Comparing Volume of Oval vs Circle: Joe's First Post

[turbojoe]

This is my first post here and any help is appreciated. I belong to a drag racing forum and
this has been a hot topic of discussion.

If you have a 4 inch round pipe by 2 inches tall and insert the pipe into a vice and make it oval shaped it would somehow change the volume.

Please see video below.

http://www.youtube.com/watch?v=B24PtgujPOo&feature=youtu.be

thread from racing forum.

http://www.yellowbullet.com/forum/showthread.php?t=435379

I was under the assumption that the volume would not change. I suppose I'm wrong.

TIA,
Joe

 

[DivisionByZro]

The volume does change, this can be seen from the limit case that the pipe is crushed flat. If crushed flat enough, there is no volume left inside the pipe. However, to know how much the volume has changed at any instant before this limit case, well, that's a little more difficult. The crushing of the pipe distorts it irregularly and creates some kinks as well. It is very hard to model a situation like that exactly. To me, it seems hard to choose a best fitting ellipse to model the shape he has in the video. I'm not sure if you were looking for how to measure the volume directly (using integrals) or if you just wanted to know for sure if the volume does, in fact, decrease. Well it does (Technically the volume is infinite as the solid is not a closed one, one has to restrict the cylinder with two planes).

 

[turbojoe]

thanks for your response.. isoperimetric inequality seems to be the best explanation