View source for Talk:Bernoulli's principle

{{talkheader}}
{{WikiProject banner shell|class=B|vital=yes|1=
{{WikiProject Physics|importance=high|fluid-dynamics=yes}}
}}
{{Notice|header=Caveat|1=Over the years this article has attracted many editors who insist that Bernoulli's principle is not relevant to the lift on an airfoil.  When we explore the views of these editors we discover that they think Bernoulli's principle is the [[Lift_(force)#False_explanation_based_on_equal_transit-time|''Equal-transit time theory'']].   (Everyone agrees that the ''Equal-transit time theory'' is so excessively simplified that it is incorrect.)  Bernoulli's principle is a valid scientific statement that has stood the test of time since 1738.  Many of us have flown inverted, or flown aircraft with upside-down airfoils, but this does NOT show that there is anything suspicious about Bernoulli's principle.  <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/69.1.23.134|69.1.23.134]] ([[User talk:69.1.23.134|talk]]) 23:22, 27 August 2010 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->}}
{{User:MiszaBot/config
|archiveheader = {{talkarchivenav|noredlinks=y}}
|maxarchivesize = 100K
|counter = 5
|minthreadsleft = 5
|algo = old(180d)
|archive = Talk:Bernoulli's principle/Archive %(counter)d
}}

== Removed GF content in March ==

The equation 
v^2/2 +gz + p/row  = constant<br />
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.<br />
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<br />
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.<br />
0.5.M.V^2 + M.g.h + P.Volume = k<br />
i.e. Volume = M/row
  
What Bernoulli did was yet another example of the Conservation of Energy Principle.<br />
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)<br />
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.<br />
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.<br />
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.<br />
Bert Vaughan <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Bert Vaughan|Bert Vaughan]] ([[User talk:Bert Vaughan|talk]] • [[Special:Contributions/Bert Vaughan|contribs]]) </span></small><!-- Template:Unsigned -->

== 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? &mdash; Cheers, [[User:Steelpillow|Steelpillow]] ([[User Talk: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. [[User:Mr swordfish|Mr. Swordfish]] ([[User talk: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. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 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; "[https://www.scientificamerican.com/article/no-one-can-explain-why-planes-stay-in-the-air/ No One Can Explain Why Planes Stay in the Air]," Space & Physics, ''Scientific American'' website, 1 February 2020. &mdash; Cheers, [[User:Steelpillow|Steelpillow]] ([[User Talk: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. [[User:Mr swordfish|Mr. Swordfish]] ([[User talk: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. &mdash; Cheers, [[User:Steelpillow|Steelpillow]] ([[User Talk: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... [[User:Mr swordfish|Mr. Swordfish]] ([[User talk:Mr swordfish|talk]]) 00:44, 14 June 2023 (UTC)
::::::{{u|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. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 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? [[User:Mr swordfish|Mr. Swordfish]] ([[User talk:Mr swordfish|talk]]) 14:39, 14 June 2023 (UTC)
:::::::{{reply|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. &mdash; Cheers, [[User:Steelpillow|Steelpillow]] ([[User Talk: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 ... ...” [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 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. &mdash; Cheers, [[User:Steelpillow|Steelpillow]] ([[User Talk: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]]. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 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. &mdash; Cheers, [[User:Steelpillow|Steelpillow]] ([[User Talk: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_(fluid_dynamics)|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. [[User:Mr swordfish|Mr. Swordfish]] ([[User talk: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? &mdash; Cheers, [[User:Steelpillow|Steelpillow]] ([[User Talk:Steelpillow|Talk]]) 06:51, 16 June 2023 (UTC)
::::::::::::If your question can be presented as “when a gas is compressed its <s>volume decreases</s> 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. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 03:03, 17 June 2023 (UTC)
:{{Outdent|::::::::::::}} 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''.  &mdash; Cheers, [[User:Steelpillow|Steelpillow]] ([[User Talk:Steelpillow|Talk]]) 08:05, 17 June 2023 (UTC)

== Explanation on the molecular level ==

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

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

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

:Bernoulli's Hydrodynamica was the seminal work in [[Statistical Mechanics]], and that's probably worth mentioning in the article, but I'm skeptical that a statistical approach to the topic will provide much in the way of an intuitive understanding of the BP. Of course, I'd be willing to look at a draft. That's what our sandboxes are for.
:I'd be careful with the ''molecules can only have so much velocity, and if that velocity is in the direction of flow, less velocity is available to make pressure.'' argument - it's been somewhat refuted in this article:  [[https://files.eric.ed.gov/fulltext/EJ1050910.pdf]]
:The reason so many people get an incorrect understanding of BP is that so many presentations get it backwards - they say the fluid speeds up for some reason (call it reason X) and this ''causes'' the pressure to drop. The problem with all these ''reason X'' explanations is that they are always wrong.  If you start with pressure differences, it is easy to see that more pressure behind will exert a force that accelerates the fluid (and more pressure in front will decelerate it).  The pressure differences cause the speed changes, not the other way around.
:Granted, the equations don't talk about cause and effect, but for any intuitive understanding of force and acceleration, we humans are predisposed to think of forces ''causing'' acceleration, not the other way around.  When you try to present the phenomena as "acceleration causes the force to appear" it's counter-intuitive. [[User:Mr swordfish|Mr. Swordfish]] ([[User talk:Mr swordfish|talk]]) 14:06, 31 July 2023 (UTC)
::Good call on the sandbox. And thank you for link and your thoughts on how to better help people understand. At first glance the paper makes a leap on the perpendicular speed concept... I’ll look into it more.  --'''[[User:Zojj|Zojj]]''' [[User_talk:Zojj|t]][[Special:Contributions/Zojj|c]] 12:24, 2 August 2023 (UTC)

:::A word of caution is appropriate here. On all scientific topics, Bernoulli included, newcomers appreciate intuitive explanations and newcomers often identify analogies and simple explanations that help them climb the ladder of understanding. It is easy to find such helpful explanations on the internet but they don't constitute reliable sources. Wikipedia works on the principle that everything that is likely to be challenged should be verifiable using a reliable published source ([[WP:VERIFY]]). It is not sufficient for the source to be published on the internet - it must be a reliable source. Given the state of knowledge of Bernoulli's principle, these popular, helpful, easy-to-understand are incompatible and peripheral to that state of knowledge. I have not seen the "molecular level" explanation of Bernoulli so I think it might be impossible to find a reliable published source to support it. It should not be added to Wikipedia unless it can be supported by a genuinely reliable published source, regardless of how helpful you might find it in helping you assimilate the information about Bernoulli.

:::With all due respect to Mr Swordfish's considerable expertise on these topics, ideas about "cause and effect", and whether pressure causes acceleration or vice versa, are outside the mainstream of Bernoulli's principle, and outside the state of knowledge of most topics in physics. Daniel Bernoulli correctly avoided writing anything about cause and effect, or acceleration causing pressure change. Similarly, Newton correctly avoided writing anything about these things. The cause and effect approach to physical laws is something developed since these laws were published; something developed by well-meaning people looking for a simple and intuitive way to understand or explain these profound physical laws. In the case of Bernoulli's principle, pressure and speed change simultaneously - it is incorrect to imagine that one causes the other; the thing that is the original cause of both is the change in cross-section area of the stream tube or the pipe in which the fluid is flowing.

:::Newton's second law of motion is another example. People commonly write that it is always the force that causes the acceleration. This may be true some of the time, but it isn't true all the time. An example of my point is a passenger vehicle accelerating. All passengers experience the same acceleration. The force acting on each passenger is this common value of acceleration multiplied by the mass of the passenger. It is the common acceleration which determines the magnitude and direction of the forces on the passengers. A more profound point to be taken from this is that, for the purpose of applying Newton, it is not necessary or meaningful to decide which one of force or acceleration is the primary cause; Newton's 2nd law simply says that the magnitude and direction of force and acceleration are related by the well-known equation, and they occur simultaneously. There is no time lag, and there is no cause and effect. It is often meaningful to talk about what causes what, but don't imagine that is a discussion about Newton's 2nd law. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 13:14, 2 August 2023 (UTC)
::::''...ideas about "cause and effect", and whether pressure causes acceleration or vice versa, are outside the mainstream of Bernoulli's principle, and outside the state of knowledge of most topics in physics''
::::Really?  So all those allegedly reliable sources we cite in the reference for this page that clearly discuss ''cause and effect'' are outside the mainstream?
::::For instance Bauman is pretty clear about it:
:::::Bernoulli’s principle is typically stated in the form that increasing the speed of a gas lowers the pressure. This illogical interpretation casts aspersions on Bernoulli’s equation, which is a direct application of Newton’s second law. Consequently, authors have sought alternative explanations, including an isoergic model and the “bounce” model, inconsistent with physics. The difficulties are removed by recognizing that '''Bernoulli’s equation tells us that a pressure difference causes a change in speed''', and pressure differences are caused by curvature of flow, interpreted locally as producing a centrifugal force.<ref>{{cite web |title=The Bernoulli Conundrum |first=Robert P. |last=Bauman |publisher= Department of Physics, University of Alabama at Birmingham |website= introphysics.info| url=http://www.introphysics.info/Papers/BernoulliConundrumWS.pdf |access-date=June 25, 2012 |url-status= dead |archive-url= https://web.archive.org/web/20120225115505/http://www.introphysics.info/Papers/BernoulliConundrumWS.pdf |archive-date=February 25, 2012 }}</ref>(emphasis mine)
::::You'll also find discussions of "cause and effect" in the works by John D. Anderson, Doug McClean, John S. Denker, Holger Babinsky, Klaus Weltner etc.  Just read the footnotes to this article, or the others that we work on together.  It's not an "outside the mainstream" view. 
::::Granted, there are some physicists who take an agnostic view and say that there are only equations, not causes and effects.  I don't know how mainstream this view is, but it doesn't help with an intuitive understanding of physics. [[User:Mr swordfish|Mr. Swordfish]] ([[User talk:Mr swordfish|talk]]) 19:29, 2 August 2023 (UTC)
:::::Thanks for the pdf of the essay by Robert Bauman. I have read it closely and I am most disappointed that a Professor of Physics has written such a low-grade article on this topic. Bauman's essay is not mainstream science. It contains much that is misleading or incorrect. Two of the most egregious errors are as follows:
:::::*At Criticism 1, Bauman writes "The equation is derived for motion along a streamline, ... so it should only be applied along a single streamline." This nonsense deserves a place down there with the equal transit-time theory! See responses, including your own response dated 24 Aug 2021, at [[Talk:Lift (force)#Oversimplification]].
:::::*"Pressure differences are caused by curvature of flow, ..." Bauman probably meant to write "curvature of flow is caused by a pressure gradient" but that is not what he wrote. Converging flow in a nozzle is an example of falling pressure and increasing speed, but all streamlines are straight - there is no curvature of flow. Bauman concludes this sentence by writing "... interpreted locally as producing a centrifugal force." This is incompatible with Wikipedia's view on [[centrifugal force]] which is that it is a pseudo force or fictitious force.
:::::This article by Bauman offers much, considering his status as a Professor of Physics, but it delivers little of value. It is embarrassing. It should not be regarded as a reliable source on the subject. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 13:17, 3 August 2023 (UTC)
::::::So, Holfger Babinski gets it wrong too?
:::::::With these assumption we can now derive the rules governing fluid motion by considering the resultant pressure force acting on an individual fluid particle and applying '''Newton’s second law, which states that force causes acceleration.'''
::::::http://www3.eng.cam.ac.uk/outreach/Project-resources/Wind-turbine/howwingswork.pdf
::::::Or John D. Anderson who states in Introduction to Flight:
:::::::...differences in pressure from one point to another in the flow create '''forces that act on the fluid elements and cause them to move'''. Hence, there must be some relation between pressure and veloc�ity, and that relation is derived in this section.
::::::and
:::::::The pressure distribution acting over the surface of the wing is the '''fundamental cause of lift.'''
::::::Or Klaus Weltner
::::::: ...it is shown that the high streaming velocity at the upper side of the aerofoil is not the reason for the low pressure. To the contrary, '''the low pressure generated by the aerofoil is the reason for the high streaming velocity.'''  [[https://ui.adsabs.harvard.edu/abs/1987AmJPh..55...50W]]
:::::::The conventional explanation of aerodynamical lift based on Bernoulli’s law and velocity differences mixes up ''cause'' and ''effect''. The faster flow at the upper side of the wing is the consequence of low pressure and not its cause.[[https://www.angelfire.com/dc/nova/flight/PHYSIC4.html]]
::::::I could go on, but I'll stop here.  You are entitled to think these reliable sources get it wrong, and say so here on the talk page, but what we put in the article is based on reliable sourcing. The notion that ''forces cause acceleration'' is hardly out of the mainstream.  Curious what you've been reading to think that it is. [[User:Mr swordfish|Mr. Swordfish]] ([[User talk:Mr swordfish|talk]]) 14:57, 3 August 2023 (UTC)
:::::::{{u|Mr swordfish}} We appear to be at cross purposes. I'm not aware of what it is that I have written to prompt you to quote Babinski, Anderson and Weltner. I don't believe I have ever challenged the notion that ''forces cause acceleration'' (your words) because that is exactly what Newton's FIRST law of motion is all about. Perhaps I wrote that ''forces cause acceleration'' is not Bernoulli's principle and you interpreted my words as doubting that forces cause acceleration.
:::::::You and I are both aware of many instances of eminent authors and institutions that have published documents advocating the equal transit time theory of aerodynamic lift. Despite the number of these documents Wikipedia is not seduced by the credentials of their authors. We repudiate the equal transit time theory. Well meaning attempts to simplify complex topics by resort to intuition, analogy and misplaced theories don't begin and end with the equal transit time theory. We must be willing to be alert at all times that something we see published may, in fact, be unreliable. Red warning lights should definitely be flashing when we see an annoyingly complex topic reduced to refreshing simplicity; or when an isolated attempt to explain a topic omits some of the essential elements used by all the acknowledged specialists and all mainstream publications. We must avoid being seduced by such strategies as denigrating the efforts of a large number of others, followed by a claim by the author that he (or she) has found a simple, easy-to-understand, explanation that anyone can comprehend. For example: "The conventional explanation of aerodynamical lift based on Bernoulli’s law and velocity differences mixes up cause and effect." I recall that this strategy was common in the equal transit time documents.
:::::::The conventional explanations of aerodynamic lift using Bernoulli's law say nothing whatsoever about cause and effect, so how can they mix them up? Why does Weltner even make this claim? I think it is a claim that is likely to catch unsuspecting readers, and perhaps that is why it appealed to Weltner. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 13:55, 4 August 2023 (UTC)
::::::Dolphin.
:::::::  Bauman is correct about "Pressure differences are caused by curvature of flow" and he shows a case correctly, but he does not explain WHY that lower pressure occurs at the end of the tube and neither do others with a Bad Bernoulli YouTube video.  He does, however, describe a standard static pressure probe when he adds that flat surface so the flow is no longer disturbed.  (I have also talked with Evan Jones)
::::::: That thing  -  that tube in the flow disturbs the flow. This points to an important concept. 
::::::: WHENEVER you introduce a surface AND there is relative fluid-surface motion, you have a new condition – a new constraint that must be considered. 
::::::: To start simple, I start with wind that everyone understands.  It blows on you and you feel the pressure.  What you must realize is that this is in INCREASE above atmospheric pressure.
::::::: Did I mention Inertia.? Air’s Inertia resists being slowed (accelerated) by a surface that it approaches and this causes a pressure increase.
::::::: Well, Guess what. ..  The converse is also true.  If you can convince air, or get it started to try travel away form a surface, you will see a pressure decrease because of Inertia.  And that is what happens in Bauman and above a wing.
:::::::: In other words, when we move things around in a fluid, pressures can increase or decrease determined by the motion.
:::::::: The best way to interpret this is that it takes Pressure Gradients to Accelerate the fluid *WHEN* all you have is fluid and different pressures near-by. However, pressures will also be modified by air’s Inertia as it resists Accelerating due to surfaces.
::::::This is also explained at Millersville Aspirator Experiment
::::::: www.millersville.edu/physics/experiments/093/
::::::: : . . . . . . . . . . . .
::::::[[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 23:59, 3 May 2025 (UTC)
::::Regarding the Acceleration of car passengers from Dolphin.
::::: This is an example of looking in the wrong place. Every person in the car adds up to a combined, total mass, along with every single component of the car.  The engine only produces some amount of torque, which is the FORCE to Accelerate the total mass.
::::::: Try this
:::::: If we put more people in the car it will accelerate less. It’s no longer the same.  Houston, we have a problem.  It looks like, NOW, mass affects acceleration.  Of course it does, Mass is the resistance to force.
:::::: A fundamental Property of mass is Inertia and it is a RESISTANCE to force.
::::::  So. It is the Inertia of each of those individual masses that resists the force and, THEREFORE is Responsible for the force applied to it.  Each mass/Inertia determines the fraction of force that gets applied to it.
::::::  THINK - - IF a brick had no Inertia, there would be no resistance to a force; Newton’s Third Law wouldn’t exist and there could be NO force possible  in the first place !  The brick would just move along with whatever came along and tried to provide the “force”.
::::: Therefore, it is each person’s MASS aka Inertia that is responsible for the fraction of the engine’s force that it gets. The adult with more mass/Inertia gets more force than a child with less mass/Inertia. Therefore, it is the mass/Inertia that is the reason for the force value.
:::::: I understand this seems like circular reasoning, but we cannot forget about Inertia and I Submit that it must be considered this way. It is very significant because it is ALSO the most significant factor in WHY air pressures change around a moving object.
::::[[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 23:42, 3 May 2025 (UTC)
::Ok I’ve digested Eastwell’s paper and agree with everything in it. The leap was conflating what I wrote (''molecules can only have so much velocity, and if that velocity is in the direction of flow, less velocity is available to make pressure'') with what Eastwell wrote (''Since perpendicular vectors are independent, any net force that changes the motion of air particles in one direction (e.g., speeds up the air) will have no effect on the speed of these particles in a perpendicular direction. '').  Both statements are true, the difference being that I am not applying any work/force/acceleration to the molecules, while Eastman is.  This is key and many people do not understand it.
::As to Swordfish’s other notion that the pressure drop is essentially caused by pressure drop in the flow direction, I agree there is truth to this too. But to Dolphin’s point, it is also not as easy as it looks to say one aspect is the cause of the other. My goal is to solve this apparent paradox.
::I see we all agree there is very little out there explaining what happens on the molecular level. And I agree I can’t just write what is happening, that would be taken as opinion.  So I’ll try to find something before editing the article… FWIW here there is a video on youtube, “Bernoulli’s Principle on Atomic Scale”, with good intentions, but it is still not 100% right / clear.
::--'''[[User:Zojj|Zojj]]''' [[User_talk:Zojj|t]][[Special:Contributions/Zojj|c]] 12:53, 3 August 2023 (UTC)
:::So I just found this: {{cite web|title=Misunderstanding Flight Part 1: A Century of Flight and Lift Education Literature|url=https://www.mdpi.com/2227-7102/13/8/762}}
:::It has talk of molecules and simulations.  Anyone with access able to see if any of those are helpful? --'''[[User:Zojj|Zojj]]''' [[User_talk:Zojj|t]][[Special:Contributions/Zojj|c]] 04:57, 4 August 2023 (UTC)
::::This url seems to bring up the article. [[https://www.mdpi.com/2227-7102/13/8/762]]
::::Quickly scanning it, I'm not seeing much about statistical mechanics.  There's some discussion of the applicability of the  model of the fluid as a [[continuum assumption|continuum]] (which the author mistakenly calls the [[continuum hypothesis]]), but the author basically concedes that it's almost universally accepted.
::::This article [[https://ui.adsabs.harvard.edu/abs/2011AmJPh..79..214F/abstract]] may be what you are looking for but I don't have access to the full text.
::::I'll take some time to read it more carefully, along with the cited articles - I thought I had read most of what's out there, but the article contains cites to many resources that I'm unfamiliar with. It's certainly an excellent compendium of links to aerodynamics and lift articles, even if I disagree with some of his conclusions. [[User:Mr swordfish|Mr. Swordfish]] ([[User talk:Mr swordfish|talk]]) 15:57, 5 August 2023 (UTC)
:::::Mr. Swordfish states: ''The notion that forces cause acceleration is hardly out of the mainstream.'' However, this statement – interpreting Newton's second law in terms of force being the cause and acceleration the effect – is not correct.{{cn}} See e.g. [https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/newtons-laws-of-motion/ this NASA page], or the section "Determinism (or, what causality is not)" of [[Causality (physics)]]. The same is of course true for Bernoulli's principle relating changes in velocity to changes in pressure etc. in a fluid flow under certain assumptions/conditions. -- [[User:Crowsnest|Crowsnest]] ([[User talk:Crowsnest|talk]]) 20:50, 12 September 2023 (UTC)
::::::The NASA page: "Considering the momentum equation, a force causes a change in velocity; and likewise, a change in velocity generates a force. The equation works both ways." -- [[User:Crowsnest|Crowsnest]] ([[User talk:Crowsnest|talk]]) 06:14, 13 September 2023 (UTC)
:::::::I have no argument with the statement that "the equation works both ways".  But the NASA article also states:
::::::::Example of force involving aerodynamics:
:::::::::An aircraft’s motion resulting from aerodynamic forces, aircraft weight, and thrust.
:::::::IOW, the aircraft's motion is a ''result'' of the forces on it.  The notion that forces ''result'' in acceleration is hardly "outside the mainstream of physics." Or perhaps you think NASA is outside the mainstream?
:::::::I am familiar with the idea that there are no causes and effects in physics, only mathematical equations that express the relationship among certain quantities.  And sometimes that may be the best way to think about things.  But I don't know how common that school of thought is among physicists, and many mainstream reliable sources describe forces as ''causing'' acceleration, and that acceleration is an ''effect'' of the applied force.  See the quotes above from Anderson and Babinsky for instance.
:::::::Doug McLean offers criticism of the Weltner paper on page 280 of his book.  It's an interesting critique, and I'm inclined to agree with McLean, but note that he doesn't claim that Weltner is ''wrong'', only that the idea is "...not entirely correct...".  If Weltner was "outside the mainstream" I doubt McLean would bother addressing the paper; certainly nothing McLean has written could be interpreted as claiming Weltner was "outside the mainstream".
:::::::If there's some source that claims "The notion that forces cause acceleration is out of the mainstream" I haven't seen it yet. I'd be curious to read it, assuming one exists. [[User:Mr swordfish|Mr. Swordfish]] ([[User talk:Mr swordfish|talk]]) 22:00, 13 September 2023 (UTC)
::::::::Accelerations are always caused by unbalanced forces. That knowledge is found in Newton’s FIRST law of motion. It is not found in Newton’s second law, and it is not found in Bernoulli’s principle or any other principle of physics. We all know of many reliable published sources that associate this concept with Newton’s FIRST law, but I don’t recall any reliable source that associates it with Bernoulli’s principle. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 22:51, 13 September 2023 (UTC)
:::::::::The classic derivation of Bernoulli's equation (i.e. not using conservation of energy) is simply a direct application of Newton's second law to the unbalanced forces encountered in a flow field with changing pressure. 
:::::::::Holger Babinsky clearly explains this in English (and provides the math in the appendix) in his article "How do Wings Work"  [https://www3.eng.cam.ac.uk/outreach/Project-resources/Wind-turbine/howwingswork.pdf]
::::::::::If the particle is in a region of varying pressure (a non-vanishing pressure gradient in the {{mvar|x}}-direction) and if the particle has a finite size {{mvar|l}}, then the front of the particle will be 'seeing' a different pressure from the rear. More precisely, if the pressure drops in the {{mvar|x}}-direction ({{math|{{sfrac|d''p''|d''x''}} < 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).
:::::::::[[User:Mr swordfish|Mr. Swordfish]] ([[User talk:Mr swordfish|talk]]) 12:50, 14 September 2023 (UTC)
::::::::::If we have a vector equation R = P x Q where R and Q are vectors, does R cause Q, or does Q cause R? I think our vector equation provides no information to assist with this question; if there is a causal relationship between R and Q, we must look elsewhere to find it. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 13:50, 14 September 2023 (UTC)
::::::::::''If the particle is in a region of varying pressure ...''
::::::::::The important premise is already in this ''If'', which assumes a non-interaction between the velocity field and the (independent) pressure field. 
::::::::::There are discussions going on for a very long time whether ''cause-and-effect'' are a subject of physics or of philosophy/metaphysics. Personally, I would prefer to stay away from this tricky subject regarding this article on Bernoulli's principle. The more since the dominant case is for application in steady flow, where time does not play a role in the ''dynamics'' (Bernoulli equation) – only in the ''kinematics'' through the relationships between the position, velocity and acceleration of a fluid parcel. Without time being a variable in the system dynamics, how can there be cause and effect? And to my opinion this is also in full agreement with Dolphin51's above argument. -- [[User:Crowsnest|Crowsnest]] ([[User talk:Crowsnest|talk]]) 22:01, 15 September 2023 (UTC)
::::::From "Understanding Aerodynamics", Doug McLean (2012), p. 3:
::::::"Another is that the basic equations define implicit relationships between flow variables, not one-way cause-and-effect relationships. Because of these difficulties, misconceptions have often arisen, and many of the physical explanations that have been put forward over the years have flaws ranging from subtle to fatal." -- [[User:Crowsnest|Crowsnest]] ([[User talk:Crowsnest|talk]]) 06:49, 13 September 2023 (UTC)
:::Zojj,
:::::: '''Regarding a "directional" pressure drop.'''
:::: Saying: “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 see it said here, that people will more easily understand things at the molecule level; yet EVERY TIME I see someone trying to do that, they get it wrong.  
:::: Molecules are trading momentum amongst themselves at supersonic rates, randomly, due to collisions in ALL directions.
:::: It is YOU that added the energy to get it flowing in the first place. You ADDED Energy.!.  The molecules do NOT modify their bouncing-around pattern.  They will always exchange momentum in all directions equally.  It is a fundamental property pf pressure called isotropic.
:::: What you see is all this molecular momentum exchange activity riding along on the overall mass flow.  There is vector addition of the linear, along the flow mass speed to the molecule motions, but amongst themselves (if you ride along with the flow speed) you see the same totally random motions.
:::: The potential energy of the ‘high pressure’ in your lungs accelerates air out, thus converting that potential energy into the kinetic energy in the speeding air, This energy conversion occurs as the air goes from the low speed, high pressure in your lungs to high speed, low pressure (atmospheric) jet outside.
:::: This tells us that Bernoulli’s Principle is about Acceleration, NOT speed.  And as already pointed out, further down in the article it says that it is a Pressure Gradient that provides the Force to Accelerate the fluid = Newton.
:::.
::::: For a direct analogy, bounce a basketball on the ground.   Each bounce transfers some momentum. Now walk around – it STILL transfers the same momentum per bounce.  NOW do that out of a car window at 60 MPH.  Each bounce STILL transfers the same amount of momentum. !  The car is adding the horizontal, kinetic energy and not changing the vertical.
:::Regards. [[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 23:35, 3 May 2025 (UTC)

==  Error in lead paragraph ==  
Folks.  I guess it's been over a year since I checked. . . I had been telling students that the article is a good reference for the correct wording of Bernoulli's Principle (*accompanies* rather than causes), but I see the lead Paragraph was changed and the most important sentence is wrong and makes no sense. It appears no one caught it since it violates all authoritative sources. The sentence is:
: "Bernoulli's principle states that an increase in the speed of a parcel of fluid occurs simultaneously with a decrease in either the pressure or the height above a datum" 

The velocity DOES NOT change with height above a datum, unless there is something like a pipe diameter change.

It should be reverted to the original. 
Or, if you really want the height part there, is can say: Static Pressure decreases with a speed increase or height increase.  
However, I believe it is customary to leave the height part out in the basic, initial statement and retain just: "an increase in the speed occurs simultaneously with a decrease pressure."

It is in:  Revision as of 22:01, 18 May 2024  By Dolphin.

I see much discussion and should come back and review it as the common misconception of the Principle has been part of my focus due to a training responsibility I was asked to assume 10 years ago and had to get pretty serious about this and some related things and and can help add come clarity if needed.

If I did this wrong, it's been a while since I did much editing. . 
Regards, [[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 08:35, 2 May 2025 (UTC)

:Good catch {{u|EngineerSteve}}! My mistake - I must have been having a bad hair day. I will fix the problem immediately. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 11:19, 2 May 2025 (UTC)

:[[File:TorricelliLawDiagram.svg|alt=|frame|The velocity of a parcel of fluid escaping from the vessel increases as the height of the parcel above the datum decreases. The pressure of the fluid outside the vessel is uniformly equal to atmospheric pressure.]]
:The statement that the velocity of a fluid changes with height above the datum is correct in the example of a thin stream of liquid escaping from a storage vessel. At every point outside the vessel the pressure is uniform and equal to atmospheric pressure. The velocity of a parcel of fluid increases as the parcel approaches the datum, thereby conserving mechanical energy.
:The objective in the lead paragraph is to provide an introduction that can be understood by the widest possible audience. The current wording is not as clear as it could be. I will work on it. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 13:17, 2 May 2025 (UTC)
::: I think so.  That tank with holes is a classical way to indicate the change in *static PRESSURE* with Depth of a vertical column - the "Pressure Head" in the  tank.  Those "jet" speeds are an indication of the pressure difference between the pressure head in the tank and atmospheric pressure outside.  That is one of the most fundamental concepts to understand. I can't recall if I've looked at any Clancy. 
::.
::: I can only assume you understand that this is where we see the conversion of the potential energy of the tank's static pressure (at low/zero speed) INTO the kinetic energy in those 'faster' jets outside the tank.  Therefore conserving energy, just converting it between forms.  One thing I emphasize to student's is that Bernoulli is about Acceleration. not simply 'speed'. Those 'speeding' streams are all at atmospheric pressure - NOT below it (static pressure within the stream).
::: I see people using the words 'conservation of energy' without understanding where the two energies reside that get converted/conserved, then think that any 'fast' fluid is lower in (static) pressure than any other 'slow' fluid. 
::: I call the misconception that fundamentally, speed is the cause of lower pressure "Bad Bernoulli". 
::: While this 'tank depth' is a demonstration of Bernoulli 'happening' between those two locations, that sentence just blew me away because the emphasis must be that the wording must be clear to not indicate a cause because as John D. Anderson indicates in one of his historical notes, there is nothing in Bernoulli's notes to indicate he knew the cause. That came with Euler's follow-up work.
::: I did a brief scan of the discussions in Talk and it seems there is considerable confusion/discussion in tis area.   I'll go though it and if needed, show the cause/effect chain in one of the more confusing situations where Bernoulli gets Bass-Ackwards. . . 
::: It is SO frustrating with people repeating it over and over.  Three friends recently alerted me to a new video where the author goes completely off the rails applying a child-like physics, thinking he's just fixed all the mistaken experts who don't understand this stuff, YET has a video with all the common Bad Bernoulli demos.!..
::. . . Sigh. . . Regards, [[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 14:20, 2 May 2025 (UTC)
::This is still not fixed.  I believe he original should read,
::: Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in [[static pressure]] or the [[fluid]]'s [[potential energy]]
::I'll still try to review the above thread and comment later today. Regards [[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 14:55, 3 May 2025 (UTC)
:The common form of Bernoulli's equation is
{{NumBlk||<math display="block">\frac{v^2}{2} + gz + \frac{p}{\rho} = \text{constant}</math>|{{EquationRef|A}}}}

:It relates three quantities (assuming gravitational constant and fluid density are constant): pressure, speed, and height.
:Any one of the three may change if either of the other two change. However, in the case of a fluid flowing through a circular tube of constant diameter that varies in height, the speed remains constant and only the pressure and height vary.  I think that's the crux of the criticism by [[User:EngineerSteve|-- Steve --]].  I agree that the current wording is misleading and should be changed.
:I'm not convinced that the previous wording is optimal:
::'''Bernoulli's principle''' is a key concept in [[Fluid dynamics|fluid dynamics]] that relates pressure, speed and height. Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in [[static pressure]] of the [[Fluid|fluid]]'s [[potential energy]].
:The lead paragraph should be employ the common terms of speed and pressure rather than more abstract concepts like potential energy.
:I'm failing to come up with a simple correct statement that relates all three quantities, so perhaps restricting the language to the simplified case of constant height would make it more readable:
::'''Bernoulli's principle''' is a key concept in [[fluid dynamics]] that relates pressure, speed and height. For example, for a fluid flowing horizontally Bernoulli's principle states that an increase in the speed  occurs simultaneously with a decrease in [[static pressure|pressure]].
:[[User:Mr swordfish|Mr. Swordfish]] ([[User talk:Mr swordfish|talk]]) 16:15, 2 May 2025 (UTC)
::Thanks to EngineerSteve and Mr Swordfish for your thoughtful replies.
::It occurs to me that there are four distinct cases that are necessary to comprehensively explain Bernoulli:
::#constant height above datum. Each change in speed is associated with a change in pressure of equal magnitude but opposite sign. This is the case we use when dealing with horizontal flows such as the airflow around a wing that is generating lift.
::#constant static pressure. Each change in speed is associated with a change in height (or head or gravitational potential energy) of equal magnitude but opposite sign. This is the case of the thin stream of liquid falling through the atmosphere.
::#constant speed. Each change in height is associated with a change in static pressure of equal magnitude but opposite sign. This is the case of a pipe (or hose or storage vessel) that is NOT horizontal and the pipe is filled with liquid. The liquid may be flowing upwards or downwards, or in the case of a storage vessel the fluid velocity is zero.
::#A combination of the above three. This is a slightly more complex case so warrants a slightly more complex explanation. It is useful to use the concept of total pressure and say static pressure plus dynamic pressure plus gravity head are equal to total pressure which remains constant throughout the body of fluid in the absence of non-conservative forces.
::I am attracted to Mr Swordfish’s suggestion that for the lead paragraph it may be best to confine attention to the case of constant height. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 22:32, 2 May 2025 (UTC)
:::As Steve says above:
::::I believe it is customary to leave the height part out in the basic, initial statement and retain just: "an increase in the speed occurs simultaneously with a decrease pressure."
:::So we seem to be batting 3 for 3 here.  Other opinions? [[User:Mr swordfish|Mr. Swordfish]] ([[User talk:Mr swordfish|talk]]) 00:26, 3 May 2025 (UTC)
:::Dolphin,
:::I’m afraid that I must be candid. &nbsp;&nbsp; I see you are struggling with this, but you have a way to go with the subject matter and terminology.
:::.
:::First, for cases 1, 4 –Speed and pressure are different quantities all together, and can’t have equal ‘magnitudes’. &nbsp;It’s like saying 3 feet is the same magnitude as 25 seconds.
:::If I read you correctly, #2 has TWO fundamental changes: height and diameter
:::Then, #3 is no different with or without flow, head pressure. .
:::Your 4 cases make it too complex.&nbsp; I see here, &nbsp;talk about keeping it simple to begin with, so jumping to those complex situations makes it very difficult.
:::Many on-line tutorials start with a varying pipe diameter and change in height right off the bat with the full equation.
:::To be honest, I think the treatment is ok, but I haven't read it all to give a good assessment.
:::. . .
:::. . . 
:::My position, for full treatment, is that it is FAR, FAR better to cover each fundamental concept alone, BEFORE combining them – if at all.
:::Namely:
:::1 – Varying diameter, horizontal pipe showing speed changes with the ‘inverse’ *related* pressure change.
:::2 – Constant diameter Pressure change with elevation.
:::.
:::.
:::.
:::I’ll look over the above comments in the next day or two.
:::Regards [[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 01:33, 3 May 2025 (UTC)
:: Swordfish If that first response is for my benefit, Summary:
::My dad got his private license in his late teens in ’37 IN a biplane and recertified in the 60s for a seaplane rating (SES), so I, therefore, spent lots of time hangar flying with friends at Palwaukee airport, building plastic & balsa models, on to flying U-Control and RC, winding up as a test pilot for other RC builders in the Navy. . .
::Something I got from my Father, also an engineer, is a deep desire to understand things to the nth degree following all well-known, applicable principles.
::Fast forward. . . About ten years ago was asked to manage a very sophisticated, full-cockpit B-737 flight simulator, donated the local Challenger Learning Center.
::Knowing I’d be asked anything, I decided to brush up on aviation things and immediately ran into the fire hose of misconceptions about Bernoulli and lift with so many well-meaning, but lousy YouTube videos, etc. Getting some of the major Aero text books and talking with some of the authors to clarify various points, I haven’t managed to crawl out of this rabbit hole since. . .
::. . .
::So. . .You might say that you are singing to the choir director. . .
::.
::I understand, on one hand wanting to be ‘correct’ but also the need to stay simple and not include too much so as to be confusing to the neophytes. I’ve also taught in two county colleges.
::In this case, I recommend leaving the elevation out since most other sources only mention the speed increase and accompanying pressure decrease.
::I also make a clear distinction between Bernoulli’s Principle and Bernoulli’s Equation. The Principle is the concept that had to come before we could find the equation(s) that mimic the physical world.
::I’m also very sensitive to the “intuitive” focus. Doing STEM demos for two schools, scouts and the local Challenger Learning Center, that is very important, talking to kindergarteners to professionals.
:: challenger.org
::For this subject, most people are quite unaware of the atmosphere we are submerged in and I start with the wind as something everyone can understand as something that is actually a small increase of the already existing atmospheric pressure.
::I’ll look over these comments in the next day or two.
::Regards.
::: I now see there are more comments. . .
::[[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 00:41, 3 May 2025 (UTC)
:::I see my statements {{tq|Each change in speed is associated with a change in pressure of equal magnitude but opposite sign}} are in error. (We have all misled in this way when we have used words such as "an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure".)
:::Focussing on Bernoulli's equation, what I intended was that each change in the ''speed term'' <math>\tfrac {V^2}{2}</math> is associated with a change in the ''pressure term'' <math> \tfrac{P}{\rho}</math> of equal magnitude but opposite sign. Alternatively that each change in the kinetic energy term <math>\tfrac {1}{2} \rho V^2</math> is associated with a change in the pressure term <math>P</math> of equal magnitude but opposite sign. Of course, every term in the equation must share [[coherent units]] because that is true of all equations that rely on units of measurement, derived units etc. (EngineerSteve: 3 feet and 25 seconds are not coherent units.)
:::We happily write that "an increase in the speed" is associated with "a decrease in the pressure". We know that Bernoulli's principle is much more precise and powerful than this. The Bernoulli equation can be used to equate two terms and predict the change in pressure, or the change in speed, with mathematical precision. That precision is available if we use half the square of the speed rather than simply the speed; and the pressure divided by fluid density rather than simply the pressure. Mathematical precision is also available if we use the pressure, and the kinetic energy per unit volume rather than simply the speed. Coherent units must always be used throughout. 
:::However, all this is too complex for the lead paragraph. The preferred approach might be to write that Bernoulli's principle applies the law of conservation of energy to the flow of fluids; and then "for example, when a fluid is flowing horizontally any increase in speed is associated with a decrease in pressure, and any decrease in speed is associated with an increase in pressure." [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 14:55, 3 May 2025 (UTC)
::::Dolphin.
::::: Re: "Each change in speed is associated with a change in pressure of equal magnitude but opposite sign"
::::My objection was the 'equal magnitude' part. 
::::How can you equate the magnitude of a speed to the magnitude of a pressure? 
::::Is 1 PSI equal in magnitude to 1 meter per second?   1 = 1
::::If you think so, then:
::::: If I measure in feet per second...
:::::: Is a magnitude of 1 PSI equal in magnitude to 3.28084 feet per second?
::::.
::::You seem confused with the use of terms. [[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 00:13, 4 May 2025 (UTC)
:::::{{u|EngineerSteve}} Your previous post (dated 00:13, 4 May 2025) tells me that you haven't read my previous post (dated 14:55, 3 May 2025), immediately above yours. Please read it. Here is the [https://en.wikipedia.org/w/index.php?title=Talk:Bernoulli%27s_principle&diff=prev&oldid=1288572807 diff] leading to my previous post to make sure you are reading the correct one. Thanks. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 08:11, 4 May 2025 (UTC)
:::::''How can you equate the magnitude of a speed to the magnitude of a pressure?''
:::::You can't. At least not directly. But you can equate the kinetic energy associated with speed with the energy that is inherent in fluid pressure.  See my post under the Equations section below for details. [[User:Mr swordfish|Mr. Swordfish]] ([[User talk:Mr swordfish|talk]]) 01:02, 5 May 2025 (UTC)
::::::Dolphin, (and Swordfish)
::::::I did find following this thread confusing and haven't done much on Wiki in quite some time. I did see things out of order. . . In this interchange, I also missed an email notice and tried to comment on too many things at once.
::::::.  I'll apologize to you folks for that, but after doing such serious research and talking with some of the well-known names in Aerodynamics. I am quite firm in my understanding.  I fully understand that you all have good intensions and I do see some good discussion, particularly about when to go tp more advanced concepts.  My technique comes from teaching all ages and using common experiences (what you may call intuitive) to start folks on the right foot. This is long, but I must explain myself. 
::::::.
::::::Because I often refer students here for the correct wording of THE Principle, I decided to check and found what was alarming, so I decided to point it out and engage, ESPECIALLY because I found that it had been sitting there for about a year. . . 
::::::.
::::::In my second comment on Dolphin's use of 'magnitude'  I attempted to make my position clearer because reading my First, I didn't think I was.  
::::::Now,  I did see another email and found these last two comments.
::::::.
::::::Swordfish, 
::::::I'm fully aware of the energies.  In fact, so many people, even some PhDs describe what I call "Bad Bernoulli" as real physics.  Bad Bernoulli is: "Fast fluid/air has/causes a lower pressure (in a jet blown into the atmosphere).  
::::::.
::::::People do not know where these energies are located and simply do the demos, then robot-talk the "conservation of energy" phrase willi-nilly without realizing the real physics.  After studying this for ~10 years and seeing all the well-intentioned people trying to explain it and discuss it, I've accumulated 41 pages of on-line examples, good and bad (mostly).
::::::. . .    
::::::The common demos of blowing over a drooping paper or between two balls or cans do NOT prove that the high speed jet exiting the blower is below atmospheric pressure.  They are misinterpreted. 
::::::.
::::::What recently reminded me to look here was a new video that no less than 3 friends alerted me to, and what has to be THE worst explanation of lift to date.  Even worse than Neil de Grasse Tyson's video explaining the Equal Transit fallacy. . . Yep, if you haven't seen it on his "Star TALK" channel and Face Book,  he uses Bad Bernoulli as most others do. Then, I see Neil has another video (on sundials) where he demonstrates ZERO knowledge of how Earth's tilt affects the Sun's path across the sky. . . sigh.  
::::::Links below.
::::::. 
::::::Well,   This new 'lift' guy, Jason Gibson, is selling STEM DVDs !  After seeing his lift video, I decided to see if he had a Bernoulli's Principle video (since he doesn't really describe his understanding of Bernoulli there), and sure enough - ALL the BAD demos.  . . . THEN. . . 
::::::I find he has a previous Bernoulli Principle video, where he ALSO does the bad demos (Bernoulli "Bag" and all) . . . THEN. . . THEN *correctly* explains potential and kinetic energy of a roller coaster.!.!.  
::::::I tried to save him some embarrassment by asking to talk to him directly to educate him and take them down, but his assistant just says he's busy. . . 
::::::.
::::::::::LINKS.  My personal Bernoulli Principle link at the very bottom.
::::::: Enjoy.
::::::Jason Gibson, Lift.  An hour. First 11 minutes dissing Equal Transit; followed by a child-like explanation flirting with physics at 30 minutes, followed by the last half hour of more added nonsense than you can shake a stick at. . . 
::::::: https://www.youtube.com/watch?v=CT5oMBN5W5M 
::::::.
::::::: Jason’s all examples Bad Bernoulli Video:
::::::::  https://www.youtube.com/watch?v=C-HWOM-UVUo    (Posted March 2025)
:::::: 
::::::: Same Bad Bernoulli with Roller Coaster explaining energy conversions and conservations, later in video:
::::::::  https://www.youtube.com/watch?v=fyy_85lKvtA   (Posted in 2023)
::::::.
::::::: Neil deGrasse Tyson TERRIBLE Lift Video: How Do Airplanes Fly? | Neil deGrasse Tyson Explains... 
::::::::: https://www.youtube.com/watch?v=VhReoAJZzpE&t=233s      
:::::: 
:::::::: Neil deGrasse Tyson’s incorrect Sun elevation video. Why Do Clocks Run Clockwise?  Starts at 58sec.
::::::::: https://www.youtube.com/watch?v=P5rBJ746F1g&t=58s 
::::::.
:::::::: Noskowicz:
::::::: Understanding Bernoulli's Principle Correctly.  I will take suggestions at cleaning it up because every time I go through it I see something that could be better and/or simpler. I Highly prefer phone, FaceTime or Zoom to clear misunderstanding up quickly (US Central time, GMT-6).   It also links to my Lift article:
::::::::: https://kyuoyckftflurrpq.quora.com/  
::::::Sorry is I have some screwy formatting here, but I tried to make the final product readable, with what little formatting I recall.
::::::Regards, folks. [[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 01:17, 7 May 2025 (UTC)
:::::::{{u|EngineerSteve}} I see you have numerous anecdotes about people who have published poor explanations of Bernoulli’s principle but I don’t see what point you are making for the improvement of this Wikipedia article. Are you suggesting a way in which this article can be improved? If so, please explain what way you have in mind. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 01:49, 7 May 2025 (UTC)
::::::::Sure,  Yes of course.  That occurred to me earlier.  AND. . .
::::::::If you don't have a good command of the physics and the terminology, should you be trying to contribute to the article. . . OR . . . It can help to discuss things in order to find the best way to "get across to" those other people who also don't understand this.
::::::::.
::::::::Having taught and mentored much, it is an important concept that you know your student enough to provide a good explanation that they will understand. . . "Speak to your audience" is an old saying.
::::::::. . . . 
::::::::So, in effect this is also saying that it may be a good idea to discuss the concepts to get to a good coverage for the general Wiki audience. . . 
::::::::.
::::::::Not having gone through the whole article now. . . 
::::::::My suggestion is that you make is clear that, although the original wording gives no cause and effect because as John D. Anderson says in his Aerodynamics book, there is no indication in Bernoulli's notes that he understood the cause, then, that Euler is credited with first figuring out that it follows Newton's laws where it is a Pressure Gradient that is the cause of fluid acceleration, just as a force is the cause of acceleration of any solid mass. I submit that that is a good teaching comparison. 
::::::::.
::::::::So. . . Emphasizing that Bernoulli's Principle is about Acceleration along a flow and not simply speed would / should clearly describe it. 
::::::::: My opinion, I'd prefer something to help dispel the common misconception about "fast air has lower pressure" and everybody believing the blown air is below atmospheric pressure.  
::::::::.
::::::::So, I CAN see discussion on whether the original wording should be retained, then adding clarification,  
::::::::OR
::::::::Change it at the start, clearly correcting the misconception at the start.  
:::::::: HOWEVER, then it probably requires adding something to the effect that so many other places use the old wording. . . . 
::::::::.
::::::::If I think anything is important, it's that making it clear, somewhere in the article, that the Speed increase is caused by a Pressure Gradient.
::::::::.
::::::::.
::::::::Along this same lines, for some time I've thought that Newton's laws are also awkwardly worded, possibly to preserve Newton's best translation to honor him.   If we see that the first law says that force is the cause of acceleration, it might then be easier to see that a Pressure Gradient is the cause here.  I believe you have touched on that here, above.
::::::::However, then this assumes one knows what acceleration is (in general) and that is what "newton's" words refer to with: "remain at rest...Straight line, constant speed, UNLESS acted on. . . "
::::::::So. . . If an "object" won't spontaneously accelerate by itself, so won't a fluid. 
::::::::.
::::::::You'll see Newton's First described the Law of Inertia.  Well, fluids have mass and inertia. . . 
::::::::FWIW, [[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 03:10, 7 May 2025 (UTC)
{{od|:::::::}}To refocus the discussion on how to improve the article (as opposed to being a [[WP:NOTFORUM|forum]] for discussion of the topic itself), I suggested above a change to the second sentence in the lead, and it seemed to have received positive reception.   Seeing that, I've implemented it in the article.  I can't say that it is the optimal solution, but it's correct, reliably sourced, and likely easily understandable.  I'm happy to discuss alternatives. [[User:Mr swordfish|Mr. Swordfish]] ([[User talk:Mr swordfish|talk]]) 00:06, 5 May 2025 (UTC)

:Thanks, Swordfish,  I thought of that earlier, but neglected to say it. [[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 01:20, 7 May 2025 (UTC)

{{reflist-talk}}
== A General Comment - Equations ==
Regarding some comments made.

My view is that equations, though important to us, never explain WHY things happen - the physics cause/effect.<br>
For one, there is normally no indications of independent and dependent variables.<br>
They only mimic the physical world.<br>
We first did experiments on the physical world and observed what happened, how things related and measure things like position speed, acceleration, force and mass and see these thing relate in regular ways. We also see that mathematics shows regular relationships and WE found the equations that mimic the physical world.  So it was an understanding of what happened that came before the equation.<br>

[[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 00:25, 4 May 2025 (UTC)

:Some equations are more easily translated into readily understood concepts or clear physical interpretations. For instance, the equation in the current article that expresses the basic equation is
{{NumBlk|:|<math display="block">\frac{v^2}{2} + gz + \frac{p}{\rho} = \text{constant}</math>|{{EquationRef|A}}}}
:If we multiply both sides by <math>\rho</math>, we get
{{NumBlk|:|<math display="block">\rho\frac{v^2}{2} + \rho gz + p = \text{constant}</math>|{{EquationRef|B}}}}
:Equation B expresses the terms of the equation in units of energy per unit volume, while the units of equation A are velocity squared or  distance/time squared which is not very illuminating - I know of no physical principle that says velocity squared is conserved.  Looking at equation B, it seems obvious (to me anyway) that it's an expression of conservation of energy i.e. it states that the total energy per unit volume is constant.
:Anyone who's done even a little bit of physics should know that kinetic energy is <math>{m}\frac{v^2}{2}</math> and that potential energy is <math>mgz</math> (or more commonly <math>mgh</math>).  Switching ''m'' for <math>{\rho}</math> gives the energy per unit volume. 
:It's not so obvious that pressure is energy per unit volume; usually pressure is thought of as force per unit area, but if you check the units it's also energy per unit volume.  Granted, dimensional analysis is insufficient to derive the equation, but once the equation is derived it becomes "obvious" that pressure ''is'' energy per unit volume.
:I'm not sure why equation A is used in the article when equation B has a much better physical interpretation.  Pending hearing objections here, I propose switching out equation B for equation A. [[User:Mr swordfish|Mr. Swordfish]] ([[User talk:Mr swordfish|talk]]) 00:44, 5 May 2025 (UTC)
::Thanks Mr Swordfish. I don’t disagree with anything you have written here. The units of Equation A are units of energy per unit mass.
::I can’t see Equation B (except by going into Edit mode.) I think there are some formatting problems within Equation B. For example, in a couple of places you have put a pair of curly brackets around \rho, and this seems to be a problem. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 01:14, 5 May 2025 (UTC)
:::1) I'm not very conversant with math markup in wikipedia.  It looked good in my browser, but I've removed unnecessary curly braces from equation B, so hopefully it will display correctly for you now.
:::2) I hadn't thought of equation A as being an expression of energy per unit mass.  But considering energy per unit mass vs energy per unit  volume,  I think the latter is more intuitive. But "intuitive" is a very subjective thing. [[User:Mr swordfish|Mr. Swordfish]] ([[User talk:Mr swordfish|talk]]) 01:51, 5 May 2025 (UTC)
::::The presumption that equation A expresses energy per unit of volume is wrong, it expresses energy per unit of mass, see e.g. Batchelor, "Introduction to fluid mechanics", 1983 reprint, page 158 -- [[User:Crowsnest|Crowsnest]] ([[User talk:Crowsnest|talk]]) 22:15, 8 May 2025 (UTC)
:::::Hi {{u|Crowsnest}}! We aren’t saying Equation A (alpha) is energy per unit of volume. We are saying A is energy per unit of mass, so I think we are all in agreement.
:::::Mr Swordfish and I are saying Equation B (bravo) is energy per unit of volume. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 22:31, 8 May 2025 (UTC)
::::::Yes, I was far from clear. The presumption that the Bernoulli equation should more fundamentally be expressed in terms of energy per unit of volume, equation B, is wrong. The "basic equation" is equation A in terms of energy per unit of mass, expressing a constant (specific) [[enthalpy]], see e.g. Batchelor, "Introduction to fluid mechanics", 1983 reprint, page 158, and other basic textbooks on the derivation of the Bernoulli equation from first principles with the least amount of restrictions on the fluid and flow. -- [[User:Crowsnest|Crowsnest]] ([[User talk:Crowsnest|talk]]) 23:03, 8 May 2025 (UTC)
:::::::Thanks {{u|Crowsnest}}. I looked at p.158 of Batchelor, and adjacent pages, but didn’t see anything to discourage the writing of Bernoulli’s equation in units of energy per unit of volume. Perhaps you can clarify your comment.
:::::::In ''Fluid Mechanics'' by Victor Streeter, Section 3.7 (4th Ed.) he writes:
::::::::“By multiplying by <math>\rho</math>,
::::::::<math>\rho g z + \frac{\rho v^2}{2} + p = constant </math> (Equation 3.7.4)
::::::::”In this form each term is ft-lb/ft<sup>3</sup> or energy per unit volume.”
:::::::[[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 08:49, 9 May 2025 (UTC)
::::::::Yes, but Streeter here obviously considers from the start of deriving the Bernoulli equation that density <math>\rho</math> is a constant. The 4th edition begins §3.7 with "Integration of Equation (3.6.5) for constant density yields the Bernoulli equation ..." 
::::::::His Eq. (3.6.5) contains the term <math>dp/\rho</math> which for an isentropic flow – the main premise for Bernoulli's equation to be possible, i.e. the flow has to be thermodynamically reversible, no irreversible heat losses and friction losses – can be shown to be <math>dw=dp/\rho</math>, with <math>w</math> the specific enthalpy (enthalpy per unit of mass), see e.g. Landau & Lifschitz (1987) "Fluid Mechanics", 2nd ed., §2 & §5. The result is: <math>\tfrac12 v^2 + w + gz =</math> constant along a streamline. The specific enthalpy <math>w</math> is the sum of internal energy <math>E</math> and <math>p/\rho</math>, Batchelor p. 160. So for the case of negligible changes in constant internal energy along a streamline, Eq. A (alpha) results, while more generally <math>\tfrac12 v^2 + E + p/\rho + gz =</math> constant. -- [[User:Crowsnest|Crowsnest]] ([[User talk:Crowsnest|talk]]) 21:43, 12 May 2025 (UTC)

== My comments on the article structure ==
.
Engineer Steve
:
I reviewed the article, except for the equations, and have these recommendations.  While I see that it does cover many important points, I think more emphases is needed in some areas, especially for the common misconception of speed causing lower pressure. This may be the most wide-spread fallacy in all physics.
:
In fact, I suggest that you consider moving the equations section down, or at least put the Misconceptions earlier, even first after the lead, since the main misconception is so widely repeated and believed.
:
I’ll explain my recommendations carefully and do not plan to enter into long discussions, but if someone wants clarification, I am numbering these for easy reference.
:
: A - In general, I make a distinction between Bernoulli’s Principle and Bernoulli’s Equation.  I consider the simplified wording, such as that second sentence, to be the Principle, but simply stated. This is a qualitative description of the *concept* - - at least the pressure/Acceleration part. 
: Bernoulli’s Equation including the three terms for static, dynamic and height shows the quantitative relationship of the values/quantities.  This mimics what happens to the *quantities* in the physical world.  However, it does not show cause and effect – independent and dependent variables.
.
: I will also state that while all physics formulas / equations are very useful, they never show cause and effect. They only mimic the real world values and are derived from an understanding of the concepts. 
. . . 
: B - Also I saw talk about starting with explanations that are intuitive, which is good.  However, you must know that we aren’t born with this knowledge. We learn things in our every-day lives and it best to find those kinds of things as a basis for explaining other things. Having done mentoring, teaching, STEM demos for a wide range of ‘students’ and read many You Tube comments, I’ve gathered many such starting points and analogies. 
. . . 
: #1 –  2nd sentence. Statement of the Principle.
I would prefer that second sentence say something like “The most common wording of Bernoulli’s Principle is. . . “
I think the part about constant height is option
:
Also, I see some references add that the converse of decrease in speed and increase in pressure is also part of the Principle. So you can discuss including that.   Some references do this by saying that the Principle also describes “the inverse relationship of pressure and speed”.
. . 
Then, right after that, I think it is a good idea to clearly and explicitly state that it does NOT say speed “Causes” a pressure reduction.
.

I also think that the fallacy of blowing a jet of air that is below atmospheric pressure should be mentioned very early in the article because it is so prevalent and few people will read down, past the long equations section, to the misconceptions to get to that one.  See #6, Misconceptions.

. . . 
: #2 – There is a contradiction in the article.
Bernoulli vs. Euler.
:
The first Paragraph has: “. . .it was Leonhard Euler in 1752 who derived Bernoulli's equation in its usual form.[4][5]”  
John D. Anderson’s Historical notes also says that Euler actually derived the equations we now use with Bernoulli’s name and, also determined that pressure is isotropic and that a Pressure Gradient is the cause of fluid acceleration, just as a force causes acceleration of an ‘object’ per Newton.. 
Anderson Historical Note 6th ed Pg 305
:
However, the contradiction is in the section APPLICATIONS: “the lift forces can be calculated (to a good approximation) using Bernoulli's equations,[24] which were established by Bernoulli over a century before the first man-made wings were used for the purpose of flight.” 
That second one should be corrected, or omitted, since it was Euler..   AND I see no reason to mention flight in this article.

. . . 
: #3 – The text under the Venturi meter image needs improvement.
It draws a relation between kinetic energy to pressure.  It should mention kinetic energy and potential energy, which is pressure. 
:
I suggest:
:
“The kinetic energy of speed, increases at the expense of the potential energy of fluid pressure, as shown by the difference in height of the two columns of water.”  Also see my #4 about “expense”.
Because everyone stresses conservation of energy, I think energies should be explicitly explained for this and other situations. 
:
When describing various situations, I submit that the locations of these potential and kinetic energies must be made clear. 
I.E. Where there is low speed there is high pressure which then changes to high speed low pressure –  This is potential energy being converted to kinetic energy.
:
It is also WITHIN a flow -  also frequently stated as ‘along a streamline’.

. . . 
: #4 – Within the early text it talks about conservation of energy, but doesn’t explain where the energies are located, nor where the conversion between potential and kinetic occur; as I point out for the Venturi meter image.  
So, for the Venturi Meter image, rather than “kinetic energy of speed, increases at the expense of” potential energy, I recommend something like: 
:
“The kinetic energy of speed was converted from the potential energy of fluid pressure, as shown by the difference in height of the two columns of water.”
:
OR 
:
: Better yet, turn it around thus:
“The potential energy in the higher pressure region is converted into the higher kinetic energy in the accelerated region.”
:
OR

: “The higher kinetic energy in the accelerated region came from the higher potential energy in the slower region with the higher pressure.”
:
OR
:
: The higher potential energy of pressure in the slower region gets converted to higher kinetic energy of speed, and thus gets conserved in the accelerated, lower pressure region. 
: 
It should be stressed that “potential energy gets converted to kinetic energy” and visa-versa where appropriate.
For example, when blowing, the potential energy of pressure is inside our lungs and the kinetic energy is in flow in the atmosphere. The pressure drop and the conversion between potential and kinetic energies occurs at the mouth exit. Therefore, the pressure decreases to atmospheric pressure NOT below it.  This should be VERY explicitly explained since it is the common fallacy repeated over and over.
:
As you see, I prefer pointing out that one form of energy gets “converted to” the other, thus conserving it in another form.
A roller coaster is a good way to see that the potential energy is at the top of a hill and kinetic energy is at the bottom.  It’s not so clear in fluids.

. . . 
: #5 - In Applications Section, the difference between explaining and calculating must be made clear. ”Explaining” is a qualitative description such as Newton’s First Law and Bernoulli’s Principle in words, of how things generally behave.  
Calculating is Bernoulli’s Equation and Newton’s Second Law where actual values are derived..  
In this regard, calculating lift-force in the two ways is the purpose of Eastlake’s paper.   I discussed this with him.  This does not explain WHY things happen, just that the lift-force can be calculated two ways.


: #6 - Misconceptions 
The very first misconception shown should be the common fallacy that speed causes lower pressure, or that any fluid moving faster than some other fluid has the lower pressure.  
:A moving fluid does not have a lower pressure.
:“Fast” air does not have, nor cause a lower pressure.
:If this was true, you could close a jar with just air in it and the pressure would decrease in a moving vehicle.
Bernoulli is not about speed, but Acceleration.
:
People who say “conservation of energy” then show some ‘blowing air’  demo, do not know where the potential and kinetic energies are. Those people never give that a thought, they just blindly parrot: “Conservation of energy.”
Something I like to point out is the fact that speed is relative to your inertial frame of reference, but Acceleration is not. Relative to the ground (moving wing), the peak magnitude of the speed of air Below a wing is a Greater than that Above the wing. Yes, the speed is higher below the wing. Therefore, using speed as a reference for Bernoulli’s Principle won’t yield the same result observing from difference inertial frames and it MUST be the same.  While Accelerations will be observed as the same.  This is physics.
:
Shown in Fig 7 here:  
::rxesywwbdscllwpn.quora.com/ 
:
:
Those are my comments from years of seeing many videos / articles with the misconceptions just getting repeated without truly understanding the physics AND reading comments, where I see how others think about these things
Bernoulli’s Principle and the misconceptions are all carefully covered, along with the misconceptions, here:
:
::/kyuoyckftflurrpq.quora.com/  
: 
:
Regards.   
[[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 00:50, 15 May 2025 (UTC)

:{{u|EngineerSteve}} I have perused your comments but I'm not much wiser just yet. Let's have a look at your section A. You make some routine comments, and then you make a most momentous statement: {{tq|This may be the most wide-spread fallacy in all physics.}} Wow, that is a big statement. However, I don't see what you mean by the word "This". Your momentous statement is about "the most wide-spread fallacy in all physics" but it looks like you clean forgot to indicate what the fallacy is; or what viewpoint is a fallacy. That is a significant oversight because it means we readers have no way of seeing what you are talking about.
:You say that Bernoulli's equation "does not show cause and effect". At this point we readers are getting ready for an important revelation about how Bernoulli's equation fails to show cause and effect ... drum roll! Sadly, in the next paragraph you say "all physics formulas/equations ... never show cause and effect"! So it seems there is nothing unique about Bernoulli's equation and its failure to show cause and effect - all physics equations are like that. That makes we readers wonder why you bothered to mention cause and effect in relation to Bernoulli.
:By "cause and effect" perhaps you are referring to the fact that a force is required if a body is to undergo an acceleration - a change in either speed or direction or both. However, that is Newton's FIRST law of motion; not his second law, and certainly not Bernoulli's equation. So why are you talking about cause and effect in relation to Bernoulli's equation? Can you illustrate your point by giving an example of how one person who understands cause and effect correctly might apply Bernoulli's equation correctly, but another person who doesn't understand cause and effect correctly might apply Bernoulli's equation incorrectly?
:If we are to consider your proposed improvements to the article we need to be clear on what you are proposing, and why. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 12:48, 15 May 2025 (UTC)
::RE: "This may be the most wide-spread fallacy in all physics."   Sorry. My editing error. I let these comments sit and returned several times to proofread for continuity and for that kind of error, but missed that one.   That sentence belongs in #6.
:::
::"This" refers specifically the all-too common fallacy that "fast air has / causes a lower pressure."  This is all over the place in the vast majority of videos and papers about Bernoulli-P. It needs to be clearly addressed by Wikipedia.  There is EVEN a NASA video with an astronaut showing a demo on the Space Station where the "low pressure" jet out of his mouth causes two floating equipment cases to drift together.!. NASA Explains it incorrectly - SO be careful what you accept from NASA. I highly suspect they contract others to write some of their stuff and I have seen things thay have that are fully wrong -- some of which has been removed. 
:::
::. . .
:::
::I talk about 'cause and effect" and equations because people frequently (usually Physics students or PhDs) jump to the  Navier-Stokes  equations as being the end-all and be-all, full proof that "fully explains" Bernoulli's Principle.
:::
::Yes.  Force causes Acceleration.
:::
:::
::Why talk about cause and effect in relation to Bernoulli's equation? Because: In Bernoulli's Equation, it is a Pressure Gradient that causes fluid Acceleration. This is directly analogous to Newton's Force and Acceleration.  It is the same physics. A Pressure Gradient provides a net force on fluid.  
:::
::Understanding science / physics is understanding the cause and effect (C&E). 
:::
::. . .
:::
::Examples:
::: Someone who understands C&E: "The fluid increase in speed entering the narrow section of a Venturi tube is causd by the decreasing Pressure Gradient between the fat and narrow sections."
:::
::: Someone who understands C&E: "When blowing into the large "Bernoulli Bag" from a distance, the larger volume of entrained air around your blown jet, fills the bag much faster than just the full lung volume.
::: . . . 
:::
::: Someone who doesn't understand C&E: The lower pressure in the narrow Venturi section is caused by the faster speed, per Bernoulli's Principle.
:::
::: Someone who doesn't understand C&E: Blowing above a curved paper makes the paper rise because the fast air from your mouth, above the paper, has a lower pressure than the still air below the paper, which, then pushes the paper up."
:::
::: Someone who doesn't understand C&E: The low pressure of the air you blow, draws in more air to fill the large "Bernoulli Bag". [This is the long bag that one breath won't fill] 
:::
::. . .
:::
::So, YES.  Newton's First Law is the Qualitative physics.  The explanation of WHY things happen - Cause & Effect.
:::
::Newton's second law gives the relationship of values: F = MA, etc.. [[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 03:51, 17 May 2025 (UTC)
::I Moved that sentence to the end of the very first paragraph where I first mention the fallacy, so it won't confuse others. This is why doing this in text can be awkward - Discussing things by voice could quickly get this corrected. Sorry. [[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 10:38, 17 May 2025 (UTC)
:::Rather than get distracted by discussions that won't lead directly to improvements in the article, I have replied on my [[User:Dolphin51/Sandbox3]]. There, I pose an engineering question requiring the application of Bernoulli's equation. I give my calculations and my answer, and I invite you to do the same. Feel free to reply on my Sandbox3. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 14:43, 17 May 2025 (UTC)
::::I spelled out my specific article recommendations above: "My comments on the article structure".
:::::
::::I understand your interest may be on the equation, but my focus is on the physics concepts, not the equation.
:::::
::::. .
::::I must be honest that the way you modified the Article second sentence last year and subsequent comments showed that you are struggling with fundamental concepts.   I am also surprised that it wasn't caught at first.   
:::::
::::. . 
::::I again recommend that you read this reference.  It is the result of about ten years of doing STEM demos and talks with all ages:
:::::: https://kyuoyckftflurrpq.quora.com/
:::::
::::. . 
:::::
::::Since Wikipedia is where many people go for good information, I focus in the environment we are now in. This is where the Fallacy that: 'fast air causes lower pressure" (I call it Bad Bernoulli), is all over the web - even in a NASA Video - Yes a NASA video falsely "demonstrates" it.
:::::
::::I am suggesting that the article needs to clearly address that problem.  It has many of the correct physics concepts, but I feel it falls short on this one as I described above.
:::::
:::::
::::[[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 19:17, 18 May 2025 (UTC)
:::::{{u|EngineerSteve}} I have begun reading your article “Understanding Bernoulli’s Principle Correctly” at the quora.com website you provided.
:::::You make the following statement {{tq|Approaching the inward sloping wall of the narrow section of the Venturi (or any surface), the air approaching the surface has inertia which pushes more and increases the pressure there. The air “running into the surface” pushes more than still air, thus increases the pressure.}}
:::::This is clearly in error. The narrow working section of a Venturi has air at low pressure and high speed. As the air approaches that narrow working section its speed increases and its pressure decreases. As the air leaves the narrow working section its speed decreases and its pressure increases. It looks like you are 100% wrong on this point. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 08:47, 20 May 2025 (UTC)
::::::No, it is correct physics in fluids. You gloss over the word "there".  
:::::::
::::::Then, you change the subject to the narrow section.  
:::::::
::::::There are fluid fundamentals it appears that you still struggle with.
:::::::
::::::. .
::::::The pressure is increased in the WIDE section of the pipe. 
::::::I'll go through it, but this is all covered in my Quora Blogs.
:::::::
::::::. . 
::::::A carefully ''designed ''experiment shows this is true physics - Changing Only ONE THING as follows:
::::::Maintaining a '''constant flow rate''' in a constant diameter pipe; decrease the cross section of the pipe in one section and the pressure rises  '''UPSTREAM ''' - rises.  FACT. 
:::::::
::::::. .
::::::Fluid approaching a surface INCREASES the pressure on the surface above ambient pressure. This increased pressure also occurs in the fluid and causes an acceleration of the fluid, depending on the angle between the original flow and surface  This applies if the direction is perpendicular to the surface, or any angle with a component perpendicular toward the surface. 
::::::Have you never felt the wind?   This should be "intuitive" to you.
:::::::
::::::.
::::::This Acceleration is what causes the flow near the pipe wall to change direction and follow the inward-sloping wall.
:::::::
::::::.
::::::This pressure also propagates '''upstream'''.  
::::::It is fundamental to fluids, that pressure acts in all directions and why pressure in fluid is called isotropic.
::::::The primary factor that causes this is the fact that the fluid has mass and, therefore, '''Inertia'''. Inertia resists acceleration - why Newton's First Law is called the Law of Inertia. 
:::::::
::::::. . 
::::::It even is easy to see at the molecular level, '''provided '''you correctly understand the molecular level of Pressure. Remember momentum is '''MV'''.  The flow speed vectorially adds that speed to the velocity of the molecules '''(v+x)''' toward the surface, therefore transferring more momentum to the surface - THUS more pressure.
::::::The very SAME physics applies in the pipe.
:::::::
::::::. .
::::::A surface is a NEW constraint that can not be ignored as so many people do.  
:::::::
::::::...
::::::These are fundamentals you should understand before trying to change the presentation of Wiki articles. 
:::::::
::::::...
::::::The pressure in the narrow section is another subject.  The constraint of the pipe wall changes there and must now be considered correctly.
::::::Regards, [[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 19:01, 21 May 2025 (UTC)
:::::::This discussion has drifted away from improvements to the article on Bernoulli's principle, towards a general discussion on the topic. Article Talk pages are not a forum for general discussions. For this reason, I have replied to {{u|EngineerSteve}} on his [[User talk:EngineerSteve|Talk page]]. See my [https://en.wikipedia.org/w/index.php?title=User_talk:EngineerSteve&diff=prev&oldid=1293752261 diff]. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 13:34, 3 June 2025 (UTC)
::::::::Thanks.  I didn't know a User Talk Page was available and move there - -
::::::::  
::::::::However, I understand the purpose of Article Talk, but because that second sentence was so far off target, I had to see that it got corrected - after being up there for so long uncorrected. 
::::::::I did engage in some discussions, also providing a link to my blog to help the Talk readers understand the material better, but was reminded it was inappropriate.  - So,  subsequently that is why I started this section and tried my best to only address recommendations for the article, thus the title: "My comments on the article structure" of 15 May [[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 13:49, 4 June 2025 (UTC)
:::::::::In the previous edit {{u|EngineerSteve}} has written {{tq|because that second sentence was so far off target, I had to see that it got corrected - after being up there for so long uncorrected.}} (See the [https://en.wikipedia.org/w/index.php?title=Talk:Bernoulli%27s_principle&diff=prev&oldid=1293924886 diff].) The “second sentence” to which Steve refers said: {{tq|Bernoulli's principle states that an increase in the speed of a parcel of fluid occurs simultaneously with a decrease in either the pressure or the height above a datum.}} I have explained previously that this sentence is not incorrect although it is perhaps a little too complex for the first paragraph in the lead. (The lead is intended to be understandable by the widest possible audience.)
::::::::: 
:::::::::The sentence has now been changed to present one example of one application of Bernoulli’s principle. (See the [https://en.wikipedia.org/w/index.php?title=Bernoulli%27s_principle&diff=prev&oldid=1288831677 diff].) The second sentence now says {{tq|For example, for a fluid flowing horizontally Bernoulli's principle states that an increase in the speed  occurs simultaneously with a decrease in pressure.}}
::::::::: 
:::::::::This example is restricted to fluid flowing horizontally but there must be no implication that Bernoulli’s principle only applies to horizontal flows. Bernoulli applies equally to fluid flows regardless of the orientation to the gravitational field. I accept that one example, confined to horizontal flows, is appropriate in the first paragraph in the lead because the lead is intended to be an introduction to the article and understandable by the widest possible audience.
::::::::: 
:::::::::The example in the second sentence could just as correctly be confined to vertical flows because they come within the applicability of Bernoulli. In that case, the second sentence would begin “For example, for a fluid flowing '''vertically '''Bernoulli’s principle states …”
::::::::: 
:::::::::Here is a challenge for everyone reading this Talk page: Complete the following sentence: {{tq|For example, for a fluid flowing vertically Bernoulli's principle states that an increase in the speed  occurs simultaneously with … …}}
::::::::: 
:::::::::Here is a hint, the response to my challenge will consist of two cases: firstly, the case of a fluid flowing vertically in a conduit such as cylindrical pipe.
::::::::: 
:::::::::Secondly, the case of a plume of water rising or falling under the influence of gravity such as when pouring water out of a pitcher, or a stream leaking out of a small hole in a bucket of water. In this case the plume of water is entirely exposed to atmospheric pressure. (Here is another hint: In our article on [[Torricelli's law]], in the lead it says {{tq|It was later shown to be a particular case of Bernoulli's principle.}})
::::::::: 
:::::::::I will offer my own model response to my challenge in a few days. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 03:50, 5 June 2025 (UTC)
::::::::::Hi Dolphin, et al,
::::::::::Though I thought we were moving to my User Talk Page and I already replied to your previous comment over on My Talk Page, I address your vertical experiment like this, here:
::::::::::.
::::::::::First, I know this is discussing the physics, not addressing how the article is organized.
::::::::::.
::::::::::But. . . Since you insist discussing physics, I continue (sorry other folks):
::::::::::.
::::::::::: The very common, simplified statement for Bernoulli's Principle that is currently the second Article sentence, CORRECTLY SAYS: "for a fluid flowing horizontally, Bernoulli's principle states that an increase in the speed occurs simultaneously with a decrease in pressure." {I added the comma}
:::::::::::: Switching to a vertical flow, is a different situation and has the added constraint of the vertical head pressure change due to changing elevation in a gravity field.  This ALONE, WITHOUT ANY speed change, will show a pressure decrease with increasing elevation.  It is common knowledge that pressure decreases as you go UP in air or under water.
::::::::::::: Continuing: including the speed increase will still be accompanied by a pressure decrease (to supply the Acceleration-causing Pressure Gradient).
:::::::::::: So, a first look at this NEW set of constraints, suggests that there is an additional pressure decrease (compared to EITHER individual constraint alone) under those new conditions (a speed increase and upward moving flow)...
::::::::::.
::::::::::So, completing your sentence [I don't know how to make the color change]: 
::::::::::: "For example, for a fluid flowing upward vertically, Bernoulli's principle is that an increase in the speed occurs simultaneously with a decrease in pressure that is greater than either the speed increase, or elevation increase alone.".
:::::::::::: Now, I must add that IF that vertical flow is directed DOWNWARD, the pressure change will be the net difference (algebraic sum) that comes with the speed increase and elevation decrease. The pressure change depends on the amount of elevation decrease and speed increase. {pressure increase and decrease, respectively)
::::::::::.
::::::::::So, we see that under this new, vertical flow setup, we see the gravity / height term assuming its role in Bernoulli's EQUATION. 
::::::::::.
::::::::::.
::::::::::Therefore, making it a general statement for EITHER up or down flow, I believe it is correct to say: 
::::::::::: "For example, for a fluid flowing vertically,  Bernoulli's Equation shows that an increase in the speed occurs simultaneously with a change in pressure that the net difference (algebraic sum) that comes with the speed increase and elevation change. (The amount and direction of pressure change depends on the amount and direction of elevation change and speed increase.)
::::::::::.
::::::::::I am quite confident that is the correct Physics.
::::::::::: **** AND to be PERFECTLY CLEAR, I am in NO way suggesting that this be used in the Article.  NOPE.
::::::::::.
:::::::::::Sorry to be explaining Physics, folks. . . 
::::::::::.
::::::::::::::: SO. . . . Regarding Article Content.  
::::::::::I RECOMMEND that Second sentence should remain for the horizontal ONLY flow because that is what is VERY commonly stated in zillions of places, all over the world as "Bernoulli's Principle".  People come here for validation of *THAT* common usage.
::::::::::::I believe the situation of elevation change is covered by the full equation for those more deeply interested in the more advances conditions.
::::::::::Regards [[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 06:23, 5 June 2025 (UTC)
:::::::::::::  Thinking just a bit more, I can summarize that this can be flow in a pipe that is decreasing in diameter in the direction of flow.
:::::::::::::: The  first case, the pipe is directed upward in the direction of flow.
:::::::::::::: The second case,  the pipe is directed downward in the direction of flow.
:::::::::::[[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 11:48, 5 June 2025 (UTC)
::::::::::::We are presently discussing the potential for improvements to the article; not general discussion about the topic. On 2 May {{u|EngineerSteve}} wrote: {{tq|the most important sentence is wrong and makes no sense. It appears no one caught it since it violates all authoritative sources. The sentence is: "Bernoulli's principle states that an increase in the speed of a parcel of fluid occurs simultaneously with a decrease in either the pressure or the height above a datum." The velocity DOES NOT change with height above a datum, unless there is something like a pipe diameter change.}} See the [https://en.wikipedia.org/w/index.php?title=Talk:Bernoulli%27s_principle&diff=prev&oldid=1288386139 diff].
:::::::::::: 
::::::::::::On 4 June EngineerSteve wrote {{tq|but because that second sentence was so far off target, I had to see that it got corrected - after being up there for so long uncorrected.}} See the [https://en.wikipedia.org/w/index.php?title=Talk:Bernoulli%27s_principle&diff=prev&oldid=1293924886 diff].
:::::::::::: 
::::::::::::It appears we are now in agreement that the second sentence in its original form is not incorrect, does not violate any authoritative source, and is not “so far off target”. It was presenting too much information for the first paragraph in the lead, and would not have been understandable by the widest possible audience, but it was not incorrect. The situation has been improved by changing the sentence to one which gives an example of Bernoulli’s principle confined to a horizontal flow field. The new sentence is an example of one type of flow field but it is not a comprehensive statement or even a summary of Bernoulli’s principle.
:::::::::::: 
::::::::::::I think we are also in agreement that the original second sentence could be used later in the article where greater detail is to be found. In fact the sentiment that {{tq|an increase in the speed of a parcel of fluid occurs simultaneously with a decrease in … … the height above a datum}} is already implied in the section [[Bernoulli’s principle#Incompressible flow equation|Incompressible flow equation]] where it states the equation as:
:::::::::::: 
::::::::::::<math>\frac{v^2}{2} + gz + \frac{p}{\rho} = \text{constant}</math>
:::::::::::: 
::::::::::::This equation clearly shows that in any region of the flow field where the pressure is uniform, the speed squared v<sup>2</sup> and the height above the datum z can vary but only in such a way that any increase (or decrease) in v<sup>2</sup> is exactly matched by a decrease (or increase) in z. An example of this is a stream of water flowing over a waterfall – at every point in the stream the pressure is equal to atmospheric pressure; as each parcel of water gets closer to the pond at the bottom of the waterfall its height above the pond decreases and its speed increases precisely in accordance with the Bernoulli equation. Furthermore, the Bernoulli equation shows that a stream of water falling from a height z above the datum reaches exactly the same speed v as a solid object falling from the same height z. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 14:10, 5 June 2025 (UTC)
.
.
::No.  YOU did not discuss the article's structure.
:
:'''YOU''' entered: "Here is a challenge for everyone reading this Talk page: Complete the following sentence: For example, for a fluid flowing vertically Bernoulli's principle states that an increase in the speed occurs simultaneously with … …"
::THAT is what I responded to.
.
I originally referred to the change that YOU made last year to the second sentence, as being way off target - YOUR change.
That sentence, BEFORE you changed it was CORRECT.  YOUR change was way off what Bernoulli's Principle commonly state.
.
YOUR VERSION was NOT providing 'too much information'.  As you subsequently admitted here, it was referencing a completely different situation of Pressure change with elevation. YOU provided the image to show your thinking.
.
As you suggested, I went to my User talk Page and responded.

Please stop jumping around.
[[User:EngineerSteve|&#32;-- Steve -- ]] ([[User talk:EngineerSteve|talk]]) 22:32, 5 June 2025 (UTC)

:On 5th June (time 03:50) I invited interested Users to suggest an end to the sentence "For example, for a fluid flowing vertically Bernoulli's principle states that an increase in the speed occurs simultaneously with … … "
:I posed this question to see what other Users were thinking about the way the pressure in a fluid might change when flowing vertically. I have been thinking about it over recent days. My model answer is ""For example, for a fluid flowing vertically Bernoulli's principle states that an increase in the speed occurs simultaneously with a decrease in either the pressure or the elevation, or a combination of the two."
:#In a fluid flowing vertically, an increase in speed with a decrease in pressure is what we observe when the diameter of a vertical pipe decreases in the direction of flow.
:#In a fluid flowing vertically, an increase in speed with a decrease in elevation is what we observe in the illustration of [[Torricelli's law]]. In the lead of our article on Torricelli's law, it says {{tq|It was later shown to be a particular case of Bernoulli's principle.}}
:In the first case: "increase in speed with a decrease in pressure" where the diameter of a pipe decreases in the direction of flow, the situation is exactly the same as with a fluid flowing horizontally. (In this case it can be argued effectively that the change in speed is unrelated to Bernoulli's principle, and instead is completely determined by continuity of mass. Mass continuity is applicable in all flow situations including the presence of [[shock wave|shocks]] whereas Bernoulli's principle is only applicable to incompressible fluids that flow without friction, no heat transfer etc.)
:I'm not advocating that a statement confined to vertical flow should be inserted into the lead. [[User:Dolphin51|<i style="color: green;">''Dolphin''</i>]] ''([[User talk:Dolphin51|<span style="color: blue;">t</span>]])'' 13:03, 15 June 2025 (UTC)