Reynolds number

Reynolds Number

The Reynolds number (dimensionless quantity) is a fundamental concept in the field of fluid dynamics and heat transfer. It is named after the British scientist Osborne Reynolds (1842–1912), who introduced this concept in the 1880s.

Definition

The Reynolds number is defined as the ratio of inertial forces to viscous forces and is used to predict the onset of turbulence in fluid flow. It is represented by the formula:

Re = ρuD/μ

where:

• Re is the Reynolds number,
• ρ is the density of the fluid,
• u is the velocity of the fluid,
• D is the characteristic linear dimension (typically the hydraulic diameter),
• μ is the dynamic viscosity of the fluid.

Applications

The Reynolds number is used in the analysis and design of fluid flow systems, including the study of aerodynamics, hydrodynamics, and heat transfer. It helps in predicting the transition from laminar to turbulent flow, which is critical in many engineering applications such as pipe flow, heat exchangers, and aerodynamic design.

Reynolds Number and Flow Regimes

The Reynolds number can be used to predict the behavior of fluid flow:

• Re < 2000: The flow is laminar, characterized by smooth, constant fluid motion.
• 2000 < Re < 4000: The flow is in a transition state, neither fully laminar nor fully turbulent.
• Re > 4000: The flow is turbulent, characterized by chaotic, eddy currents.

See also

• Froude number
• Mach number
• Prandtl number
• Strouhal number