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Bernoulli's equation

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Old 02-16-2004, 08:01 PM
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elmerfud
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Default Bernoulli's equation

Ok. If I have this correct,,,, in Bernoulli's equation,, he came to the conclusion(in a nutshell or laymans terms) that when the velocity of air is sped up…it will cause lower pressure.(over an airplane wing for example)
Or if the speed of liquid is sped up.. it would cause lower pressure.. (through a venturi in a pipe for example)
Hence..the airflow going over the symmetrical wing(top side in this case) will be going faster then the flat bottom side(also for this example). So low pressure will be above the wing. And higher pressure will be below the wing… causing it (the wing)to have lift. With me so far>?
So if the wing is symmetrical. On both sides… does that not make this equation for creating lift no good>? Because pressure would be the same on both sides>? No lift/same pressure on both top and bottom>?

photo has formula.(below)
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Old 02-16-2004, 08:12 PM
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David Cutler
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Default RE: Bernoulli's equation

The lift is created by a combination of angle of attack and the Bernoulli effect you mentioned.

Especially with a thick wing section, when you get a positive angle of attack, the effective centre of the leading edge moves downwards, thus making it a longer distance over the top of the wing compared with the underside.

I'm sure it's more complex than this, but I reckon that's why a thick section works better at slower speeds than a thin section. If you have a thicker leading edge then the forward-most point of the wing at positive angles of attack moves further down so greater lift is created by the differential between the top and the bottom distance.

-David C.
Old 02-16-2004, 08:48 PM
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elmerfud
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Default RE: Bernoulli's equation

ah that makes sense... the "angle of attack"....i know if you increase the angle of attack. you get more drag though... so it takes more power to fly at same speed with the higher angle... thats why i would assume. they tell newbie`s to start with a flat bottomed wing.//// more stable at lower speeds... ect ect.
Old 02-16-2004, 09:57 PM
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David Cutler
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Default RE: Bernoulli's equation

True.

Actually, lift is proportional to drag in all circumstances.

That's why, when you make a turn by rolling with the ailerons, then applying up elevator there is a tendency to yaw away from the turn, and to make a fully coordinated turn you have to apply a little rudder towards the turn. The outside wing is creating more lift (hence the roll into the turn) and therefore, more drag, so it yaws towards the wing with the greater lift, that is, away from the turn.

-David C.
Old 02-16-2004, 10:03 PM
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LouW
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Default RE: Bernoulli's equation

This subject was beat to death last year, and if you look up the thread, I think you will find more than you want to know. Basically, Bernoulli was describing flow in pipes, not in a free field. Every wing section, both cambered and symmetrical, has an angle at which it produces no lift. If angle of attack is measured from this “zero lift” line rather the chord line it becomes obvious that there is no other explanation for lift other than angle of attack. Lift depends on asymmetrical flow regardless of the shape of the airfoil. The shape of the section only becomes important when it is desired to produce lift with a minimum of drag.
Old 02-16-2004, 10:15 PM
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David Cutler
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Default RE: Bernoulli's equation

Lift depends on asymmetrical flow regardless of the shape of the airfoil. The shape of the section only becomes important when it is desired to produce lift with a minimum of drag.
If that's true, then how come a ball moves towards the flow if you blow over just one edge of it? There is no angle of attack effect as you aren't blowing over the bottom and pushing it upwards. It must be caused by a lowering of the pressure in' free air' over the top.

-David C.
Old 02-16-2004, 11:30 PM
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Tall Paul
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Default RE: Bernoulli's equation

" This subject was beat to death last year,.."
It truly was... The Bernoullis vs the Newtonians..
No one wins.
Old 02-16-2004, 11:55 PM
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LouW
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Default RE: Bernoulli's equation

Actually, Paul, both sides win. They are just two ways of looking at the same thing. One side sees only trees, the other side sees a forest. Both are right.
Old 02-17-2004, 07:58 AM
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rmh
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Default RE: Bernoulli's equation

Lift is the drag in the direction you wanted
Drag is lift in the direction you didn't want.
Yin and Yang
Old 02-17-2004, 10:47 AM
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banktoturn
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Default RE: Bernoulli's equation

LouW,

I don't know what particular problem Bernoulli had in mind when he did his work, but the "Bernoulli equation" is valid for flow around a wing, as well as for flow in pipes. In particular, one can use the Bernoulli equation to calculate the variation in pressure as a result of variations in velocity, along a streamline. As long as you apply it along a streamline, this works for pipes, wings, sneezes, ... whatever. Pressure really does go down when velocity goes up, along a streamline, and this phenomenon really does explain one of the main reasons wings generate lift. It is not correct or useful to say that angle of attack is the only explanation of lift. It is also incorrect to assert that Newton explains lift and Bernoulli doesn't. It is correct to note that a symmetric wing must be operated at a positive angle of attack to generate lift.

banktoturn
Old 02-17-2004, 10:50 AM
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David Cutler
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Default RE: Bernoulli's equation

ORIGINAL: banktoturn

LouW,

I don't know what particular problem Bernoulli had in mind when he did his work, but the "Bernoulli equation" is valid for flow around a wing, as well as for flow in pipes. In particular, one can use the Bernoulli equation to calculate the variation in pressure as a result of variations in velocity, along a streamline. As long as you apply it along a streamline, this works for pipes, wings, sneezes, ... whatever. Pressure really does go down when velocity goes up, along a streamline, and this phenomenon really does explain one of the main reasons wings generate lift. It is not correct or useful to say that angle of attack is the only explanation of lift. It is also incorrect to assert that Newton explains lift and Bernoulli doesn't. It is correct to note that a symmetric wing must be operated at a positive angle of attack to generate lift.

banktoturn
FWIW, I agree totally!

-David C.
Old 02-17-2004, 11:18 AM
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JimTrainor
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Default RE: Bernoulli's equation

Mr B.'s equation is an energy balance.

Potential (static pressure)
+
Kinetic ( 1/2 row V^2 )
=
Constant

... as such, of course it applies anywhere and everywhere energy is conserved. It easier to apply to pipe than it is to a free flow. Applying it to a sneeze may be grand challenge computing territory.
Old 02-17-2004, 11:31 AM
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banktoturn
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Default RE: Bernoulli's equation

Jim,

Yes, it applies anywhere and everywhere that energy is conserved, but you have to make sure that you are dealing with the same 'piece' of air, which is why one can only take advantage of the relation along a streamline. It is 'easy' to apply when you know the path of a streamline. For attached flow around a wing, this is easy, since we know that one streamline follows the surface of the wing, from the leading edge (stagnation point) to the trailing edge. For the turbulent flow in a separation region, it isn't feasible. Same for pipe flow (meaning that there are situations in which the paths of streamlines are known, and there are situations in which they aren't).

banktoturn
Old 02-17-2004, 11:48 AM
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David Cutler
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Default RE: Bernoulli's equation

Applying it to a sneeze may be grand challenge computing territory.
Oh I dunno. Somebody at our flying field recently sneezed and his head imploded from excess pressure!



-David C.
Old 02-17-2004, 12:48 PM
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LouW
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Default RE: Bernoulli's equation

Actually the Bernoulli equation is a mass balance (conservation of mass). It simply states that within the confines of a stream tube , the mass passing through each section must be equal. Obviously if the section gets smaller, the velocity of the mass must increase. This increase in velocity can only happen if there is an unbalanced force. To exist, this force demands a lower pressure at the smaller section in order to accelerate the mass. It is only valid for a fluid that is incompressible (which air is not) and inviscid (which air is not), and for flow confined within a stream tube. Within the limits of its’ derivation, it is an extremely useful concept.

It is not a matter of whether Bernoulli or Newton is right. In fact they are simply two ways of looking at the same thing. If you are designing wing sections and need to explore the pressure field around an airfoil, Bernoulli is the only way to go, but if you are flying an aircraft that is already designed and built, Newton gives a better understanding of what is going on.

In fact the air is not flowing at all. It is essentially still, and the airplane is moving through it. This doesn’t make any difference as far as the pressure distribution around the wing is concerned, but is highly significant to a pilot, who is trying to move along a certain path through the air.

In either case, the overly simplified explanation of lift, usually seen in popular books involving a flat bottom airfoil, is not quite accurate. Bernoulli works just as well for a flat plate moving at some angle of attack as it does for a Clark Y. As I stated before, if angle of attack is related to the zero lift line (rather than the chord) it becomes obvious that it is really the secret of lift.
Old 02-17-2004, 12:55 PM
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acropilot_ty
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Default RE: Bernoulli's equation

The awnser to your questions comes from a better understanding of Pressure. At any given point in the atmosphere you have a given static pressure, which is just created by the stack of air on top of it pushing down due to gravity. At sea level this static pressure is about 15 PSI. When you give air velocity you add dynamic pressure to the static pressure due to the momentum of the air molecules (which have mass). This combined pressure is called Total Pressure. Total pressure must be conserved... so at a given Aircraft Velocity there is a given total pressure. Lets say that the dynamic pressure is 2 PSI for the sake of aurgument... that would mean that the total pressure is 17 PSI... As the air flows over the aircraft the total pressure can not exceed 17 PSI, pressure can't just be created like that, and at the same time total pressure can not be disipated (except through skin friction, or flow separation which disipates pressure through heat, sound, vibration ect...). So as the air speeds up to get around the airplane the dynamic pressure increases, lets say it goes up to 3 PSI... that means that the static pressure drops down to 14 PSI. You can see that the shape at a given angle of attack can be changed to either speed up, or slow down air and therefore increase or decrease pressure. But, this has very little affect when compared to changing the angle of attack, which results in large differences in flow velocity between two sides of a surface (like a wing)... I fly decathlons inverted every day... they have two percent camber to tailor the wing for upright flight... give it enough angle of attack inverted and it'll fly just fine, in fact I have done several outside loops in the decathlon even with this positive cambered airfoil.

Ty
Old 02-17-2004, 02:59 PM
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Tall Paul
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Default RE: Bernoulli's equation

"So as the air speeds up to get around the airplane the dynamic pressure increases, lets say it goes up to 3 PSI... that means that the static pressure drops down to 14 PSI."
???
Whuffo you can't change total pressure, but you can change static pressure? There's so much more of it !
The highest pressure the airplane sees is that air which strikes the surface directly.. At the "stagnation point" on an airfoil, or the front opening in a pitot tube reads this pressure.
This pressure is compared to the static pressure the airplane is flying in, and the result is dynamic pressure. Which is another word for airspeed.
The total pressure then diminishes from the impact point as the air moves around the surface.
The static pressure remains static and is read by the orifices around the sides of the pitot tube, some calculuated back from the tip.
The orifice which reads static presssure for the altimeter and airspeed indicator is generally located where there will no interference with the flow from anything upstream. (The "Keep this area free" notation on a shiny round patch on a plane.)
In a simple pneumatic airspeed indicator, the total pressure is fed into a curved tube in the instrument case, blocked so there's no flow in the tube.
The static pressure is fed into the case of the instrument. Vented to atmosphere, in essence thru the static port on the side of the fuselage.
As the pressure increases in the dynamic pressure tube, it uncurves, and moves a gear set which moves the indicator needle.
If the static pressure field could change around the airplane, then possibly there might be a burp in the indicated airspeed, but that would be something extremely unusual.
Old 02-17-2004, 04:38 PM
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LouW
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Default RE: Bernoulli's equation

Actually, acropilot_ty has it nailed. But the explanation may be just a little hard to follow. You are both saying the same thing regarding total pressure being constant (as long as the airspeed is constant). And furthermore it consists of dynamic pressure at the stagnation point plus the remote static pressure of the air the airplane is operating in. This remote static is read from a port located so as not to be affected by speed.

He is saying that as the air is forced around the airplane and over the wing it speeds up and the local dynamic pressure increases and the local static pressure decreases a corresponding amount. This is exactly what happens.

Furthermore, if the pitch attitude is such that the wing is moving into the air at it’s zero lift angle. The net sum of change of local static pressures will be zero and no lift will be generated (duh). If the angle of attack is increased, lift will be produced proportional to that angle up to the point that the wing stalls. Angle of attack produces lift. It does it by changing the pressure field around the wing in accordance with Bernoulli’s principles. It will do so regardless of the shape of the airfoil, even if it is a flat plate. The shape only determines how much drag will result, and how far the angle can increase before it stalls.
Old 02-17-2004, 05:15 PM
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David Cutler
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Default RE: Bernoulli's equation

I understand your points, but, surely, it's simpler to think of it this way:-

If it is, indeed, a greater distance across the top of a wing than the bottom, the air relative to the wing, has to it has to travel further in the same time, therefore it travels faster, and conservation of energy tells us that this increase in kinetic energy has to come from somewhere

Two places it can come from are heat (the energy in the temperature of the air; it cools down, contributing to the creation of vapor trails as the water comes out of saturated solution at the lower temperature), and from potential energy in the pressure, thus reducing the pressure on the top of the wing.

Maybe!

Of course, this implies that lift can be created at zero angle of incidence with an asymmetric airfoil, and I'm open to suggestions that this isn't true!


-David C.
Old 02-17-2004, 06:52 PM
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Tall Paul
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Default RE: Bernoulli's equation

ORIGINAL: LouW

Actually, acropilot_ty has it nailed. But the explanation may be just a little hard to follow. You are both saying the same thing regarding total pressure being constant (as long as the airspeed is constant). And furthermore it consists of dynamic pressure at the stagnation point plus the remote static pressure of the air the airplane is operating in. This remote static is read from a port located so as not to be affected by speed.

He is saying that as the air is forced around the airplane and over the wing it speeds up and the local dynamic pressure increases and the local static pressure decreases a corresponding amount. ...
.
Well, no.
The postulated 1 psi change in static pressure to keep the total pressure the same is a change in indicated airspeed from 144 knots to 246 knots!.
This can't happen.
....
Running some numbers thru an airspeed program..
Conditions: Alt = 2500'
OAT=15° C
Ps=27.3 in. hg. 13.4 psi
CAS=144 knots
Pt=28.3 in. hg. 13.9 psi
q=1 in. hg., .49 psi
............
CAS=202 knots
Pt=29.3 in. hg., 14.3 psi
q=2 in. hg. .98 psi
.........
CAS= 246 knots
Pt=30.3 in. hg. 14.9 psi
q=3 in. hg, 1.47 psi
.
Changing the Ps to 1000 feet from the 2500 feet above is equivalent to a 1 psi change.
The q value remains the same as does the airspeed.
The delta pressure change of 1 psi is STILL equivalent to an indicated change of 102 knots, whether the dynamic or static changes.
Not representative of the real world.
Old 02-17-2004, 07:03 PM
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95tequesta
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Default RE: Bernoulli's equation

Just something to think about.
Can make a barn door fly? That is produce lift sufficient enough to be controlled.
Old 02-17-2004, 08:42 PM
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Tall Paul
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Default RE: Bernoulli's equation

ORIGINAL: 95tequesta

Just something to think about.
Can make a barn door fly? That is produce lift sufficient enough to be controlled.
.
OFF TOPIC!
Old 02-17-2004, 08:57 PM
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BruceDana
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Default RE: Bernoulli's equation

Here is some good reading if you are trying to understand what is going on:

http://www.aa.washington.edu/faculty/eberhardt/lift.htm

http://www.eskimo.com/~billb/wing/airfoil.html

The debate is like religion, the other explanation is wrong because it is not belived by me...
Old 02-17-2004, 09:47 PM
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LouW
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Default RE: Bernoulli's equation

I think you are taking his example too literally. His choice of figures aren't real world and I suspect he just pulled them from his head without running them through a program, just to illustrate his point, which is a valid point. That is, as the air speeds up to go around/above the airplane. local static pressures go down in accordance with the now infamous Bernoulli.
Old 02-17-2004, 10:45 PM
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elmerfud
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Default RE: Bernoulli's equation

well... i have had some great reading..i had no idea. on the perverbial "can of worms" i was opening..


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