I was thinking about the pressure build up in a system that is squeezed equally from all sides (or at least in two dimensions, like squeezing a tube of toothpaste), and I ran into a conundrum. If the pressure increases as the area decreases, then the pressure inside a circle that's squeezed radially should approach infinity as we approach the center of the circle. I'm attaching a picture to illustrate this. View attachment Pressure Pic.bmp Consider the area as the circumference of the circle - the outside of the tube of toothpaste, for example. As I squeeze it with any force at all, doesn't the pressure (P = F/A) become greater and greater without limit as we consider smaller and smaller inner circles? When I squeeze the tube, why doesn't the lid burst off the toothpaste under billions of Pascals of pressure, or why doesn't a needle-thin stream of toothpaste spray out from the center when the lid's off? What's happening to prevent that? I understand that viscosity will try to limit this, but again, at the very center of the tube, shouldn't the pressure approach infinity?