Reynolds Number: Formula, Calculator Guide, and Solved Examples

What is the Reynolds Number?

The Reynolds number (Re) is a dimensionless quantity that predicts flow behavior inside a pipe: laminar (smooth, ordered) or turbulent (chaotic, with eddies).

It's one of the most important parameters in hydraulic engineering because it determines which friction equation to use.

Formula

Re = (V × D) / ν

Where:

• V = mean fluid velocity (m/s)
• D = pipe internal diameter (m)
• ν = kinematic viscosity (m²/s)

For water at 20°C: ν = 1.004 × 10⁻⁶ m²/s

Flow Regime Classification

In practice, 95% of pressurized water systems operate in turbulent flow (Re > 10,000 is common). Laminar flow is rare in pressurized pipes.

Why It Matters

The flow regime determines the friction factor equation:

• Laminar: f = 64/Re (exact, no pipe roughness needed)
• Turbulent: Colebrook-White or Swamee-Jain (requires pipe roughness)

Using the wrong formula gives incorrect friction losses, which leads to incorrect pump sizing.

Water Kinematic Viscosity Table

Example 1: 2-inch PVC Pipe

Data: 2" PVC (ID = 52.5 mm), flow 2 L/s, water at 20°C.

V = 0.002 / (π × 0.0525²/4) = 0.924 m/s
Re = (0.924 × 0.0525) / (1.004 × 10⁻⁶) = 48,316

Result: Turbulent flow. Use Swamee-Jain for friction factor.

Example 2: Very Low Flow in Large Pipe

Data: 6" steel (ID = 152.4 mm), flow 0.2 L/s, water at 20°C.

V = 0.0002 / (π × 0.1524²/4) = 0.011 m/s
Re = (0.011 × 0.1524) / (1.004 × 10⁻⁶) = 1,669

Result: Laminar flow. Use f = 64/Re.

Example 3: Hot Water at 60°C

Data: 1" copper (ID = 25.4 mm), flow 0.5 L/s, water at 60°C.

V = 0.0005 / (π × 0.0254²/4) = 0.986 m/s
Re = (0.986 × 0.0254) / (0.474 × 10⁻⁶) = 52,846

Result: Turbulent. Hot water has lower viscosity, producing higher Re at the same velocity.

Common Mistakes

1. Wrong units: diameter must be in meters, not inches or mm
2. Using dynamic instead of kinematic viscosity: the formula uses ν (kinematic), not μ (dynamic)
3. Ignoring temperature: viscosity at 60°C is half that at 20°C
4. Assuming turbulent without checking: low flows in large pipes can be laminar

Automate It

HydroApp Pro calculates Reynolds number automatically for every pipe segment. Select the water temperature, and viscosity adjusts automatically. The app uses the correct friction equation based on the flow regime — no manual decision needed.

Try HydroApp Pro — $99 one-time payment.

Related Articles

• Darcy-Weisbach equation explained
• Pipe friction loss guide
• Centrifugal pump sizing guide