What flow regime do common Reynolds numbers represent?

Re 4000: turbulent. For pipe flow, most water-distribution and HVAC duct flow is fully turbulent (Re > 10⁴). Lab-scale flow and high-viscosity fluid handling can be laminar.

What's Reynolds number used for?

Re determines flow regime, which dictates which friction factor formula applies, whether boundary layer is laminar or turbulent, and how heat/mass transfer correlations behave. It's the most important dimensionless number in fluid mechanics.

How do I compute Reynolds number for non-circular ducts?

Replace pipe diameter D with hydraulic diameter D_h = 4A/P, where A is cross-sectional area and P is wetted perimeter. For a square duct, D_h = side length. For rectangular: D_h = 2ab/(a+b).

What is the formula for Reynolds number?

Re = V·L/ν = ρ·V·L/μ, where V is mean velocity, L is characteristic length (pipe diameter D for round pipes, hydraulic diameter D_h for non-circular), ν is kinematic viscosity, ρ is density, μ is dynamic viscosity. Reynolds number is dimensionless.

Why is the laminar threshold different for pipes vs open channels?

Pipe flow has solid boundaries on all sides; instability needs to overcome confinement before turbulence develops. Open-channel flow has a free surface that adds instability — turbulence develops at lower Re (typically 500). Therefore: pipe Re < 2,300 = laminar; channel Re < 500 = laminar.

What is critical Reynolds number?

For internal pipe flow, critical Re is approximately 2,300 — the value at which laminar flow becomes unstable. Below 2,300, perturbations decay; above, they grow into turbulence. For flow over a flat plate, critical Re ≈ 5×10⁵ (transition to turbulent boundary layer).

How does temperature affect Reynolds number?

Higher temperature reduces viscosity, increasing Re for the same V and D. Water viscosity drops 50% from 40°F (1.66×10⁻⁵ ft²/s) to 100°F (0.74×10⁻⁵). Same flow at higher temperature is more likely to be turbulent.

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Reynolds Number Calculator

Compute Re for a pipe or open-channel flow and read the regime: laminar, transitional, or turbulent.

Units

Geometry

Velocity, Vft/s

Characteristic length, Lft

Kinematic viscosity, νft²/s

Reynolds number, Re——

Flow regime——

Defaults are water at 60°F (ν = 1.21 × 10⁻⁵ ft²/s) in a 6-inch pipe at 5 ft/s.

$$ Re = \frac{V L}{\nu} $$

V mean velocity · L characteristic length (= pipe diameter D, or hydraulic radius R_h for open channel) · ν kinematic viscosity of fluid.

Regime thresholds — by geometry

Reynolds-number boundaries between flow regimes for common configurations
Geometry	Laminar	Transitional	Turbulent
Round pipe (internal flow)	< 2,300	2,300–4,000	> 4,000
Non-circular duct (use D_h)	< 2,300	2,300–4,000	> 4,000
Open channel (use R_h)	< 500	500–2,000	> 2,000
Flat plate boundary layer	< 5×10⁵	5×10⁵	> 5×10⁵
Sphere drag (transition to wake)	< 1	1–10⁵	> 10⁵
Cylinder cross-flow (vortex shed.)	< 40	40–10⁵	> 3×10⁵

The open-channel limits look lower only because they are written with L = R_h. For a full pipe R_h = D/4, so 500 and 2,000 on an R_h basis correspond to 2,000 and 8,000 on a diameter basis. Engineering practice usually treats pipe flow above Re = 2,300 as effectively turbulent and uses rough-pipe friction formulas conservatively in the transitional band.

Kinematic viscosity ν of common fluids

Kinematic viscosity at typical engineering temperatures
Fluid / temperature	ν (US ft²/s)	ν (SI m²/s)
Water, 32°F (0°C)	1.92×10⁻⁵	1.79×10⁻⁶
Water, 40°F (4°C)	1.66×10⁻⁵	1.55×10⁻⁶
Water, 50°F (10°C)	1.41×10⁻⁵	1.31×10⁻⁶
Water, 60°F (16°C)	1.21×10⁻⁵	1.13×10⁻⁶
Water, 70°F (21°C)	1.06×10⁻⁵	9.84×10⁻⁷
Water, 80°F (27°C)	9.30×10⁻⁶	8.64×10⁻⁷
Water, 100°F (38°C)	7.39×10⁻⁶	6.87×10⁻⁷
Air, 60°F	1.58×10⁻⁴	1.47×10⁻⁵
SAE 10W oil, 60°F	1.0×10⁻³	9.3×10⁻⁵
SAE 30 oil, 60°F	4.1×10⁻³	3.8×10⁻⁴
Glycerin, 70°F	6.5×10⁻³	6.0×10⁻⁴
Mercury, 60°F	1.21×10⁻⁶	1.13×10⁻⁷

Worked examples

Example 1 — 6-inch water main at 5 ft/s

Given: 6-inch (D = 0.5 ft) pipe, V = 5 ft/s, water at 60°F (ν = 1.21×10⁻⁵ ft²/s).

Find: Reynolds number and regime.

Re = V·D/ν = 5·0.5/(1.21×10⁻⁵)

Re = 2.07×10⁵

Re ≈ 207,000 — fully turbulent. Use Swamee-Jain for friction factor.

Example 2 — Hydraulic-oil cooler line, small diameter

Given: ½-inch line, V = 2 ft/s, SAE 30 oil at 60°F (ν = 4.1×10⁻³ ft²/s).

Find: Re and regime.

D = 0.5/12 = 0.0417 ft

Re = 2·0.0417/(4.1×10⁻³) = 0.0833/0.0041 = 20.3

Re = 20 — strongly laminar. Use f = 64/Re = 3.15 in Darcy-Weisbach.

Reference: White, F.M. (2011). Fluid Mechanics (7th ed.). McGraw-Hill. Original concept: Reynolds, O. (1883). "An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous." Phil. Trans. Royal Soc. London, 174, 935–982.

Common mistakes

Mixing length conventions. Pipe thresholds (2,300 / 4,000) assume L = D. Open-channel thresholds (500 / 2,000) assume L = R_h. If a source uses 4R_h for channels, its thresholds are about four times larger. Match the threshold to the length you entered.
Using dynamic viscosity μ in VL/ν. This calculator takes kinematic viscosity. In US units μ/ν for water is the density, about 1.94 slug/ft³, so the wrong one is off by roughly a factor of two.
Assuming 60°F water in winter or in process piping. Viscosity of water nearly halves between 40°F and 100°F. Use the table above.
Reading “turbulent” as “supercritical”. Reynolds number separates laminar from turbulent. The Froude number separates subcritical from supercritical, and the two are independent.

When this calculator doesn’t apply

The thresholds are for steady, fully developed flow of a Newtonian fluid. Flow just downstream of an entrance or fitting, pulsating flow and heated pipes transition at different values. Sludges, slurries and polymer solutions are non-Newtonian and need a generalized Reynolds number. Flow through soil or filter media uses a particle-based Reynolds number, and Darcy’s law is valid only at low values of it.