# Navier-Stokes equations

The Navier-Stokes equation is an equation in fluid mechanics that states:

$\rho \frac{D \mathbf{V}}{D t} = -\nabla p + \mu \nabla^2 \mathbf{V} + \rho \mathbf{g}$

where $\nabla p$ is the pressure difference (expressed as the partial derivative of pressure in each dimension), $\frac{D \mathbf{V}}{D t}$ is the total derivative of velocity, $\mu \,$ is the kinematic viscosity of the fluid, $\rho \,$ is the density of the fluid, and $\mathbf{g}$ is the gravitational acceleration. [1]

## References

1. A.J. Smits, "A Physical Introduction to Fluid Mechanics," John Wiley & Sons, ISBN 0-471-25349-9