Reynolds number

The Reynolds number is the ratio of inertial to viscous forces in a fluid flow. It helps characterize whether flow is laminar, transitional, or turbulent.

Navier–Stokes equations: Differential equations describing the motion of viscous fluids through conservation of momentum. Their inertial and viscous terms supply the force balance represented by the Reynolds number.
Pipe flow: Fluid motion through a conduit with a bounded cross-section. Pipe-flow regime estimates commonly use Reynolds number based on pipe diameter.
Laminar flow: Fluid motion in orderly layers with little mixing across them. It commonly occurs at low Reynolds numbers, though geometry and disturbances also matter.
Osborne Reynolds: A nineteenth-century British engineer and physicist known for research on fluid flow and turbulence. His experiments and analysis gave the dimensionless ratio its name.
Inertial force: The effect of a body's momentum resisting changes in its motion. This is the force contribution that grows relative to viscosity as Reynolds number increases.
Critical Reynolds number: A threshold value associated with a change in flow stability or regime for a specified system. It marks transitions whose value depends on geometry and disturbances.
Turbulence: Irregular fluid motion featuring fluctuating velocities and enhanced mixing. High Reynolds number makes turbulent motion more likely but does not guarantee it.
Reynolds' dye experiment: An experiment in which colored dye reveals changes in water flow through a glass tube. It demonstrated the transition from orderly to irregular pipe flow.
Viscosity: A fluid's resistance to deformation and internal flow. Dynamic viscosity appears in the denominator of the standard Reynolds number.
Drag coefficient: A dimensionless measure of drag force relative to fluid density, speed, and reference area. Reynolds number helps determine drag correlations for bodies moving through fluids.

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