The flow of a fluid will experience turbulence, a fluid flow in which layers mix together via eddies and swirls, at high velocities.

Turbulence is a fluid flow in which layers mix together via eddies and swirls. It has two main causes. First, any obstruction or sharp corner, such as in a faucet, creates turbulence by imparting velocities perpendicular to the flow. Second, high speeds cause turbulence. The drag between adjacent layers of fluid and between the fluid and its surroundings can form swirls and eddies if the speed is great enough.

An indicator called the Reynolds number (Re) can reveal whether flow is laminar or turbulent. For flow in a tube of uniform diameter, the Reynolds number is defined as

Re = (2ρvr)/η

where ρ is the fluid density, v its speed, η its viscosity, and r the tube radius. The Reynolds number is a dimensionless quantity. Experiments have revealed that Re is related to the onset of turbulence. For Re below about 2000, flow is laminar. For Re above about 3000, flow is turbulent.

For values of Re between about 2000 and 3000, flow is unstable—that is, it can be laminar, but small obstructions and surface roughness can make it turbulent, and it may oscillate randomly between being laminar and turbulent. In fact, the flow of a fluid with a Reynolds number between 2000 and 3000 is a good example of chaotic behavior. A system is defined to be chaotic when its behavior is so sensitive to some factor that it is extremely difficult to predict. It is difficult, but not impossible, to predict whether flow is turbulent or not when a fluid’s Reynolds number falls in this range due to extremely sensitive dependence on factors like roughness and obstructions on the nature of the flow. A tiny variation in one factor has an exaggerated (or nonlinear) effect on the flow.

Key Points

• Laminar flow is characterized by smooth flow of the fluid in layers that do not mix.

• Turbulence is characterized by eddies and swirls that mix layers of fluid together.

• The Reynolds number (Re) can reveal whether flow is laminar or turbulent. It is Re = (2ρvr)/η.

• For Re below about 2000, flow is laminar. For Re above about 3000, flow is turbulent. For values of Re between 2000 and 3000, it may be either or both.

Key Terms

Laminar flow: A smooth flow of the fluid in layers that do not mix.

Turbulent flow:A fluid flow in which layers mix together via eddies and swirls.

Reynolds number (Re): the ratio of inertial forces to viscous forces within a fluid. Re < 2000 for laminar flow and Re > 3000 for turbulent flow.