A worked example: 50mm pipe, 100m long, 2 m/s water flow
Water flowing at 2 m/s through a 100m length of 50mm pipe loses 87.955 kPa of pressure to friction — equivalent to a head loss of 8.966 meters, with a Reynolds number of 100,000 (turbulent) and a Darcy friction factor of 0.021989.
The formula: ΔP = f × (L/D) × (ρV²/2)
Pressure drop scales directly with pipe length (twice the length, twice the friction loss) and with the fluid's kinetic energy term (ρV²/2) — velocity matters a lot, since it's squared. The friction factor f captures everything about the flow regime and pipe roughness that isn't already covered by length, diameter, and velocity.
Two very different ways to find the friction factor
For laminar flow (Re < 2,300), the friction factor is simply 64 ÷ Re — a clean, direct formula. For turbulent flow, no such simple formula exists; this calculator uses the explicit Swamee-Jain approximation (accurate to within about 1%) instead of the more precise but implicit Colebrook equation, which would otherwise require iterative solving.
A laminar example: narrower pipe, much slower flow
The same water crawling at 0.05 m/s through a 20mm pipe over 50m has a Reynolds number of just 1,000 (laminar), giving a friction factor of exactly 0.064 (64 ÷ 1,000) and a much smaller pressure drop of just 0.2 kPa — both the slower flow and the laminar friction formula contribute to the far smaller loss.
What this calculation deliberately leaves out
This covers straight-pipe friction loss only — fittings, valves, bends, and entrance or exit effects add additional "minor losses" on top of this figure, not included in the Darcy-Weisbach calculation itself.