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Darcy–Weisbach Head Loss

Also known as friction head loss · pipe friction loss

hf=f LD v22gh_f = f \, \frac{L}{D} \, \frac{v^{2}}{2g}
sig figs

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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Constant used: built into this formula, no need to enter
gn=9.80665 m/s2g_{n} = 9.80665\ \text{m/s}^{2}Standard acceleration of gravity · exact

Where Darcy–Weisbach Head Loss fits

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Total Dynamic HeadHydraulic GradientNet Positive Suction Head Available (NPSHa)
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See also

Hazen–Williams Head Loss: Both use friction head loss and pipe length.Pipe Internal Volume: Both use pipe length and inside diameter.Weymouth Gas Pipeline Flow (Flow from the Pressure Drop): Both use pipe length and inside diameter.Equivalent Length of a Fitting: Both use darcy friction factor and inside diameter.Swamee–Jain Friction Factor: Both use darcy friction factor and inside diameter.Colebrook–White Friction Factor: Both use darcy friction factor and inside diameter.
5 more relatedMinor Loss from K Factor: Both use friction head loss and flow velocity.Laminar Friction Factor (f = 64/Re): Both use darcy friction factor.Net Positive Suction Head Available (NPSHa): Both use friction head loss.Total Dynamic Head: Both use friction head loss.Hydraulic Gradient: Both use friction head loss.
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Darcy–Weisbach Head Loss explained

hfvfLD

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

hf=f LD v22gh_f = f \, \frac{L}{D} \, \frac{v^{2}}{2g}
Where
  • hfh_f= Friction head loss (m)
  • ff= Darcy friction factor
  • LL= Pipe length (m)
  • DD= Inside diameter (mm)
  • vv= Flow velocity (m/s)
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Pipe friction losses

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

Revised 31 October 2026
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formula.expert. (2026, October 31). Darcy–Weisbach Head Loss Formula & Calculator. https://formula.expert/solvers/darcy-weisbach-head-loss

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