Equation of the Week [July 1, 2013]

The Navier-Stokes equations describe the motion of fluid substances. The derivation begins with the conservation of momentum, an application of Newton's second law of motion.In an inertial frame of reference, the general form of the equation of fluid motion is



where  is the flow velocity,  is the fluid density,  is the pressure,  is the deviatoric component of the total stress tensor,  represents the body forces acting on the fluid, and  is the del operator.

Assuming constant viscosity and assuming incompressible flow, the Navier-Stokes equations will read, in vector form



where  is the (constant) dynamic viscosity.