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Physical meaning of potential flow

  1. Apr 24, 2008 #1
    Under which conditions can we describe the speed of the liquid with a potential flow? I know that the liquid must be incompressible, so that we get equation:

    div(v)=0 or Laplace(fi)=0

    But the velocity field must also be conservative, so that it's potential fi exists. Does this follow from non-viscosity of the fluid? How do we prove it?
  2. jcsd
  3. Apr 24, 2008 #2


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    Liquid flow is not, in general, a conservative vector field (equivalently, it is not the gradient of a scalar potential.) Consider a whirlpool (and please excuse my ascii math):

    (Integral) v(dot)dr
    is path-dependent.

    Hope this makes sense.
  4. Apr 25, 2008 #3
    I know that general flow is not potential. The flow must not include whirlpools or more exactly: the rotor of v must be zero everywhere.
    But this does not help to estimate the validity of aproximation: why would I care about accuracy of the aproximation if I already had an exact solution? I think that (non)conservativeness of the flow must be predicted in advance (before the calculation of velocity field), from some physical causes.
    Last edited: Apr 25, 2008
  5. Apr 27, 2008 #4


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    If you're asking under what physical conditions or situations flow will be conservative, I don't know. Sorry.
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