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Open integration problem

  1. May 1, 2010 #1
    1. The problem statement, all variables and given/known data
    The relative velocity of two small spheres subjected to a constant force in a liquid is given by u = uo/f where f is the drag correction factor and u0 is the relative velocity of the spheres when they are far apart. The drag coefficient factor, f, is a function of (r/a) where a is the radius of each sphere and r is the center-to-center distance. Given the following data for the correction factor estimate the time at which it takes the spheres to travel apart from r=22 μm to r=32 μm when u0=1 mμ/s and a=10 μm
    using an appropriate open integration formula. (Hint: dt=dr/u )
    r/a: 2.1 2.5 3.0 3.5
    f: 4.03 1.72 1.37 1.24


    2. Relevant equations



    3. The attempt at a solution
    I don't understand the problem, can you explain what i should do firstly?
     
  2. jcsd
  3. May 1, 2010 #2

    gabbagabbahey

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    Let's imagine for a second, that you were given the exact functional form of [itex]f\left(\frac{r}{a}\right)[/itex]....what would you do to find the time it takes the spheres to travel apart from r=22 μm to r=32 μm?
     
  4. May 2, 2010 #3
    Re: integration problem

    Can you give me the function which i should integrate, the problem is very complex and difficult to solve for me
     
    Last edited: May 2, 2010
  5. May 2, 2010 #4

    gabbagabbahey

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    Again, all I'm asking is that if I gave you [itex]f\left(\frac{r}{a}\right)[/itex]...what would you do to find the time it takes the spheres to travel apart from r=22 μm to r=32 μm?
     
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