Reynix

Meet Reynix, a stream of water who flows smoothly until she starts to swirl.

Flowing fluids come in two main styles. In laminar flow the fluid moves in neat parallel layers. In turbulent flow it breaks up into chaotic swirls and eddies. The Reynolds number is a single pure number that predicts which style you will get.

It is defined as Re = ρvL/η, where ρ is the fluid density, v its speed, L a size such as a pipe diameter, and η the viscosity. Water at 0.1 m/s in a pipe 2 cm wide gives Re = 1000 × 0.1 × 0.02 / 0.001 = 2000. In pipes, flow is usually laminar below about 2000 and turbulent above about 4000.

The number compares the push of the fluid's momentum with the smoothing effect of its viscosity. A high value means momentum wins and swirls form.

Engineers use the Reynolds number to scale up models, since flows with equal values behave alike.