Learn: Darcy–Weisbach friction loss
Flow along a pipe loses mechanical energy through wall friction. The Darcy–Weisbach relationship converts pipe length, diameter, speed and a supplied friction factor into an equivalent lost head.
What the formula is saying
First form L/D, the number of pipe diameters along the length. Multiply by the Darcy friction factor and the velocity head v²/(2g). A long narrow pipe produces more loss at the same velocity and friction factor.
Read the symbols in plain language
- f
- Darcy friction factor
Dimensionless Darcy–Weisbach pipe-loss factor. It is four times the Fanning factor for the same flow.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- L
- Pipe length
Pipe length. Dividing two lengths gives the dimensionless length-to-diameter ratio.
mMetres measure length; 1 m = 1000 mm.
- D
- Diameter
Diameter. Dividing two lengths gives the dimensionless length-to-diameter ratio.
mMetres measure length; 1 m = 1000 mm.
- v
- Velocity
Velocity. Friction loss scales with squared speed rather than speed alone.
m/sUse m/s as the base unit shown here. L and internal diameter D must use the same length unit, here m. f is the Darcy factor, dimensionless; velocity is m/s and g is m/s². The result is m of liquid head, not pressure in Pa.
- g
- Gravity
Gravity. Friction loss scales with squared speed rather than speed alone.
m/s²Use m/s² as the base unit shown here. L and internal diameter D must use the same length unit, here m. f is the Darcy factor, dimensionless; velocity is m/s and g is m/s². The result is m of liquid head, not pressure in Pa.
- hf
- Result to find
Darcy–Weisbach friction loss. Multiplying the dimensionless factors by velocity head yields head loss.
m
Sort out the units first
L and internal diameter D must use the same length unit, here m. f is the Darcy factor, dimensionless; velocity is m/s and g is m/s². The result is m of liquid head, not pressure in Pa.
Assumptions before calculating
Assume steady incompressible flow through a constant-diameter full pipe, with a Darcy factor appropriate to Reynolds number and relative roughness. Use an average velocity for that pipe reach.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find hf and explain the result in the stated output unit.
- f · Darcy friction factor
- 0.02
- L · Pipe length
- 100 m
- D · Diameter
- 0.2 m
- v · Velocity
- 2 m/s
- g · Gravity
- 9.81 m/s²
Count pipe diameters along the reach
Dividing two lengths gives the dimensionless length-to-diameter ratio.
(100) ÷ (0.2) = 500Find the velocity-head scale
Friction loss scales with squared speed rather than speed alone.
(2)^2 ÷ (2 × (9.81)) ≈ 0.2038735984 mApply the Darcy friction factor
Multiplying the dimensionless factors by velocity head yields head loss.
(0.02) × (500) × (0.2038735984) ≈ 2.038735984 m
Does this worked answer make sense?
At fixed f, L and D, doubling speed multiplies loss by four. Zero length or zero speed gives zero friction loss within this model.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- f · Darcy friction factor
- 0.025
- L · Pipe length
- 80 m
- D · Diameter
- 0.15 m
- v · Velocity
- 1.8 m/s
- g · Gravity
- 9.81 m/s²
Count pipe diameters along the reach
Dividing two lengths gives the dimensionless length-to-diameter ratio.
(80) ÷ (0.15) ≈ 533.3333333Find the velocity-head scale
Friction loss scales with squared speed rather than speed alone.
(1.8)^2 ÷ (2 × (9.81)) ≈ 0.1651376147 mApply the Darcy friction factor
Multiplying the dimensionless factors by velocity head yields head loss.
(0.025) × (533.3333333) × (0.1651376147) ≈ 2.201834862 m
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- f · Darcy friction factor
- 0.018
- L · Pipe length
- 120 m
- D · Diameter
- 0.25 m
- v · Velocity
- 2.5 m/s
- g · Gravity
- 9.81 m/s²
Find: Learn: Darcy–Weisbach friction loss
A hint, not the answer
First form L/D, the number of pipe diameters along the length. Multiply by the Darcy friction factor and the velocity head v²/(2g). A long narrow pipe produces more loss at the same velocity and friction factor.
L and internal diameter D must use the same length unit, here m. f is the Darcy factor, dimensionless; velocity is m/s and g is m/s². The result is m of liquid head, not pressure in Pa.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Count pipe diameters along the reach
Dividing two lengths gives the dimensionless length-to-diameter ratio.
(120) ÷ (0.25) = 480Find the velocity-head scale
Friction loss scales with squared speed rather than speed alone.
(2.5)^2 ÷ (2 × (9.81)) ≈ 0.3185524975 mApply the Darcy friction factor
Multiplying the dimensionless factors by velocity head yields head loss.
(0.018) × (480) × (0.3185524975) ≈ 2.752293578 m
Avoid the common trap
Do not substitute a Fanning factor directly: the Darcy factor is four times the Fanning factor. Do not use pipe radius for D or add this head loss to a pressure without conversion.
When this method applies — and when it does not
The factor is supplied here; it must come from a suitable laminar or turbulent relation. Fittings and entrances create additional losses. Changing diameter at fixed discharge also changes velocity, so the fixed-velocity comparison is not a complete resizing study.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Darcy–Weisbach friction loss. Water-measurement principles; for discharge devices, read the orifice/weir chapters and the installation and head-measurement conditions, not only the coefficient formula.
- U.S. Bureau of Reclamation — Water Measurement Manual, 3rd edition (1997; revised reprint 2001)
- Dawei Han, University of Bristol — Concise Hydraulics (2008, Ventus Publishing)
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.