Streamline and Turbulent Flow; Critical Velocity

When a fluid flows, the individual particles making up the fluid can move past one another in one of two fundamentally different ways, and telling these two ways apart is the first step in understanding any problem in fluid flow.

Streamline (or laminar) flow. At sufficiently low speeds, a fluid moves in an orderly, predictable way: every particle of the fluid that passes through a particular point in the flow follows exactly the same path as every particle that passed through that point before it. This path is called a streamline. Because different streamlines never cross one another (if they did, a fluid particle arriving at the crossing point would have two different possible velocities at once, which is impossible for steady flow), the fluid can be pictured as moving in smooth, distinct layers that slide past one another without mixing. Water flowing gently and smoothly from a tap that is only barely turned on, or the smooth flow of honey poured slowly from a jar, are everyday examples of streamline flow. Flow of this kind is also called laminar flow, from the Latin lamina, meaning a thin layer or sheet -- a direct reference to the layered picture just described.

Turbulent flow. As the speed of the flow is increased, past a certain characteristic speed called the critical velocity, this orderly layered pattern breaks down completely. The fluid's velocity at any fixed point in the flow now fluctuates rapidly and unpredictably, both in magnitude and in direction, and the fluid develops swirling regions called eddies and vortices, with considerable mixing between what were previously separate layers. Water gushing turbulently from a tap that has been turned on fully, the visibly chaotic flow just downstream of a rock in a fast-moving stream, and smoke rising from an incense stick (smooth and streamline near the source, then breaking up into swirling turbulence higher up as its speed and the surrounding disturbances increase) are everyday examples of turbulent flow. …