The Darcy-Weisbach equation is the most physically general way to find pipe friction loss: it works for any Newtonian fluid, any temperature, and any pipe, because it derives the friction factor from the Reynolds number and the relative roughness rather than from a water-only correlation. Head loss equals the friction factor times length over diameter times velocity head, or h_f = f (L/D)(v²/2g), measured in feet or metres.
Worked example
Water at 60 °F flows at 100 gpm through 100 ft of 3-inch Schedule 40 steel pipe (inside diameter 3.068 in, roughness 0.045 mm):
- Velocity: 4.34 ft/s; Reynolds number ≈ 91,700 (turbulent)
- Friction factor (Swamee-Jain): f ≈ 0.021
- Head loss = 0.021 × (100 / 0.256) × (4.34² / 64.35) ≈ 2.40 ft (1.04 psi)
Why show Reynolds number and the friction factor?
The Reynolds number decides the flow regime: below about 2,300 the flow is laminar and f = 64/Re; above about 4,000 it is turbulent and f comes from the Swamee-Jain approximation to the Colebrook equation. Between those values (transitional) the friction factor is genuinely uncertain, so the calculator flags it. Seeing f and Re — which most calculators hide — lets an engineer sanity-check the result against a Moody chart.
When to use Darcy-Weisbach — and when Hazen-Williams
Use Darcy-Weisbach whenever the fluid is not room-temperature water, when viscosity matters, or when you want a defensible physical result. The empirical Hazen-Williams method is quicker for cold-water systems but is valid only for water near 60 °F at moderate velocities; outside that range it can be materially wrong. Add fittings with the built-in K-factor panel, and take the resulting head loss into the total dynamic head calculator.