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Fluid Mechanics

The Moody Chart Explained

What the Moody chart shows and how engineers use it — the Reynolds-number axis, relative roughness ε/D, the Darcy friction factor, the laminar line, the transitional caution band, and turbulent smooth/rough behaviour. Includes the Darcy-vs-Fanning trap and why calculator results differ slightly from a chart reading.

TypeEngineering guide — concept explainer

Definition

The Moody chart (or Moody diagram) is a single graph that gives the Darcy friction factor f for pipe flow as a function of two dimensionless inputs: the Reynolds number Re (on a logarithmic horizontal axis) and the relative roughness ε/D (a family of curves). You enter with Re and ε/D, read off f, and feed that friction factor straight into the Darcy-Weisbach equation to get friction head loss or pressure drop. It is essentially a graphical solution of the laminar f = 64/Re relation and the turbulent Colebrook-White equation plotted together.

Why it matters

Before explicit correlations and calculators, the Moody chart was how every engineer obtained a friction factor, and it remains the standard mental picture of how f behaves. Reading it tells you at a glance which regime you are in, how strongly roughness matters at your Reynolds number, and whether you are near the fully rough plateau where f stops changing with Re. Even when a calculator does the arithmetic, understanding the chart stops you from trusting a friction factor that sits in the uncertain transitional band or from applying a smooth-pipe value to a corroded line.

Formula

Laminar region
f = 64 / Re
Turbulent (Colebrook-White)
1/√f = −2 log₁₀( ε/(3.7D) + 2.51/(Re√f) )
Swamee-Jain (explicit)
f = 0.25 / [ log₁₀( ε/(3.7D) + 5.74/Re⁰·⁹ ) ]²
Relative roughness
ε/D
Darcy ↔ Fanning
f_Darcy = 4 × f_Fanning

Units involved

  • •f — Darcy friction factor, dimensionless
  • •Re — Reynolds number, dimensionless
  • •ε — absolute roughness, mm or m (same unit as D)
  • •D — internal pipe diameter, mm or m
  • •ε/D — relative roughness, dimensionless

Concept diagram

f (Darcy)Reynolds number (log)10³10⁴10⁵10⁶laminar f = 64/Retransitionε/D largesmooth

Worked example

Find the Darcy friction factor for turbulent flow at Re = 100,000 in a pipe with relative roughness ε/D = 0.001, using the Swamee-Jain approximation the Moody chart represents.

  1. 01ε/(3.7D) = 0.001 / 3.7 = 2.703 × 10⁻⁴
  2. 02Re^0.9 = 100,000^0.9 ≈ 31,623, so 5.74/Re^0.9 = 5.74 / 31,623 = 1.815 × 10⁻⁴
  3. 03Sum inside the log = 2.703 × 10⁻⁴ + 1.815 × 10⁻⁴ = 4.518 × 10⁻⁴
  4. 04log₁₀(4.518 × 10⁻⁴) = −3.345, squared = 11.19
  5. 05f = 0.25 / 11.19 = 0.0223
Result

f ≈ 0.0223 — a Moody chart reading for the same Re and ε/D would give roughly 0.022–0.023.

Common mistakes

  • •Reading a Fanning-based chart but using the value in the Darcy-Weisbach equation (or vice versa) — the two friction factors differ by a factor of 4.
  • •Trusting a precise friction factor in the transitional band (Re ≈ 2300–4000), where the chart is deliberately uncertain and no curve is reliable.
  • •Using a smooth-pipe curve for an old, scaled, or corroded line — real relative roughness can be many times the new-pipe value.
  • •Forgetting that ε/D, not ε alone, sets the curve: the same absolute roughness is far more significant in a small pipe than a large one.
  • •Expecting a calculator to match a hand-read chart exactly — the chart is read by eye to two figures, while a correlation returns more digits.

When to use the calculator

Use the Friction Factor calculator to get f directly from Reynolds number and relative roughness without reading a chart. Use the Reynolds Number calculator to find the axis position first, and the Pipe Pressure Drop or Darcy-Weisbach Pressure Drop calculators when you want the friction factor turned into an actual head loss or pressure drop.

Friction Factor Calculator →Reynolds Number Calculator →Pipe Pressure Drop Calculator →Darcy-Weisbach Pressure Drop Calculator →Pipe Head Loss Calculator →

FAQ

What three quantities does the Moody chart relate?
The Reynolds number (horizontal log axis), the relative roughness ε/D (the family of curves), and the Darcy friction factor (vertical axis). Given any pipe flow you compute Re and ε/D, then read f off the chart.
Why does the friction factor flatten out at high Reynolds number?
In fully rough turbulent flow the friction factor depends almost entirely on relative roughness and barely on Reynolds number, so each ε/D curve becomes horizontal. There f is essentially constant — the "fully rough" plateau.
Why might a calculator give a slightly different friction factor than the chart?
The chart is read by eye to about two significant figures, while calculators evaluate the Colebrook-White equation or an explicit approximation such as Swamee-Jain to more digits. The small difference is reading precision, not a real disagreement.
Is the Moody chart the same as the Darcy-Weisbach equation?
No. The Moody chart supplies the friction factor f; the Darcy-Weisbach equation then uses that f to compute head loss or pressure drop. They are used together — see the Darcy-Weisbach Equation Explained guide.

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