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Perfect fluid
 
 
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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, a perfect fluid is a fluid
Fluid

A fluid is defined as a substance that continually deforms under an applied shear stress. All liquids and all gases are fluids. Fluids are a subset of the Phase and include liquids, gas, Plasma physics and, to some extent, plasticity ....
 that can be completely characterized by its rest frame energy density
Energy density

Energy density is the amount of energy stored in a given system or region of space per unit volume, or per unit mass, depending on the context, although the latter is more formally specific energy ....
 ρ and isotropic pressure
Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
 p.

Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in which these possibilities are neglected. Specifically, perfect fluids have no shear stress
Shear stress

File:Shear stress.JPGA shear stress, denoted , is defined as a stress which is applied parallel or tangent to a face of a material, as opposed to a normal stress which is applied perpendicularly....
es, viscosity
Viscosity

Viscosity is a measure of the Drag of a fluid which is being deformed by either shear stress or extensional stress. In everyday terms , viscosity is "thickness"....
, or heat conduction
Heat conduction

Heat conduction or thermal conduction is the spontaneous heat transfer through matter, from a region of higher temperature to a region of lower temperature, and acts to equalize temperature differences....
.

In tensor notation, the energy-momentum tensor
Stress-energy tensor

The stress-energy tensor is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress of Newtonian physics....
 of a perfect fluid can be written in the form where U is the velocity
Velocity

In physics, velocity is defined as the Derivative of Position vector. It is a vector physical quantity; both speed and direction are required to define it....
 vector field
Vector field

In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space.Vector fields are often used in physics to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic field or gravity for...
 of the fluid and where is the metric tensor of Minkowski spacetime.

Perfect fluids admit a Lagrangian
Lagrangian

The Lagrangian, , of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics known as Lagrangian mechanics....
 formulation, which allows the techniques used in field theory to be applied to fluids.






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Encyclopedia


In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, a perfect fluid is a fluid
Fluid

A fluid is defined as a substance that continually deforms under an applied shear stress. All liquids and all gases are fluids. Fluids are a subset of the Phase and include liquids, gas, Plasma physics and, to some extent, plasticity ....
 that can be completely characterized by its rest frame energy density
Energy density

Energy density is the amount of energy stored in a given system or region of space per unit volume, or per unit mass, depending on the context, although the latter is more formally specific energy ....
 ρ and isotropic pressure
Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
 p.

Real fluids are "sticky" and contain (and conduct) heat. Perfect fluids are idealized models in which these possibilities are neglected. Specifically, perfect fluids have no shear stress
Shear stress

File:Shear stress.JPGA shear stress, denoted , is defined as a stress which is applied parallel or tangent to a face of a material, as opposed to a normal stress which is applied perpendicularly....
es, viscosity
Viscosity

Viscosity is a measure of the Drag of a fluid which is being deformed by either shear stress or extensional stress. In everyday terms , viscosity is "thickness"....
, or heat conduction
Heat conduction

Heat conduction or thermal conduction is the spontaneous heat transfer through matter, from a region of higher temperature to a region of lower temperature, and acts to equalize temperature differences....
.

In tensor notation, the energy-momentum tensor
Stress-energy tensor

The stress-energy tensor is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress of Newtonian physics....
 of a perfect fluid can be written in the form where U is the velocity
Velocity

In physics, velocity is defined as the Derivative of Position vector. It is a vector physical quantity; both speed and direction are required to define it....
 vector field
Vector field

In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space.Vector fields are often used in physics to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic field or gravity for...
 of the fluid and where is the metric tensor of Minkowski spacetime.

Perfect fluids admit a Lagrangian
Lagrangian

The Lagrangian, , of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics known as Lagrangian mechanics....
 formulation, which allows the techniques used in field theory to be applied to fluids. In particular, this enables us to quantize
Quantization (physics)

In physics, quantization is a procedure for constructing a quantum field theory starting from a classical field . This is a generalization of the procedure for building quantum mechanics from classical mechanics....
 perfect fluid models. This Lagrangian formulation can be generalized, but unfortunately, heat conduction and anisotropic stresses cannot be treated in these generalized formulations.

Perfect fluids are often used in general relativity
General relativity

General relativity or the general theory of relativity is the Geometry Theoretical physics of gravitation published by Albert Einstein in 1916....
 to model idealized distributions of matter
Matter

In common usage, matter is anything that has both mass and volume . A more rigorous definition is used in science: matter is what atoms and molecules are made of....
, such as in the interior of a star.

See also

  • equation of state
    Equation of state

    In physics and thermodynamics, an equation of state is a relation between thermodynamic variables. More specifically, an equation of state is a thermodynamic equations describing the state of matter under a given set of physical conditions....
  • ideal gas
    Ideal gas

    The ideal gas model is a model of matter in which the molecules are treated as non-interacting point particles which are engaged in a random motion that obeys conservation of energy....
  • fluid solutions in general relativity
    Fluid solution

    In general relativity, a fluid solution is an exact solutions in general relativity of the Einstein field equation in which the gravitational field is produced entirely by the mass, momentum, and stress density of a fluid....


External links


  • Mark D. Roberts, [A Fluid Generalization of Membranes http://www.arXiv.org/abs/hep-th/0406164 hep-th/0406164].


Note: Mark Roberts is an occasional Wikipedia editor Markdroberts. He contributed to this article.