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How It Works
The Reynolds number is a dimensionless quantity that predicts the flow regime in fluid mechanics. It represents the ratio of inertial forces to viscous forces within a fluid and is used to determine whether flow will be laminar or turbulent.
The formula is Re = ρVL/μ, where ρ is the fluid density, V is the flow velocity, L is a characteristic length (such as pipe diameter), and μ is the dynamic viscosity. Low Reynolds numbers (Re < 2,300 for pipe flow) indicate laminar flow, while high Reynolds numbers (Re > 4,000) indicate turbulent flow. The range between 2,300 and 4,000 is the transitional region.
Example Problem
Water (ρ = 998 kg/m³) flows at 1.5 m/s through a pipe with an inner diameter of 0.05 m. The dynamic viscosity of water at 20°C is approximately 0.001002 Pa·s. What is the Reynolds number?
- Re = ρVL / μ = 998 × 1.5 × 0.05 / 0.001002
- Re = 74.85 / 0.001002 = 74,700.6
Because Re > 4,000, the flow is fully turbulent. Engineers would need to account for turbulent friction losses when designing this piping system.
Frequently Asked Questions
What is the Reynolds number?
The Reynolds number (Re) is a dimensionless number that describes the ratio of inertial forces to viscous forces in a flowing fluid. It equals ρVL/μ, where ρ is density, V is velocity, L is a characteristic linear dimension, and μ is the dynamic viscosity. It is named after Osborne Reynolds who popularized its use in 1883.
What are the critical Reynolds number values for pipe flow?
For flow in a circular pipe, Re < 2,300 indicates laminar flow, Re > 4,000 indicates turbulent flow, and the range 2,300–4,000 is the transition zone where flow may alternate between laminar and turbulent. These thresholds can vary depending on surface roughness and flow disturbances.
What is the characteristic length in the Reynolds number?
The characteristic length depends on the geometry. For internal pipe flow, it is the pipe diameter. For flow over a flat plate, it is the distance from the leading edge. For flow around a sphere, it is the sphere diameter. Choosing the correct characteristic length is essential for accurate Reynolds number calculations.
How does temperature affect the Reynolds number?
Temperature primarily affects viscosity and, to a lesser extent, density. For liquids, viscosity decreases with increasing temperature, so the Reynolds number increases (flow becomes more turbulent). For gases, viscosity increases with temperature, so the Reynolds number decreases.
Can the Reynolds number be used for non-Newtonian fluids?
A generalized Reynolds number can be defined for non-Newtonian fluids, but the standard formula Re = ρVL/μ applies only to Newtonian fluids with constant viscosity. For power-law fluids, a modified Reynolds number accounts for the shear-rate-dependent viscosity.
Related Calculators
- Darcy-Weisbach Calculator — calculate friction head loss in pipes using the Darcy-Weisbach equation.
- Pipe Flow Calculator — compute flow rate, velocity, and pressure drop for pipe systems.
- Colebrook Equation Calculator — determine the Darcy friction factor for turbulent pipe flow.
- Bernoulli Theorem Calculator — apply Bernoulli's principle to fluid flow problems.
- Fluid Pressure Calculator — calculate pressure at depth in a fluid.