Physical meaning of potential flow

In summary, to accurately describe the speed of a liquid using potential flow, the liquid must be incompressible and the velocity field must be conservative. The conservation of the flow is necessary for the existence of a potential function. However, general liquid flow is not always conservative, as seen in the example of a whirlpool. This non-conservativeness must be taken into consideration when estimating the accuracy of the potential flow approximation. The physical causes for the flow to be conservative or not are not fully understood.
  • #1
Lojzek
249
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?
 
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  • #2
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.
 
  • #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:
  • #4
If you're asking under what physical conditions or situations flow will be conservative, I don't know. Sorry.
 

1. What is potential flow?

Potential flow is a mathematical model used to describe the motion of an ideal fluid, which is a fluid that is inviscid (has no internal friction) and incompressible (has a constant density). It assumes that the flow is irrotational, meaning that the fluid particles do not rotate as they move.

2. What is the physical significance of potential flow?

The physical significance of potential flow is that it provides a simplified representation of fluid motion, which can be used to study and understand more complex fluid dynamics problems. It also helps in the design and analysis of various engineering systems, such as airfoils, wings, and fluid pumps.

3. How is potential flow different from real flow?

Potential flow is an idealized model and does not account for certain real-world factors, such as viscosity and turbulence, which can significantly affect the flow of fluids. In real flow, the fluid particles do experience internal friction and can rotate, leading to more complex flow patterns.

4. What are the limitations of potential flow?

Potential flow has several limitations, including its inability to accurately predict flow separation, boundary layer effects, and the formation of vortices. It also assumes that the flow is two-dimensional and incompressible, which may not always be the case in real-world situations.

5. How is potential flow used in practical applications?

Potential flow is widely used in various engineering fields, such as aerodynamics, hydrodynamics, and fluid mechanics. It is used to analyze and design aircraft, ships, and other vehicles that move through fluids. It is also used in the design of pumps, turbines, and other fluid machinery.

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