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

[jartsa]

I thought of that explanation too, and believed it to be correct for a couple of weeks. But about a week before I started this thread, I dismissed it as incorrect because if it's correct, then it's impossible to create a high pressure stream of air. (Applied to a high pressure stream, the argument leads to a contradiction).

Let's break this down to something even simpler. If we shoot a high-speed N₂ molecule horizontally into the atmosphere at a location where there's no wind (i.e. at a location where the average velocity is zero), would it increase or decrease the pressure along the molecule's path? Since it increases things like density, average speed, average momentum and average kinetic energy, it seems to me that the pressure should increase, not decrease.

What kind of thing is a high pressure stream of air? It must be held together by pressure, otherwise it explodes, like high pressure things in low pressure environment do.

 

[Justintruth]

Ok consider two finite length walls and some tennis balls. The balls are given two independent velocities by two devices. One gives a velocity parallel to the wall and the other gives a velocity perpendicular to the wall. What happens to one of these balls as it is fired in a way that its position upon entering the space between the walls makes it right between the walls exactly. It can strike either wall only if the velocity in the perpendicular direction is fast enough for the ball to traverse half the distance between the walls before the velocity parallel to the walls takes it out from between the walls. It depends on the ratio of the velocities and the ratio of the length of the wall to the separation. I won't go through the geometry in detail but its easy to see that if the parallel kicker imparts a very high velocity or if the length of the wall is very short then you get fewer collisions and if the perpendicular kicker gives a very high velocity or the separation between the walls is low then you get more collisions.

Now this is true for two cans in a vacuum. In that case the cans move out not together as long as the geometry is such that some balls strike the walls. Else they don't move. But they never move together. There is a clue right there. Its due to the random balls that make the fired balls not operate "in a vacuum".

But if there are many other balls around and you must consider not just the kickers but subsequent collisions. Still, the kicker firing balls into the slot will cause the balls that were already bouncing there randomly to start to move toward the exit and get there before their velocities cause them to hit the sides of the wall more given that they spend less time in the slot. This is because of subsequent collisions.

And since fewer balls hit on this side and the same on the other, non-slot side the walls move together. If I am right and you make a very long wall and constrain the motion so that the walls cannot rotate then blowing will not move them together at all but rather apart. There will be some kind of torsion on the wall resisted by whatever makes the constraint that the walls can only move together or apart not rotate. This is because the long wall can overcome the velocity difference between the thermal velocities (random) and the velocity parallel to the wall.

Now we must also give gravity its due for it is gravity that maintains the pressure. Absent gravity and no container in which the experiment is done the balls all over will become less and less present and soon it will be the vacuum case and the cans will move apart.

All of this can be modeled mathematically I think. And gravity increases the pressure. If this is right as you decrease the pressure less motion together or if you do it on a mountain, less motion together everything being equal.

Continuum mathematics always introduces elements that I can't get my head around. Consider a solid torus made of a continuum and put it in rotation about the line passing through the center of the torus as far from intersecting the torus as possible. Note that the torus does rotate but if there is truly a homogenous continuum there is nothing to differentiate the material that moved in from the material that moved out. And so you enter the strange realm of haecity. Or this-ness. It is "this" piece of material that moves in and "that" piece of material that moves out and so there "really is" matter and independent of its properties. We have to enter philosophy and the subject of ontology to fully parse this. The ontology of material objects obviously has a lot of problems and they are accentuated by using notions of continuum mechanics. That is my way of saying it.

The idea that a planes wing develops lift because the continuous air has to go a longer distance is as repeated as it is ridiculous. Consider a simple right wedge wing who's cross section is a right triangle and which flies with one leg of the right triangle parallel to the ground. The path length over the top of the wedge is the same no matter which of either directions the wing is flown. It is always longer by the Pythagorean theorem. Do you think that a wedge flying with point forward will produce lift? Also do you think if I mount the wings of an aeroplane on backwards that the wings will work as well? Still we use that notion of having a longer path so the wind needs to go faster and the pressure drops.

I remember very distinctly being in a "physical science" class and being taught that and everyone nodding their heads up and down. It was almost as scary as the last election.

 

[Fredrik]

What kind of thing is a high pressure stream of air? It must be held together by pressure, otherwise it explodes, like high pressure things in low pressure environment do.

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?

 

[Fredrik]

some tennis balls.

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.

 

[rcgldr]

What kind of thing is a high pressure stream of air? It must be held together by pressure, otherwise it explodes, like high pressure things in low pressure environment do.

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.

what's the pressure at the open end of a pipe into atmosphere when the velocity is $v$ ?

Atmospheric pressure.

What if it's air being blown out of the pipe instead of water, such as a hair dryer, a leaf blower, or a ducted fan?

 

[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.