Reynolds number, abbreviated as Re, a dimensionless number, measures the ratio of inertial forces (forces that remain at rest or in uniform motion) to viscosity forces in the fluid flow (the resistance to flow). It is used to predict the flow regimes of a fluid or gas.
Reynolds Number Interpretation
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Low Reynolds Number (Re << 1) - Viscous forces dominate over inertial forces. The flow is laminar, meaning it moves in smooth, predictable layers with minimal mixing. This happens in slow flows, highly viscous fluids (like honey), or very small systems (like microfluidics). For example, a tiny bug swimming in water experiences a low Re world where friction rules.
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High Reynolds Number (Re >> 1) - Inertial forces dominate over viscous forces. The flow becomes turbulent, characterized by eddies, swirls, and chaotic motion. This occurs in fast flows, low viscosity fluids (like air or water in large pipes), or big systems (like a river or an airplane wing). Think of a rushing river or windstorm, turbulence takes over.
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Transitional Range (Re ≈ critical value) - There’s a crossover region where flow shifts from laminar to turbulent, depending on the system. For pipe flow, this transition typically starts around Re ≈ 2000 and becomes fully turbulent above Re ≈ 4000. The exact threshold varies with geometry (pipes vs. flat plates) and disturbances in the flow.
Reynolds Number Formula |
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\( Re \;=\; \dfrac{\rho \cdot v \cdot l_c }{ \mu } \) (Reynolds Number) \( \rho \;=\; \dfrac{Re \cdot \mu }{ v \cdot l_c} \) \( v \;=\; \dfrac{Re \cdot \mu }{ \rho \cdot l_c } \) \( l_c \;=\; \dfrac{ Re \cdot \mu }{ \rho \cdot v } \) \( \mu \;=\; \dfrac {\rho \cdot v \cdot l_c }{ Re } \) |
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| Symbol | English | Metric |
| \( Re \) = Reynolds Number | \( dimensionless \) | \( dimensionless \) |
| \( \rho \) (Greek symbol rho) = Fluid Density | \( lbm \;/\; ft^3 \) | \( kg \;/\; m^3 \) |
| \( v \) = Fluid Velocity | \( ft \;/\; sec \) | \( m \;/\; s \) |
| \( l_c \) = Characteristic Length or Diameter of Fluid Flow | \( in \) | \( mm \) |
| \( \mu \) (Greek symbol mu) = Fluid Dynamic Viscosity | \( lbf-sec \;/\; ft^2\) | \( Pa-s \) |
It's important to note that these Reynolds number ranges are general guidelines, and the transition from laminar to turbulent flow can be influenced by factors such as surface roughness, disturbances, and the specific geometry of the flow. Engineers use these flow regimes to predict and analyze fluid behavior in various applications, including pipe flow, aerodynamics, and heat transfer.
