liminfoMoody Diagram Tool
Free web tool: Moody Diagram Tool
Colebrook-White Equation
About Moody Diagram Tool
The Moody Diagram Calculator solves the Colebrook-White equation iteratively to compute the Darcy-Weisbach friction factor (f) for internal pipe flow. The friction factor is a dimensionless quantity used in the Darcy-Weisbach equation to calculate head loss due to friction in pipes and ducts. It is fundamental to hydraulic system design, HVAC duct sizing, process piping, and water distribution network analysis.
The tool supports all three flow regimes automatically. For laminar flow (Reynolds number Re < 2300), the friction factor is simply 64/Re — an exact analytical result. For the transition zone (2300 ≤ Re < 4000), results are shown but interpreted with caution as flow behavior is unpredictable. For turbulent flow (Re ≥ 4000), the implicit Colebrook-White equation is solved using 50 iterations of fixed-point iteration, achieving convergence to within 10⁻¹⁰ accuracy.
Beyond the numerical result, the calculator renders an interactive Moody diagram on an HTML5 canvas. The diagram plots friction factor (log scale, y-axis) against Reynolds number (log scale, x-axis) with turbulent curves for nine relative roughness values from smooth pipe (ε/D = 0) to very rough pipe (ε/D = 0.05). Your computed point is marked with a red dot, making it easy to see where your operating condition falls on the diagram relative to standard roughness bands.
Key Features
- Solves the Colebrook-White equation: 1/√f = −2 log₁₀(ε/D/3.7 + 2.51/(Re√f)) via iterative convergence
- Handles all three flow regimes: Laminar (f = 64/Re), Transition, and Turbulent
- Interactive Moody diagram rendered on HTML5 canvas with log-log axes
- Nine turbulent roughness curves plotted from smooth (ε/D = 0) to rough pipe (ε/D = 0.05)
- Current operating point marked as a red dot on the diagram for visual reference
- Dark mode-aware canvas rendering — diagram colors adapt to light and dark themes
- Displays friction factor to 6 decimal places for precision engineering use
- 100% client-side — all calculations run in the browser with no server calls
Frequently Asked Questions
What is the Moody diagram?
The Moody diagram (or Moody chart) is a graph relating the Darcy-Weisbach friction factor to the Reynolds number and relative pipe roughness. Developed by Lewis Moody in 1944, it is one of the most widely used charts in fluid mechanics and is included in virtually every engineering handbook. It allows engineers to quickly find the friction factor needed to calculate pressure drop and head loss in pipe systems.
What is the Colebrook-White equation?
The Colebrook-White equation is an implicit formula for the Darcy friction factor in turbulent pipe flow: 1/√f = −2 log₁₀(ε/D/3.7 + 2.51/(Re√f)). It is "implicit" because f appears on both sides, requiring iterative numerical methods to solve. This equation was proposed by Colebrook and White in 1939 and remains the industry standard for turbulent friction factor calculation.
What is relative roughness (ε/D)?
Relative roughness is the ratio of the average surface roughness height (ε, epsilon) to the inner pipe diameter (D). It is dimensionless. Typical values range from near 0 for smooth drawn tubing (commercial steel ε ≈ 0.046 mm) to 0.05 for corroded or very rough cast iron. Lower relative roughness means the pipe behaves more like a smooth pipe at high Reynolds numbers.
What Reynolds number indicates turbulent flow?
Flow in a pipe is considered laminar when Re < 2300 and fully turbulent when Re > 4000. The range 2300 < Re < 4000 is a transition zone where the flow is unstable and can switch between laminar and turbulent. In practice, most industrial pipe flows operate well into the turbulent regime, often at Re values of 10⁵ to 10⁷.
How accurate is the iterative solver?
The solver uses fixed-point iteration starting from an initial guess of f = 0.02, running up to 50 iterations. It stops early when the change between consecutive iterations is less than 10⁻¹⁰, which is far more accurate than any practical engineering requirement. For most conditions, convergence is achieved in 5–15 iterations.
What is the friction factor used for in engineering calculations?
The friction factor f is used in the Darcy-Weisbach equation: ΔP = f × (L/D) × (ρV²/2), where ΔP is pressure drop, L is pipe length, D is diameter, ρ is fluid density, and V is flow velocity. This equation is used to size pumps and fans, design piping systems, calculate energy consumption, and verify that pressure drops stay within acceptable limits.
Why does the laminar friction factor decrease linearly on the log-log diagram?
In laminar flow, f = 64/Re. Taking logarithms: log(f) = log(64) − log(Re). This is a linear relationship with slope −1 on a log-log plot, which is why the laminar region appears as a straight diagonal line on the Moody diagram. This line is exact and universal — it does not depend on pipe roughness because viscous forces dominate over inertial and roughness effects.
Can I use this for non-circular ducts?
Yes, with modification. For non-circular ducts, replace the diameter D with the hydraulic diameter Dh = 4A/P, where A is the cross-sectional area and P is the wetted perimeter. Then enter Dh as your pipe diameter when computing Re and ε/D. This approach is an approximation that works reasonably well for turbulent flow in rectangular, annular, and other duct geometries.