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Bernoulli's Principle

  1. Nov 17, 2009 #1
    1. The problem statement, all variables and given/known data
    This isn't a homework question, but more like a theory question that my teacher and I are having trouble figuring out. We're trying to figure out why this ball, more or less, stays still in a high speed stream of air:


    2. Relevant equations
    Bernoulli's Principle, gravity, balancing vector diagrams.

    3. The attempt at a solution
    The stream of air is going from the bottom/left to the top/right, and we had a couple theories. I think the ball is spinning clockwise, and bernoulli's is causing a lift perpendicular to the stream. The force of gravity is acting down, and the reason there isn't a net movement to the left is because the stream itself pushes the ball to the right. Therefore, the forces cancel out and the ball, more or less, stays still. However, my professor thinks the ball is actually spinning counterclockwise, and in that case Bernoulli's wouldn't explain why the ball is floating in midair; it would actually cause the ball to be pushed downward, correct? Is there someting we're missing here? What're your thoughts?
  2. jcsd
  3. Nov 17, 2009 #2
    The only thing I know that I can say about it is that Bernoulli's doesn't actually apply because of all kinds of viscous effects, but instead you'd have to apply the momentum equation (one of the navier-stokes equations) and also/alternatively you could apply the energy equation, but you definitely can't use Bernoulli because of the presence of viscous boundary layers around the ball. Navier-stokes would be able to tell you what is going on since they are partial differential vector equations, but in order to use those navier-stokes equations you'd really have to run a computer simulation and numerically evaluate the equations because of the inherit complexity of those partial derivatives.
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