Laminar Friction Factor (f = 64/Re)
Worked example: Re = 1600 → f = 0.04 — press Try an example to run it live, then adjust anything.
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Laminar Friction Factor (f = 64/Re) explained
This is one of the few exact results in pipe hydraulics: integrate the parabolic Hagen–Poiseuille velocity profile and the Darcy friction factor falls out as precisely 64/Re, with no empirical fitting anywhere. At Re = 1600 that is f = 0.04. Because it is exact, it also anchors the left-hand edge of every Moody diagram ever drawn — the straight line of slope −1 on log-log paper that all the roughness curves eventually peel away from.
The striking implication is that roughness is irrelevant in laminar flow. A rusty pipe and a glass pipe give identical pressure drop, because the fluid nearest the wall is not moving and the flow never sees the bumps. Above Re ≈ 2300 the assumption collapses; in the 2300–4000 transition band no correlation is reliable and prudent engineers simply design out of it, usually by choosing a diameter that puts velocity solidly into turbulent territory.
Laminar Friction Factor (f = 64/Re) formula
- = Darcy friction factor
- = Reynolds number
Missing one of these? Work it out first, then come back
- Darcy friction factor — Darcy–Weisbach Head Loss, Swamee–Jain Friction Factor
- Reynolds number — Reynolds Number, Swamee–Jain Friction Factor