I've been doing rather insane amounts of preserving tomatoes in various ways lately. And whether I'm making Tomato Conserva or Sun Dried Tomatoes, I end up with a big bowl of seeds and watery juice after I've prepped the tomatoes.
I really don't like food waste, so I've taken to straining it. The result is a fresh, flavorful, refreshing tomato beverage.
If there weren't a thicker, heavier thing already widely known as "tomato juice," I'd call this juice, but since that name is taken, I think "tomato water" describes this beautifully. And hey, if you want to jazz it up with a shot of vodka or gin and a bit of pepper, I won't tell anyone.