Darcy–Weisbach Head Loss
Also known as friction head loss · pipe friction loss
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Julius Weisbach published this in 1845 and Henry Darcy supplied the experimental friction factors; nearly two centuries on it is still the only pipe-friction equation with no fluid, temperature or material restrictions. The structure is transparent: velocity head v²/2g is the currency, L/D counts how many diameters of pipe you are traversing, and f is the price per diameter. Water at 2 m/s through 100 m of 100 mm pipe with f = 0.02 loses 0.02 × 1000 × (4/19.613) ≈ 4.08 m.
Two traps. The Darcy friction factor is four times the Fanning friction factor used in chemical engineering — mixing them up produces a 4× error, and the giveaway is that Fanning f for laminar flow is 16/Re rather than 64/Re. And D must be the true inside diameter, not the nominal size: 4 in Schedule 40 steel is actually 4.026 in, while 4 in Schedule 80 is 3.826 in, and since head loss scales as roughly D⁻⁵ at constant flow that 5% difference is a 28% error in pressure drop.
- = Friction head loss
- = Darcy friction factor
- = Pipe length
- = Inside diameter
- = Flow velocity
- Friction head loss — Hazen–Williams Head Loss, Total Dynamic Head
- Darcy friction factor — Laminar Friction Factor (f = 64/Re), Swamee–Jain Friction Factor
- Pipe length — Poiseuille's Law, Hazen–Williams Head Loss
- Inside diameter — Swamee–Jain Friction Factor, Hazen–Williams Head Loss
- Flow velocity — Dynamic Pressure (q = ½ρv²), Reynolds Number