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 $v = 0.849 \times 130 \times 0.05^{0.63} \times 0.01^{0.54} \approx 1.39$ 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 $1.318 \times 0.3048^{0.37} \approx 0.849$. 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.