Head loss and pressure drop for a pipe run, by either standard method — Darcy-Weisbach with a Colebrook friction factor, or Hazen-Williams with a C-factor — plus velocity, Reynolds number, minor losses and a Moody chart.
Inputs
Hazen–Williams: intended for water in full pressurized pipes, normally under turbulent flow. Use Darcy–Weisbach for other liquids or viscosity-sensitive calculations.
Use actual bore, not nominal size or outside diameter.
Indicative values only; use project, utility, manufacturer or measured data for design.
1.0×10⁻⁶ m²/s ≈ water at 20°C
Used only to convert head loss into pressure loss.
Convenient for early estimates; total K is more physically transferable.
Results
Method: Hazen–Williams · water-service screening
Flow velocity—
Reynolds number—
Flow regime—
Hazen C-factor—
Straight-pipe friction loss—
Minor loss—
Total dynamic loss—
Pressure loss—
Hydraulic gradient—
v = Q/A, Re = vD/ν
Hazen–Williams: hf = 10.67LQ1.852/(C1.852D4.8704) Darcy–Weisbach: hf = f(L/D)v²/(2g), with f = 64/Re for laminar flow and a turbulent friction-factor approximation otherwise. Minor loss: hm = ΣK·v²/(2g), or an early-stage percentage allowance.
Elevation head and inlet/outlet pressure differences are not included.
Hazen–Williams
Use for quick estimates of water flow in full pressurized pipes. The empirical C-factor represents pipe condition. It is not suitable for gases, arbitrary liquids or laminar flow.
Darcy–Weisbach
Use when viscosity and pipe roughness matter. It applies more generally to liquids and handles laminar and turbulent regimes through the friction factor.
Model boundary
The result is dynamic hydraulic loss only. Static elevation, boundary-pressure differences, pumps, water hammer, networks and partially filled pipes are outside this calculation.
For 50 m³/h of water through 100 m of 100 mm internal-diameter PVC pipe, C = 150 and a 10% allowance:
Velocity = 1.77 m/s.
Reynolds number = 176,839, turbulent.
Hazen–Williams straight-pipe loss = 2.683 m.
Minor allowance = 0.268 m.
Total dynamic loss = 2.952 m, approximately 29.0 kPa for water.
Actual internal diameter and pipe condition dominate the result. Nominal size alone is not sufficient.
Moody chart — friction factor on its own
The calculator above derives the friction factor from the pipe, fluid and flow you enter. Use this when you already know the Reynolds number and relative roughness, or to read an operating point off the diagram.
Friction factor inputs
For a 100 mm pipe with 0.045 mm roughness, ε/D = 0.00045.
Reynolds number must be positive and relative roughness must lie between 0 and 0.1.
The transitional range has no single reliable friction-factor curve.
Friction factor results
Darcy friction factor
—
Flow regime
—
Fanning factor
—
Fully rough limit
—
Reading: —
Laminar: f = 64/Re Turbulent: 1/√f = −2log₁₀[ε/(3.7D) + 2.51/(Re√f)]
The displayed factor is the Darcy factor, four times the Fanning factor.
Moody diagram
Solid curves: constant ε/DOrange point: current inputShaded bands: laminar / transition / turbulent regions
The chart is generated locally; both axes are logarithmic, matching the standard Moody diagram convention.
Which method to use
Both methods are on this page because each is right in a different situation, and the choice changes the answer by more than most people expect.
Darcy-Weisbach
The general method, valid for any fluid, any temperature and any flow regime, because it works from the physics: hf = f · (L/D) · v²/2g. The friction factor f comes from the Reynolds number and relative roughness through the Colebrook-White equation.
Use it for anything that is not cold water: oils, chemicals, glycol mixtures, hot water, gases. It is also the only correct choice when the flow may be laminar.
Hazen-Williams
An empirical correlation fitted to water in the turbulent range, using a single roughness descriptor C instead of a friction factor. It is simpler, needs no viscosity, and is written into much water-industry practice.
It is valid for water near 10-25 °C, in pipes above roughly 50 mm, at velocities under about 3 m/s. Outside that envelope it drifts, and it has no laminar branch at all.
Matched properly, the two methods agree more closely than their reputation suggests. Take the default run — 50 m³/h through 100 mm of 100 m pipe, minor losses off. In smooth PVC (ε = 0.0015 mm with C = 150) Darcy-Weisbach gives 2.57 m and Hazen-Williams 2.68 m, about 4% apart. In heavily aged cast iron (ε ≈ 1 mm with C = 100) they give 6.10 m and 5.69 m, about 7% apart. Neither is wrong; they are fitted to different evidence, and where the answer matters you should size on Darcy-Weisbach and use Hazen-Williams as the cross-check.
The trap is mismatching the two descriptors. The C-factor and the roughness are chosen independently on this page, because each method needs its own. Pair an aged C = 100 with the new cast-iron roughness of 0.26 mm and the results diverge by 37% — not because the methods disagree, but because you have described two different pipes. Always set both to the same pipe condition.
Choosing the roughness input
Each method needs a different descriptor of the same pipe, and the two are not interchangeable.
Pipe
Absolute roughness ε (mm) — Darcy
C-factor — Hazen-Williams
Drawn tubing, PVC, smooth plastic
0.0015–0.007
150
Copper, brass
0.0015–0.01
140
Commercial steel, welded
0.045
120–130
Galvanised iron
0.15
120
Cast iron, new
0.26
130
Cast iron, aged / tuberculated
1–3
80–100
Concrete, smooth to rough
0.3–3
100–140
Design for the pipe at the end of its life, not on the day it is installed. Tuberculation and scaling can take cast iron from C = 130 to C = 80 over decades. Because head loss scales as C−1.852, that is a factor of (130/80)1.852 ≈ 2.5 — two and a half times the head loss at the same flow. A pump selected on new-pipe figures will be undersized long before the pipe is replaced.
Reading the friction factor
Laminar, Re < 2300. f = 64/Re exactly, and roughness is irrelevant — the friction factor depends only on Reynolds number. Hazen-Williams does not apply here at all.
Transitional, Re 2300–4000. No reliable correlation exists. Behaviour switches unpredictably between laminar and turbulent, so treat any number from this band as indicative and design away from it.
Turbulent, Re > 4000. The Colebrook-White equation applies, solved iteratively. At moderate Re the factor still depends on both Re and roughness; as Re rises the curves flatten.
Fully rough. Above the flattening point f depends on relative roughness alone and stops changing with flow rate. The calculator reports this limit, and when your operating point is close to it you can treat f as fixed across the operating range — a useful simplification for pump curves.
Darcy or Fanning? The Darcy friction factor is exactly four times the Fanning factor. Both are reported here because the literature uses both, and mixing them is a factor-of-four error in head loss. Chemical engineering texts tend to use Fanning; civil and mechanical sources tend to use Darcy. If a value looks four times too large or small, this is why.
Assumptions and what is not included
Steady, full-bore, single-phase flow in a circular pipe of constant diameter. Partially full pipes, two-phase flow and slurries need different treatment.
Minor losses are an allowance, not a calculation. Enter them either as a percentage of straight-pipe loss or as a total K-factor. A run with many fittings, a control valve and a strainer can easily exceed the straight-pipe loss, so for anything valve-dominated build the K-total explicitly rather than accepting a percentage.
No static lift and no equipment. This is the friction component only. Total pump head must add the static difference in elevation, the pressure difference between the end points, and the losses across heat exchangers, filters and control valves.
Fluid properties are yours to supply. Density and viscosity change substantially with temperature: water viscosity nearly halves between 10 and 40 °C, which moves the Reynolds number and the friction factor with it.
No ageing, no cavitation, no surge. Design for end-of-life roughness, check NPSH separately on the suction side, and treat rapid valve closure as a separate surge analysis.
Standards and what to do next
Method references: Colebrook-White (1939) for the turbulent friction factor, with Swamee-Jain as an explicit approximation within about 1%. The Moody diagram (1944) is its graphical form. Crane Technical Paper No. 410 is the standard practical reference for fitting losses and K-factors.
Water industry: Hazen-Williams C-factors and their application appear in AWWA design guidance and in EN 805 for water supply systems. ISO 4064 and EN 1267 cover flow measurement and valve resistance testing.
Next steps: take the total dynamic loss into a pump duty calculation, adding static lift and equipment losses, then check the duty point against a real pump curve and confirm NPSH available exceeds NPSH required. Re-run the calculation at end-of-life roughness to see how far the duty point moves over the system's life, and at minimum flow to check the velocity stays high enough to avoid sedimentation — usually above about 0.6 m/s for water carrying solids.