South Africa · Science & Engineering
Friction Loss Calculator
Change the roughness coefficient
Enter the flow, the internal diameter and the length. The calculator returns head loss in metres, kPa and bar, checks the velocity, and shows why diameter matters far more than length.
How is friction loss in a pipe calculated?
The Hazen-Williams equation gives head loss as 10.67 × length × flow^1.852, divided by the roughness coefficient^1.852 × diameter^4.87, with flow in cubic metres per second and diameter in metres. The diameter exponent of 4.87 is why one pipe size up cuts the loss by roughly two thirds.
How to use this calculator
- Use the internal diameterNot the nominal size. A 22 mm copper tube has an internal bore around 20.2 mm, and because diameter is raised to the power 4.87, that 8 per cent difference changes the answer by about 45 per cent.
- Add an equivalent length for fittingsEvery bend, tee and valve costs pressure. The usual method converts each fitting into an equivalent length of straight pipe — roughly 30 diameters for an elbow, 60 for a tee taking the branch.
- Set the roughness coefficient for the material and its ageNew plastic is around 150, new copper 140, and old galvanised steel can drop below 100. Ageing pipework loses capacity for exactly this reason.
- Check the velocity as well as the lossAbove about 2.5 m/s pipework gets noisy and erodes; below about 0.6 m/s sediment settles out. The breakdown flags both.
How the calculation works
Hazen-Williams is an empirical equation fitted to measurements of water flowing in full pipes. It is not derived from first principles like Darcy-Weisbach, and in exchange for that it is far easier to use — no need to iterate on a friction factor or evaluate a Reynolds number.
The two exponents are where the physical insight sits. Flow is raised to 1.852, so doubling the flow rate roughly triples the loss. Diameter is raised to 4.87 in the denominator, so increasing the bore by a quarter — say from 20 mm to 25 mm — cuts the loss to roughly a third.
That asymmetry drives almost every practical decision about pipework. When a system does not deliver enough pressure at the far end, the instinct is to shorten the run. Length enters linearly, so halving it halves the loss. Going one pipe size up is usually easier and does considerably more.
The roughness coefficient C works in the opposite direction to intuition: a higher C means a smoother pipe and less loss. It also degrades over time as scale and corrosion build up, which is why an old system can fail to deliver flows it managed comfortably when installed.
hf = 10.67 × L × Q^1.852 ÷ (C^1.852 × D^4.87)Roughness coefficients
| Material and condition | Hazen-Williams C |
|---|---|
| PVC, PE and other plastics, new | 150 |
| Copper and brass, new | 140 |
| Cement-lined ductile iron | 130 – 140 |
| Galvanised steel, new | 120 |
| Cast iron, 10 years old | 110 |
| Cast iron, 20+ years old | 90 – 100 |
| Old, heavily tuberculated steel | 60 – 80 |
The spread between new plastic at 150 and old steel at 80 is not a rounding difference. Because C appears raised to 1.852, that change alone roughly triples the friction loss for the same flow through the same bore — which is why replacing an old main frequently solves a pressure problem that adding a pump did not.
Worked example: a garden irrigation run
Thirty litres per minute through 25 metres of 22 mm copper, with an additional 5 metres equivalent length for elbows and a valve, so 30 metres effective.
Converting: 30 L/min is 0.0005 m³/s, and 22 mm nominal copper has a 20.2 mm bore, or 0.0202 m. With C at 140, the equation gives a head loss of about 1.6 metres, which is roughly 15.7 kPa or 0.16 bar. Velocity works out at about 1.56 m/s — comfortably inside the sensible range.
Now change the pipe to 15 mm copper, with a 13.6 mm bore. The same flow gives a head loss over 11 metres of head and a velocity above 3.4 m/s — noisy, erosive, and losing most of the available pressure to friction. One pipe size down has made the run unusable.
That is the practical lesson: for a given flow, diameter is not a minor optimisation. It is the design decision.
Where Hazen-Williams stops being valid
The equation is fitted to water at ordinary ambient temperatures flowing in full pipes at velocities within a normal engineering range. Outside that, it drifts.
It should not be used for other fluids. Viscosity does not appear anywhere in the equation, which is fine for water and wrong for oil, glycol mixtures or anything appreciably thicker. For those, use Darcy-Weisbach with a properly evaluated friction factor.
It also assumes the pipe runs full. Partially full gravity drainage is a different problem entirely, handled by Manning's equation rather than this one. And it says nothing about static head — the pressure gained or lost from height change is separate arithmetic that has to be added or subtracted afterwards.
Within its range, though, it is accurate enough for the vast majority of water distribution, irrigation and building services work, and it has the considerable advantage of being solvable directly rather than iteratively.
Total pressure at the outlet is static head plus supply pressure minus friction loss. This calculator gives only the friction component. A run that climbs 10 metres loses about 1 bar to static head before any friction is considered.
Assumptions and limitations
- Valid for water at ordinary temperatures in full pipes — not for other fluids or partially full flow
- Viscosity is not modelled, so results for anything thicker than water will be wrong
- Fitting losses are entered as an equivalent length rather than calculated from loss coefficients
- The roughness coefficient degrades with age and the calculator cannot know the condition of your pipe
- Static head from height change is not included and must be added separately
- Not suitable for compressible flow, steam, or velocities far outside the normal engineering range
Questions people ask about this in South Africa
How do you calculate friction loss in a pipe?
The Hazen-Williams equation gives head loss as 10.67 × length × flow^1.852 ÷ (C^1.852 × diameter^4.87), with flow in cubic metres per second and diameter in metres. The result is in metres of head, which you can convert to kPa by multiplying by 9.807.
The diameter exponent of 4.87 is the important part — a small change in bore has a very large effect on the loss.
Does pipe diameter or length matter more for friction loss?
Diameter, by a wide margin. Length enters the equation linearly, so halving it halves the loss. Diameter is raised to the power 4.87, so increasing the bore by a quarter cuts the loss to roughly a third. Going one pipe size up is almost always more effective than shortening the run.
What is a good Hazen-Williams C value?
150 for new plastic pipe, 140 for new copper, 130 to 140 for cement-lined ductile iron, and 120 for new galvanised steel. Old cast iron and tuberculated steel fall to 100 or below, and that degradation alone can triple the friction loss in an ageing system.
What water velocity should I design for?
Broadly 0.6 to 2.5 metres per second. Below 0.6 m/s sediment settles out; above 2.5 m/s pipework becomes noisy and erosion accelerates, particularly at bends. Domestic hot and cold services are usually designed toward the lower half of that range to keep noise down.
How do I account for bends and valves?
Convert each fitting to an equivalent length of straight pipe and add it to the run. A standard elbow is roughly 30 pipe diameters, a tee taking the branch about 60, and a fully open gate valve around 8. On a run with many fittings this can exceed the straight length.
Should I use Hazen-Williams or Darcy-Weisbach?
Hazen-Williams for water at ordinary temperatures, where it is accurate enough and solves directly. Darcy-Weisbach for anything else — other fluids, unusual temperatures, or velocities outside the normal range — because it accounts for viscosity properly, at the cost of needing an iterative friction factor.
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Method, source and review date
- How it is worked out
- Hazen-Williams equation for water in full pipes, SI units
- Formula used
hf = 10.67 × L × Q^1.852 ÷ (C^1.852 × D^4.87)- Basis
- Hazen-Williams head loss equation
- Last reviewed
- Confidence
- Medium
Hazen-Williams is an empirical equation valid for water at ordinary temperatures in full pipes. It is not suitable for other fluids, for very high or low velocities, or for compressible flow. The roughness coefficient degrades as pipes age.
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Disclaimer
This is a planning estimate, not a substitute for a design signed off by a qualified engineer. Anything structural, electrical or gas-related must be checked and certified by a competent person before it is built or connected.