Mass density in the context of "Perfect fluid"

In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the mean position of all the points in the figure. The same definition extends to any object in ${\displaystyle n}$-dimensional Euclidean space.

In geometry, one often assumes uniform mass density, in which case the barycenter or center of mass coincides with the centroid. Informally, it can be understood as the point at which a cutout of the shape (with uniformly distributed mass) could be perfectly balanced on the tip of a pin.

In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in coulombs per cubic meter (C⋅m), at any point in a volume. Surface charge density (σ) is the quantity of charge per unit area, measured in coulombs per square meter (C⋅m), at any point on a surface charge distribution on a two dimensional surface. Linear charge density (λ) is the quantity of charge per unit length, measured in coulombs per meter (C⋅m), at any point on a line charge distribution. Charge density can be either positive or negative, since electric charge can be either positive or negative.

Like mass density, charge density can vary with position. In classical electromagnetic theory charge density is idealized as a continuous scalar function of position ${\displaystyle {\boldsymbol {x}}}$, like a fluid, and ${\displaystyle \rho ({\boldsymbol {x}})}$, ${\displaystyle \sigma ({\boldsymbol {x}})}$, and ${\displaystyle \lambda ({\boldsymbol {x}})}$ are usually regarded as continuous charge distributions, even though all real charge distributions are made up of discrete charged particles. Due to the conservation of electric charge, the charge density in any volume can only change if an electric current of charge flows into or out of the volume. This is expressed by a continuity equation which links the rate of change of charge density ${\displaystyle \rho ({\boldsymbol {x}})}$ and the current density ${\displaystyle {\boldsymbol {J}}({\boldsymbol {x}})}$.

The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor field quantity that describes the density and flux of energy and momentum at each point in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields. This density and flux of energy and momentum are the sources of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity.

In chemistry and related fields, the molar volume, symbol V_m, or ${\displaystyle {\tilde {V}}}$ of a substance is the ratio of the volume (V) occupied by a substance to the amount of substance (n), usually at a given temperature and pressure. It is also equal to the molar mass (M) divided by the mass density (ρ):$${\displaystyle V_{\text{m}}={\frac {V}{n}}={\frac {M}{\rho }}}$$

The molar volume has the SI unit of cubic metres per mole (m/mol), although it is more typical to use the units cubic decimetres per mole (dm/mol) for gases, and cubic centimetres per mole (cm/mol) for liquids and solids.