Textbook fluid dynamics teaches that pipe flow transitions to turbulence at a Reynolds number of approximately 2,000. This number appears in every introductory course, every engineering handbook, every design standard. It is one of the most widely taught constants in physics.
It is not a constant. It is not even a property of the flow.
Experimentally, laminar flow can be maintained at Reynolds numbers exceeding 100,000 — fifty times the textbook value — by carefully controlling inlet disturbances. The transition from laminar to turbulent flow is not triggered by the Reynolds number alone but by the amplitude of perturbations at the inlet. Smooth the inlet, suppress the disturbances, and laminar flow persists far beyond what any textbook would predict.
This means Re ≈ 2,000 is not a physical constant of pipe flow. It is an engineering approximation reflecting typical pipe roughness, typical inlet conditions, typical manufacturing tolerances. Real pipes are imperfect, and their imperfections generate perturbations that trigger turbulence at modest Reynolds numbers. The “critical Reynolds number” is a property of the pipe's imperfections, not the flow itself.
The distinction matters: a fundamental constant would mean turbulence is inevitable above a threshold. An engineering approximation means turbulence is the product of specific conditions that can, in principle, be controlled. The same data point — Re ≈ 2,000 — carries completely different implications depending on whether it describes the phenomenon or the apparatus. When a constant depends on experimental conditions, it is not a constant of the phenomenon but of the measurement.