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Why an Airplane Flies (Bernoulli's Principle vs. Newton's Third Law)


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Studiot, you say, “Fuel is expended and work done to fill the balloon …”

I say, “the work done in inflating the balloon displaces a volume of air equal to the volume of the balloon according to Archimedes, (ignoring the contribution of Aesop 300 years before him). This means the air in the atmosphere will rise by an equal volume. As the atmosphere rises it increases it potential energy.

However, the balloon already has less mass than the air. Hence

 

Potential energy……….m(air)gh > m(helium)gh

 

Gravity pulls more on the heavier air than the helium, hence air descends and the balloon rises. Eventually, because the air gets lighter with height the balloon will occupy the same as an equal volume of air that has the same potential energy. Gravity then pulls equally on the air and the balloon, and the balloon stops rising.

 

Potentail energy……….m(air)gh = m(helium)gh

 

You continue, “or drive the aeroplane”.

I say, “Newton’s first law states ‘every body continues in its state of rest or uniform motion in a straight line except in so far as it is compelled by external forces to change that state.” This law says the airplane will continue in a straight line unless an external force acts on it. The only new force acting on the airplane is drag. Once up to level flying speed the engine no longer provides the airplane with lift, it only counteracts the drag.

A glider incurs drag which in stationary air causes it to lose height. I.e., it loses potential energy. This lost energy manifests itself as kinetic energy in the air that is dragged along with the airplane, vortices and all. The energy needed from an engine in countering the drag is therefore the same as the kinetic energy in the air, is the same as the potential energy lost by the air.

A satellite in space travelling at orbital velocity does not require any engines to keep it up, because there is no drag in space.

 

In your last post, you say, “Talos, do you just wish to preach or are you interested in discussion, which involves acknowledging the contributions of others present in the discussion?”

I say, “No, I don’t want to preach, but I do want to correct errors, misconceptions and wrong ideas. If this is preaching, then so be it.

 


John Cuthber, you say, “When a helium balloon rises up it gains potential energy. No it doesn't.”

I say, yes it does.

 

You continue, “If I have a big He balloon at ground level, I can tie a string to it and wrap that sting round the shaft of a generator. If I let go of the balloon I can get electricity from the generator.

I agree.

You continue, “If I start with the balloon further up I can't get as much electricity before the lift from the balloon is too small to turn the shaft. So, as the balloon rises it looses potential energy.

I say, “If you start with the balloon further up it has already acquired potential energy but it still has some more to acquire. You’re forgetting about the energy already extracted from the air.” Your argument is like saying “if I start with a half full tank I can’t get as much energy from the tank.

 

You continue, “How does the displacement theory explain where the energy comes from?” You tell me- it's not my theory.

I say, “At the risk of rolling Archimedes over in his grave, the displacement theory is a simple illustration of a more complex issue. The issue is concerned with energy. Everything contains energy, whether it be potential energy, kinetic energy or strain energy, or some other form of energy. In essence, a change of one type of energy results in a different form of energy. Hence, air that descends, like everything that descends, loses potential energy and this must go somewhere. It can only go into the balloon; so the balloon gains potential energy as it rises.

 

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Talos

“No, I don’t want to preach, but I do want to correct errors, misconceptions and wrong ideas. If this is preaching, then so be it.

 

Well I would say your last post was not preaching, since it contains attempts to explain your statements, based on views which I assume are honestly held.

So I see no reason for negative points.

 

However the good news is that opening the discussion as you have now done has provided the opportunity for you to reappraise your applications of the laws of mechanics.

 

Firstly the powered aircraft.

 

Yes Newton's laws apply, but you have forgotten an external force.

 

There is a force developed by the propellor or the reaction from a jet, which counters the drag, ans supplies the acceleration force when accelerating.

Both of these arise from the body of air.

 

(A rocket in space is also subject to the reaction from the exhaust when the rocket motor is operational)

 

As to the balloon you have just put the opposite argument since you (appear to) claim that bouyancy forces do not exist, (or have forgotten them).

Therefore by Newton's law, just as you enunciated it, the inflated balloon, sitting on the ground, will not move.

 

Of course we all know that this is not so.

 

You error lies in considering 'potential energy' in this case, but failing to distinguish between gravitation PE, which does not change during the inflation process, and a new potential that arises within the air fluid, due to the inflation process and exactly equls the work done (as you correctly observe) in inflating the balloon.

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Studiot, you say, “Fuel is expended and work done to fill the balloon …”

I say, “the work done in inflating the balloon displaces a volume of air equal to the volume of the balloon according to Archimedes, (ignoring the contribution of Aesop 300 years before him). This means the air in the atmosphere will rise by an equal volume. As the atmosphere rises it increases it potential energy.

However, the balloon already has less mass than the air. Hence

 

Potential energy……….m(air)gh > m(helium)gh

 

Gravity pulls more on the heavier air than the helium, hence air descends and the balloon rises. Eventually, because the air gets lighter with height the balloon will occupy the same as an equal volume of air that has the same potential energy. Gravity then pulls equally on the air and the balloon, and the balloon stops rising.

 

Potentail energy……….m(air)gh = m(helium)gh

 

You continue, “or drive the aeroplane”.

I say, “Newton’s first law states ‘every body continues in its state of rest or uniform motion in a straight line except in so far as it is compelled by external forces to change that state.” This law says the airplane will continue in a straight line unless an external force acts on it. The only new force acting on the airplane is drag. Once up to level flying speed the engine no longer provides the airplane with lift, it only counteracts the drag.

A glider incurs drag which in stationary air causes it to lose height. I.e., it loses potential energy. This lost energy manifests itself as kinetic energy in the air that is dragged along with the airplane, vortices and all. The energy needed from an engine in countering the drag is therefore the same as the kinetic energy in the air, is the same as the potential energy lost by the air.

A satellite in space travelling at orbital velocity does not require any engines to keep it up, because there is no drag in space.

 

In your last post, you say, “Talos, do you just wish to preach or are you interested in discussion, which involves acknowledging the contributions of others present in the discussion?”

I say, “No, I don’t want to preach, but I do want to correct errors, misconceptions and wrong ideas. If this is preaching, then so be it.

 

John Cuthber, you say, “When a helium balloon rises up it gains potential energy. No it doesn't.”

I say, yes it does.

 

You continue, “If I have a big He balloon at ground level, I can tie a string to it and wrap that sting round the shaft of a generator. If I let go of the balloon I can get electricity from the generator.

I agree.

You continue, “If I start with the balloon further up I can't get as much electricity before the lift from the balloon is too small to turn the shaft. So, as the balloon rises it looses potential energy.

I say, “If you start with the balloon further up it has already acquired potential energy but it still has some more to acquire. You’re forgetting about the energy already extracted from the air.” Your argument is like saying “if I start with a half full tank I can’t get as much energy from the tank.

 

You say "yes it does", but I explained why it doesn't.

 

 

“If you start with the balloon further up it has already acquired potential energy but it still has some more to acquire. "

It doesn't acquire energy by giving it away as electricity.

 

"Your argument is like saying “if I start with a half full tank I can’t get as much energy from the tank."

Well, saying “if I start with a half full tank I can’t get as much energy from the tank."

is, of course, right.

So you agree that my argument is right.

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Studiot,

When we inflate a helium balloon it displaces an equal volume of air. Do you not agree?

This causes the atmosphere to rise by an equal volume. Do you not agree?

When the atmosphere rises it increases its potential energy. Do you not agree?

When we release the balloon the air around it descends. Do you not agree?

The descending air then begins to lose some of the atmosphere’s increase of potential energy that inflating the balloon caused. Do you not agree?

The descending air’s loss of potential energy has to go somewhere. Do you not agree?

It can only go into the balloon. Do you not agree?

If the helium escapes or the balloon bursts at any height it will descend to the ground changing its potential energy to kinetic energy as it falls. Do you not agree?

The balloon therefore gained potential energy when it rose. Do you not agree?

 

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You seem to be muddling up two things.
The rubber from which the balloon is made gains potential energy when it rises.

However, the helium in the balloon loses potential energy as it rises.

So, if the balloon bursts then the rubber falls - fair enough.

But if you consider the balloon and the helium together (and that's what the phrase "helium balloon" means then it loses potential energy as it rises.

 

And I'm not going to repeat the details but the fact that the balloon loses potential energy as it rises is the reason why you could extract energy from the system with a bit of string and a generator.

If, as you claim, the balloon ends up with more energy after it has done work turning the generator, where did that energy come from?

 

 

The other thing you have missed is this

"It can only go into the balloon. Do you not agree?"

Yes, but it goes initially into the kinetic energy of the balloon and it subsequently dissipated as heat by viscosity.

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No I do not agree with your chain of 'reasoning' and I have already stated why.

 

You state that the balloon causes the atmosphere to rise.

Why so?

 

Suppose I removed some air adjacent to the balloon (perhaps by freezing it) and equal in volume to the balloon,

Would the atmosphere now rise?

Would the balloon still rise when released?

 

What would happen if I filled the balloon with carbon dioxide instead of helium by mistake?

Would the balloon skin not still push back the atmosphere by the same amount?

 

The point is that the apparatus that inflates the balloon causes the balloon volume to increase against the pressure of the atmosphere around the balloon skin.

Work is done against this pressure and is equal to the volume change times the pressure.

Since this work is done against the atmospheric pressure energy is transferred to the atmosphere as pressure energy, not gravitational potential.

That is what I mean by saying that you need to distinguish types of potential energy.

 

I also mentioned bouyancy force.

 

This is independent of the balloon (once inflated) and is the same upward force regardless of the weight of the balloon.

 

So if the weight of the balloon is less than the BF the balloon will rise, and Newton's First Law is not violated.

 

Work is then done by the bouyancy force minus gravity on the balloon.

 

This work appears as increased gravitational potential energy of the balloon.

Edited by studiot
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You state that the balloon causes the atmosphere to rise.

Why so?

Archimedes and Aesop.

 

Suppose I removed some air adjacent to the balloon (perhaps by freezing it) and equal in volume to the balloon,

Would the atmosphere now rise?

No.

 

Would the balloon still rise when released?

No. It requires the displaced air to descend. The atmosphere hasn’t risen so it doesn’t descend. Archimedes again.

 

What would happen if I filled the balloon with carbon dioxide instead of helium by mistake?

Would the balloon skin not still push back the atmosphere by the same amount?

Yes. But the carbon dioxide has greater potential energy than the air. So the air will not descend.

 

The point is that the apparatus that inflates the balloon causes the balloon volume to increase against the pressure of the atmosphere around the balloon skin.

Work is done against this pressure and is equal to the volume change times the pressure.

Since this work is done against the atmospheric pressure energy is transferred to the atmosphere as pressure energy, not gravitational potential.

You’re wrong. Where do you think the atmospheric pressure comes from?

 

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Suppose I removed some air adjacent to the balloon (perhaps by freezing it) and equal in volume to the balloon,

Would the atmosphere now rise?

No.

 

 

Yes. But the carbon dioxide has greater potential energy than the air. So the air will not descend.

Demonstrably wrong.

All over the world there are compressed air containers that are full of high pressure air.

Someone already took lots of air from the atmosphere and put it into those containers.

Yet balloons still rise

 

And why is there a difference between a heavy gas and a light gas? They both push the atmosphere up equally well. If that was the cause of lift they would both float equally well.

 

 

Also, you have not explained how a balloon on a string can generate electricity by rising unless that energy is taken from the potential energy of the balloon.

If energy is taken from it as it rises then it must have less potential energy when it's high up.

Edited by John Cuthber
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You’re wrong. Where do you think the atmospheric pressure comes from?

 

You are so nearly there it is a shame if you don't want to listen.

 

Or are you, perhaps, just repeating something you half heard sometime ago?

 

You have a balloon sitting limply on the ground, showing no signs of going anywhere.

 

Newtons First Law : A body continues in its state of rest or steady motion unless acted on by a (net) Force.

 

So the limp balloon is not being acted on by a force.

 

You come along and inflate the balloon so that it rises off the ground.

 

So Newton requires there to be a force acting on the balloon.

 

Can you name this force and describe it please?

Edited by studiot
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Where do you think the atmospheric pressure comes from? I take it that you don’t know.

 

I am aware of the laws of hydrostatics.

 

But that doesn't matter to the question I asked you or to Newton's laws of motion or to the Laws of thermodynamics.

 

Particularly as you denied their truth

 

 

You’re wrong

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Swansont,

If the conjecture is right, then if you inflate a helium balloon in a closed room, it shouldn't rise, since the displaced air can't simply go up. I think we can conclude that this isn't the case.

Inflating a balloon in a closed environment will still displace a weight of air equivalent to the volume of the helium. The displacement however comprises air which is compressed. This again means it has greater potential energy, just as if it had risen, as before.

 

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Swansont,

If the conjecture is right, then if you inflate a helium balloon in a closed room, it shouldn't rise, since the displaced air can't simply go up. I think we can conclude that this isn't the case.

Inflating a balloon in a closed environment will still displace a weight of air equivalent to the volume of the helium. The displacement however comprises air which is compressed. This again means it has greater potential energy, just as if it had risen, as before.

 

So, if I inflate a balloon with carbon dioxide in a sealed room, it should rise.

 

Do you know that the rules of this forum require that you respond to reasonable questions?

 

So, once again. why is there a difference between a heavy gas and a light gas? They both push the atmosphere up (or compress the air in the room) equally well. If that was the cause of lift they would both float equally well.

 

 

Also, you have not explained how a balloon on a string can generate electricity by rising unless that energy is taken from the potential energy of the balloon.

If energy is taken from it as it rises then it must have less potential energy when it's high up.

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When we inflate a helium balloon it displaces an equal volume of air. Do you not agree?

This causes the atmosphere to rise by an equal volume. Do you not agree?

When the atmosphere rises it increases its potential energy. Do you not agree?

When we release the balloon the air around it descends. Do you not agree?

The descending air then begins to lose some of the atmosphere’s increase of potential energy that inflating the balloon caused. Do you not agree?

The descending air’s loss of potential energy has to go somewhere. Do you not agree?

It can only go into the balloon. Do you not agree?

If the helium escapes or the balloon bursts at any height it will descend to the ground changing its potential energy to kinetic energy as it falls. Do you not agree?

The balloon therefore gained potential energy when it rose. Do you not agree?

 

 

Talos, I suggest we construct a scale model to study this phenomenon. Ideally, air would be the best choice but we cannot create a scale model of the atmosphere that possesses a graduated decrease going from the highest pressure at its base to nearly zero at the models highest point.

 

But water would work well for a proxy. If we had a clear plastic cylinder 50 meters high containing water, it would have approximately 5 bars of pressure at its base and half that at 25 meters, and thus can effectively graduate the hydrostatic pressures so forth for its entire height.

 

To start with, we will lower a weighted balloon into the empty cylinder, the balloon is ballasted to have a neutral buoyancy at approximately 2.5 bars at 25 meters in depth.

 

Next, we will slowly fill the cylinder from below with water from a measured source.

 

I believe the balloon will not lift off the cylinder’s bottom until the water reaches above 25 meters. Do you agree?

 

When the water reaches 26 meters the balloon will be one meter off the bottom. Do you agree?

 

Do you believe the water moves down to raise the balloon?

 

As water is added the balloon will rise in proportion, this is neutral buoyancy. If the cylinder was full to the top and the balloon was released from the bottom it would rise to the 25 meter level and stop.

 

To do so the water above it will have to move down past the balloon as it rises, I think this detail is over complicating your understanding of this process. For example, when something sinks the water moves past the object.

 

Is this water pushing the object down?

 

This is negative buoyancy. Is there really a void to fill, the pressure is from all directions at any given point and is immediately filled in by the nearest source, molecule by molecule.

 

Does this simple model seem to be in accord with your hypothesis?

 

The water, or air for that matter, moving past the rising (or sinking) object is not doing so to fill the void and thus propel the balloon any more than the air you're car is driving trough is moving your car forward.

 

Any buoyant object is in direct opposition to the hydrostatic pressure surrounding it, and is being moved upwards by the higher pressure from below, and as it does this it is continually moving to a lower pressure state above. In the simplest of terminology, it is being squeezed and is moving in the path of least resistance.

 

 

When we inflate a helium balloon it displaces an equal volume of air.

This causes the atmosphere to rise by an equal volume.

 

As compared to the rather small proportional differences of the balloon and cylinder of the model, the balloon in proportion to the atmosphere is inconsequential to the atmospheres volume.

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All over the world there are compressed air containers that are full of high pressure air.

Someone already took lots of air from the atmosphere and put it into those containers.

Yet balloons still rise

John, if all the compressed air in these containers were discharged back into the atmosphere it would rise and increase it potential energy. Also, It’s not the atmosphere’s height that causes balloons to rise, but the potential energy they contain compared to an equal volume of air around them. This is true for a carbon monoxide balloon; so it can’t rise, whether in the atmosphere or a closed environment.

I haven’t forgotten your question about the generator and will answer it in due course.

 

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Swansont,

If the conjecture is right, then if you inflate a helium balloon in a closed room, it shouldn't rise, since the displaced air can't simply go up. I think we can conclude that this isn't the case.

Inflating a balloon in a closed environment will still displace a weight of air equivalent to the volume of the helium. The displacement however comprises air which is compressed. This again means it has greater potential energy, just as if it had risen, as before.

 

 

Only the air above compresses? How does that work, exactly?

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All of you, here’s your answer; taken from question and answers at Department of Physics. University of Illinois at Urbana-Champaign.

 

Question: Consider the three statements 1)Air pressure acts from all directions 2)Air pressure is due to the motion of air molecules 3)Air pressure is caused by the weight of air above Statements 1 and 2 seem logical to me. Statement 3 seems illogical to me -obviously pressure in gases is dependent upon temperature and pressure and will decrease as one rises in the atmosphere but not because of a decrease in the weight of air molecules pushing down from above. My question. is there a fault to my reasoning? Many thanks for your help Stephen
- Stephen (age 57)
Risch, Zug, Switzerland

 

Answer: Many questions about causation raise philosophical issues, since the meaning of causation isn't very clear. Here I think we all have no problem with the first statement, which is just an empirical fact. Your second statement is a pretty non-controversial one as well, since if you take away the air molecules the pressure goes away and if you keep the same density but have them move slower the pressure is reduced. In fact, you might say that the moving air molecules are the proximate cause of the pressure.

 

So the third statement is the one that bugs you. The atmospheric weight isn't quite as proximate a cause of the pressure as is the local atmosphere. If you quickly removed all the atmosphere above say 1 km (see Spaceballs) it would take a little bit of time before the pressure down here dropped. Essentially no effect would be noticed until time of 1km/(speed of sound) or about 3 seconds. Still, if you removed that weight pretty soon the pressure here would indeed drop, so there's a decent sense in which you can say the weight causes the pressure. The basic point is this: The net force on a column of air above us is zero, in equilibrium. The downward force on it is just gravity, its weight. The upward force is just the pressure of the air down here times the cross-sectional area of the bottom of the column. So the weight does determine the pressure, in equilibrium although not quite instantly.

 


Swansont,

Only the air above compresses? How does that work, exactly?

The inflated balloon has the same pressure inside as the air outside.

 

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Swansont,

Only the air above compresses? How does that work, exactly?

The inflated balloon has the same pressure inside as the air outside.

 

 

If the air above compresses, the pressure goes up. The air below is at the same pressure, so you have created a situation where there is a pressure difference at the height of the top of the balloon. That's not a stable condition. How does the system maintain the pressure differential?

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Studiot, So, Talos, your University link says that you were wrong and everybody else was right.

Re read it. It confirms everything I say.

 


If the air above compresses, the pressure goes up. The air below is at the same pressure, so you have created a situation where there is a pressure difference at the height of the top of the balloon. That's not a stable condition. How does the system maintain the pressure differential?

The air pressure below is not at the same pressure, it is increased because the head of air has risen; Archimedes again.

 

 

 

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