# How a faster air flow creates a lower air pressure on an airplane wing? [duplicate]

• An airplane wing creates a faster air flow on the upper side and slower air flow on the lower side.
• Pressure of a gas and the speed of the gas molecules are directly related. If the speed of molecules increases, pressure will also increase.

Are these assumptions correct? If not can you correct it? If they are not wrong: can you please help me understand how an higher speed of air flow creates a lower air pressure? A higher speed of airflow does not mean a higher average molecule speed as well?

Another question, that might be related with this: Suppose we have a sealed room that no molecules and heat can escape or enter. We started to run a fan which has a motor that do not produce any heat. So the air start to flow inside the room. Will the room temperature and pressure increase?

I hope these questions are not too stupid. I don't have Physics or Math education (but I have a great admire on them), and its really hard for me to understand the equations. Explanations that would help me visualize how things are happening is very appreciated.

Edit: My question was set as "duplicate" to a question to which I cannot see-understand how it is same with my question. My aim is just to understand, please help. Thank you.

Edit2: My actual question here is not to understand how a wing creates a lift, but to understand how this is possible:

## marked as duplicate by John Rennie, Cosmas Zachos, Kyle Kanos, Aaron Stevens, ZeroTheHeroNov 11 '18 at 1:13

• Possible duplicate of What really allows airplanes to fly? – Wasserwaage Nov 8 '18 at 14:50
• @Wasserwaage I've tried to find read all the questions related to my questions including the one you have mentioned. I could not find (or understand) an answer to how a speeded up air creates less pressure. – Koray Nov 8 '18 at 14:57
• Have you read about the Bernoulli effect? – md2perpe Nov 8 '18 at 16:31
• Do you understand the origin of the pressure in a gas? That's important here. Check out this website and see if it helps: av8n.com/how – Bill N Nov 8 '18 at 16:52
• Actually, I my self have same kinds of questions. @Koray Bernoulli equation is actually a conservation of energy equation. Pressure drop is an experimental fact. But, how can we explain this in the frame of kinetic theory, escapes me also. I can just say that average, irregular motion of molecules is used to explain pressure of gas but air flow is not the same. Air flow is regular motion. In one definite direction. But again, why would this effect pressure, or why would faster flow of water molecules in a tube effect pressure, i do not know also. – Žarko Tomičić Nov 8 '18 at 19:43

My actual question here is not to understand how a wing creates a lift, but to understand how this is possible: picture of the Venturi effect

TL;DR when something moves through the air mass it causes the random motion of the air molecules to be interrupted and that causes a different distribution of velocities in the air. At the macroscopic level, we interpret that distribution as pressure.

Long version:

What follows is a toy model, but outlines the basic concept of "what's going on".

Let's start by considering what gas "really is", a mixture of atoms and molecules moving about randomly. Quite quickly too, the thermal velocity of room temperature air is about 1000 m/s, or 2200 mph! It is also important to remember that their speeds are distributed according to the Maxwell-Boltzman distribution, so there's some slow-moving stuff, some fast-moving stuff, and a whole bunch around 1000.

So consider a little bit of air for a moment. If you could take a snapshot and see all the molecules and where they were going, you could plot them in 3D with their angle from the origin being their line of motion and the distance being their speed. The result would be a sort of fuzzy ball. Note this is not a graph of their locations, it's a graph of their velocities. Do you see that? It's kind of key to what follows.

Now you have all these particles whizzing about, but the net speed is zero. Do you see why that is? In any given volume of air, for every particle at 1,1,1 on your graph, there's one at -1,-1,-1, going the opposite direction and angle. When you add the two, they cancel out. The entire bit of air does this, which is why you don't feel a 2200 mph wind all the time.

Now let's add an open tube to our system. Consider that tiny bit of air you plotted sitting at one end. Which particles on your graph can enter the tube? Well if the tube is to the right and runs off to the right, it's any of the ones who's vector is somewhere along the X axis. The ones up on Z, for instance, are flying off in the wrong direction.

Ok now instead of a complete venturi, consider just the inlet. It's basically a cone:

So now consider just the front part (on the left) and we're going to seal off its outlet (around the middle in this image) with a piece of paper. Ok, now take that bit of air we were considering earlier, and put it inside the cone. Now what happens when you take the piece of paper away? Well, for that instant at least, the only molecules that can get through the new opening are the ones travelling in that direction.

So then if we consider just those ones, they aren't evenly distributed in velocity, you're selecting just the ones moving to the right very quickly. So the average speed of the air in the tube is very fast indeed!

This illustration leaves out an important point - there's already air on the other side of the cone when we open the hole, so it can't really flow like this because the molecules going the opposite direction on the other side of the paper are going into the tube from the back as fast as our slug of air is going the other way.

But that's not the case when you push air into the "front" cone, either by increased pressure or by moving the aircraft you're attached to. In that case the "back pressure" is lower. What is pressure? The number and energy of impacts from the molecules. So if we set the number of particles to be the same on either side, which is a good bet in the case of a plane for instance, then the difference is due to the speed distribution. So the distribution of velocities on the front are different than on the back, which means there's some tiny leftover net velocity towards the rear. And if you consider the fact that you've selected those particles travelling along the tube, you can immediately see their trajectories result in less impacts on the side of the tube, which means lower pressure inside the tube.

I said this is a toy model. That's because air doesn't really move like this, in most cases any one particle gets maybe a couple of nanometers before bumping into another molecule and quickly randomizing everything. So it's not like you have these "left-going molecules" getting all the way through the pipe, they're barely inside the entrance before they're all over the place again. But I suspect you can see that even this tiny effect causes the overall distribution to change, at a very small degree, and that's what you measure in a venturi.

Ok, now let's close this off by looking at your original question.

Take the venturi and saw the top off, and put a flat plate of metal there. I think you can see the overall effect will still be there, but modified. Now you don't get every particle moving "close enough to +X" getting into the pipe, because the ones moving slightly downward hit the plate. So now you get the ones moving along X and the ones moving along +X and a little +Z. So that means there's a little bit of unbalanced force... upwards. That is what you call lift.

Now take the plate off and replace it with the entire atmosphere. Airplane wing.

This may sound all very hand-waving, and it is, but this is precisely how modern aerodynamics is actually calculated. What you do is make a huge 3D matrix in memory, and fill it with a number representing the velocity of that little cell of air. So for instance, in our case we might fill it with 50,0,0, meaning the air is moving 50 m/s to the right (which is easier than moving the plane 50m/s to the left).

Now you say that any cell that touches the object reflects from it. And then in the next iteration that cell bumps into the cell beside it, and so on. And you keep iterating until you (hopefully) get a steady state. Like this:

You can see all of the effects we're talking about in that image. You can see how the air goes down the intake it gets squeezed, and that sort of squeezes it into the restriction. Then it passes the restriction and spreads out again.

This is an example of "do it on the computer" that really works; instead of using mass flow formulas and stuff you just stick the object in the computer and you'll know what really happens.

• TL;DR means "I didn't read all of your question" I guess. I want to say: VL;BGETILEWOI --> Very Long But Great Explanation That I Loved Every Word Of It! I think I have understood clearly! I was thinking about this for years. Thank you very much. – Koray Nov 9 '18 at 18:58
• I think this also explains: when I squeeze the tip of a hose, the water comes out faster when the hole becomes smaller and smaller. However, after a certain radius, the water start to come out slover. I can't put it into words, but your answer also explain this, I think. (water pressure diminishes so much that atmospheric pressure wins perhaps) – Koray Nov 9 '18 at 19:25
• Yeah, I'm always frustrated at the number of pages (and replies) that just say "conservation of mass!" like that's explaining anything. CoM tells you what has to happen, it doesn't tell you anything whatsoever about how it happens, but it seems many people are willing to ignore that. – Maury Markowitz Nov 9 '18 at 20:55

My actual question here is not to understand how a wing creates a lift, but to understand how this is possible: picture of the Venturi effect

Assume for simplicity that the gas is not compressible, so its density does not change when the width of the tube changes. Then the number of molecules that pass by a given point every second must be the same no matter how wide or narrow that part of the tube is. The only way to achieve this without changing the density is for the gas to move faster through the narrow part of the tube. But in order for the gas to move faster in the narrow part, there must be a net force that gives it a push as it's entering the narrow part. This means that the pressure in the wide part of the tube must be higher than the pressure in the narrow part. The push comes from this difference in pressure. Pressure is omnidirectional, so the pressure on the walls of the wide part is also higher than the pressure on the walls of the narrow part. This explains the Venturi effect. (This is just a wordier version of md2perpe's explanation.)

• Your second para has got too many kinetics in it... Total Energy is conserved - not kinetic energy alone. The kinetic energy actually increases as the gas moves through the constriction. This energy is taken from the static pressure (i.e., potential energy), which drops. Also, you're mixing the statistical mechanics model (bulk gas) with the microscopic explanation (per molecule). I would delete the three kinetics and the per molecule and see how that reads. – Oscar Bravo Nov 9 '18 at 7:42
• (+) and thank you very much for trying to explain the meaning behind equations that I can't understand. I'm not in a level to judge you are wright or not; but your answer gave me a tought: Fluid in the thicker pipe has a pressure. If we can say that pressure is the potential energy, when the fluid accelerates in the thinner pipe, kinetic energy increases so the potential energy == pressure drops, to conserve the total energy. (I hope I'm not seriously wrong) But why? Why fluid accelerates and kinetic energy increases? What is happening in the molecular level? – Koray Nov 9 '18 at 9:39
• @OscarBravo Oops - you're absolutely right. That's what I get for trying to "check the math" in my head. I deleted the incorrect second part. Thanks for catching this! – Chiral Anomaly Nov 9 '18 at 12:44
• @Koray Oscar Bravo's comment is correct. My energy-based argument was wrong. I was mistakenly treating the kinetic energy as being conserved, but (like Oscar said) only the total energy is conserved. The kinetic energy by itself is not. Sorry for the confusion; next time I'll actually check things on paper instead of trying to "check" them in my head when I'm sleepy. – Chiral Anomaly Nov 9 '18 at 12:46
• @OscarBravo Even though I deleted the incorrect section, I would recommend leaving your comment there because I think it adds a good insight to the post. And thanks again for catching my blunder. I don't want to perpetuate any misconceptions. – Chiral Anomaly Nov 9 '18 at 12:54

Re. your: "Pressure of a gas and the speed of the gas molecules are directly related. If the speed of molecules increases, pressure will also increase."

This is wrong--the pressure will decrease--but not because of increased speed of the air flow on the upper surface.

See https://phys.org/news/2012-01-wings.html “What actually causes lift is introducing a shape into the airflow, which curves the streamlines and introduces pressure changes – lower pressure on the upper surface and higher pressure on the lower surface,” clarified Babinsky, from the Department of Engineering. “This is why a flat surface like a sail is able to cause lift – here the distance on each side is the same but it is slightly curved when it is rigged and so it acts as an aerofoil. In other words, it’s the curvature that creates lift, not the distance.” (italics are mine)

Also see for the common incorrect explanation:

https://www.grc.nasa.gov/www/k-12/airplane/wrong1.html

• Thank you for your explanations. Your answer lead me to this two small videos: video1, video2 – Koray Nov 8 '18 at 18:48
• But I'm trying to understand why this occurs. – Koray Nov 8 '18 at 18:55
• – user45664 Nov 8 '18 at 19:57

TL;DR: Newton's 2nd law

What makes a fluid accelerate? A fluid has mass, and to accelerate mass you need a force. For a fluid the force is given primarily by a pressure difference; there must be higher pressure behind the accelerating volume than in front of it. And opposite; it the fluid decelerates, the pressure must be higher in front of it than behind it.

• Hmmm...interesting, but why is the pressure in a tube where fluid flows everywhere with the same speed constant? And then, all of a sudden, when it enters the tube of smaller diameter and starts going faster, pressure drops? – Žarko Tomičić Nov 8 '18 at 19:49
• @ŽarkoTomičić. If the velocity is constant, then there can be no pressure gradient, because a pressure gradient would make the velocity change. It's not the speedup that makes the pressure drop when the fluid enters the region of smaller diameter; it's the pressure drop that makes the fluid speed up. – md2perpe Nov 8 '18 at 20:17
• I thought you are getting at that. So what kind of a pressure drop or increase speeds up the molecules in a pipe with smaller diameter? And what does that has to do with the pressure exerted on the walls of the tube? – Žarko Tomičić Nov 8 '18 at 20:20
• @ŽarkoTomičić. It's the pressure drop from the thicker pipe to the thinner pipe that makes the fluid speed up. It's not the different diameters per se that generates the pressure drop, but if the flow is constant, then the fluid must have a higher speed where the area is smaller, and for the fluid to be able to speed up we must provide a pressure drop. – md2perpe Nov 8 '18 at 20:31
• Yes there must be higher pressure behind the accelerating fluid in the smaller pipe to make it accelerated; and it is observed so. But I can't understand why? how? When the fluid is accelerated, isn't the kinetic energy increased (like the room example of my question)? Why pressure drops? – Koray Nov 9 '18 at 9:19