There's an old expression, "water seeks its level." The physics behind water's tendency to flow until all of it is at the same level is related to potential energy— energy stored in forces such as those of gravity. The higher water is, the more gravitational potential energy it has. Water, like everything else, accelerates in whatever direction reduces its total potential energy as quickly as possible. In the case of water that's not level in an open container, the higher water accelerates toward the lower water so that the higher water reduces its potential energy as quickly as possible. Open water always accelerates so as to level itself.
It's easy to understand how water seeks its level when you pour water from a higher open container to lower one. But when you connect those two containers with a pipe, the level-seeking process becomes much more mysterious. As long as the water goes only downhill through the pipe, the mystery seems minimal, but sometimes the pipe starts upward before it bends downward. This siphon shape is very puzzling. What allows the water to go upward as part of its level-seeking process?
The answer lies in the fact that water has more than one type of potential energy. In addition to gravitational potential energy, water has potential energy associated with its pressure. High-pressure water has more potential energy than low-pressure water, which explains why water tends to accelerate from high pressure toward low pressure—from high potential energy to low potential energy—even in the absence of gravity. Moreover, the pressure of water in a sealed pipe decreases with altitude, so the higher you look in that pipe, the less pressure potential energy you'll find. Because of this pressure effect, the total potential energy (gravitational plus pressure) of water in a closed pipe doesn't change, even as that water rises a short distance upward inside the pipe! Sure, the gravitational potential energy of the water is increasing as the water rises, but its pressure potential energy is decreasing by an equal amount.
In a siphon, where the pipe goes first upward from the higher container and then downward to the lower container, the weight of water in descending portion of the pipe actually decreases the pressure inside the rising portion of the pipe. As a result of this extra pressure drop, water in the high container can reduce its total potential energy by accelerating toward and then through the pipe. Water begins flowing through the pipe, even though it has to go upward for a short time during that passage. Surprisingly enough, its total potential energy is decreasing the whole time, even as it rises, because the pressure potential energy drops quickly enough in the pipe to more than make up for the rise in gravitational potential energy. This continuous drop in total potential energy helps to keep the water flowing smoothly, despite some of the slowing effects of friction in the pipe. As always, water seeks its level and the higher container empties into the lower container.
This siphon effect relies on atmospheric pressure to allow the pressure and pressure potential energy to drop as the water travels upward inside the sealed pipe. But eventually the pressure of the rising water reaches zero and no further reductions in pressure and pressure potential energy are possible. That failure of the siphon effect occurs when the water is about 30 feet (10 meters) above the higher container. You can't use a siphon to lift water higher than 30 feet because above that height, an empty region will develop at the top of the pipe and stop the siphon process.
Answered by Louis A. Bloomfield of the University of Virginia