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# Circular Ring - Temperature Expansion

## Calculate ring (or pipe) diameter expansion or contraction when temperature changes.

The circumference of a thin ring, a pipe or tube, can be expressed as

c0 = 2 π r0                                 (1)

where

c0 = initial circumference (m, inches)

π = 3.14...

r0 = initial radius (m, inches)

The change in circumference due to temperature change can be expressed as

dc = c1 - c

=  2 π r0 dt α                                 (2)

where

dc = change in circumference (m, inches)

c1 = final circumference (m, inches)

dt = temperature change (oC, oF)

α = linear expansion coefficient (mm/moC, μin/inoF)

The final circumference can be expressed as

c1 = 2 π r1                                           (3)

where

r1 = final radius (m, inches)

Equation 1, 2 and 3 can be expressed as

dc = 2 π r1 - 2 π r0

= 2 π r0 dt α

or transformed to

r1 = r0 dt α + r0

= r0 (dt α + 1)                                    (4)

Equation 4 can be modified with diameters to

d1 = d0 (dt α + 1)                                     (5)

### Example - Steel Pipe Diameter Temperature Expansion

A stainless steel pipe with nominal diameter 10 inches (outside diameter 10.750 inches) is heated from 68oF to 98oF. The expansion coefficient for stainless steel S30100 is 9.4 μin/inoF.

The final outside diameter can be calculated

d1 = d0 [dt α + 1]

= (10.750 in) [((98 oF) - (68 oF)) (0.0000094 in/inoF) + 1]

= 10.753 inches

### Circular Ring - Temperature Expansion Calculator

Calculate the final diameter of a thin circular ring after temperature expansion. The calculator can be used for metric and imperial units as long as the use of units are consistent.

d0 - initial diameter (m, mm, in)

dt - temperature difference (oC, oF)

α - temperature expansion coefficient (m/moC, mm/mmoC, in/inoF)

## Related Topics

• Temperature Expansion - Thermal expansion of pipes and tubes - stainless steel, carbon steel, copper, plastics and more.

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## Citation

• Engineering ToolBox, (2010). Circular Ring - Temperature Expansion. [online] Available at: https://www.engineeringtoolbox.com/thin-circular-ring-radius-temperature-change-d_1612.html [Accessed Day Mo. Year].

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