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Aerodynamics and hydrodynamics

  1. Nov 28, 2004 #1
    Let's tie a sphere, drop it into a water and trawl it with a boat. How do we calculate the angle between a vertical line and rope?
    Actually I don't know much about aerodynamics and hydrodynamics so I don't know how drag force is calculated from shape, mass and speed of an object. Recently I have started using Simulink and Matlab so it would really help me to get a some formula so I could try to do some model.
    Thank you,
  2. jcsd
  3. Nov 28, 2004 #2
    Well you need quite a bit of knowledge of these fields to properly do the calculations. For instance engineers usually model the drag force by using the empirical relation:

    [tex]F_D=C_D(Re)A\frac{1}{2}\rho v^2[/tex]

    With A the frontal surface of your sphere. rho the density of water and v your velocity. The drag coefficient ([itex]C_D[/tex]) depends on the Reynolds number so imlicitly on the velocity. If you want to find the drag force for a certain fixed velocity of the boat you could calculate the Reynolds number from its definition:

    [tex]Re=\frac{\rho v D}{\mu}[/tex]

    With D the characteristic length scale, in your case the diameter of the sphere and [itex]\mu[/tex] the dynamic viscosity of water. Next you could look up the drag coefficient in a graph or something, only for certain Reynolds numbers (<1) this can be analytically found:

    [tex]C_D= \frac{24}{Re}[/tex]

    But for Re<1 your boat would have to move very! slowly. For 1E3<Re<2E5 the drag coëfficiënt is approximately constant (~0,4). See: http://www.uh.edu/engines/spheredrag.jpg for an example of how to find the drag coefficient from the Reynolds number.

    With the drag coëfficient you can calculate the drag with the first formula. But again, I think a good calculation involves a lot of knowledge of the fields you mention and will be quite labourous, so you might still want to change your mind...
  4. Nov 28, 2004 #3
    Well, giving it another thought. If you discard the effect of the boat on the water, so you can evaluate the flow as homogeneous, a first approximation is not too difficult.
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