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Apologies first, if this has been asked and answered. What I want to do is create a constant flow of water for my dog bowl. I dont want to use a float valve or anything else that might fail since this is on the 2nd floor of my house. My thoughts are to use a sealed 5 gallon bucket, with a flexible line from the bottom of the 5 gallon bucket, that drains into the dog bowl. If the end of the line from the bucket is placed into the dog bowl, will water drain until it reaches that line? What would keep it from overflowing? Since it is an air tight supply container, once water covers the other end of the line in the bowl, would that lack of air supply stop the water from draining? As long as the supply bucket is higher than the bowl, it would drain automatically until the water covers the line and keeps air from displacing water in the supply bucket. Or, would the water continue to drain into the bowl?

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This will work as long as the line slopes downward the entire way from the bottom of the bucket to the bowl, and the diameter of the line is large enough--say at least a couple of centimeters. If you allow any local maxima in the elevation of the line or it's too skinny, the water will not continue to come out of the bucket after a partial vacuum develops inside. There will be no way for air to get in. A large line sloping upward the whole way will allow bubbles to travel up it, until as you suggest the bottom end gets sealed by the rising water level.

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