Navier-Stokes equations

Navier-Stokes equations [nä′vyā ′stōks i‚kwā·zhənz]

(fluid mechanics)

The equations of motion for a viscous fluid which may be writtendV/dt= -(1/ρ)∇p+ F + ν∇²V + (⅓)ν∇(∇·V), wherepis the pressure, ρ the density,Fthe total external force per unit mass, V the fluid velocity, and ν the kinematic viscosity; for an incompressible fluid, the term in ∇·V (divergence) vanishes, and the effects of viscosity then play a role analogous to that of temperature in thermal conduction and to that of density in simple diffusion.