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Testing Drag Force on a Sphere

  1. Dec 3, 2014 #1
    Hi all. This is my first question on these forums.

    I am given a task to test out whether or not FD=1/2 CDAρv2 is a good model to test drag force.
    Where CD is described by Reynold's Number.

    We have a balloon a small ball and a myriad of basic physics lab equipment.

    What is a experiment I could do that would test this model and its reliability?

    I'm thinking of dropping the ball into the graduated cylinder and timing it hitting the bottom to get its velocity. I have the density of water, as well as the cross sectional area (it's half the area of the ball, right?). When it comes to CD, the drag coefficient, I'm simply confused about determining linear size of the object to obtain Reynold's number. After I figure that out though, I think I'll be good.

    Is this a good idea? Will it accurately test the model? My only confusion is that if I'm testing to see if it's reliable, don't I need something to compare? I have nothing else.

  2. jcsd
  3. Dec 3, 2014 #2
    Sounds pretty good. Just make sure that the cylinder diameter is large compared to the diameter of the ball. Consider using other fluids in addition to water, so you have a range of viscosities and densities. Consider using different ball diameters and different ball densities. Make sure you wait long enough in the experiment for the fall to reach terminal velocity. Don't let the ball come too close to the bottom of the cylinder. You should do calculations in advance to make sure that you cover the wide range of Reynolds numbers present in the correlations in the literature. Try to measure the temperature of the liquid so that the viscosity is known in each test.

  4. Dec 3, 2014 #3
    Thank you!

    Also, I think I figured out that the linear distance is the diameter of the ball, right?
  5. Dec 3, 2014 #4
    Yes. Also check out web sites on Falling Ball Viscometry and Falling Ball Viscometer Corrections.

  6. Dec 3, 2014 #5


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    The cross-sectional area of the ball is not equal to half the surface area of the ball, but the area of a circle whose diameter is the same as that of the ball.

    The cross-section, i.e. the section obtained when cutting the ball in two, is a circle.
  7. Dec 4, 2014 #6
    Ohh thank, you! Saved me.
  8. Dec 8, 2014 #7

    Andy Resnick

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    Just to chime in: don't forget about:

    1) the graduated cylinder confines the fluid through which the ball falls, altering the flow field and complicating the measurement.
    2) the ball's velocity is not a constant- but a measurement of the 'terminal velocity' may suffice
    3) If the object is rotating while it falls, there will be another complication you have to account for.

    Otherwise, go for it!
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