Head loss is the energy the water loses as it flows through the pipe: by friction with the wall along the reach, and at each fitting (elbows, valves, tees…). It is expressed as a head of water.
How it works
How to use the calculator
- Choose what you want to calculate: the head loss, the diameter needed for a maximum head loss, or the discharge the pipe conveys.
- Choose the friction formula and the material: the calculator proposes its C or its ε, which you can change.
- Enter the inputs in the unit you prefer: each field has its own selector. You can type decimals with a point or a comma.
- Add the fittings of the reach or a percentage for minor losses, and press “Calculate”.
Diameter and discharge
In “Diameter” mode, the calculator looks for the internal diameter at which the total head loss — friction plus minor losses — equals the maximum head loss. It is a theoretical diameter: choose the commercial pipe with an equal or larger internal diameter and enter it as the adopted diameter to obtain the actual head loss.
In “Discharge” mode, it looks for the discharge at which the total head loss equals the maximum head loss: this is the capacity of the pipe for that head loss.
Assumptions and limits
- Water flowing full under pressure, in steady flow.
- Water at 20 °C: kinematic viscosity ν = 1.0·10⁻⁶ m²/s.
- With Darcy-Weisbach, turbulent flow (Re ≥ 4000): the Swamee-Jain equation is not valid in laminar or transitional flow.
- Hazen-Williams is an empirical formula for water; it should not be used with other fluids.
- Acceleration due to gravity g = 9.81 m/s².
Formulas and method
Hazen-Williams
hf = 10.67 · L · Q1.852 / (C1.852 · D4.87)
Empirical formula for water at ordinary temperatures. In SI units: Q in m³/s; D and L in m; h_f in m.
Darcy-Weisbach and Swamee-Jain
hf = f · (L/D) · V2/(2g)
f = 0.25 / [log10(ε/(3.7·D) + 5.74/Re0.9)]2, with Re = V·D/ν
The friction factor f is obtained from the explicit Swamee-Jain equation, valid in turbulent flow.
Minor losses
hm = ΣK · V2/(2g)
Each fitting adds a loss proportional to the velocity head. Alternatively, minor losses can be estimated as a percentage of the friction loss.
Coefficients by material
Typical values for pipes that are new or in good condition. The actual value depends on the condition and age of the pipe and on the water quality.
| Material | C (Hazen-Williams) | ε (mm) |
|---|---|---|
| PVC / HDPE | 150 | 0.0015 |
| Copper | 140 | 0.0015 |
| Commercial steel | 140 | 0.045 |
| Cement-lined ductile iron | 140 | 0.1 |
| Concrete | 130 | 0.3 |
| Galvanized steel | 120 | 0.15 |
| Cast iron | 130 | 0.26 |
K coefficients of fittings
Typical values from Crane (TP-410). They depend on the manufacturer, the diameter and the type of joint.
| Fitting | K |
|---|---|
| Standard 90° elbow | 0.9 |
| Long-radius 90° elbow | 0.6 |
| 45° elbow | 0.4 |
| Tee, flow through run | 0.6 |
| Tee, flow through branch | 1.8 |
| Gate valve, fully open | 0.2 |
| Butterfly valve, fully open | 0.3 |
| Globe valve, fully open | 10 |
| Check valve | 2.5 |
| Square-edged entrance | 0.5 |
| Exit to reservoir | 1 |
Frequently asked questions
Which formula should I use, Hazen-Williams or Darcy-Weisbach?
Hazen-Williams is common in drinking-water networks and simple to use, but it is empirical and only for water. Darcy-Weisbach is general and more accurate over a wide range of diameters and velocities, at the cost of needing the absolute roughness. If the standards of your project require one of them, use that one.
Why must I give the internal diameter?
The head loss depends on the diameter the water actually flows through. The nominal size of a commercial pipe does not match its internal diameter, which depends on the wall thickness and the pressure class.
What do I do with the theoretical diameter?
Choose the commercial pipe with an equal or larger internal diameter and enter it as the adopted diameter: the calculator gives the actual head loss and velocity with that pipe.
Which units does the calculator work in?
You can type each input in the unit you prefer (L/s, gal/min, mm, inches, metres or feet of water…) or change them all at once with the unit system selector. The calculation is always made in SI units.
References
- Saldarriaga, J. (2007). Hidráulica de tuberías. Alfaomega.
- White, F. M. (2011). Fluid Mechanics (7th ed.). McGraw-Hill.
- Crane Co. (1988). Flow of Fluids Through Valves, Fittings and Pipe (Technical Paper 410).