Well, you can see where all of this is leading. Let’s turn the
can around fill it with hot not-very-dense air and we’ll get a
similar pressure distribution (Figure 7). Here again, the pressure
at the throat is zero and increases as you go up toward the crown
due to all of the hot little molecules pushing up on each other.
Unlike water, however, air is somewhat compressible. You don’t
quite get nice linear behavior in pressure with height above the
throat (For you purists, the pressure differential gradient in a
balloon is exponential just like the Earth’s atmosphere). For our
purposes though, we will assume it to be linear. This will work
well enough to give us some nice approximations.