What is the primary factor in determining whether fluid flow is laminar or turbulent?

The primary factor in determining whether fluid flow is laminar or turbulent is the Reynolds number. The Reynolds number is a dimensionless quantity that provides insight into the flow characteristics of a fluid. It is calculated using the fluid's density, viscosity, flow velocity, and characteristic length scale (such as diameter in pipe flow).

When the Reynolds number is low (typically below 2000 for flow in a circular pipe), the flow tends to be laminar, characterized by smooth, orderly layers of fluid that slide past one another. In contrast, a high Reynolds number (typically above 4000) indicates turbulent flow, where the motion of the fluid becomes chaotic and mixed, with eddies and vortices forming. The transition between laminar and turbulent flow occurs in this intermediate range of Reynolds numbers, making it a crucial factor in the analysis of fluid mechanics.

While fluid density, viscosity, and flow velocity are indeed factors that contribute to the calculation of the Reynolds number, it is the Reynolds number itself that ultimately dictates the nature of the flow, establishing it as the key determinant in identifying laminar versus turbulent flow regimes.