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)

Applications: black-tailed prairy dog

The mechanism proposed in the cited article on the wind-induced ventilation in the burrows of prairy dogs seems very implausible to me. As is well known, the pressure in a boundary layer, such as in the wind flow near the Earth surface, remains constant at different elevations at the same cross section (normal to the surface). Bernoulli's principle for such a flow with vorticity is applicable along a streamline, and not for different streamlines at different elevations. Although I do think (my "original research") that Bernoulli's principle – on different grounds as used in the cited paper – may to a certain extend be used to explain the natural ventilation, as induced by the different shaped mounds at the different entrances of the burrow. But due to lacking secondary sources on the proposed mechanism in established fluid-dynamics journals and books I suggest to remove this example. -- Crowsnest (talk) 20:33, 20 April 2021 (UTC)

Thank you for your concern and explanation. This is beyond my realm of expertise, so I will remove the example for now until I have a better understanding of the topic or another party weighs in. Thanks again Viséan (talk) 20:40, 20 April 2021 (UTC)

Thanks. Sorry I could not support the proposed mechanism in your interesting example of natural ventilation. -- Crowsnest (talk) 20:46, 20 April 2021 (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)

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)

Compressible flow

Our article contains a section titled Bernoulli's principle#Compressible flow equation. This section explains that:

Bernoulli developed his principle from observations on liquids. His equation is applicable only to incompressible fluids but it can be used with minimal error at speeds up to approximately Mach number 0.3 in compressible fluids. It is possible to use the fundamental principles of physics to develop similar equations applicable to compressible fluids. There are numerous equations, each tailored for a particular application, but all are analogous to Bernoulli's equation and all rely on nothing more than the fundamental principles of physics such as Newton's laws of motion or the first law of thermodynamics.

This is a summary of compressible flow that is most appropriate in the article about Bernoulli's principle. However, what follows are three sub-sections with the following titles:

1. Compressible flow in fluid dynamics
2. Compressible flow in thermodynamics
3. Unsteady potential flow

I think the most appropriate place for this information is our article on Compressible flow rather than our article on Bernoulli's principle. I suggest these three sub-sections should be cut from our article on Bernoulli's principle and pasted into Compressible flow.

My reasoning for proposing the relocation of these three sub-sections includes:

• The quotation above explains that Bernoulli’s equation is strictly applicable only to incompressible fluids. It is contradictory to then present detailed information about compressible fluids; especially when we have an article dedicated to compressible fluids.
• These three sub-sections contain high-level physics and math. In particular, the math is more advanced even than the math presently found in our article Compressible flow. The math is out of place in Bernoulli's principle.
• The great strength of Bernoulli's principle is that in regions of irrotational flow the Bernoulli constant is the same along all streamlines and so can be applied broadly to large regions of steady flow around streamlined bodies. This is stated explicitly in the section Simplified form. However, as explained by Crowsnest in this edit, in compressible flows the equivalent of Bernoulli's constant is only applicable along a streamline and so does not display the same broad applicability that exists for Bernoulli's constant.

What do others think? Dolphin (t) 12:40, 7 April 2022 (UTC)

Moving this material to the compressible flow article makes sense to me. Mr. Swordfish (talk) 20:47, 7 April 2022 (UTC)

To my opinion these general forms of the Bernoulli equation should be here. Both Batchelor (1967, §3.5) and Landau & Lifshitz (1987, §6) start with deriving the Bernoulli equation for the general case, i.e. as given in the sections valid for compressible flow. They mention that Daniel Bernoulli derived them first for incompressible flow. Also "Prandtl's Essentials of Fluid Mechanics" (2004, §4.1.1) clearly states that the compressible flow formulation is "... the general form of the Bernoulli equation ...", the subject of this article. Crowsnest (talk) 20:11, 8 April 2022 (UTC)

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)