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PDE solution

  1. Aug 19, 2010 #1
    Hi, I'm doing some research on my own, but my math is pretty bad and I am stuck trying to find the solution to this problem:
    (1/r) ∂/∂r (r√(C/r))=

    I've seen these solutions of similar-looking problems:
    (1/r) ∂/∂r (r^2 (Ω))=2Ω
    (1/r) ∂/∂r (r K/r)=0, except when r=0, in which case the solution is infinite.

    Thank you very much!
  2. jcsd
  3. Aug 19, 2010 #2


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    Usually equations have something on both sides of the equal sign...:wink:
  4. Aug 19, 2010 #3
    Hi, sorry, guess the thing on the other side would matter. It happens to be vorticity or, in cylindrical coordinates, ω_z.
  5. Aug 19, 2010 #4


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    What coordinate variables does the vorticity depend on (i.e. does it depend on [itex]r[/itex],[itex]\phi[/itex] and/or[itex]z[/itex])?
  6. Aug 19, 2010 #5
    Out of the 3 cylindrical coordinates, there is only vortical motion wrt z, which motion is dependent on r, as the equation shows, I think.
    Last edited: Aug 19, 2010
  7. Aug 19, 2010 #6
    I've been still looking at the problem too, and I think I noticed that in the example solution I gave:
    ωz = (1/r) ∂/∂r (ruφ ) = (1/r) ∂/∂r (r2Ω) = 2Ω

    it seems as though it was solved like a regular differential equation using only the rule for the derivative of powers:
    If f(x)=xn, then f'(x)=nxn-1

    Can I just do that to solve mine, too, in which case, I would get f'(x)=(1/2)r-1/2 to give me:
    ωz = C1/2/2rr1/2?
    Last edited: Aug 19, 2010
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