A cast iron pipe has an inside diameter of d= 208mm and an outside diameter of D= 236mm. The length of the pipe is L= 3.0m. The coefficient of thermal expansion for cast iron is α1 = 12.1 * 10^-6/°C. Determine the dimension changes caused by an increase in temperature of 70°C.

Question

A cast iron pipe has an inside diameter of d= 208mm and an outside diameter of D= 236mm. The length of the pipe is L= 3.0m. The coefficient of thermal expansion for cast iron is [latex]{ \alpha }_{ 1 }=12.1 imes { 10 }^{ -6 }/°C[/latex]. Determine the dimension changes caused by an increase in temperature of 70°C.

Accepted Answer

The thermal strain caused by a temperature increase of 70°C is given by
[latex]{ \varepsilon }_{ T }=\alpha \Delta T=\left( 12.1 imes { 10 }^{ -6 }/°C ight) \left( 70°C ight) =0.000847mm/mm[/latex]
The dimension changes caused by a temperature increase of 70°C are
[latex]\Delta D={ \varepsilon }_{ T }D=\left( 0.000847mm/mm ight) \left( 236mm ight) =0.1999mm [/latex]
[latex]\Delta d={ \varepsilon }_{ T }d=\left( 0.000847mm/mm ight) \left( 208mm ight) =0.1762mm[/latex]
[latex]\Delta L={ \varepsilon }_{ T }L=\left( 0.000847mm/mm ight) \left( 3.0m ight) =0.002541\quad m=2.54mm[/latex]

Question : A cast iron pipe has an inside diameter of d= 208mm and an o...

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