Blowing between two objects -- Why is the pressure low?

[Fredrik]

I was thinking of what happens to water flowing out of a pipe, in which case the exit pressure is about ambient.

I know that's what you meant. I just don't understand why the water pressure at the exit is equal to the air pressure.

Sure it must be fast to get the air out.

But in the case of the straw an impulse will travel between molecules very quiclkly else the speed of sound will be lower.

The average speed of the N₂ molecules in the air is 530 m/s. The speed of sound is only 340 m/s.

make sure some of the air leaves the gap before it collides. is there any other way?

My issue with the (probably correct) narrative that we're somehow blowing away molecules from the region between the cans is that a stream of air will also push molecules into that region. To turn the narrative into an explanation, this must be addressed.

 

[Fredrik]

I found this interesting so I threw together a quick CFD model just to see what can be learned. This model relies on symmetry so only one can is shown. I chose 6cm for the can diameter and 6mm for the straw diameter. Below are some results. I arbitrarily chose 50 m/s air velocity, but qualitative results are the same as for slower speeds I checked, down to 5 m/s. This is a steady state solution.

Your plots are interesting, especially the velocity vector plot. I'm curious what assumptions you fed into the software. In particular, have you (or the software) calculated that the stream will have lower pressure, or is that somehow part of the initial conditions?

 

[Fredrik]

So, along any given streamline, the flow must always maintain the same $p_0$, which is why, if you take any two points along said streamline, you get
\dfrac{1}{2}\rho v_1^2 + p_1 = \dfrac{1}{2}\rho v_2^2 + p_2.

I keep running into apparent contradictions that undoubtedly just highlight that I still don't understand the basics. Here's one of them:

Isn't there a streamline that starts in the person's lungs, goes through the straw and continues in a straight line until the velocity has dropped to zero? At that point, the pressure should be equal to the ambient air pressure. So if we compare that point to a point inside the lungs on the same streamline, then since the velocity at both locations is zero, we get p_lungs=p_ambient.

 

[boneh3ad]

I keep running into apparent contradictions that undoubtedly just highlight that I still don't understand the basics. Here's one of them:

Isn't there a streamline that starts in the person's lungs, goes through the straw and continues in a straight line until the velocity has dropped to zero? At that point, the pressure should be equal to the ambient air pressure. So if we compare that point to a point inside the lungs on the same streamline, then since the velocity at both locations is zero, we get p_lungs=p_ambient.

It's true that eventually the air coming out of a straw along some streamline (or all of them, really) will come to rest and be at ambient pressure, but this is because viscosity works to slowly lower the total pressure of that stream until it is both the same as ambient. Since Bernoulli's equation does not admit dissipative phenomena, you cannot use it to analyze those sort of phenomena. In using Bernoulli's equation, you are assuming that the flow does not have any phenomena that would lower the total pressure along a streamline, so from that point of view, the fluid would keep moving forever. That's why it is only an approximation. It just turns out that in many situations, it's a good approximation.

 

[Justintruth]

My issue with the (probably correct) narrative that we're somehow blowing away molecules from the region between the cans is that a stream of air will also push molecules into that region. To turn the narrative into an explanation, this must be addressed.

I think it has to do with the velocities. Look at just one molecule and see how the momentum transfer to the walls is affected by the velocity of the particle. Only the velocity perpendicular to the walls can contribute to momentum transfer to the wall. But it turns out that the velocity parallel to the wall also will affect it provided the wall is sort enough down the channel. It does this by causing the particle to miss the wall. So given the same number of particles between the walls velocity parralel will reduce the number hitting.

And it gives another prediction. Back the straw up away from the gap and the cans will at some point move out not in - for the collisions can transfer energy to particles and as long as the momentum away from and toward the wall is equal will eventually result in increased velocity toward the wall and away (momentum sum added=0 because of vector sum) But the wall only sees the toward part and thst only upon colision.

Consider a particle halfway between the walls and halfway down the channel between the walls in a direction parralell to the wall. if it has some velocity perpendicular to the wall but none parallel it will strike the wall. But if I now add momentum parallel to the wall by adding a second component of the velocity then if i add enough so that the particle exits before it hits the wall then it will not transfer momentum to the wall. Particles closer to the wall will be least affected. They must move faster parallel to the wall to miss it while particles toward the center of the gap have less a requrement for parralel velocity because the have farthrvto go and therefoe take mor time to hit.

So let me address your issue directly. We are adding particles to the gap as you say but those particles initially have higher velocity parallel to wall. The motion of the cm of the particles must be parallel to the wall predominately. Collisions with the other particles in the gap must transfer momentum parallel to the wall because of momentum conservation. Those same colisions can also thransfer momentum toward the wall as long as they transfer an equal amounnt away from the wall. So if the densities are right. you get less collisions at the wall and less momentum transfer but if you get it wrong you can increase the momentum against the wall. You can see this my imagining a single stationary particle being given a glanncing blow so it mives toward the wall.

I think - not quite sure - that if you increase the density of air between the cans so that the energy of the incomming stream is deposited in the molecules in the gap before it gets out you will also push out. The momentum will still be increased in the direction parallel to the wall but momentum toward the wall can be generated by depositing energy in such a way that the momentum toward the wall is balanced by momentum moving away from the wall. That can move particles toward the wall faster and cause more collisions. So the density of the air must be such that one effect dominates.

This toy model is just a cartoon of the molecular theory. it can be made quantitative by using the same tennis ball model and using random variables to model the momentum transfer as the expectation values of the ensemble. Tennis balls rotate and are even inelastic so the model can be pushed a long way.

The curved can helps because the wall falls away. i suspect it introduces the nonzero curl into the velocity field. .

 

[Justintruth]

My issue with the (probably correct) narrative that we're somehow blowing away molecules from the region between the cans is that a stream of air will also push molecules into that region. To turn the narrative into an explanation, this must be addressed.

I think it has to do with the velocities. Look at just one molecule and see how the momentum transfer to the walls is affected by the velocity of the particle. Only the velocity perpendicular to the walls can contribute to momentum transfer to the wall. But it turns out that the velocity parallel to the wall also will affect it provided the wall is sort enough down the channel. It does this by causing the particle to miss the wall. So given the same number of particles between the walls velocity parralel will reduce the number hitting.

And it gives another prediction. Back the straw up away from the gap and the cans will at some point move out not in - for the collisions can transfer energy to particles and as long as the momentum away from and toward the wall is equal will eventually result in increased velocity toward the wall and away (momentum sum added=0 because of vector sum) But the wall only sees the toward part and thst only upon colision.

Consider a particle halfway between the walls and halfway down the channel between the walls in a direction parralell to the wall. if it has some velocity perpendicular to the wall but none parallel it will strike the wall. But if I now add momentum parallel to the wall by adding a second component of the velocity then if i add enough so that the particle exits before it hits the wall then it will not transfer momentum to the wall. Particles closer to the wall will be least affected. They must move faster parallel to the wall to miss it while particles toward the center of the gap have less a requrement for parralel velocity because the have farthrvto go and therefoe take mor time to hit.

So let me address your issue directly. We are adding particles to the gap as you say but those particles initially have higher velocity parallel to wall. The motion of the cm of the particles must be parallel to the wall predominately. Collisions with the other particles in the gap must transfer momentum parallel to the wall because of momentum conservation. Those same colisions can also thransfer momentum toward the wall as long as they transfer an equal amounnt away from the wall. So if the densities are right. you get less collisions at the wall and less momentum transfer but if you get it wrong you can increase the momentum against the wall. You can see this my imagining a single stationary particle being given a glanncing blow so it mives toward the wall.

I think - not quite sure - that if you increase the density of air between the cans so that the energy of the incomming stream is deposited in the molecules in the gap before it gets out you will also push out. The momentum will still be increased in the direction parallel to the wall but momentum toward the wall can be generated by depositing energy in such a way that the momentum toward the wall is balanced by momentum moving away from the wall. That can move particles toward the wall faster and cause more collisions. So the density of the air must be such that one effect dominates.

This toy model is just a cartoon of the molecular theory. it can be made quantitative by using the same tennis ball model and using random variables to model the momentum transfer as the expectation values of the ensemble. Tennis balls rotate and are even inelastic so the model can be pushed a long way.

The curved can helps because the wall falls away. i suspect it introduces the nonzero curl into the velocity field. .

 

[rcgldr]

"Pressure drop with length" http://hyperphysics.phy-astr.gsu.edu/hbase/pber2.html#pdrop

I was thinking of what happens to water flowing out of a pipe, in which case the exit pressure is about ambient.

I just don't understand why the water pressure at the exit is equal to the air pressure.

After rethinking this, I'm not sure if this is an idealization. I'm also wondering about a possible pressure gradient perpendicular to the stream, higher in the center, lower at the edges.

My issue with the (probably correct) narrative that we're somehow blowing away molecules from the region between the cans is that a stream of air will also push molecules into that region. To turn the narrative into an explanation, this must be addressed.

It's more like the molecules surrounding the stream are being sucked into the stream (entrainment) due to viscosity, resulting in lower pressure surrounding the stream, but not lower pressure at the center of the stream. There's also the issue of Coanda effect, where the streams tendency to attempt to follow both convex surfaces of the two cans does result in lower than ambient pressure, with reduced deflection compared to the deflection caused by a single can.

Isn't there a streamline that starts in the person's lungs, goes through the straw and continues in a straight line until the velocity has dropped to zero? At that point, the pressure should be equal to the ambient air pressure. So if we compare that point to a point inside the lungs on the same streamline, then since the velocity at both locations is zero, we get p_lungs=p_ambient.

Bernoulli doesn't hold here because the lung perform work on the air. The reason the stream exists in the first place is because higher pressure air is being blown through the straw and the stream accelerates as its pressure decreases to ambient, which can occur beyond the exit end of the straw.

Consider the case of the stagnant pressure zones at the front and back of a bus moving through air. The stagnant zone at the front of the bus has somewhat higher than ambient pressure, while the stagnant zone at the rear of the bus has lower than ambient pressure, but both stagnant zones move at the same speed. The bus performs work on the air which violates one of the assumptions used for the basic Bernoulli equation.

 

[Justintruth]

I keep running into apparent contradictions that undoubtedly just highlight that I still don't understand the basics. Here's one of them:

Isn't there a streamline that starts in the person's lungs, goes through the straw and continues in a straight line until the velocity has dropped to zero? At that point, the pressure should be equal to the ambient air pressure. So if we compare that point to a point inside the lungs on the same streamline, then since the velocity at both locations is zero, we get p_lungs=p_ambient.

I think you need to separate momentum and energy and also consider the center of mass of the ensemble and include the momentum imparted to the blower himself. If you look at momentum considerations you will see that the stream of air emitted has both an energy and momentum and while the energy can be dissipated as it is a scalar, momentum must be conserved. So if you start thermal - the vector sum of velocities is zero - no linear momentum (and no curl or angular momentum) - and then blow - transferring momentum to the guy blowing him back and to the stream blowing it forward then that forward momentum cannot be dissipated by the gas. In the end the velocity of the expelled gas/sream ensemble will not be zero unless it hits some other object. You can transfer energy into the gas and randomize it but the vector summed velociy of the ensemble will have to be non zero.

Slightly off topic but not totally, I read an article once on guys doing Very Long Based Interferometry (VLBI) on quasars. They were able to detect "seasonal exchanges of momentum between the atmosphere and the Earth's crust". So their measurements were so sensitive that they picked up some of the effect of the wind blowing on the mountains and moving the Earth's crust over the magma.

Sort of makes it credible that blowing on a straw will contribute to the momentum of the guy, his chair, house, etc.

 

[mfig]

Your plots are interesting, especially the velocity vector plot. I'm curious what assumptions you fed into the software. In particular, have you (or the software) calculated that the stream will have lower pressure, or is that somehow part of the initial conditions?

Hello,

There are always several assumptions that go into any model. This model assumes:

• constant velocity jet
  
• turbulent flow, with the k-ε turbulence model and non-slip, standard wall treatments
  
• air as the material, with viscous effects enabled
  
• ideal gas density behavior, which is a more than adequate at such low speeds and pressures
  
• ambient pressure of 101325 Pa
• ambient temperature of 300 K
• Zero back-pressure outlets (the top and right walls are system outlets)
  
• Flow field was solved from an initial guess that basically has the entire field at near constant pressure and velocity
• Mesh adaption was used so that both energy and mass were balanced to within 1 part in 10^-4 for the system. If I were trying to get a more accurate model, I would drop this down to 10^-6.

So, yes, the low pressure area under the can is calculated, and not part of the initial conditions. The initial conditions are very general and are not similar at all to the final solutions.

 

[Justintruth]

...The vector plot shows that a circulation zone develops around the can in a clockwise manner at this point, making me wonder if there is a possibility for the can to rotate at some x distance from the straw (I doubt it, but it is interesting to consider

I have been thinking about this. There is something called standing friction and moving friction. Both are non-zero. A lot of the models that I have seen assume that a gas has zero velocity at the wall and some boundary layer undergoes torsion and forms vortices that dissipate energy with the stream flowing only away from the wall. Eliminating this and producing laminar flow then becomes a big goal in a lot of designs. I remember marveling at the way a seal glides through the water. Not that its fins produce thrust but after that the length of its glide seems way off compared to when I swim. My understanding is that early models did not show any dependence of friction on the velocity of the air and that that was fixed but understanding how these boundary layers operate. Boundary layers are very important. But...

I do think that it is possible to get flow between the can and the gas - at least given very precise control of the gas molecules - and assuming that this is possible and there is then moving friction between the gas and the can, then a torque on the can will be applied. Then if you can get the friction down between the bottom of the can and the table you will get rotation.

I don't know exactly how to get the shearing to be at the can and not have a static layer of air near the can, and the torsion in the gas velocity.

I am also remembered about the famous thought experiment of the pail full of water that demonstrates Mach's principle. There the water is started spinning by the friction between it and the pail. So something like that can occur with a liquid.

So my "vote" - after all physics is democratic no? - is that the you can get a force parallel to the surface of the can and that it will be friction and could cause a torque on the can - probably a very small one not able to overcome the standing friction between the can bottom and the table. .

Cheers.

 

[rcgldr]

Bernoulli doesn't hold here because the lung perform work on the air. The reason the stream exists in the first place is because higher pressure air is being blown through the straw and the stream accelerates as its pressure decreases to ambient, which can occur beyond the exit end of the straw.

Just experienced a large scale version of this that I hadn't thought of in a while. I was at a very large indoor shopping mall which uses a positive pressure ventilation system. When any door way is opened, a substantial stream of air flows out, and from what I recall about positive pressure ventilation systems, the pressure will remain above ambient for some distance beyond the door way as the air flow accelerates and its pressure decreases back to ambient. Another example similar to the flow produced by a fan or propeller.

Getting back to why cans or balloons tend to be drawn together by a stream where the core of the stream has higher than ambient pressure, I suspect a combination of entrainment of the surrounding air and a Coanda like effect to result in lower than ambient pressure air surrounding the stream.

 

[BvU]

The faster moving core has lower than ambient pressure. That's why the cans are pulled together. Simple Bernoulli. When you feel air speed you only think it's pressure.

 

[rcgldr]

The faster moving core has lower than ambient pressure. That's why the cans are pulled together. Simple Bernoulli. When you feel air speed you only think it's pressure.

In the scenarios I've mentioned, because work was performed on the air to produce the initial stream, the pressure starts off above ambient, then accelerates and decreases in pressure until it reaches ambient pressure. Take a look at this Nasa article, which is somewhat idealized, ignoring viscosity effects with the surrounding air, but the "exit" point where the streams pressure returns to ambient is well downstream from the source of the stream:

http://www.grc.nasa.gov/WWW/K-12/airplane/propanl.html

 

[Capn'Tim]

Forgive me for jumping in here. For me the answer as a aviation professional seems clear and obvious... However I can understand the need for clarification for those not having previous experience with the phenomena known as the Bernoulli's Principal. Without this effect no aircraft ever designed (to my knowledge) would ever fly. it is a cornerstone of aerodynamics. I will not contribute any equations here as it is not my area of expertise :). When you blow through the straw, as it exits the straw the pressure within the straw expands and is largely converted to velocity (air movement). Also remember that any airstream in free air will create a effect of motivating the free air around it to also move, to some degree increasing the flow as friction drags a portion of that air along with it. As the airflow moves toward the cans there is no increased pressure as it is not constrained as in the straw, as it is relatively at ambient atmospheric pressure. Bernouli's Principal states that when airflow passes through a constriction it will accelerate. This acceleration will cause a low pressure area to develop just beyond the point of maximum restriction. This is the active mechanism of a venturi which is what we have just described by two cans in close proximity to each other. Notable is the curved surface between the two cans which perfectly represent a venturi. The low pressure is proportional to the area of flow, mass quantity and the velocity. As the pressure between the two cans is reduced a pressure differential is created which is manifested as a force and atmospheric pressure at the outside perimeter pushes the two cans together (Boyles Law?) seeking entropy. On an aircraft wing (Airfoil) the curved surface of the wing acts as one half of the venturi and the undisturbed airflow above the wing is the other half which creates the constricted path of airflow, resulting in airflow acceleration and ultimately lift from the air pressure difference above and below the wing.

 

[BvU]

Hello captain,

 

[Capn'Tim]

Greetings :)

 

[rcgldr]

On an aircraft wing (Airfoil) the curved surface of the wing acts as one half of the venturi and the undisturbed airflow above the wing is the other half which creates the constricted path of airflow, resulting in airflow acceleration and ultimately lift from the air pressure difference above and below the wing.

A wing does not act like half a venturi. Instead if the wing is not stalled, then the air flow tends to follow a convex surface. The curved path of the air is associated with centripetal acceleration and a pressure gradient perpendicular to the streamline, with the lower pressure on the inside of the curve. The pressure gradient perpendicular to the flow also affects acceleration of air in the direction of flow, but to apply Bernoulli to the inside flow versus outside flow requires separating the flow into multiple streamlines.

 

[Capn'Tim]

You are referring to laminar flow. Laminar flow is important mainly to prevent airflow separation from the wing upper surface which creates turbulence, decreases velocity and results in loss of pressure differential, i.e, lift (wing stall). There are indeed multiple streamlines if measuring pressure gradient and velocity across the wing surface and the free air stream. At the wing surface the velocity is lower due to parasitic drag and higher at some point just above the surface- a gradient. The pressure differential between top and bottom side also tends to move the airflow outboard to the point of least resistance where the high pressure under the wing attempts to fill the low pressure void on top creating wing tip vortices - a major contributor to lift induced drag. Because of the above it is important keep the wing surface very clean in order to support the laminar flow efficiency. To be more complete though, one has to factor in equal and opposite action. deflection of airflow beneath the wing creates an equal and opposite force contributing to lift. This however is more prominent during low speed high angle of attack (angle of airfoil to airflow). In my previous explanation I alluded incorrectly to the velocity creating low pressure. The opposite is true. The low pressure at the rear of the wing created by wing bow wave effects creates an initial pressure differential causing acceleration. The primary lifting moment comes from entrainment of the air just behind the highest area of effective camber creating low pressure.

 

[rcgldr]

You are referring to laminar flow.

On high end gliders and some powered aircraft, the wing surface may be roughed up and/or turbulator strips used to deliberately induce turbulent flow to reduce what would be a separation laminar flow bubble which would increase profile drag. The turbulent flow tends to remain attached longer (separates further downstream):

http://en.wikipedia.org/wiki/Turbulator

Induced drag can be defined as the drag related to diversion of air flow. You could assume an ideal wing that diverts a flow with no change in speed or energy of the flow. After diversion, the relative free stream flow (with respect to the wind) is reduced, and a flow perpendicular to the free stream flow is induced (the total speed remains unchanged, only the direction of the flow is changed). Induced drag would be related to the reduction in the relative free stream flow due to diversion by an ideal wing.

http://en.wikipedia.org/wiki/Lift-induced_drag

 

[Capn'Tim]

The techniques for controlling boundary layer separation vary some what depending on manufacturer and type of aircraft. Low speed flight at LD/Max is obviously of peak importance in a glider, so the parasitic drag they cause at those speeds is not very significant vs lift benefits. In a high speed aircraft like a jet turbulators and vortex generators etc. tend to lend additional drag as airspeed increases reducing their desirability. You will indeed find them on production jet aircraft though, quite often as a low cost fix to aerodynamic deficiencies found during flight test and certification rather than redesigning the wing at significant cost .Dassault is very "anal" about not using any flow modification protuberances on their aircraft and spend considerable engineering and development time on wings and structure to promote the most efficient design. They are truly a work of art to behold... No rivets, very smooth and curvilinear. Even the extra expense of area rule fuselage around the engines is used to reduce interference drag between engines and fuselage. For the longest time they refused to use winglets because it violated their perceived clean wing philosophy. Finally they gave into the trend and implemented a very efficient design increasing wing efficiency by about 5%

 

[boneh3ad]

A wing does not act like half a venturi. Instead if the wing is not stalled, then the air flow tends to follow a convex surface. The curved path of the air is associated with centripetal acceleration and a pressure gradient perpendicular to the streamline, with the lower pressure on the inside of the curve. The pressure gradient perpendicular to the flow also affects acceleration of air in the direction of flow, but to apply Bernoulli to the inside flow versus outside flow requires separating the flow into multiple streamlines.

It's certainly true (and important) to note that a wing is not like half of a Venturi, as has been discussed at great length on this site before. However, your statements about streamline curvature and the resulting conclusions are not accurate. It is certainly true that curved streamlines, as with any other curved path, require a centripetal force and that force is provided by a pressure gradient. The pressure therefore decreases in the direction of the center of curvatures. However, this pressure gradient points exactly normal to the flow direction and the only role it plays in accelerating the flow is that of the centripetal acceleration, i.e. it changes the velocity of the flow since it "causes" curvature, but it doesn't change the magnitude of the velocity. If there is any tangential acceleration to the flow, it is not related to the streamline curvature through the centripetal acceleration.

Additionally, in situations such as an airfoil where the typical frame of reference is a uniform free stream moving over an airfoil, then every streamline starts with the same total pressure and Bernoulli's equation applies everywhere, not just along a single streamline and regardless of your so-called streamline curvature effect. The exception is when a streamline enters the boundary layer region, at which point viscosity is non-negligible and Bernoulli's equation no longer applies.

You are referring to laminar flow. Laminar flow is important mainly to prevent airflow separation from the wing upper surface which creates turbulence, decreases velocity and results in loss of pressure differential, i.e, lift (wing stall).

Quite the opposite, actually. laminar flow is exceptionally susceptible to boundary-layer separation/stall, which turbulent flow is much more resistant to separation. In situations where high angle of attack maneuvers are common (e.g. fighter jets) there are often elements of the design intended to ensure turbulent flow over the wings so that separation does not occur.

There are indeed multiple streamlines if measuring pressure gradient and velocity across the wing surface and the free air stream. At the wing surface the velocity is lower due to parasitic drag and higher at some point just above the surface- a gradient.

For air blowing over a stationary airfoil, the flow velocity at the surfaces isn't just lower. It's zero. This is not due to "parasitic drag", but due to viscosity, which leads to one component of total drag: skin friction drag. If you instead imagine stationary air with a wing moving through it, this is the equivalent of the wing dragging some of the air along with it since the flow velocity relative to the surface must be zero at the surface.

For now it is easier to work in the frame of reference of a stationary wing with air moving over it. The two frames are equivalent anyway. So, at the surface the velocity is zero, and a short distance away, the velocity is the same as that predicted by inviscid theory, often called the edge velocity. The relatively thin region near a surface that features the smooth change from zero to the edge velocity is called the boundary layer. As luck would have it, nature loves us and the pressure gradient in the wall-normal direction through the boundary layer is very nearly zero, so when we do simple inviscid simulations to come up with the edge velocity, we can treat that corresponding pressure as if it was touching the surface anyway.

Because of the above it is important keep the wing surface very clean in order to support the laminar flow efficiency.

Keeping the boundary layer laminar over the wings of a transport/cargo plane (i.e. one that doesn't do a lot of high angle maneuvering) would be very nice in terms of efficiency. In fact, it's estimated that laminarizing the boundary layers on the wings of a Boeing 737 would result in a 15% fuel savings. However, this process is extraordinarily more complicated than just keeping the wing surface clean. Even if it was that simple, that would be nigh on impossible in any real-world situation.

To be more complete though, one has to factor in equal and opposite action. deflection of airflow beneath the wing creates an equal and opposite force contributing to lift. This however is more prominent during low speed high angle of attack (angle of airfoil to airflow).

This is literally always the case, not just during high angle of attack situations. The momentum change of of the air due to the deflection caused by the wing is exactly equal to the forces on the wing, both lift and drag. This is always true. The Bernoulli explanation and the flow deflection explanation are not two different mechanisms contributing to lift. They are, in fact, two sides of the same coin, and each individually can account for 100% of the lift.

The primary lifting moment comes from entrainment of the air just behind the highest area of effective camber creating low pressure.

Given that a symmetric airfoil (with zero camber) can generate lift, that should tell you that camber is not required for lift, and therefore cannot be somehow fundamental to lift.

 

[rcgldr]

... pressure gradient perpendicular to the streamline, with the lower pressure on the inside of the curve. The pressure gradient perpendicular to the flow also affects acceleration of air in the direction of flow ...

your statements about streamline curvature and the resulting conclusions are not accurate. It is certainly true that curved streamlines, as with any other curved path, require a centripetal force and that force is provided by a pressure gradient. The pressure therefore decreases in the direction of the center of curvatures. However, this pressure gradient points exactly normal to the flow direction and the only role it plays in accelerating the flow is that of the centripetal acceleration.

Thanks for getting back to this thread.

Wouldn't the pressure gradient in the direction of flow correspond to the changes in pressure related to curvature of flow? Wouldn't the lowest pressure and highest velocity of flow occur at the point of greatest centripetal acceleration (above a wing), a coexistent relationship?

 

[boneh3ad]

Thanks for getting back to this thread.

I get to be pretty busy at the end of the semester. I neglected basically the entire forum for the last few weeks.

Wouldn't the pressure gradient in the direction of flow correspond to the changes in pressure related to curvature of flow? Wouldn't the lowest pressure and highest velocity of flow occur at the point of greatest centripetal acceleration (above a wing), a coexistent relationship?

Not necessarily. The pressure gradient in the direction of the flow, by definition, is tangential to any curves in the streamlines and is therefore not coupled in any way to the associated centripetal acceleration. Now, the pressure and velocity fields are coupled, so the two can't be completely separated, but any acceleration in the streamwise direction must come from a streamwise pressure gradient, not the stream-normal pressure gradient that accompanies curved streamlines. In fact, the lowest pressures over an airfoil do not tend to correspond exactly with the areas with the largest streamline curvature. The largest curvature is at the leading edge where the flow rapidly deflects out of the way of the airfoil. This also happens to be where the highest pressure typically occurs. Of course, there are also low pressure regions that are in the vicinity of high curvature as well. The important takeaway is that you can't assume high curvature means low pressure. All you can assume is that there is a negative pressure gradient in the direction of the center of pressure.

 

[Capn'Tim]

I think you misunderstood (or I poorly worded) when I said "The primary lifting moment comes from the entrainment of air just behind the highest area of effective camber" I was not speaking to the entire lifting moment of the wing. I was intending to infer to the lift generated by that portion of the aerodynamics apportioned to the Bernoulli effect. I full well realize there are other contributors. Synopsis statements sometimes don't adequately convey intended meaning. In reality the force vector of the wing is a composite of all the pressure points along the chord line of each given section, and when those pressure points are aggregated and averaged it tends to be a point somewhere to the rear of the peak camber (with exceptions like super-critical design for example). As to the value of camber itself, with little exception nearly every viable wing design incorporates camber. Yes you can make a flat plate fly, but it is terribly inefficient and economically useless. Yes some supersonic aircraft utilize wing designs with very little if any perceptible camber, but from low speed high lift designs to high sub-sonic super critical designs there is always camber. The question is how much? And what combination of negative and positive camber over the length of the chord to effect the final "effective camber". to meet the design goals?
On another note though, looking back at my old dusty Aerodynamic primer books from the early 1970's I realize they didn't have it quite right! I am a professional and as such always learning and willing to change my thinking when either proven in error or a better explanation comes along. The venturi example is indeed a poor descriptor of the Bernouli effect as it applies to airfoils. And even NASA still is saying that the Bernouli effect causes acceleration which results in low pressure (though the explanation that the difference in pressure at the entry side of the restriction vs the exit side seems more appropriate to me). Though NASA gives recognition to both Bernouli and to Newtonian contribution to lift, they say the true cause is neither of these but the downward deflection of airflow that makes a wing fly! So there we go... :)
Best Regards!

 

[boneh3ad]

I think you are back on the correct track, but there are still a few things you are saying that are at best misleading. For instance:

The venturi example is indeed a poor descriptor of the Bernouli effect as it applies to airfoils. And even NASA still is saying that the Bernouli effect causes acceleration which results in low pressure (though the explanation that the difference in pressure at the entry side of the restriction vs the exit side seems more appropriate to me).

This may be part of the issue. There really isn't such a thing as "the Bernoulli effect." Bernoulli's princple, or the Bernoulli equation, is essentially just an equation describing the relationship between pressure and velocity in an inviscid, incompressible flow. It says nothing about cause and effect. It is simply a statement of conservation of energy (originally and most straightforwardly, although you can also cast it in terms of conservation of momentum). In other words, if you know the velocity distribution around an airfoil, you can use that to relate the velocity to the pressure, and then use the pressure to explain and/or quantify lift. This is, in fact, a quite common method of calculating lift. It does not, however, tell you anything about why the air moves faster in certain locations. Similarly, it doesn't tell you why the flow speeds up in a Venturi tube, only that the acceleration accompanies a decrease in pressure and vice versa. It is actually conservation of mass that explains why the flow speeds up in a Venturi tube.

Though NASA gives recognition to both Bernouli and to Newtonian contribution to lift

Bernoulli and Newton do not both "contribute" to life. Rather, each one can independently be used to describe lift. Using Bernoulli's equation, you can say the pressure distribution resulting from the velocity field will provide a net upward force that we call lift. Using Newton, you can say that any deflection of the air downward by the wing requires force, and the equal and opposite reaction to this is the upward force we call lift. If you used either of these to actually calculate lift, they would give the same answer. Both Newton and Bernoulli can completely and on their own explain all of lift. They are not independent contributions.

they say the true cause is neither of these but the downward deflection of airflow that makes a wing fly! So there we go... :)

The downward deflection of air is the Newtonian explanation of lift, and is, at its heart, probably the most fundamental method of qualitatively explaning lift while simultaneously being the most useless method for quantifying lift.

 

[Capn'Tim]

Bernoulli and Newton do not both "contribute" to life. Rather, each one can independently be used to describe lift. Using Bernoulli's equation, you can say the pressure distribution resulting from the velocity field will provide a net upward force that we call lift. Using Newton, you can say that any deflection of the air downward by the wing requires force, and the equal and opposite reaction to this is the upward force we call lift. If you used either of these to actually calculate lift, they would give the same answer. Both Newton and Bernoulli can completely and on their own explain all of lift. They are not independent contributions.

It is fair to say that neither airflow deflection (Newtonian) or the velocity/pressure (Bernouli) by themselves account for lift independently of each other. Nor do the two when aggregated accurately reflect the lift of a given airfoil. This much is evident through wind tunnel testing as both independently fall short of predicting the true lift of a given airfoil. Hence, all airfoils require wind tunnel testing regardless the intensity of calculation expended in the design. My recount of the NASA position was not a direct quote... rather than deflection they say curvature in a downward direction (when applied to overcoming gravity specifically). Like weather prediction which escapes exact and accurate results, aerodynamics remains to some degree dependent on observation after the fact. The entire truth of first causes remains somewhat elusive else there would be far less vigorous discussion :)

I am not a scientist or an engineer. I am a practitioner of applied science in aviation. As such I focus on trying to understand the physics principals at work vs the science itself. Most pilots unless they have a background in physics don't feel compelled to fully understand the principals at work, focusing on the other myriad of subjects they must apply in doing their work.

Some decades ago when I was a much younger gentleman, I was flying into Hong Kong Kai Tak on a B747 Classic as the First Officer. I was flying with the #1 Captain who was also a training captain. We were slated to do the famous IGS Approach into Rwy 13. Unfortunately there was a thuderstorm parked on the approach area that made that approach too dangerous to complete. The captain elected to do a downwind approach to land on Rwy 31 with a 10 knot tailwind. Windshear Advisories were in effect due to the storm. As such the captain elected to carry an additional 20 knots of airspeed during the approach due to the prospect of encountering windshear ( which in retrospect was incorrect since any windshear we encountered would likely be performance increasing rather than decreasing). In any case, this decision resulted in an increase of ground speed with the tail wind of about 30 knots. Our target approach speed at maximum landing weight was 157 knots ... A groundspeed of 187 knots (215 mph) crossing the landing threshhold. When the Captain tried to set the aircraft down it resisted touchdown due to increased ground effect and we floated some distance additionally down the runway before the Captain spoke an expletive and applied full speed brakes to kill the lift! The aircraft fell unceremoniously onto the runway and using moderate to heavy breaking we came to a stop within the remaining 6000 feet of runway with a few hundred feet to spare. As we turned off the runway I asked the captain if we shouldn't have the Flight Engineer check the brake energy charts. His response was that it was not necessary because the aircraft would sit over night in HKG... Right then and there I realized the captain had not grasped the physics reality of bringing 630,000 lbs of mass to rest within 6000 feet! The total inertial energy had to go somewhere, and that somewhere was massive heat in the braking assembly! What is not comprehended by many is that the majority of the heating does not occur at the brake surfaces (frictional heating) but deep within the brake assembly itself as the brakes absorb all that energy. It takes about 15 minutes for the heat to migrate to the surface of the assembly. To make an even longer story short, by the time we reached the gate the aircraft was on fire as the bimetallic brake assemblies melted, dripped onto the asphalt and created combustion - fire! We could have lost the whole aircraft if the fire dept had not been prompt and did a good job. As it was we lost 5 brake assemblies and three tires to the incident. Later in my hotel room I ran the brake energy chart and it ended in the RED ZONE with a danger note " Evacuate the aircraft immediately as brake fire will occur".

 

[boneh3ad]

It is fair to say that neither airflow deflection (Newtonian) or the velocity/pressure (Bernouli) by themselves account for lift independently of each other. Nor do the two when aggregated accurately reflect the lift of a given airfoil. This much is evident through wind tunnel testing as both independently fall short of predicting the true lift of a given airfoil. Hence, all airfoils require wind tunnel testing regardless the intensity of calculation expended in the design. My recount of the NASA position was not a direct quote... rather than deflection they say curvature in a downward direction (when applied to overcoming gravity specifically). Like weather prediction which escapes exact and accurate results, aerodynamics remains to some degree dependent on observation after the fact. The entire truth of first causes remains somewhat elusive else there would be far less vigorous discussion :)

I am sorry, but you are objectively incorrect here according to the previous 100+ years of aerodynamic research. If you know the pressure field accurately, you know 100% of the lift. If you know the velocity field accurately, then through the Bernoulli equation, you know 100% of the lift. If you somehow knew the change in vertical momentum in the flow resulting from the wing (i.e. if you quantified the downwash/flow deflection) then you know 100% of the lift. That is fact.

Lift is "easy". Drag is why you really need wind tunnel testing. Lift-induced drag is relatively easy to quantify, but viscous drag is essentially impossible to calculate, and so must be measured. The biggest problem in calculating drag is laminar-turbulent transition. Viscous drag increases by an order of magnitude when the boundary layer is turbulent, so knowing the transition point accurately is important to predicting drag, but that's something that we generally cannot do computationally at this point in time. There's also the matter of the wake and any separation that might occur, which will affect drag in a way that is difficult to calculate.

In short, you can get lift pretty easily and completely from pressure, velocity (Bernoulli), or downwash (Newton), but drag remains impossible to accurately calculate and requires testing. Even wind tunnels only get you so far. Eventually you will need full-scale flight testing to make sure it works as intended.

I am not a scientist or an engineer. I am a practitioner of applied science in aviation. As such I focus on trying to understand the physics principals at work vs the science itself. Most pilots unless they have a background in physics don't feel compelled to fully understand the principals at work, focusing on the other myriad of subjects they must apply in doing their work.

I am an engineer who does wind tunnel testing for a living. I promise that the above is true. The physics principles at work are, generally, conservation of mass, momentum, and energy. Newton's laws can be used to derive the conservation of momentum equations that describe fluid flow (the Navier-Stokes equations) and any change in momentum requires force. Therefore, deflecting the flow requires a force exerted by the wing, and the equal and opposite force on the wing is lift. If you have another source of upward force, I invite you to try to discuss how it arises and why it doesn't also contribute to the flow deflection.

Similarly, if you have some pressure distribution on the wing that predicts and upward force, then there must be a balancing equal and opposite force assuming the wing is at steady, level flight. That opposite force is what deflects the air flow, and again, if you are trying to say that there is some other force in addition to this integrated pressure field, then I invite you to consider what that force may be and why it doesn't show up in the pressure field, since pressure is how a fluid transmits normal force to a surface.

Some sources:
How Does an Airplane Work: A Primer on Lift, an Insight I wrote for this site
https://www.amazon.com/dp/0078027675/?tag=pfamazon01-20
https://www.amazon.com/dp/1259129918/?tag=pfamazon01-20
https://www.amazon.com/dp/0521665523/?tag=pfamazon01-20