The simplicity of a law does not imply simplicity of the consequences.

The Navier-Stokes equations describe how fluids move by relating velocity, pressure, density, viscosity, and external forces. They are essentially Newton’s laws applied to flowing liquids and gases, tracking how momentum changes from one point to another. The equations can model everything from water curling around a ship’s hull to air streaming over a wing. Their nonlinear terms allow turbulence, vortices, and other complicated behavior to emerge, which is exactly what makes them both powerful and notoriously difficult to solve. In many real systems, numerical approximation is essential.

The design is the vector form of the incompressible Navier–Stokes momentum equation for a Newtonian fluid with constant viscosity (More specifically, the non-conservative, material-derivative form).