OpenSpecEngineering

Finds the friction head loss in a full, pressurized water pipe for a given flow, or the flow a pipe carries for a given head loss. It also gives the velocity and the hydraulic gradient. Civil and municipal engineers use it to size water mains, fire lines and irrigation laterals, and to check how much pressure a run of pipe will cost.

Equation

The page uses the SI form of the Hazen–Williams equation [1][3]:

h_f = 10.67·L·Q^1.852 / (C^1.852·D^4.87)     V = Q / (πD²/4)

h_f is the friction head loss in meters of water, L the pipe length in m, Q the flow in m³/s, D the inside diameter in m and V the mean velocity. C is the Hazen–Williams coefficient, a smoothness factor: the higher C, the smoother the pipe and the lower the loss. Choosing a Pipe Material fills C from a table [4][5], or you can type your own. The hydraulic gradient is h_f/L. To solve for flow, the page inverts the same equation.

Inputs

The Pipe Size list gives the inside diameters of steel pipe to ASME B36.10M [2][6]. PVC (AWWA C900) and ductile-iron (AWWA C151) water mains have other inside diameters for the same nominal size, so pick Custom and enter the actual bore from the maker’s data.

Limits and common mistakes

• The equation is empirical and holds for water near 15 °C in turbulent flow. Do not use it for oil, other viscous fluids, hot water or very low velocities. Use the Darcy–Weisbach equation for those.
• C drops as a pipe ages. Unlined cast iron falls from about 130 new to about 100 after 20 years, which raises the loss by over 60 %. Design for the C the pipe will have, not the C it has on day one.
• Use the inside diameter, not the nominal size. A loss varies with D^4.87, so a few millimeters matter.
• The head loss is friction only. Add fittings, valves and any change in elevation separately.

Worked example

A new 200 mm cement-mortar-lined ductile-iron main runs 800 m to a housing development. It must deliver 40 L/s at peak demand. How much head does the pipe lose?

1. Choose Solve For Head loss (given flow) and enter Flow Rate (Q) 40 L/s.
2. Choose Pipe Material Ductile iron, cement-mortar lined, which sets Hazen–Williams Coefficient (C) to 140.
3. Leave Pipe Size at Custom and enter Inside Diameter (D) 200 mm and Pipe Length (L) 800 m.
4. Press Solve. The Solution shows: Flow rate Q: 40 L/s
   Velocity V: 1.27324 m/s
   Head loss hf: 5.9105 m
   Hydraulic gradient hf/L: 0.00738813 m/m
   Head loss per 100 m: 0.738813 m

Check with the US form of the equation, h_f = 4.52·q^1.852/(C^1.852·d^4.87) in psi per foot, with q in gpm and d in inches. 40 L/s is 634 gpm and 200 mm is 7.874 in, which gives 0.003203 psi/ft. Over 2,625 ft that is 8.41 psi, or about 5.92 m of water, within 0.2 % of the page. The velocity, 1.27 m/s, is normal for a water main.