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Thin Circular Ring - Temperature and Expanding Radius

Calculate change in pipe diameter with changed temperature

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Pipe or tube - change in diameter or radius with changed temperature

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 - 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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