Plumbing Pipe Size and Flow Rate Calculator
Calculate pipe flow rate, velocity, and required pipe diameter using the Hazen-Williams equation and basic fluid dynamics.
Formula
Hazen-Williams Equation (Flow Rate):
Q = 0.4322 × C × d2.63 × S0.54
- Q = Flow rate (US gallons per minute, GPM)
- C = Hazen-Williams roughness coefficient (dimensionless)
- d = Pipe inner diameter (inches)
- S = Friction slope = hf / L (ft/ft)
- hf = Head loss (ft) = Pressure drop (psi) × 2.30659
- L = Pipe length (ft)
Required Diameter:
d = (Q / (0.4322 × C × S0.54))1/2.63
Flow Velocity:
V = Q / A where A = π × (d/2)2
Assumptions & References
- The Hazen-Williams equation is valid for water at typical temperatures (40–75°F / 4–24°C) and turbulent flow conditions.
- Pressure drop is converted to head loss using: 1 psi = 2.30659 ft of water at standard conditions.
- Recommended flow velocity for plumbing systems: 2–8 ft/s (ASHRAE / ASPE guidelines). Below 2 ft/s risks sediment deposition; above 8 ft/s risks erosion and noise.
- Standard pipe inner diameters are based on Schedule 40 nominal pipe sizes (IPS).
- Hazen-Williams C values: PEX/Plastic ≈ 150, Copper/New Steel ≈ 140, Galvanized ≈ 130, New Cast Iron ≈ 120, Old Cast Iron ≈ 100, Corroded Steel ≈ 80.
- This calculator does not account for minor losses (fittings, valves, bends). Add 10–30% to pipe length as an equivalent length allowance for fittings.
- Reference: Hazen, A. & Williams, G.S. (1920). Hydraulic Tables. ASPE Plumbing Engineering Design Handbook.