Moody Lab
Explore how Reynolds number and relative roughness determine the Darcy friction factor across pipe-flow regimes.
Interactive Moody chart
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Selected relation
About this chart
Pipe resistance appears to depend on many quantities at once: velocity, diameter, viscosity and wall roughness. The Moody chart makes the problem manageable by collapsing them into Reynolds number, relative roughness and the Darcy friction factor.
Three quantities, one map
Reynolds number describes the balance between inertial and viscous effects. Relative roughness ε/Dh compares the wall roughness with the pipe size. Once those two are known, the chart gives the friction factor f.
From chart to energy loss
The friction factor enters the Darcy–Weisbach equation for head loss, pressure drop and required pumping head. The chart therefore turned a difficult resistance relation into a practical engineering tool.
Three friction stories
In laminar flow, f = 64/Re and roughness is irrelevant. In fully rough turbulent flow, f depends mainly on ε/Dh. Between these limits, viscosity and roughness act together. The path through this transition also depends on the shape, spacing and arrangement of the roughness elements.
Why compare relations
Several all-regime relations, including Cheng and Bellos–Nalbantis–Tsakiris, were fitted directly to Nikuradse’s measurements and can reproduce the transition almost perfectly. That does not make the transitional path universal. Commercial, aged, corroded, machined and natural surfaces can behave differently even at the same ε/Dh. A beautiful fit to sand roughness is therefore not necessarily the most accurate description of actual pipes.