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Why is it right that the irrotational flow must have the velocity potential?

  1. Mar 15, 2012 #1
    When I am studying the ratation of the fluid, I found one sentence: "The irrotational flow must have the velocity potential." Why? Can someone tell me the derivation of this equation?
     
  2. jcsd
  3. Mar 15, 2012 #2

    tiny-tim

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    Hi Chuck88! :smile:
    It's the Helmholtz theorem, see http://en.wikipedia.org/wiki/Helmholtz_decomposition#Statement_of_the_theorem

    If F is irrotational, and if φ is defined as shown there, you can check that φ = F :wink:
     
  4. Mar 15, 2012 #3
    Thanks for your reply and from the materials you provided, I have known some of the knowledge I did not know before. Another question is that suppose I have alreadly got the value of a curl, which is not equal to zero, how can I prove reversely that the potential does not exist?
     
  5. Mar 15, 2012 #4

    tiny-tim

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    Hi Chuck88! :smile:
    Because curl grad = 0.

    So if the flow F has a potential φ,

    then F = φ.

    so x F = x φ = 0. :wink:
     
  6. Mar 15, 2012 #5
    Thanks for your reply. I have found one link which could is also quite useful.
    http://mathinsight.org/curl_gradient_zero
     
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