Free pipe thermal expansion

Estimate unconstrained axial length change using a supplied thermal-expansion coefficient.

How this calculation works

Enter the original pipe length, initial and final temperatures, and a linear expansion coefficient appropriate to the material and temperature interval. The coefficient is specified in micrometers per meter per kelvin and is converted to inverse kelvin before use. Multiplying it by the original length and signed temperature change gives the free length change. A warmer final temperature produces expansion; cooling produces contraction. Adding that signed change to the original length gives final free length. This constant-coefficient model assumes uniform pipe temperature and no restraint. It cannot predict the stress or anchor forces that develop when movement is constrained. Expansion loops, support arrangements and material behavior over the actual temperature range need separate evaluation rather than being inferred from the free movement alone.

Inputs and units

Original pipe length (m)
Linear expansion coefficient (µm/(m·K))
Initial temperature (°C)
Final temperature (°C)

Method and formula

ΔL = α L0(Tfinal−Tinitial); Lfinal = L0+ΔL. Convert α from µm/(m·K) to 1/K by multiplying by 10⁻⁶.

Worked example

Example inputs

Original pipe length: 30 m
Linear expansion coefficient: 12 µm/(m·K)
Initial temperature: 20 °C
Final temperature: 80 °C

Calculation steps

Temperature change = 80 − 20 = 60 K. Coefficient = 12 × 10⁻⁶ per K.
Free length change = 12 × 10⁻⁶ × 30 × 60 = 0.0216 m = 21.6 mm.
Final free length = 30 + 0.0216 = 30.0216 m.

Example results

Signed length change: 21.6 mm
Final free length: 30.0216 m

Assumptions

Unrestrained uniform-temperature pipe with a constant user-supplied coefficient.
Positive change is expansion; negative change is contraction.

Limitations

Does not calculate restrained stress, anchor forces, expansion loops or support spacing.
Use a coefficient valid for the material and temperature interval.
Preliminary educational check; verify inputs and equipment data before design or operation.

Sources

Spears Manufacturing: Pipe and Hangers Technical: Printed page 34: free thermal expansion; ΔL = 12αLΔT with feet-to-inch conversion