Why pressure drops along a pipe
Water rubbing against pipe walls and against itself loses energy. That loss, called friction loss or head loss, shows up as lower pressure at the far end of the pipe. Too much friction loss means weak showers upstairs, sprinklers that do not reach, or a pump that has to work harder.
The Hazen-Williams equation
For water at normal temperatures in full pipes:
hf = 10.67 × L × Q^1.852 ÷ (C^1.852 × d^4.87)
with hf and L in meters, Q in m³/s and d in meters. In US units, the loss per 100 ft is 0.2083 × (100 ÷ C)^1.852 × gpm^1.852 ÷ d^4.8655, with d in inches. Feet of head convert to psi by dividing by 2.31.
Roughness coefficients
| Pipe | C |
|---|---|
| PVC, CPVC, PEX, HDPE | 150 |
| Copper | 140 |
| Lined ductile iron | 130 |
| New steel | 120 |
| Old galvanized steel | 100 or less |
Worked example
10 gpm through 100 ft of 3/4 in type L copper (inner diameter 0.785 in):
- Head loss ≈ 25.6 ft.
- Pressure loss ≈ 25.6 ÷ 2.31 ≈ 11.1 psi.
- Velocity ≈ 6.6 ft/s, within the usual limit for cold water.
At 6 gpm in the same pipe, the loss falls to about 4.3 psi, because friction grows with flow to the power 1.85: a 40% cut in flow cuts loss by 61%.
The power of diameter
Friction loss falls with the diameter to the power 4.87. Going from 3/4 in to 1 in type L copper cuts the loss by about 73% at the same flow. On long runs, upsizing the main line is usually the cheapest fix for low pressure.
Fittings and valves
Each elbow, tee and valve adds loss. Add its equivalent length to the pipe length:
| Fitting (3/4 in) | Equivalent length |
|---|---|
| 90° elbow | about 2 ft |
| Tee, flow through branch | about 4 ft |
| Gate valve, open | about 0.5 ft |
| Check valve | 5 to 10 ft |
Pressure budget
A typical plumbing design starts from the street or tank pressure, subtracts the elevation (0.433 psi per foot of rise), the water meter and the friction loss, and checks that at least 15 to 20 psi remains at the most remote fixture. Many fixtures need more: a pressure-balanced shower valve works best at 30 psi or more.
Limits
Hazen-Williams applies to water between about 40 and 75 °F in turbulent flow. For hot water, other fluids or small, slow flows, the Darcy-Weisbach equation with the Colebrook friction factor is more accurate.