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Fluid Mechanics Ideal Flow Problem

  1. Sep 27, 2009 #1
    1. The problem statement, all variables and given/known data

    Calculate flow velocity and magnitude at a point (2,-2)

    Sink at origin with strength 20 m2/s
    Vortex at (0,2) with strength 25 m2/s
    Uniform flow in +x with strength of 10 m/s

    3. The attempt at a solution

    [tex]\phi[/tex] = [tex]\phi[/tex]1 + [tex]\phi[/tex]2 + [tex]\phi[/tex]3

    [tex]\phi[/tex]1 = -Ux = -U r cos([tex]\theta[/tex])
    [tex]\phi[/tex]2 = -[tex]\mu[/tex]s ln r
    [tex]\phi[/tex]3 = [tex]\mu[/tex]v [tex]\theta[/tex]

    vr = d[tex]\phi[/tex]/dr
    =-U * cos [tex]\theta[/tex] - [tex]\mu[/tex]s * (1/r)
    =-10 cos([tex]\pi[/tex]/4) - 20 / 2.83
    =-14.14

    v[tex]\phi[/tex] = (1/r) d[tex]\phi[/tex] / dr
    = (1/r) (-14.14)
    = -5

    u = .5 (14.14) + .5(5) = -9.57
    v = -.5(14.14) + .5(5) = 4.57


    I know that I have butchered this because the solutions is supposed to be

    V = 12.5 m/s
    u = 10 m/s
    v = 7.5 m/s
    [tex]\alpha[/tex] = 37 degrees

    Could someone please point out the obvious flaw in my logic and point me in the right direction?

    Thank you very much in advance!
     
  2. jcsd
  3. Sep 28, 2009 #2
    Nevermind! I was making this problem a lot harder than I thought it was. I took a step back and looked at the units that I needed for my solution along with what the correct solution and was able to work it out.
     
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