# Physical meaning of potential flow

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?

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Redbelly98
Staff Emeritus
Homework Helper
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.

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:
Redbelly98
Staff Emeritus