Outer diameter = 256 mm
Inner diameter = 230 mm
The material is Aluminum
Temperature ranges from 23 °C to 200 °C.
Solid cylinder formula is, d1=d0(dt*α+1).
Where, α = 15.2 ×10-6 /K (approx)
How to consider when the cylinder is hollow?
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1$\begingroup$ You should show some effort towards a solution. $\endgroup$– Solar MikeNov 24, 2021 at 6:19
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$\begingroup$ I have calculated for solid cylinder, I dont know how to consider, when it is hollow. And I am interested to know, how much expansion is happening in inner diameter $\endgroup$– Kanaga Senthil RajaNov 24, 2021 at 6:24
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$\begingroup$ if you have considered for a solid cylinder, I ask: what is its height after thermal expansion and why? Think about what is happening in this even, unloaded thermal expansion. It is certainly different from reality where gradients and forces are everywhere. $\endgroup$– AbelNov 24, 2021 at 12:47
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1$\begingroup$ A hollow tube (or cylinder) of same material and same dimensions as a solid object will expand exactly equally. They will both grow the same amount. The hole's diameter will also increase in proportion. $\endgroup$– r13Nov 24, 2021 at 16:18
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1 Answer
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Assuming the cylinder wall is thin an approximate method to calculate the expansion of circumference is:
Let's call the initial circumference, $C_0=2\pi r_0=2\pi* 230mm .$
The change in diameter due to temperature is $$ \ d_c=c_1 - c_0= 2 π r_0 \Delta t *α \quad\\ \rightarrow dc = 2 π r_1 - 2 π r_0 = 2 π r_0 \Delta t* α $$.
- $\alpha=$ linear expansion coefficient.
