Physical meaning of potential flow

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Discussion Overview

The discussion centers on the conditions under which liquid flow can be described as potential flow, focusing on the requirements for incompressibility and conservativeness of the velocity field. Participants explore the implications of these conditions and the physical reasoning behind them.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant states that for potential flow, the liquid must be incompressible, leading to the equations div(v)=0 or Laplace(fi)=0.
  • Another participant argues that liquid flow is generally not a conservative vector field, using the example of a whirlpool to illustrate path-dependence.
  • A different participant acknowledges that general flow is not potential and emphasizes that the rotor of the velocity field must be zero everywhere for potential flow to hold.
  • One participant expresses uncertainty about the physical conditions that would make flow conservative, indicating a lack of knowledge on the topic.

Areas of Agreement / Disagreement

Participants express differing views on the nature of liquid flow and its conservativeness, with no consensus on the specific physical conditions that would allow for potential flow.

Contextual Notes

There are limitations in the discussion regarding the assumptions needed to determine the conservativeness of flow, and the dependence on specific physical conditions remains unresolved.

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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