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Hazen–Williams Equation

V = 0.849 C R^{0.63} S^{0.54} (SI), V = 1.318 C R^{0.63} S^{0.54} (US)

Empirical mean-velocity formula for water in pipes (typically 5–25 °C). C is a dimensionless roughness coefficient (new smooth pipe ~130–150; older tuberculated pipe much lower). S is the hydraulic gradient h_f/L. Not for gases or non-Newtonian fluids.

C

Hazen–Williams coefficient

R

(m or ft)

Hydraulic radius

S

Hydraulic gradient h_f/L

V

(m/s or ft/s)

Mean velocity

Step-by-step solved example

Full 300 mm pipe, C = 140, S = 0.004. Find V (SI).

Full-pipe empirical friction. Same two-section pipe as Darcy.

1. Hydraulic radius
R = D/4 = 0.300/4 = 0.075 m. R^{0.63} = 0.075^{0.63} = 0.1955.
2. Slope term
S^{0.54} = 0.004^{0.54} = 0.05075.
3. Velocity
V = 0.849×140×0.1955×0.05075 = 1.18 m/s.
$V = 1.18 m/s$

Answer: V = 1.18 m/s

10 practice questions

0/10 correct

1.Hazen–Williams is intended primarily for

2.If C increases 20% (same R, S), V

3.Typical C for new cement-lined ductile iron is nearest

4.If slope S is multiplied by 4, V multiplies by about

5.Aging / tuberculation of a water main typically

6.The US customary coefficient 1.318 is replaced in SI by

7.Full pipe: if D doubles, R doubles and V multiplies by about

8.Hazen–Williams S is

9.Compared with Darcy–Weisbach, Hazen–Williams

10.C = 100, R = 1 ft, S = 0.01 (US). V is nearest