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 - c0
= 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)
