Darcy–Weisbach Head Loss

Also known as friction head loss · pipe friction loss

h_f = f \, \frac{L}{D} \, \frac{v^{2}}{2g}

Worked example: f 0.02, 100 m of 100 mm pipe at 2 m/s → h_f = 4.0789 m — press Try an example to run it live, then adjust anything.

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g_{n} = 9.80665\ \text{m/s}^{2}

Standard acceleration of gravity · exact

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Darcy–Weisbach Head Loss explained

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.

Darcy–Weisbach Head Loss formula

h_f = f \, \frac{L}{D} \, \frac{v^{2}}{2g}

Where

$h_f$ = Friction head loss (m)
$f$ = Darcy friction factor
$L$ = Pipe length (m)
$D$ = Inside diameter (mm)
$v$ = Flow velocity (m/s)

Missing one of these? Work it out first, then come back

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, Colebrook–White Friction Factor
Flow velocity — Dynamic Pressure (q = ½ρv²), Reynolds Number

Part of this formula set

Pipe friction losses

9 formulasDarcy–Weisbach, Hazen–Williams, friction factors, minor losses and equivalent length — every way the trade computes head loss in pipe.