How Friction Loss Is Calculated in Pipes: Hazen-Williams and Darcy-Weisbach
Learn how friction loss in pipes is calculated using the Hazen-Williams and Darcy-Weisbach equations. Covers C factors, Reynolds number, and pressure drop for fire suppression and plumbing systems.
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What Is Friction Loss in Pipes?
Friction loss is the reduction in fluid pressure caused by the fluid's interaction with the pipe wall as it flows. It's also called head loss or pressure drop. Every foot of pipe and every fitting causes friction loss — understanding it is essential for sizing pumps, designing fire suppression systems, and ensuring adequate water pressure.
Two Primary Methods
Method 1: Hazen-Williams (Practical Plumbing and Fire Systems)
Formula (English units): V = 1.318 × C × R^0.63 × S^0.54
Or more commonly as pressure drop per 100 feet: P_loss = 4.52 × Q^1.85 / (C^1.85 × D^4.87)
Where: - Q = flow rate in gallons per minute (GPM) - C = Hazen-Williams roughness coefficient - D = internal pipe diameter (inches) - P_loss = pressure drop in PSI per 100 feet
Hazen-Williams C Coefficients:
Example: 50 GPM through 2-inch PVC pipe (C = 150): P_loss = 4.52 × (50)^1.85 / (150^1.85 × 2^4.87) = 4.52 × 1,380 / (12,870 × 29.2) = 6,238 / 375,804 = 0.0166 PSI per foot = 1.66 PSI per 100 feet
Method 2: Darcy-Weisbach (Engineering, Accurate All Fluids)
Formula: h_f = f × (L/D) × (V²/2g)
Where: - h_f = head loss (feet of fluid) - f = Darcy friction factor (dimensionless) - L = pipe length (feet) - D = pipe diameter (feet) - V = velocity (ft/s) - g = gravitational constant (32.2 ft/s²)
The friction factor f is determined by the Reynolds Number and pipe roughness, typically using a Moody diagram or the Colebrook-White equation.
Reynolds Number: Re = V × D / ν Where ν = kinematic viscosity (for water at 60°F: 0.0000122 ft²/s)
For laminar flow (Re < 2,300): f = 64/Re For turbulent flow (Re > 4,000): use Colebrook-White or Moody chart
Comparing the Two Methods
NFPA 13 (fire sprinkler systems) mandates Hazen-Williams. Darcy-Weisbach is preferred for petroleum pipelines and engineering applications.
Minor Losses: Fittings and Valves
Fittings (elbows, tees, valves) add friction loss expressed as equivalent pipe lengths:
Multiply by pipe diameter to get equivalent feet of straight pipe, then include in total L for calculation.
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Frequently Asked Questions
- What is the Hazen-Williams formula for friction loss?
- Pressure drop (PSI/100 ft) = 4.52 × Q^1.85 / (C^1.85 × D^4.87), where Q is flow in GPM, C is the roughness coefficient (150 for PVC, 130 for new cast iron), and D is internal diameter in inches. Hazen-Williams is standard for water pipe systems including fire suppression (NFPA 13).
- What is the C factor in Hazen-Williams?
- The C coefficient represents pipe roughness/smoothness. Higher C = smoother pipe = less friction. Common values: PVC = 150, new steel = 120, cast iron = 130, old cast iron = 80–100. Using an incorrect C factor significantly changes friction loss calculations — older pipes with corrosion may have C values 20–40 lower than when new.
- How do you calculate friction loss for fire suppression systems?
- NFPA 13 requires using the Hazen-Williams method. Start from each sprinkler, calculate flow at that head (based on area/density requirements and K factor), then sum flows and calculate pressure drop along each pipe segment working back to the supply. A hydraulic calculation table documents each segment's Q, L, C, D, and resulting pressure loss.
- What is minor loss in pipe systems?
- Minor losses are friction losses from fittings, valves, elbows, and transitions — distinct from pipe wall friction (major losses). They're expressed as equivalent lengths of straight pipe and added to the total L in calculations. Globe valves cause significant minor loss (equivalent to ~340 pipe diameters of straight pipe); ball valves cause very little (3 pipe diameters).
Last updated 7/28/2026