Physical meaning of potential flow

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SUMMARY

The discussion centers on the conditions necessary for describing liquid speed using potential flow, specifically emphasizing that the fluid must be incompressible, leading to the equations div(v)=0 and Laplace(fi)=0. Additionally, the velocity field must be conservative, which is contingent upon the fluid being non-viscous. The conversation highlights that general liquid flow is not conservative due to the presence of whirlpools, where the rotor of v is non-zero. The participants seek to understand the physical conditions that determine whether a flow can be classified as conservative.

PREREQUISITES
  • Understanding of incompressible fluid dynamics
  • Familiarity with the mathematical concepts of divergence and Laplace's equation
  • Knowledge of conservative vector fields and their properties
  • Basic principles of fluid viscosity and its effects on flow
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Fluid dynamics researchers, physicists, and engineers interested in the theoretical aspects of potential flow and its applications in various fluid systems.

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

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