Sprinkler System Pipe Sizing Calculator
Calculate the required pipe diameter and friction head loss for a sprinkler irrigation system using the Hazen-Williams equation. Enter the flow rate, pipe length, and system parameters to determine the optimal pipe size.
Formulas Used
1. Minimum Diameter from Velocity Constraint:
D = √(4Q / (π · vmax))
where Q = flow rate (ft³/s), vmax = maximum allowable velocity (ft/s)
2. Hazen-Williams Friction Head Loss:
hf = 10.67 · L · Q1.852 / (C1.852 · D4.8704)
where hf = friction head loss (ft), L = pipe length (ft), Q = flow rate (ft³/s), C = Hazen-Williams roughness coefficient, D = inside pipe diameter (ft)
3. Pressure Conversion:
h (ft) = P (PSI) × 2.3077 | P (PSI) = h (ft) / 2.3077
4. Elevation Pressure Effect:
Pelev = Δz / 2.3077 (positive elevation = pressure loss)
5. Residual Outlet Pressure:
Presidual = Pavailable − hf,PSI − Pelev,PSI
6. Flow Velocity:
v = Q / A = Q / (π/4 · D²)
Assumptions & References
- The Hazen-Williams equation is valid for turbulent flow of water at typical temperatures (40–75°F / 4–24°C).
- Pipe inside diameters are based on PVC Schedule 40 nominal sizes (ASTM D1785). Actual IDs vary by material and schedule.
- Recommended maximum flow velocity: 5 ft/s (1.5 m/s) for main lines, up to 7 ft/s (2.1 m/s) for lateral lines (ASABE/ANSI S376.2).
- Minor losses (fittings, valves, etc.) are not included. Add 10–20% to pipe length as an equivalent length allowance for minor losses.
- Water density assumed at 62.4 lb/ft³ (fresh water at ~60°F).
- Hazen-Williams C values: PVC = 150, Polyethylene = 140, Galvanized Steel = 120, Cast Iron = 100, Concrete = 110–140 (AWWA M23).
- The calculator selects the smallest standard pipe size that simultaneously satisfies the velocity limit and maintains positive residual pressure.
- References: Hazen & Williams (1920); ASABE EP405.1; AWWA M23; Irrigation Association Design Standards.