Pressure and Lift around a Wing

[rcgldr]

For an "idealized" wing, the flow is diverted, but the speed is not changed. The components of velocity are changed, the horizontal component is decreased, and the vertical component is increased (from zero to some non-zero "exit" velocity). The aerodynamic force vector points upwards (lift) and a bit backwards (induced drag). The point here is that lift induced drag is related to the diversion of flow, not dissipation of mechanical energy being converted into heat, such as friction or viscous related drag.

I can see how the 'in vacuo' approach to this whole business leads to arguments and confusion. How is the paradox explained that air has to be deflected (along with its KE) in order to follow N3, yet no Energy is lost in the process

I updated my last post (included in the quote in this post), that might help clarify my point. In an "ideal" circumstance, Newton laws would still apply, but without requiring any loss in energy, Bernoulli principle is an example of such an idealized case where it's assumed that there are no energy losses, where a flow is accelerated as it transitions into a narrower section of pipe and decelerated as it transitions into a wider section of pipe.

 

[boneh3ad]

You have to be careful when discussion an "ideal" flow around a wing, because you will predict zero drag. This is a concept called D'Alembert's paradox, so named because D'Alembert formulated the first mathematical theory of forces on an object moving through a fluid and it predicted zero drag despite there clearly being drag when observed in the real world. In order to predict a nonzero value of lift on an infinite ideal wing, one must consider viscosity, which leads to viscous drag and form drag due to boundary-layer separation. The other option is induced drag, which only affects finite wings. The induced drag on an infinite wing is zero (thus the reason gliders typically have very large wingspans).

 

[fog37]

boneh3ad,

For a steady flow, I see how the isotropic pressure on the surface of a fluid parcel moving at a constant speed inside a horizontal pipe decreases with an increase in the fluid parcel speed based on energy arguments: From a thermodynamic point of view, why does the external isotropic pressure on the surface of the fluid parcel decreases is moving at a higher speed?

 

[boneh3ad]

Conservation of energy is the First Law of Thermodynamics, so I am not sure where the disconnect here is. Bernoulli's equation is essentially a statement of the First Law of Thermodynamics and can be derived directly from the energy equation.

 

[rcgldr]

The induced drag on an infinite wing is zero (thus the reason gliders typically have very large wingspans).

I find conflicting articles about this. The main issue seems to be the case of an infinite wing producing a finite amount of lift, in which case the angle of the diversion of airflow approaches zero as the wing span approaches infinity. If instead the infinite wing produces some finite amount of lift per finite unit of length of the wing, then the angle of diversion of airflow and the corresponding effective angle of attack are non-zero, and there is lift induced drag since there is a non-zero angle of diversion.

 

[sophiecentaur]

D'Alembert formulated the first mathematical theory of forces on an object moving through a fluid and it predicted zero drag

That's fine as a basis for preliminary calculations but not for the sort of discussion in this thread which attempts to describe "what's really happening". Any deeper understanding of a phenomenon can't ignore the Energy considerations, can it?

 

[fog37]

Thanks boneh3ad

But doesn't Bernoulli's equation come from the Euler equation (which is NS with zero viscosity) when the flow is time steady and has zero vorticity?

 

[boneh3ad]

That's fine as a basis for preliminary calculations but not for the sort of discussion in this thread which attempts to describe "what's really happening". Any deeper understanding of a phenomenon can't ignore the Energy considerations, can it?

I was replying to @rcgldr and his use of an idealized flow. If the question is about lift, you can get a very, very accurate answer and understand all the fundamental ideas with that approach. It simply provides no insight into drag.

 

[boneh3ad]

Thanks boneh3ad

But doesn't Bernoulli's equation come from the Euler equation (which is NS with zero viscosity) when the flow is time steady and has zero vorticity?

You can derive it from the Euler equation. You can also derive it from the Reynolds transport theorem applied to energy.

 

[fog37]

Conservation of energy is the First Law of Thermodynamics, so I am not sure where the disconnect here is. Bernoulli's equation is essentially a statement of the First Law of Thermodynamics and can be derived directly from the energy equation.

Thanks for the patience. In hydrostatics, I get a clear picture of what is going on: at a certain depth inside water, the static pressure on a the walls of an infinitesimal fluid parcel located at point $P$ is isotropic and due to all the other fluid parcels surrounding the fluid parcel positioned at $P$.

When the fluid is in motion, instead, to the right at speed $V$, the isotropic pressure at the same point $P$ is lower compared to when the fluid is at rest. Of course, different fluid parcels will occupy point $P$ at different instants of time. But, without using energy arguments, I was wondering if I could get some insight from a more elementary point of view of the forces acting on the passing by fluid parcel at point $P$ and understand why the pressure would be reduced if the fluid is moving...

 

[jbriggs444]

When the fluid is in motion, instead, to the right at speed VVV, the isotropic pressure at the same point PPP is lower compared to when the fluid is at rest. Of course, different fluid parcels will occupy point PPP at different instants of time. But, without using energy arguments, I was wondering if I could get some insight from a more elementary point of view of the forces acting on the passing by fluid parcel at point PPP and understand why the pressure would be reduced if the fluid is moving...

There is no reason for the parcels in a moving fluid to be at a different pressures than in a stationary fluid. Whether the fluid is "moving" or "stationary" is, after all, decided when you pick a frame of reference. The choice of frame of reference cannot affect the pressure.

If you choose a single body of fluid which is moving in one region and stationary at another, now you have a real physical effect to look at. What does change pressure is the fact that a fluid parcel that is moving slowly as it passes one point and moving more rapidly as it passes another point must have accelerated to do so. That acceleration is the result of a pressure gradient.

 

[russ_watters]

There is no reason for the parcels in a moving fluid to be at a different pressures than in a stationary fluid. Whether the fluid is "moving" or "stationary" is, after all, decided when you pick a frame of reference. The choice of frame of reference cannot affect the pressure.

I'll add that for airplanes this should be particularly obvious. There are thousands of planes zooming around at different speeds at any given time, and the air may be considered moving with respect to any of them or stationary with respect to the surface of the Earth, and that doesn't affect the freestream static pressure.

...but it may be less obvious for flow in a wind tunnel or pipe, where there would seem to be a preferred reference frame (but doesn't have to be) and other factors affecting static pressure (such as loss through the pipe/duct, Venturi effects, etc.).

 

[olivermsun]

...without using energy arguments, I was wondering if I could get some insight from a more elementary point of view of the forces acting on the passing by fluid parcel at point $P$ and understand why the pressure would be reduced if the fluid is moving...

Consider Newton’s 2nd law along a stream line. The acceleration on a parcel of water is due to the net force on the parcel, here equal to the difference in pressure dp/dx, where x is along the streamline. If the flow is accelerating, then the net force must be positive in the direction of the flow, and hence the pressure gradient must be negative.

 

[boneh3ad]

@olivermsun gave the explanation I would have here. You can view Bernoulli from either a force persective or an energy perspective, and you can derive it from either direction as well. I suspect, perhaps, that it would be useful if I wrote another Insight article about Bernoulli's equation.

 

[fog37]

Thanks olivermsun and boneh3ad.

Given a fluid parcel moving along a straight streamline in the positive x-direction, I see that a pressure difference between two points (one before and one after point $P$) would cause a force $F$ on the fluid parcel which would accelerate. But what if the parcel is moving at constant speed? The force would zero and the pressure gradient would be zero. In that case, being pressure isotropic, the parcel experiences the same force from the back, from the front, from the top and from the bottom. This isotropic pressure is smaller compared to the static pressure at the same point $P$ when the fluid is not moving at all. I am not sure how to justify the fact that the speed makes the pressure smaller without using Bernoulli's equation.

 

[boneh3ad]

You are sort of running in circles here. The best way to address that question again goes back to the consideration of energy. A given fluid parcel has a finite total energy (represented by total pressure in Bernoulli's equation). If it is accelerated to some constant velocity further downstream (e.g. after a pipe constriction) and experiences no non-conservative forces, then it still has the same total energy but it now has higher kinetic energy. The energy stored as static pressure must therefore decrease.

 

[FactChecker]

Thanks olivermsun and boneh3ad.

Given a fluid parcel moving along a straight streamline in the positive x-direction, I see that a pressure difference between two points (one before and one after point $P$) would cause a force $F$ on the fluid parcel which would accelerate. But what if the parcel is moving at constant speed? The force would zero and the pressure gradient would be zero. In that case, being pressure isotropic, the parcel experiences the same force from the back, from the front, from the top and from the bottom. This isotropic pressure is smaller compared to the static pressure at the same point $P$ when the fluid is not moving at all. I am not sure how to justify the fact that the speed makes the pressure smaller without using Bernoulli's equation.

After the velocity has increased and the pressure has decreased, it is hard to figure things out if you ignore what happened to cause the velocity to increase. You can't intuitively understand the difference between point A and point B while ignoring everything in between.

Suppose you wanted to compare the velocity of a car at the top of a hill with the same car after it has rolled down the hill without considering the obvious speed up as it rolled down. You want a reason why the velocity at the bottom is faster. In addition, you are trying to rule out consideration of the potential vs kinetic total energy trade-offs. That is asking for too much.

 

[fog37]

Ok, thank you. I look forward to boneh3ad insight article :)

 

[boneh3ad]

I have a rough draft made up but it needs some figures, which may take a while to actually put together, especially with the end of the semester rapidly approaching. It might have to wait until mid-May.

 

[Joseph M. Zias]

For your information: I have found a very good web book on flying that includes a very readable section of wings and lift. Look up "See How it Flies" by
John S. Denker, a physicist and flight instructor.

 

[sophiecentaur]

For your information: I have found a very good web book on flying that includes a very readable section of wings and lift. Look up "See How it Flies" by
John S. Denker, a physicist and flight instructor.

That guy knows a lot about flying and planes and the book is certainly entertaining as well as informative. I didn't read from cover to cover, of course, but one bit leaped out of the screen at me:

"Downwash behind the wing is relatively easy to understand; the whole purpose of the wing is to impart some downward motion to the air."

He is obviously aware of Newton's Third Law so he is, by definition 'A Good Lad" and gets the general principle.

 

[DarioC]

I don't understand fog37's initial statement that the air flowing over the top of the wing causes a downward pressure on the top of the wing.

None the less:There was (is) an excellent video online of wind tunnel airflow over an airfoil with the flow shown by pulsed smoke. It really changed my view of what happens. What I saw was that the air velocity near the wing speeds up compared to the general tunnel flow as it goes up to the high point on the airfoil and then slows back down as it curves down to the trailing edge of the wing. This is displayed by the vertical lines of the smoke pulses.

The second part that conflicted with what I thought I knew about wings was that the "smoke lines" indicated the flow slowed down as it passed under the wing. Interestingly enough, if that is correct, it would still produce a downward vortex, and therefore lift, from the trailing edge of the wing.

I fail to see any conflict between the downward flow of air from a helicopter, the rearward flow from a propeller, or the lift from a wing. I can personally vouch for the vortex from a wing as I well remember having my light airplane flipped almost 90 degrees by a vortex from a larger corporate aircraft just as I was turning final following it

Don't have a link for that video now as it was lost on my older computer when it crashed. I'll look around and post if I find it.

 

[fog37]

Hello DarioC,

Let me see if I can be more clear if what I was trying to describe: if the air above the wing far from the surface is at regular atmospheric pressure and the air right above the wing surface is at pressure lower than atmospheric pressure, I would envision a pressure gradient directed toward the wing surface.

 

[Joseph M. Zias]

That guy knows a lot about flying and planes and the book is certainly entertaining as well as informative. I didn't read from cover to cover, of course, but one bit leaped out of the screen at me:

"Downwash behind the wing is relatively easy to understand; the whole purpose of the wing is to impart some downward motion to the air."

He is obviously aware of Newton's Third Law so he is, by definition 'A Good Lad" and gets the general principle.

Dr. Denker also has a LOT of comments on theorems in physics and reviews (very critical at times) on textbooks. Take a look at his website: http://www.av8n.com/physics/

 

[boneh3ad]

That guy knows a lot about flying and planes and the book is certainly entertaining as well as informative. I didn't read from cover to cover, of course, but one bit leaped out of the screen at me:

"Downwash behind the wing is relatively easy to understand; the whole purpose of the wing is to impart some downward motion to the air."

He is obviously aware of Newton's Third Law so he is, by definition 'A Good Lad" and gets the general principle.

I am amused by his view of the purpose of a wing. I'd argue that the purpose of the wing is to hold up the plane, and imparting some downward motion to the air is the means by which it achieves this purpose, not the other way around. Otherwise I'd agree.

 

[sophiecentaur]

it achieves this purpose, not the other way around.

How would you feel about saying that the purpose of a planes propellor is to push air backwards or that an aircraft's engine is there to turn the propellor or that the fuel is put into make the engine go? Or even that the pilot is there to make the passengers arrive at JFK.
Causes and effects.

 

[boneh3ad]

How would you feel about saying that the purpose of a planes propellor is to push air backwards or that an aircraft's engine is there to turn the propellor or that the fuel is put into make the engine go? Or even that the pilot is there to make the passengers arrive at JFK.
Causes and effects.

Well, I might argue that the pilot is there so he can earn his paycheck and eat.

 

[sophiecentaur]

Well, I might argue that the pilot is there so he can earn his paycheck and eat.

The toe bone's connected to the foot bone, the foot bone's connected to the ankle bone . . . . . now hear de word of de lawd.

 

[Joseph M. Zias]

I am amused by his view of the purpose of a wing. I'd argue that the purpose of the wing is to hold up the plane, and imparting some downward motion to the air is the means by which it achieves this purpose, not the other way around. Otherwise I'd agree.

From the frame of reference of the pilot - yep, keeping that plane up is Primary. Take a look at his physics site:

http://www.av8n.com/physics/

 

[Joseph M. Zias]

Well, I might argue that the pilot is there so he can earn his paycheck and eat.

Well as a private pilot I spend my money to fly - unfortunately the money tree has lost most of its leaves.

 

[sophiecentaur]

Well as a private pilot I spend my money to fly - unfortunately the money tree has lost most of its leaves.

I sit in my garden and watch guys like you, flying overhead every day. I can hear the cool person of hard earned cash disappearing down a black hole. As a former boat owner, I can sympathise (by a factor of ten, at least).

 

[DarioC]

Fog37, In reply I think you might want to look at what happens at the leading edge of the wing. I am getting close to the limits of my understanding here.
The air running into the leading edge curve is flung/forced upwards which compacts the air above the wing, at the same time making a lower pressure near the surface of the wing. The pressure layers higher up cannot exert downward force because they are being constantly compacted and separated from the wing by the up flow from the curved leading edge.
Pretty cool question you asked, as it made me reorganize what I "knew" about airfoils and think about the details more.
Thanks
DC
Added: Are you familiar with the triangular strips of metal that are put on the leading edge of the wings, near the fuselage to make that part of the wing stall before the outboard part where the ailerons are?
Rather interesting little detail on real-world wings.

 

[OCR]

I am getting close to the limits of my understanding here.

This should "get you over the top" then... .

Click, SHOW MORE, to see more about Doug McLean ...
.

 

[FactChecker]

This should "get you over the top" then... .

Click, SHOW MORE, to see more about Doug McLean ...
.

I think this is an excellent video. As an interested amateur, I wish that I had seen this decades ago. It really gives one a clue that any simple explanation necessarily omits too much and is misleading when predicting lift and drag. That is why CFD programs are used in spite of the huge amount of computer power required and the limitations of the answers.

 

[DarioC]

I think this is the video I mentioned. Pulsed smoke flow in wind tunnel. Check at about 47 seconds.