Hazen–Williams Velocity

This is Hazen–Williams in its original velocity form, and it is the version that handles part-full sewers and open channels as well as pressure pipes, because everything geometric enters through the hydraulic radius R = flow area ÷ wetted perimeter. For a full circular pipe R is simply D/4, so a 200 mm main is R = 0.05 m; at C = 130 on a 1% gradient that gives v = 0.849 × 130 × 0.05^0.63 × 0.01^0.54 ≈ 1.39 m/s.

The constant carries the units, and this is where careless work goes wrong. In SI, with R in metres and v in metres per second, the coefficient is 0.849; the familiar American form v = 1.318 C R^0.63 S^0.54 wants R in feet and returns feet per second, and the two are related by 1.318 × 0.3048^0.37 ≈ 0.849. S is dimensionless in both systems — head loss per unit length, so 12 ft per 1000 ft is S = 0.012, not 12. Enter it as a plain ratio here.