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That air in the upper side has accelerated to pass through an smaller cross section than it occupied before and after (there was other mass or air a bit further away from the wing that didn't want to make more space for it and a solid wing below). See how the lines got closer in the upper side and further apart from each other (so the air slowed down and increased in cross section) in the lower side. It is like a small constriction, as in Bernoulli, only the constriction is relatively open and only closed in one side. Or at least that is one way to look at it (I am a Newtonian and think in terms of individual molecules behaving like a collective).

Edit: very interesting how much air that seemed bound for the lower side chooses to go to the upper side instead. I guess this is another effect that would be lost with my zero thickness leading edge.
Edit 2: I just tested it in this CFD toy for iPhone and the effect is still there with sharp, flow aligned leading edges (which by the way, made a decent-ish wing in the toy). I guess the accelerated flow from the convex side manages to suck in/enthrall some flow that would otherwise belong in the concave side. And interesting, that effect, just by itself, effectively creates a roundish effective leading edge.

tok-tokkie wrote:Here is the Cambridge video:
http://www.youtube.com/watch?v=UqBmdZ-BNig

It clearly shows that the air does flow faster on the upper side.
What puzzles me is what happens afterwards?
If the leading edge of the upper & lower flows never got back into sync then there would be an accumulation of air along the upper path - because there is more air leaving the upper trailing edge each second.
Obviously that is nonsense since precisely the same quantity of air is entering each path of the system on the left so the same quantity must be leaving each path of the system on the right.
OK the video is not showing the air leaving the system on the right - that is still further to the right & it is in that unshown area that the mass balance must be restored.
What happens? Just a lot of turbulance as it sorts itself out?
But that contradicts what Kiril says in the post above this.
Going back to the statement I made that there is more air leaving the upper trailing edge each second. That does not make sense because where did the extra air come from?


The air has expanded to fill a bigger volume?
So if it has expanded then it is not incompressible flow?

Not so much “more” air as faster air at lower pressure, i.e. less dense according to Bernoulli.

Bernoulli's equation applies to incompressible flows: it can be modified for a compressible version, but we are not seeing that in the movie.

Check wiki:
http://en.wikipedia.org/wiki/Bernoulli's_principle

or this good pdf from an american uni:
http://www.google.it/url?sa=t&rct=j&q=b ... 7112,d.ZWU

@olefud: with "less dense" you mean with lower pressure but the same density, isn't it?

In low Mach numbers (definetly the ones seen by a F1 car, I posted it once, don't remember right now) air is treated as incompressible.

shelly wrote:Bernoulli's equation applies to incompressible flows: it can be modified for a compressible version, but we are not seeing that in the movie.

Check wiki:
http://en.wikipedia.org/wiki/Bernoulli's_principle

or this good pdf from an american uni:
http://www.google.it/url?sa=t&rct=j&q=b ... 7112,d.ZWU

@olefud: with "less dense" you mean with lower pressure but the same density, isn't it?

Bernoulli’s principle in my frame of reference says that speeding up a fluid flow will lower its pressure/density. When air molecules speed up they essentially become spaced further apart thus lowering the pressure. This works for wings and a carburetor venturi for instance. The equations may differ for compressible and incompressible fluids but the principle is sound for both.

There’s a standing argument as to whether a wing develops lift/downforce because of the pressure difference on opposing surface sides (Bernoulli) or because of the reaction to movement of air in the up/down wash (Newton). The former is supported by the calculable center of pressure on the wing where the resolved ΔP forces act. The latter by the up/down wash being equal in the mass x acceleration force to the actual lift/downforce though it occurs at the trailing edge of the wing. My view is that both views are right and the effects are integrally related.

What happened to the circulation theroy? Back in the day I grasped the concept and it made everything else pretty easy to figure out.
http://www.onemetre.net/design/downwash ... Circul.htm

No Lotus wrote:A rounded edge is necessary to give a broader drag bucket. What that means is that the airfoil performs well at a broader range of angles of attack. A sharp edge is actually fine IF the airfoil is kept at its designed angle of attack.

While I know little about aerodynamics, your comment seems to make sense. The bluff LE works better with changes in AoA. This would seem to make sense with an airfoil used for aircraft wings or horizontal stabilizer surfaces, that are subject to large variations in AoA due to directional pitch changes. But for a race car wing that is subject to relatively small pitch changes, wouldn't a sharper LE profile give better performance?

riff_raff wrote:

No Lotus wrote:A rounded edge is necessary to give a broader drag bucket. What that means is that the airfoil performs well at a broader range of angles of attack. A sharp edge is actually fine IF the airfoil is kept at its designed angle of attack.

theres a lot more to it or everyone would just have thick foils. For one drag buckets are less useful for a race car than an airplane because there isnt a cruising attitude and its rare to have only a single element wing in that sort of AOA range. Anything with that advanced of aero work will be something with more downforce and probably two+ element wing(s).

Sometimes I will do a thinner foil and vary the alpha across the span to reduce pitch sensitivity.... always weighing compromises and what makes sense all things considered, especially adjustment range (which exactly the opposite need of pitch sensitivity) and drag. If you have front wings it gets easier to be more efficient overall since you can trim via front adjust and optimise the rear wing for a fixed position, like they do in F1. Rear wing will have much more effect on total drag so you can get a more efficient package overall like that if you address sensitivity in other ways.

olefud wrote:...When air molecules speed up they essentially become spaced further apart thus lowering the pressure...

No, they do not become spaced further apart, if the flow is surrounded by more gas at similar pressure. The volume of a portion of gas does not change (within uncompressible conditions), only it's shape as you squeeze it through a narrower cross section, the same as wide and narrows sections of a river. When gas speeds up its molecules use some of their internal kinetic energy (random motion) to create net kinetic energy as the total energy content is constant. With less internal energy, the relative motion of one molecule respective to the others is reduced (random Browninan motion is reduced) and you have less collisions with any given surface, less energetic collisions, or both, and that is what you observe as reduced pressure. The relative distance between molecules stays constant (within reasonable limits which produce incompressible flow) and the gas density stays constant. If accelerated flows had reduced density they would float.

olefud wrote:There’s a standing argument as to whether a wing develops lift/downforce because of the pressure difference on opposing surface sides (Bernoulli) or because of the reaction to movement of air in the up/down wash (Newton). The former is supported by the calculable center of pressure on the wing where the resolved ΔP forces act. The latter by the up/down wash being equal in the mass x acceleration force to the actual lift/downforce though it occurs at the trailing edge of the wing. My view is that both views are right and the effects are integrally related.

Of course both are solid laws of physics. If they assumptions hold, they both must be obeyed and hold. Real life flows obey both Newton and Bernoulli. They are just different ways to describe (in language) the same overly complicated phenomenon. So we agree, but I would remove the "in my view" part. They are proven laws of physics.

Edit: I hope this didn't sound too harsh. I might be wrong as my statistical thermodynamics knowledge has been rusting for years. Thinking of the simplified "expansion against a vacuum" system, but with a partial vacuum only, would indeed suggest that expansion takes place as well (and cooling, so maybe that's why there is no floating?), but when one considers the real life counterpart where the gas is surrounded by other gases at the same temperature and pressure which must be taken into acount, and that pressure effects travel back and forth at the speed of sound, it all gets so hopelessly complicated!

Thanks for the discussion. It made me realise during the night that I was considering just the X direction. It is, in fact, similar to a thin stream of falling water. Always the same volume (and mass) passing any point - but as the velocity increases the stream stretches = decreased Y dimension in the case of the air flowing over the wing.


A thicker slower moving stream below the wing is moving just as much air as the faster thinner stream above the wing. I had not appreciated that previously. Also the upper stream unites with a portion of the lower stream that was ahead of it in the free stream ahead of the wing.

'----------------------------------------------


Here is the exam question.
In this picture it is clear that the lower white streams get thicker as they slow down.
Conversely the dark streams get thinner. How is that possible?
Discuss for 10 marks.

tok-tokkie wrote: Here is the exam question.
In this picture it is clear that the lower white streams get thicker as they slow down.
Conversely the dark streams get thinner. How is that possible?
Discuss for 10 marks.

Isn't this(the thicker and thinner streamlines) just the effect of turning the smoke stream on and off?
Watch the video and look at the streamlines before they reach the profile, they already have this shape right from the start.

hollus wrote:

olefud wrote:...When air molecules speed up they essentially become spaced further apart thus lowering the pressure...

No, they do not become spaced further apart, if the flow is surrounded by more gas at similar pressure. The volume of a portion of gas does not change (within uncompressible conditions), only it's shape as you squeeze it through a narrower cross section, the same as wide and narrows sections of a river. When gas speeds up its molecules use some of their internal kinetic energy (random motion) to create net kinetic energy as the total energy content is constant. With less internal energy, the relative motion of one molecule respective to the others is reduced (random Browninan motion is reduced) and you have less collisions with any given surface, less energetic collisions, or both, and that is what you observe as reduced pressure. The relative distance between molecules stays constant (within reasonable limits which produce incompressible flow) and the gas density stays constant. If accelerated flows had reduced density they would float.

olefud wrote:There’s a standing argument as to whether a wing develops lift/downforce because of the pressure difference on opposing surface sides (Bernoulli) or because of the reaction to movement of air in the up/down wash (Newton). The former is supported by the calculable center of pressure on the wing where the resolved ΔP forces act. The latter by the up/down wash being equal in the mass x acceleration force to the actual lift/downforce though it occurs at the trailing edge of the wing. My view is that both views are right and the effects are integrally related.

Of course both are solid laws of physics. If they assumptions hold, they both must be obeyed and hold. Real life flows obey both Newton and Bernoulli. They are just different ways to describe (in language) the same overly complicated phenomenon. So we agree, but I would remove the "in my view" part. They are proven laws of physics.

Edit: I hope this didn't sound too harsh. I might be wrong as my statistical thermodynamics knowledge has been rusting for years. Thinking of the simplified "expansion against a vacuum" system, but with a partial vacuum only, would indeed suggest that expansion takes place as well (and cooling, so maybe that's why there is no floating?), but when one considers the real life counterpart where the gas is surrounded by other gases at the same temperature and pressure which must be taken into acount, and that pressure effects travel back and forth at the speed of sound, it all gets so hopelessly complicated!

Constructive criticism is always welcome –how else will I become more knowledgeable?

My thinking on further apart goes like this –In a compressible gas the net mean velocity of the gas at rest is zero in that velocity is a vector quantity. As a portion of the gas is accelerated in a common direction, as over wing camber, the net mean velocity of the accelerated gas differs from that at rest. Thus over the accelerating volume the two volumes of gas, each having mutually differing net mean velocities, move apart. Air molecules are free to do this while water, being incompressible, is not.

A crude example is a stream of auto traffic moving from a low speed limit to a higher one. As each vehicle reaches the change area it accelerates and increases the distance from the following vehicle that has yet to accelerate.

Newton vs. Bernoulli is a bit like torque vs. horsepower –it’s better not to ruffle feathers.

The scenario you described is the same as in expansion of a gas against a vacuum, and leads to expansion and cooling of the gas left behind. the car example is a bit like that, that car group does not change in cross section. Nor are they surrounded by other cars that want the same space. The situation here is more akin to people leaving a concert venue through a narrow corridor only to find another agglomeration on the other side. The acceleration is temporary, not permanent.
The concept of expanding is incompatible with the assumption of incompressibility, but then, with gas molecules moving each at 500m/s, I don't dare to say that it doesn't happen to a fraction of 1 percent.

Edit: Loving the discussion, by the way, and nice to get a functional answer to the original question as well.

olefud wrote: Bernoulli’s principle in my frame of reference says that speeding up a fluid flow will lower its pressure/density. When air molecules speed up they essentially become spaced further apart thus lowering the pressure. This works for wings and a carburetor venturi for instance. The equations may differ for compressible and incompressible fluids but the principle is sound for both.

Bernoulli's equation says that when speed increase pressure decreases while density remains constant. Air behaves like water at slow speeds - density stays constant.
The exmple of the car you made is a bit misleading. 1d-traffic equations are hyperbolic - i.e. have the same mathematical character of navier-stokes equations when air flow is supersonic, that is so fast that air behaves as compressible.

At slow speeds air is treated as incompressible - it is a mathematical model that cuts out the energy equation (which is a modelling semplification) but it works very well.

As far as Newton and Bernoulli, besides advising everybody to try and find and read "How airplanes really fly - Stop abusing Bernoulli" what I can say is that bernoulli's equation is nothing else that the newtonian momentum conservation equation rewritten under some hypotesis (irrotational motion,no viscous effects etc) - but I agree with you: better not stir it up (otherwise we would brake the non viscous, irrotational hypoteses!)

shelly wrote:

olefud wrote: Bernoulli’s principle in my frame of reference says that speeding up a fluid flow will lower its pressure/density. When air molecules speed up they essentially become spaced further apart thus lowering the pressure. This works for wings and a carburetor venturi for instance. The equations may differ for compressible and incompressible fluids but the principle is sound for both.

Bernoulli's equation says that when speed increase pressure decreases while density remains constant. Air behaves like water at slow speeds - density stays constant.
The exmple of the car you made is a bit misleading. 1d-traffic equations are hyperbolic - i.e. have the same mathematical character of navier-stokes equations when air flow is supersonic, that is so fast that air behaves as compressible.

At slow speeds air is treated as incompressible - it is a mathematical model that cuts out the energy equation (which is a modelling semplification) but it works very well.

As far as Newton and Bernoulli, besides advising everybody to try and find and read "How airplanes really fly - Stop abusing Bernoulli" what I can say is that bernoulli's equation is nothing else that the newtonian momentum conservation equation rewritten under some hypotesis (irrotational motion,no viscous effects etc) - but I agree with you: better not stir it up (otherwise we would brake the non viscous, irrotational hypoteses!)

Point taken. I may have got caught up in one of the simplifying metaphors rampant in aero. Let’s not move on to vortices. And the comment about Bernoulli’s equation treating air as incompressible –as opposed to applying only to incompressible fluids- is now understood.