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Category:Integral calculus |
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<math>\int\limits_{V_f} \rho(\vec x, t) d\Omega = 0</math>
Applying the [[Reynolds transport theorem]], one can change the reference to an arbitrary (non-fluid) [[control volume]] <var>V<sub>c</sub></var>. Further assuming that the [[density|density function]] is continuous (i.e. that our fluid is monophasic and thermodinamically metastable) and that <var>V<sub>c</sub></var> is not moving relative to the chosen system of reference, the equation becomes:
<math>\int\limits_{V_c} \left [ {{\partial \rho} \over {\partial t}} + \nabla \cdot (\rho \vec v) \right ] d\Omega = 0</math>
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