Talk:Bernoulli's principle

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 (talk • contribs)

Possible error in reference [15]

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

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

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

Misunderstandings about the generation of lift

This section should be closely reviewed, and perhaps removed. For one thing, some of the references are IMO not of sufficient grade to serve as reference for an encyclopedia entry on fluid dynamics. E.g. an article in a pilots magazine is hardly a good reference for a fluid dynamics topic. Often such articles are themselves based on Wikipedia information and therefore create circular references, rather than reliable ones. But the main reason this section needs work is that it feeds the very misconception it claims to dispel. It clearly assumes a connection between the flow above and below the wing via Bernoulli's law, which is incorrect. Just read this very article. Bernoulli's principle establishes a relation between different points upstream/downstream of one another within the same flow. There is no relationship that this principle establishes between different flows. The flows above and below a wing are different flows, physically separated by the wing. Thus Bernoulli's principle does not establish any relationship between the respective velocities or pressures. — Preceding unsigned comment added by 73.189.225.197 (talk) 17:55, 23 March 2022 (UTC)

Actually, as explained in one of Charles Eastlake's papers, Because the energy ahead of the wing is the same for both the soon to be upper and lower flows (streamlines), Bernoulli's Equation does indeed provide a reasonably good *calculation* of the lift force, but it in no way explains the physics. I spoke with Eastlake myself to clarify his paper. It is easily searchable. The Physics Teacher Vol 40 March 2001 : "An Aerodynamicist’s View of Lift, Bernoulli, and Newton" 19:07, 14 September 2022 (UTC)

-- Steve -- (talk) 19:07, 14 September 2022 (UTC)

Just to make sure this does not simply remain a comment. This https://www.youtube.com/watch?v=XWdNEGr53Gw youtube video shows a lecture about the basics of lift. From minute 29 through minute 31 the lecturer addresses this very topic. The flows above and below the wing have no relationship that relates through Bernoulli's Principle. — Preceding unsigned comment added by 73.189.225.197 (talk) 01:10, 27 March 2022 (UTC)

I disagree. At its most basic level, Bernoulli’s principle applies only to points along one streamline. But in a region of irrotational flow, the Bernoulli constant is the same along every streamline. (I think our cited source for this is Victor Streeter’s textbook - see reference No 6 which applies to the third para in the lead.) The flow outside the boundary layer is irrotational so streamlines above and below are part of the one region of irrotational flow, and they all share the same Bernoulli constant. Dolphin (t) 01:18, 27 March 2022 (UTC)

I have watched the YouTube video you identified above. Prof Babinsky is talking about blowing with his mouth across the top of a piece of paper. He is also talking about using a hair dryer to blow across the top of an airfoil. (He is not talking about an airfoil moving through the atmosphere.) He correctly states that “in general, the Bernoulli constant along one streamline is different to the constant along any other streamline.” That is true in general, where the generality includes the flow in boundary layers and other regions of rotational flow. But explaining lift by using Bernoulli’s principle uses a much simpler model of the flowfield where we ignore the presence of the boundary layer.

Prof Babinsky explicitly mentions streamlines flowing out of a reservoir and says all those streamlines might share a common Bernoulli constant, and he is correct. The atmosphere is a large region of uniform energy and therefore streamlines in the atmosphere around a wing share a common Bernoulli constant, just like the streamlines flowing out of a reservoir.

In summary, when Prof Babinsky focuses on the fact that the Bernoulli constant above is different to that below, he is not talking about a wing moving through the atmosphere; he is talking about blowing over a piece of paper, and other classroom experiments. Dolphin (t) 06:56, 27 March 2022 (UTC)

Well, number one, this article is about Bernoulli's principle and not about lift. As such, it is important to be clear about the fact, that the principle only applies along a streamline. You can't argue that point. As such, any statement that pulls this into question is problematic and reduces the quality of the article.

Second, it does not matter if there is a piece of paper between two random streamlines, a wing, some other object or nothing at all. The same constant does not apply. In that it also does not matter how a flow is generated, from a reservoir, from one's mouth, a hair drier or some more sophisticated method. Therefore arguing that there is an example with a piece of paper, but a wing is something very different, is just word play. It has no practical meaning.

Third, Prof. Babinsky is very clear that while man might not make too big a numeric error by assuming the same constant in a narrow field of parallel flow, the values are very different between the top and bottom of a wing indeed.

The obvious intent here is to further a misconception, in that Bernoulli's principle somehow is the cause of the different pressures above and below a wing. This is wrong. Besides, this sort of discussion is off topic for this article as it does not concern itself with lift, but with Bernoulli's principle as such. 73.189.225.197 (talk) 18:05, 27 March 2022 (UTC)

I would suggest reading Holger Babinsky's article on the subject: http://www3.eng.cam.ac.uk/outreach/Project-resources/Wind-turbine/howwingswork.pdf Paying particular attention to the following passage:

However, the fact is often overlooked that Bernoulli’s equation applies only along a stream-line. There is no explicit relationship between the pressure and velocity of neighbouring streamlines. Sometimes, all streamlines in a flow originate from a region where there is uniform velocity and pressure (such as a reservoir or a uniform free-stream) and in such a case it is possible to apply Bernoulli’s equation throughout the flow.

Perhaps it would help clear up some of the confusion.

As for the section under consideration, I do think it could be improved and I'll have some suggestions in a day or so. Mr. Swordfish (talk) 19:18, 27 March 2022 (UTC)

In Fundamentals of Aerodynamics by John D. Anderson Jr (1984, McGraw Hill) on page 117 it states

For a general, rotational flow, the value of the constant in Eq. 3.14 will change from one streamline to the next. However, if the flow is irrotational, then Bernoulli’s equation holds between any two points in the flow, not necessarily just on the same streamline. For an irrotational flow, the constant in Eq. 3.14 is the same for all streamlines, and:

$p+{\frac {1}{2}}\rho v^{2}=const$ throughout the flow.

This quote shows the importance for aerodynamicists of always clarifying that they are talking about irrotational flow. The editor who initiated this thread does not mention the word irrotational so I assume he is unaware of its significance. Dolphin (t) 04:59, 28 March 2022 (UTC)

My takeaway at this point is that this section may be confusing, at least to some readers. The statement:

Several of these explanations use the Bernoulli principle to connect the flow kinematics to the flow-induced pressures. In cases of incorrect (or partially correct) explanations relying on the Bernoulli principle, the errors generally occur in the assumptions on the flow kinematics and how these are produced.

is certainly correct and well sourced, but seems overly general and difficult to follow for someone who is not already familiar with the material. The terms "flow kinematics" and "flow-induced pressures" are likely unfamiliar to the majority of our readers. Rather than trying to craft a general statement that applies to the many different incorrect applications of BP to lift I think it would better serve the reader to highlight the most common one as a specific example and link to the article on Lift for further exposition. Seems to me that the section should make the following points

1. A very common explanation of lift mis-applies BP (with a very brief summary of equal transit time and why it's incorrect)
2. The fact that BP is commonly misused in this circumstance does not imply anything is wrong with BP
3. BP is commonly used correctly as part of a mathematical treatment of lift.

I'm not convinced that this is the best place to delve into the Bernoulli v Newton "controversy", but I'm ok with it remaining as long as we keep it short. Looking for feedback on this approach from other editors; if received positively I'll take a crack at crafting a draft. Mr. Swordfish (talk) 18:14, 31 March 2022 (UTC)

I agree that the sentences you quote are inappropriate in this article. Removing them will be an improvement. Your proposal looks good - I encourage you to go ahead with developing the three points you have given us. Dolphin (t) 23:24, 31 March 2022 (UTC)

A quick comment about your points 1 and 2: The equal transit-time fallacy is based on false reasoning for the essential kinematics of the flow field; subsequent application of Bernoulli’s principle is entirely separate from speculation about the kinematics; application of BP shouldn’t be characterised as mis-application or misuse. Application of BP to any region of irrotational flow is appropriate and correct but if the assumed kinematics are inaccurate or incorrect, the resulting pressures will be equally inaccurate or incorrect, but that doesn’t constitute misuse or mis-application of BP. Dolphin (t) 13:34, 1 April 2022 (UTC)

Yes, you are correct. The Equal Transit Time Fallacy (ETT) does not misapply Bernoulli's equation; it starts with a "nonsensical" physical assumption about why the air is faster over the top of the wing and proceeds to correctly apply the equation to infer a lower pressure due to the increased speed. I'll be careful about the wording in the draft. Mr. Swordfish (talk) 23:45, 1 April 2022 (UTC)

I have composed a draft revision of this section in my sandbox https://en.wikipedia.org/wiki/User:Mr_swordfish/sandbox. Comments cheerfully accepted. It does not contain any references yet. If it receives positive responses I will add them. Thanks. Mr. Swordfish (talk) 20:50, 7 April 2022 (UTC)

I have made some suggestions on Mr Swordfish's sandbox. See my diff. Dolphin (t) 12:59, 8 April 2022 (UTC)

There is now a release candidate draft in my sandbox. I'll release it in a few days unless there is further comment. Mr. Swordfish (talk) 11:57, 9 April 2022 (UTC)

A single word was recently added to this section:

One of the most common erroneous explanations of aerodynamic lift ...

And this is certainly a correct and supportable statement.

However, it is also correct and supportable without the qualifier "erroneous", which is a stronger statement. i.e. it's not just one of the most common erroneous statements, it's one of the most common explanations, full stop. My preference is to remove the qualification, but let's try to come to a consensus before making that change. Further discussion? Mr. Swordfish (talk) 02:24, 13 April 2022 (UTC)

The word “erroneous” has recently been added to the new text constituting this sub-section: see the diff.

My preference is to retain the word erroneous because I think it more accurately reflects the situation described in the cited sources. The previous statement, that the Equal Transit Time explanation was “one of the most common explanations of aerodynamic lift” appears to me to overstate the situation:

1. How many different explanations are commonly used is unknown, or at least uncited,
2. The number of times each explanation is used is also unknown, and unknowable,
3. The number of times the ETT is used is also unknown and unknowable.

So we can’t honestly say the ETT is one of the most common explanations of aerodynamic lift. However, we have a better idea of the small number of incorrect explanations of aerodynamic lift, and we can be confident that the ETT is prominent among them. Therefore I don’t have any objection to saying the ETT is one of the most common erroneous explanations …

The first of the cited sources, Physics that Works by Kendall Hunt Pub Co., says “One of the most widely circulated, but incorrect, explanations …” This citation uses the word “incorrect” so doesn’t support our original statement that the ETT is one of the most common explanations of lift.

The second of the cited source, Norman F Smith in The Physics Teacher, doesn’t use the word “erroneous” or any synonym, but it is dated November 1972, almost 50 years ago. I am biased against this sentiment because my first serious physics book, Physics by Resnick and Halliday, was widely used in Universities and Colleges and first copyrighted in 1960. In Chapter 18, Fluid Dynamics, it contains an accurate description of aerodynamic lift. It contains an accurate diagram of the streamlines around an airfoil. There is not the slightest hint of the ETT explanation of the kinematics. I don’t doubt that the ETT was widely used in literature aimed at student pilots and newcomers to aviation but serious literature such as that by Resnick and Halliday, aimed at millions of students of science and engineering, presented a description of aerodynamic lift that must be considered scrupulously correct even today. Dolphin (t) 12:46, 13 April 2022 (UTC)

Our role here is to summarize the information provided by reliable sources and present it to our audience in a readable form. To answer your points 1,2, and 3 above, we don't need to (and shouldn't) research it ourselves; we simply look to the reliable sources and see what they have to say.

Smith refers to ETT as "...the textbook explanation that is more or less standard in the United States..."

The NASA website describes it as "... one of the most widely circulated, incorrect explanations." Note the use of the comma, which implies that it is both widely circulated and incorrect. If they were trying to say it was the one of the most widely circulated incorrect explanations, they would have omitted the comma. (https://web.archive.org/web/20140427084226/http://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html)

Holger Babinsky describes it simply as "...the most widely used explanation of lift..." (http://www3.eng.cam.ac.uk/outreach/Project-resources/Wind-turbine/howwingswork.pdf)

Anderson & Eberhart describe it as "...the popular explanation that most of us were taught..." indicating that it is perhaps the most widely circulated explanation, but surely is one of the most.

Your reading of the excerpt from Physics that Works is very different than mine. The author seems to be saying that ETT is one of the most widely circulated explanations, and that it is also incorrect. Not that it is just one of the most widely circulated incorrect explanations.

The cites above show that we would have a very solid basis for omitting the word erroneous. The fact that ETT is one of the most widely circulated explanations should be uncontroversial. Is there anyone claiming that it is not one of the most widely circulated explanations?

And if you're still not convinced that it is widespread, have a look at https://en.wikipedia.org/wiki/User:Mr_swordfish/List_of_works_with_the_equal_transit-time_fallacy

My takeaway here is that whether to include erroneous or not is an editorial decision about what to emphasize, rather than a disagreement on the facts as supported by reliable sources. We do need to be clear that ETT is incorrect and including erroneous in the first sentence emphasizes that fact, but the title of the section and the second paragraph seem to be sufficiently clear to make the insertion of the word erroneous superfluous. Mr. Swordfish (talk) 22:19, 13 April 2022 (UTC)

A further comment on the Norman Smith article: I think you are missing the context, since he goes on to say

"Unfortunately, this explanation [fails] on three counts. First, an airfoil need not have more curvature on its top than on its bottom. Airplanes can and do fly with perfectly symmetrical airfoils; that is with airfoils that have the same curvature top and bottom. Second, even if a humped-up (cambered) shape is used, the claim that the air must traverse the curved top surface in the same time as it does the flat bottom surface...is fictional. We can quote no physical law that tells us this. Third—and this is the most serious—the common textbook explanation, and the diagrams that accompany it, describe a force on the wing with no net disturbance to the airstream. This constitutes a violation of Newton's third law."

This paper is to the best of my knowledge the first clear refutation of ETT in peer-reviewed literature. Yes, it's 50 years old, but it still stands up. I think you would enjoy reading it. Mr. Swordfish (talk) 22:21, 13 April 2022 (UTC)

This discussion thread shows that some readers believe Bernoulli's equation is only of limited value because it is only valid along a streamline. This misunderstanding comes as no surprise because our article repeatedly mentions Bernoulli's principle in the context of the streamline. All reliable published sources describe the application of the Bernoulli constant along a streamline simply as a learning aid; these sources then proceed to clarify that where the energy per unit of mass of fluid, or the energy per unit of volume, is uniform the Bernoulli constant does not vary among streamlines. In the flow of an inviscid fluid, in regions of frictionless flow, and regions of irrotational flow, the Bernoulli constant is uniform throughout the region. The energy per unit of mass of a fluid is uniform throughout a reservoir; therefore where a region of flow is driven by a fluid leaving a reservoir, the energy per unit of mass is uniform and the Bernoulli constant is the same on all streamlines. Bernoulli's equation can then be applied throughout the region.

I have erased the multiple mentions of the streamline from the article. See my diffs. Hopefully the article now makes it easier for readers to see that Bernoulli's principle has much broader applicability than just along a streamline. Dolphin (t)

If?

If we cannot explain the lifting effect of an airfoil, or the reasoning of why a ball can remain suspended in an airstream using the Bernoulli Principle, how can we explain these phenomenon? Science teachers need a reasonable explanation so as not to confuse young'un's. Flight Risk (talk) 21:21, 12 September 2022 (UTC)

We can explain the lift force that acts on an airfoil. There are several ways to explain lift, all valid, and Bernoulli’s principle is is one of them. We can explain a ball remaining suspended in an airstream.

These phenomena are relatively complex and not entry-level topics for young’uns. A more appropriate topic for newcomers to the physical sciences is Bernoulli’s principle in general, using the venturi and the airfoil merely as examples of phenomena for which we make use of Bernoulli when explaining their principal characteristics. Dolphin (t) 22:18, 12 September 2022 (UTC)

There are people who can. Amateurs need to stay out of it because they are just repeating / spreading misconceptions. This includes Ed Regis 'technical author' who wrote the Feb 2020 Scientific American article after ignoring the advice he got.

Science teachers do need it, badly, but there is so much bad information out there that it is virtually impossible to get anything good.

Bernoulli's Principle does not 'explain' why or how lift occurs, nor the ball-centering. Most people stating how it works, while well meaning, misunderstand it - and what Euler said in the mid 1700s while following up on Bernoulli's work.

THE FUNDAMENTALS ARE SIMPLE, but there are quite a few that apply and few people understand them and know that they apply.

I know they want to be helpful because they were told / taught something by someone who spoke with authority, but it was wrong, so well meaning amateurs need to stay out of it.

The Talk page is not supposed to be to learn the topic. If you want good information for yourself, please go here: https://rxesywwbdscllwpn.quora.com/

-- Steve -- (talk) 18:47, 14 September 2022 (UTC)

Adjustment to the lead

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

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

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

Not how but why?

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

The third paragraph contains the following two sentences:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

It's like the following hypothetical article:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Explanation on the molecular level

There is a lot of misinformation on Bernoulli, allowing many people to get an incorrect understanding of how it works. And the correct explanations use abstract terms like internal energy and dynamic pressure, that while correct, are unintelligible to most people. If we were able to explain it on the molecular level, as balls bouncing around, I would think that people would have an easier time understanding the concept. There are few articles and videos explaining how it works on the molecular level, and they are not as clear as I would like. So my question - what does the community think about having a section in the article explaining what is going on at the molecular level, in a way that is fairly easy for average readers to understand? Showing that the molecules can only have so much velocity, and if that velocity is in the direction of flow, less velocity is available to make pressure. I’m happy to write it and make illustrations. But I’m also wary that there may be significant resistance from some editors; I’m not interested in an edit war. Thoughts? Thanks! --Zojj tc 21:04, 30 July 2023 (UTC)