# How to calculate the thermal expansion of hollow cylinder

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?

• You should show some effort towards a solution. Nov 24, 2021 at 6:19
• 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 Nov 24, 2021 at 6:24
• 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.
– Abel
Nov 24, 2021 at 12:47
• 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.
– r13
Nov 24, 2021 at 16:18

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.