A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied...

known properties of divergence and gradient we can use the mass continuity equation, which represents the mass per unit volume of a homogenous fluid...

can be derived from an appropriate scaling of the continuity equation. The full continuity equation for a general fluid flow is: ∂ ρ ∂ t + ∇ ⋅ ( ρ u )...

This equation is called the mass continuity equation, or simply the continuity equation. This equation generally accompanies the Navier–Stokes equation. In...

process Continuity equations applicable to conservation of mass, energy, momentum, electric charge and other conserved quantities Continuity test for...

is considered continuous and therefore can be described using the continuity equation for continuous steady flow. Spatially-varied flow The discharge of...

has almost zero mass diffusivity), hence the transport equation is simply the continuity equation: ∂ c ∂ t + v ⋅ ∇ c = 0. {\displaystyle {\frac {\partial...

in 3D. Continuity equation Heat equation Fokker–Planck equation Fick's laws of diffusion Maxwell–Stefan equation Radiative transfer equation and diffusion...

form of the continuity equation, but rather of the energy equation, as it will become clear in the following). Notably, the continuity equation would be...

x^{\alpha }} is the four-gradient. This is the continuity equation. In general relativity, the continuity equation is written as: J α ; α = 0 , {\displaystyle...

write down a continuity equation for W, from which all other equations can be derived and which we will call therefore the "master” equation. — Nordsieck...

Functional equation Functional equation (L-function) Constitutive equation Laws of science Defining equation (physical chemistry) List of equations in classical...

Klein–Kramers equation. The case with zero diffusion is the continuity equation. The Fokker–Planck equation is obtained from the master equation through Kramers–Moyal...

theorem in classical mechanics, and mathematically similar to the continuity equation. Poynting's theorem states that the rate of energy transfer per unit...

In plasma physics, the Vlasov equation is a differential equation describing time evolution of the distribution function of collisionless plasma consisting...

current density) is related to the probability density function via a continuity equation. The probability current is invariant under gauge transformation...

of aortic valve is not routinely performed.[citation needed] The continuity equation states that the flow in one area must equal the flow in a second...

displacement) has been found, the vertical velocity can be recovered via the continuity equation. Situations in fluid dynamics where the horizontal length scale is...

is solenoidal (see next section), so the divergence theorem and continuity equation imply that the flux through any surface with boundary C, with the...

ρ = | ψ | 2 {\displaystyle \rho =|\psi |^{2}} , this equation is exactly the continuity equation, appearing in many situations in physics where we need...

conservation law is usually expressed mathematically as a continuity equation, a partial differential equation which gives a relation between the amount of the...

of ρ {\displaystyle \rho } obeys an 2n-dimensional version of the continuity equation: ∂ ρ ∂ t + ∑ i = 1 n ( ∂ ( ρ q ˙ i ) ∂ q i + ∂ ( ρ p ˙ i ) ∂ p i...

at least two variables. Whereas the "wave equation", the "diffusion equation", and the "continuity equation" all have standard forms (and various special...

hydrodynamic stability problems are the Navier–Stokes equation and the continuity equation. The Navier–Stokes equation is given by: ∂ u ∂ t + ( u ⋅ ∇ ) u − ν ∇ 2...

general. Since charge is conserved, current density must satisfy a continuity equation. Here is a derivation from first principles. The net flow out of...

formulation of energy conservation is generally not in the form of a continuity equation because it includes contributions both from the macroscopic mechanical...

\rho (x,y,z,t)=\rho {\text{ (a constant)}}} Then, starting with the continuity equation: ∂ ρ ∂ t + ∇ ⋅ ( ρ v → ) = 0 {\displaystyle {\frac {\partial \rho...

}} , that satisfies the continuity equation ∂ μ j μ = 0 {\displaystyle \partial _{\mu }j^{\mu }=0} . The continuity equation represents a conservation...

clearly not enough, as there are only 14 equations (10 from the field equations and 4 from the continuity equation) for 20 unknowns (10 metric components...

In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including...