Editing Bernoulli's principle (section)

== Misconceptions ==
{{main|Lift (force)}}

=== Airfoil lift ===
[[File:Equal transit-time NASA wrong1 en.svg|thumb|right|586px|An illustration of the incorrect equal transit-time explanation of airfoil lift]]

One of the most common erroneous explanations of aerodynamic lift asserts that the air must traverse the upper and lower surfaces of a wing in the same amount of time, implying that since the upper surface presents a longer path the air must be moving over the top of the wing faster than over the bottom. Bernoulli's principle is then cited to conclude that the pressure on top of the wing must be lower than on the bottom.<ref>{{cite book |author=Technical education research center|title=Physics That Works |publisher=Kendall Hunt |location= |year= 2006 | pages= |isbn= 0787291811 | quote = One of the most widely circulated, but incorrect, explanations can be labeled the “Longer Path” theory, or the “Equal Transit Time” theory. |oclc=61918633}}</ref><ref>{{cite journal|quote=The airfoil of the airplane wing, according to the textbook explanation that is more or less standard in the United States, has a special shape with more curvature on top than on the bottom; consequently, the air must travel over the top surface farther than over the bottom surface. Because the air must make the trip over the top and bottom surfaces in the same elapsed time ..., the velocity over the top surface will be greater than over the bottom. According to Bernoulli's theorem, this velocity difference produces a pressure difference which is lift. |title=Bernoulli and Newton in Fluid Mechanics |first=Norman F. |last=Smith |journal=The Physics Teacher |date=November 1972 |volume=10 |issue=8 |page=451 |doi=10.1119/1.2352317 |bibcode=1972PhTea..10..451S |url=http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PHTEAH000010000008000451000001&idtype=cvips&doi=10.1119/1.2352317&prog=normal|url-access=subscription }} {{dead link|date=January 2018|bot=InternetArchiveBot|fix-attempted=yes}}</ref>

Equal transit time applies to the flow around a body generating no lift, but there is no physical principle that requires equal transit time in cases of bodies generating lift. In fact, theory predicts – and experiments confirm – that the air traverses the top surface of a body experiencing lift in a ''shorter'' time than it traverses the bottom surface; the explanation based on equal transit time is false.<ref>{{cite journal|quote=...it is often asked why fluid particles should meet up again at the trailing edge. Or, in other words, why should two particles on either side of the wing take the same time to travel from S to T? There is no obvious explanation and real-life observations prove that this is wrong. |title=How do wings work? |first=Holger |last=Babinsky |journal=Physics Education |volume=38 |issue=6 |date=2003 |pages=497–503 |doi=10.1088/0031-9120/38/6/001 |bibcode=2003PhyEd..38..497B |s2cid=1657792 |url=https://www3.eng.cam.ac.uk/outreach/Project-resources/Wind-turbine/howwingswork.pdf }}</ref><ref>"The actual velocity over the top of an airfoil is much faster than that predicted by the "Longer Path" theory and particles moving over the top arrive at the trailing edge before particles moving under the airfoil."<br>{{cite web|url=https://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html |date=Aug 16, 2000 |title=Incorrect Lift Theory #1 |author=Glenn Research Center|publisher=NASA |access-date=June 27, 2021| archive-url=https://web.archive.org/web/20140427084226/http://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html|archive-date=April 27, 2014}}</ref><ref>{{cite book|last=Anderson|first=John|title=Introduction to Flight|publisher=McGraw-Hill Higher Education|location=Boston|year=2005|isbn=978-0072825695|page=355|quote=It is then assumed that these two elements must meet up at the trailing edge, and because the running distance over the top surface of the airfoil is longer than that over the bottom surface, the element over the top surface must move faster. This is simply not true. Experimental results and computational fluid dynamic calculations clearly show that a fluid element moving over the top surface of an airfoil leaves the trailing edge long before its companion element moving over the bottom surface arrives at the trailing edge.}}</ref> While the equal-time explanation is false, it is not the Bernoulli principle that is false, because this principle is well established; Bernoulli's equation is used correctly in common mathematical treatments of aerodynamic lift.<ref>{{cite web|quote=There is nothing wrong with the Bernoulli principle, or with the statement that the air goes faster over the top of the wing. But, as the above discussion suggests, our understanding is not complete with this explanation. The problem is that we are missing a vital piece when we apply Bernoulli’s principle. We can calculate the pressures around the wing if we know the speed of the air over and under the wing, but how do we determine the speed? |website=How Airplanes Fly: A Physical Description of Lift |first1=David |last1=Anderson |first2=Scott |last2=Eberhardt |url=http://www.allstar.fiu.edu/aero/airflylvl3.htm|title=How Airplanes Fly|access-date=26 January 2016|url-status=live|archive-url=https://web.archive.org/web/20160126200755/http://www.allstar.fiu.edu/aero/airflylvl3.htm|archive-date=January 26, 2016}}</ref><ref>{{cite book|title=Introduction to Flight |first=John D. |last=Anderson |edition=8th |date=2016 |publisher=McGraw-Hill Education |chapter=Chapter 4. Basic Aerodynamics}}</ref>

=== Common classroom demonstrations ===
There are several common classroom demonstrations that are sometimes incorrectly explained using Bernoulli's principle.<ref>"Bernoulli's law and experiments attributed to it are fascinating. Unfortunately some of these experiments are explained erroneously..."  {{cite web |title= Misinterpretations of Bernoulli's Law |last1=Weltner |first1=Klaus |last2=Ingelman-Sundberg |first2=Martin |publisher=Department of Physics, University Frankfurt |url=http://www-stud.rbi.informatik.uni-frankfurt.de/~plass/MIS/mis6.html |access-date=June 25, 2012 |url-status=dead |archive-url= https://web.archive.org/web/20120621073812/http://www-stud.rbi.informatik.uni-frankfurt.de/~plass/MIS/mis6.html |archive-date= June 21, 2012 }}</ref> One involves holding a piece of paper horizontally so that it droops downward and then blowing over the top of it. As the demonstrator blows over the paper, the paper rises. It is then asserted that this is because "faster moving air has lower pressure".<ref>{{cite web| quote= This occurs because of Bernoulli’s principle — fast-moving air has lower pressure than non-moving air.| work= MAKE Magazine |title= Origami Flying Disk| first= Cy |last= Tymony| url= http://makeprojects.com/Project/Origami-Flying-Disk/327/1 |archiveurl= https://archive.today/20130103152803/http://makeprojects.com/Project/Origami-Flying-Disk/327/1%23.UOWjZ33LdRw |archivedate=2013-01-03 }}</ref><ref name=Minnesota>{{cite web| quote= Faster-moving fluid, lower pressure. ... When the demonstrator holds the paper in front of his mouth and blows across the top, he is creating an area of faster-moving air.| title= Bernoulli Effects| publisher= School of Physics and Astronomy, [[University of Minnesota]]| url= http://www.physics.umn.edu/outreach/pforce/circus/Bernoulli.html |archiveurl= https://web.archive.org/web/20120310190206/http://www.physics.umn.edu/outreach/pforce/circus/Bernoulli.html |archivedate= 2012-03-10 }}</ref><ref>{{cite web| quote= Bernoulli's Principle states that faster moving air has lower pressure... You can demonstrate Bernoulli's Principle by blowing over a piece of paper held horizontally across your lips. |publisher= Tall Ships Festival – Channel Islands Harbor |title= Educational Packet |url=http://www.tallshipschannelislands.com/PDFs/Educational_Packet.pdf |access-date=June 25, 2012 |url-status=usurped |archive-url=https://web.archive.org/web/20131203014334/http://www.tallshipschannelislands.com/PDFs/Educational_Packet.pdf |archive-date=December 3, 2013 }}</ref>

One problem with this explanation can be seen by blowing along the bottom of the paper: if the deflection was caused by faster moving air, then the paper should deflect downward; but the paper deflects upward regardless of whether the faster moving air is on the top or the bottom.<ref>{{cite web| quote= If the lift in figure A were caused by "Bernoulli's principle," then the paper in figure B should droop further when air is blown beneath it. However, as shown, it raises when the upward pressure gradient in downward-curving flow adds to atmospheric pressure at the paper lower surface. |first=Gale M. |last=Craig |title=Physical Principles of Winged Flight |url= http://www.rcgroups.com/forums/showatt.php?attachmentid=5305482 |access-date=March 31, 2016 | via= rcgroups.com}}</ref> Another problem is that when the air leaves the demonstrator's mouth it has the ''same'' pressure as the surrounding air;<ref>{{cite journal| quote= In fact, the pressure in the air blown out of the lungs is equal to that of the surrounding air...| title= How Do Wings Work | first= Holger |last= Babinsky |year= 2003 | journal= Physics Education| volume= 38 | number= 6| page= 497 |url= http://iopscience.iop.org/0031-9120/38/6/001/pdf/pe3_6_001.pdf| via= iopscience.iop.org| publisher= IOP Publishing| doi= 10.1088/0031-9120/38/6/001 | bibcode= 2003PhyEd..38..497B | s2cid= 1657792 |access-date= April 7, 2022}}</ref> the air does not have lower pressure just because it is moving; in the demonstration, the static pressure of the air leaving the demonstrator's mouth is ''equal'' to the pressure of the surrounding air.<ref>{{cite journal|quote = ...air does not have a reduced lateral pressure (or static pressure...) simply because it is caused to move, the static pressure of free air does not decrease as the speed of the air increases, it misunderstanding Bernoulli's principle to suggest that this is what it tells us, and the behavior of the curved paper is explained by other reasoning than Bernoulli's principle.|first = Peter|last = Eastwell|title = Bernoulli? Perhaps, but What About Viscosity?|journal = The Science Education Review|volume = 6|issue = 1|date = 2007|url = http://d1vdx9ifs4n5d7.cloudfront.net/s3fs-public/davidson_images/eastwell-bernoulli.pdf|access-date = 2018-03-18|archive-date = 2018-03-18|archive-url = https://web.archive.org/web/20180318183632/http://d1vdx9ifs4n5d7.cloudfront.net/s3fs-public/davidson_images/eastwell-bernoulli.pdf|url-status = dead}}</ref><ref>{{cite web| quote= Make a strip of writing paper about 5&nbsp;cm × 25&nbsp;cm. Hold it in front of your lips so that it hangs out and down making a convex upward surface. When you blow across the top of the paper, it rises. Many books attribute this to the lowering of the air pressure on top solely to the Bernoulli effect. Now use your fingers to form the paper into a curve that it is slightly concave upward along its whole length and again blow along the top of this strip. The paper now bends downward...an often-cited experiment, which is usually taken as demonstrating the common explanation of lift, does not do so...| first= Jef |last= Raskin | title= Coanda Effect: Understanding Why Wings Work| url= http://karmak.org/archive/2003/02/coanda_effect.html| date= February 2003| website= karmak.org| publisher= | access-date= }}</ref> A third problem is that it is false to make a connection between the flow on the two sides of the paper using Bernoulli's equation since the air above and below are ''different'' flow fields and Bernoulli's principle only applies within a flow field.<ref name=Babinsky2>{{cite journal| quote= Blowing over a piece of paper does not demonstrate Bernoulli’s equation. While it is true that a curved paper lifts when flow is applied on one side, this is not because air is moving at different speeds on the two sides... ''It is false to make a connection between the flow on the two sides of the paper using Bernoulli’s equation.''| first= Holger |last= Babinsky |title= How Do Wings Work |journal= Physics Education | year= 2003 |volume= 38| number= 6| page= 497 | url= http://iopscience.iop.org/0031-9120/38/6/001/pdf/pe3_6_001.pdf |via= iopscience.iop.org| publisher= IOP Publishing| doi= 10.1088/0031-9120/38/6/001 | bibcode= 2003PhyEd..38..497B | s2cid= 1657792 |access-date= April 7, 2022}}</ref><ref>{{cite journal|quote =An explanation based on Bernoulli’s principle is not applicable to this situation, because this principle has nothing to say about the interaction of air masses having different speeds... Also, while Bernoulli’s principle allows us to compare fluid speeds and pressures along a single streamline and... along two different streamlines that originate under identical fluid conditions, using Bernoulli’s principle to compare the air above and below the curved paper in Figure 1 is nonsensical; in this case, there aren’t any streamlines at all below the paper!|first =Peter|last =Eastwell|title =Bernoulli? Perhaps, but What About Viscosity?|journal =The Science Education Review|volume =6|issue =1|date =2007|url =http://d1vdx9ifs4n5d7.cloudfront.net/s3fs-public/davidson_images/eastwell-bernoulli.pdf|access-date =2018-03-18|archive-date =2018-03-18|archive-url =https://web.archive.org/web/20180318183632/http://d1vdx9ifs4n5d7.cloudfront.net/s3fs-public/davidson_images/eastwell-bernoulli.pdf|url-status =dead}}</ref><ref>{{cite journal| quote= The well-known demonstration of the phenomenon of lift by means of lifting a page cantilevered in one’s hand by blowing horizontally along it is probably more a demonstration of the forces inherent in the Coanda effect than a demonstration of Bernoulli’s law; for, here, an air jet issues from the mouth and attaches to a curved (and, in this case pliable) surface. The upper edge is a complicated vortex-laden mixing layer and the distant flow is quiescent, so that Bernoulli’s law is hardly applicable.| first= David |last= Auerbach | title= Why Aircraft Fly| journal= [[European Journal of Physics]]| volume= 21 |page= 295| url= http://iopscience.iop.org/0143-0807/21/4/302/pdf/0143-0807_21_4_302.pdf | via= iopscience.iop.org| access-date= }}</ref><ref>{{cite news| quote= Millions of children in science classes are being asked to blow over curved pieces of paper and observe that the paper 'lifts'... They are then asked to believe that Bernoulli's theorem is responsible... Unfortunately, the 'dynamic lift' involved...is not properly explained by Bernoulli's theorem.| first= Norman F. |last= Smith |title= Bernoulli and Newton in Fluid Mechanics| work= The Physics Teacher | date= November 1972| publisher= | access-date= }}</ref>

As the wording of the principle can change its implications, stating the principle correctly is important.<ref>{{cite web| quote= Bernoulli’s principle is very easy to understand provided the principle is correctly stated. However, we must be careful, because seemingly-small changes in the wording can lead to completely wrong conclusions.| title= Bernoulli's Principle| work= See How It Flies| first= John S.| last= Denker | url= http://www.av8n.com/how/htm/airfoils.html#sec-bernoulli| via= av8n.com| publisher= | date= | access-date= }}</ref> What Bernoulli's principle actually says is that within a flow of constant energy, when fluid flows through a region of lower pressure it speeds up and vice versa.<ref>{{cite journal| quote= A complete statement of Bernoulli's Theorem is as follows: 'In a flow where no energy is being added or taken away, the sum of its various energies is a constant: consequently where the velocity increases the pressure decreases and vice versa.'| first= Norman F. |last= Smith |title= Bernoulli, Newton and Dynamic Lift Part I| journal= School Science and Mathematics | year= 1973 | volume= 73 | number= 3| pages= 181–186 | doi= 10.1111/j.1949-8594.1973.tb08998.x | url= http://onlinelibrary.wiley.com/doi/10.1111/j.1949-8594.1973.tb08998.x/pdf| via= wiley.com| access-date= | url-access= subscription }}</ref> Thus, Bernoulli's principle concerns itself with ''changes'' in speed and ''changes'' in pressure ''within'' a flow field. It cannot be used to compare different flow fields.

A correct explanation of why the paper rises would observe that the [[Plume (fluid dynamics)|plume]] follows the curve of the paper and that a curved streamline will develop a pressure gradient perpendicular to the direction of flow, with the lower pressure on the inside of the curve.<ref>{{cite journal| quote= ...if a streamline is curved, there must be a pressure gradient across the streamline, with the pressure increasing in the direction away from the centre of curvature.| title= How Do Wings Work | first= Holger |last= Babinsky |year= 2003 | journal= Physics Education| volume= 38 | number= 6| page= 497 |url= http://iopscience.iop.org/0031-9120/38/6/001/pdf/pe3_6_001.pdf| via= iopscience.iop.org| publisher= IOP Publishing| doi= 10.1088/0031-9120/38/6/001 | bibcode= 2003PhyEd..38..497B | s2cid= 1657792 |access-date= April 7, 2022}}</ref><ref>{{cite journal| quote= The curved paper turns the stream of air downward, and this action produces the lift reaction that lifts the paper.| first= Norman F. |last= Smith |title= Bernoulli, Newton and Dynamic Lift Part II| journal= School Science and Mathematics | year= 1973 | volume= 73 | number= 4| page= 3333| doi= 10.1111/j.1949-8594.1973.tb09040.x | url= http://onlinelibrary.wiley.com/doi/10.1111/j.1949-8594.1973.tb09040.x/pdf| via= wiley.com| access-date= | url-access= subscription}}</ref><ref>{{cite book| quote= The curved surface of the tongue creates unequal air pressure and a lifting action. ... Lift is caused by air moving over a curved surface.| title= Aeronautics: An Educator's Guide with Activities in Science, Mathematics, and Technology Education| publisher= NASA | page= 26 | url= http://www.nasa.gov/pdf/58152main_Aeronautics.Educator.pdf| via= nasa.gov| access-date= }}</ref><ref>{{cite web| quote= Viscosity causes the breath to follow the curved surface, Newton's first law says there a force on the air and Newton’s third law says there is an equal and opposite force on the paper. Momentum transfer lifts the strip. The reduction in pressure acting on the top surface of the piece of paper causes the paper to rise.| title= The Newtonian Description of Lift of a Wing| first1= David F.| last1= Anderson| authorlink1= David F. Anderson| first2= Scott| last2= Eberhardt| page= 12| url= http://www.integener.com/IE110522Anderson%26EberhardtPaperOnLift0902.pdf| via= integener.com| access-date= | archive-date= 2016-03-11| archive-url= https://web.archive.org/web/20160311011153/http://www.integener.com/IE110522Anderson%26EberhardtPaperOnLift0902.pdf| url-status= dead}}</ref> Bernoulli's principle predicts that the decrease in pressure is associated with an increase in speed; in other words, as the air passes over the paper, it speeds up and moves faster than it was moving when it left the demonstrator's mouth. But this is not apparent from the demonstration.<ref>{{cite book| quote= 'Demonstrations' of Bernoulli's principle are often given as demonstrations of the physics of lift. They are truly demonstrations of lift, but certainly not of Bernoulli's principle.| first1= David F.| last1= Anderson | first2= Scott |last2= Eberhardt | title= Understanding Flight| page= [https://books.google.com/books?id=52Hfn7uEGSoC&pg=PA229 229]| isbn= | access-date= | via= Google Books}}</ref><ref>{{cite book| quote= As an example, take the misleading experiment most often used to "demonstrate" Bernoulli's principle. Hold a piece of paper so that it curves over your finger, then blow across the top. The paper will rise. However most people do not realize that the paper would ''not'' rise if it were flat, even though you are blowing air across the top of it at a furious rate. Bernoulli's principle does not apply directly in this case. This is because the air on the two sides of the paper did not start out from the same source. The air on the bottom is ambient air from the room, but the air on the top came from your mouth where you actually increased its speed without decreasing its pressure by forcing it out of your mouth. As a result the air on both sides of the flat paper actually has the same pressure, even though the air on the top is moving faster. The reason that a curved piece of paper does rise is that the air from your mouth speeds up even more as it follows the curve of the paper, which in turn lowers the pressure according to Bernoulli.| title= The Aeronautics File | first= Max |last= Feil | url= https://www.mat.uc.pt/~pedro/ncientificos/artigos/aeronauticsfile1.ps |archiveurl= https://web.archive.org/web/20150517081630/https://www.mat.uc.pt/~pedro/ncientificos/artigos/aeronauticsfile1.ps |archivedate=May 17, 2015 }}</ref><ref>{{cite web| quote= Some people blow over a sheet of paper to demonstrate that the accelerated air over the sheet results in a lower pressure. They are wrong with their explanation. The sheet of paper goes up because it deflects the air, by the Coanda effect, and that deflection is the cause of the force lifting the sheet. To prove they are wrong I use the following experiment: If the sheet of paper is pre bend the other way by first rolling it, and if you blow over it than, it goes down. This is because the air is deflected the other way. Airspeed is still higher above the sheet, so that is not causing the lower pressure.| first= Pim |last= Geurts| website= sailtheory.com | url= http://www.sailtheory.com/experiments.html | title= Some simple Experiments| date= | archiveurl= https://web.archive.org/web/20160303212343/http://www.sailtheory.com/experiments.html |archivedate= 2016-03-03 | publisher= | access-date= April 7, 2022}}</ref>

Other common classroom demonstrations, such as blowing between two suspended spheres, inflating a large bag, or suspending a ball in an airstream are sometimes explained in a similarly misleading manner by saying "faster moving air has lower pressure".<ref>{{cite web|quote=The Bernoulli effect is commonly—and incorrectly—invoked to explain:  :why two suspended balloons or table tennis balls move toward each other when you blow air between them; :why paper rises when you blow air over it; :why a pitched baseball curves; :why a spoon is drawn toward a stream of water; :why a ball remains suspended in an air jet.  Here’s the news: None of these phenomena is the result of the Bernoulli effect. 
|website=Science 101 |title=Q: Is It Really Caused by the Bernoulli Effect? |first=Matt |last=Bobrowsky |publisher=National Science Teaching Association |url=https://www.nsta.org/q-it-really-caused-bernoulli-effect}}</ref><ref>{{cite journal| quote= Finally, let’s go back to the initial example of a ball levitating in a jet of air. The naive explanation for the stability of the ball in the air stream, 'because pressure in the jet is lower than pressure in the surrounding atmosphere,' is clearly incorrect. The static pressure in the free air jet is the same as the pressure in the surrounding atmosphere...| first= Martin |last= Kamela | title= Thinking About Bernoulli| journal= The Physics Teacher | url= http://tpt.aapt.org/resource/1/phteah/v45/i6/p379_s1| publisher= American Association of Physics Teachers| date= September 2007 | volume= 45 | issue= 6 | pages= 379–381 | doi= 10.1119/1.2768700 | bibcode= 2007PhTea..45..379K |archiveurl= https://archive.today/20130223130448/http://tpt.aapt.org/resource/1/phteah/v45/i6/p379_s1| archivedate= February 23, 2013| access-date= | url-access= subscription }}</ref><ref>{{cite journal| quote= Asymmetrical flow (not Bernoulli's theorem) also explains lift on the [[ping-pong ball]] or [[beach ball]] that floats so mysteriously in the tilted vacuum cleaner exhaust...| first= Norman F. |last= Smith |title= Bernoulli and Newton in Fluid Mechanics| journal= The Physics Teacher | date= November 1972| volume= 10 | issue= 8 | page= 455| doi= 10.1119/1.2352317 | bibcode= 1972PhTea..10..451S | access-date= }}</ref><ref>{{cite web| quote= Bernoulli’s theorem is often obscured by demonstrations involving non-Bernoulli forces. For example, a ball may be supported on an upward jet of air or water, because any fluid (the air and water) has viscosity, which retards the slippage of one part of the fluid moving past another part of the fluid. |title=The Bernoulli Conundrum |first=Robert P. |last=Bauman |publisher= Department of Physics, University of Alabama at Birmingham |website= introphysics.info| url=http://www.introphysics.info/Papers/BernoulliConundrumWS.pdf |access-date=June 25, 2012 |url-status= dead |archive-url= https://web.archive.org/web/20120225115505/http://www.introphysics.info/Papers/BernoulliConundrumWS.pdf |archive-date=February 25, 2012 }}</ref><ref>{{cite web| quote= In a demonstration sometimes wrongly described as showing lift due to pressure reduction in moving air or pressure reduction due to flow path restriction, a ball or balloon is suspended by a jet of air. |first=Gale M. |last=Craig |title=Physical Principles of Winged Flight |url=http://www.rcgroups.com/forums/showatt.php?attachmentid=5305482 |access-date= March 31, 2016}}</ref><ref>{{cite web| quote= A second example is the confinement of a [[ping-pong ball]] in the vertical exhaust from a [[hair dryer]]. We are told that this is a demonstration of Bernoulli's principle. But, we now know that the exhaust does not have a lower value of ps. Again, it is momentum transfer that keeps the ball in the airflow. When the ball gets near the edge of the exhaust there is an asymmetric flow around the ball, which pushes it away from the edge of the flow. The same is true when one blows between two ping-pong balls hanging on strings.| title= The Newtonian Description of Lift of a Wing| first1= David F.| last1= Anderson| first2= Scott| last2= Eberhardt| page= 12| url= http://www.integener.com/IE110522Anderson%26EberhardtPaperOnLift0902.pdf| via= integener.com| access-date= | archive-date= 2016-03-11| archive-url= https://web.archive.org/web/20160311011153/http://www.integener.com/IE110522Anderson%26EberhardtPaperOnLift0902.pdf| url-status= dead}}</ref><ref>{{cite web |quote= This demonstration is often incorrectly explained using the Bernoulli principle. According to the INCORRECT explanation, the air flow is faster in the region between the sheets, thus creating a lower pressure compared with the quiet air on the outside of the sheets.| title= Thin Metal Sheets – Coanda Effect |publisher= Physics Lecture-Demonstration Facility, University of Maryland |website= physics.umd.edu |url= https://www.physics.umd.edu/lecdem/services/demos/demosf5/f5-03.htm |access-date=October 23, 2012 |url-status=dead |archive-url= https://web.archive.org/web/20120623121737/http://www.physics.umd.edu/lecdem/services/demos/demosf5/f5-03.htm |archive-date=June 23, 2012 }}</ref><ref>{{cite web| quote= Although the Bernoulli effect is often used to explain this demonstration, and one manufacturer sells the material for this demonstration as 'Bernoulli bags,' it cannot be explained by the Bernoulli effect, but rather by the process of entrainment. |title= Answer #256 |publisher= Physics Lecture-Demonstration Facility, University of Maryland | website= physics.umd.edu |url= https://www.physics.umd.edu/deptinfo/facilities/lecdem/services/QOTW/arch13/a256.htm |access-date=December 9, 2014 |url-status=dead |archive-url= https://web.archive.org/web/20141213125404/http://www.physics.umd.edu/deptinfo/facilities/lecdem/services/QOTW/arch13/a256.htm |archive-date= December 13, 2014 }}</ref>