Mathematical form of Mass Conservation for continuum body:
Integral form | Differential form | ||||
---|---|---|---|---|---|
|
|
where
t | time |
{\bf r } | position vector |
\rho(t, {\bf r}) | continuum body spatial density distribution |
{\bf u}(t, {\bf r) | continuum body spatial velocity distribution |
\dot m = \frac{dm}{dt} | mass generation rate |
For the stationary fluid flow:
(3) | \frac{\partial \rho}{\partial t} = 0 \rightarrow \nabla (\rho \, {\bf u}) = 0 |
See also
Natural Science / Physics / Mechanics / Continuum mechanics