# Thermal expansion of a metal round disk with hole in the middle

1. Sep 16, 2010

### tbone_nl

This is my first post on this forum because I have a question that I cannot seem to answer myself.

At my working place we have a machine where a metal conveyor belt is running through a section of the machine where the temperature is constant at 320 degrees Celcius. On this conveyor belt are metal round disks with a hole in the middle.

I know that when such a disk is heated from room temperature to higher temperature, the inner diameter of the disk (so in fact the diameter of the hole) gets smaller (right ?)

I also know that the outside diameter of the disk itself will get larger.

But the question is: how do I calculate this ?

Let's say the outer diameter of the disk is 10 cm and the inner diameter of the hole is 8 cm at room temperature. How do I calculate these diameters at 320 C.

I need an answer badly because inside the hot part of the machine there is resitricted space and we want to put disks through the machine that fit at room temperature, but we are not sure if they fit at high temperature. We can easily test this, but there is a risk that we damage the machine if the disks would become to large.

The disks are in the machine long enough to reach 320 C themselves before they arrive at this restriction.

2. Sep 16, 2010

### nasu

All dimensions (inner diameter or radius included) will increase when temperature is increased.
The hole gets bigger when the temperature is increased.
A good approximation is given by the formula for linear expansion
l=lo(1+alpha * deltaT)
where lo is the initial value of the linear dimension (diameter, thickness, etc), alpha is the coefficient of thermal expansion for the material and deltaT is the increase in temperature.
For common metals alpha has typical values of the order of 10^(-5). So for a temperature increase of 300 Celsius, I would expect that the change in dimensions will be of the order of a few percent.

3. Sep 16, 2010

### Redbelly98

Staff Emeritus
Actually, no, the hole gets larger. This is a common misconception.

4. Sep 17, 2010

### Lsos

Yeah, it get larger. They even asked me this question at my current job interview. I answered that "it gets larger" even though I did have a hint of a doubt in my mind.

The guy then said "are you sure?"....but luckily he started laughing before I managed to say "No...."