Where it appears
The Darcy-Weisbach equation gives the friction pressure drop in a full round pipe: dp = f × (L / D) × (ρ v² / 2), with L the length, D the inside diameter, ρ the density and v the mean velocity. Everything about the wall and the flow regime sits in f. To run the full calculation, including fittings and elevation, use the pipe pressure drop calculator.
Step 1: Reynolds number
Re = ρ v D / μ, where μ is the dynamic viscosity. Below about 2 300 the flow is laminar, above about 4 000 it is turbulent, and in between it is unstable.
Step 2: friction factor
- Laminar: f = 64 / Re. Roughness does not matter.
- Turbulent: Colebrook-White, 1/√f = −2 log10( (e/D)/3.7 + 2.51 / (Re √f) ), solved by iteration. e is the absolute roughness, e/D the relative roughness.
- Explicit shortcut: Haaland, 1/√f = −1.8 log10( (e/D / 3.7)1.11 + 6.9 / Re ), within about 2 % of Colebrook.
Typical values (Colebrook)
| Reynolds number | Smooth pipe | e/D = 0.0001 | e/D = 0.001 | e/D = 0.01 |
|---|---|---|---|---|
| 10,000 | 0.0309 | 0.0310 | 0.0324 | 0.0431 |
| 100,000 | 0.0180 | 0.0185 | 0.0222 | 0.0385 |
| 1,000,000 | 0.0116 | 0.0134 | 0.0199 | 0.0380 |
Notice that f falls as Re rises, then flattens: at high Re and high roughness the friction factor depends almost only on e/D (fully rough flow). Commercial steel pipe is roughly e = 0.045 mm (0.0018 in), drawn tubing about 0.0015 mm.
Worked example
Water at 20°C (ρ = 998.2 kg/m³, μ = 1.002 mPa·s) flows at 300 L/min (79 gpm) through 100 m of 50 mm commercial steel pipe (e = 0.045 mm, e/D = 0.0009). Velocity v = 2.55 m/s, Re = 126 800, Colebrook gives f = 0.02135. Then dp = 0.02135 × (100/0.05) × (998.2 × 2.546² / 2) = 1.38 bar (20 psi) of friction loss. These are the default inputs of the calculator, which adds fittings and elevation on top.
Common mistakes
- Mixing Darcy and Fanning factors (a factor of four).
- Using the nominal instead of the inside diameter.
- Using the turbulent formula below Re 2 300.
- Forgetting that old pipe can be several times rougher than new.
Related: hydraulic cylinder force calculator for flow and speed, all calculators.
FAQ
What is the Darcy friction factor?
It is the dimensionless number f in the Darcy-Weisbach equation, dp = f (L/D) (rho v^2 / 2). It folds the effect of wall friction into one coefficient that depends on the Reynolds number and the relative roughness e/D of the pipe.
What is the difference between the Darcy and Fanning friction factor?
The Darcy factor is four times the Fanning factor. Most mechanical and civil references use Darcy (f about 0.02 for turbulent water flow), many chemical engineering texts use Fanning (about 0.005). Check which one an equation expects before using a value.
What is the friction factor for laminar flow?
f = 64 / Re for Reynolds numbers below about 2 300. It does not depend on roughness. At Re = 1 000, f = 0.064.
How do you solve the Colebrook equation?
It has f on both sides, so iterate: guess f = 0.02, evaluate the right-hand side, and repeat until the value stops changing, which takes fewer than ten passes. The Haaland equation is an explicit approximation that is within about 2 % over normal ranges.
Is the Moody chart still needed?
No. The chart is a plot of the Colebrook equation, so a calculator gives the same answer with more digits. The chart is still useful to see how f falls with Reynolds number and levels off at high Re where roughness dominates.
Engineering aid for guidance only. Verify critical designs.