Navier-Stokes equations

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

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

where $\nabla p$ is the pressure difference (expressed as the partial derivative of pressure in each dimension), ${\frac {D\mathbf {V} }{Dt}}$ 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.