A million-dollar question

Fluids take the shape of their container, unlike solids, which have definite shapes. A fluid is also a continuous substance that flows automatically. Fluids are everywhere. Air in the Earth's atmosphere is a fluid. Water in the oceans is a fluid. The black liquid that flows through pipes from refineries is a fluid. Stars consist of fluids. Even atomic nuclei, which are protons and neutrons held together, behave like a liquid that obeys quantum laws. It is easy to see, therefore, that the laws of fluid mechanics govern the entire universe. Understanding fluid mechanics helps scientists understand all the phenomena mentioned above. It also explains much of what happens on Earth and elsewhere, including inside human bodies.

All fluids largely behave the same way, except for two key features: density and viscosity. Understanding this general behaviour is a hard scientific problem. Human beings designed machines governed by fluid dynamics long before they understood how their creations worked. The most famous example is the building of an aeroplane. Records suggest that the Wright brothers did not know — or possibly did not fully understand — the concept of lift or Bernoulli's principle that governed lift when they designed the world's first plane in 1903. They used empirical methods, better known as trial and error, to develop a plane that flew. Since then, physicists have understood the laws of fluid mechanics much better, yet the deep truth still eludes their grasp.

The problem is a solution to the Navier-Stokes equation, the most fundamental equation of fluid mechanics. They were developed from 1822 to 1845 by French engineer Claude-Louis Navier and Irish physicist George Gabriel Stokes, with contributions from other scientists. They apply Newton's laws of motion to the specific case of fluids. Fluids contain billions of molecules, each of which moves based on the forces it experiences from other molecules that are also moving with it. These molecules are also subjected to external pressures. The Navier-Stokes equation combines all of these into a neat equation that purports to predict the future of the liquid. You plug the current state of the fluid into the equation, and it is supposed to give a future state as output — except that it never works so neatly.