# Limit of Acrylic Rod embedded in a Hole

Let's suppose an acrylic sheet with a hole on it

I want to insert something into that hole, let's say an acrylic rod

The hole has a diameter of x and the rod has a diameter of x-y. If I increase y, the cylinder is not going to enter, if I decrease y, is not going to embed, so, How do I know what are the limit values of y so that the cylinder stays in the hole?

I am not quire sure about how to address this problem, but I find it many times in my life

Should I use a probability distribution where y is the probability of the cylinder being embedded correctly?, How much does the material of the cylinder and the sheet with the hole matter? How much the values of y change if the value of X is increased (A hole with a bigger diameter)?, Could you give suggestions of how to solve this problem

Edit. I am asking because I want to make an acrylic case for an electronic project, like this:

The acrylic sheets I am using have a diameter of 2.5 mm and 1.75 mm .. So I would like to know what should be the size of the holes .. And a way to apply the same method for any other thickness .. The holes are not exactly circles, they are rectangles, but I think it is easy to analyse it with circles and rods ..