Type a line (30 m carbon steel 20 to 180 °C; 12 m stainless 316 from 15 °C to 95 °C; movement 40 mm 25 m carbon steel) or fill in the fields: the line and the fields stay in step.
Enter the length of a pipe run, the installation and the working temperature, and the linear expansion coefficient, your own or an example figure for one of five materials, and the calculator gives the free thermal expansion of the run in mm and in mm per metre. When the pipe cools below its installation temperature, the result is a contraction. In reverse, it gives the temperature difference at which the run moves by a stated amount, or the length of run for a stated movement. The working is shown with your numbers, a drawing sets the run cold against the run hot, and the result is a line you can copy or add to a request.
The movement only: the calculator does not size a bellows, an expansion joint or a pipe loop, works out no forces, anchor loads or stresses and names no allowable movement of any product. The coefficient is a mean over a temperature range; the pipe material certificate or the maker data govern.
delta L = alpha x L x delta T = 12 x 1e-6 1/K x 30000 mm x 160 K = 57.6 mm for a carbon steel run of 30 m from 20 to 180 °C, that is 1.92 mm per metre. The diameter and the wall do not enter. The 12 here is the example figure, a mean up to 100 °C; up to 180 °C the mean is higher, so the figure to use comes from the maker data.
When the working temperature is below the installation temperature, delta T is negative: a copper line of 20 m from 25 to -10 °C gives 16.8 x 1e-6 x 20000 mm x (-35 K) = -11.76 mm, a contraction of 11.76 mm. The copper figure is a mean from 20 to 100 °C, so below 20 °C it is an estimate.
delta T = delta L / (alpha x L): 40 mm on 25 m of carbon steel is 133.3 K. L = delta L / (alpha x delta T): 50 mm from 20 to 180 °C is 26.04 m. Both use the example figure 12, a mean up to 100 °C; above 100 °C the mean is higher.
| Material | Mean over | 1e-6 1/K | mm/m per 100 K | mm on 10 m at 100 K |
|---|---|---|---|---|
| Carbon steel | 0 to 100 °C | 12.0 | 1.20 | 12.0 |
| Stainless steel 1.4401 / 316 | 20 to 100 °C | 16.0 | 1.60 | 16.0 |
| Copper Cu-DHP | 20 to 100 °C | 16.8 | 1.68 | 16.8 |
| Copper-nickel 90/10 | 20 to 300 °C | 17.0 | 1.70 | 17.0 |
| Aluminium EN AW-6061 | 20 to 100 °C | 23.6 | 2.36 | 23.6 |
These are examples, not the figures of your pipe: the coefficient depends on the alloy, and the mean coefficient rises with temperature, so a mean over a range up to a higher temperature is higher. There is no example for 304 (1.4301) or for plastic pipes, where the references differ; enter the figure from the certificate.
The movement is plain arithmetic: delta L = alpha x L x delta T, and the reverse. Each example coefficient is offered only where two independent references agree to 0.5 x 1e-6 1/K over the stated range: for carbon steel, the design value for steel in EN 1993-1-1 and handbook data for low carbon steels; for stainless steel 1.4401 / 316, the EN 10088-1 table as a stainless steel association gives it and a supplier grade data sheet; for copper Cu-DHP, copper-nickel 90/10 and aluminium EN AW-6061, the material data of two different companies and a metals handbook. For 1.4301 / 304 the references differ by 1.2 x 1e-6 1/K (16.0 and 17.2), so there is no example. 1 ft = 0.3048 m and 1 in = 25.4 mm are exact by definition. The pipe material certificate and the maker data always come first.
The free movement is delta L = alpha x L x delta T: the mean linear expansion coefficient, times the length of the run, times the temperature difference between installation and work. A carbon steel run of 30 m laid at 20 °C and working at 180 °C, with alpha 12 x 1e-6 1/K, grows by 12 x 1e-6 x 30000 mm x 160 K = 57.6 mm, that is 1.92 mm per metre. The 12 is the example figure for carbon steel, a mean up to 100 °C; the mean up to 180 °C is higher, so for a real run take the figure for the range from the maker data. The diameter and the wall do not enter: a free run grows by the same amount whatever its size.
The mean coefficient over your temperature range, from the pipe material certificate, the pipe standard or the maker data. It depends on the alloy and on the range: a mean over a wider range is higher, for stainless steel 1.4401 16.0 x 1e-6 1/K from 20 to 100 °C and 16.5 from 20 to 200 °C in the EN 10088-1 table. The page offers example figures only where two references agree to 0.5 x 1e-6 1/K: carbon steel 12.0, stainless steel 1.4401 / 316 16.0, copper Cu-DHP 16.8 and aluminium EN AW-6061 23.6 (each up to 100 °C), and copper-nickel 90/10 17.0 (20 to 300 °C). There is no pick for 304, where the references differ by 1.2, nor for plastic pipes, where the figures differ by grade and maker: enter the figure from the certificate.
Then delta T is negative and the run contracts. A copper line of 20 m laid at 25 °C and cooled to -10 °C: 16.8 x 1e-6 x 20000 mm x (-35 K) = -11.76 mm, a contraction of 11.76 mm. The copper figure is a mean from 20 to 100 °C, so below 20 °C it is an estimate; the maker data govern.
Turn the formula round. The temperature difference is delta T = delta L / (alpha x L): 40 mm on a 25 m carbon steel run is 40 / (12 x 1e-6 x 25000) = 133.3 K, so from 20 °C about 153.3 °C. The length is L = delta L / (alpha x delta T): 50 mm on carbon steel from 20 to 180 °C is 50 / (12 x 1e-6 x 160) = 26042 mm, about 26.04 m. Both use the example figure 12, a mean up to 100 °C; above that the mean is higher and the maker data govern.
No. It states the free movement of a straight run between two points only. It does not size a bellows, an expansion joint or a pipe loop, and it gives no forces, anchor loads, stresses or allowable movements of any product: the maker of the joint or the piping designer works those out from the movement, the pipe size, the media, the pressure and the temperatures. The result line carries the movement to a request, with room for the pipe size and the media.
The length in m, mm, cm, ft or in (1 ft = 0.3048 m and 1 in = 25.4 mm exactly), the temperatures in °C and a difference in K (a difference of 1 °C is 1 K), the movement in mm, cm, m or in. The coefficient in 1e-6 1/K (12 or 12e-6), in mm/m per 100 K (1.2) or in mm/(m K) (0.012), which are the same figure for carbon steel. Temperatures in °F are not taken.
The calculator works out the movement only. When a bellows expansion joint or other piping parts are needed, send the movement, the pipe size, the media, the pressure and the temperatures, with a photograph of the old joint and its plate if there is one, and Vessel Core checks the details before an offer goes back.
