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Mathematical form of Mass Conservation for continuum body:
| Integral form | Differential form |
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| LaTeX Math Block |
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| \frac{d}{dt} \iiint_\Omega \rho \, dV = \dot m = \frac{dm_\Omega}{dt} |
| | LaTeX Math Block |
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| \frac{\partial \rho}{\partial t} + \nabla (\rho \, {\bf u}) = \ |
|
dotm where
| time |
| LaTeX Math Inline |
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| body | --uriencoded--%7B\bf r %7D |
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| position vector |
| LaTeX Math Inline |
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| body | --uriencoded--\rho(t, %7B\bf r%7D) |
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| continuum body spatial density distribution |
| LaTeX Math Inline |
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| body | --uriencoded--%7B\bf u%7D(t, %7B\bf r) |
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|
| continuum body spatial velocity distribution |
| LaTeX Math Inline |
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| body | --uriencoded--\dot m = \frac%7Bdm%7D%7Bdt%7D |
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|
| mass generation rate |
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