Potential flow

In fluid dynamics, potential flow, also known as irrotational flow (of incompressible fluids) is steady flow defined by the equations

Related Topics:
Fluid dynamics - Incompressible fluids

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

: abla imes mathbf{v} = 0 (zero rotation = no viscosity)

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

: abla cdot mathbf{v} = 0 (zero divergence = volume conservation)

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Equivalently,

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

: mathbf{v} = abla Phi ; ,

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

where:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• v is the vector fluid velocity
• Φ is the fluid flow potential, scalar
• " ×" is curl
• " ·" is divergence.

The equations above imply abla^2 Phi=0 , or Laplace's equation, holds.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Together with the Navier-Stokes equations and the Euler equations, these equations can be used to calculate solutions to many practical flow situations. In two dimensions, potential flow reduces to a very simple system that is analysed using complex numbers (see below).

Related Topics:
Navier-Stokes equations - Euler equations - Complex number

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Potential flow does not include all the characteristics of flows that are encountered in the real world. For example, potential flow excludes turbulence, which is commonly encountered in nature. Richard Feynman considered potential flow to be so unphysical that the only fluid to obey the assumptions was "dry water".

Related Topics:
Turbulence - Richard Feynman

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Potential flow also makes a number of invalid predictions, such as d'Alembert's paradox, which states that the drag on any object moving through an infinite fluid otherwise at rest is zero.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

More precisely, potential flow cannot account for the behaviour of flows that include a boundary layer.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Nevertheless, understanding potential flow is important in many branches of fluid mechanics. In particular, simple potential flows (called elemental flows) such as the free vortex and the point source possess ready analytical solutions. These solutions can be superposed to create more complex flows satisfying a variety of boundary conditions. These flows correspond closely to real-life flows over the whole of fluid mechanics; in addition, many valuable insights arise when considering the deviation (often slight) between an observed flow and the corresponding potential flow.

Related Topics:
Elemental flow - Free vortex - Point source - Superposed

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Potential flow finds many applications in fields such as aircraft design. For instance, in computational fluid dynamics, one technique is to couple a potential flow solution outside the boundary layer to a solution of the boundary layer equations inside the boundary layer.

Related Topics:
Computational fluid dynamics - Boundary layer - Boundary layer equations

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Since the flow is inviscid and free of shear forces, this means that any streamline can be replaced with a solid boundary with no change in the flow field, a technique used in many aerodynamic design approaches. Another technique would be the use of Riabouchinsky solids.

Related Topics:
Shear force - Riabouchinsky solid

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

 
Potential flow: Analysis ►