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Drag can happen in extremely low-viscosity fluids

  1. Jan 25, 2008 #1
    First, let me introduce myself. I am new to these forums, but not new to sharing ideas that cause argument. If you think anything I say is wrong, please speak up.

    The reason I joined was because of this outrageous 2+ year old thread: https://www.physicsforums.com/showthread.php?t=70227

    The idea was that even if air molecules did not ever collide with eachother, there would still be drag. To me, this is obvious, but this guy russ_watters thinks otherwise. Let me try to explain to Russ, if he bothers to read this, why drag occurs even if air molecules did not collide with each other.

    First, I think we all need to have a conception of pressure. Air pressure is not measured by the collision of gas molecules with each other, but by the collision of gas molecules with the walls of the container. If anyone has ever seen a half-inflated balloon put in a vacuum, you know that there must be a tremendous amount of collisions of air molecules with the balloon membrane each second. If you haven't seen a balloon in a vacuum, watch this: The balloon in the vacuum illustrates what happens when you take away the pressure normally exerted on the balloon by our atmosphere. To get an idea of how much pressure this is, try to compress a fully inflated balloon to half its size; it's more than many people would imagine - about 14.7 PSI (pounds per square inch). As the typical adult has a surface area of 1.8m^2 or about 2,800 square inches, this means typically you have about 40,000 pounds of force compressing your body. Normally, however, you are not pushed in any one direction by this force. Usually the force is distributed throughout your body.

    A mole of air (6.02x10^23 molecules) takes up about 22.4 liters, which means there are about 0.045 moles of air in a liter. Water, on the other hand, has about 55.5 moles per liter, which means water has about 1,200 times the number of molecules per unit volume as air at STP. If you picture water as a bunch of marbles bouncing around in a shaken bag, then air could be pictured as tennis balls on the ends of arrows being shot around in a large gymnasium. They don't hit each other nearly as often as they do in the bag. Now imagine that these tennis balls bounce off the walls with the same energy that they hit them with; now people who have shot the arrows can leave the gymnasium and just let the tennis balls bounce. You can imagine that the balls are hitting the walls of the gymnasium much more often than they are hitting each other. In other words, it would seem more likely for a tennis ball to reach another wall than to be hit by a stray tennis ball at any one time. To fully give you an idea of what air is like, I think it's necessary to know that air molecules move with an average speed of 1,100 miles per hour, so collisions with the walls and each other are happening many times per second, but still in the same proportion to each other as if they were moving slowly. This gymnasium, however, would only represent a very small volume of actual air. If you make the walls of the gymnasium much farther apart, the number of collisions of air molecules with each other increases relative to the number of collisions of air molecules with the walls of the gymnasium. When the frequency of mid-air collisions increases, the molecules start to move more slowly from a macroscopic viewpoint. In other words, since the air molecules are hitting each other more often, it becomes less likely that an air molecule would bounce all the way from one corner of the gym to another to another without hitting other molecules. So it becomes more likely a molecule spends time bouncing around between other molecules instead of flying freely in whatever direction it is traveling in until it hits a wall. Some people argue that drag is a result of these collisions of air molecules with each other. They argue this tendency of air molecules to hit each other causes the viscosity of air, meaning an object moving through it has a tougher time moving it out of the way (drag). They argue that if the air molecules did not collide with each other, when an object went to go through this fluid, it could simply push the molecules out of the way without any speed lost. I believe, however, that even if air molecules didn't collide with each other, there would still be drag.

    First, we already know that the atmoshpere is pushing on you with about 40,000 pounds of force, but this force is normally spread out evenly on your body. This force comes from the fact that a huge number of small air molecules are bombarding you each second at very high speeds in all directions. Not all the molecules are moving at the same speed or direction, but on average they aren't going in any one direction. You can assume the the average velocity of the air around you is the same as the earth you are standing on (except for the occasional gust of wind). Say, however, you start running in one direction (for this example, we will be running North) and there is no wind. On average, there are an equal number of air molecules going South as North relative to the ground, but because you are moving north relative to the ground, air molecules are on average moving south at the opposite velocity you are running north at. If the 40,000 pounds of force was normally split into 10,000 on your front and 10,000 on your back, you would expect more than 10,000 pounds of force on your front and less than 10,000 pounds on your back when you are running. This is mostly because the air molecules that are going South with a certain speed are traveling South relative to you with that speed plus your speed, and the air molecules that were going North with a certain speed are now traveling North relative to you will that speed minus your speed. So, not only is there an additional force pushing you backwards, but there is a lack of force pushing you forwards which would normally be there (in other words, a vacuum is formed behind you pulling you back). This is called drag, and this is all without any interactions between air molecules. The amount of drag depends only on velocity in this situation, not position or acceleration. Another way to think about this is that when you are driving down the highway, you pass more cars go by going the opposite direction as you than cars going the same direction pass you, and the cars going the opposite direction as you are moving faster relative to you. If each one of the cars made a scratch mark on your car when they passed by, you would have more marks on the front of your car than the back.

    Now let's look at the effects of air molecules colliding. Let's have the same scenario as before, but this time those air molecules you push out of the way collide with other air molecules. In the previous example, there was high pressure directly in front of you, and low pressure directly behind you. Each second, more molecules would be hitting you from in front of you than behind. Each molecule you hit would bounce off you and never be seen again. If you were to measure the density of air molecules at any one time while running, however, you would find that a cubic foot of air in front of you contains more air molecules than a cubic foot of air behind you. This is because the air molecules in front of you are now hitting you and bouncing to the space in front of you instead of continuing to the space behind you like if you weren't there. This density shift does not have an effect on drag if the air molecules don't collide because the additional molecules in front of you are all traveling away from you, as would the lost molecules behind you. If the air molecules do collide, however, the increased density of air in front of you resulting from you running causes more molecules to be shot back your way, increasing the pressure in the front. In this case, the molecules you push out of the way don't stay out of the way. This has a number of effects which people who study aerodynamics find interesting. Not only can it increase the drag resulting from molecules hitting you on the front, but if the molecules you hit tend to be pushed sideways instead of forward, they can actually increase the pressure behind you, decreasing drag resulting from the lack of pressure behind you.

    EDIT: With air molecules colliding, air acts more like a spring. The first nanosecond you start moving, there is not much of an increased density in front of you, but as you continue going at that same speed, the density of the air in front of you increases, causing increased pressure acting on your front. When air molecules don't collide, the drag from when you first start moving at a certain speed will remain the same for the rest of the time you travel at that speed. This is all assuming there are no other objects to restrict the flow of air. In a room, pressure would build up in front of you because of air bouncing off the wall in front of you.

    Well, that's pretty much it.
    Last edited by a moderator: Sep 25, 2014
  2. jcsd
  3. Jan 25, 2008 #2

    Andy Resnick

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    You are describing something called "d'Alembert's paradox", and has been solved for quite some time. Inviscid motion produces no drag for steady flow only. In unsteady flow, although the velocity distribution may be the same, the pressure distribution is different. The work done against the drag as an obstacle is accelerated through a fluid provides a change in kinetic energy to the fluid.

    See, for example, "Physical Fluid Dynamics", D. J. Tritton, pp18-119.
  4. Jan 25, 2008 #3
    There is something called conservation of momentum. It exists. With an object moving through the air, we can assume the collision between the object and the air molecules is 100% elastic (otherwise we need to account for the heat generated in the deformation of the object and whatnot). Assuming no outside forces, the combined momentum of the air molecules and the object will remain constant throughout the experiment. As the air molecules cannot pass through the object, collisions between the moving object and an air molecule cause a force to be applied to both the object and the molecule. By Newton's laws, these forces are equal. After the collision, because the object is so large relative to the air molecules, the collided air molecules will be traveling at a slightly lower speed away from the object as they were when they were heading towards the object. By conservation of momentum, if the momentum of an air molecule is changed from heading in one direction (let's say South) to heading another (North), the opposite change in momentum must be applied to the object. This means the object has slowed down as a result of the air. This is called drag. The air molecules do not need to collide with each other for this to be true.

    If you define viscosity as the resistance to an object moving through it, then you could say even gases without gas molecules colliding or interacting with each other have viscosity. Then again, that would be the same definition as of drag. If you define inviscid as "not producing drag" then of course you can say what you are saying, but I don't think that's the best definition for people who say viscous fluids must have colliding/interacting molecules.
  5. Jan 25, 2008 #4

    Do you like to see yourself talk? Why did you take multiple paragraphs to tell us about pressure in a baloon? I can see that you are on the road to commiting several fallacies.
  6. Jan 25, 2008 #5
    The balloon talk was necessary for people to understand the number of collisions of air molecules with you every second. Otherwise, my explanation of drag would have made little sense.
  7. Jan 25, 2008 #6

    Andy Resnick

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    Air is not inviscid, first off. The dynamic viscosity of air is the same as water.

    Second, trying to reduce viscosity to molecular interactions is a fool's errand. Viscosity is a dissipative process. Fluid mechanics (and more generally continuum mechanics) is valid only in a particular limit- relevant length scales must be much larger than atomic distances. The definition of the inviscid limit is quite clear and straightforward in continuum mechanics.

    Third, I'm sure what the point of your post is- do you think you have discovered some new concept? Perhaps it would help to state your idea more clearly and consisely.
  8. Jan 25, 2008 #7
    Okay, here is my statement: "Even if the molecules in a fluid did not collide with eachother, there would still be drag."

    It seems I misread some of the things russ_watters had posted, and thought he was arguing that Thomas2 was wrong that there would be drag if the molecules in a fluid did not collide with eachother.
  9. Jan 25, 2008 #8
    That is not true. You could have simply used the information you postulate to derive the number of collisions.

    You come off as a person who attempts to validate their position simply by using a vast amount of material. Argument by Nauseum.
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