When I am reading the paper in fluid mechanics, I found a paragraph and two equations:(adsbygoogle = window.adsbygoogle || []).push({});

"Since the ﬂuid is considered Newtonian and incompress-

ible of density ρ and constant viscosity μ, the dimensionless

mass and momentum balance equations are:"

[tex]

\nabla \cdot \mathbf{v} = 0

[/tex]

[tex]

Re[\frac{d\mathbf{v}}{dt}+(\mathbf{v} - \mathbf{x}^t) \cdot \nabla \mathbf{v}] = \nabla \cdot \mathbf{T}

[/tex]

"Where ##\mathbf{T} = -p/Ca \mathbf{I} + (\nabla \mathbf{v} + \nabla \mathbf{v}^T)## is the Cauchy stress tensor"

Can someone provide me with the information about the "mass and momentum balance?" Also, what does ##Re## mean in the formulae?

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# Momentum and mass balance in fluid mechanics

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