Reynolds Number Calculator

Q: 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.

Q: 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.

Our fluid mechanics calculator computes reynolds number accurately. Enter measurements for results with formulas and error analysis.

Reviewed by Manoj Kumar, Mathematics Educator

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\nRe >> 4000 → Turbulent flow\nCritical velocity = 2300 × 0.001 / (998 × 0.05) = 0.046 m/s\nFriction factor (Blasius) = 0.3164 / 99800^0.25 = 0.0178\nEntrance 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\nRe < 2300 → Laminar flow ✓\nFriction factor = 64/Re = 64/182.5 = 0.3507\nCritical velocity = 2300 × 0.24 / (876 × 0.1) = 6.30 m/s\nEntrance 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.

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.

References

Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy