Notes on Computational Fluid Dynamics: General Principles

6.1 Reynolds experiment

Reynolds distinguished the laminar and turbulent flow regimes in his influential experiments in the early 1880s.¹ At that time, Poisueille’s law predicted correctly that the resistance to flow in a pipe for laminar flow at speed , which typically occurs at small and/or diameter . Reynolds wanted to understand why, at higher and/or , resistance (approximately).

His experiment used a large, glass-walled tank filled with water. A glass tube with a flared intake passed through the tank and out through one wall. Water from the tank flowed along the tube at speed , controlled by an outlet valve. A jet of liquid dye was injected at the inlet to the tube to visualise the flow.

The observed behaviour is shown in Reynolds’s original drawings on the following page. At sufficiently low speed, the streak of dye followed a straight line along the tube, indicating laminar flow. The speed was increased in small steps until at some distance from the tube intake (typically, 30) the dye would mix with the water, rapidly filling the tube. This marked the transition to turbulent flow.

Reynolds made the following important observations.

• Distinct eddies were visible during turbulent flow, see above.
• The transition speed was very sensitive to disturbances in the water entering the tube, even due to the temperature variations in the water.
• Before full transition was reached, intermittent “spots” of turbulence appeared and disappeared.

Reynolds number

Reynolds argued that the transition is controlled by the Reynolds number, from Eq. (2.68 ), using the characteristic length in a pipe. His deduction was based on the idea of scale similarity, introduced in Sec. 2.21 .

He observed that with minimal disturbance in the tank, the transition to turbulent flow occurred at  13000. When disturbances were evidently present, the transition occurred at  2000. An updated view for pipe flow is that for  2000, all disturbances will decay preventing the onset of turbulent flow. For  2000, transition depends on initial disturbances and the roughness of the pipe wall.