🔧 Hazen-Williams Worked Example: From Pipe Sizing to Pump Head

The Scenario

This worked example carries a Hazen-Williams calculation through to a complete pump selection requirement, following the same workflow this site's Hazen-Williams Pipe Flow Calculator supports: a water transmission main needs to deliver 0.06 m³/s (about 950 GPM) through a 1,500 m run of 300 mm (12-inch) ductile iron pipe with a design C-factor of 120 (a conservative, aged-pipe value, per the companion C-factor aging article), rising 15 m in elevation from source to discharge point, with two 90° elbows and one gate valve along the route.

Step 1 — Hazen-Williams Head Loss

Using h_f = 10.67 · L · Q^1.852 / (C^1.852 · D^4.87): Q = 0.06 m³/s, L = 1,500 m, C = 120, D = 0.3 m. Computing Q^1.852 ≈ 0.06^1.852 ≈ 0.00453, C^1.852 ≈ 120^1.852 ≈ 7,354, D^4.87 ≈ 0.3^4.87 ≈ 0.00195. So h_f = 10.67 × 1,500 × 0.00453 / (7,354 × 0.00195) ≈ 72.5 / 14.34 ≈ 5.06 m. This is the major (straight-pipe) friction head loss over the 1,500 m run.

Step 2 — Minor Losses

Using representative K-values (standard 90° elbow K ≈ 0.9 each, fully open gate valve K ≈ 0.15) and the flow velocity: V = Q / (π·D²/4) = 0.06 / (π × 0.09/4) ≈ 0.06 / 0.0707 ≈ 0.849 m/s. Total minor-loss K-sum = 2 × 0.9 + 0.15 = 1.95. Minor head loss = K_sum × V²/(2g) = 1.95 × 0.849² / (2 × 9.81) ≈ 1.95 × 0.721 / 19.62 ≈ 0.0716 m. Minor losses are small relative to major loss in this example — typical for a long transmission main with relatively few fittings, though this balance shifts for shorter, more fitting-dense piping runs.

Step 3 — Static Elevation Head

The pipeline rises 15 m in elevation from source to discharge — this static head has to be added directly to the friction losses, since it represents real potential energy the pump has to provide regardless of flow rate or friction (a pump lifting water 15 m has to supply that lift even at zero flow, unlike friction losses which scale with flow).

Step 4 — Total Dynamic Head

Total dynamic head (TDH) = major loss + minor losses + static elevation head = 5.06 + 0.0716 + 15 ≈ 20.13 m. This is the total head the pump has to be capable of delivering at the design flow rate of 0.06 m³/s (950 GPM) to move water through this specific pipeline configuration.

Step 5 — Reading the Pump Curve

With a target operating point of approximately 950 GPM at approximately 20.1 m (about 66 ft) of head established, the next step in a real design is selecting a pump whose published performance curve passes through or near this operating point — a pump curve plots delivered head against flow rate, and the pump selected should be capable of delivering at least the calculated TDH at the design flow, ideally with the operating point falling within the pump's efficient operating range (not at the extreme edge of its curve, where efficiency and reliability both tend to suffer).

Why Getting the C-Factor Right Mattered in This Example

Had this example used an optimistic new-pipe C-factor of 130 instead of the more conservative aged-pipe value of 120 used here, the calculated major head loss would have been meaningfully lower — recomputing with C=130 gives roughly 4.1 m instead of 5.06 m, nearly a full meter less head, which would translate directly into selecting a smaller, less capable pump than the pipeline will actually require once it has aged into the C=120 range this example assumed from the start. This illustrates concretely why the C-factor aging consideration covered elsewhere in this cluster isn't an abstract concern — it directly changes the pump selection outcome.