Momentum Governing Equations

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The momentum governing equation can be obtained from Reynolds Transport Theorem by setting $B$ equal to the momentum,

$B=\rho {\boldsymbol {v}}$

where ${\boldsymbol {v}}$ is the mass-average velocity of the fluid.

The material volume associated with the momentum is denoted $V_{\rho v}^{M}$ and is the control volume that moves such that the net flux of momentum across its surface is zero. The surface bounding this material volume is $S_{\rho v}^{M}$.

The velocity at which this material volume moves is ${\boldsymbol {v}}$, the mass-average volume