Darcy friction factor calculator

This free Darcy friction factor calculator returns the Colebrook-White / Moody chart friction factor from the Reynolds number and the relative roughness, or straight from your fluid, velocity and pipe diameter. It reports the Fanning factor alongside, flags the flow regime, handles laminar flow (f = 64/Re) automatically, and works in metric or imperial units. It is the same friction relationship Fluid Network Studio solves internally on every pipe.

Method

• Laminar: f = 64 / Re, independent of roughness (the calculator applies this exact law up to Re = 2000).
• Turbulent: the Colebrook-White equation,

1 / sqrt(f) = -2 log10( (epsilon/D) / 3.7 + 2.51 / (Re sqrt(f)) )

where epsilon/D is the relative roughness. It is implicit in f, and the Moody chart is its graphical form. Fluid Network Studio evaluates it with the explicit Churchill (1977) correlation, which reproduces Colebrook-White across all regimes with no iteration. The explicit Swamee-Jain equation is another approximation of similar accuracy.

This is the Darcy friction factor. The Fanning friction factor used in some chemical-engineering texts is one quarter of it (f_Darcy = 4 f_Fanning). The primary sources for all three correlations are linked in the references at the foot of this page.

Limits. Fully developed, single-phase flow in a circular pipe. The flow is labelled laminar below Re 2300, transitional to about 4000 (where any correlation is uncertain), then turbulent.

Inputs

• Reynolds number and relative roughness epsilon/D, or
• a fluid preset (or custom density and viscosity) with velocity, internal diameter and absolute roughness, to compute them.

Outputs

• Darcy friction factor f (the headline value), and the Fanning factor.
• The flow regime, and in the second mode the Reynolds number and epsilon/D.

Absolute roughness of common pipe materials

Relative roughness is the absolute wall roughness divided by the internal diameter in the same units. The last column shows it for a 100 mm bore as a guide.

Moody (1944) and Crane TP-410 class values for new, clean pipe unless noted, the same material presets the Studio and the pipe pressure drop calculator use. These figures are equivalent sand-grain roughnesses, referred back to Nikuradse's rough-pipe experiments. Corrosion and scaling can raise roughness by an order of magnitude, so verify against your pipe condition for design work.

Darcy friction factor values (Colebrook-White)

Solved from the implicit Colebrook-White equation, the relationship the Moody chart plots. In laminar flow (Re below about 2300) use f = 64/Re instead, and roughness has no effect. The calculator's explicit Churchill (1977) evaluation matches these values within about 2 per cent, and about 3 per cent right at Re 4000 where the correlation blends the transition.

Worked example

Turbulent: at Re = 100,000 and relative roughness epsilon/D = 0.001, the calculator reads f = 0.0223 from its Churchill evaluation, against 0.0222 from the implicit Colebrook-White equation.

Laminar: Re = 1500 gives f = 64 / 1500 = 0.0427, regardless of roughness.

Frequently asked questions

Is this the Darcy or the Fanning friction factor?

The headline value is the Darcy factor, and the calculator also reports the Fanning factor, which is exactly one quarter of it, in the same result panel. Use Darcy in the Darcy-Weisbach equation and Fanning in chemical-engineering texts that expect it.

What is a typical Darcy friction factor?

Most turbulent pipe flow sits between about 0.015 and 0.05: smooth pipe at Re 100,000 gives about 0.018, commercial steel in that range typically 0.02 to 0.03, and a very rough pipe at ε/D = 0.05 about 0.072. In laminar flow it is 64/Re, so it can be far higher at low Reynolds numbers.

Do I need to iterate the Colebrook-White equation?

No. Colebrook-White is implicit in f, but this calculator evaluates the explicit Churchill (1977) correlation, which reproduces Colebrook-White within about two per cent across all regimes, so the result is instant with no iteration. The explicit Swamee-Jain equation is another common approximation of similar accuracy.

What relative roughness should I enter?

Relative roughness is the absolute wall roughness divided by the internal diameter in the same units, so commercial steel (0.045 mm) in a 100 mm bore gives ε/D = 0.00045. The roughness table above covers common materials, or switch to the second mode and enter the absolute roughness and diameter directly and the calculator reports the resulting ε/D.

Does roughness matter in laminar flow?

No. Below about Re 2300 the factor is 64/Re regardless of roughness, and the calculator flags the regime for you. Between about Re 2300 and 4000 the flow is transitional and any correlation is uncertain, so treat results there with caution.

Can I calculate it without knowing the Reynolds number?

Yes. Switch to the second mode, pick a fluid preset (water, seawater, glycols, fuels, oils and more) or enter a custom density and viscosity, then give the velocity, internal diameter and absolute roughness. The calculator computes the Reynolds number, relative roughness, regime and both friction factors, in metric or imperial units.

References

• Colebrook, C. F. (1939), "Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws", Journal of the Institution of Civil Engineers. doi.org/10.1680/ijoti.1939.13150
• Moody, L. F. (1944), "Friction factors for pipe flow", Transactions of the ASME. The chart form of the same relationship. ASME Digital Collection
• Churchill, S. W. (1977), "Friction-factor equation spans all fluid-flow regimes", Chemical Engineering, Vol. 84, No. 24, pp. 91-92. The explicit correlation this calculator evaluates.
• Swamee, P. K. and Jain, A. K. (1976), "Explicit equations for pipe-flow problems", Journal of the Hydraulics Division, ASCE. The other common explicit approximation. doi.org/10.1061/JYCEAJ.0004542
• Nikuradse, J., Laws of Flow in Rough Pipes, NACA Technical Memorandum 1292 (English translation of the 1933 paper). The origin of equivalent sand-grain roughness. NASA NTRS
• Crane Co., Technical Paper No. 410: Flow of Fluids Through Valves, Fittings and Pipe. tp410.com

Related

• Pipe pressure drop calculator
• Reynolds number calculator
• Hazen-Williams calculator
• Rectangular duct pressure drop calculator
• The Darcy-Weisbach equation in the glossary, or how Fluid Network Studio evaluates friction.
• Open the Studio for full networks.