What this calculator does
Friction loss is the pressure a fluid loses as it flows through a pipe, caused by drag against the pipe wall. For water flowing through a pipe, the Hazen-Williams formula is the standard way to work this out without needing an iterative friction-factor calculation: hf = 10.67 × L × Q^1.852 ÷ (C^1.852 × D^4.871), giving the head loss in metres directly from the flow rate, pipe length, pipe diameter and a roughness coefficient C.
The C coefficient is what carries the pipe material and condition: a smooth new plastic pipe might use C = 150, while old, corroded steel pipe can drop to C = 100 or lower. Getting C roughly right matters more than most of the other inputs, since it is raised to the same power as the flow rate in the formula.
The formula
Convert the flow rate to cubic metres per second and the diameter to metres, then apply hf = 10.67 × L × Q^1.852 ÷ (C^1.852 × D^4.871). The result is the head loss in metres of water, which converts to a pressure loss by multiplying by 9.80665 kPa per metre of head.
| Term | Meaning |
|---|---|
| hf | Head loss due to friction, in metres of water. |
| Q | Flow rate through the pipe. |
| L, D | Pipe length and internal diameter. |
| C | The Hazen-Williams roughness coefficient: higher means smoother, lower friction. |
The inputs explained
| Field | What to enter |
|---|---|
| Flow rate (L/s) | The flow rate of water through the pipe, in litres per second. |
| Pipe internal diameter (mm) | The internal diameter of the pipe, not the outside diameter. |
| Pipe length (m) | The total length of the pipe run. |
| Hazen-Williams coefficient C (PVC ≈ 150, new steel ≈ 120, old steel ≈ 100) | The Hazen-Williams coefficient for the pipe material and condition. PVC and plastic pipe is typically around 150, new steel around 120, and old or corroded steel can drop to 100 or below. |
When to use it
Sizing a pump for a pipe run
A pump has to overcome friction loss as well as any static lift, so working out the head loss over the full pipe run at the design flow rate is a direct input into pump selection.
Checking whether a smaller pipe diameter is acceptable
Friction loss rises steeply as diameter shrinks, since D is raised to nearly the fifth power in the formula, so a seemingly small reduction in pipe size can produce a large jump in pressure loss.
Diagnosing low pressure at the far end of a long pipe run
If pressure at the end of a long irrigation or supply line is lower than expected, calculating the friction loss for the actual length and flow shows whether that alone explains the shortfall.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How friction loss changes with flow rate
The same pipe, at a range of flow rates.
| Flow rate | Head loss over the pipe run | Pressure loss over the pipe run |
|---|---|---|
| 5 L/s | 0.405 m | 3.97 kPa |
| 10 L/s | 1.462 m | 14.34 kPa |
| 15 L/s | 3.099 m | 30.39 kPa |
| 20 L/s | 5.279 m | 51.77 kPa |
| 25 L/s | 7.980 m | 78.26 kPa |
| 30 L/s | 11.186 m | 109.70 kPa |
How friction loss changes with pipe condition
The same flow, length and diameter, across a range of Hazen-Williams coefficients from old corroded steel to new plastic pipe.
| Hazen-Williams C | Head loss over the pipe run |
|---|---|
| 100 | 3.099 m |
| 110 | 2.597 m |
| 120 | 2.211 m |
| 130 | 1.906 m |
| 140 | 1.662 m |
| 150 | 1.462 m |
Questions
What is the friction loss formula for a pipe?
This calculator uses the Hazen-Williams formula, hf = 10.67 × L × Q^1.852 ÷ (C^1.852 × D^4.871), which is the standard empirical approach for water flowing through a pipe and avoids the iterative friction-factor solve that the more general Darcy-Weisbach equation needs.
What Hazen-Williams C value should I use?
It depends on pipe material and age. PVC and other plastics are typically around 150, new steel or ductile iron around 120 to 130, and older or corroded metal pipe can fall to 100 or lower. Use a manufacturer figure where one is available.
Does this work for fluids other than water?
No. The Hazen-Williams formula and its coefficients were developed specifically for water at typical ambient temperatures. Other fluids, especially anything more viscous, need the more general Darcy-Weisbach approach with a fluid-specific friction factor.
Why does pipe diameter matter so much?
Diameter is raised to the power 4.871 in the formula, so even a modest reduction in pipe size produces a large increase in friction loss. Halving the diameter at the same flow rate multiplies the head loss by roughly 58 times.
For laminar flow through a narrow pipe or tube, where the physics is different again, see Poiseuille's law. For the viscosity figures that feed into pipe flow calculations, see the water viscosity calculator.