Reading 1.6-2.3

This is some good stuff in this reading. So I've got a question but it's mainly about how the stress tensor has to do with thinking about in regard to fluids:

Is the stress tensor the location in your e.o.m. where you would effectively specify whether a blob of fluid or gunk is suspended in air as opposed to sitting in a tank? I mean, gravity has something to do with the difference between those situations. Ok--lets say I actually meant the difference between fluid sitting in a tank and fluid in a blob doing infinite free-fall into the fiery pits of Pandemonium. What about then?