# Thermal Expansion

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### Description

This sheet is a very simple and quick way to calculate linear thermal expansion in typical metal piping materials. Also valid for non-piping components of the same type of materials.

Linear thermal expansion occurs when materials expand or contract as a result of temperature changes. To calculate the linear thermal expansion of a metal pipe, you'll need to know the pipe's initial length, the material's coefficient of linear thermal expansion, and the change in temperature.

The formula for linear thermal expansion is:

ΔL = L0 * α * ΔT

Where:

ΔL = Change in length due to thermal expansion (inches, mm) L0 = Initial length of the pipe (inches, mm) α = Coefficient of linear thermal expansion (inches/inch/°F, mm/mm/°C) ΔT = Change in temperature (°F, °C)

Coefficients of linear thermal expansion (α) for some typical metal piping materials are:

• Carbon steel: 6.5 x 10^-6 inches/inch/°F (11.7 x 10^-6 mm/mm/°C)
• Stainless steel: 9.6 x 10^-6 inches/inch/°F (17.3 x 10^-6 mm/mm/°C)
• Copper: 9.3 x 10^-6 inches/inch/°F (16.6 x 10^-6 mm/mm/°C)
• Aluminum: 13 x 10^-6 inches/inch/°F (23.4 x 10^-6 mm/mm/°C)

Please note that these coefficients are approximate and can vary depending on the specific alloy, manufacturing process, and temperature range.

To calculate the linear thermal expansion, follow these steps:

1. Determine the initial length (L0) of the pipe.
2. Determine the change in temperature (ΔT).
3. Identify the coefficient of linear thermal expansion (α) for the specific metal pipe material.
4. Plug the values into the formula and calculate the change in length (ΔL).

Example:

Calculate the linear thermal expansion of a 100-foot-long carbon steel pipe when the temperature increases by 50°F (28°C).

L0 = 100 ft (initial length) ΔT = 50°F (change in temperature) α = 6.5 x 10^-6 inches/inch/°F (coefficient of linear thermal expansion for carbon steel)

ΔL = L0 * α * ΔT ΔL = 100 ft * (12 inches/ft) * (6.5 x 10^-6 inches/inch/°F) * 50°F ΔL ≈ 0.39 inches

The carbon steel pipe would expand approximately 0.39 inches due to the temperature increase.

07 Apr 2009
25 Apr 2023
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