I found recently that water fills a bottle quicker through only observation if I hold the tube away from the filling water than if I leave the tube inside the bottle. why does that happen? does potential energy have anything to do with this? 
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$\begingroup$ If you leave the tube inside, the water doesn't even fully leave the tube - so be a little more precise in which sense you understand "filling the bottle". If you just mean you stick the tube in and wait till no water flow happens anymore, then it's because if the water has to leave the tube and enter the bottle underneath, the water cloumn in the bottle presses against the water column inside the tube. $\endgroup$– Nikolaj-KCommented Oct 21, 2013 at 11:00
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I'm not totally clear what exactly you are asking, but I think the answer is backpressure.
This "purifier" thing is apparently just a source emitting water out of the bottom end of a vertical tube. In your right drawing, the pressure at the bottom of the tube trying to push the water back up the tube is just the ambient air pressure.
In the left drawing, the top of the liquid in the tank is at ambient air pressure, so the pressure at the end of the tube is that plus the water pressure at the depth of the end of the tube. This higher pressure pushing back up the tube slows the water flow.
answered Oct 21, 2013 at 12:30