Talk:Bernoulli's principle/Archive 1

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Wikipedia:Be bold, if you know it's wrong, correct it! :) Dysprosia 02:38, 16 Oct 2003 (UTC)

(THIS IS NOT TRUE) is not a good way of correcting. :) -- Jake 02:45, 16 Oct 2003 (UTC)

In other words anon, could you provide the correct information? Thanks Dysprosia 02:46, 16 Oct 2003 (UTC)

Wow I can tell a bunch of ME's wrote this stuff bc they use the simplified versions, call them selves college grads too

Everybody relax. Both explanations are right. They are equivalent. I'll fix this to make that a little more clear.

What about Bernoulli's Theorem in discrete mathematics? I think that either Bernoulli's Theorem should not be redirected to here or that there should be a disambiguation page. (Sorry, don't have time to make an article.)

Removed "There are other ways of understanding aerodynamic lift that many novices find more intuitive (see Coanda Effect)." The Coanda effect is not a valid explanation of airfoil lift - it is completely explained by the existence of a bound vortex, and can be fully explained in the absence of viscosity (i.e., potential flow); Bernoulli's equation is a convenient way of relating the pressure and velocity at one point to another point as an inviscid fluid moves from one place to another (i.e from upstream to above/below a wing). Fluid-dynamic lift is independent of the completely viscous corner-turning Coanda effect, which is actually a type of vectored thrust. --Knotnic 00:37, 8 August 2005 (UTC)

see [1] for a well-written discussion by a physicist and flight-instructor

"Bernoulli's principle...is named for the Dutch/Swiss mathematician/scientist Daniel Bernoulli, though it was previously understood by Leonhard Euler and others." Could someone please clarify what was understood by others before Bernoulli, and what (if anything) Bernoulli added? --Judah

Why Bernoulli's Principle should not be merged with Lift Force

There are several different lift forces, notably the magnus force, the force from the coanda effect, and (the most common explanation for aerodynamic lift) Bernoulli's principle. Furthemore, there are many applications of Bernoulli's Principle that do not have to do with aerodynamic lift -- notably the venturi effect and choked flow. (I also mentioned this in the discussion linked-to by ther "merge" block). If you are going to merge Bernoulli's Principle with Lift Force please adress this concern first. zowie 23:21, 22 October 2005 (UTC)

Since nobody seems to have spoken out for merging Bernoulli Principle and Lift Force in quite a while, I took the liberty of removing the merge tag. zowie 23:28, 22 October 2005 (UTC)

---

Some corrections... 1) the coanda effect has nothing to do with viscosity. A gas will follow a curved surface, because if it doesnt, then it leaves the surface... and as it flows past the surface, it drags out some of the stationary gas between the moving gas stream and the fixed surface. This continues until there is no stationary gas between the two. In reality, we dont have this detached-then-reatached behaviour. Any tendency for the gas flow to leave the surface immediately results in the gas in the stationary pocket being dragged out. Coanda effect only explains why the gas (or liquid) WILL follow a convex surface. That gas diversion and the gas diversion under a wing explains ALL of the effect of wing lift. No other explanation is necessary. Several other mathematical relationships exist, but they do not explain how a wing works. The Bernoulli equation will give a precise relationship between the gas velocity and pressure etc. and this is often assumed to show that it this explanation for wing lift is correct. It is not correct because the assumed cause and effect relationship is invalid. It is the pressure differences that cause the velocity profile, not visa vers.

2) the Bernoulli equation is an energy balance equation. It states that the energy at all points in a steady state flow will have the same energy. It does not say any one item causes the other.

3) No mass EVER accelerates without an applied net force. In gasses, this means that the acceleration (Change in velocity) of any particle of gas is ALWAYS the result of the pressure gradient along the flow path. Common sense (as well as complex physics proof)shows that where the velocity distribution is entirely the result of the pressure gradient, the pressure gradient cannot be the result of the velocity gradient.

The confusion relatated to venturi effect and Bernoulli that has reinforced this plethora of incorrect derived associated theory, is because it is difficult to understand how the lowest pressure in a venturi can be lower than any externally applied pressure. The function is easier to understand if you consider air as a bunch of lumps each having mass, and each being pushed uppon by other surrounding air acting like springs in all directions. Now simplify the model further... a row of masses with springs between them. All springs in compression. If we push one end toward the middle, we would expect the whole assembly to start moving. If we apply a restriction (some drag force) to one of the mass's in the middle, and continue pushing the mass at one end, then we get a build up in the spring compression on one side (increase in prssure). Now allow the restricted mass to escape, grabbing the next one as it gets to your restriction. The released one, jumps away.. and if we kept everything else still, that released one would then jump back and vibrate back and forth. BUT if we were to allow the next mass to go just as the first one was as far away from the second as possible, then there is less spring force difference to make the second one spring back. If we continue this rapidly and continuously we will have each succesive mass moving faster, and having less spring force on both sides of it, than all of the springs started with. This model would gradually reach a state of dynamic equilibreum. If we then added a controlled movement rate to the exit side of this model, we would similarly find that the fast moving middle masses with lightly compressed springs between them would slow and join the exit flow, and the springs between them would compress back to the initial level because it took a certain level of force, and absorbed energy to slow each of the moving masses.

If you want to prove or disprove any of this model of the venturi. Go back to first principles. Consider one atom, or one cubic millimetre of air. Then as WHY will it change speed. Why will it change pressure. If you really think about the cause and effect relationships, your answers will not include the word Bernoulli. F=ma adequately, simply, and completely describes all such gas flows without exception. It also describes all sub sonic wing lift without circulation theory, without using the word Coanda, and without the need for maths. Dave Fowler B.E.(Mech) UNSW M APESMA

Proposed merge of Bernoulli's principle and Bernoulli's equation

There seems to be redundancy here and it would be better to have a single page.--NHSavage 22:13, 28 April 2006 (UTC)

I'd support that. moink 22:23, 28 April 2006 (UTC)

I support it too - moreover, I support the original idea: to merge the Bernoulli effect with the coverage of the equation or principle. Eric Deeson UK 29 Apr

A draft for the merge is at: User:NHSavage/sandbox. Please feel free to comment and edit. I will leave it up there for a whole to see what comments emerge. I need to sort the interwikis.--NHSavage 08:48, 30 April 2006 (UTC)

As it all seems quite and comments here are positive I have finished the merge.--NHSavage 21:37, 2 May 2006 (UTC)

Can someone please explain how the Bernoilli equation causes lift on an airfoil.

I ask this question because the Bernoulli Equation relates to forces, velocities, pressures along streamlines.

1. How does a streamline cause lift, when all but one streamline actually touches the airfoil?

2. How too can the Bernoulli Equation apply to the flow along the airfoil itself when the velocity at the base of the boundary layer is basically zero and the fluid has basically stopped? Is the Bernoulli equation then supposedly invalid? Or is some convenient workaround available?

3. If forces are supposed to be transmitted at right angles to the streamlines in the boundary layer, to generate lift, then why isnt the same principle applied to the whole flow field?

It seems presumptious that the Bernouilli principle is merged with Lift (Force), when these basic questions remain unresolved. —Preceding unsigned comment added by 58.110.88.205 (talk) 18:39, 5 November 2007 (UTC)

New Source

This theorem is explained in the following (excellent) book. Hydrodynamics Horace Lamb, 1932 Chapter 2, Art (21) Pg. 20

I'm not sure how to add it as a source in wikipia, if someone could that would be great. thanks, -Jonathan

Disagreement with the rating of this article

Hello,

The article has been listed as A class, however I would consider myself to have a reasonably good grasp of Bernoulli's principle and how it applies to general fluid flow, however I must admit the layout and content of the article seemed unclear to me. I was going to mark this with a cleanup tag, then i spotted the A class rating! I was somewhat surprised by this, especially when a reasonably non intuitive effect such as that of a Venturi nozzle was not given a diagram in its section (for example). Also uses/examples appear before an explanation of what it Bernoulli's principle is.

It is also not made clear that Bernoulli's is a way of accounting for the energy components of a fluid, perhaps something (very roughly) along the lines of

Bernoulli's principle is an important principle in fluid mechanics, it arises from the consideration of the different forms that energy can take in a fluid. There are several key forms for which a fluid can take, kinetic, pressure and gravitational potential. Bernoulli's principle implies that all these forms of energy (in an ideal fluid) must be conserved. This means that if there is an increase in velocity (kinetic energy, say over the top surface of a wing when compared to the lower surface) the energy must have been obtained from somewhere, and if no work is performed on the fluid, the fluid itself must have converted another form of energy into that increase in velocity, in this case pressure. Furthermore it explains why fluids can flow downhill (but not why, that requires the use of entropy) and so on.. HI72.10.127.110 17:50, 21 March 2007 (UTC)

Thanks User A1 12:21, 12 December 2006 (UTC)

Radiative shocks?

Could this bit please be explained further?

An exception to this rule is radiative shocks

Thanks --Chriswaterguy talk 13:38, 5 March 2007 (UTC)

Bernoulli's Equation is crap?

I am a physics student and my egineering/physics instructor was talking about how bernoulli's equation is pretty much crap and most of the stuff you learn about it doesn't apply to most cases. He was explaining how just about the only case that it applies to would be something like mercury flowing through a glass pipe because in that situation mercury has very low friction with itself and it doesn't compress easily and the adhesive forces and friction forces with the glass are extremely low. Otherwise you have adhesive forces and friction which completely change how the liquid flows and completely destroy how bernoulli's equation works.

He also explained how it can't be used for airfoil lift at all because the air compresses and is of course viscous and it has adhesive forces with the wing. Rather instead what causes the lift is a high pressure center above the wing toward the front and a lower pressure center toward the back and lower and that pressure difference causes a downward vector force which thus has an equal and oppsite compression on the wing moving the wing upwards. This seemed to explain lift much better than the age old, "The air splits and goes over the wing and because the distance across the top is longer the air has to speed up and this causes a lower pressure at the top and it sucks the wing up." For what reason if any does the air have to speed up? There is no reason what so ever why the same air that splits at the beginning of the wing has to meet up at the end of the wing.

Someone correct me if I am wrong on all this but this seems seriously messed up here. Ergzay 18:17, 6 April 2007 (UTC)

As far as i understand, the air over the top speeds up argument has been clearly proven incorrect. This is due to the fact that there is no need for a given set of air to "meet up" at the back of the wing, thus there is no need to speed up. So you are correct. There is a more complex analysis, of which I have not got to understanding sufficiently. However what I can say is that when solving the Navier stokes equation for a 2D wing, then calculating the integral of pressure over the wing, you do end up with an upwards force on the wing. The exact reason for this to me is somewhat unclear, but is definitely an effect predicted by Navier-Stokes in a steady state turbulent flow scenario (and is clearly a function of angle of attack).

Furthermore Bernoulli's equation is not "crap", but it definitely has assumptions built into it. You can actually take into account viscous losses as a "friction work" factor, which can then be calculated theoretically in the case of laminar flow, or you can work it out using correlations based around Reynold's number. Just remember that many calculations we do are simply a useful model of what is really going on, and this is also true here. Bernoulli's equation is a great way to figure out how much shaft work you need to drive low velocity newtonian fluids up a hill for example, and also predicts the siphoning effect User A1 14:28, 7 April 2007 (UTC)

Inertia?

Hello,

The article states "... an increase in velocity occurs simultaneously with decrease in pressure or a change in inertia"

Surely bernoulli's equation does not relate to the inertia of an object, should this not be gravitational potential enegy (deltaZ)? Eeach term in the equation relates to a particular manifestation of energy for the system, static pressure, kinetic and gravitational potential. Inertia is not a form of energy, and is independent of g. Quoting from inertia itself "t should be emphasised that 'inertia' is a scientific principle, and thus not quantifiable. " So how can it be present in an equation? If there are no complaints to the contrary i will change it in ~12 hrs. Thanks. User A1 01:59, 16 April 2007 (UTC)

Working on it?

"with no work being performed on the fluid" Like, maintenance work? Elaborate. If the definition of work is different in this context then we need a link explaining it, I think.207.81.30.83 17:59, 4 June 2007 (UTC)

Why not? I've made it link to Mechanical work. Or more like, why not link it yourself when you thought so? This is a wiki: be bold, go on and edit it! --朝彦 (Asahiko) 12:44, 5 June 2007 (UTC)

Mildly off-topic quips and musings

The first paragraph, which states that "Bernoulli's Principle states that..." makes me think of alpine skiing. The ideal fluid is Utah powder on a bright crisp morning after a storm, I'm not working, and I can feel the work-stress pressure decrease as my gravitational potential decreases in bounds as I kangaroo from one swooping turn to the next. Fun.

Drinking my soda with a straw.

Hey, so I went to panda express today and I got a soda with a straw. Due to a bad habit, I was chewing on the straw and punctured a hole in it. I can't drink my soda now :(. Is that bernoulli's principle? If not, than what would my soda example be?

This can be explained by bernoulli's priniciple. You have put a hole between the liquid surface and the straw, as such it is now impossible to reduce the pressure in the straw enough (by sucking in air) to cause the liquid to flow up the tube due to a pressure difference, (the deltaP component) (the (z2-z1)g component of the equation). You will find that you are just sucking on air, as less work is required to move the air than the liquid, so the air moves (bad) rather than the liquid (good). If you could examine the straw in a miniscule detail, you would actually see the liquid move a tiny amount when you attempt to use the straw. User A1 02:13, 17 August 2007 (UTC)

Hello. I reproduced the text recently added by Tordivel, needs some polishing and referencing before introducing into the article. Perhaps removal of words such as "grave" some good wikilinking etc. Will get there myself eventually.:

Common misunderstandings about bernoullis effect

It is often stated that fast moving fluid has an inherently lower pressure than the surrounding fluid. This is a grave misunderstanding. The experiment where one blows between two suspended pieces of paper is a clear example of this. In this experiment one will see that the two pices of paper will move towards the airflow. This is only due to the fact that the fast moving air, due to friction, will remove the surrounding air from its original position. When the air is removed, it needs to be replaced. This will attract the air further out to the sides, thus bringing the pieces of paper towards the airflow. The air in the airstream does indeed have a lower pressure, but only related to its original pressure, in the lungs of the blower. Another grave misappliance of the Bernoulli Effect originates from messing with dimensions. The common form of the Bernoulli Equation is strictly one-dimensional. The pressure-speed relationship is usually expressed along the X-axis. The Equal-Transit-Time theory, to explain lift on an aerofoil, is an example of this misappliance. The lenght of the cord line over a wing is only longer than the equivalent under the wing due to its two-dimensional form. Along the X-axis the two cordlines are equally long. Tordivel 02:36, 13 September 2007 (CET)

Thanks User A1 08:11, 13 September 2007 (UTC)

Hello. I see that there is already a reference, in the article to the invalidity of using the example with the pieces of paper to explain lift. http://www.physicsmyths.org.uk/bernoulli.htm However, it doesen’t say anything about the internal pressure in the airflow, and how Bernoulli’s principle relates to this. It is very easy to disprove the statement that fast moving fluid always has a lower pressure than its surroundings.

I will use an example to illustrate my point.

Consider a non-compressible frictionless fluid that emits from a nozzle into a big space. Such a fluid doesn’t really exist, but for the purpose of the experiment it is practiable to use it. Now, when the flow has been established, it will theoretically continue forever because it is not slowed down by friction. I will claim that, in this system, it is impossible that the sorruonding fluid has a higher internal pressure that the internal pressure in the flow. Because it is a fundamental fact that a pressure gradiant over an area (as the boundary area between the flow and the sorrunding fluid) will cause movement; Newtons 2nd Law. If there was a pressure difference the flow would laterally contract. Because the fluid is incompressible, it would still occupy the same volume, thus it would have to become elongated. This means that the flow would need to speed up, and thus its kinetic energy would increase. And as the speed of the flow increases, the internal pressure should, supposedly, decrease accordingly. Then the flow would contract even more making the flow move even faster, and so on. You see, the whole “fast fluid = low pressure” thing is in complete violation of the princip of Conservation of Energy.

The whole mystery with the moving papers makes so much more sence when one adds a bit of friction. When there is friction between the flow and the surrounding fluid the flow will slow down and the fluid, surrounding it, will start moving, thus being removed from its original position. Then it must be replaced by fluid further out to the sides of the flow.

This is, in fact, the same fenonomen that one observes when water in a stream runs through a narrow gap between two rocks. One will see that eddies will form on both sides of the fast moving water. If one sticks a piece of paper into the water, to the side of the flow, right behind one of the rocks, one will see that the swirling water will move it towards the flow.

Now, about the “messing up the dimensions” part. I must admit that my example about the upper and lower cord length along the x-axis was not particularly good. The point I wanted to make was that one needs to consider the direction as well as the speed of a flow when one uses The Bernoulli Principle. When the air rushes down the trailing end of the wing it has got a certain downward speed. Whenever fluid is accelerated there will be a corresponding difference in pressure. It is like when one blows directly at a surface. The airflow hits the surface and fans out. If one disregard the friction loss the air will have the same speed after the impact, but it has been diverted 90 degrees. If one just consider the speed along the axis it first travelled, it has gone from whatever speed it had to zero. This is reflected in the high-pressure area at the impact point that again pushes on the surface. It is easy to use Bernoullis equation here, but one needs to separate between the speed of the flow along the different axes. Of course, one will easily arrive at all kind of wrong conclusion if one disregards that the flow around an airfoil is indeed more than one-dimensional. Tordivel 00:15, 15 September 2007 (CET)

Help! Do we even know how the Bernoulli principle works?

It is totally amazing that this article can drag on and on with all that differential math and completely miss the point of explaining how it works! When laymen and kids look at this article all the see is a bunch of useless math. If they needed math, they sure wouldn't be looking here, they would go to a trustworthy textbook. Is this another case where we use math to cover up our ignorance. We are pathetic! (myself included, because I don't have a clue how it works.)

I can recite the dogma: "When air moves through a venturi, or over a wing, the pressure drops to conserve energy." But why? At a molecular level, what happens to the molecules that enables all this energy conservation. For example, if I have a hole drilled in the throat of a venturi, the pressure in that hole will be lower if air moves through the venturi. If the molecules passing through the throat are moving parallel to the hole, why do they scavenge more molecules out of the hole than they deposit in it? I think we need to replace this article with something helpful, if anyone is up to it. Can someone rescue us with an articulate explanation and intelligent diagram (sin math)? John 04:33, 23 September 2007 (UTC)

Well, from my understanding, Bernoulli's prinicle works because of the Law of Continuity. A simple example of this is when a stream of water is moving and it goes through constriction that cuts the room for the water to move in half, the speed of the water must go twice as fast so as to not cause a slowdown of the water.

I was reading a book about this theory, and how Bernoulli came up with this theory. In the following days I will add an appropriate column. Simply put, he used two equations of Viz Viva (Energy) and amplied them to a fluid.63.136.116.155 (talk) 23:41, 12 February 2008 (UTC)

Does this help Image:Venturi-nomaths.svg?

The explanation is like this:

Assume that the system is at steady state (ie nothing is changing as time goes on). The application of Bernoulli's principle to this example is an argument based around the conservation of energy. Note that the mass of the fluid flowing through the venturi meter is the same at both points A and B, and there is nothing doing any Mechanical work on the fluid nor is the fluid transferring energy to its surroundgings (ignore friction losses), therefore no energy is being transferred to or from the fluid. So what Bernoulli tells us is that there are three ways that the fluid can store energy, through gravitational potential (a height difference), through pressure or through velocity. As the fluid cannot transfer energy it can only switch between the different storage forms.

In this example we can see that there is no significant changee in height, as the meter is horizontal, so therefore we can eliminate the height difference as a source of energy. The only two forms of energy that remain are kinetic and pressure. If we note that the mass flowing through A and B must be the same in order to maintain steady state, and knowing that the mass flow through a given cross section is the velocity times the cross sectional area, we see that the velocity at B must be higher than A.

So where does the energy come from to speed up the flow at B? Well it comes from the only source of energy available to the fluid, its pressure. The pressure energy (static pressure) at A is converted to kinetic energy as the flow becomes more constricted. The conversion mechanism at the molecular level is probably quite complicated itself, so I won't address that, but i would suggest it relates to the mean free path of the fluid. If you use continuum models to explain it (as i have done here), then it is relatively straightforward.

I hope that clears up the venturi meter case. User A1 06:40, 23 September 2007 (UTC)

Thank you, but this explanation boils to saying "push the 'I believe' button, it just is". You are probably correct, at least thats the dogma, but is not at all clear that you have exhaustively considered all possibilities for where the energy could have come from, that isn't even possible, so that is not even a closed-form explanation, just astute speculation. This explanation says there is a shortage of energy that must come from somewhere, but individual molecules don't know squat about the average group energy, they are slaves to forces on them. Energy is irrelevant to explaining why this works. Conservation of energy per se doesn't cause anything, this principle is only (probably) consistent with energy conservation. Why do the net average forces on the molecules coax them out of the hole in the venturi throat? From another viewpoint, as a venturi moves through still air, it does something to an air molecule to discourage it from colliding with the throat of the venture. Surely there is a simple-minded summary. The mechanism at the molecular level may be complicated, but can we sum it up in a few words? Hasn't anyone ever wondered why? John 14:59, 23 September 2007 (UTC)

Hi John, we can say that as we know there is a reduced pressure, tapping a hole into the venturi throat would cause a suction (ignoring diffusive effects for the flow).

One point to make is in regards to the following comment:

is not at all clear that you have exhaustively considered all possibilities for where the energy could have come from,

The explanation has constructed a situation whereby there are no other sources of energy and thus doesn't need to consider them. It is merely a model for a physical process, one which is used to organise thought to prevent it being contradictory. Care must be taken to not confuse the model with the real process, and to realise that acceptances of shortcomings in the model do not render the model entirely useless. We could add energy into the equations perhaps via reactions or some form of local inhomogeneities causing exotheric/endothermic behaviour, however its just too complicated/specific to have as a general construct. To some extent it says not "i believe" but "in order to make have consistent thought, ther model must be consistent" and therefore (hopefully) "it is close enough to observation of real systems" and subsequently useful. It should be recalled that the idea of a molecule/ball/field is only an approximation as well. There are no balls of Oxygen or Nitrogen flying around at all, but it hurts to much to think about it, so generally dogma says don't unless its really necessary. I must admit I can't see good reasons for the balls to behave as they do without resorting back to continuum arguments User A1 17:48, 23 September 2007 (UTC)

Did you consider the string theory of mass gain from monopoles transferring energy from a black hole at the center of the earth :-). OK then, I guess you are right. Anyway, I'm good with not talking about molecules, I don't think a layman's explanation should really do that anyway. Can we talk about a homogeneous fluid? Aside from the fact that we firmly hope it never violates conservation of energy, how does it really work? John 21:31, 23 September 2007 (UTC)

Errors and Inconsistencies in this Article

There are some glaring errors and inconsistencies in this article:

First of all, it hurts to see Newton's second law written as m*dv/dt=-F in the derivation section. Surely, the acceleration can not be directed oppositely to a force.

Secondly, if the condition of 'inviscid' implies 'no internal friction', then this strictly speaking means that there are no collisions of molecules with each other. This however means that different volumes of the fluid can not interact with each other at all (and therefore not exert forces on each other either). To illustrate this point and its consequence for the Bernoulli principle, consider a large tank containing gas with a pipe attached to it which leads into a vacuum space. Assume first this pipe is closed at the end; then the flow velocity in the pipe is zero because the molecules heading outwards will be reflected at the end and reverse their velocity (assume for simplicity that the molecules do not collide with each other but only with the walls of the pipe and the tank). If one now opens the pipe, the only thing that changes is that the molecules heading outwards will not be reflected anymore at the end but simply carry on heading into the vacuum space (with the corresponding loss of molecules being replaced from the large tank). So we now have a net flow velocity without that either the density nor the speed of the molecules has changed in any way. This means that the pressure exerted on the inside wall of the pipe is unchanged despite the fact that we now have a net flow velocity within it.

So it seems to be very much inconsistent and incorrect to associate Bernoulli's principle with an inviscid gas or fluid (of course, this does not just apply to this article, but also to the sources on which it is based).

See also my pages http://www.physicsmyths.org.uk/bernoulli.htm and http://www.physicsmyths.org.uk/drag.htm, where the asssumption of a strictly inviscid gas is applied ot the aerodynamic lift and drag.

Thomas —Preceding unsigned comment added by 81.103.111.58 (talk) 09:15, 4 October 2007 (UTC)

Bernoulli Principle and Lift Force (Open Questions)

The Bernoulli Equation relates to forces, velocities and pressures along streamlines.

Question 1.

How do streamlines directly cause lift, when only one streamline, the stagnation streamline, actually touches the airfoil?

How does Newtons Laws of Motion apply in this case?

Question 2.

How can the Bernoulli Equation apply to the streamlines along the airfoil when the velocity at the base of the boundary layer is basically zero?.

So, where does the pressure come from to lift the airfoil, if the Bernoulli principle/equation is invalid at the boundary layer?

Question 3.

If forces are supposed to be transmitted at right angles to the streamlines in the boundary layer, as a workaround to the Bernoulli equation, then why isn't the same principle of transverse presure gradients generating lift, then applied to the whole flow field instead?

NOTE: A successful theory of lift should be compatible with these questions.

Cold-logic 12:00, 9 November 2007 (UTC)

A common misconception about wings

The history of Bernoulli's principle shows there have been numerous attempts to expose the fallacy of the equal transit-time idea by denouncing it in relation to Bernoulli's principle. Another attempt appeared in Bernoulli's principle on 20 December 2007. The perpetrators display their lack of understanding of Bernoulli's principle when they write that it is a fallacy to use this principle in explaining the lift on an airfoil!

It is true that there is a terrible fallacy in using the idea of equal transit-time in attempting to explain the lift on an airfoil. See List of works with the equal transit-time fallacy. This equal transit-time idea and Bernoulli's principle are two very different ideas! The equal transit-time idea is a fallacy when applied to the lift on an airfoil, but Bernoulli's principle is NOT a fallacy when applied in this way!

The lift on an airfoil can be explained adequately using a number of different scientific principles:

• Newton's Second Law of Motion
• Law of conservation of momentum
• Newton's Third Law of Motion
• Prandtl's thin airfoil theory
• Theory of the Horseshoe vortex
• The Kutta condition and Kutta-Joukowski Theorem

The article Bernoulli's principle presently proclaims earnestly that "The actual mechanism generating lift on an airfoil is Newton's Third Law of Motion"! It is true that lift can be explained using Newton's third law, but it is false to suggest that this is the ONLY principle that can correctly explain lift. Every one of the above principles can be used to legitimately explain lift, and each principle has its advantages and disadvantages. Some are more powerful and more complex than others. There is no single correct explanation.

The Kutta-Joukowski Theorem and the Kutta condition can be used to explain that when an airfoil generates lift the fluid travels past one side of the airfoil faster than it passes the other side. A century of aviation has shown that the side of the airfoil that has the high speed fluid flow also experiences a lower fluid pressure than the other side. These two things are inextricably linked. There is never reduced fluid pressure in the absence of higher speed fluid flow, and higher speed fluid flow never occurs in the absence of reduced fluid pressure. Can we explain the association of fluid speed and fluid pressure, as observed on an airfoil generating lift? YES! For over 200 years we have had the benefit of Bernoulli's principle to give us confidence in predicting that air flowing faster over one side of an airfoil than the other will generate lift. There is no legitimacy in suggesting any sort of misconception in the application of Bernoulli's principle to the generation of lift on an airfoil. When the Kutta condition and Kutta-Joukowski theorem are used to explain lift, it is essential to include Bernoulli's principle to complete the picture.

Let's get rid of these suggestions that Bernoulli's principle has no place in explaining why an airfoil generates lift. Let's confine discussion about the fallacy to the article Equal transit-time. Dolphin51 (talk) 04:46, 31 December 2007 (UTC)

While the full theory of lift includes a heck-of-a-lot more fine print than just Newton's Third, let's remind ourselves to the fact that this article is about Bernoulli's Principle. That means that this page should not explain the full theory of lift here. That will be at the appropriate pages. This page should only explain that Bernoulli's Principle is not - as is commonly believed - the main mechanism behind lift. The Equal Transit Time fallacy does not work without BP because without BP there is nothing to explain why the faster movign air has lower pressure. BP is always, in one form or another, mentioned when the Equal Transit Tiem fallacy is used to explain lift.

Hence there is most certainly legitimacy to include a section that mentions that BP is not the main mechanism about lift... because the Equal Transit Time fallacy never comes without it. In fact, if you check the history and see my first edit here you will see that I removed a section that said just that! This hints how common the minconception is and therefoer there I see a very good reason for keeping the current section.

And while Newton's Third is not the full explanation about lift, in all its nitty gritty and not-yet-fully-understood glory that lets us take to the skies, it is still perfectly acceptable to say that 1) BP is not the main mechanism behind lift and 2) the main mechanism that generates lift is Newton's Third. Regarding the fine print we should most definately avoid to bog down this page with six-seven different theories on lift. But we cannot just say "BP does not generatte (the main part) of lift" and not include at least a quick mention of what actually generates lift.

If you wish to clarify that the onion has many more layers than this, feel free to do so in a comment along the lines of "For more information about the many theories of lift, please see..." and wiki-link to those pages. But we cannot remove the section that dispells BP as a major source of lift - because the minsconception is so dreadfully common - and we cannot become excessively wordy in that section. Keep that in mind when you edit. --J-Star (talk) 12:23, 31 December 2007 (UTC)

J-Star has boldly made the statement that "2) the main mechanism that generates lift is Newton's Third Law". This is a common misconception and J-Star, like all the others, fails to offer any information to support this sweeping statement. Newton's Laws, including the Third, have universal application. Newton's Laws are relevant to every force that exists, and has ever existed, no matter how small or large, or for what time period the force acted. Whenever a body A exerts a force F on another body B, Newton's Third Law gives us confidence that body B also exerts a force F in the opposite direction on body A. But Newton's Third Law says nothing whatsoever about the cause or origin of the force. It therefore provides little or no explanation about why the force exists. It certainly provides no information about why an airfoil generates lift and why non-airfoil shapes generate no lift.

Consider this. The needle of a magnetic compass deflects when a direct current begins flowing in a nearby electrical conductor. If someone enquires as to why the needle deflects it is possible to give the explanation that it is because of Newton's Third Law. Although Newton's Third Law is applicable to the needle and the conductor, most people would find it an inadequate explanation. If there is a small number of people who find it adequate they too will become sceptical when they observe that the needle deflects in the opposite direction when the flow of direct current reverses direction and they are told that the reversal of direction is also because of Newton's Third Law. Newton's Third Law is an inadequate explanation of why an airfoil can generate lift for exactly the same reason it would be inadequate if it was offered as the reason a compass needle deflects when a direct current begins flowing in a nearby conductor. There is nothing unique about the lift force generated by an airfoil. It is just another force, like every other force, and saying "the main mechanism that generates lift is Newton's Third Law" is plainly as inadequate as suggesting that compass needles deflect in the presence of electric currents because of Newton's Third Law.

J-Star has also suggested that the Equal-time fallacy is always accompanied by Bernoulli's principle and therefore Bernoulli's principle should not be mentioned in connection with the lift on an airfoil. This suggestion is foolish. The Kutta condition, and the Kutta-Joukowski Theorem are legitimate elements in aerodynamics. They have stood the test of time for over a century. To complete the picture of how an airfoil generates lift the Kutta condition and the K-J Theorem rely on Bernoulli's principle and for that reason it is entirely legitimate to mention the lift on an airfoil in an article on Bernoulli's principle. The problem in all of this is the Equal-time fallacy. The problem is NOT Bernoulli's principle although many people mistakenly think it is. Dolphin51 (talk) 12:27, 1 January 2008 (UTC)

Basically, I think Dolphin51 is right.

How is lift generated? One can look at this from the Bernoulli persepective. Basically, air flowing past an aerofoil is impeded on the underside and accelerated on the upper side. This is not because of geometry. For example, a thin flat piece of paper held at angle to a stream of air will generate lift, even though the distance travelled by the air across the upper surface is the same as the distance travelled by the air across the lower surface. Higher speed at top = lower pressure, so overall pressure force acts upwards.

If we angled the paper 'downwards' rather than 'upwards' (ie - the paper facing towards the oncoming freestream is lower than the aft end of the paper - I know this really needs a diagram to explain it properly) then a downforce, rather than lift will be generated. Engineers call the angling of any aerofoil to the freestraem the angle of attack (or alpha) of the aerofoil.

As has been pointed out in the main article, there is no absolute requirements for air to pass over the upper surface in the same time as air passing over the lower surface. However, as far as I can see, the Kutta condition does NOT exclude this from happening - it's just not neccesary and highly improbable. However, one can envisage at least in theory of an irregular flowfield which does generate lift and does meet this conditon in theory!

So why is the flow impeded on the lower surface and accelerated on the upper surface?

This is because effectively the angling of the aerofoil means that if the flow were to continue undeflected, it would hit the airfoil.. Therefore, the flow is deflected downwards, away from the airfoil. This deflection slows the air down. The nature of this deflection is not at all intuitive - it occurs contiuously along the every point of the chord of the airfoil. Each point along the wing is deflecting - to a greater or lesser degree - air at every single point in the flow field - not just the fluid in immediate contact with it. An example of this counterintuitive process: the centre of pressure caused this complex deflection activity occurs at the airfoil quarter chord point, not the intuitive half chord point. Knowing which areas of the wing are changing which bits of momentum of the airflow is an involved, difficult calculation (An expression exists from the Lanchester - Prandtl theory which involves a horrible integro - differential equastion...).

Netwon's law of action and reaction is another valid way of analysing the situation. The total deflective force downards applied to the oncoming air mass must be equal to the total force pushing the wing upwards. Bernoulli can be derived using Newton's 3rd law, so this is hardly suprsing, so essentially, the two different ways of analysing the situation are utterly compatible.

Some contributors have talked of Bernoulli being invalid because of viscosity effects. I think this is a bit of a red herring. One can meaningfully apply Bernoulli to low speed idealised flows and obtain results which match pretty closely with the reality - especially in the low speed regime.

90.241.44.54 (talk) 13:24, 1 January 2008 (UTC)

On 22 December a new sub-heading was added, titled "A common misconception about wings". This new text included the sentence "The actual mechanism generating lift on an airfoil is Newton's Third Law of Motion." On 1 January I attached a Citation needed flag to this sentence. On 2 January Cerireid kindly added a citation to the book Understanding Flight by Anderson and Eberhardt, pages 15-30. I have checked this reference and found that it contains nothing similar to the above sentence. On the contrary, it contains various sentences acknowledging the legitimacy and accuracy of Bernoulli's principle, so I have inserted two such sentences into the article. On 7 January I re-attached a Citation needed flag to the offending sentence quoted above.

In their book, Anderson and Eberhardt are not attempting to discredit Bernoulli's principle, nor to say it does not apply to airfoils. The authors are aiming to explain aeronautics and flight in simple terms, readily understandable to students, pilots and enthusiasts, without recourse to mathematics or concepts that are outside everyday experience. For this reason they have used concepts that are alternatives to Bernoulli's principle, but they are not attempting to repudiate Bernoulli's principle or its application to airfoils.

I have also added a Citation needed flag to the opening sentence: "While lift generated by an airfoil is often attributed to Bernoulli's Principle, it cannot be used to explain this."

If proponents of the 'Bernoulli doesn't explain lift' school of thought are unable to substantiate their ideas their comments must be erased from the article. Dolphin51 (talk) 23:33, 6 January 2008 (UTC)

I strongly disagree with the 'Bernoulli doesn't explain lift' section. I think it should be completely removed. The assertion that 'An airfoil is always flown at an angle of attack' is false. Cambered airfoils produce lift at zero angle of attack. This can be seen in thin-airfoil theory. The claim that the lift is produced by the downward deflection of the air is backwards. Though it is true that the air must be deflected downwards to produce a lift force via conservation of momentum this has nothing to do with the mechanism of lift generation.

The basis of lift can be considered in the context of inviscid incompressible flow. The Kutta condition is key in determining the circulation around the the airfoil. Once the circulation is fixed, the potential flow can be used to determine the velocities around the airfoil. This velocity distribution then determines the pressure on the airfoil via Bernoulli. The integrated pressure is the lift. Though this simplification neglects viscous effects, it can be used on the exterior of the boundary layer as long as the flow is not separated.

Any reference to flat plates and supersonic aircraft with zero camber are irrelevant to the discussion. Though it is possible to produce lift with a flat plate and to have a lift to drag ratio of greater than 1 allowing for flight with thrust to weight ratios under 1, this mechanism of lift production is much different than that of laminar flow. Early flight attempts failed because the engines of the time could not overcome the drag resulting from flow separation.

Almost all sub-sonic aerobatic aircraft use symmetrical airfoils so that inverted flight uses the same angle of attack as normal flight, and the lift to drag ratio isn't that poor. Not all airfoils have positive camber, here are links to pictures of a flat top, curved bottom flying body glider, and it's powered version (reached a speed of mach 1.6) m2-f2.jpg m2-f3.jpg Jeffareid (talk) 01:04, 16 March 2008 (UTC)

As discussed at the beginning of the first chapter in John D. Anderson Jr.'s Fundementals of Aerodynamics, Netwon originally tried to solve the problem of fluid mechanics using solid body dynamics directly. The entire second book of Newton's Principia was devoted to fluid mechanics. This approach was shown to be invalid 100 years later by d'Alembert for angles of attack less than 50 degrees. At the same time, Leonhard Euler developed equations based on the pressure distribution and shear stress around the body.

I would have deleted the section myself, but have never edited and article on Wikipedia and wasn't confident about the correct etiquette. If credentials matter, I received my B.S. in Aerospace Engineering from Iowa State University in 2004, my M.S. in Engineering Sciences focusing on computational fluid dynamics at the University of California San Diego in 2007, and am currently enrolled as a doctoral student continuing CFD research at UCSD. (I'm also unclear on how I am supposed to sign this so I'll try to copy what I see on other posts.) Rsmartin 5:28, 7 January 2008 (UTC) --Rsmartin (talk) 05:32, 7 January 2008 (UTC)

• Hi Rsmartin. Welcome to Wikipedia. You are doing just fine. Thanks for contributing to the discussion. I'm glad you didn't just delete the offending sentences. I think there is too much of that going on - people don't understand something so they delete it. The more mature approach is to place a "Citation needed" flag adjacent to the offending statement(s). That gives proponents of the statement the opportunity to give a reference to support the idea. If a week or so passes and no reference or supporting argument appears you would be justified in deleting the statement, and amending the whole paragraph if that is appropriate. Another mature strategy is to use the Discussion page to add your thoughts to the debate, and give the opposing side the opportunity to add their thoughts. If the opposing side remains silent you have added justification in believing their thoughts are unsound. Keep up the good work in bringing a rigorous scientific perspective to Fluid Dynamics.

• There is a discussion going that I initiated on Static pressure. I would be grateful if you would run your eye over Talk:Static pressure and, if you wish, add your thoughts or at least make a comment on which of the two points of view you favour. Dolphin51 (talk) 11:56, 7 January 2008 (UTC)

Just to be a pain, I am going to wade in here. I do believe there are two effects that are being mixed up for low-speed flows, that is the force due to the deflection of the velocity vector, hence exerting an impaction force which will be seen via a vector application of Bernoulli's (scalar application won't cut it as flow direction is changed), and secondly there is the assumption of increase of velocity over the wing - I believe the complication is due to the correct application of Bernoulli's in one (change of velocity vector), and the incorrect in the other (decreased top pressure due to increased path length). Just my two cents User A1 (talk) 07:40, 7 January 2008 (UTC)

Hello all. Seems I kicked up a real hornet's nest and for that I am truly glad, believe it or not. :)

It seems we have some experts on the subject here, people who know a helluva lot about this than me. Here is the rundown on the situation:

• The Equal Transit Time fallacy and Bernoulli's Principle are often used to describe lift to laymen. The very section I slashed is evidence of the latter and the ETT fallacy has its very own section under Lift.
• I think - and I am certain many agree - that the section that I slashed cannot remain. It does not properly describe the part played by Bernoulli's Principle in regards to lift and analysis of the same.
• Hence, we have to replace that section and more properly describe what part BP plays in aerodynamics.
• Also, we should keep a comment that BP is often wrongly used in laymens' descriptions of lift.

Don't be afraid to edit and rip out entire sections. As per WP:BOLD you should stick your chin out a bit. The important part is to source your statements (which is - of course - where I erred, but still I feel the current discussion is a huge gain). So go ahead, put your expert knowledge in the subject to use.

A note: titles mean little. That is - in the worst case - Appeal to authority. Sourcing is everything. Just as long as you source your statements, feel free to slash and edit all you like. --J-Star (talk) 12:40, 7 January 2008 (UTC)

Hi J-Star. Thanks for returning to this debate. You suggest that "we should keep a comment that BP is often wrongly used in laymen's descriptions of lift" but you have provided nothing to support your suggestion. Is that simply your personal view, or is there some independent source that holds that view? As you can see from this Talk page, this is a highly controversial subject so it is vital that assertions must be supported by some reference to a source.

Well seeing that the subject is controversial, that itself speaks for the slashed section not returning until the matter is settled. This would also mean removing the big section I wrote for the time being. If you feel that this should be done because what I wrote is too vague, then by all means go ahead.

Do remember that we do not need to keep things just for the sake of keeping them. If a section is wrong or too unsourced, it is perfectly allright to just cut it out. Besides... the history of a page always allows a section to be restored. --J-Star (talk) 14:17, 9 January 2008 (UTC)

Secondly, you have made several references to "the section I slashed". Would I be correct in assuming you are referring to the following text? If so, why do you say it "cannot remain"?

The air flowing past the top of the wing of an airplane, or the rotor blades of a helicopter, is moving very much faster than the air flowing past the under-side of the wing or rotor blade. The air pressure on the top of the wing or rotor blade is much lower than the air pressure on the under-side, and this explains the origin of the lift force generated by a wing or rotor blade to keep the airplane or helicopter in the air. The fact that the air is moving very fast over the top of the wing or rotor blade, and the air pressure is very low on the top of the wing or rotor blade, are fine examples of Bernoulli's Principle in action, even though Bernoulli established his famous principle over a century before the first man-made wings were used for the purpose of flight. (Bernoulli's Principle does not explain WHY the air flows faster past the top of the wing and slower past the under-side. To understand WHY, it is necessary to see the Kutta-Joukowski Theorem.) Dolphin51 (talk) 22:44, 7 January 2008 (UTC)

Bernoulli's equation can be derived from the momentum equation Navier_Stokes by dotting it with the velocity under the approximations of incompressible, inviscid flow as seen in the section entitled "Mechanical Energy and Bernoulli Equations" in Panton This means that the claim that Bernoulli's equation does not explain lift is akin to saying that the approximations to the momentum equation are invalid when explaining lift. It is true that the Kutta condition is necessary to correct the the inviscid simplifications as mentioned in Section 4.5.1 entitled 'Without Friction Could We HAve Lift?' of Anderson's 'Fundamentals of Aerodynamics'. The combination of Bernoulli and Kutta are sufficient for the estimation of lift produced. Though lift can be explained with these approximations, drag cannot. This is the basis of D'Alembert's Paradox D'Alembert's_paradox.

The concept of what 'causes' lift seems to be more of a philosophical debate. The vertical force resulting from the pressure integration is the lift. The pressures can be obtained from the flowfield via Bernoulli. However, the Kutta condition (or viscosity) is necessary in determining the correct flowfield. Does that mean that the lift is 'caused' by viscous effects or pressure forces? It seems to me that it's only the combination of the two that 'causes' lift. The momentum equation 'causes' lift, but the combination of potential theory, Bernoulli, and the Kutta condition is a reasonable approximation to the momentum equation. --Rsmartin (talk) 01:48, 9 January 2008 (UTC)

On 20 December 2007 a new sub-heading titled A common misconception about wings was inserted in the article Bernoulli’s principle. Under this sub-heading numerous claims were made about the non-applicability of Bernoulli’s principle as an explanation of why wings generate lift. For example, on 20 December the following claims were inserted:

• “While lift generated by an airfoil is often attributed to Bernoulli's Principle, it cannot be used to explain this.”

• “The actual mechanism generating lift on an airfoil is Newton's Third Law of Motion.”

• “Bernoulli's Principle cannot be used to explain the lifting mechanism.”

Little attempt was made to justify these statements, and no attempt was made to source them. On 31 December 2007 a debate about the legitimacy of these statements commenced in Talk:Bernoulli's principle.

On 1 January 2008 I posted “Citation needed” flags against the above three statements. On 2 January Cerireid kindly posted a reference to the book Understanding Flight by David F. Anderson and Scott Eberhardt. No page number or chapter identification was included and I have been unable to find anything in Understanding Flight that exactly matches the sentence for which the book was offered as a source.

Since 2 January no attempt has been made by anyone to post a source for any of the above three statements, or anything else under the sub-heading.

On 7 January Rsmartin wisely posted an “Accuracy disputed” flag on the sub-heading “A common misconception about wings”.

There is indeed a common misconception about wings and lift and Bernoulli’s principle, but it is not the one intended by the original author of this sub-heading! I have done substantial research into the matter and comprehensively re-written this sub-heading, including sources to my claims and quotations.

I would welcome other editors contributing constructively to this sub-heading, but unless you can quote a legitimate source for your contribution please keep out. Dolphin51 (talk) 02:21, 29 January 2008 (UTC)

Hello again, I have populated several OR tags onto this page, and I said I would make some comments on the talk page, and I didn't. So here I am trying to rectify matters somewhat. So before I launch into my rant, I realise that I may well be opening a can of worms here, as there has been much discussion on this already; so here goes.

I am somewhat ambivalent about this sections existence, whilst it both serves as a deterrent to people placing incorrect/questionable, but well meaning assertions onto the page here(diff) and to a lesser extent here(diff). My memory has me recall this as a more regular issue, but a light perusal of the logs fails to verify this.

Anyway the idea of dispelling incorrect invocations of Bernoulli's Principle (BP) is good, and well to be applauded, however I feel that this section involves more interpretation and derived opinion than one would expect on an article that is quite technically oriented. It almost seems as if the editor of the article has read a book, which oversimplifies the subject in order to explain a complex physical phenomenon and has been taken aback by this. In response the editor writes this section in the hope that anyone who has previously read this reference will be illuminated. I would expect this editorial style to be more approriate in a text where one *can* assume that the readership would be familiar with these texts, such as if one is of an aeronautical background (not engineers, but pilots, manufacturers etc). Finally it seems to diverge into a detailed and well thought out discussion on why these particular texts are incorrect - which is in my opinion somewhat less than helpful in an encyclopaedia article.

To conclude my rather verbose rant, I shall suggest that something of the following form could be written to simply inform the reader that the situation is complicated and requires a good level of understanding in wider fluid mechanics, my suggestion is as shortly follows. It is my hope that it does *not* generate too much dicussion, rather a single editor adopts the concept and moulds it to suit, rather than simply imposing my view on the article.

As Bernoulli's principle cannot be used to explain all of the fluid phenomena that directly contribute to the generation of lift due to the flow of air past an airfoil, explanations that solely use Bernoulli's principle are usually in error. The misapplication stems from several possible misconceptions, firstly the use of the equal transit time theory, Secondly, the seemingly simple but incomplete explanation of lift generation due only to angle of attack deflecting the air flow and allowing for a simple force balance. Thirdly, the misues of the Coandă effect - a result of shear in the fluid flow.

To correctly calculate the lift on the wing, one must first solve the fluid flow field around the object, either analytically or numerically, then integration_(mathematics) the forces applied to the object due to this flow. Such a technique will yield a good approximation to the actual lift, limited by the numerical accuracy of the solution and the applicability of the Navier-Stokes equations to describing the physics of the fluid flow

So in summary, I'm not really keen on whats there at the moment, even though I understand why. I think something that is less of a discourse into the world of bad explanations for lift is in order, and have made a suggestion.

If you read that, then I hope that my comment was worth your time! User A1 (talk) 11:00, 21 February 2008 (UTC)

Hi User A1. You are correct when you observe that there are editors who have worked on this article who don't trust Bernoulli, and want to write about how Bernoulli really shouldn't be applied to the wing of an aircraft. Let's call these editors "Bernoulli sceptics". The Level 2 Headline "A common misconception about wings" wasn't created by me - it was created by one of our Bernoulli sceptics.

I suspect you are one of these Bernoulli sceptics. You propose saying "As Bernoulli's principle cannot be used to explain all of the fluid phenomena that directly contribute to the generation of lift due to the flow of air past an airfoil, explanations that solely use Bernoulli's principle are usually in error." Where did you get this theory from? Do you intend quoting a source for your proposed text, or is this your original research? If you intend quoting a source please post the details on this Talk page.

Your proposed text seems to be saying the lift generated by a wing is such an incredibly complex phenomenon that people should not attempt to explain it using simple principles like that of Bernoulli. You appear to be confident in use of the Navier-Stokes Equations, but much less confident about the application of Bernoulli.

Bernoulli's principle is nothing more than some very fundamental principles of mechanics applied to steady, inviscid fluid flow. Bernoulli's equation can be derived using Newton's second law or the Work-energy theorem. Suggesting that Bernoulli isn't reliable, or isn't applicable to the lift generated by a wing is tantamount to suggesting that you have found a situation in which Newton's second law fails, or the Work-energy theorem fails. Prove those things and you are guaranteed to win the Nobel prize in Physics because, apart from Albert Einstein, no-one has ever managed to disprove those fundamental physical principles or find a situation in which they are less than 100% accurate.

Bernoulli's equation is precisely correct and totally relevant to the generation of lift by an airfoil, providing only that we are looking outside the boundary layer. It is misleading to suggest that application of Bernoulli to a wing is a misapplication, or a misconception, or is only an approximation. How does a parcel of air know whether it is flowing around a wing or a golf ball or the sail of a yacht or the hull of a boat? How does this parcel know whether it should behave in accordance with Bernoulli's principle, or misbehave when it is in the vicinity of a wing?

A number of Bernoulli sceptics have contributed to this article, but not one has posted a source which supports the sceptic's claim. The Bernoulli sceptics are relying on little more than someone else's original thinking. The Bernoulli sceptics must start quoting sources if they want to be taken seriously - this is an encyclopedia. Dolphin51 (talk) 12:59, 21 February 2008 (UTC)

I consider it, umm interesting that I am a "bernoulli skeptic" in my defence, I believe (and I may well be wrong) that I know what it is and how it works. I find the theorem extremely useful but often misapplied. It is not a question of if the equation is right or wrong - its right; It's more that the equation is often invoked where it isn't helpful - it merely relates the energies of a stream tube/line. In the end it is very simple fluid mechanics User A1 (talk) 13:25, 21 February 2008 (UTC)

Hi again User A1. You can take off the Bernoulli Sceptic hat and put on a Bernoulli Believer hat! Bernoulli may be often misapplied, and his equation may be invoked where it isn’t helpful, but how could you quote a source for these two statements? Has there been some research?

As you know, Bernoulli’s principle relates pressure, speed and elevation at two or more points. If one of these is unknown it can be determined using Bernoulli’s equation. To determine the pressure at one or more points, the fluid speed must be known at those points. Bernoulli’s principle doesn’t presume to be able to provide both the fluid speed and the pressure at a point, and consequently more than Bernoulli’s equation is needed to determine the pressure distribution around a wing of known dimensions. I see no need to state the things Bernoulli’s equation cannot do (eg “BP cannot be used to explain all of the fluid phenomena that directly contribute to the generation of lift due to the flow of air past an airfoil …”) This would be a bit like inserting a paragraph in Newton’s Second Law saying “N2L cannot be used to calculate the mass of propellant in a solid fuel rocket to achieve a specified performance.”

I agree that the tricky part in explaining the lift on a wing using Bernoulli is explaining the velocity distribution around the wing, and particularly the higher speed across one surface. The equal transit-time theory is one attempt, albeit an inaccurate one, but it understates rather than overstates the speed across the top surface so I consider the inaccuracy relatively inoffensive. The Bernoulli sceptics focus on the equal transit-time theory and then conclude that Bernoulli must be equally in error when applied to a wing. When applying Bernoulli to the phenomenon of lift on a wing one should begin with the fact that the fluid speed over one surface is significantly faster than over the other, and then use Bernoulli to explain why this speed distribution is accompanied by a pressure distribution. Exactly why the speed is faster over one surface than the other is not relevant to the application of Bernoulli, and no apology needs to be made for the fact that the speed distribution cannot be determined using Bernoulli.

However, the article in question is about Bernoulli’s principle and what it can achieve. It is not about explaining the lift on a wing. I see no need to include statements about Bernoulli being unable to fully explain lift. I also see no need to include statements that if Bernoulli is misapplied it leads to incorrect results – that is universally true. Dolphin51 (talk) 10:51, 23 February 2008 (UTC)

---moved discussion here---- Stick and Rudder explains why wings generate lift by using the fact that wings push the air down. The book does not explain why wings push the air down. This approach is in danger of leading to a circular argument: Why do wings push the air down? Because wings generate lift. 05:26, 26 February 2008 (UTC)

Rotation

This article is becoming a bit messy, psuedo-explanations appear to abound. I have removed the following from the article, as I believe that it confuses some of the concepts going on here:

• As water drains from a bowl it usually spins in a circular fashion around the axis of the drain pipe. It spins faster close to the axis of the drain than at the edge of the bowl. Bernoulli's Principle states that the water pressure near the floor of the bowl must be lower near the drain where the water speed is fastest, than at the edge of the bowl where the speed is slowest. In a liquid, lower pressure means lower water depth and that is why the water is not as deep near the axis of the drain, and the surface of the water is not flat but slopes downwards towards the axis of the drain. The result is that the surface of the water in the bowl displays a characteristic shape with a distinct depression above the drain.

I think the proper analysis is more complex than this is puporting, with several components to consider. In the analysis of a draining system, which is perfectly rotationally symmetrical, simple application of Bernoulli's principle will not predict any rotation associated with the discharge. The fluid stream tubes should be uniformly distributed across the system and directly heading for the drain. Other real effects will cause the initial rotation.

As for the "charachteristic shape", I believe that it is true that the static pressure at the centre of rotation is lower than at the edge, however the impact pressure should be the same, much as for a venturi tube. However lower pressure does *not* mean lower depth, consider a horizontal venturi tube after this draining tank, there will be *no* change in liquid level, however there is an associated pressure drop. The shape is probably better explained using a conservation of angular momentum explanation, rather than direct application of bernoulli's principle. User A1 (talk) 09:21, 1 January 2008 (UTC)

Hi User A1. Thanks for participating in the debate. You have deleted a whole paragraph of text from the article, and then you have used the Talk page to report that you have deleted it! I suggest you have the two steps back to front. It would be much more in the spirit of Wikipedia if you used the Talk page to give your point of view, and argue your case as to why the text that offends you should be deleted. Others may want to disagree with your reasoning.

You have written "simple application of Bernoulli's principle will not predict any rotation associated with the discharge". You must have missed the sentence saying "As water drains from a bowl it usually spins in a circular fashion around the axis of the drain pipe."

You have also written "I believe that it is true that the static pressure at the centre of rotation is lower than at the edge, however the impact pressure should be the same." You believe correctly, but what is the relevance of the impact pressure in this context? There are many, many examples of observable differences at different places in a fluid flow due to differences in static pressure, even though total pressure is constant throughout the flow.

You have also written "lower pressure does not mean lower depth". Readers of this Talk page would be very interested to see your explanation of that one in the context of a liquid with a free surface!

You conclude by saying "The shape is probably better explained using a conservation of angular momentum explanation, rather than direct application of bernoulli's principle." The text you have cut from Bernoulli's principle was intended to illustrate Bernoulli's principle. The intention was NOT to explain the shape of the free surface of rotating liquid bodies!

I suggest you reinstate the text you deleted, and then use the Talk page to provide a much better explanation of why you believe the paragraph in question should be deleted. Dolphin51 (talk) 12:58, 1 January 2008 (UTC)

Hello Dolphin51,

In the spirit of wiki I was being bold, also in the spirit of wiki you to umbridge to this and then replied on the talk page. As this has generated (most likely good) discussion, both of these events are good. Sometimes I do the talk/delete combination, other times I do the delete/talk combination, and other times still I just delete. Most of the time people don't discuss it, but they should at all times be free to, and thus I think this is exactly what Wiki is about, but enough wiki-philosiphy (if you are really keen you can drop me a line on my talk page)!

I shall address your concerns in list form if I may. If I am unclear in any point, please do tell me and I shall do my best to be a bit clearer or to backtrack, whichever is needed ;) :

• You have written "simple application of Bernoulli's principle will not predict any rotation associated with the discharge". You must have missed the sentence saying "As water drains from a bowl it usually spins in a circular fashion around the axis of the drain pipe.

I feel that the paragraph was not clear that Bernoulli's princple was not responsible, and a casual reader could confuse the rotation as an effect of Bernoulli's, rather than a separate observation.

• You have also written "lower pressure does not mean lower depth". Readers of this Talk page would be very interested to see your explanation of that one in the context of a liquid with a free surface!

As per before, impact pressure will not, static pressure will. As for lower pressure != lower depth when in the presence of I shall elaborate. With a free surface the relation that static pressure and depth are equivalent will only be true for static (flow) problems, not completely true in a dynamic problem (I know i am getting picky, but so often is Bernoulli's principle mis-invoked, people do take things at face value often, and finkicky people like me get upset when they use something out of context). The lower pressure at lower depth is simply Bernoulli's equation without the velocity term. As a counter example, in a system that is at steady state and flowing such as the horizontal venturi meter this is not the case, and one can add a free liquid surface above it if needed.

To illustrate simply place a tank above horizontal venturi, with the drain of the tank in the centre of the tank at the base. Connect the horizontal venturi to the drain, such that the base of the tank is above the venturi. Now provide the tank with a non-zero inflow (and of course a non-zero outflow to satisfy steady state :) ), draw a system boundary such that it encompasses the tank & free liquid surface as well as the venturi meter (consider the outflow of the venturi to be at the end of the system). In the throat of the venturi meter the static pressure will be reduced possibly beyond the pressure of the inlet pipe, even though the entire throat will be above some of the pipe leading into the venturi meter (I find textual descriptions difficult sometimes, if this is unclear I can make a quick sketch and upload it).

• You conclude by saying "The shape is probably better explained using a conservation of angular momentum explanation, rather than direct application of bernoulli's principle." The text you have cut from Bernoulli's principle was intended to illustrate Bernoulli's principle. The intention was NOT to explain the shape of the free surface of rotating liquid bodies!

I know that was not the intention, but again I felt that it was easily possible for a reader to draw a link between the two, even if the intent to do so was not there.

I am a bit tired at the moment (happy new year!), so I may not have been entirely clear in my discussion above. If you want to reinstate the text, I shall leave that up to you, but I would ask that the example be adjusted to address a couple of my concerns. If you like I shall return later and adjust the content to what I feel comfortable with, then ask you if you approve of the modifications.

Thanks User A1 (talk) 13:48, 1 January 2008 (UTC)

Hi User A1. Thanks for your very prompt response. I am willing to reinstate the text but my strong preference is that you reinstate it and make whatever adjustments or discussion you think appropriate to improve the presentation.

Your response contains one or two suggestions that "the paragraph was not clear ..." and "a casual reader could confuse ...", and so you deleted the paragraph. The way Wikipedia moves forward is surely for knowledgeable people to identify ambiguous text and improve it, rather than simply deleting it. I agree that Wikipedia advocates being bold, but I don't believe casual deletion of someone else's work qualifies as bold. Being bold is best achieved by adding to Wikipedia.

You have continued with your analogy of the horizontal venturi tube connected to the drain of a tank. (My comment referred to a liquid with a free surface. A liquid in a venturi doesn't have a free surface - venturis are completely filled with fluid.) You seem to be saying that a horizontal venturi demonstrates that "lower pressure does not mean lower depth". I disagree. Some fluid dynamics laboratories have a piece of apparatus comprising a venturi with three standpipes made of transparent tubing - one connected to the inlet to the venturi, the second connected to the throat, and the third connected to the exhaust. The venturi is fed with water from a low-pressure source. With no water flowing through the venturi the water is at the same level in the three standpipes. When water is allowed to flow through the venturi the level drops markedly in the standpipe at the throat, demonstrating the reduced pressure in the throat where the flow is fastest. This experiment demonstrates my point very well - that fluid depth and static pressure are in a functional relationship, not only in fluid statics but in steady-state fluid dynamics too. I continue to be puzzled by your comment that "static pressure and depth are equivalent" but "not completely true in a dynamic problem". I would appreciate your further attempt to explain this one because it is at the heart of your reasoning for deleting the paragraph.

The reason I am pursuing you on these things is because, if you are correct, then the paragraph which offended you must be improved or deleted. If you are incorrect then the paragraph must be reinstated without change. Dolphin51 (talk) 02:14, 2 January 2008 (UTC)

Hello Dolphin51, Everything you state is true, however they are different situations, and I have performed that experiment before, most likely we are explaining two sides of the same coin. I have tried to explain myself more clearly at Image:Venturi-explain-talk.svg; sorry about the late reply User A1 (talk) 05:28, 7 January 2008 (UTC)

Alternate example would be a vertical venturi Image:Venturi-explain-talk2.svg User A1 (talk) 06:03, 7 January 2008 (UTC)

Bernoulli effect

The typical reader will come to this article for an understanding of the "Bernoulli effect". They will glance at the article and leave frustrated, none the wiser.

The article needs a new introduction in plain English stating what the BE is, and giving examples from common life. If there are any! Or say straight out that there aren't, and maybe list the common misconceptions?

If flying airplane wings are really not an example, maybe there are no true examples in ordinary experience?

The article should specifically address relevance to computer technology, real or supposed. Certainly the term is used there!

BBC News 2006:

'Without Daniel Bernoulli we would not have a name for the effect that we rely on to make the hard disk work.

The Bernoulli Effect is what happens when a wing moves through the air - it floats. Just like an aeroplane's wing, the read head of a hard disk floats across the top of the disk.

"As the disk spins this lifts the head up off the media," explained Ian Keene of hard drive manufacturers WD.

He added: "Many people think the head is actually touching the media, but the distance between the head and the media is in the distance of 100 angstroms; to give you some idea of what an angstrom is, a human hair is about one million angstroms." ' -69.87.199.68 (talk) 20:51, 24 January 2008 (UTC)

Half-venturi

Please identify "who says" many books contain this fallacy or the section will have to be removed. (Even if many books do contain this, and it is wrong, it still does not belong in Wikipedia unless it is verifiable.) ComputerGeezer (talk) 03:32, 17 February 2008 (UTC)

I agree. This paragraph does not belong in WP. Get rid of it. Go for it ComputerGeezer. Dolphin51 (talk) 12:07, 17 February 2008 (UTC)

"A common misconception about wings" Section

This section appears to consist almost entirely of the author's criticism of the books in question, take this paragraph here (emphasis mine):

"Stick and Rudder explains why wings generate lift by using the fact that wings push the air down. The book does not explain why wings push the air down. This approach is in danger of leading to a circular argument: Why do wings push the air down? Because wings generate lift."

The bolded section is simply an assertion written by whomever wrote this article. Criticism of these books should come from a valid source, like a reviewed journal. There are similar problems in the section about Understanding Flight

"Anderson and Eberhardt also make some statements about Bernoulli’s Equation and flight that are not consistent with a modern understanding of aeronautics."

Again, this may or may not be a valid criticism, but some random guy on Wikipedia is NOT a valid source. There are several more instance of this in the next few paragraphs, which I've marked.

In my opinion, it would be much better to provide an explanation of how Bernoulli's principle relates to the creation of lift, rather than to try and criticize specific books. The lift article has some better-cited explanations of how lift is created, and I think theirs would be a good example to follow. I'm going to leave this up for a while to see if anyone responds, but if not, I'll start working on killing this section and replacing it with something better. User:!jim^talk _contribs 01:55, 24 February 2008 (UTC)

I agree that we need to properly source our material. But the reason it is in the article is that the books in question were used as (flawed) sources in an attempt to "debunk" Bernoulli’s Equation. The entire section should probably be moved to the talk page. This would simplify the article while retaining the information to ensure that the same mis-interpretation does not make its way back into the article. ComputerGeezer (talk) 05:02, 24 February 2008 (UTC)

I believe that rather than addressing the books themselves, it would be more useful to provide a sourced, correct explanation of the relationship between Bernoulli's principle and lift. If we do that, people coming to this page with the misconception will hopefully read it and improve their understanding of the principle. If they don't, we'll have a good base that we can refer them to if they add their incorrect interpretations again. User:!jim^talk _contribs 18:09, 24 February 2008 (UTC)

Hi User:!jim. Welcome to this debate. I am the culprit who wrote the text you see today under the Headline "A common misconception about wings". To understand why I wrote my text please read what existed under this Headline at 24 January 2008 or earlier. There were numerous bold assertions that Bernoulli's principle could not be used in an explanation of why wings generate lift. No sources were quoted. I posted "Citation needed" flags on some of the worst examples of outrageous claim and Cerireid kindly responded by nominating Understanding Flight by Anderson and Ebehardt. However, after reading that book carefully I found no statement of the kind for which Anderson and Eberhardt was offered as a source. The reference proved to be useful because it led me to Wolfgang Langewiesche's book Stick and Rudder and he does make the statement that the correct explanation for lift on a wing is Newton's Third Law. Both A & E and Langewiesche have written introductory books for aviation enthusiasts and student pilots. Neither of these books is an advanced work in the field of aerodynamics and yet we have seen numerous Bernoulli Sceptics adding text to the article in question boldly exclaiming that Bernoulli has no place in explaining the lift on wings. As well as adding fanciful text about how the true explanation of lift lies only in Newton's Third Law, we have seen the Bernoulli Sceptics deleting entirely sound and reasonable text about the way Bernoulli's principle contributes to our understanding of the phenomenon of lift.

I agree that my present text will probably one day be deleted from Bernoulli's principle (probably by an outraged Bernoulli Sceptic) but hopefully it is serving at present to challenge the thinking of those who have embraced the notion that Bernoulli's principle is irrelevant to our understanding of the phenomenon of lift. Hopefully it is helping the Bernoulli Sceptics realise that the sources of their scepticism are introductory books written for readers for whom Bernoulli is still too advanced a concept. (The Sceptics never actually quote a source.) As I wrote above, before you go further please read Bernoulli's principle as it stood prior to 24 January 2008. Dolphin51 (talk) 12:15, 24 February 2008 (UTC)

I read through your changes, and see that they are an improvement in one sense, in that they are at last factual. However, they still consist of you personally addressing the misconceptions, rather than a citation of a verifiable source doing the same. I once again suggest that we add an explanation along the lines of what lift has. That allows us to offer a fairly simple explanation of the relation between Bernoulli's principle and lift. I don't have time to add this section now, but I will in the new next few days. User:!jim^talk _contribs 18:03, 24 February 2008 (UTC)

Hi again !jim. I look forward to reading your new section. I think we might be successful in deterring the Bernoulli Sceptics from corrupting Bernoulli's principle. Today I have restored a paragraph I added a few months ago on lift and Bernoulli - it was deleted by one of the Bernoulli Sceptics. Dolphin51 (talk) 22:45, 25 February 2008 (UTC)

In my opinion, the section "A common misconception about wings" should be removed or moved (and adapted) to somewhere else on WikiPedia. This article is about Bernoulli's principle, which relates the given kinematics of a flow to the resulting pressure dynamics. So this article is not about flow kinematics and should not describe misconceptions on how the flow kinematics are derived, like the equal transit-time fallacy or split ventury pipe fallacy. Neither are the subsections "Stick and rudder" and "Understanding flight" helpfull, since the author of these subsections suggests that Bernoulli's principle is different from Newton's law of motion, while in the sections above it is shown at length how to derive Bernoulli's principle from Newton's laws. The only difference being, that Bernoulli's principle is about describing the local forces (called pressure) while lift is an integral force. Discussions on how to derive these integral forces using different approaches should be made in the relevant articles (or associated talk pages) where they are described, not here. Given the correct flow kinematics, Bernoulli's principle will produce the correct pressures and lift force (provided the assumptions necessary for Bernoulli's principle to be accurate, are fullfilled). Crowsnest (talk) 00:43, 28 February 2008 (UTC)

I agree that this section needs to be removed, and will be working on a section that explains the relation (for lack of a better word) between lift and Bernoulli's principle to replace this one. If you were to beat me to doing the same I would support you, as I'm very busy. I do think that a section on this relationship (for lack of a better word) is appropriate, as the history of this article (and this talk page) will show repeated wars between people who understand BP and lift and people who don't. User:!jim^talk _contribs 04:54, 28 February 2008 (UTC)

Is air at low M an incompressible fluid?

Hi !jim. I have just undone your amendment in which you expanded the example of an incompressible fluid to include "air at low Mach numbers". I think it is foolish to suggest that air is an incompressible fluid, regardless of the qualification about low Mach number. (Air is a gas and therefore compressible - air at low M and air at high M are not two different gases). Bernoulli's principle already contains ample explanation about how the incompressible equation can be applied without excessive error to gases moving with low Mach number - see Heading 1.2. There is no justification for including it as an example in line one, where the simplest introduction to the subject should be found. Dolphin51 (talk) 05:28, 27 February 2008 (UTC)

Dolphin,

The comment is trying to say that air at low velocities is well approximated by the incompressible model. There is less than a 1% difference in impact pressure for the incompressible and compressible models of air for velocities of up to 60m/s at RTP. You can see that from the equation or it is mentioned in Coulson & Richardson "Chemical Engineering" volume 1 6th edition (fluid flow, heat transfer & mass transfer); pp 243. ("little difference" is the phrase used) 60m/s at rtp is approximately Mach 0.18 User A1 (talk) 08:01, 27 February 2008 (UTC)

Hi User A1. I am well aware that gases moving at low Mach number are well approximated by the incompressible equation, but that is not the comment I deleted from Bernoulli's principle. What I deleted was a few words giving "air at low Mach numbers" as an example of an incompressible fluid. The two statements are very, very different. I deleted the words from the opening sentence, not somewhere deep in the article among all the details and differential equations. The beginning of an article should make sense to readers who are completely new to a subject, and it should begin in simple terms. More complex information should come later in an article. In the fields of physics and fluid dynamics, Bernoulli's principle is an elementary principle whereas Mach number is much more advanced. When readers begin to grasp the concept of Bernoulli's principle they should not be confronted by the concept of Mach number. I am totally in favour of Bernoulli's principle explaining that gases moving at low Mach numbers are well approximated by the incompressible equation. Heading 1.2 is the ideal place for that to happen by way of explanation - not the opening sentence where it is introduced by way of a paradoxical example in parenthesis. Those of you who are sufficiently knowledgeable to talk about the applicability of the incompressible form of Bernoulli to gases moving at low Mach number should add some well-researched explanatory text at Heading 1.2, not insert a paradoxical example in the first sentence. Dolphin51 (talk) 23:12, 27 February 2008 (UTC)

I added that sentence off-the-cuff and should have made a better effort to integrate into the article, and for that I apologize. That being said, I think that if we're going to single out fluids to which BP applies (or may apply), we ought to include air in that somehow, as it may be confusing to readers who comes here expecting to read about things like air and lift to find that BP does not apply to air. User:!jim^talk _contribs 04:54, 28 February 2008 (UTC)

Bernoulli's principle is already well-organized with Headings devoted to incompressible fluids and compressible fluids. As I have written twice before, I see no grounds for trying to insert the subtlety of "the incompressible equation being applicable to compressible fluids" in the opening sentence. There is a place for everything, but the opening sentence isn't that place. I removed the offending paradox but User A1 re-inserted it so I won't engage in a duel - I will wait a while to see if User A1 (or anyone else) removes it; possibly replacing it with some eloquent explanation at an appropriate place in the article. Dolphin51 (talk) 05:31, 28 February 2008 (UTC)

I have made some amendments to Bernoulli's principle, including an amendment to delete the reference in the opening sentence to incompressible fluids, and particularly to delete the reference to liquids and air at low Mach number as examples of incompressible fluids. Prior to my amendment there had been two examples given of incompressible fluids - liquids, and air at low Mach numbers. The Wiki editors responsible for including "air at low Mach number" most likely intended to give "air at low Mach number" as an example of a compressible fluid that can be analysed using the incompressible form of Bernoulli's equation with an acceptably low amount of error. Unfortunately, what resulted was tantamount to a statement that "air at low Mach number" is an example of an incompressible fluid. To eliminate the problem in a way that is hopefully acceptable to all parties, I have deleted the reference in the opening sentence to "incompressible fluids" and replaced it simply with "fluids". The article gives comprehensive information about compressible fluids so it is misleading for the opening sentence to give the appearance that what follows will be confined to incompressible fluids. Dolphin51 (talk) 10:16, 12 March 2008 (UTC)

In my opinion, quite an improvement. I added that the fluid should be inviscid for Bernoulli's principle to be applicable. Crowsnest (talk) 23:23, 12 March 2008 (UTC)

• Thanks Crowsnest. It is great to find an editor on Bernoulli's principle who doesn't want to write that air is an example of an incompressible fluid; or that Bernoulli's principle doesn't apply to the wings of an aircraft!

I have some discomfort reading that Bernoulli's principle applies (only) to inviscid fluids. Most readers will be aware that air, water, and all the other fluids we consider in fluid dynamics have finite viscosity. Therefore Bernoulli's principle doesn't apply to these fluids? Right? No, wrong. There is a great opportunity for someone to explain Prandtl's hypothesis which says fluids with low viscosity can be considered to be inviscid throughout the flow field except at the boundary of the flow. Therefore Bernoulli's principle can be applied to viscous fluids throughout the flow field except in the boundary layer (and the boundary layer is usually extremely thin). Alternatively, it is reasonable to omit references to inviscid fluids in the introduction to Bernoulli's principle, and introduce the complexities of boundary layers and Prandtl's hypothesis further down in the article, down among all the partial derivatives and complex stuff. Dolphin51 (talk) 00:23, 13 March 2008 (UTC)

Yes, I agree that it applies to viscous fluids provided the effects of viscosity are confined to thin boundary layers (e.g. for many wings, or the oscillatory boundary layers in water waves or acoustics). But there are also many flows where Bernoulli's principle is not applicable throughout (the whole of) the flow: e.g. the hydraulic jump, due to (for a large extend) viscous dissipation in and behind the jump. So to my opinion there should be something on this in the opening of the article.

All models are only approximate, so in that sense there is nothing wrong if it is said that Bernoulli's principle is applicable to fluid flows in which viscous effects may to good approximation be neglected. A similar wording circumvents the objection to refer to inviscid fluids, which are very rare (superfluids). This also applies to incompressibility, if it is not referred to as a property of the fluid, but the consequence of an approximation in mathematical-physical modeling. Crowsnest (talk) 01:03, 13 March 2008 (UTC)

By the way, liquids are also compressible, e.g. water with a speed of sound of about 1450 m/s in pure water (without dissolved gases) at air temperature and atmospheric pressure, see speed of sound. It drops fast when there is dissolved gas, which makes it much more compressible while the mass density hardly changes. Only in most cases the Mach numbers are very low in most cases. An exception is water impacts, when a fast-moving (almost) flat-surfaced object hits the water surface. Or the other way around, when the moving water surface hits an object with the surfaces almost parallel. Crowsnest (talk) 01:26, 13 March 2008 (UTC)

Is there no work being done by gravity ???

In the first sentence it is said both that Bernoulli's principle is valid for flows with no work being performed on the fluid and at the same time about changes in the gravitational potential energy. This is inconsistent since the gravitational force performs work at a rate of ρg DZ/Dt if Z is the vertical coordinate of a fluid particle in a Lagrangian frame of reference. I do not have access to the reference cited, but since Bernoulli's principle is valid for flows in a conservative force field, the statement that no work is performed must be wrong. I removed it. Crowsnest (talk) 10:38, 13 March 2008 (UTC)

Bernoulli's principle and lift

An aircrafts generates lift and drag by performing work on the air. When an aircraft flies through a volume of air, it increases the total energy of the air equal to the work done on the air; the velocity of the air is increased, without an equal decrease in pressure. Bernoulli equations need to be adjusted to deal with the increase in total energy.

It's easier to visualize this if the air itself is the frame of reference, such as an observer in a hovering balloon. When a aircraft flies through a volume of air, the affected air is accelerated mostly downwards (corresponding to lift), and some forwards (corresponding to drag).

Given suffiencient air speed and effective angle of attack (downwards acceleration of air), just about any "airfoil", including a flat board, will generate lift. Small solid balsa wood gliders use flat airfoils and glide just fine. When an aircraft passes through a volume of air, the affected air experiences an increase in total energy, based on the work done by the aircraft.

Regarding the idea that wings must be symmetrical or cambered, here is a link to a picture of a flat top, curved bottom, lifting body glider used as a pre-shuttle prototype, called the M2-F2, which flew just fine. Note that the flat top of the M2-F2 is nearly horizontal. The chase plane in the picture is a F104 jet.

M2-F2.jpg

The rocket powered version of this model, the M2-F3, reached a peak speed of mach 1.6, so it's not a high drag airfoil.

M2-F3.jpg

Regarding this ariticle, why not remove the part about how wings generate lift, since it's apparently controversial? There's already a good article on Venturi effect. Jeffareid (talk) 01:13, 16 March 2008 (UTC)

Static ports on airfraft are not affected by the air flowing across them.

On civilian aircraft, such as a Cessna 182, there is a static port, basically a circular hole in the side of the fuselage that is connnected via a pipe to a chamber used for the altimeter, vertical speed indicator, and 1/2 of the airspeed indicator. The other port is a pitot port that faces into the airstream, also connected via a pipe to the other half of the airspeed indicator.

In spite of the fact that the air stream flows across the static port, there's no Bernoulli like reduction of pressure with increase in air speed. The pressure from the static port is almost identical to the ambient pressure of the air at that altitude, independent of the aircraft's airspeed (within the range of airspeed that an aircraft like a Cessna 182 can achieve).

Pitot-static_system

Search for the small reference to static port at this site, one of the sites complained about in the section "A common misconception about wings", but it's difficult to argue with the reality that static ports work.

lift.htm

Jeffareid (talk) 05:43, 16 March 2008 (UTC)

In most cases, with respect to the Earth, the plane is moving much faster than the "real" airspeed. So, first take a frame of reference with respect to the air, such that the air is stagnant and the plane is moving. If the static port is at a position where the flow speed induced by the moving plane is small, the static port opening just moves along different positions with (near) stagnant air, and it will measure the ambient pressure. However, the pitot port in this reference frame is pushing against the air it encounters, moving the air aside as the pitot port passes. In fact we have a instationary flow since fluid parcels, first at rest before the plane arrives, will accelerate and decelerate as the plane passes. The versions of the Bernoulli equation in this article are all for stationary flow, and are invalid for instationary flow (although, for potential flow, versions exist for instationary flow, incorporating time-derivatives of the velocity potential).

So, it is more convenient to study the situation from a reference frame attached to the plane, which is stationary and where the air moves. Because of Galilean invariance both reference frames must be equally valid to describe this situation, provided the plane is flying at constant speed. In this reference frame where the air is flowing, the pitot port is at a stagnation point of the air flow, and the static port is at a point where the air speed is (almost) equal to the incoming air speed V, so by Bernoulli's principle the pressure is lowered by the amount ½ρV² at the static port and far ahead of the plane in the free air stream. Therefor the static port is again measuring the ambient pressure (provided it is located in a suitable location where the air speed is near V). Crowsnest (talk) 21:35, 16 March 2008 (UTC)

My point is similar to that of the link just above; that the same argument for relative air flow across a wing being responsible for lift should also apply to the static port, but that the static port pressure is the same as ambient, indepenent of the aircraft's speed (within the range of a Cessna 182). Regarding lift, it's not the velocity, but rather the acceleration of air that creates lift and drag. I prefer to use an air based frame of reference, because it's clear that air is mostly accelerated downwards (inducing a lifting reaction force), and forwards (inducing a drag reaction force), and it's easier to visualize lift to drag ratios using the air as a frame of reference. I think the Nasa link at the end of the ariticle does a good job, in explaining lift while trying to avoid all the differing explanations for it. My concern is all too often, Bernoulli based explanations of lift involve "hump theory" and/or include diagrams that don't show any downward component of airflow behind an airfoil. Jeffareid (talk) 06:46, 17 March 2008 (UTC)

• Hi Jeffareid. The hump theory (or equal transit-time theory) is wrong. Everyone agrees on that point. Bernoulli's principle is not wrong. Sadly, a lot of people (including Anderson & Eberhardt in Understanding Flight) think you can only discard the equal transit-time theory if you also discard Bernoulli's principle. Anderson & Eberhardt deserve to be pilloried in the aviation hall of infamy. Some of their comments are no more valid than saying 'Newton's Laws of Motion are incorrect because the earth is not flat.' (Linking the hump theory and Bernoulli is like linking Newton and the flat-earth theory.) Dolphin51 (talk) 06:58, 17 March 2008 (UTC)

My issue with hump theory was more generic, that aifoils need positive camber, in which case I post a link of a picture of my favorite exception, the m2-f2.jpg. My issue with Bernoulli lift explanation, is not equal transit, but that all too often, web site diagrams show horizontal air flow in front and behind the wing, as opposed to showing downwards flow behind the wing. It is known that wings peform work on air, and the penalty is induced drag, along with formulas to caculate it: induced drag. However I haven't seen how these formulas could be derived from a Bernoulli based explanation of lift. My personal preference for explaining lift is that wings deflect air downwards (lift) and a bit forwards (drag) (I really don't care how), and in the case of a typical cambered airfoil, it's a combination of Coanda and what some refer to as void effect (a solid passing through the air leaves a void behind it, and with an effective angle of attack, this void is above as well as behind a wing). Jeffareid (talk) 08:48, 17 March 2008 (UTC)

Is your argument that Bernoulli's principle is wrong?

No, just that it's not a good method to explain lift.

Or that positive camber has no effect on lift?

The main goal of positive camber is to improve lift to drag ratio. Increasing effective angle of attack will increase lift with any reasonable airfoil, positive camber or not. If a typical positive cambered air foil is flown backwards, it will have a much worse lift to drag ratio than a symmetrical airfoil, so it's not just positive camber, but the actual airfoil design, (the "hump" needs to be near the front if on top, and near the back if on the bottom).

Or that static ports would work just as well if you put them on the top of the wing on your Cessna?

Nope, only that static ports work just fine regardless of the air speed of an aircraft such as a Cessna.

...Any of these assertions would require extraordinary proof... If your argument is that some people misunderstand or misapply Bernoulli, I think that is already over-explained in the "misconceptions" section. (I'll add a link to the pitot tube page in case so readers can consider the mathematical relationship between static and dynamic pressure used to calculate airspeed.) ComputerGeezer (talk) 15:07, 17 March 2008 (UTC)

I'm not concerned about the pitot tube or airspeed indicator. Both the altimeter and vertical speed inidcator only use the static port (and don't use the pitot port). Jeffareid (talk) 01:27, 18 March 2008 (UTC)

Lift cannot be "explained" by Bernoulli's principle. For given flow kinematics, Bernoulli's principle gives a means to calculate the dynamics, which is the pressure (just outside the boundary layer). But the kinematics have to be determined beforehand, and that is a different story. So, in my opinion, trying to explain lift or misconceptions about that is outside the realm of this article.

I like Jeffareid's association of lift with downward acceleration (and resulting downward flow) of the air, which is a nice demonstration of Newton's laws of motion. Crowsnest (talk) 17:24, 17 March 2008 (UTC)

Real World Application

On 25 March the use of wing lift to illustrate Bernoulli's principle was deleted from Real World Application by an anonymous editor. (This is not the first time it has been deleted.) I reinstated the deletion, but it was deleted again, with the suggestion it was a dubious example (although no explanation of why it might be dubious.) The deleted text contained the following reference:
When a stream of air flows past an airfoil, there are local changes in velocity round the airfoil, and consequently changes in static pressure, in accordance with Bernoulli’s Theorem. The distribution of pressure determines the lift, pitching moment and form drag of the airfoil, and the position of its centre of pressure.” Clancy, L.J., Aerodynamics , Section 5.5
This is a very, very powerful reference in support of the notion that the lift on a wing is a good example of Bernoulli's principle in action. In contrast, none of the Bernoulli Sceptics who have deleted this text or others like it, have ever provided a reference of any kind to support their scepticism about the applicability of Bernoulli to the lift on a wing.

The threshold for inclusion in Wikipedia is verifiability, not truth. See WP:Verifiability. Why is it that the Bernoulli Sceptics feel they are exempt from the general principle in Wikipedia that sources must be quoted? Why is it that the example of lift on a wing, comprehensively supported by a reference to L.J. Clancy's excellent book Aerodynamics, is deleted but the explanation that accompanies that deletion is conspicuously devoid of any reference or source, except perhaps a suggestion that editors should look at the Talk page to see all the debate there. (WP Talk pages are not sources!)

Can we agree that the spirit of WP:Verifiability is that if an inclusion cannot be supported by an adequate reference it can be deleted; and if deletion of an adequately sourced statement cannot be supported by a reference, that deletion should be reverted? Dolphin51 (talk) 12:10, 25 March 2008 (UTC)

Dolphin, first off I am not the editor in question, when I edit this page, unless I forget, I log in. Secondly stop calling people "bernoulli sceptics". Its a with us/against us type label the use of which in unacceptable, and dances around WP:NPA - they are editors and their thoughts are more complex than such classifications allow. I am abstaining from commenting on this paragraph in the text. Apologies for the slightly rant like remark, and if there exist concerns about this comment, lets move it to my talk page. Kind regards User A1 (talk) 22:49, 25 March 2008 (UTC)

I wasn't involved either, but I'll offer a critique that is almost relevant. I notice the section contains phrases like "very much faster", "much lower" and "very fast". In technical material, adverbs are poor substitute for quantitative information. In my experience, the words "much" and "very" are correlated with with bogus ideas and myths. 75.16.46.75 (talk) 23:00, 26 March 2008 (UTC)

• It would be nice to be able to write something like "the air flows around one side of a wing 37% faster than around the other side", but unfortunately that wouldn't be true. The velocity distribution around a given wing section varies with airspeed, lift coefficient, Reynolds Number and Mach number. It is possible to grasp the situation by seeing Joukowsky transform. At the end of the day, Bernoulli's principle is not about the velocity distribution around solid bodies. It can be used to bridge the gap between the velocity distribution and the pressure distribution. As the article says, "Bernoulli's principle does not explain WHY the air flows faster past the top of the wing and slower past the under-side." Dolphin51 (talk) 00:30, 27 March 2008 (UTC)

Intended replacement "A common misconception about wings"

I intent to remove A common misconception about wings, and replace it by a section on how to compute lift using given flow kinematics and an appropriate form of the Bernoulli equation. The reason is that the section "A common misconception about wings" is not about whether Bernoulli's principle is right or wrong, not even about misusing Bernoulli's principle, but about ways to calculate lift. The idea is to replace it with a new "Integral force" or "lift force section", giving some equations how to calculate force from pressure, plus:

• refer to the Lift (force) page, and
• say that there are misconceptions about how to calculate lift, giving links to e.g. lift (force)#Equal_transit-time,
• that there are other ways to calculate lift than by the Bernoulli equation (again link to lift article).

I intent to copy the present "Misconception" section to this talk page, and say something about it on the talk page of lift (force). Crowsnest (talk) 20:41, 27 March 2008 (UTC)

Hi Crowsnest. Thanks very much for raising your intentions on this Talk page, and giving other editors the opportunity to contribute. So many editors simply delete an area of text, leaving other editors to rectify the damage.

You say you intend to remove A common misconception about wings. The reason you give is that this section “is not about whether Bernoulli's principle is right or wrong, not even about misusing Bernoulli's principle, but about ways to calculate lift.” Your meaning is not clear, but I assume you are saying this section should be about ways to calculate lift. I disagree. The article is about Bernoulli’s principle, not about lift, and certainly not about calculating lift. There is an abundance of information about calculating lift here. The section “A common misconception about wings” is not about calculating lift, nor should it be. I agree that the title “A common misconception etc” is not an accurate summary of the information that follows, but that is for historical reasons – see this section prior to my comprehensive re-write on 29 January 2008. I wrote the present content of “A common misconception” and I would welcome someone else coming up with a more accurate title. The present content in “A common misconception” gives an accurate and honest coverage of two alternative views of Bernoulli’s principle and its application to lift on wings. These alternative views are entirely legitimate and are accompanied by appropriate citations. Removing these two alternative views of Bernoulli’s principle would be tantamount to censorship and I would object to it. Placing these two views on the Talk page would not be an acceptable alternative.

You propose adding to Bernoulli's principle a new section giving equations on how to calculate force from pressure. I suggest such equations are appropriate to Lift (force) but are not appropriate to Bernoulli’s principle. Lift (force) already has a suitable opening for more such equations here. Such equations are unrelated to the information about “Stick and Rudder” and “Understanding Flight”, so such equations should not be considered a replacement for the information about these two books. I would be very happy to see people considering improving the information about these two books, but I would not be happy to see the information deleted, regardless of whether it is replaced by equations about how to calculate lift.

You propose writing that the equal transit time myth is an example of a misconception of how to calculate lift. The equal transit time myth is not about calculating lift. It is about explaining lift for student pilots and newcomers to aviation for whom Bernoulli’s principle is too advanced.

You also propose making a comment that there are alternatives to Bernoulli when calculating lift. Would this serve any purpose? For example, conservation of momentum can be used as an alternative to Newton’s Second Law of Motion, but do you see any value in amending the WP article on Newton’s Second Law of Motion to point out that there are alternatives to this Law when doing calculations in kinematics? Do you see any value in amending the WP article on momentum to point out that there are alternatives to the principle of conservation of momentum?

You have made a number of additions to Wikipedia articles but I don’t recall any citations accompanying your additions to confirm their verifiability. The threshold for inclusion in Wikipedia is verifiability, not truth - see WP:Verifiability. Please ensure that your substantial additions are adequately supported by citations in the form of references that confirm the verifiability of those additions. Happy editing. Dolphin51 (talk) 23:48, 27 March 2008 (UTC)

Well, there seems to be nothing wrong with the amount of references in this section, but all is wrong with it being here in the first place. Bernoulli's principle is about a constant of motion along streamlines (or for potential flows in the whole fluid domain), which can be used to determine the local flow dynamics (pressure) for given flow kinematics, not on how to determine (directly) an integral lift force on wings. To obtain the lift force, you need to compute the flow kinematics, which is outside the scope of Bernoulli's principle.

Further, the first two examples are more like book reviews of two individual books, than an encyclopedic topical description of common misconceptions. In my opinion, while interesting, and containing many references to other sources, such book reviews contesting the claims of the authors are original research. Some more comments on the three topics in this section:

• "Stick and Rudder" is just giving the POV of Langewiesche on the ways how he likes to explain lift. Not about the validity of Bernoulli's principle. Further it is misleading: the reader may easily get the impression that Bernoulli's principle is different from Newton's 2nd law of motion, while it is just determined as a first integral of the momentum equation.
• "Understanding Flight", is also about different ways to explain lift. Misconceptions on the Coandă effect relation with lift are clearly already explained in Lift (force).
• "Equal transit-time fallacy" doe not even mention Bernoulli's principle, and is already described well on Lift (force). Further there is the List of works with the equal transit-time fallacy.

Bernoulli's principle is a tool, very handy in many applications, but (perhaps) not to "explain" lift. I think the emphasis in this article should be on how to use Bernoulli's principle. The hammer article, for instance, also does not contain a section: how not to use a hammer.

Just removing this section and leaving a copy on the talk page, and linking to Lift (force) is a good solution, in my opinion. I think it better to refrain from adding a lift section here, given all controversies about lift.

Crowsnest (talk) 09:21, 28 March 2008 (UTC)

While reading through the section I ran across a seeming contradiction in the article. There is this quote from Anderson and Eberhardt which the section claims is incorrect:

“The acceleration of air over the top of a wing is the result of the lowered pressure and not the cause of the lowered pressure.”

The article intro says:

"(when) the speed increases it can only be because the fluid on that section has moved from a region of higher pressure to a region of lower pressure"

which sounds completely consistent with the supposedly incorrect quote from Anderson and Eberhardt's -- both say that acceleration is the result of a pressure gradient. How is it that one of the statements is wrong? Spiel496 (talk) 22:40, 28 March 2008 (UTC)

The problem is that Bernoulli does not say whether velocity change causes pressure change, or pressure change causes velocity change; it just relates the two. Whether one "causes" the other should be argued in lift (force), not here.

I think a "misunderstandings about Bernoulli" section might be appropriate if properly referenced. But the existing section is really OR that should not be on the main page. (It is, however, valuable work which we should preserve to prevent the original error from being re-introduced on the main page.) ComputerGeezer (talk) 23:35, 28 March 2008 (UTC)

Bernoulli's principle, for incompressible flow without additional forcing by e.g. gravity, just says that pressure changes are balanced by velocity changes. It does not say anything directly about cause and effect, in that respect.

However, Bernoulli's principle is derived from Newton's 2nd law of motion for a fluid parcel, describing the change of momentum due to forcing. In that respect pressure changes, if considered as external forces, could be described as causing the velocity changes. But, the pressure changes are also the result of the interacting fluid parcels: in incompressible flow the pressure is ensuring that the volume of fluid elements does not change.

So, there is an interaction between pressure and velocity (momentum, kinetic energy), not a one-way action.

In that respect, the first statement is formally incorrect, since it states that velocity changes are caused by pressure changes. The second statement is correct, since it implies a balance between pressure changes and associated velocity (kinetic energy) changes. Crowsnest (talk) 23:52, 28 March 2008 (UTC)

Talk page archive

The talk page is growing very long. Any objection to it being archived? Ongoing discussions will be left here. Crowsnest (talk) 10:29, 28 March 2008 (UTC)

I have no objection to the oldest material being archived. Dolphin51 (talk) 12:10, 28 March 2008 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Bernoulli's principle/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

=Bernoulli%27s_principle&oldid=91607917 version reviewed This is a very good article. The intro mentions Euler might have got there first but I have read the contrary. More historical perspective in the introduction. The lift section has more space rubbishing an incorrect theory. Has the basic theory could do with some more explanation in the maths. Rex the first talk | contribs

Last edited at 02:16, 3 December 2006 (UTC). Substituted at 20:04, 2 May 2016 (UTC)