Navier-Stokes is actually Newton’s second law of motion in disguise. The left-hand side is the acceleration of a small fluid region, and the right-hand side is the forces that act on it: pressure, stress, and internal body forces. This formula provides a really accurate way to calculate how fluids move, and it is a key feature of innumerable scientific and technological problems. Navier-Stokes led us to modern passenger jets, fast and quiet submarines, Formula-1 racing cars that stay on the track at high speeds, and medical advances on blood flow in veins and arteries.

## Discover Maths

Mathematics is much more than routine calculations. That's what David Darling aims to show in this series of mathematics videos.