Hazen–Williams Head Loss

Allen Hazen and Gardner Williams fitted this in 1905 to thousands of waterworks measurements, and its great virtue is that all the pipe's character collapses into one number, C, that a utility can measure by fire-flow test and track over decades. New plastic runs C = 150, cement-lined ductile iron 140, new steel 130, twenty-year-old unlined cast iron 100 or worse. Push 50 L/s through 100 m of 200 mm pipe at C = 130 and you lose about 1.28 m — comfortably inside the 3 m per 100 m that most distribution standards allow.

The formula is emphatically not general. It is calibrated for water near 15 °C at velocities under about 3 m/s in pipes 50 mm and larger; use it on glycol, on oil, on steam or on hot water and the answer is wrong by an amount nobody can bound, because viscosity appears nowhere in it. That is also its charm — fire-protection codes such as NFPA 13 mandate Hazen–Williams precisely because it needs no fluid properties and no iteration, and every sprinkler hydraulic calculation in North America runs on it. For anything but cool water, use Darcy–Weisbach.