Zet

I get it. I was wrong. (Well, I don't totally get it. I need to spend some time studying this area of physics. But I get, I think, the basic overall logic of it.) So, when we have two electromagnets attracted to one another (and they have been for some time) the "center of energy density" is halfway between them (assuming the two electromagnets are the same). They are accelerating towards one another. One is then turned off. It stops accelerating. But the other one (the still turned on one) continues to accelerate for a while. This increased amount of momentum of the one electromagnet in one direction is offset by the "center of energy density" moving in the opposite direction towards this still accelerating magnet (the still turned on magnet). And so increased motion in one direction is matched by increased motion in the other direction. The increased mass times velocity of the accelerating electromagnet is equally matched by the mass times velocity of the moving "center of energy density" (and the decreasing amount of energy density) in the opposite direction. If I've stated this right, then I get it. ("Get it" is the broadest of meanings.) Cool. Thank you. I realize my snootiness is not forgivable, but I do apologize. Take care!

. Yes, the supplicant has the burden of proof and not the pedagogue, if he is trying to prove something. However, if the supplicant asks a question and the pedagogue does not directly answer the question but rather points to a field of study, then, presumably, the teacher is saying that the answer lays in that area of study, and simply leaves it to the student to put the pieces together. So, in the thought experiment above where there are two electromagnets and they are turned on and off in such a way that the one is set into greater motion towards the other, if the response to “how is momentum is conserved?” is “electromagnetic fields have momentum” then presumably the answer lays in this aspect of physics (and it is just up to the student to put the pieces together). So, we have the one mass (the one electromagnet) set into more motion in one direction, and if momentum is conserved because “electromagnetic fields have momentum” then this must mean that the electromagnetic field moving towards this now moving magnet speeds up to offset the magnet’s increased velocity. But this would mean that the electromagnetic field is now moving faster than the speed of light. And it cannot. So, yes, this tangent was ignored in the statement of the thought experiment. But noting this absence, and noting it in such a way as to suggest that in it lays the answer to how this law is not violated is misleading at best. It appears to answer, or it appears to point to an answer, to the question but it does not. And this should then be called out. Yes? No? When the one electromagnet is set into more motion than the equal mass of the other electromagnet, how is Newton’s Third Law not violated? ? .

There is nothing in your last post that I disagree with. However, there is nothing in you last post that addresses the issue. No one is asking you to give us a MOOC on electromagnetic theory. The issue raised is whether or not the third law of motion is violated in this case. And no one is even asking you in particular to address this either. However, if you seemly purport to have addressed it and seemly purport to have put the matter to rest, but you actually don't, then you are going to get called out on it. You seem to conclude with the speed of changes in a magnetic field in a vacuum transmit at the speed of light ( c ). Okay? Again, I don't disagree with you, but what does this have to do with addressing the issue? As far as I can tell, this is not a conclusion as to why there is not a violation, but rather this is a restatement of an initial premise.

"Newton's third law is only seemingly violated in such situations. You need to remember that the electromagnetic field itself carries momentum." - ajb Okay. So make your case. Assertions are like opinions ... everybody's got one.

. Um ... ? .

. hey moth ... I believe I understand your point. In a closed system, the amount of energy in that system, is frame dependent. If you move from one inertial frame of reference to another, say in a system such as the Universe, the total amount of energy within that system will change. And so if you look at things from the faster moving magnet at rest and from the slower moving magnet at rest, you will get two different amounts of total energies between the two systems. Is this what you’re getting at? If so, I tried to address this in endnote #9 (but, again, the endnotes are superfluous to the question). Let me know what you think. And thank you for already telling me some of what you think! - Zet (PS: I am mistrustful of large font arguments too. That’s why I consider post #24 to be a failed “reductio ad absurdum with font formatting” attempt. At no time have I enlarged my fonts; only diminished them and grayed them. I simply offered to enlarge my fonts, if that is what he was complaining about in post #24. I don’t know.) .

. I don’t. My original post is an easy read but it is very long. And I totally understand the idea that no one wants to waste their time reading that much text “knowing” that there must be some simple flaw (or flaws) buried somewhere in all that text. I get it. That’s why I spent time working with the issue to present it in another way and in a much shorter form (post #21). I don’t see how anyone could read your post #24 as anything other than a complaint about my use of fonts and their formatting. If there is another hidden implication in your single sentence response, I missed it. If anyone (“people”) other than John Cuthber is reading this, do you also find the text of the question in post #21, as written, something that has to be “struggled” with in order to get through? I’d like to know. I tried to make the issue as simple as possible. And I had believed that I had succeeded in this in post #21. But, now, John Cuthber is making the claim that the language and/or concepts are not clear in post #21 and if any of you others in the forum have attempted to understand it it was a “struggle” for you. Others, please let me know if this “struggle” is, in fact, also true for you. Thank you. - Zet .

. I guess I would characterize your response as “reductio ad absurdum with font formatting.” That’s it? Am I to understand that the problem with my question in post #21 is not logical or factual but rather “an improper use of fonts”? The endnotes in post #21 are superfluous to the question and so are accordingly diminished in size. They are merely there in anticipation of the kinds of tangential issues that may arise when addressing the question. The actual question itself should be easily readable. I realize the original post in this thread is very long and probably no one (or hardly anyone) read it. But the reformulated question in post #21 (sans endnotes) only takes a couple of minutes to read. Does anyone have anything to say about the substance of the issue raised in post #21? (BTW: I can repost the text of post #21 in a large plain format such as 18 point Courier New. Would you like me to do so?) .

. Silence, generally, means consent. “Silence implies consent” http://c2.com/cgi/wiki?SilenceImpliesConsent “he who is silent is taken to agree” http://en.wikipedia.org/wiki/Silence_procedure “Silence means consent” https://www.englishclub.com/ref/esl/Sayings/S/Silence_means_consent_925.htm “Silence gives consent” http://idioms.thefreedictionary.com/Silence+gives+consent Can I take the collective silence of the members of Science Forums to mean that I found a violation of the Law of Conservation of Energy in post #21? (I realize my original post in this thread is very long, but I worked hard to present the issue in a much shorter form in post #21 (especially if you just look at the question and ignore the endnotes).) Or, is my question in post #21 so embarrassingly stupid that it’s not worth anyone’s time to comment? Or, something else? ? .

. Hello. If anyone has the time, could you please show me why the question in post #21 does not lead to a violation of the Law of Conservation of Energy? Thank you. - Zet I’m always willing to learn. I worked hard on the question. .

. (Please note: I posted this question as its own new separate thread ... I thought it was distinct enough to warrant a new conversation ... I was wrong ... I misjudged the parameters of the rules of this forum ... I apologize ... I hope that I am now able/allowed to post it here, in this thread, even though I've already posted it in its own separate (and locked) thread ... thank you ... and, again, I apologize for my misjudgment.) There is an even simpler form of this question; with demagnetized and moving magnets. There are two closed systems. In terms of energy each system is identical. In each system, there are two magnetically aligned ferromagnets. One is fixed in place, and the other one is in motion moving towards the fixed one due to their mutual attraction. In each system, there is a chemical heat pack. If the chemicals are exposed to one another thermal energy will be generated. The temperature in the vicinity of the heat pack after the chemical exposure will be greater than the Curie temperature of the ferromagnets. (And after that, the thermal energy will then dissipate throughout the rest of the system.) The chemical heat pack is placed at one location in the one system and in the other system the chemical heat pack is placed near the fixed magnet. In both systems, when the two magnets in the two sets are the same distance apart, and when the moving magnet is near the heat pack in the one system, the chemicals are exposed to one another. The temperature in the vicinity of heat pack increases to more than the Curie temperature of the ferromagnets. One magnet is each system becomes demagnetized. (The magnets are close enough to one another to be attracted to one another (even if only slightly) while far enough away from one another so that the magnetic field of the other non-demagnetized magnet is not strong enough to keep the heated magnet externally significantly magnetically aligned.) There is a of loss mutual attraction between the two magnets. The remaining amount of potential energy between them as they have gotten closer is now gone. The demagnetized magnet is immediately cut off from the mutual attraction. But the lack of mutual attraction takes some time to make its way across the distance to the still magnetized magnet. It remains attracted to the other magnet for a while longer. The means in the case where it is the moving magnet that is demagnetized the moving demagnetized magnet immediately ceases to continue to accelerate, while in the other case where it is the fixed magnet that is demagnetized the moving still magnetized magnet continues to accelerate for a little while longer. In the end, in both systems, the thermal energy will dissipate throughout the entire closed system and both magnets within it will be raised above their Curie temperatures. The two moving magnets, in the two different systems, will continue to move. In the end the two systems are identical in many respects. There is the same decrease in chemical potential energy. There is the same increase in energy in the form of the magnets’ demagnetizations. And there is an increase in thermal energy. In the one system, there is, however, more kinetic energy in the end than in the other. And since both systems started out identical energy-wise they must end up with identical total amounts of energy, according to the logic of the Law of Conservation of Energy. And so, in the end, in the case with more kinetic energy there must be less of another form of energy, and in the other case with less kinetic energy there must be more of this other form of energy. What is it? Or, is there a flaw in the logic of the “Laws of Physics” in this situation? ? --- Endnotes. 1: The demagnetized state is the higher energy state and the magnetized state is the lower energy state (but this is irrelevant to the issue presented here). 2: It is a loss in thermal energy that demagnetizes each magnet and thus raises each magnet’s energy state. 3: The only possibility I can see is, in the end, there must be less thermal energy in the system with more kinetic energy and more thermal energy in the system with less kinetic energy. This means it must take more energy to demagnetize the fixed magnet (a greater decrease in thermal energy) and where the moving magnet continues to accelerate, and less energy to demagnetize the moving magnet (a lesser decrease in thermal energy) and where the moving magnet immediately discontinues to accelerate. But if anything it seems as if the exact opposite should be true. As the moving magnet moves towards the fixed magnet the strength of the moving magnet’s field moves too. Whereas the moving magnet moves across positions where the strength of the fixed magnet is already there. And so, at the time of demagnetization of each different magnet in the two cases, when the distance between the two magnets in both sets is identical, the strength of the magnetic field from the fixed magnet on the moving magnet could be stronger than the strength of the magnetic field from the moving magnet on the fixed magnet. And it stands to reason that the stronger the external magnetic field is on the demagnetizing magnet the more energy it would take to demagnetize it. But this leads to the exact opposite conclusion needed. This leads to that it would then take more energy to demagnetize the moving magnet, which is also the case where there is less kinetic energy in the end, and so there would both be less kinetic energy and less thermal energy than in the other case. This only exacerbates the problem. 4: There is also an empirical answer, if one has the skills and resources to find it. However, regardless of what the empirical answer turns out to be, the logic must work first or no matter what the empirical answer turns up to be it will not be one where energy is conserved. 5: If the loss of mutual attraction does not take time to cross the distance between the two magnets and to the still magnetized magnet, but is rather instantaneous, then this would lead to all sorts of Special Theory of Relativity paradoxes. 6: The “demagnetized” magnet will never fully become magnetically disaligned. And so, the moving magnets will continue to accelerate after the “demagnetization” of itself or the other magnet. However the residual magnetic alignment and the remaining continued acceleration are so minuscule so as to be reasonably ignored. 7: In reality, no mutually attracted body is “fixed in place.” They both are moving towards one another. But if the “fixed in place” magnets in the two systems above are connected to a massive body such as planet Earth, then the acceleration of the “fixed in place” magnet and the associated massive body is so miniscule so as to be reasonably ignored. There is an equal increase in momentum in opposite directions between the “moving” magnet and the “fixed in place” magnet and associated massive body (p = mv), but the increase in kinetic energy of the “fixed in place” magnet and associated massive body is miniscule compared to the increase in kinetic energy of the “moving” magnet and so can be reasonably ignored (ke = ½mv2). (However, whether it is the “moving” magnetic that continues to accelerate for a time while the other demagnetized body and associated massive body does not or whether it is the “fixed in place” magnet” and associated massive body continues to accelerate for a while while the other demagnetized body does not, either way, there is also a possible violation of the Law of Conservation of Momentum.) 8: The fact that one magnet is in motion relative to the chemical heat pack and the other magnet is not is irrelevant unlike other aspects of magnetic movement, such as Lenz’ Law, where the nature of any relative motion is a factor. 9: When two bodies are in two different motions, such as the faster moving magnet in the one system versus the slower moving magnet in the other system, they are in two different frames. And the total amount of energy can vary between frames. However, the two frames in comparison here are the two “fixed in place” frames and not the frames from the perspective of the “moving” bodies at rest, and so the total amount of energies between the two systems considered are in the same frame and so must end up with the same total amounts of energy in each for the logic of the Law of Conservation of Energy to not be violated. .

. A Question about the Logic of the Law of Conservation of Energy with Demagnetized and Moving Magnets. There are two closed systems. In terms of energy each system is identical. In each system, there are two magnetically aligned ferromagnets. One is fixed in place, and the other one is in motion moving towards the fixed one due to their mutual attraction. In each system, there is a chemical heat pack. If the chemicals are exposed to one another thermal energy will be generated. The temperature in the vicinity of the heat pack after the chemical exposure will be greater than the Curie temperature of the ferromagnets. (And after that, the thermal energy will then dissipate throughout the rest of the system.) The chemical heat pack is placed at one location in the one system and in the other system the chemical heat pack is placed near the fixed magnet. In both systems, when the two magnets in the two sets are the same distance apart, and when the moving magnet is near the heat pack in the one system, the chemicals are exposed to one another. The temperature in the vicinity of heat pack increases to more than the Curie temperature of the ferromagnets. One magnet is each system becomes demagnetized. (The magnets are close enough to one another to be attracted to one another (even if only slightly) while far enough away from one another so that the magnetic field of the other non-demagnetized magnet is not strong enough to keep the heated magnet externally significantly magnetically aligned.) There is a of loss mutual attraction between the two magnets. The remaining amount of potential energy between them as they have gotten closer is now gone. The demagnetized magnet is immediately cut off from the mutual attraction. But the lack of mutual attraction takes some time to make its way across the distance to the still magnetized magnet. It remains attracted to the other magnet for a while longer. The means in the case where it is the moving magnet that is demagnetized the moving demagnetized magnet immediately ceases to continue to accelerate, while in the other case where it is the fixed magnet that is demagnetized the moving still magnetized magnet continues to accelerate for a little while longer. In the end, in both systems, the thermal energy will dissipate throughout the entire closed system and both magnets within it will be raised above their Curie temperatures. The two moving magnets, in the two different systems, will continue to move. In the end the two systems are identical in many respects. There is the same decrease in chemical potential energy. There is the same increase in energy in the form of the magnets’ demagnetizations. And there is an increase in thermal energy. In the one system, there is, however, more kinetic energy in the end than in the other. And since both systems started out identical energy-wise they must end up with identical total amounts of energy, according to the logic of the Law of Conservation of Energy. And so, in the end, in the case with more kinetic energy there must be less of another form of energy, and in the other case with less kinetic energy there must be more of this other form of energy. What is it? Or, is there a flaw in the logic of the “Laws of Physics” in this situation? ? --- Endnotes. 1: The demagnetized state is the higher energy state and the magnetized state is the lower energy state (but this is irrelevant to the issue presented here). 2: It is a loss in thermal energy that demagnetizes each magnet and thus raises each magnet’s energy state. 3: The only possibility I can see is, in the end, there must be less thermal energy in the system with more kinetic energy and more thermal energy in the system with less kinetic energy. This means it must take more energy to demagnetize the fixed magnet (a greater decrease in thermal energy) and where the moving magnet continues to accelerate, and less energy to demagnetize the moving magnet (a lesser decrease in thermal energy) and where the moving magnet immediately discontinues to accelerate. But if anything it seems as if the exact opposite should be true. As the moving magnet moves towards the fixed magnet the strength of the moving magnet’s field moves too. Whereas the moving magnet moves across positions where the strength of the fixed magnet is already there. And so, at the time of demagnetization of each different magnet in the two cases, when the distance between the two magnets in both sets is identical, the strength of the magnetic field from the fixed magnet on the moving magnet could be stronger than the strength of the magnetic field from the moving magnet on the fixed magnet. And it stands to reason that the stronger the external magnetic field is on the demagnetizing magnet the more energy it would take to demagnetize it. But this leads to the exact opposite conclusion needed. This leads to that it would then take more energy to demagnetize the moving magnet, which is also the case where there is less kinetic energy in the end, and so there would both be less kinetic energy and less thermal energy than in the other case. This only exacerbates the problem. 4: There is also an empirical answer, if one has the skills and resources to find it. However, regardless of what the empirical answer turns out to be, the logic must work first or no matter what the empirical answer turns up to be it will not be one where energy is conserved. 5: If the loss of mutual attraction does not take time to cross the distance between the two magnets and to the still magnetized magnet, but is rather instantaneous, then this would lead to all sorts of Special Theory of Relativity paradoxes. 6: The “demagnetized” magnet will never fully become magnetically disaligned. And so, the moving magnets will continue to accelerate after the “demagnetization” of itself or the other magnet. However the residual magnetic alignment and the remaining continued acceleration are so minuscule so as to be reasonably ignored. 7: In reality, no mutually attracted body is “fixed in place.” They both are moving towards one another. But if the “fixed in place” magnets in the two systems above are connected to a massive body such as planet Earth, then the acceleration of the “fixed in place” magnet and the associated massive body is so miniscule so as to be reasonably ignored. There is an equal increase in momentum in opposite directions between the “moving” magnet and the “fixed in place” magnet and associated massive body (p = mv), but the increase in kinetic energy of the “fixed in place” magnet and associated massive body is miniscule compared to the increase in kinetic energy of the “moving” magnet and so can be reasonably ignored (ke = ½mv2). (However, whether it is the “moving” magnetic that continues to accelerate for a time while the other demagnetized body and associated massive body does not or whether it is the “fixed in place” magnet” and associated massive body continues to accelerate for a while while the other demagnetized body does not, either way, there is also a possible violation of the Law of Conservation of Momentum.) 8: The fact that one magnet is in motion relative to the chemical heat pack and the other magnet is not is irrelevant unlike other aspects of magnetic movement, such as Lenz’ Law, where the nature of any relative motion is a factor. 9: When two bodies are in two different motions, such as the faster moving magnet in the one system versus the slower moving magnet in the other system, they are in two different frames. And the total amount of energy can vary between frames. However, the two frames in comparison here are the two “fixed in place” frames and not the frames from the perspective of the “moving” bodies at rest, and so the total amount of energies between the two systems considered are in the same frame and so must end up with the same total amounts of energy in each for the logic of the Law of Conservation of Energy to not be violated. .

. The demagnetized state is the higher energy state and magnetized state is the lower energy state. “... this torque tends to line up the magnetic moment with the magnetic field B, so this represents its lowest energy configuration” http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html “... the energy is lowest when the magnetic moment is aligned with the magnetic field.” http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magpot.html “This reduces the electrostatic energy of the electrons when their spins are parallel compared to their energy when the spins are anti-parallel, so the parallel-spin state is more stable.” http://en.wikipedia.org/wiki/Ferromagnetism “This "spin flip" places some of the spins in their higher energy state. If the radio frequency signal is then switched off, the relaxation of the spins back to the lower state ...” http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/nmr.html But this is irrelevant to the issue presented here. .

Yeah. I tried to set up my thought experiment to avoid issues of “thrust” or “different amounts of initial kinetic energy” and just get to where I’m having a problem (different decreases in pressures on the top and bottom adding to the rise of the airfoils). I tried, ... but I don’t think I succeeded. Airfoils are complicated things, and I probably should stay away from them. I do thank you all for adding to my understanding of the issue. Whether you all believe me or not, I have learned from this discussion. Thank you for all of your time, effort, and ... patience!

. So, when the fluid moves over the airfoil there is a certain amount of "dynamic" potential energy. If the airfoil is free to rise, it will. When it rises this potential energy becomes kinetic energy. Okay ... cool. What then happens to this "dynamic" potential energy when the airfoil does not rise ... and after the fluid passes and this potential energy is then gone? The Law of Conservation of Energy states that energy can change forms, but the total amount remains. Are you suggesting that there was an amount of energy in the form of "dynamic" potential energy in the non-rising case and then this amount of energy is then gone (without an offsetting change in another form of energy)? If so, you are suggesting a violation of the Law of Conservation of Energy. ?

Right. If the neutrally buoyant solid starts out in the fluid and then rises in the fluid and remains in the fluid, then there is no increase in gravitational potential energy in both the non-rising and rising cases. There is, rather, an increase in the vertical kinetic energy of the rising solid and displaced fluid downwards in the rising case that does not occur in the non-rising case. This is one way to formulate the question. However, if the non-rising solid and the rising solid (neutrally buoyant when in the fluid when static) emerge from the fluid in the end, then, with the one solid is higher than the other, there is a difference in gravitational potential energies. This is another way to formulate essentially the same question. (I find it easier to talk about differences in gravitational potential energies between the two airfoils in the end, rather than differences in vertical kinetic energies. But, either way, the logic and the issue remain the same.)

Okay, I misunderstood you when I said it would seem strange to me but not to you that there would be the same lesser increases in the swirl in the rising cases where airfoils of equal masses and volumes but of different shapes rise. Cool. But, I think, you are still saying that (it is not strange to you that) there would be the same overall decrease in the kinetic energy (in all off its various forms, including horizontal and swirling motions) of the fluid (when the differently shaped airfoils of equal mass and equal volume all rise the same distance) to offset the same increases in gravitational potential energy (in the form of these differently shaped risen airfoils)? Yes? No? If I now have your position right ... it still seems strange to me. For me, this is counterintuitive. I would think that when differently shaped airfoils of equal mass and volume all rise the same distance that there would be different amounts of swirl plus horizontal motion and that it wouldn’t all add up in the end to be the same decrease in kinetic energy (overall) in every case. But, that’s just my gut. Or maybe I still don’t understand your position. The “input” energy in this system is a certain amount of gravitational potential energy in the L shaped container of fluid. As the fluid drains out of the container (and so there is a decrease in this gravitational potential energy) there is an increase in kinetic energy in the form of the moving fluid. When the moving fluid encounters the airfoil in the horizontal part of the L shaped container, there is a greater decrease in the pressure pushing down on the top of the solid and a lesser decrease in the pressure pushing up on the bottom of the solid. And so, the otherwise neutrally buoyant body will rise (if allowed to do so). The “input” energy at this point (the only option for the rise of the airfoil) is the kinetic energy of the moving fluid (the original gravitational potential energy of the fluid is beyond the scope of the analyses at this point as the fluid moves horizontally across the bottom of the L. And we can assume that this fluid ends up in the same bucket at the same height below the same L shaped container in every case in the end and so there is the same decrease in gravitational potential energy in the form of falling fluid in each case. And so this cannot be the offsetting form of energy for the increase in gravitational potential energy in the rise of differently shaped airfoils). And so, if differently shaped airfoils (all of equal mass and volume) are all in frictionless tracks that allow them to rise the same distance (and if the original height of the L shaped column of fluid and so the subsequent flow of fluid is far beyond that needed to get all of the differently shaped airfoils to all rise that same small little height), then there is the same increase in gravitational potential energy in this form, in the end, in each case, and so ... for energy to be conserved ... there must be the same decrease in another (the “input”) form of energy. It is the flow of the fluid over and under the airfoil (and the subsequent different decreases in pressures) that causes the airfoil to rise. But, I would expect, as it appears perhaps you do too, that the “input” energy (the (gravitational potential energy turned into) kinetic energy) would be different (different amounts of kinetic energy (in all its various motions)) in the end. No? So, perhaps I’m still missing your point. (I do that a lot.) The idea that there would be the same decrease in the overall amount of kinetic energy (in all of its various forms) in the end for each rising differently shaped airfoil case seems counterintuitive ... to me. (But, that my intuitions are wrong, is no surprise either.) ? Right. There are two different ... related and overlapping ... analyses here. One is the mechanics of a rising airfoil with no angle of attack. The other is the analysis of how energy is conserved. And while they are two different analyses they both must work in tandem. When an airfoil rises the mechanics of this dynamic must work out in such a way so as energy is conserved. If, mechanically, when an airfoil rises as opposed to when it does not then if in the end there is less overall motion of the fluid (less kinetic energy) then this (mechanical reason) resolves the overlapping conservation of energy analysis where the increase in gravitational potential energy of the rising airfoil (plus the increase in vertical kinetic energy) is offset (logically) by an equal decrease in the overall kinetic energy of the moving fluid. (Whether this is happening in real physical life is another matter and only answered by experimentation, but, for the purposes in this thread, the logic works.) And then, in the next step in this line of analysis where I compared differently shaped airfoils of equal mass and volumes all rising the same difference, I used these two overlapping analysis in the reverse (to find the former). If we know energy must be conserved (which is must in this forum) then we know that when the differently shaped airfoils of equal mass and volume all rise the same distance (and so there is the same increase, in the end, in gravitational potential energy, in this form) that (... even though it seems counterintuitive to me ...) there must be mechanically the same decrease in the overall amount of kinetic energy of the moving fluid (in all of it various motions) in each differently shaped rising case in order for energy to be conserved (since there are no other energy change options). And we can know this to a logical certainty. So, you’re right, I did dodge the direct question of the mechanics of differently shaped airfoils rising and whether or not this would lead to the same lesser overall kinetic energy in the rising versus the non-rising cases. But, logically, I got there just the same. For energy to be conserved, there must be the same lesser amount of kinetic energy (in all it various motions) of the fluid for every risen differently shaped airfoil of equal mass and equal volume to offset the equal increases, in the end, in gravitational potential energy (in the form of these risen bodies). No? And if the Mechanics of Physics are within the bounds of logic (which it must be) then we know this is mechanically what happens ... and we know this to a logical certainty. No? ? --- I don’t know. If it is, I’m cool with changing it from an L to a U. The logic and the issue remain the same. Yep. Yep. Yep. For energy to be conserved, then in the non-rising case the fluid must reach the same height (on the right side) as when it first started (on the left side). And, for energy to be conserved, then in the rising case (where there is an increase in gravitational potential energy in the form of the risen body) there must be an equal decrease in another form of energy. And the only energy change option is the kinetic energy of the moving fluid as it passes over and under the airfoil and thus the height is rises to on the right hand side. The logic and the issue remain the same. Cheers!

Larry, The link to SU2 was fascinating (post #108). I was a c (… not a c++ …) programmer back in the mid-nineties. And … I’m guessing some things have probably changed by now. (If you ever need a mean DOS batch file programmer, I’m your guy.) I couldn’t get the NASA link to work (post #112). I reloaded Java and downloaded the Java Control Panel and followed their instructions under “security settings” for Windows 8 and greater but I couldn’t get the Java Control Panel to let me type or paste in the web site URL in the excepted list box. I guess I’m getting old. It looks cool, and perhaps very promising for perhaps resolving this thread. I’ll keep trying to get it to work on my (new but very low end) laptop. Could this piece of software (even if only in beta and even if only approximately) answer/address whether or not there would be the same decrease in the swirl for differently shaped airfoils of equal mass and volume all rising the same distance as opposed to when they don’t rise? That would be exciting. --- And, whether or not it is okay to stipulate a perfectly incompressible fluid in a thought experiment, I don’t know. I trust you that it is. But, if it’s not, this doesn’t change the logic of the issue. In post #83 I wrote: “The fluid is incompressible and has zero viscosity.” But … perhaps … I should have written: “The fluid is as theoretically close to incompressible as possible which is something greater than zero and the viscosity of the fluid is as low as theoretically possible which is greater than zero.” (Again, assuming it’s not simply okay to just stipulate zero compressibility and zero viscosity.) And then I could have gone on (in a thus modified post #83) to say, “And with the compressibility of the fluid so miniscule and so therefore with any internal pressure energy changes so minor, any pressure changes in the fluid itself in this thought experiment can reasonably (or “justifiably”) be ignored for the ease of analysis … and ditto for the impacts of a something greater than zero amount of viscosity.” No? ? --- J.C.MacSwell, Are you saying whether not there is an upward “dynamic buoyant” force on an otherwise neutrally buoyant body that this is not a factor in whether or not it rises? (Or, are you saying it is not part of “lift” … that word? If so, and if the presence of a “dynamic upward buoyant” force is a factor in whether or not the body rises (along with the rest of the factors falling under “lift”), then the body rises, in part, due to the “non-lift” factor (or whatever you want to call it) of an increased upward “dynamic buoyant” force. No?) ? ?

Essay: ""But I find it physically doubtful." Why? Not me; it seems very straightforward, about the extra turbulence, that each would be different, though very difficult to measure accurately enough to see the relatively tiny and chaotic differences." This can be argued a different way … at this point … and in the inverse. In this forum we must assume all of the Laws of Physics as axioms. One of those is energy can change forms but the total amount of energy always remains. (The Law of Conservation of Energy). And so, your intuition must be right and mine must be wrong. It seems strange to me that each one of the differently shaped airfoils all of equal mass and volume all produce the same lesser increase in the overall amount of kinetic energy in the decrease in the swirl in the rising case than in the non-rising case in the fluid in the end, but to you it does not. However, if energy is conserved (… and it must …) and if the only energy change option available is the same decrease in the overall amounts of kinetic energy in the fluid in the end when differently shaped airfoils of equal mass and volume all rise the same distance then they must all have the same lesser increase in the swirl in the rising case than in the non-rising case. Accepting the premises of Physics, one of which is the total amount of energy must always remain the same, then the only way for this to happen is your intuition must be right and my intuition must be wrong. And we can know this to a logical certainty. I’m sure I’ll never be fully comfortable with this answer ( … just to honest … ) but I accept the logic. Thank you all for helping me out with this! Cheers! --- A possible test. Sheldon on tv told a story about Archimedes measuring the amount of gold in the king’s crown by submersing it in a fluid. In a real friction filled world , such as ours , the motion of the fluid in both cases will come to a stop. There will be a decrease in kinetic energy and an equal increase in thermal energy. So, we could measure the temperatures of the two cases in the end (after all of the motion of the fluid has come to a stop) and the one should be higher than the other. Or … mass energy equivalence … after the end the of thought experiment the one airfoil is lowered half the distance and the other airfoil is raised half the distance between them , and so different actual motions but similar that any energy change difference between the two will be negligible if not zero , and then weight the two cases and the one should weight more than the other. So, two possible tests. ?

K?

Are you comfortable with “The increase in vertical kinetic energy and in gravitational potential energy is offset by an equal decrease in the kinetic energy of the fluid” (if that, in fact, is how it is offset)? --- If there is more force on an object in one direction (more force from the pressure pushing up on the bottom of the solid) and if there is less force on the same object in the other direction (the force from the pressure pushing down on the top of the object plus its weight) then it will move (upwards) if it is free to do so (and it will not move upwards, even though there is an overall upward force on it, if it is fixed in place). When it moves upwards there is an increase in vertical kinetic energy (in the form of the moving solid upwards and displaced fluid downwards) and there is an increase in gravitational potential energy (and if it is prevented from moving then there will not be these same energy increases). And so … for energy to be conserved … there must be a decrease (an equal decrease) in another form (or forms) of energy (that does not also occur when the airfoil is prevented from rising). When MigL suggested adding an angle of attack (in his thought experiment of a tilted flat hand outside the window of a moving car) that could be addressed in and of itself (the bottom of the airfoil will collide with the fluid and the airfoil will be redirected upwards and the air will be redirected downward due to this. There is an increase in vertical kinetic energy and there will be an equal decrease in horizontal kinetic energy. Energy is conserved.) There was no need to address and include every other aspect of this system to understand this part of it. The same thing here. If there is more upward force than downward force then the solid will rise if it is free to do so and it will not if is prevented from doing so. And if it rises then there is an increase in vertical kinetic energy and in gravitational energy. And so there must be a decrease in another form of energy that does not occur when it does not. What is it? --- J.C.MacSwell’s logic works. There is an increase in vertical kinetic energy and in gravitational potential energy in the one case that does not occur in the other. And so, if there is an equal decrease in the kinetic energy of the fluid (overall in all of its various motions) in the one case that does not occur in the other then (… ta-da! …) energy is conserved. The logic works, but we still need a link to a reputable web site showing that this in fact physically the case. (Just because this logically works out, does not mean that this necessarily is what is happening in the real physical world.) And (assuming for the moment that this is right, that there is a greater decrease in the overall kinetic energy of the moving fluid in the rising case than in the non-rising case), there is still a problem then with the next step in this conservation of energy analysis. If (in the thought experiment in post #83) there are differently shaped neutrally buoyant airfoils all of equal masses and of equal volumes in the horizontal part of the L shaped container, then when the fluid drains out of the L shaped container there will a greater decrease in pressure pushing down of the top of each one and a lesser decrease in pressure pushing up on the bottom each one. If they are free to rise then they will do so. In the end (since each differently shaped airfoil is of the same mass and volume) there will be the same increase in gravitational potential energy. (There is not only an increase in gravitational potential energy when the airfoils rise but also an increase in vertical kinetic energy. And so, the odds are that when each differently shaped airfoil rises they will do so at differently velocities (thus different vertical kinetic energies). If what brings the rising airfoils to a stop (when the reach the top of the frictionless track that allows them to move vertically but not horizontally) is a perfectly elastic collision (such as compressing a hypothetically perfect spring) then all of the vertical kinetic energy of the rising solid will become an equal amount of elastic potential energy. Energy is conserved. This will balance out in and of itself. And the vertically moving fluid displaced downwards becomes part of the rest of the overall movement of the fluid.) If (… if …) energy is conserved when the airfoil rises because there is a greater decrease in the overall kinetic energy of the fluid than when it is prevented from rising, then this additional decrease in the kinetic energy of the fluid must be the same in every rising case and regardless of the shape of the airfoil. It could be. The logic works. But I find it doubtful. When each differently shaped airfoil is held in place and the fluid passes over it (the odds are) there will different amounts of drag and turbulence in each case. And when each differently shaped airfoil rises, it stands to reason, that if there is an lesser increase in the turbulence that it would be different lesser increases in each case due to them having different shapes (and not regardless of their shapes). The logic works. But I find it physically doubtful. ? --- (Modesty? Your post was very detailed.) I understand that the rise of an airfoil can be explained in terms of Newton’s Third Law of Motion (or also in terms of the Law of Conservation of Momentum). But this still doesn’t get around the fact that when a fluid and an airfoil are in relative motion then there is an overall upward force on an otherwise neutrally buoyant body and it will rise if free to do so. And so, regardless of whatever else is causing this rising airfoil to rise (and regardless of the conservation of energy analyses involved in those other aspects), there must be a decrease in another form of energy to offset the increase in gravitational potential energy from this contributing factor. (And I’m guessing you and I are in agreement about this.) Yep. (I keep using the terms “dynamic pressure” and “dynamic buoyant force” but I just made those up because they seem descriptively accurate but I don’t know if they are, in fact, the correct terms I should be using. You said “static pressure.” Is that right? Typo?) Yep. All of your questions are also my questions. Thanks for the links! --- ? --- (And while J.C.MacSwell is the only one who has come up with a workable (logically workable) answer in this thread (... as far as I can tell ...), I’m still hesitant about it, and not so sure this is, in fact, how the real physical world works (based on the next step in the analysis where then differently shaped rising airfoils of equal mass and volume would all have to have the same lesser increase in turbulence … for energy to be conserved). We need some links!) --- ?

I have no reason to doubt you. But, if you are right, this, I believe, only compounds my problem. This would mean that, in the end, in the case where there is more gravitational potential energy there is also more kinetic energy and, in the end, in the case where there is less gravitational potential energy there is also less kinetic energy. No? --- I have a bad habit of streamlining the description of the example in order to get to, highlight, the part of it I’m having trouble with (e.g. “simply stipulating the fluid is in motion and not including how is was set in motion”). I think this more literal approach seems to work better. I know that there is not just horizontally moving fluid after it encounters the airfoil but also swirling fluid (and downwardly moving fluid). (By just illustrating horizontally moving air I was just trying to (simplify and) get to the point that the fluid must be moving faster in the one case and slower in the other case after encountering the airfoils for energy to be conserved … as it is the only energy change option I can see). The point (that I was trying to make) is the motion (in whatever direction and of whatever type) of the fluid must be less in the one case and more in the other case to offset the different amounts of gravitational potential energies in the two cases in the end (unless there is another energy change option available and I just can’t see it). I hope this more literal drawing works better. --- In a friction filled world, when a fluid is in motion over the surface of a solid, the faster the relative velocity means the greater the skin friction and so the more thermal energy is generated. If a body remains at rest while a fluid flows around it then the relative velocity between the fluid and the solid is greater than if the solid moves along somewhat with and in the direction of the moving fluid. And so if it remains at rest (again, in a friction filled world) there is more skin friction and so more thermal energy generated and if it moves along with the fluid somewhat there is less skin friction and so less thermal energy generated. Friction both generates thermal energy and decreases kinetic energy. And so, in the resting case there is a greater increase in thermal energy and an equal greater decrease in the kinetic energy of the fluid and in the moving along somewhat case there is a lesser increase in thermal energy and an equal lesser decrease in the kinetic energy of the fluid. Energy is conserved. And if a body remains at rest while a fluid flows over it there is no increase in kinetic energy in the form of the moving body while if moving fluid sets the body into motion along with it (if the force from the pressure from the fluid on the body is the cause of that motion) then there is an increase in kinetic energy in the form of the moving solid and there is an equal decrease in kinetic energy in the form of the moving fluid. Energy is conserved. Are you saying that the more or less skin friction there is between a fluid and a solid the more or less pressure there is from that fluid on that solid? (If so, I’ve never heard of this. Do you have a link?) I read (and reread) your post several times, but I didn’t understand the point of “fluid pressure is also a function of heat.” I have never heard of this before. And I would be grateful for a link (!). (The temperature of a fluid affects the density of the fluid and so, in turn, affects the pressure of that fluid at a given depth. But I don’t think you’re saying this?) (And if I have misunderstood you, I apologize. I’m trying.) Are you saying that when a (initially) horizontally moving fluid encounters a horizontally fixed airfoil there is a decrease in the amount of skin friction between them if that airfoil moves vertically that does not occur when the airfoil remains also vertically fixed in place and so less thermal energy is generated when the airfoil rises? If so (but I don’t believe this is or could be the case, unless the velocity of the fluid slows down in the rising case in a way that it doesn’t in the non-rising case (which is what I’ve been saying I think must occur for energy to be conserved all along)) then, since friction both increases thermal energy and decreases kinetic energy, in the non-rising case there would be a decrease in kinetic energy in the form of the moving fluid and an equal increase in thermal energy, while in the rising case there would be a lesser decrease in kinetic energy in the form of the moving fluid and an equal lesser increase in thermal energy. (Energy is, would be, conserved.) If this is what you’re saying (that there less skin friction between the moving fluid and the airfoil when the airfoil vertically rises) then this would balance out in and of itself. --- In this thought experiment, the horizontally fixed and otherwise neutrally buoyant airfoils have different decreases in pressures on the top and bottom of them (as per Bernoulli) when the fluid is in motion, which, in turn, creates an overall upward (dynamic buoyant) force. If allow to rise, the airfoil will. And when the airfoil rises (due to this “dynamic buoyant force”) there is an increase in vertical kinetic energy and in gravitational potential energy that does not occur when the airfoil remains in place. For energy to be conserved there must be a decrease in another form of energy in the rising case that does not occur in the non-rising case. What is it? Yep (in a friction filled world). And this balances out in and of itself. No. In this thought experiment, in the end, there is an increase in gravitational potential energy in the one case that does not occur in the other. And so, for energy to be conserved, there must be a decrease in another form of energy in the one case that does not occur in other. If, after the end of this thought experiment, the one higher up airfoil then falls back down to its original position (where the other airfoil remained) then this greater amount of gravitational potential energy in the one system than in the other becomes a greater amount of kinetic energy in the one system than in the other. (And, you could take it a step further, and you could point out when the falling airfoil comes to a stop there is a decrease in kinetic energy. But there will be an equal increase in thermal energy. And, so, in the one system is more thermal energy than in the other ... unless there was a decrease in another form of energy that does not occur in the other when the imbalance between the two cases in gravitational potential energy was first created.) This simply begs the question. When the airfoil rises there must be a decrease in another form of energy that does not occur when it does not … for energy to be conserved. What is it? --- Whether it is acceptable to stipulate zero viscosity in a thought experiment or not, I don’t know. I trust you that it is. But, if it’s not, it really doesn’t change anything. The logic, and the issue, remain the same. It just makes this thought experiment slightly more complicated if we have to stipulate that “the fluid has the lowest amount of viscosity theoretically possible, which is something greater than zero” rather than “the viscosity of the fluid is zero.” If we stipulate the former, then since the viscosity is so minuscule its impact on this system will then be so minor and so it can be justifiably ignored for the ease of analysis, while if we stipulate the latter, then since there is no viscosity to factor in then it is also not a factor. The logic, and the issue, remain the same. --- This could be it! And so my illustrated simplification of having the fluid after it encounters the airfoils continue on only horizontally was not just trivial, it is a problem. So, if I understand you correctly, in the end there is overall more motion the non-rising case and there is overall less motion in rising case. And it’s just that the difference in kinetic energy between the two cases necessary for energy to be conserved is found in the swirl of the fluid itself (less by the difference in horizontal motion). And, again if I understand you correctly, while, in the end, there is a greater decrease in the horizontal motion of fluid in the non-rising than in the rising case, this is offset and surpassed by an greater increase in the swirling of the fluid in itself in the non-rising case and a lesser increase in the swirling of the fluid in the rising case. And so, in the end, there is less kinetic energy in the rising case (in the form of the moving fluid in all its various motions) and more kinetic energy in the non-rising case (in the form of the moving fluid in all its various motions) and this offsets the different amounts of gravitational potential energy between the two cases (and by a precisely equal amount). Ta-da! If this is right, then this resolves this portion of the conservation of energy analysis! Thank you very much. Do you have a link(s) for this? --- Now, the big question is: does anyone else think J.C.MacSwell (post #89) is right? And, if so, does anyone have a link for that? ? (Essay: I wrote this before reading your post #94. I will read it now and respond to it next time.) Cheers!

Please excuse me for not initially directly addressing the recent comments, but, rather, let me, if it is okay, restate the issue, in a much more literal way and in light of the recent comments, which will hopefully address them in course and eliminate as much extraneous elements as I am able in order to highlight the specific problem I’m having. --- There is an L shaped container of fluid. This is in a closed system and in a frictionless world. The fluid is incompressible and has zero viscosity. In the horizontal part of the container there is a submerged solid. The solid is up above the floor of the container and fixed in place on top of a pole. The solid is neutrally buoyant (it has the same density as the fluid it displaces). And, at the end of the horizontal part of the container there is a door and it is closed. The door is opened and the fluid flows out of the container. All of the fluid drains out of the container. In the end, there is a decrease in gravitational potential energy and there is an equal increase in kinetic energy. (Again, it is frictionless world for the ease of analysis.) Energy is conserved. The same thing is done again. But this time, the submerged solid is curved on the top and flat on the bottom. As the fluid drains out of the container and so moves over and under the submerged solid, due to the shape of the solid there is a greater decrease in pressure on the top and a lesser decrease in pressure on the bottom (as per Bernoulli). So there is now an overall upward force on the otherwise neutrally buoyant solid. The solid is fixed to the end of the pole and does not (cannot) move. All of the fluid drains out of the container. In the end, there is a decrease in gravitational potential energy and there is an equal increase in kinetic energy. Energy is conserved. The same thing is done again for a third time. But this time the submerged solid is not fixed in place on top of the pole but, rather, is in a frictionless track that allows it to move vertically but keeps it in place horizontally. As the fluid drains out of the container and so moves over and under the submerged solid, due to the shape of the solid there is a greater decrease in pressure on the top and a lesser decrease in pressure on the bottom (as per Bernoulli). So there is now an overall upward force on the otherwise neutrally buoyant solid. It is free to rise and so it will. And after it rises, and before all of the fluid drains out of the container, it is fixed in place at its new height. All of the fluid drains out of the container. --- In the second case, where the solid is fixed in place and does not (cannot) rise, in the end, there is a decrease in gravitational potential energy in the form of the falling fluid and there is an equal increase in kinetic energy in the form of the falling fluid. Energy is conserved. In the third case, there is the same decrease in gravitational potential energy in the form of the falling fluid and there is also an increase in kinetic energy in the form of the falling fluid. However, in the third case, where the solid rises, in the end, there is also an increase in gravitational potential energy in the form of the risen solid (and there was also an increase the vertical kinetic energy in the form of the rising solid and displaced fluid downwards), and so there must be a decrease in another form of energy does not occur in the second case. What is it? Less kinetic energy in the falling fluid? (Is it: the moving fluid slows down when the submerged solid rises as opposed to when it is held in place?). Less thermal energy (even though there is no friction)? (Is it: there must be a decrease in friction (and so it cannot be stipulated that there is no friction in this thought experiment) when the submerged solid rises as opposed to when it is held in place?) Less of some other form of energy? (What could it be?) ? --- If my car is running (and so there is a decrease in chemical potential energy) then there must be an equal increase in another form of energy (or energies) for energy to be conserved. Whether this increase is in the form of kinetic and thermal energies or if this increase in all just in the form of thermal energy, either way, energy is conserved. When the airfoil rises there is an increase in gravitational potential energy (and vertical kinetic energy). When the airfoil does not rise there is not an increase in gravitational potential energy (and there is not the same increase in vertical kinetic energy). And so, when the airfoil rises there must be a decrease in another form of energy that does not occur when the airfoil does not (cannot) rise … for energy to be conserved. What is it? --- You are right. I did. I thought being abstract and just stipulating the fluid is “in motion” would be enough. Perhaps I was wrong about that. Hopefully this more literal restatement of the case (with the cause of the motion of the fluid, gravitational attraction, included) works better. --- If an airfoil has an angle of attack, then the bottom of the airfoil collides with the fluid and the fluid is set in motion downwards and the airfoil is set in motion upwards. There is an increase in vertical motion and an equal decrease in horizontal motion (assuming no friction). Energy is conserved. In this thought experiment there is no angle of attack. And this was done on purpose to highlight better the specific issue I’m having with the conservation of energy analysis of a rising airfoil. I believe you and I are in agreement that there must be a decrease in the velocity of the wind (and so a decrease in kinetic energy) when the airfoil rises as opposed to when it does not (since there are no other energy change options, ... at least that I can see). And I believe you and are in agreement that the only mechanical reason for this to happen (that I can see) is that there must be an additional amount of drag when the airfoil rises that does not occur when it is held in place (post #47). Correct? --- I’m not sure I understand what you are saying. Are you saying that when an airfoil rises (and so there is an increase in vertical kinetic energy and gravitational potential energy) that there is an equal decrease in thermal energy? If so, I’m not so sure how this would work (mechanically-wise). --- Thank you all for trying to help me out with this. --- ? .

Is it “thrust”? Did I use that word wrong? If so, I apologize. If a ball is rolling across the floor, and so is in motion, and there is nothing else acting on it, is it simply “in motion” or is there “thrust”? And if there is motion within a fluid and there is nothing else acting on it is it simply “in motion” or is there “thrust”? Yes, the original formulation of this question was about a moving airfoil, and so I ended up in an extended conversation about “thrust” that I didn’t feel helped answer my question. So, in post #46 I changed it so that it was the fluid that is in motion and not the airfoil. I had hoped that this would eliminate this conversation about “thrust” and better highlight my issue. For the wind to be in motion there must have been something that set it in motion. And so, if I understand the word correctly, something must have “thrust” it into motion. But once it is in motion, I believe, if there is nothing else acting on it, then we are beyond “thrust” and, at this point, it is simply “in motion.” No? Again, if I used the term incorrectly I apologize. Perhaps I may have seemed to suggest that the wind will last indefinitely, in which case, you may be suggesting that there needs to be “thrust” to maintain this. If I gave you that impression, I did not mean to. The wind is in motion. It passes over and under the airfoil. And then it moves on. What happens to it after that (when it eventually comes to a stop) is beyond the scope of this thought experiment. (And how it was originally set or “thrust” into motion is beyond the scope of this thought experiment.) ?

(In the thought experiment in post #46 the airfoil is more dense than the fluid. Now it has been changed so that the solid and the surrounding fluid are of the same density. The logic, and the issue, are essentially the same.) Yeah. In this thought experiment there is no “thrust.” The “wind” is simply stipulated to be in in motion before encountering the “airfoil.” And when the moving fluid encounters the “airfoil” it will move more quickly over the top than it does under the bottom (as has been experimentally demonstrated). And so there will be more of a decrease in pressure pushing down on the top and less of a decrease in pressure pushing up on the bottom (as per Bernoulli’s principle). This will cause the otherwise neutrally buoyant “airfoil” to rise. And so there will be an increase in kinetic energy in the form of the vertically rising “airfoil” and in the form of the displaced fluid downwards. And so, for energy to be conserved, there must be a decrease in another form of energy. The obvious answer is a slowing of the “wind” (and so a decrease in kinetic energy in this form) when the “airfoil” rises which does not also occur when the “airfoil” is held in place and does not (cannot) rise. --- Different decreases in pressures on the top and bottom as per Bernoulli’s principle, and so a “dynamic buoyant force” (or whatever it should be called). If the fluid is incompressible, then whether the “wind” moves up or down or in circles or whatever after encountering the “airfoil” then there is no change in the gravitational potential energy of the fluid in and of itself. Again, the obvious answer is that there must be a decrease in the velocity of the “wind” when the “airfoil” rises that does not occur when the “airfoil” kept from rising. (And so the increase in vertical kinetic energy of the rising “airfoil” and falling displaced fluid is offset by an equal decrease in the kinetic energy of the “wind”). I think it must. There is an increase in vertical kinetic energy and so there must be a decrease in another form of energy (... for energy to be conserved). And in this simple scenario there is really only one energy change option: a slowing of the “wind” and so a decrease in kinetic energy in this form. ? .