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Why does pipe flow change from laminar flow to turbulent flow over a range of Reynolds numbers?

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differential manometer, Torricellian barometer, and siphon — fluid mechanics Figure 1: Schematic representations of (A) a differential manometer, (B) a Torricellian barometer, and (C) a siphon.

In fluid mechanics, the transition from laminar flow to turbulent flow occurs because of the nonlinear nature of fluid motion. As flow velocity increases, small periodic perturbations in the fluid grow parasitically, eventually causing the flow to become grossly disturbed and irregular.1

This transition is governed by the Reynolds number, a dimensionless quantity representing the ratio of inertial forces to viscous forces. While laminar flow is characterized by smooth, parallel layers, turbulence involves irregular fluctuations and mixing.234

The shift does not happen at a single, universal value because it is highly sensitive to external factors, such as the smoothness of the pipe's entry. Consequently, the transition typically occurs across a range, often beginning between 1,000 and 2,000 and extending up to 5,000. In practical engineering, turbulence often sets in at lower values if the pipe entry is not carefully flared, whereas in highly controlled conditions, it may persist until higher Reynolds numbers are reached.21