Definition:Continuity Equation

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