# Momentum and mass balance in fluid mechanics

1. Feb 27, 2012

### Chuck88

When I am reading the paper in fluid mechanics, I found a paragraph and two equations:

"Since the ﬂuid is considered Newtonian and incompress-
ible of density ρ and constant viscosity μ, the dimensionless
mass and momentum balance equations are:"

$$\nabla \cdot \mathbf{v} = 0$$

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

"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?

Last edited: Feb 28, 2012
2. Feb 28, 2012

In this context, $\mathrm{Re} = \frac{\rho u L}{\mu}$ is the Reynolds number - a nondimensional number representing the ratio of inertial forces to viscous forces in the fluid.