Reynolds Number Calculator
Calculate Reynolds number, determine flow regime (laminar/transitional/turbulent), and find critical velocity.
Reynolds Number Calculator
Calculator
Adjust values & calculateEnter your values below. Every result is computed in your browser — no data is sent to any server.
Formula: Re = ρvD/μ = vD/ν | Laminar: Re < 2300 | Turbulent: Re > 4000
Worked example — Re = 99,800 | Turbulent | f = 0.0178 | v_crit = 0.046 m/s
Formula
Re = ρvD/μ = vD/ν | Laminar: Re < 2300 | Turbulent: Re > 4000
The Reynolds number equals the product of fluid density, velocity, and characteristic length divided by dynamic viscosity (or velocity times length divided by kinematic viscosity). Flow is laminar below Re 2300, transitional between 2300-4000, and turbulent above 4000 for internal pipe flow.
Worked Examples
Example 1: Water Flow in Pipe
Problem:Water at 20°C (ρ = 998 kg/m³, μ = 0.001 Pa·s) flows at 2 m/s through a 50mm diameter pipe. Determine the flow regime.
Solution:Re = ρvD/μ = 998 × 2 × 0.05 / 0.001 = 99,800 Re >> 4000 → Turbulent flow Critical velocity = 2300 × 0.001 / (998 × 0.05) = 0.046 m/s Friction factor (Blasius) = 0.3164 / 99800^0.25 = 0.0178 Entrance length ≈ 4.4 × Re^(1/6) × D = 4.4 × 6.81 × 0.05 = 1.50m
Result:Re = 99,800 | Turbulent | f = 0.0178 | v_crit = 0.046 m/s
Example 2: Oil Flow in Pipeline
Problem:SAE 30 oil at 40°C (ρ = 876 kg/m³, μ = 0.24 Pa·s) flows at 0.5 m/s in a 100mm pipe. Is the flow laminar?
Solution:Re = ρvD/μ = 876 × 0.5 × 0.1 / 0.24 = 182.5 Re < 2300 → Laminar flow ✓ Friction factor = 64/Re = 64/182.5 = 0.3507 Critical velocity = 2300 × 0.24 / (876 × 0.1) = 6.30 m/s Entrance length = 0.06 × 182.5 × 0.1 = 1.10m
Result:Re = 183 | Laminar | f = 0.3507 | v_crit = 6.30 m/s
Frequently Asked Questions
What is the Reynolds number?
The Reynolds number (Re) is a dimensionless quantity that predicts flow patterns in fluid mechanics. It represents the ratio of inertial forces to viscous forces: Re = ρvD/μ = vD/ν, where ρ is fluid density, v is flow velocity, D is characteristic length (pipe diameter), μ is dynamic viscosity, and ν is kinematic viscosity. Named after Osborne Reynolds who demonstrated in 1883 that fluid flow transitions from smooth (laminar) to chaotic (turbulent) at a predictable Re value. It is arguably the most important dimensionless number in fluid mechanics.
What do the flow regimes mean?
Flow regimes describe the behavior of fluid motion: Laminar flow (Re < 2300) — fluid moves in smooth, parallel layers with no mixing between them. Velocity profile is parabolic. Predictable and easy to analyze. Transitional flow (2300 < Re < 4000) — flow alternates between laminar and turbulent, is unstable and unpredictable. Design should avoid this range. Turbulent flow (Re > 4000) — chaotic, irregular motion with mixing and eddies. Flat velocity profile. Higher friction and pressure drop but much better heat and mass transfer. Most industrial flows are turbulent.
What is the difference between dynamic and kinematic viscosity?
Dynamic viscosity (μ, mu) measures a fluid's resistance to shear flow — the 'thickness' of the fluid. Units: Pa·s or kg/(m·s). Water at 20°C: μ = 0.001 Pa·s. Kinematic viscosity (ν, nu) is dynamic viscosity divided by density: ν = μ/ρ. Units: m²/s. Water at 20°C: ν = 1.004×10⁻⁶ m²/s. Kinematic viscosity represents how quickly momentum diffuses through the fluid. Both are needed in Reynolds number: Re = ρvD/μ = vD/ν. Dynamic viscosity is a fluid property; kinematic viscosity combines fluid properties with density.
What is the critical velocity?
Critical velocity is the flow velocity at which the transition from laminar to turbulent flow begins. For pipe flow, it corresponds to Re = 2300: v_critical = 2300ν/D = 2300μ/(ρD). Below this velocity, flow is laminar; above it, transition begins. The critical velocity depends on pipe diameter and fluid properties. For water at 20°C in a 25mm pipe: v_crit = 2300 × 1.004e-6 / 0.025 = 0.092 m/s. This is quite low, which is why most practical water flows are turbulent. Increasing viscosity or decreasing pipe diameter raises the critical velocity.
How does Reynolds number affect friction and pressure drop?
In laminar flow, the Darcy friction factor f = 64/Re (Hagen-Poiseuille). Pressure drop is proportional to velocity (linear). In turbulent flow, friction depends on both Re and pipe roughness. For smooth pipes, the Blasius correlation gives f = 0.3164/Re^0.25. The Moody chart or Colebrook equation provides friction factors for rough pipes. Pressure drop is proportional to v² (quadratic). Doubling velocity in turbulent flow roughly quadruples pressure drop. The pressure drop formula is ΔP = f(L/D)(ρv²/2), where L is pipe length and D is diameter.
How do you choose the characteristic length for a non-circular duct?
Replace the diameter with the hydraulic diameter, D_h = 4A / P, where A is the cross-sectional flow area and P is the wetted perimeter. A 300 mm by 200 mm rectangular duct has A = 0.06 m^2 and P = 1.0 m, so D_h = 0.24 m. For a concentric annulus the result reduces neatly to the outer diameter minus the inner diameter. Using D_h keeps the same laminar and turbulent thresholds roughly valid, though very flat or sharply cornered sections shift the transition somewhat.
What is entrance length and why does it matter for flow measurement?
Downstream of an inlet or a fitting the velocity profile is still developing, and the entrance length is the run needed before it settles. Laminar flow needs about 0.06 Re D, which at Re = 1800 in a 25 mm pipe is roughly 2.7 metres, while turbulent flow develops far faster at about 4.4 Re^(1/6) D. Orifice plates, venturis, and ultrasonic meters are calibrated on fully developed profiles, which is why installation standards demand a straight run of many diameters upstream.
Does the Re 2300 threshold apply to flow over a wing or a sphere?
No. The 2300 and 4000 limits are specific to internal pipe flow with the diameter as the length scale. External flows use their own scale and their own critical values: boundary-layer transition on a smooth flat plate is usually taken near Re_x of 5 x 10^5 based on distance from the leading edge, and the drag crisis on a smooth sphere or cylinder occurs near Re of 3 x 10^5 based on diameter. Always state which length scale a quoted Reynolds number uses.
Why does temperature change the Reynolds number so much?
Re depends on kinematic viscosity, and viscosity is strongly temperature dependent. Liquids thin out when heated, so water going from 20 to 60 degrees C drops from about 1.00 x 10^-6 to 4.75 x 10^-7 m^2/s, roughly doubling Re at the same velocity and diameter. Gases behave in the opposite way, since molecular momentum transfer rises with temperature and their viscosity increases. A pipeline that is comfortably laminar with cold heavy oil can turn turbulent once the line is heated.
Why do engineers match Reynolds number when testing scale models?
Dynamic similarity requires the model and the full-size object to share the same dimensionless groups, so a one-tenth scale model must run at ten times the velocity in the same fluid to keep vD constant. Because that is often impossible, wind tunnels raise density with pressurisation or use cryogenic nitrogen to cut kinematic viscosity instead. Matching Re makes the measured drag coefficient, separation point, and pressure distribution transfer to the prototype; missing it by an order of magnitude can put the model in a different flow regime entirely.
References
Background & Theory
Reynolds Number and Flow Regime
The Reynolds number is a dimensionless ratio of inertial forces to viscous forces in a moving fluid, and it's the single most important parameter for predicting whether a flow will be smooth and orderly (laminar) or chaotic and mixing (turbulent). The same Re value predicts the same qualitative flow behavior regardless of whether the fluid is water in a pipe or air over a wing, because the ratio itself captures the relevant physics.
| Reynolds number range | Flow regime (pipe flow) |
|---|---|
| Re < 2,300 | Laminar — smooth, layered flow with no mixing between layers |
| 2,300 - 4,000 | Transitional — unstable, can flip between laminar and turbulent |
| Re > 4,000 | Turbulent — chaotic mixing, higher friction losses but better heat/mass transfer |
Honey poured slowly from a jar (very low Re due to high viscosity) flows in smooth laminar sheets, while water from a fully open faucet (much higher Re due to low viscosity) becomes turbulent almost immediately — the same underlying physics, just at opposite ends of the Reynolds number scale.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
Related Calculators
🧮Acceleration Calculator
Calculate acceleration with inputs, formulas, and instant results.
🧮Motion on Incline with Friction Calculator
Calculate motion on incline with friction with inputs, formulas, and instant results.
🧮Relative Velocity Calculator
Calculate relative velocity with inputs, formulas, and instant results.
🧮Velocity Calculator
Calculate velocity with inputs, formulas, and instant results.
🧮Coupled Spring Damper Calculator
Calculate coupled spring damper with inputs, formulas, and instant results.
🧮Friction Force Calculator
Calculate friction force with inputs, formulas, and instant results.
🧮Impulse Calculator
Calculate impulse with inputs, formulas, and instant results.
🧮Variable Mass System Calculator
Calculate variable mass system with inputs, formulas, and instant results.