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Hazen-Williams Equation Calculator

The water-distribution engineer's everyday equation. Empirical, calibrated for water at typical temperatures, no Reynolds number required.

in
ft
gpm
ft/s
ft
ft/ft

Defaults: 8-inch ductile iron water main (C = 120), 500 gpm flow, 1000 ft long.

US customary (Q in gpm, D in inches, hf in ft of water per ft of pipe):
$$ h_f / L = \frac{4.52 \, Q^{1.852}}{C^{1.852} \, D^{4.87}} $$
SI (Q in m³/s, D in m, hf/L in m/m):
$$ h_f / L = \frac{10.67 \, Q^{1.852}}{C^{1.852} \, D^{4.87}} $$
Q volumetric flow rate · D internal pipe diameter · L pipe length · C Hazen-Williams roughness coefficient (higher = smoother) · hf friction head loss.

Hazen-Williams C-factor table

The C-factor depends on material and condition. Higher C = smoother = less head loss. For end-of-life capacity analysis on unlined ferrous pipe, drop C by 10–30 from the new-pipe value.

Hazen-Williams C-factors by pipe material and condition
Pipe material / conditionC (new)C (aged)
PVC, schedule 40/80150140
HDPE150140
Copper, drawn140130
Ductile iron, cement-mortar lined140135
Concrete pipe (precast, smooth)140120
Steel, riveted, new120100
Steel, welded, new130110
Steel, galvanized120100
Ductile iron, unlined12090
Cast iron, unlined, new130
Cast iron, 10 years old110
Cast iron, 30 years old90
Cast iron, tuberculated (40+ yr)60–80
Asbestos cement140120
Vitrified clay (sewer)110100

Source: AWWA Manual M14 — Recommended Practice for Backflow Prevention and Cross-Connection Control; AWWA M11 — Steel Pipe. Distribution-system models commonly default to C = 130 for new mains and C = 100 for older systems.

Worked examples

Example 1 — 8-inch ductile iron water main, 1500 ft, 600 gpm

Given: 8-inch cement-lined ductile iron (C = 140), L = 1500 ft, Q = 600 gpm.
Find: Friction head loss hf, velocity, and slope.
hf = 4.52 · 1500 · (600)1.852 / [(140)1.852 · (8)4.87]
= 4.52 · 1500 · 154,200 / (8,580 · 26,000)
A = π·(8/12)²/4 = 0.349 ft²; V = (600/448.8) / 0.349 = 3.83 ft/s ✓ (in 3–6 ft/s design range)
hf ≈ 4.7 ft  ·  S = hf/L = 0.0031 ft/ft

Example 2 — Sizing for fire flow (1500 gpm, max hf/L = 0.01)

Given: Need to convey 1500 gpm with friction slope ≤ 0.01 ft/ft. New ductile iron (C = 130).
Find: Minimum pipe diameter.
Solve for D: D = [4.52 · Q1.852 / (C1.852 · S)]1/4.87
= [4.52 · (1500)1.852 / ((130)1.852 · 0.01)]1/4.87
= [4.52 · 853,000 / (7,460 · 0.01)]1/4.87 = (51,700)0.205
D = 9.6 in → use 10-in standard pipe (round up).
D = 10 in  ·  verify: hf/L = 0.0072 ft/ft ✓  ·  V = 6.1 ft/s

When NOT to use Hazen-Williams

Hazen-Williams is empirical and calibrated for water at roughly 60°F flowing turbulently. It systematically over-predicts head loss in laminar or transitional flow, and is invalid for fluids other than water (oils, slurries, hot water above 100°F or below 40°F). For fire flow (where Re is very high) or any non-water application, use Darcy-Weisbach.

What does C = 120 actually mean?

The C-factor is empirical and not directly traceable to a physical roughness. Higher C means smoother pipe and less friction loss. The exponent 1.852 comes from Hazen and Williams' 1905 fitting of velocity data; it is approximately the Reynolds number exponent for fully rough turbulent flow, which is why the equation works for water-distribution conditions and breaks down outside that range.

Aging

Pipe roughness increases over time as scaling, tuberculation, and biofilm accumulate. C-factor decreases by 10–30 over 20–30 years for unlined ferrous pipe. Cement-lined and plastic pipes are essentially stable for the design life. Use lower C-values when designing for end-of-life capacity.

Reference: AWWA Manual M14 — Design and Construction of Distribution Mains. Original: Williams, G.S., Hazen, A. (1933). Hydraulic Tables (3rd ed.).

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