Chicken Waterer using Communicating Vessels First, I apologize if I don't use proper terms. I'm not very educated when it comes to physics. That being said...
I want to make a watering station for my chickens. I have built the attached image.

My problem is, when the bucket is filled, lid on, and valve turned on, the water doesn't stop flowing when it goes above the hole I drilled in the downpipe. My assumption was that once the hole was covered, it wouldn't get air to drain, and it would stop. What's more, bubbles come out the bottom.
Assuming the bucket is air-tight, is this because the head pressure is so great it forces itself out or?? That's all I got. I've searched for hours for an answer, without knowing the proper terms to search for, I can't find anything.
Thanks, in advance!
UPDATE
The reason I put this valve in is so I can stop flow, take the lid off and fill the bucket without it flowing out of control down to the watering portion. Would a check valve accomplish this, or would it not have enough pressure to work correctly?
 A: Even an air-tight bucket lid will not keep the water from spilling out of the trough.  As water is pulled downward, a partial vacuum forms between the lid of the bucket and the surface of the water.  This is similar to blocking the tip of a syringe with your finger and pulling the plunger - air is simply too compressible/stretchable to be used in this fashion.
I recommend installing a float-valve at the bottom of the vertical 3/4" pipe.
A: Have a look at the tube arrangement for a hamster waterer (sealed upended vertical tube full of water with an exit nozzle of smaller diameter than the tube). this principle (sometimes referred to as a "bubbler") may be of use in the design of your watering system. 
A: The system as described should work as planned.  
Assume that the bucket is only partially filled with water when the lid is sealed in place and the valve opened.
The pressure at the bottom of the fill tube from the combination of air and water in the delivery system will exceed atmospheric pressure, causing water to flow out the fill tube and fill the drinking trough.  As the water flows out of the bucket, the air in the bucket will expand and the air pressure in the bucket will drop.  Eventually, the combined pressure at the bottom of the fill tube will drop to atmospheric pressure, and the initial outflow will stop.  The closer to full the bucket is at the beginning, the less the amount of this outflow.
When the thirsty chickens drop the level in the trough below the bottom of the fill tube, some air will work its way into the fill tube and up into the bucket.  Here, the air raise the pressure in the bucket.  More water will then flow out of the fill tube (sealing off the flow of air into the fill tube), the air in the bucket will expand, its pressure will drop back down, and the outflow will stop.
One possible explanation for the constant outflow you experience is leakage of air into the delivery system.  Apart from the seal around the lid of the bucket, I see six places where air could leak into the delivery system: both sides of the elbow, both sides of the valve, the packing on the valve stem, and the connection to the bottom of the bucket.  At each of these, the system is at less than atmospheric pressure.  Air sucked in here could show itself as bubbles at the drinking trough.
