Fluid Network Studio

Darcy friction factor calculator

Relative roughness: the wall roughness epsilon against the bore diameter DA zoomed view of the pipe inner wall showing the absolute roughness epsilon as a jagged texture about the mean surface, relative to the bore diameter D.flowmean surfaceepsilonD
epsilon/D = 1.00e-3 - f = 0.0223 (turbulent)

Result

Darcy friction factor
0.0223
Fanning friction factor
0.0056
Flow regime
Turbulent

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The Darcy friction factor sets how much head a pipe loses to wall friction. This calculator returns it from the Reynolds number and the relative roughness, using the Colebrook-White equation in the turbulent range: the same relationship the Moody chart plots and that Fluid Network Studio solves internally.

Method

  • Laminar (Re < 2300): f = 64 / Re, independent of roughness.
  • 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, so it is solved iteratively; the explicit Swamee-Jain equation is a good approximation and starting guess. The Moody chart is the graphical form of these relationships. Fluid Network Studio evaluates it with the Churchill (1977) correlation, an explicit form that reproduces Colebrook-White across all regimes.

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). Citation: Colebrook, C. F. (1939); Moody, L. F. (1944).

Limits. Fully developed, single-phase flow in a circular pipe. In the transitional band (roughly Re 2300 to 4000) the factor is uncertain and both correlations should be treated with caution.

Inputs

  • Reynolds number (or fluid, velocity and diameter to compute it).
  • Relative roughness epsilon/D, or absolute roughness epsilon (mm) with diameter D (mm).

Outputs

  • Darcy friction factor f.
  • Flow regime, and the equivalent Fanning factor.

Worked example

Turbulent: Re = 100,000 and relative roughness epsilon/D = 0.001 give, from Colebrook-White, f = 0.0222.

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

Frequently asked questions

Darcy or Fanning?

This is the Darcy factor. Multiply the Fanning factor by four to get it, or divide Darcy by four to get Fanning.

Why is it iterative?

The Colebrook-White equation has f on both sides, so it cannot be rearranged for f in closed form. The solver iterates to convergence; the Swamee-Jain equation gives an explicit value within about 1 per cent.

Related

New to the terms? See the glossary and how it works, or browse all calculators.