The continuity equation expresses conservation of mass and has the form


\begin{displaymath}\frac{\partial \rho}{\partial t}+\frac{\partial}{\partial x_{i}}(\rho u_{i}) = 0 \notag
\end{displaymath}  

where $\rho$ is the fluid density and $u_{i}$ is the component of the velocity vector $\vec{u}$ in the $i$ th direction. If we assume that the fluid isincompressible and the density constant, the equation above simplifies to


\begin{displaymath}\frac{\partial u_{i}}{\partial x_{i}} = 0 \notag
\end{displaymath}  

or in vectorial form to


\begin{displaymath}\nabla.\vec{u} = 0 \notag
\end{displaymath}  



Timothy S Choe
2003-03-15