# Difference between revisions of "Navier-Stokes equation"

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The Navier-Stokes equation describes the motion of fluids. It is derived from applying Newton's second law to fluid systems, and assumes that the fluid stress is the sum of a viscous term and a pressure term. The general form of the equations of fluid motion is

$\rho \left(\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v}\right) = -\nabla p + \nabla \cdot\mathbb{T} + \mathbf{f},$

where $\mathbf{v}$ is the flow velocity, $\rho$ is the fluid density, p is the pressure, $\mathbb{T}$ is the stress tensor, and $\mathbf{f}$ represents body forces per unit volume acting on the fluid.