Get Re, flow regime, and full step-by-step working — plus 3 solved practice problems
kg/m³
m/s
m
Pa·s (kg/m·s)
Reynolds Number:
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What is the Reynolds Number?
The Reynolds number (Re) is a dimensionless quantity used to predict whether flow in a pipe will be smooth (laminar) or chaotic (turbulent). It is calculated as:
Re = (ρ × v × D) / μ
where ρ is fluid density, v is flow velocity, D is the pipe's internal diameter, and μ is the fluid's dynamic viscosity.
Flow Regimes
Reynolds Number
Regime
Description
Re < 2300
Laminar
Smooth, orderly flow in parallel layers
2300 ≤ Re ≤ 4000
Transitional
Unstable, switches between laminar and turbulent
Re > 4000
Turbulent
Chaotic, mixing flow with eddies
Why It Matters
Engineers use the Reynolds number to select the right friction factor correlation, predict pressure drop, and size pumps correctly. Using a laminar-flow formula on turbulent flow (or vice versa) gives badly wrong pressure drop estimates.
Solved Examples (Practice Problems)
Click "Try This Example" to auto-fill the calculator above and see the full step-by-step working.
Example 1 — Water in a pipe (turbulent)
Water (ρ = 998 kg/m³, μ = 0.001 Pa·s) flows at 2.5 m/s through a 50 mm diameter pipe. Find the Reynolds number and flow regime.
Example 2 — Lubricating oil in a pipe (laminar)
A lubricating oil (ρ = 900 kg/m³, μ = 0.29 Pa·s) flows at 0.6 m/s through a 25 mm diameter pipe. Find the Reynolds number and flow regime.
Example 3 — Air in a duct (transitional zone)
Air (ρ = 1.2 kg/m³, μ = 0.000018 Pa·s) flows at 2 m/s through a 25 mm diameter duct. Find the Reynolds number and flow regime.
Frequently Asked Questions
What is a good Reynolds number for turbulent flow?
For flow inside a circular pipe, Re above 4000 is generally treated as fully turbulent. Between 2300 and 4000 the flow is transitional and unstable — in practice, engineers usually design to avoid operating in this range because pressure drop becomes unpredictable.
Can I calculate Reynolds number without knowing density?
Yes — switch to "Kinematic Viscosity" mode above. Instead of Re = ρvD/μ, it uses Re = vD/ν, where ν (kinematic viscosity) already accounts for density. This is common when working from a fluid properties table that lists ν directly, such as for air or steam.
Does pipe diameter use inside diameter or outside diameter?
Always use the internal (inside) diameter — the actual cross-section the fluid flows through, not the pipe's nominal or outer diameter. For non-circular ducts, use the hydraulic diameter instead.
Why does Reynolds number matter for pump and pipe sizing?
The flow regime determines which friction factor correlation is valid. Laminar flow uses f = 64/Re; turbulent flow requires the Colebrook or Moody chart approach. Using the wrong one gives a badly wrong pressure drop, which leads to an under- or over-sized pump.
Related Tool
Already have your Reynolds number? Use it directly to find pressure drop with the Friction Factor & Head Loss Calculator — it picks up right where this one leaves off.