Thin Circular Ring - Temperature and Expanding Radius
Calculate change in pipe diameter with changed temperature
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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 - Temperature and Change in Steel Pipe Diameter
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
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