This isn't a homework problem janny boy so please don't delete it. This is a personal project, I'm building a machine and need to attain a better understanding of the physics before I'm able to build a machine that can get the job done. (see this thread if you really give a fuck http://boards.4channel.org/g/thread/73483873)

Suppose you've got some material jammed in a pipe or a hole of some sort, that is it's surrounded on all sides by metal, it has some depth L, and some cross sectional diameter D. What is the theoretical calculation you could do that would quantify how much force you'd need to push this thing out?

In the orientation my machine will be in, the material is held up entirely by friction, the weight of the material itself is negligible. I've been looking into some pressure vessel equations as a guide to understand the situation when it's static, but I'm not sure if that is even valid. The material is hard and doesn't infinitely deform under shear, so I don't think any of the equations from fluid mechanics would be useful as a guide either.

I have many questions that will follow once I properly understand how much force is required to push the material out, but those can wait for other threads.