Darcy or Fanning friction factor?

They describe the same physics but the Darcy friction factor is exactly four times the Fanning factor. The Darcy–Weisbach equation uses the Darcy factor (laminar value 64/Re). Mixing the two is a classic 4× error — always check which your correlation reports.

When is flow laminar vs turbulent?

Below a Reynolds number of about 2300 pipe flow is laminar and f = 64/Re exactly. Above roughly 4000 it is fully turbulent and f depends on relative roughness via Colebrook–White. The 2300–4000 range is a transitional region where predictions are uncertain.

Why use Swamee–Jain instead of Colebrook?

Colebrook–White is implicit in f, so it must be solved iteratively. Swamee–Jain is an explicit approximation that matches it within about 1% over the normal engineering range, which is convenient for spreadsheets and quick checks.

Transport · guide

Pipe pressure drop with Darcy–Weisbach

Single-phase pressure drop in a pipe comes down to one equation and one dimensionless friction factor. Get the Reynolds number and the relative roughness right and the rest follows. Here is the full chain, including the friction-factor correlations.

The Darcy–Weisbach equation

The frictional pressure drop over a length L of pipe with internal diameter D, carrying fluid of density ρ at mean velocity v, is:

Δp = f · (L / D) · (ρ · v² / 2)

where f is the Darcy friction factor. Everything hard about pipe flow is hidden inside f.

Step 1 — Reynolds number

Re = ρ · v · D / μ

with μ the dynamic viscosity. Re decides the flow regime and which friction-factor law applies.

Step 2 — friction factor

In laminar flow the friction factor is exact and independent of roughness:

f = 64 / Re (Re < ~2300)

In turbulent flow it depends on the relative roughness ε/D through the implicit Colebrook–White equation, well approximated by the explicit Swamee–Jain formula:

f = 0.25 / [ log₁₀( ε/(3.7·D) + 5.74/Re^0.9 ) ]²

ε is the absolute roughness of the pipe wall (e.g. ~0.045 mm for commercial steel, far less for drawn tubing). The ratio ε/D is what the Moody chart plots against.

Step 3 — add the fittings

Valves, bends and entrances add minor losses, handled either with loss coefficients K or as equivalent lengths:

Δp_minor = ( Σ K ) · (ρ · v² / 2)

For a fitting-heavy run the minor losses can rival the straight-pipe friction, so don't drop them.

Open the calculatorPipe pressure-drop calculator →Compute Re, the regime, the friction factor (Colebrook/Swamee–Jain) and the total Δp including minor losses, with the velocity profile and Moody point.

Common mistakes

The recurring errors are the Darcy/Fanning 4× mix-up, using gauge instead of absolute roughness, applying a turbulent correlation in laminar flow, and forgetting that density and viscosity are temperature- (and for gases, pressure-) dependent. For compressible or two-phase flow this single-phase equation no longer applies — use the compressible or two-phase methods instead.

Frequently asked

Darcy or Fanning friction factor?: They describe the same physics but the Darcy friction factor is exactly four times the Fanning factor. The Darcy–Weisbach equation uses the Darcy factor (laminar value 64/Re). Mixing the two is a classic 4× error — always check which your correlation reports.
When is flow laminar vs turbulent?: Below a Reynolds number of about 2300 pipe flow is laminar and f = 64/Re exactly. Above roughly 4000 it is fully turbulent and f depends on relative roughness via Colebrook–White. The 2300–4000 range is a transitional region where predictions are uncertain.
Why use Swamee–Jain instead of Colebrook?: Colebrook–White is implicit in f, so it must be solved iteratively. Swamee–Jain is an explicit approximation that matches it within about 1% over the normal engineering range, which is convenient for spreadsheets and quick checks.

References

C.F. Colebrook, "Turbulent Flow in Pipes...," Journal of the Institution of Civil Engineers, 1939.
P.K. Swamee, A.K. Jain, "Explicit equations for pipe-flow problems," Journal of the Hydraulics Division, ASCE, 1976.
L.F. Moody, "Friction factors for pipe flow," Transactions of the ASME 66, 1944.
F.M. White, "Fluid Mechanics," McGraw-Hill.

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