Question

Define Ideal Fluids​

Answer 1

Answer:

an Ideal fluid is a fluid that can be completely characterized by its rest frame mass density and isotropic pressure p. Real fluids are "sticky" and contain heat. Perfect fluids are idealized models in which these possibilities are neglected.

Answer 2

In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame mass density {\displaystyle \rho _{m}} \rho_m and isotropic pressure p.

The stress–energy tensor of a perfect fluid contains only the diagonal components.

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 space-positive metric signature tensor notation, the stress–energy tensor of a perfect fluid can be written in the form

{\displaystyle T^{\mu \nu }=\left(\rho _{m}+{\frac {p}{c^{2}}}\right)\,U^{\mu }U^{\nu }+p\,\eta ^{\mu \nu }\,} T^{{\mu \nu }}=\left(\rho _{m}+{\frac {p}{c^{2}}}\right)\,U^{\mu }U^{\nu }+p\,\eta ^{{\mu \nu }}\,

where U is the 4-velocity vector field of the fluid and where {\displaystyle \eta _{\mu \nu }=\operatorname {diag} (-1,1,1,1)} {\displaystyle \eta _{\mu \nu }=\operatorname {diag} (-1,1,1,1)} is the metric tensor of Minkowski spacetime.

In time-positive metric signature tensor notation, the stress–energy tensor of a perfect fluid can be written in the form

{\displaystyle T^{\mu \nu }=\left(\rho _{\text{m}}+{\frac {p}{c^{2}}}\right)\,U^{\mu }U^{\nu }-p\,\eta ^{\mu \nu }\,} {\displaystyle T^{\mu \nu }=\left(\rho _{\text{m}}+{\frac {p}{c^{2}}}\right)\,U^{\mu }U^{\nu }-p\,\eta ^{\mu \nu }\,}