# Pipes and Tubes - Temperature Expansion

## Pipes expands when heated and contracts when cooled. The expansion of the pipes can be expressed with the expansion formula

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The temperature expansion of pipes depends on the start and final temperature of the pipe and the expansion coefficient of the piping material at the actual temperature. The general 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)

Mean expansion coefficient may vary with temperature as:

Mean Expansion Coefficient - α - (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 Heated Alloy Steel

*100 feet* of alloy steel pipe 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 feet) (12 in/ft) ((212^{o}F) - (32^{o}F))

= 1.728 inches

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