About Reynolds Number & Friction Factor Calculator
The Reynolds number calculator evaluates the dimensionless Reynolds number for flow in a circular pipe, the resulting flow regime, and the Darcy friction factor used in head-loss calculations. Enter the mean velocity (or a volumetric flow rate and pipe diameter), the fluid density and dynamic viscosity, and the absolute pipe roughness.
The Reynolds number Re = rho*v*D/mu compares inertial to viscous forces and governs whether flow is laminar, transitional, or turbulent. The tool classifies the regime (laminar below 2300, transitional 2300 to 4000, turbulent above 4000), computes the friction factor (f = 64/Re for laminar flow, or the implicit Colebrook-White equation for turbulent flow), and plots a Moody-style friction-factor curve so you can size pipework and estimate pressure drop.
How It Works
- Choose whether to enter the mean velocity directly or a volumetric flow rate Q (the tool then computes v = Q / (pi/4 * D^2)).
- Enter the pipe internal diameter D, fluid density rho, dynamic viscosity mu, and absolute pipe roughness e.
- The calculator computes Re = rho*v*D/mu and the relative roughness e/D, then classifies the regime against the 2300 and 4000 thresholds.
- It evaluates the Darcy friction factor (64/Re for laminar flow, Colebrook-White solved by iteration for turbulent flow) and plots f against Re at the current relative roughness.
Worked Example
Water (rho = 1000 kg/m^3, mu = 0.001 Pa.s) flows at v = 2 m/s through a D = 0.1 m commercial-steel pipe with roughness e = 0.000045 m. The Reynolds number is Re = rho*v*D/mu = 1000 * 2 * 0.1 / 0.001 = 200000, which is well above 4000 so the flow is turbulent. The relative roughness is e/D = 0.000045 / 0.1 = 0.00045. Solving the Colebrook-White equation gives a Darcy friction factor f = 0.0186 (Swamee-Jain returns 0.0187 as a cross-check). The kinematic viscosity is nu = mu/rho = 1e-6 m^2/s.
Formulas
- Reynolds number
Re = rho * v * D / mu = v * D / nu- Velocity from flow rate
v = Q / (pi/4 * D^2)- Flow regime
laminar Re < 2300 | transitional 2300 <= Re <= 4000 | turbulent Re > 4000- Laminar Darcy friction factor
f = 64 / Re- Colebrook-White (turbulent, implicit)
1/sqrt(f) = -2 log10( (e/D)/3.7 + 2.51 / (Re sqrt(f)) )- Swamee-Jain (turbulent, explicit)
f = 0.25 / [ log10( (e/D)/3.7 + 5.74 / Re^0.9 ) ]^2
Standards & References
- Reynolds (1883) laminar-turbulent transition
- Colebrook-White equation (1939)
- Swamee & Jain explicit approximation (1976)
- Moody diagram (Moody, 1944)
Frequently Asked Questions
What Reynolds number separates laminar and turbulent pipe flow?
For flow in a circular pipe the conventional thresholds are Re < 2300 for laminar flow, 2300 to 4000 for the transitional band, and Re > 4000 for fully turbulent flow. These boundaries are empirical and the transition is sensitive to disturbances, pipe vibration, and inlet conditions.
Why is the friction factor 64/Re only for laminar flow?
In laminar (Hagen-Poiseuille) flow the velocity profile is parabolic and the Darcy friction factor is exactly f = 64/Re, independent of pipe roughness. Once flow becomes turbulent the friction factor depends on both Reynolds number and relative roughness, so the Colebrook-White or Swamee-Jain correlations are used instead.
What is the difference between the Darcy and Fanning friction factors?
This calculator reports the Darcy (Darcy-Weisbach) friction factor, which is four times the Fanning friction factor. The Darcy factor is the one used in the Darcy-Weisbach head-loss equation h_f = f (L/D) v^2 / (2g). If you need the Fanning factor, divide the Darcy value by four.
How does the calculator solve the implicit Colebrook-White equation?
The Colebrook-White equation defines 1/sqrt(f) implicitly, so it is solved by fixed-point iteration seeded from the explicit Swamee-Jain approximation. Iteration continues until the friction factor converges, typically within a few steps, giving a result that matches the Moody diagram.