Engineering · Fluid mechanics

Darcy–Weisbach equation for pipe-friction loss

The Darcy–Weisbach equation expresses distributed friction loss in a straight pipe as head loss.

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Formula

h_{f} = f_{D} \frac{L}{D} \frac{v ˉ ^{2}}{2 g}

hf, L and D in m; fD dimensionless; v̄ in m/s; g in m/s²

Variables & units

Variables & units
Symbol	Meaning	Unit
$hf$	Distributed friction head loss	m
$fD$	Darcy friction factor	dimensionless
$L$	Pipe length	m
$D$	Inside diameter or appropriate hydraulic length	m
v̄	Mean flow speed	m/s
$g$	Gravitational acceleration	m/s²

LaTeX

h_f=f_D\frac{L}{D}\frac{\bar v^2}{2g}

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Derivation & background

Head loss scales with pipe length and the velocity head. The Darcy friction factor is not the Fanning factor, which is four times smaller. For turbulent flow, fD depends on Reynolds number and relative roughness. The equation assumes fully developed pipe flow and a consistent mean speed; bends, valves and fittings add separate local losses.

Exam blueprint

Validity range

Derivation steps

The Darcy–Weisbach equation expresses distributed friction loss in a straight pipe as head loss.

1State the model assumptions and list quantities with units.
2Substitute into hf = fD(L/D)(v̄²/2g); convert quantities to SI first.
3For fD=0.025, L=20 m, D=0.05 m and v̄=2 m/s, hf≈2.04 m.

Rearrangements

Base equation for the target quantity

h_f=f_D\frac{L}{D}\frac{\bar v^2}{2g}

Preserve signs, boundary conditions and units when rearranging.

Task variant

Work through the numerical example for “Darcy–Weisbach equation for pipe-friction loss” and check its unit and magnitude.

For fD=0.025, L=20 m, D=0.05 m and v̄=2 m/s, hf≈2.04 m.

Common mistakes

Substituting a related quantity that shares the same symbol.

Use variable definitions and check: hf, L and D in m; fD dimensionless; v̄ in m/s; g in m/s².

Exam context

Model distributed pressure losses and combine them with a system energy balance.

Formula cluster

Fluid mechanics

The Darcy–Weisbach equation expresses distributed friction loss in a straight pipe as head loss.

Re = ρvL/η = vL/ν

Reynolds number

p₁/ρg + α₁v₁²/2g + z₁ + hp = p₂/ρg + α₂v₂²/2g + z₂ + ht + hL

Extended Bernoulli energy equation with head loss

Dh = 4A/Pbenetzt

Hydraulic diameter

Worked example

For fD=0.025, L=20 m, D=0.05 m and v̄=2 m/s, hf≈2.04 m.

Applications

Model distributed pressure losses and combine them with a system energy balance.

How do you calculate with Darcy–Weisbach equation for pipe-friction loss?

Here is how to work through a typical Darcy–Weisbach equation for pipe-friction loss (hf = fD(L/D)(v̄²/2g)) task step by step:

1
Task
Work through the numerical example for “Darcy–Weisbach equation for pipe-friction loss” and check its unit and magnitude.
Solution path
For fD=0.025, L=20 m, D=0.05 m and v̄=2 m/s, hf≈2.04 m.

Frequently asked questions about Darcy–Weisbach equation for pipe-friction loss

What does the Darcy friction factor represent?+

fD represents friction, flow regime and relative roughness in the pipe-loss equation. It is dimensionless and obtained from an appropriate correlation or measurement. For laminar pipe flow, fD=64/Re; in turbulent flow it also depends on pipe roughness. The equation represents distributed pipe-friction loss; fittings need separate local coefficients. The Darcy factor depends on flow regime and wall roughness and is not the Fanning factor. Use consistent diameter, mean speed and head convention throughout the energy balance. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.

Why can’t I substitute the Fanning factor?+

Darcy and Fanning factors use different definitions. For the same flow, the Darcy factor is four times the Fanning factor. Substituting Fanning directly into the Darcy–Weisbach form underestimates loss by a factor of four. Check which convention a source or software uses. The equation represents distributed pipe-friction loss; fittings need separate local coefficients. The Darcy factor depends on flow regime and wall roughness and is not the Fanning factor. Use consistent diameter, mean speed and head convention throughout the energy balance. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.

Which losses are not included?+

The standard form captures distributed friction along the straight pipe segment. Bends, valves, entrances, exits and sudden area changes create local losses, often modeled by ζv²/(2g). Add them separately to the engineering energy equation and avoid counting a loss twice. The equation represents distributed pipe-friction loss; fittings need separate local coefficients. The Darcy factor depends on flow regime and wall roughness and is not the Fanning factor. Use consistent diameter, mean speed and head convention throughout the energy balance. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.

How do I check the result and units for Darcy–Weisbach equation for pipe-friction loss?+

Write the quantity and unit from the variable list next to every value: hf, L and D in m; fD dimensionless; v̄ in m/s; g in m/s². Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For fD=0.025, L=20 m, D=0.05 m and v̄=2 m/s, hf≈2.04 m. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. The equation represents distributed pipe-friction loss; fittings need separate local coefficients. The Darcy factor depends on flow regime and wall roughness and is not the Fanning factor. Use consistent diameter, mean speed and head convention throughout the energy balance. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.

Which model limit matters for Darcy–Weisbach equation for pipe-friction loss?+

The background states this starting condition: Head loss scales with pipe length and the velocity head. The Darcy friction factor is not the Fanning. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. The equation represents distributed pipe-friction loss; fittings need separate local coefficients. The Darcy factor depends on flow regime and wall roughness and is not the Fanning factor. Use consistent diameter, mean speed and head convention throughout the energy balance. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.

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Subject references and further reading

This list names subject references and further reading. A page or section number appears when it is part of the reference; these are not verbatim quotations.

[1]Engineering LibreTexts, Fluid Mechanics, Darcy-Weisbach relation and pipe head loss.

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Hagen–Poiseuille law for laminar pipe flow

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Quanta Study editorial team

Symbol

Meaning

Unit

hf

Distributed friction head loss

fD

Darcy friction factor

dimensionless

L

Pipe length

D

Inside diameter or appropriate hydraulic length

v̄

Mean flow speed

m/s

g

Gravitational acceleration

m/s²

Derivation & background

Exam blueprint

Validity range

Derivation steps

The Darcy–Weisbach equation expresses distributed friction loss in a straight pipe as head loss.

1State the model assumptions and list quantities with units.
2Substitute into hf = fD(L/D)(v̄²/2g); convert quantities to SI first.
3For fD=0.025, L=20 m, D=0.05 m and v̄=2 m/s, hf≈2.04 m.

How do you calculate with Darcy–Weisbach equation for pipe-friction loss?

Here is how to work through a typical Darcy–Weisbach equation for pipe-friction loss (hf = fD(L/D)(v̄²/2g)) task step by step:

Task

Work through the numerical example for “Darcy–Weisbach equation for pipe-friction loss” and check its unit and magnitude.

Solution path

For fD=0.025, L=20 m, D=0.05 m and v̄=2 m/s, hf≈2.04 m.

Frequently asked questions about Darcy–Weisbach equation for pipe-friction loss

What does the Darcy friction factor represent?+

Why can’t I substitute the Fanning factor?+

Which losses are not included?+

How do I check the result and units for Darcy–Weisbach equation for pipe-friction loss?+

Which model limit matters for Darcy–Weisbach equation for pipe-friction loss?+

Retain Darcy–Weisbach equation for pipe-friction loss for exams

Create a curated FSRS exam set for hf = fD(L/D)(v̄²/2g): formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.

Curated formula set · LaTeX · FSRS spaced repetition · import from Essential