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
c_{0} = 2 π r_{0} (1)
where
c_{0} = initial circumference (m, inches)
π = 3.14...
r_{0} = initial radius (m, inches)
The change in circumference due to temperature change can be expressed as
dc = c_{1 } c_{0 }
_{ } = 2 π r_{0} dt α (2)
where
dc = change in circumference (m, inches)
c_{1} = final circumference (m, inches)
dt = temperature change (^{o}C, ^{o}F)
α = linear expansion coefficient (mm/m^{o}C, μin/in^{o}F)
The final circumference can be expressed as
c_{1} = 2 π r_{1 } (3)
where
r_{1} = final radius (m, inches)
Equation 1, 2 and 3 can be expressed as
dc = 2 π r_{1}  2 π r_{0}
= 2 π r_{0} dt α
or transformed to
r_{1} = r_{0} dt α + r_{0}
= r_{0} (dt α + 1) (4)
Equation 4 can be modified with diameters to
d_{1} = d_{0 }(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 68^{o}F to 98^{o}F. The expansion coefficient for stainless steel S30100 is 9.4 μin/in^{o}F.
The final outside diameter can be calculated
d_{1} = d_{0 }[dt α + 1]
= (10.750 in) [((98 ^{o}F)  (68 ^{o}F)) (0.0000094 in/in^{o}F) + 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.
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