Pipe Thermal Expansion and Expansion Leg Calculator

Why do pipes grow?

Every material expands when heated. In a pipe run the expansion accumulates along the length: ΔL = α × L × ΔT, where α is the linear expansion coefficient of the material, L the pipe length between two anchors and ΔT the difference between installation and operating temperature.

Plastic pipes grow far more than metals. The same 10 metres heated by 50 °C grows about 6 mm in steel, 8.5 mm in copper and 75 mm in PP-R. That is why absorbing expansion is a mandatory part of the design in plastic hot water systems.

Example

A 50 m steel hot water main is installed at 20 °C and will run at 120 °C. The growth is 0.012 mm/(m·K) × 50 m × 100 K = 60 mm. If the run is anchored at both ends those 60 mm have to go somewhere: an expansion leg or a loop takes them up, or the pipe and anchors end up under large forces.

How is an expansion leg calculated?

The leg after a change of direction absorbs the growth by flexing sideways. The longer the leg, the easier it flexes.

For metal pipe the guided cantilever approximation is used: L = √(3 × E × D × δ / σ_A). E is the modulus of elasticity, D the outside diameter, δ the movement the leg must take and σ_A the allowable stress range.

For plastic pipe manufacturers give the same relation with a single material constant: L = C × √(D × δ). Example: for a 20 mm PVC-U pipe with 46.8 mm of expansion and C = 33.5 the leg is 33.5 × √(20 × 46.8) = 1025 mm.

U loops

On long straight runs without bends a U shaped loop is built at mid length. The two legs share the growth coming from both sides, each taking half. The leg is therefore 1 / √2 of the single leg length, about 71 percent.

Limits

These relations are for approximate preliminary work. The listed expansion coefficients and material constants are approximate: for plastic pipes in particular the manufacturer's manual governs. Anchor positions and forces, guide spacing and stress analysis of high temperature lines are a separate engineering task.