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Perfect fluid

In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame energy density ρ and isotropic pressure p.

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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 stresses, viscosity, or heat conduction.

In tensor notation, the energy-momentum tensor of a perfect fluid can be written in the form

$T^{\mu\nu} = (\rho + p) \, U^\mu U^\nu + p \, \eta^{\mu\nu}\,$

where U is the velocity vector field of the fluid and where $η μν$ is the metric tensor of Minkowski spacetime.

Perfect fluids admit a Lagrangian formulation, which allows the techniques used in field theory to be applied to fluids. In particular, this enables us to quantize 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 to model idealized distributions of matter, such as in the interior of a star.

References

The Large Scale Structure of Space-Time, by S.W.Hawking and G.F.R.Ellis, Cambridge University Press, 1973. ISBN 0-521-20016-4, ISBN 0-521-09906-4 (pbk.)

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

Category: Fluid mechanics