Fluid moving through pipe pays a continuous toll to wall friction, and that toll is booked as head loss — metres of energy the pump or the available pressure must make good. Two equations dominate the accounting. Darcy-Weisbach is the general instrument, valid for any Newtonian fluid in pipes or ducts, using a friction factor tied to the Reynolds number and roughness. Hazen-Williams trades that generality for convenience: one material coefficient C, no viscosity, no iteration — but it is calibrated only for water at ordinary temperatures and velocities of roughly 0.3–3 m/s.
The Hazen-Williams SI form hf = 10.67·L·Q^1.852/(C^1.852·D^4.87) makes the two big sensitivities explicit. Diameter is merciless: the D^4.87 exponent means 10% less bore costs about 59% more friction, and one commercial pipe size usually halves the loss — when a pump is marginal, a pipe size is nearly always cheaper than a pump size. Smoothness matters almost as much over a system’s life: new PVC rates C = 150 while old tuberculated cast iron falls to 100, and (150/100)^1.852 ≈ 2.12 means the aged main loses over twice the head at the same flow.
Straight-pipe friction is only part of the bill. Fittings and valves add minor losses, commonly summed as K-coefficients or equivalent pipe lengths, and elevation change enters separately — the total dynamic head a pump sees stacks all three.