Definition:Continuity Equation
(Redirected from Definition:Equation of Continuity)
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Definition
A continuity equation is an equation in physics which is applied to continuous flow of a conserved quantity.
Examples
Increase of Fluid Mass
The continuity equation for mass equates the rate of increase of mass in a volume of fluid to the net rate of flow of mass into that volume:
- $\dfrac {\partial \rho} {\partial t} + \nabla \cdot \paren {\rho \mathbf v} = 0$
where:
- $\rho$ is the density of the fluid
- $\dfrac {\partial \rho} {\partial t}$ is the rate of change of density at an arbitrary point
- $\mathbf v$ denotes the velocity of the fluid at that point
- $\nabla$ is the del operator.
Also known as
A continuity equation is also known as an equation of continuity.
Also see
- Results about continuity equations can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): continuity equation
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): continuity equation