Thermal expansion

The change in length of a pipe follows from three quantities:

ΔL = α · L · ΔT

Here α is the mean coefficient of linear thermal expansion of the material, L the length of the section considered and ΔT the difference between installation and operating temperature. Diameter and wall thickness do not appear.

An example: 50 m of carbon steel pipe, installed at 20 °C, operated at 220 °C. With α = 12 · 10⁻⁶ 1/K the result is 12 · 10⁻⁶ · 50 000 mm · 200 K = 120 mm. The line grows by twelve centimetres – whether this has been planned for or not.

The expansion coefficient depends on the material and rises slightly with temperature. For a rough estimate the orders of magnitude in the table are sufficient; for a verification the values of the material standard or the code for the actual temperature range are used.

Two things stand out. Austenitic stainless steels expand about 40 per cent more than carbon steel – a routing that works in carbon steel can be too stiff in stainless. And plastics such as polyethylene expand more than ten times as much, which is why their supports follow rules of their own.

If a straight pipe between two anchors is fully prevented from expanding, the stress is σ = E · α · ΔT. It depends neither on length nor on cross-section. For steel with a modulus of elasticity of about 200 000 N/mm², a temperature difference of only 100 K gives about 240 N/mm² – the order of magnitude of the yield strength of common pipe steels.

The associated force is stress times cross-sectional area. For a pipe of 219.1 × 6.3 mm this is about 1000 kN. No ordinary anchor and no equipment nozzle can take such a force. The conclusion is always the same: thermal expansion cannot be prevented, it has to be absorbed.

The simplest means is the routing itself. Every change of direction makes the line flexible: when one leg expands, the leg perpendicular to it bends. L-, Z- and U-shaped runs absorb the expansion without any additional component. If that is not enough, an expansion loop is provided.

Where space is lacking, expansion joints take over – with their own requirements for anchors and guides. In every case anchors divide the line into sections, each absorbing its own expansion, and guides ensure that the movement goes where it can be absorbed.

The equation is simple. The result goes wrong through the temperatures entered.