[The Goober]

So after posting this, I looked at an actual smooth stream of water from my faucet and noticed something - at the very bottom of the stream, the stream stopped narowing, and instead it broke up and started mixing with air. Clearly, there is some point (before reaching terminal velocity) where the surface tension is not enough to keep the stream as a solid column of water and instead the density does go down as the water breaks into smaller droplets. So, the viscosity / surface tension does play a pretty big part here. I imagine that if one poured out a nice big stream of syrup from a very high distance, you would see the stream get pretty damn narrow before it starts to break up (and it may not break up at all if its still a stream when it reaches terminal velocity). I think this is the only reason that it would change things if you did this in a vacuum - without air, there is no terminal velocity and even the most viscous liquid stream would eventually break up into smaller droplets.