# Turbulence

## The Reynolds Number

There is a number—called Reynolds number—whose values indicate clearly whether the motion of a fluid in a certain region is turbulent or not. It is defined as:

Whether an obstacle carries any eddies, and whether these are released into the flow downstream depends upon the speed of the incoming fluid, the size of the obstacle and the internal friction (viscosity) of the fluid, according to Karen J. Heywood writing in Physics Education. Just like a solid body, a parcel of liquid or gas has mass, and therefore inertia. Inertial force is the amount of force required to stop a body that is moving along steadily with its own inertia (for example, the force to stop a charging rhino moving towards you would be greater than that needed to stop a hummingbird at the same speed). The inertial force necessary to stop a parcel of water that occupies a unit volume (1 m3, say) is proportional to the square of its speed (v2) divided by a length typical of the obstacle (d)—say, the diameter of a stone in a river. All fluids, as they flow, present friction between their different parts. This property is called viscosity. Liquids are more viscous than gases, and, among liquids, corn syrup is much more viscous than water. The viscous force (internal friction) working on an object of diameter d moving through a fluid at speed v is proportional to h.d/d 2, where h is the viscosity coefficient of the fluid. Dividing the expression for the inertial force by that for the frictional force, we obtain R as given by the above equation.