Open Channel Reynolds Number Calculator
Enter velocity, hydraulic radius and kinematic viscosity to compute the Reynolds number Re = v·R/ν for open-channel flow.
Input Data
Results
At a glance:The Reynolds number compares inertial to viscous forces: Re = ρ·v·L/μ = v·L/ν, where ν = μ/ρ is kinematic viscosity. For open-channel flow the characteristic length is the hydraulic radius R (area/wetted perimeter) rather than diameter, so Re = v·R/ν. Flow regimes: laminar for Re < ~500, transitional 500–2000, turbulent > ~2000 (some texts use 2000/4000 thresholds). Re determines whether the flow is smooth (viscous-dominated) or turbulent (mixing-dominated), which affects friction (Manning vs Darcy-Weisbach) and sediment transport. This tool computes Re = vR/ν and labels the regime.
Formula
Re = v·R/ν
ν = μ/ρ
$$Re = \dfrac{v\,R}{\nu}$$How to Use
- Enter mean velocity v (m/s).
- Enter hydraulic radius R (m) and kinematic viscosity ν (m²/s).
- The calculator returns Re and the regime.
Case Studies
River flow
v = 1 m/s, R = 0.5 m, ν = 1e-6 m²/s.
Re = 1×0.5/1e-6 = 5×10⁵.
Highly turbulent (typical river).
FAQ
Why use hydraulic radius, not diameter?
Open channels have a free surface, so the relevant length for viscous shear is R = A/P. For a full pipe R = D/4, recovering the familiar Re = vD/ν with R=D/4.
What Re separates laminar and turbulent?
Open-channel thresholds are roughly Re < 500 laminar, 500–2000 transitional, > 2000 turbulent — lower than pipe flow because R < D/4.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.