Continuity Equation/Examples
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Examples of Continuity Equations
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.