Friction loss in a water pipe follows the Hazen-Williams equation, h = 10.67 × L × Q^1.852 ÷ (C^1.852 × d^4.87), so it falls by a factor of 3.61 when the flow is halved, by about 3 when the bore goes from 32 to 40 millimeters, and rises about 2.12 times when the roughness coefficient C drops from 150 to 100. For 400 meters of 32 millimeter plastic pipe at 0.33 liters per second the loss is about 3.07 meters at C = 140, which is 0.77 meters per 100 meters and sits below the carrier’s field rule of 1-3 meters per 100 meters because one tap is a small flow.
Part of Community Water System
Friction loss is the head a flowing pipe consumes, in meters of water, as the water drags against the pipe wall; it is subtracted from static head to give the pressure left at a tap.
The Exponents Explain Every Rule Of Thumb
The carrier says to subtract roughly 1-3 m of head for every 100 m of pipe, depending on diameter and flow. That is a field summary. The equation behind it, as used in Pipe Sizing and Distribution Network, is Hazen-Williams in SI units:
h = 10.67 × L × Q^1.852 ÷ (C^1.852 × d^4.87)
with h in meters of head, L in meters, Q in m³/s, d the internal diameter in meters, and C the roughness coefficient: about 140-150 for smooth new plastic, 100 for old cast iron and 80-100 for bamboo or wood.
Three consequences follow, and each is checked below:
- Flow enters as the 1.852th power. Halving the flow multiplies the loss by 0.5^1.852 = 0.277, a reduction of 3.61 times.
- Diameter enters as the 4.87th power. Doubling the bore divides the loss by 2^4.87 = 29.2. One standard size up, 32 to 40 mm, divides it by (40 ÷ 32)^4.87 = 2.96.
- Roughness enters as C^1.852. Dropping C from 150 to 100 multiplies the loss by (150 ÷ 100)^1.852 = 2.12.
The diameter exponent is why the cheapest correction to a failing line is the next pipe size, and why a mislabelled bore is costly: a pipe sold as 50 mm with a 45 mm bore has (50 ÷ 45)^4.87 = 1.67 times the friction of a true 50 mm.
What You Need
- Internal diameter from the pipe’s data sheet, not its label
- Length measured along the pipe
- Design flow in m³/s: 1 L/s = 0.001 m³/s
- A C value for the material and its age
- A calculator with an x^y key, or a table you have computed in advance
Method: Compute The Loss, Then Add The Fittings
Step 1: Convert units. Flow L/s ÷ 1,000 = m³/s; diameter mm ÷ 1,000 = m. A slip here shifts the answer by a factor of up to a thousand.
Step 2: Compute pipe friction with the equation.
Step 3: Add minor losses for fittings: K × v² ÷ 2g, with v the water speed and g = 9.81 m/s². Typical K values are 0.9 for a 90° elbow, 0.2 for a fully open gate valve and 0.5 for a sharp pipe entrance. These K figures are standard hydraulic-handbook values recalled, not measured here, and vary by source.
Step 4: Compare with the allowance (static head minus 5 m) and adjust diameter, not flow, if it fails.
Worked Example: 400 m Of 32 mm At One Open Tap
Inputs: L = 400 m; d = 0.032 m; Q = 0.33 L/s = 0.00033 m³/s; C = 140.
- Pipe friction: 10.67 × 400 × (0.00033)^1.852 ÷ (140^1.852 × 0.032^4.87) = 3.07 m.
- Speed: Q ÷ area = 0.00033 ÷ (π × 0.016²) = 0.41 m/s. Velocity head v² ÷ 2g = 0.0086 m.
- Fittings: 8 elbows (8 × 0.9), 2 open gate valves (2 × 0.2) and one entrance (0.5) give ΣK = 8.1, so minor loss = 8.1 × 0.0086 = 0.07 m.
- Total: 3.07 + 0.07 = 3.14 m. Fittings add about 2%.
- Per 100 m the pipe loses 3.07 ÷ 4 = 0.77 m. The carrier’s 1-3 m per 100 m is reached by 32 mm pipe at about 0.38-0.69 L/s and by 50 mm pipe at about 1.2-2.2 L/s (solving the equation for Q at C = 140), so the field rule describes a busier line than one open tap.
Now the same fittings at 2.5 L/s in a 50 mm main: speed 1.27 m/s, velocity head 0.082 m, minor loss 8.1 × 0.082 = 0.67 m, against 3.7 m per 100 m of pipe friction. Fittings matter more as speed rises, and a fully open valve is not the worry: a nearly closed valve has a K that rises steeply and can cost meters of head on its own.
Sensitivity of the 400 m example to C:
| C | Loss over 400 m |
|---|---|
| 150 | 2.71 m |
| 140 | 3.07 m |
| 100 | 5.73 m |
| 80 | 8.67 m |
On a line with a 5 m friction allowance, C = 140 passes at 3.07 m and C = 80 fails at 8.67 m, which is why bamboo, wood and old iron lines need a larger bore than new plastic for the same service.
Where The Equation Stops Being Valid
Hazen-Williams is an empirical fit for water at ordinary temperatures in turbulent flow. Check the flow regime with the Reynolds number Re = v × d ÷ ν, where ν is the kinematic viscosity of water, about 1.0 × 10⁻⁶ m²/s at 20 °C and about 1.52 × 10⁻⁶ m²/s at 5 °C (standard values, recalled). For the 32 mm example Re = 0.41 × 0.032 ÷ 1.0 × 10⁻⁶ = 13,100, comfortably turbulent. At 0.05 L/s the speed is 0.062 m/s and Re is about 2,000, which is laminar, where loss rises with the first power of flow, not the 1.852th. The loss there is tiny, 0.02 m per 100 m, so the error does not matter, but it shows that the exponent is not a law of nature.
Checking Against Reality
Compare calculated loss with the measured difference between static and flowing head (Head Calculation). A measured loss well above the calculation points to a smaller bore than assumed, a lower C from deposits or age, a partly closed valve, a leak upstream that carries flow you did not count, or trapped air.
Common Mistakes
- Putting L/s into a formula that wants m³/s. The result is wrong by a factor of 1,000^1.852, over 300,000.
- Using label diameter.
- Sizing for average flow. The line must pass the peak, set by the taps open together.
- Adding fitting loss only for valves you can see. Reducers, tees and the intake entrance count too.
Safety
A calculation is not a pressure test
A line that passes on paper can still hold air or a closed valve. Flush and bleed the line, then read the pressure at the farthest tap before relying on it. Never test plastic pipe with compressed air.
What’s Next
- Learn next: Pipe Sizing — using these losses to choose a diameter
- Combine with: Air Valves — removing the trapped air that mimics high friction