Darcy-Weisbach Pipe Friction Calculator

Calculate pressure drop and head loss in pipes from fluid flow using the Darcy-Weisbach equation.

ΔP = fLDρv²2
ΔPpressure lossPa
fDarcy friction factordimensionless
Lpipe lengthm
Dpipe inner diameterm
ρfluid densitykg/m³
vmean velocitym/s
50mm = 0.05m
Smooth pipe turbulent: ~0.01-0.04
Please check your inputs and try again.

Darcy-Weisbach Converts Pipe Friction into Head and Pressure Loss

The Darcy-Weisbach equation expresses mechanical-energy loss from wall friction in a pipe using a dimensionless friction factor. Head loss is hf=f(L/D)v²/(2g), and pressure loss is Δp=ρghf. The Darcy friction factor f depends on Reynolds number and relative roughness ε/D. In fully developed laminar circular-pipe flow, f=64/Re.

For turbulent flow, f is commonly found from the Colebrook relation or explicit approximations such as Swamee-Jain. Minor losses from valves, bends, entrances, and fittings are separate terms often written K v²/(2g).

hf=f(L/D)v2/(2g),   Δp=ρghf
SymbolMeaningWhy it appears / units
fDarcy friction factorDimensionless; not the Fanning factor.
L/DRelative pipe lengthDimensionless geometry ratio.
vMean pipe velocitym/s; loss scales with v² for fixed f.
ε/DRelative roughnessDimensionless surface roughness ratio.

Pressure drop rises strongly with velocity and pipe length and falls with larger diameter. Because f itself can change with Reynolds number, exact scaling is not always a pure v² law across different flow regimes.

Darcy–Weisbach losses should scale with the expected pipe physics. At fixed f and velocity, doubling L doubles pressure loss, while doubling D halves the L/D contribution. Because the dynamic-pressure term contains v2, a velocity increase can raise losses strongly; that trend is a useful check before accepting a result.

Worked Examples

Example 1: Water pipe: v=2m/s, D=50mm, L=100m, f=0.025
h_f=0.025×100×4/(0.05×2×9.81)
Result: h_f=10.2m, ΔP=100 kPa
Significant pressure drop in long pipes
Example 2: Laminar: v=0.1m/s, D=10mm, L=1m, water
Re=1000 (laminar), f=64/Re=0.064
Result: ΔP=3.2 kPa
Laminar flow: f=64/Re formula
Example 3: Laminar friction factor
Re=1000
Result: f=64/1000=0.064
Laminar circular-pipe friction factor is set directly by Reynolds number.
Example 4: Head loss
f=0.02, L=100m, D=0.10m, v=2m/s
Result: hf≈4.08m
A long small-diameter pipe can consume substantial pressure head.

Common Mistakes

⚠️
Mixing Darcy and Fanning friction factors

The Darcy factor is four times the Fanning factor. Use the convention required by the equation.

⚠️
Ignoring minor losses in short or fitting-heavy systems

Valves and bends can contribute losses comparable to or larger than straight-pipe friction.

⚠️
Using roughness without matching length units to diameter

Relative roughness ε/D must use compatible units before taking the ratio.

Connected Formulas

sets the friction-factor regime →Reynolds Numberadds head loss to →Bernoulli Equationsupplies mean velocity from Q →Flow Rate

Frequently Asked Questions

How to find friction factor f?
Moody chart: f = fn(Re, ε/D) where ε = pipe roughness. For turbulent smooth pipe: Colebrook equation 1/√f = −2log(ε/3.7D + 2.51/(Re√f)). For laminar (Re<2300): f = 64/Re.
Minor losses?
Major losses: Darcy-Weisbach (pipe friction). Minor losses: fittings, bends, valves. h_minor = K×v²/2g where K = loss coefficient. For long pipes (L/D>1000), minor losses are often neglected.
What is head loss physically?
It is the mechanical energy per unit weight irreversibly dissipated by friction and turbulence. It appears as a pressure requirement that pumps must overcome.
Why does diameter matter so much?
Diameter changes both L/D and flow velocity for a specified volume flow rate. Smaller diameter often causes a dramatic increase in pressure drop.
When is f=64/Re valid?
It applies to fully developed laminar flow in a circular pipe using the Darcy friction factor convention.
What is the Colebrook equation used for?
It estimates turbulent Darcy friction factor from Reynolds number and relative roughness in rough or smooth pipes, usually through iteration or an explicit approximation.
What is the difference between Darcy and Fanning friction factors?
The Darcy friction factor used in ΔP=f(L/D)(ρv2/2) is four times the Fanning friction factor. Mixing the two conventions produces a factor-of-four error. Always confirm which definition a Moody chart, correlation, textbook, or data source uses before inserting f.