Sizing process pipework by Darcy–Weisbach friction loss and velocity limits: continuity, Reynolds number, Colebrook/Swamee–Jain friction factor, self-scour velocity bands and a worked diameter comparison.
Pipe diameter is the first hydraulic decision and it cascades into everything else — pump head, energy cost, water hammer, solids deposition and capital cost. Size a line too small and friction loss and erosion soar; too large and solids settle, capital is wasted and self-cleansing velocity is never reached. The right diameter falls out of two constraints handled together: a friction-loss budget (Darcy–Weisbach) and a velocity band.
Continuity fixes velocity once a diameter is chosen:
Friction head loss along a full-flowing pipe follows Darcy–Weisbach:
hf = friction head loss (m)f = Darcy friction factor (–)L, D = pipe length and internal diameter (m)v = mean velocity (m/s), g = 9.81 m/s²The friction factor depends on the Reynolds number and relative roughness; for turbulent flow it is given implicitly by Colebrook–White, or explicitly by the Swamee–Jain approximation:
ε = absolute roughness (m) — ~0.0015 mm drawn metal, ~0.05 mm steel, ~0.0015 mm PE/PVCν = kinematic viscosity (~1.0×10−6 m²/s for water at 20°C)| Service | Typical velocity (m/s) | Why |
|---|---|---|
| Pump suction | 0.6–1.5 | Low loss protects NPSH and avoids cavitation |
| Pump discharge / process | 1.0–2.4 | Self-scouring without excess friction or hammer |
| Sludge / solids-bearing | 1.2–2.0 | Above the deposition (settling) velocity |
| Gravity sewer / drain | ≥0.7 (self-cleansing) | Prevents grit and solids accumulation |
| Long transfer mains | 0.9–1.5 | Low velocity caps pumping energy and surge |
Velocity scales with the inverse square of diameter at fixed flow (v ∝ 1/D²), and friction loss roughly with v² — so a one-size increase can cut head loss dramatically while pushing velocity toward the deposition limit. The art is landing inside the band at the diameter that minimises lifetime cost (capital + pumping energy).
Transfer Q = 40 L/s = 0.040 m³/s of water at 20°C through 250 m of steel pipe (ε = 0.05 mm).
Size the diameter and check head loss and erosional velocity with the pipe hydraulics tools.
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