes there are practical situations where the "speed can be indpendently determined or calculated, and then afterwards distribution of pressure calculated based on that". However, some people mistakenly believe that because the speed can be calculated first, it somehow causes the pressure to develop, and this is responsible for a lot of confusion.

I agree that the statement could be reversed, but the fact remains that most treatments of aerodynamic lift first calculate the speed and then derive the pressure from there. Mr. Swordfish (talk) 13:41, 29 March 2013 (UTC)

I had the impression that those vector field calculations had to take pressure differentials into account (how the air responds to pressure differentials, based on density and viscosity, as part of the process to calculate the speeds and vice versa). One example of this is a flow that follows the upper cambered surface of a wing, where part of the reduction in pressure is related to acceleration perpendicular to the direction of flow, where it would initially seem that the component of acceleration perpendicular to the direction of flow would have no effect on speed, except that the reduction of pressure itself is going to result in an increase of speed within a streamline. There's also the issue of some net work being performed on the affected air, which violates Bernoulli, but apparently it's a relatively small effect (if using the wing as a frame of reference). Assuming that the speed calculations do not require knowledge of the effects from pressure differentials, then the current statement in the article is ok. Would be nice if there was some citable reference for this. Rcgldr (talk) 20:57, 29 March 2013 (UTC).

There is a problem with this section stating "... if the air flowing past the top surface of an aircraft wing is moving faster than the air flowing past the bottom surface..." this assumption is completely wrong! For reference you can read the following paper: http://iopscience.iop.org/0031-9120/38/6/001 — Preceding unsigned comment added by Pendarify (talk • contribs) 21:49, 2 December 2014 (UTC)

Pendarify, when you say "this assumption is completely wrong!" I believe you are referring to the "Equal transit time fallacy" which asserts that the air flowing along the top of the wing must reach the trailing edge at the same time as the air flowing along the bottom. This is certainly false, as Babinsky explains in the article you cite: "How Do Wings Work" by holger Babinsky.

But please read the article carefully. While there is no basis in physics for the equal transit time fallacy, the air actually does go faster along the top of the wing than along the bottom. Babinsky (who wrote the article you cited) has prepared a video demonstrating this, which you can watch at https://www.youtube.com/watch?v=e0l31p6RIaY . Another good video explaining it is at https://www.youtube.com/watch?v=aFO4PBolwFg Mr. Swordfish (talk) 22:14, 2 December 2014 (UTC)

Fluid flowing faster across one surface of an object than across the other surface is a recognized phenomenon. See Kutta condition. Dolphin (t) 11:00, 3 December 2014 (UTC)

Derived from Euler equation?

A recent edit changed the article from saying that Bernoulli's equation can be derived from Newton's laws to saying that it can be derived from Euler's equation. I'm scratching my head over this, because the derivation included in the article starts with Newton's 2nd law, does a bit of calculus, and results in the Brnoulli equation. Euler's equation is never mentioned. Likewise, the derivation at the end of this article (http://iopscience.iop.org/0031-9120/38/6/001/pdf/pe3_6_001.pdf) starts with F=ma and proceeds without ever mentioning Euler's equation. And this article (http://user.uni-frankfurt.de/~weltner/Physics%20of%20Flight%20internet%202011.pdf) too.

Granted, it is possible to start with Euler's equation and derive BE from it, but it's not necessary - BE can be derived directly form Newton's 2nd law. So, I'm wondering what the motivation was for the change.Mr. Swordfish (talk) 12:50, 2 September 2013 (UTC)

It's been over a week, so absent any response I'm going to restore the previous version. Mr. Swordfish (talk) 13:46, 11 September 2013 (UTC)

Dear Mr. Swordfish, I definitely disagree. Bernoulli theorem applies for Euler equations and not for the general Newton's second law. As reductio ad absurdum, if the Bernoulli's principle were general as Newton's law it should be valid also for the motion of planets around the sun or for the dynamics of classical rigid bodies. If it required some additional assumptions like no viscosity and others that apply for the case of ideal fluid, they shluld be equivalent to Euler equations.

The two direct paths traced from Newton to Bernoulli that was called "derivation" lacks of the necessary mathematical rigour and should be intended as a simple informal introduction for neophytes. I do not mean they are wrong, but rather that they do not mark the assumptions made and do not formally "demonstrate" the equivalence between Newton's second law + some assumptions and Bernoulli's principle. One could try to add terms: "In the force term in general there must be also a viscosity term" or to induce wrong hypothesis: "By hypothesis the Bernoulli principle is derived considering a control mass since F=ma holds for systems with constant mass"

Finally the correct derivation of Bernoulli's theorem from Euler equations and not from Newton second law is reported in:

• hydrodynamic texts, like: Lamb, Hydrodynamics, CUP 1895, p. 22-3, https://archive.org/stream/hydrodynamics00horarich#page/n39/mode/2up, that as you can check was already cited in the text more than three times long before my contribution

• best general physics texts, like: Fenynman's physics, Vol II, Par. 40-3 Steady flow - Bernoulli's theorem, p. 40-8 that as you can check was already cited in the text more than three times long before my contribution.

• good introductory texts like Falkovich, Fluid Mechanics: A short course for Physicists, CUP 2011, p. 8-9.

Anyway, please let me know what do you think about my arguments! --87.10.61.143 (talk) 17:38, 28 December 2014 (UTC)

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.wiki.x.io/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:

$\mathbf {u} \cdot \nabla H=0$

• Connection with total head and hydraulic head: this explains why they are so important in hydraulics
• Connection with Kelvin's circulation theorem

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)

To answer your two questions:

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:

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

${\frac {D{\boldsymbol {u}}}{Dt}}+{\frac {\nabla p}{\rho }}-{\boldsymbol {g}}={\boldsymbol {0}}$

or explicitly:

${\frac {\partial {\boldsymbol {u}}}{\partial t}}+\mathbf {u} \cdot \nabla \mathbf {u} +\nabla \left({\frac {p}{\rho }}\right)-{\boldsymbol {g}}={\boldsymbol {0}}$

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:

$\mathbf {a} \cdot \nabla \mathbf {a} =(\nabla \times \mathbf {a} )\times \mathbf {a} +\nabla \left({\frac {1}{2}}a^{2}\right)$

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)

Simplify, please

"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)

Misleading terms

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:

Description	Google Search	Google Scholar	Google Books
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)