Pipe Sizing Continuity Equation
The continuity equation relates the volumetric flow rate, the cross-sectional area of the pipe, and the velocity of the fluid flow.
Where:
- Q = Volumetric flow rate
- A = Cross-sectional area of the pipe
- v = Fluid velocity
For circular pipes, the area is calculated using the internal diameter (D):
Frequently Asked Questions
Using the continuity equation Q = A * v (Flow Rate = Area * Velocity). You first find the required cross-sectional area and then solve for the inner diameter (D = sqrt(4*A/pi)).
Pipe size is determined by: required flow rate (L/s or m³/h); acceptable flow velocity (1–3 m/s for water systems); allowable pressure drop per metre; fluid properties (viscosity, density); pipe material (roughness affects friction losses); and total pipe length including equivalent lengths for fittings and valves. The Darcy-Weisbach equation is the standard method.
The Darcy-Weisbach friction head loss formula: hf = f × (L/D) × (v²/2g). Where hf is friction head loss (m), f is the Darcy friction factor (dimensionless, from Moody chart), L is pipe length (m), D is internal pipe diameter (m), v is flow velocity (m/s), g = 9.81 m/s². The friction factor f depends on Reynolds Number and pipe roughness.
Recommended maximum design velocities: Cold water domestic — 2.0 m/s; Hot water domestic — 1.5 m/s; Water mains distribution — 3.0 m/s; Chilled water systems — 2.5 m/s; Fire mains (during flow) — 5.0 m/s. Velocities above 3 m/s in copper or plastic pipe risk erosion corrosion, noise, and water hammer. Lower velocities are specified for noise-sensitive applications.
Reynolds Number Re = ρ × v × D / μ, where ρ is fluid density (kg/m³), v is velocity (m/s), D is diameter (m), and μ is dynamic viscosity (Pa·s). Re < 2,300 indicates laminar flow; Re > 4,000 indicates turbulent flow. Most water piping operates in turbulent flow. The friction factor f differs significantly between laminar (f = 64/Re) and turbulent flow (use Colebrook-White or Moody chart).
Water hammer is a pressure surge caused by rapid flow velocity changes — typically when a valve closes quickly. Pressure spikes can reach 5–10× normal working pressure. Prevention methods: slow-closing actuated valves; pressure reducing valves (PRVs); expansion vessels or surge tanks; air chambers near pump outlets; designing for maximum pipe velocities below 2 m/s; and avoiding dead-end pipe runs.