# Pipes and Tubes - Temperature Expansion

## Pipes expands when heated and contracts when cooled and the expansion can be expressed with the expansion equation.

The temperature expansion of pipes depends on start and final temperature of the pipe, and the expansion coefficient of the piping material at the actual temperature. The expansion formula can be expressed as:

dl = α L_{o}dt(1)

where

dl= expansion (m, inches)

L_{o}= length of pipe (m, inches)

dt= temperature difference (^{o}C,^{o}F)

α= linear expansion coefficient (m/m^{o}K, in/in^{o}F)

Note that the mean expansion coefficient may vary with temperature:

Mean Expansion Coefficient 10^{-6} (in/in^{ o}F, ) | ||||||||
---|---|---|---|---|---|---|---|---|

Material | Temperature Range ( ^{o}F) | |||||||

- 32 | 32 - 212 | 32 - 400 | 32 - 600 | 32 - 750 | 32 - 900 | 32 - 1100 | 32 - 1300 | |

Alloy Steel (1% Cr. 1/2% Mo) | 7.7 | 8.0 | 8.4 | 8.8 | 9.2 | 9.6 | 9.8 | |

Mild Steel (0.1 - 0.2% C) | 7.1 | 7.8 | 8.3 | 8.7 | 9.0 | 9.5 | 9.7 | |

Stainless Steel (18% Cr. 8% Ni) | 10.8 | 11.1 | 11.5 | 11.8 | 12.1 | 12.4 | 12.6 | 12.8 |

Formula *(1)* can also be used with SI units. The expansion coefficient must be adjusted to ^{o}C.

*T(*^{o}C) = 5/9[T(^{o}F) - 32]*1 in (inch) = 25.4 mm**1 ft (foot) = 0.3048 m*- Expansion coefficients for some common materials

### Example - Thermal Expansion of an Alloy Steel Pipe

An alloy steel pipe with length* 100 feet* is heated from *32 to 212 ^{o}F*. The expansion coefficient is

*8 10*.

^{-6}(in/in^{o}F)The expansion of the pipe can be calculated as:

dl =(8 10^{-6}in/in^{o}F) (100 ft) (12 in/ft) ((212^{o}F) - (32^{o}F))

= 1.728 inches