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Reynolds Number & Flow Regimes — Reference

The ratio of inertial to viscous forces — the single number that decides whether flow is laminar or turbulent, and therefore which friction relation applies.

Definition

Re = ρVL/μ = VL/ν   (ν = μ/ρ)

Characteristic length L: pipe → diameter D (full-flow); open channel → hydraulic radius R = A/P. (Some texts use 4R for channels to align with the pipe definition — check which convention a threshold assumes.)

Flow Regime Thresholds

SystemLaminarTransitionalTurbulent
Pipe flow (L = D)< 21002100–4000> 4000
Open channel (L = R)< 500500–2000> 2000
Flow around a sphere/particle< 11–1000> 1000

Kinematic Viscosity of Water

Tempν (m²/s)ν (ft²/s)
5°C / 41°F1.52×10−61.63×10−5
10°C / 50°F1.31×10−61.41×10−5
20°C / 68°F1.00×10−61.08×10−5
30°C / 86°F0.80×10−60.86×10−5
Why it matters. In laminar pipe flow the friction factor is simply f = 64/Re (roughness irrelevant). In turbulent flow you need Colebrook / Swamee-Jain with the relative roughness. The Froude number (not Reynolds) governs the sub/supercritical state of open-channel flow — Reynolds only tells you it's turbulent, which it nearly always is.

Sources: White, F.M., Fluid Mechanics. Munson et al., Fundamentals of Fluid Mechanics. Viscosity values: standard water property tables.

Checking a flow regime? Open the Reynolds calculator → · Turbulent friction? Roughness & friction factor.

Related cheat sheets and tools

Confirm the regime with the Reynolds tool, then pick the friction relation from the roughness card and compute loss in Darcy-Weisbach. For open channels, the specific-energy card covers the Froude side. For full network modeling, see HydroComplete.

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