All tools

Hazen-Williams — 12-inch Steel Water Main Worked Example

Friction loss for a welded steel transmission main between a booster station and an elevated tank. Steel is the material where the C-factor story matters most: new lined steel starts near C = 140–145, but unlined or aging steel tuberculates its way down toward C = 100 and below — and head loss climbs steeply as it does. Sources: Hazen & Williams, Hydraulic Tables; AWWA M11, Steel Pipe — A Guide for Design and Installation.

The main

Pipe	12-inch welded steel, cement-mortar lined, d = 12 in
Length L	3,500 ft
Design flow Q	1,500 gpm
C-factor (design)	130 (lined steel, mid-life; see C reference)

Step 1 · Velocity check first

Is 1,500 gpm reasonable in a 12-inch main?

Q = 1,500 gpm ÷ 448.8 = 3.34 cfs
A = π/4 · (1.0 ft)² = 0.785 ft²
V = 3.34/0.785 = 4.3 ft/s — comfortably inside the 2–6 ft/s transmission range ✓

Above ~6–7 ft/s, surge pressures and per-foot losses climb quickly in transmission service; below ~2 ft/s the pipe is oversized for the duty (capital tied up, water age grows).

Step 2 · Hazen-Williams friction loss

The design-condition number

h_f = 10.44 · L · Q^1.852 / (C^1.852 · d^4.87) [Q gpm, d in, L, h_f ft]

Q^1.852 = 1500^1.852 = 7.62 × 10⁵
C^1.852 = 130^1.852 = 8.22 × 10³
d^4.87 = 12^4.87 = 1.81 × 10⁵

h_f = 10.44 · 3500 · 7.62×10⁵ / (8.22×10³ · 1.81×10⁵)
h_f = 2.79×10¹⁰ / 1.49×10⁹ = 18.8 ft (≈ 5.4 ft per 1,000 ft)

In pressure terms: 18.8 ft ÷ 2.31 ft/psi = 8.1 psi

Step 3 · Aging sensitivity

The same main across its service life

Condition	C	h_f (ft)	Loss vs design
New, cement-mortar lined	140	16.3	−13%
Design (mid-life lined)	130	18.8	—
Unlined / tuberculated, decades old	100	30.5	+62%

Scaling shortcut: h_f ∝ (1/C)^1.852
h_f,100 = 18.8 · (130/100)^1.852 = 18.8 · 1.626 = 30.5 ft

Design both directions. For pump head and fire-flow adequacy, the low-C (aged) case governs — can the system still deliver at C = 100? For surge and velocity checks, the high-C (new) case governs — flows run highest when the pipe is smoothest. One C-factor cannot be conservative for both questions.

Step 4 · What Hazen-Williams quietly assumes

Limits of the equation

Water only, ordinary temperatures. The formula is dimensional and fluid-specific. Any other fluid, or hot water, needs Darcy-Weisbach.
Turbulent flow in the normal municipal range. Accuracy degrades at very low and very high velocities; C itself drifts with velocity in reality.
Friction only. Valves and fittings add minor losses on top — itemize with the minor loss tool or fold in via equivalent lengths. On 3,500 ft of straight main they are small; in the station piping they are not.
Static head is separate. Total pump head = static lift + friction + minor losses — the TDH tool assembles the whole stack.

Tools used in this example

Reproduce every step: Hazen-Williams tool with C from the C-factor card, then total dynamic head and pump BHP to finish the pumping picture. Companion example: 6-inch PVC distribution main.