Hazen-Williams Calculator

About Hazen-Williams Calculator — Pipe Friction Head Loss for Water

The Hazen-Williams calculator estimates friction head loss for water flowing in pressure pipe — the everyday equation of waterworks, fire-protection, and irrigation design. Enter the pipe length, internal diameter, and flow, pick the material (or enter a custom C), and the tool evaluates the SI form h_f = 10.67·L·Q^1.852/(C^1.852·D^4.87), reporting head loss, the gradient per 100 m, the equivalent pressure drop, and the mean velocity.

Hazen-Williams trades the physical generality of Darcy-Weisbach for pure convenience: one material coefficient C, no viscosity, no iteration. That works because it is calibrated for water at ordinary temperatures and velocities (roughly 0.3–3 m/s). Higher C means smoother pipe — new PVC runs about 150 while old tuberculated cast iron falls to 100, which alone more than doubles the friction loss for the same flow. For other fluids or extreme conditions, use the Darcy-based Reynolds number and pipe sizing tools instead.

How It Works

1. Enter the pipe run length and internal diameter — the actual bore, not the nominal size (a 4-inch Schedule 40 steel pipe runs 102.3 mm internally; SDR PVC differs again). The D^4.87 exponent makes head loss brutally sensitive to diameter: 10% less bore is about 59% more friction.
2. Enter the design flow in litres per second and pick the pipe material. The C values are new-pipe figures verified against published tables, except old unlined cast iron, which represents aged, tuberculated mains — water pipes roughen with decades of service, so designers often use a lower "design C" than the new-pipe value.
3. The tool computes h_f = 10.67·L·Q^1.852/(C^1.852·D^4.87) with Q in m³/s and D in m, then derives the hydraulic gradient (head per 100 m — the number pipe charts tabulate), the pressure drop (ρg·h_f, in kPa and psi), and the mean velocity Q/A.
4. Check the velocity against the equation's comfort zone: Hazen-Williams is calibrated near 0.9 m/s and stays credible from roughly 0.3 to 3 m/s in turbulent water flow. Outside that — or for hot water, glycol, oils, or any non-water fluid — switch to Darcy-Weisbach.
5. Straight-pipe friction only: add fitting (minor) losses and elevation change separately for the total pump head. The pipe & duct sizing tool handles fittings via loss coefficients.

Worked Example

A 100 m run of 100 mm-bore PVC (C = 150) carries 10 L/s (0.01 m³/s). Head loss: h_f = 10.67 × 100 × 0.01^1.852 ÷ (150^1.852 × 0.1^4.87) = 10.67 × 100 × 1.977×10⁻⁴ ÷ (10 718 × 1.349×10⁻⁵) = 1.459 m over the run — a 1.46 m per 100 m gradient, equivalent to 14.31 kPa (2.07 psi). The velocity is 0.01 ÷ (π/4 × 0.1²) = 1.27 m/s, comfortably inside the equation's validity range. Swap the pipe for old unlined cast iron (C = 100) and the same flow loses (150/100)^1.852 = 2.12× as much head — 3.09 m — which is why aging mains quietly eat pump energy.

Formulas

Hazen-Williams head loss (SI form)

h_f = 10.67 × L × Q^1.852 / (C^1.852 × D^4.87)

Derived quantities

gradient = h_f/L × 100; Δp = ρ·g·h_f; v = Q / (π/4 · D²)

C sensitivity

h_f2 / h_f1 = (C1 / C2)^1.852

Standards & References

• Hazen-Williams empirical head-loss equation, SI form with the 10.67 coefficient, as given in standard hydraulics references (e.g. Lindeburg, Civil Engineering Reference Manual; waterworks and fire-protection practice per AWWA and NFPA 13 hydraulic calculations)
• C coefficients verified against published tables (Engineers Edge Hazen-Williams coefficient table; CECALC design coefficient tables): PVC 150, copper 140, cement-lined ductile iron (new) 140, concrete 130, galvanized steel 120, old unlined cast iron 100 — values vary with age and condition
• Validity: water near ordinary temperature, turbulent flow, velocities roughly 0.3–3 m/s; for other fluids use Darcy-Weisbach (Reynolds number & friction factor tool)

Frequently Asked Questions