Circular Ring - Temperature Expansion
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 68 oF to 98 oF. 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.
Related Topics
• Temperature Expansion
Thermal expansion and expansion coefficients. Expansion pipes and tubes made of stainless steel, carbon steel, copper, plastics and more.
Related Documents
Fixed Pipes - Stress vs. Change in Temperature
Temperature changes introduces stress fixed pipes.
Linear Thermal Expansion Coefficients of Materials
Linear thermal expansion coefficients of common materials, including metals, plastics, and composites.
Linear Thermal Expansion: Formula, Coefficients & Calculator
Online linear temperature expansion calculator.
Metals - Temperature Expansion Coefficients
Thermal expansion coefficients metals.
Pipes and Tubes - Temperature Expansion
Pipes expands when heated and contracts when cooled and the expansion can be expressed with the expansion equation.
Piping Materials - Temperature Expansion Coefficients
Temperature expansion coefficients for materials used in pipes and tubes like aluminum, carbon steel, cast iron, PVC, HDPE and more.
Pressfit Pipes - Expansion Loops
Temperature expansion loops with pressfit piping.
PVC, CPVC, Carbon Steel, Stainless Steel and Fiberglass Pipes - Thermal Expansion Diagrams
Thermal expansion of PVC, CPVC, Carbon and Stainless Steel and Fiberglass pipes.
Safety Signals - Recommended Colors
American National Standards Institutes schedule for safety colors marking physical hazards.
Steam Pipes - Thermal Expansion
Thermal expansion of steam pipes heated from room temperature to operation temperature (mm pr. 100 m pipe).
Steel Pipes - Temperature Expansion
Calculate temperature expansion with carbon steel pipes.
Thermal Expansion of Steam Pipes - (inches)
Expansion of steam pipes heated from room temperature to operation temperature.
Volumetric (Cubic) Thermal Expansion
Volumetric temperature expansion calculator.