Engineering
Hazen-Williams Water Pipe Head Loss formula: 10.67 * L * Q^1.852 / (C^1.852 * D^4.8704)
Estimate straight-pipe friction head loss for turbulent water flow with SI inputs and an assumed Hazen-Williams coefficient.
An empirical straight-pipe estimate
Use length and inside diameter in metres, nonnegative flow magnitude in m³/s, and a positive Hazen-Williams coefficient C. The coefficient and exponents in this worksheet are the stated SI convention; do not combine constants from other unit systems.
This empirical relationship is intended for turbulent water flow. It does not model viscosity explicitly and should not be extrapolated to laminar flow or other fluids. Darcy-Weisbach is an alternative; its friction factor does not always require an iterative solution.
The illustrative C values are assumptions, not guaranteed material properties. Condition and age affect roughness; calibrate against suitable data. This example excludes fittings, valves, elevation changes and pump head and does not establish fire-system code compliance. Halving diameter multiplies the formula result by 2^4.8704, about 29.3, when the other inputs are fixed.
| Water Main Scenario | Inputs (L=500m, Q=0.05 m^3/s, D=0.20m) | Roughness C | Head Loss h_f & Pressure Drop |
|---|---|---|---|
| New Cement-Lined Ductile Iron | 50 L/s through 200 mm main | C = 130 | 6.41 m head (62.88 kPa) |
| Aged Tuberculated Cast Iron | Same 50 L/s & 200 mm main | C set to 100 | 10.42 m head (+62.6% loss!) |
| Static Zero-Flow Isolation | Flow Q set to 0 m^3/s | C = 100 | 0.00 m head loss |
SI Hazen-Williams Pipe Friction Head Loss h_f in meters of water
The result is the positive friction-loss magnitude, not a signed network-flow equation. Zero flow returns zero friction loss; that does not mean static pressure or elevation head is zero.
=IF(COUNT(B2:B5)<>4,"Invalid inputs",IF(OR(B2<0,B3<0,B4<=0,B5<=0),"Invalid inputs",ROUND((10.67 * B2 * (B3 ^ 1.852)) / ((B4 ^ 1.852) * (B5 ^ 4.8704)), 2)))Convert meters of water head loss into kilopascals (kPa = 9.81 * h_f)
For this conversion only, assume density 1000 kg/m³ and gravity 9.81 m/s². Multiplying by 9.81 converts metres of head to kPa. This worked example deliberately converts the displayed two-decimal head in B6; engineering calculations should normally retain unrounded intermediate values.
=IF(COUNT(B6)<>1,"Invalid inputs",IF(B6<0,"Invalid inputs",ROUND(9.81 * B6, 2)))Try the example
Use the original values or change them to test your understanding.