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Fluid Mechanics

Hazen-Williams Head Loss Calculator

The Hazen-Williams equation is an empirical relationship widely used for sizing water-distribution, fire-service, and irrigation pipework. It estimates friction head loss directly from flow, pipe diameter, length, and a roughness coefficient C — without needing the fluid viscosity, Reynolds number, or a friction factor that the physically general Darcy-Weisbach method requires. That simplicity is also its limit: the C-factor and the equation were fitted to water at ordinary temperatures, so the result is only valid for clean cold-to-warm water in turbulent flow. This calculator returns the friction head from the SI form of the equation, adds an optional elevation head, and converts the total head to an equivalent pressure drop using the density of water. It is a preliminary estimate, not a substitute for a full Darcy-Weisbach analysis or a verified pipe-network model.

TypeInteractive engineering calculator

Calculator

Velocity:
Head:
Pressure:
Result
Velocity (v)1.5719 m/s
Friction head (h_f)2.03474 m
Elevation head (h_z)0 m
Total head (h_total)2.03474 m
Equivalent pressure drop, water (ΔP)19.9539 kPa
Empirical water-service estimate only — Hazen-Williams is valid for clean water in turbulent flow, not for other fluids, slurry, gas, or two-phase flow. Use Darcy-Weisbach for a physically general result and verify before design.

Formulas

Friction head loss (SI)
h_f = 10.67 × L × Q^1.852 / (C^1.852 × D^4.871)
Velocity
v = Q / (π × D² / 4)
Total head
h_total = h_f + Δz
Equivalent pressure drop (water)
ΔP = ρ_water × g × h_total

Diagram

Hazen-Williams: h_f = 10.67·L·Q^1.852 / (C^1.852·D^4.871)Q, v = Q/A — water, C factorDLh_f = 10.67·L·Q^1.852 / (C^1.852·D^4.871)ΔP = ρ_water · g · h_total

Worked example

Water flows at 100 m³/h through a 150 mm internal-diameter pipe, 100 m long, with C = 120 and no elevation change. Find the friction head, velocity, and equivalent pressure drop.

  1. 01Q = 100 m³/h = 0.02778 m³/s; A = π × 0.15² / 4 = 0.01767 m²
  2. 02v = 0.02778 / 0.01767 = 1.57 m/s
  3. 03h_f = 10.67 × 100 × 0.02778^1.852 / (120^1.852 × 0.15^4.871) = 2.03 m
  4. 04ΔP = 1000 × 9.80665 × 2.03 = 19,950 Pa ≈ 19.95 kPa
Result

Friction head ≈ 2.03 m, velocity ≈ 1.57 m/s, equivalent water pressure drop ≈ 19.95 kPa.

FAQ

When should I use Hazen-Williams instead of Darcy-Weisbach?
Hazen-Williams is a convenient shortcut for clean water in turbulent flow — water distribution, fire mains, irrigation. Darcy-Weisbach is the physically general method: it works for any fluid and any flow regime because it uses viscosity, Reynolds number, and a friction factor. For non-water fluids, low Reynolds numbers, or final design, prefer Darcy-Weisbach.
What C factor should I use?
C depends on the pipe material, internal condition, and age. New smooth plastic or cement-lined pipe sits high (≈140–150); older or tuberculated metal pipe is much lower (≈100 or below). Because head loss scales with C^1.852, the C-factor basis is usually the largest source of uncertainty — use a value you can defend from the material and service.
Does the pressure drop assume water?
Yes. The equation itself is water-specific, and the equivalent pressure drop is computed with water density (1000 kg/m³) and standard gravity applied to the total head. It is not a general fluid pressure-drop tool.
Is the elevation term a loss?
No — elevation change is static head, not friction. A rise adds head the pump must overcome; a fall returns head. It is shown separately and added to the friction head only to give a combined total head and its water-pressure equivalent.

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