Laminar flow

In fluid dynamics, laminar flow describes how fluid particles move in smooth, orderly layers that slide past one another with minimal mixing. This happens at low velocities, where the fluid lacks cross-currents, eddies, or swirls perpendicular to the direction of flow. Particles near a solid surface travel in straight lines parallel to that surface. This flow regime is marked by high momentum diffusion and low momentum convection.

Whether flow through a closed channel—like a pipe or between two flat plates—is laminar or turbulent depends on the fluid's velocity and viscosity. Laminar flow occurs below a threshold velocity, beyond which the flow becomes turbulent. That threshold is set by the Reynolds number, a dimensionless parameter that also accounts for the fluid's density, viscosity, and the channel's dimensions. Turbulent flow, in contrast, is disorderly, featuring eddies and lateral mixing. Simply put, laminar flow is smooth; turbulent flow is rough.

The type of flow in a channel is crucial in fluid dynamics, affecting heat and mass transfer. The Reynolds number compares inertial forces to shearing forces—essentially, how fast the fluid moves relative to how viscous it is, independent of system scale. Laminar flow typically occurs when the fluid moves slowly or is very viscous. As the Reynolds number rises (for instance, by increasing flow rate), the flow transitions from laminar to turbulent over a specific range, which depends on small disturbances in the fluid or imperfections in the system. At very low Reynolds numbers (much less than 1), the fluid exhibits Stokes, or creeping, flow, where viscous forces dominate.

The exact Reynolds number calculation and the values for laminar flow depend on the system's geometry. For pipe flow, the Reynolds number is defined as Re = (ρ u D_H) / μ = (u D_H) / ν = (Q D_H) / (ν A), where D_H is the pipe's hydraulic diameter, Q is the volumetric flow rate, A is the cross-sectional area, u is the mean fluid speed, μ is dynamic viscosity, ν is kinematic viscosity (ν = μ/ρ), and ρ is density. In such systems, laminar flow occurs below a critical Reynolds number of about 2,040, with the transition range typically between 1,800 and 2,100.

For flow over external surfaces, like fluid passing objects, different Reynolds number definitions predict flow type. For example, the particle Reynolds number (Re_p) applies to particles suspended in flowing fluids. As with pipes, lower Reynolds numbers yield laminar flow, while higher ones lead to turbulence and phenomena like vortex shedding.

A common example is the smooth flow of a viscous liquid through a tube or pipe, where velocity varies from zero at the walls to a maximum at the center. The flow profile can be calculated by dividing the flow into thin cylindrical elements and applying viscous forces. Another example is airflow over an aircraft wing: the boundary layer—a thin sheet of air adhering to the wing due to viscosity—flows smoothly over the airfoil's streamlined shape at first, remaining laminar. Ludwig Prandtl applied the concept of the laminar boundary layer to airfoils in 1904. An everyday instance is the slow, smooth, optically transparent flow of shallow water over a smooth barrier. When water leaves a tap without an aerator at low force, it initially shows laminar flow, but as gravity accelerates it, the Reynolds number increases with speed, and the laminar flow downstream soon transitions.