Dane, what on earth!!!! What is with the equation? Are you like some kind of techy mathmetician (LOL, spelling?). I don't do equations. Regardless, sounds cool.
I think that the bees do not like to drink from water that is too close to their hive. Not sure, but I'm thinking that they like something a little farther away better. Maybe they are worried about feces in the water that is close (their own poopies) to their hive. I know when I first started with bees I had a container right inside their yard, never once saw one in it. Moved it about 20 feet away and there were a few, but not many. Probably didn't like what I had.
When I was out working in my new bee barn yesterday and day before I saw a whole bunch of bees, and I mean lots and lots, drinking from the stagnant mucky muck from some run off from the bathtub that the ducks love to swim in. Oh brother. To me it didn't even look like it was very wet. But they were there, sucking up moisture like there was no tomorrow. Go figure that one. I guess they filter mucky junk and take what they need. Have a wonderful day, great life. Cindi