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

[jartsa]

What kind of thing is a low pressure stream of air? Shouldn't it implode like low pressure things in a high pressure environment do?

I don't know, but maybe on the output side of a fan the pressure is normal, as there does not seem to be any explosion or implosion occurring there, while on the other side there is a under pressure, as the air seems to be imploding from all directions towards the fan there.

 

[jartsa]

The air stream on the output side of a fan or propeller has high pressure, and it continues to accelerate as it's pressure lowers to ambient. As the stream velocity increases (while its pressure decreases), it's ideal cross sectional area should decrease, but viscosity draws in the surrounding air. The stream from a fan or propeller remains a stream for some distance downstream of the fan or propeller.

How about if on the output side of a fan the pressure is normal, as there does not seem to be any explosion or implosion occurring there, while on the other side there is a under pressure, as the air seems to be imploding from all directions towards the fan there?

 

[rcgldr]

How about if on the output side of a fan the pressure is normal, as there does not seem to be any explosion or implosion occurring there, while on the other side there is a under pressure, as the air seems to be imploding from all directions towards the fan there?

Take a look at this NASA article about propellers. The flow is idealized in that viscosity effects with the surrounding air are ignored, but the main concept is that as air flows across the area swept out by a fan / propeller, there's little change in speed, with mostly an increase in pressure from below ambient to above ambient. Note that the "exit" point where the stream's pressure decreases back to ambient is well downstream of the propeller (again this is idealized).

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

 

[Justintruth]

Consider two straight walled cans with a gap between them and the walls parallel making a canyon between them.

Imagine balls are sent into the gap by giving them two kicks, one that imparts a velocity parallel to the wall and another perpendicular to the wall. Imagine the balls initially enter the gap right at the center of the gap equally far from each wall. Without going into the math clearly you can see that if the ball travels down the length of the channel between the walls before it crosses 1/2 the distance between the cans it will exit without hitting a wall. So you have 4 numbers the velocity parallel, perpendicular, the width between walls and the distance down the channel to the exit. If the parallel velocity is high enough relative to the perpendicular velocity and the channel short in length enough relative to the distance between the cans then no balls will strike the wall but change those numbers and some will. So you can control the pressure on the wall by adjusting the velocity and the lengths.

Note now that the cans only ever move apart in this situation or stay at rest. They can't move in. This is the case of the vacuum and we might predict that in a vacuum the cans move apart not in. At least its a clue!

Now imaging that there are other balls moving with some random velocity on all sides of the cans before we start. Before we start balls are hitting on all sides of the can so it doesn't move. As the kicked balls enter the chamber they will begin to collide with the balls inside and in general the balls in between the containers will start to move more parallel to the walls. So fewer will strike the walls. But the same number of balls will strike the walls on the outside (other side) of the cans. So the cans are pushed together by the imbalance.

Now we can predict that the cans will move together less if we were to lower the temperature of the random balls and we might even predict that if we lowered the temperature and maybe put fewer random balls there and made the walls long enough and the gap short enough that we could get the walls to even move apart. Say at very low atmospheric pressure.

We also must give gravity its due. Without gravity the random balls would move away and after a short time we would have the vacuum experiment and the cans would move apart.

A round can is harder because it will also be pushed away from the straw not just out or in.

In general I find using continuum mechanics a problem. For example consider a ring made of a continuous and homogenous material rotating about its center in the plane of the ring. Note that there is no way to distinguish whether there is motion because the material has exactly the same properties. We are forced to use haecity and say that "this" material moved out of a given segment of the ring and "that" material moved in. But what is the difference to what is? It is a lesson on the meaning of the term "matter" and how it cannot be reduced totally to the properties of the object involved. So we find that we are distinguishing between matter not by properties. Its a little strange at best. But this can only be solved by the philosophers.

Consider also the argument given for a wing that the path over the wing is longer so the air must go faster reducing the pressure. What a dumb argument! Imagine a wedge shaped wing whose cross section is a right triangle will one leg parallel to the ground. No one would be crazy enough to believe that that wing would provide lift if run with the point toward the velocity vector. And yet the path is longer. I can remember hearing this explanation in a physical science class and feeling a little alone in seeing that something just didn't make any sense in it.

 

[Justintruth]

Consider two straight walled cans with a gap between them and the walls parallel making a canyon between them.

Imagine balls are sent into the gap by giving them two kicks, one that imparts a velocity parallel to the wall and another perpendicular to the wall. Imagine the balls initially enter the gap right at the center of the gap equally far from each wall. Without going into the math clearly you can see that if the ball travels down the length of the channel between the walls before it crosses 1/2 the distance between the cans it will exit without hitting a wall. So you have 4 numbers the velocity parallel, perpendicular, the width between walls and the distance down the channel to the exit. If the parallel velocity is high enough relative to the perpendicular velocity and the channel short in length enough relative to the distance between the cans then no balls will strike the wall but change those numbers and some will. So you can control the pressure on the wall by adjusting the velocity and the lengths.

Note now that the cans only ever move apart in this situation or stay at rest. They can't move in. This is the case of the vacuum and we might predict that in a vacuum the cans move apart not in. At least its a clue!

Now imaging that there are other balls moving with some random velocity on all sides of the cans before we start. Before we start balls are hitting on all sides of the can so it doesn't move. As the kicked balls enter the chamber they will begin to collide with the balls inside and in general the balls in between the containers will start to move more parallel to the walls. So fewer will strike the walls. But the same number of balls will strike the walls on the outside (other side) of the cans. So the cans are pushed together by the imbalance.

Now we can predict that the cans will move together less if we were to lower the temperature of the random balls and we might even predict that if we lowered the temperature and maybe put fewer random balls there and made the walls long enough and the gap short enough that we could get the walls to even move apart. Say at very low atmospheric pressure.

We also must give gravity its due. Without gravity the random balls would move away and after a short time we would have the vacuum experiment and the cans would move apart.

A round can is harder because it will also be pushed away from the straw not just out or in.

In general I find using continuum mechanics a problem. For example consider a ring made of a continuous and homogenous material rotating about its center in the plane of the ring. Note that there is no way to distinguish whether there is motion because the material has exactly the same properties. We are forced to use haecity and say that "this" material moved out of a given segment of the ring and "that" material moved in. But what is the difference to what is? It is a lesson on the meaning of the term "matter" and how it cannot be reduced totally to the properties of the object involved. So we find that we are distinguishing between matter not by properties. Its a little strange at best. But this can only be solved by the philosophers.

Consider also the argument given for a wing that the path over the wing is longer so the air must go faster reducing the pressure. What a dumb argument! Imagine a wedge shaped wing whose cross section is a right triangle with one leg parallel to the ground. No one would be crazy enough to believe that that wing would provide lift if run with the point toward the velocity vector. And yet the path is longer. I can remember hearing this explanation in a physical science class and feeling a little alone in seeing that something just didn't make any sense in it.

 

[Justintruth]

I have tried to understand the two cans problem by considering a bunch of tennis balls shot towards the space between two trash cans. If some of the balls hit the trash cans, it would tend to push the cans apart. What makes this scenario very different from the one in post #1 is that here the cans aren't already surrounded by bouncing tennis balls on all sides. If they were, the end result would be the product of two things:

1. Some of our tennis balls hit the cans. This tends to push them apart.
2. Some of our tennis balls will collide with the tennis balls that are already bouncing around in front of our tennis ball cannon. This should knock a few of them away from the region between the cans, but it should also knock a few into that region. So it's hard to predict what the effect will be.

The result of the experiment described in post #1 (the cans move closer together) tells us that the second thing above tends to pull the cans together.

Unfortunately this argument doesn't tell us that the pressure between the cans is lower. It just gives us a rough idea what causes that low pressure.

My opinion is you should forget pressure completely and in fact forget continuum mechanics in general, and just look at the exchange of momentum between the balls and the cans. (BTW I thought this response didn't get in so I re-wrote it - scuse me). If you can see how in the vacuum case you can cause tennis balls to miss hitting the can because they pass through the gap too quick - before they can hit the wall they are out - then you can derive everything else. Just try to see that if I put a nozzle right at the centerline and could independently control the velocities parallel and perpendicular to the walls of the can that I could affect the number of balls that hit the walls. And also see that I can reduce the number - even to zero - by making the velocity down the channel fast compared to the velocity perpendicular to the channel. Only after this go to the non-vacuum case and see why the cans move in. There is nothing different between thermal velocities and regular velocities. The random motion is just motion. You could cause a nearly complete vacuum with the right blast and engineered collisions even. No balls would be between the walls then. Surely the collisions on the opposite sides of the cans would move them together. You can get a lot out of this model. The numbers of particles, gaps between the cans, length of the cans, density of the random balls and their average speed - in all these cases you can see how they affect the outcome. For one thing you can predict that if you did this experiment at higher and higher altitudes the cans at one point would stop moving together and start to move apart with the right setting of the blast from the straw of course.

 

[Justintruth]

I thought of an even easier example. Just imagine a very large hammer swinging through the gap between the cans at a velocity so high that the randomly moving balls cannot keep up with its back side. Imagine the hammer is sized to the gap with little tolerance. Surely it can knock nearly all the gas out of between the walls of the cans with one very fast blow. So you can see what is happening and what is causing the vacuum! Something is knocking the air out from between the cans. The fact that they will move together then becomes more obvious.

A vacuum is created behind the hammer because it is moving so fast that the particles thermal velocity is to slow to keep up. The hammer does not draw them toward it in any way - gravitation between the hammer and the air is negligible. This is called cavitation and is a problem sometimes in rudders.

 

[mfig]

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.

The velocity vector plot is interesting in that it shows the air is being entrained from both the near and far side of the can (as measured from the straw end), and this causes a stagnation point opposite the low pressure zone between cans. The vectors are normalized so the size doesn't mean anything. The colors display the magnitude of the velocity at the arrow's tail.

I solved this several times while moving the can further from the straw. At some point, the can more fully enters the velocity 'cone' and a stagnation point arises on that side of the can which counteracts the low pressure region between the cans. This disrupts the smooth entrainment seen when the can is close. Also, the air starts to circulate in one direction (clockwise) around the can. I can post images, if there is interest.

I am not sure how much insight this gives to others, but it was interesting to look at with CFD.

Cheers!

 

[Justintruth]

It might be interesting to make a square can and vary the length of the can in the x direction. Will a very long square can move out or in?

How short must the can be to move in?

Also, the graphic is showing 0 velocity behind the can. I think this means 0 average velocity - meaning the vector sum of all of the particles. Temperature, in other words has no effect on the color or the "velocity" reported. There must be some velocity of the particles behind the can. I bet that at absolute zero the can will not move in. Or that you can stop the motion by evacuating the air - lowering the air pressure. Does the program allow you to do that?

 

[mfig]

It might be interesting to make a square can and vary the length of the can in the x direction. Will a very long square can move out or in?

How short must the can be to move in?

Also, the graphic is showing 0 velocity behind the can. I think this means 0 average velocity - meaning the vector sum of all of the particles. Temperature, in other words has no effect on the color or the "velocity" reported. There must be some velocity of the particles behind the can. I bet that at absolute zero the can will not move in. Or that you can stop the motion by evacuating the air - lowering the air pressure. Does the program allow you to do that?

Hello Justintruth,

• The velocity is not actually zero behind the can. The vector plot shows that there is a velocity. The contour plot is deceiving that way, as it only shows a few levels so things look homogeneous.
• I edited my previous post to say I ran several models where I moved the can to the right in 5cm increments, and I did see a point where the can entered the velocity 'cone' sufficiently that a stagnation point develops on the jet side of the can, which may mark the beginning of turning point where the stream does not push the cans together. 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).
  
• Temperature is 300 K throughout, as I did not solve for thermal transport.
  
• It would be really interesting to plot the net force (y component) as a function of distance from the straw end, f(x), for a fixed y displacement.
• I am not sure what you are asking about the CFD program. Do you mean to ask if the program will allow me to turn the straw 'blowing' into the straw 'sucking' air? Yes, it will.

Cheers!

 

[Justintruth]

I am not sure what you are asking about the CFD program. Do you mean to ask if the program will allow me to turn the straw 'blowing' into the straw 'sucking' air? Yes, it will.

Reference https://www.physicsforums.com/threa...objects-why-is-the-pressure-low.893581/page-3

No. I was wondering whether you could lower the air pressure. Like moving the experiment to a mountain top then higher and higher until you reach vacuum.

 

[Fredrik]

I thought of an even easier example. Just imagine a very large hammer swinging through the gap between the cans at a velocity so high that the randomly moving balls cannot keep up with its back side. Imagine the hammer is sized to the gap with little tolerance. Surely it can knock nearly all the gas out of between the walls of the cans with one very fast blow. So you can see what is happening and what is causing the vacuum! Something is knocking the air out from between the cans. The fact that they will move together then becomes more obvious.

A vacuum is created behind the hammer because it is moving so fast that the particles thermal velocity is to slow to keep up. The hammer does not draw them toward it in any way - gravitation between the hammer and the air is negligible. This is called cavitation and is a problem sometimes in rudders.

I'm not sure this argument works. Maybe it does if the hammer is super-fast. But if its speed isn't much faster than the average speed of the tennis balls, then I think it would cause an increase in pressure before the drop in pressure.

The average speed of N₂ molecules in the air is over 500 m/s. This is much faster than the speed of the stream of air coming out of the straw.

 

[Fredrik]

The pressure within the pipe needs to be greater than ambient, but somewhere near the pipe exit, the pressure drops to ambient.

OK, so now you agree with what I read at the HyperPhysics web site. Can you (or someone) explain to me why the pressure at the exit must be equal to the ambient air pressure?

Reminder: We're talking about the picture you can see here, in the section "Pressure drop with length": http://hyperphysics.phy-astr.gsu.edu/hbase/pber2.html#pdrop

 

[rcgldr]

Can you (or someone) explain to me why the pressure at the exit must be equal to the ambient air pressure?

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

In the case of air flowing out of a pipe, I don't see why the exit pressure can't be significantly greater than ambient. To me the situation is not much different the jet produced by a fan or propeller, where the pressure remains above ambient for quite a distance downstream of the fan or propeller. A better analogy might be a ducted fan, where again, the exit pressure is well above ambient.

 

[Justintruth]

I'm not sure this argument works. Maybe it does if the hammer is super-fast. But if its speed isn't much faster than the average speed of the tennis balls, then I think it would cause an increase in pressure before the drop in pressure.

The average speed of N₂ molecules in the air is over 500 m/s. This is much faster than the speed of the stream of air coming out of the straw.

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.

Without getting into the molecular theory of gasses quantitatively from a qualitative view the only way I can see a low pressure developing is to reduce the momentum transfer in the collisions between the can and the air...this follows almost directly from the definition of pressure. How to do that? make sure some of the air leaves the gap before it collides. is there any other way?

 

[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%