Darcy (and Fanning) friction factor from Reynolds number and relative roughness — Colebrook–White solved exactly, with the Swamee–Jain explicit fit for comparison.
For laminar flow the Darcy friction factor is simply 64/Re. For turbulent flow it comes from the implicit Colebrook–White equation — the algebraic form of the Moody chart — which this tool solves by iteration. The explicit Swamee–Jain fit is shown alongside for comparison.
Worked example
Re = 100,000 in a 100 mm commercial-steel pipe (ε = 0.045 mm, ε/D = 0.00045). Darcy f ≈ 0.0201; Fanning f ≈ 0.0050. Swamee–Jain agrees to within a fraction of a percent.
Inputs
Reynolds number — ρvD/μ. Below ~2300 the flow is laminar.
Inside diameter (mm)
Roughness ε (mm) — Commercial steel ≈ 0.045 mm, drawn tubing ≈ 0.0015 mm, PVC ≈ 0.0015 mm.
Frequently asked questions
Darcy or Fanning friction factor?
This tool reports the Darcy factor by default (used in ΔP = f·(L/D)·ρv²/2), and the Fanning factor — exactly one quarter of Darcy — beside it. Mixing the two is a classic factor-of-4 error, so check which your pressure-drop equation expects.
What is the Colebrook equation?
The implicit correlation behind the Moody chart, valid for turbulent flow in rough pipes. Because f appears on both sides it must be solved iteratively; this tool does that to machine precision.
When can I use Swamee–Jain instead?
The explicit Swamee–Jain equation matches Colebrook to within about 1% for 4000 < Re < 10⁸ and 10⁻⁶ < ε/D < 10⁻² — fine for hand calculations. Outside that range, use the Colebrook value.
Assumptions
Fully developed, single-phase flow in a circular pipe.
Colebrook–White is the implicit Moody-chart correlation; Swamee–Jain approximates it to within ~1% for 4000 < Re < 10⁸ and 10⁻⁶ < ε/D < 10⁻².
Darcy factor is reported by default (ΔP = f·(L/D)·ρv²/2). Fanning = Darcy/4.
References
Colebrook, C.F. (1939), J. Inst. Civil Engineers.
Swamee, P.K. & Jain, A.K. (1976), J. Hydraulics Division, ASCE.
Related Fluid Mechanics tools
Pipe Pressure Drop — Frictional ΔP and head loss for single-phase flow in a circular pipe (Darcy–Weisbach, Swamee–Jain friction factor).
Fittings Pressure Drop (K-factors) — Minor losses through elbows, tees, and valves by the ΣK excess-head method — the companion to straight-pipe friction.
Pipe Velocity & Reynolds — Line velocity, Reynolds number, and flow regime from flow rate and pipe inside diameter.
Pipe Line Sizing (velocity) — Required pipe bore for a target line velocity, with the resulting velocity and typical service velocity guidance.