le change.
Another common misconception about siphons is that because the atmospheric pressure is virtually identical at the entrance and exit, atmospheric pressure cancels, and therefore atmospheric pressure can't be pushing the liquid up the siphon. But equal and opposite forces may not completely cancel if there is an intervening force that counters some or all of one of the forces. In the siphon, the atmospheric pressure at the entrance and exit are both lessened by the force of gravity pulling down the liquid in both tubes, but the pressure on the down side is lessened more by the taller column of liquid on the down side. In effect, the atmospheric pressure coming up the down side doesn't entirely "make it" to the top to cancel all of the atmospheric pressure pushing up the up side. This effect can be seen more easily in the two carts being pushed up a hill example. Even though the guy on the left seems to have his push canceled entirely by the equal and opposite push from the guy on the right, the guy on the left's seemingly canceled push is still the source of the force to push the left cart up.
In some situations siphons do function in the absence of atmospheric pressure and via tensile strength – see vacuum siphons – and in these situations the chain model can be instructive. Further, in other settings water transport does occur via tension, most significantly in transpirational pull in the xylem of vascular plants. While water and other liquids may seem to have no tensile strength, because when a handful is scooped up and pulled on, the liquids narrow and pull apart effortlessly, liquid tensile strength in a siphon is possible when the liquid adheres to the tube walls. Any contamination on the tube walls, such as grease or air, or other minor influences such as turbulence or vibration, can cause the liquid to detach from the walls and lose all tensile strength.
In more detail, one can look at how the hydrostatic pressure varies through a static siphon, considering in turn the vertical tube from the top reservoir, the vertical tube from the bottom reservoir, and the horizontal tube connecting them (assuming a U-shape). At liquid level in the top reservoir, the liquid is under atmospheric pressure, and as one goes up the siphon, the hydrostatic pressure decreases (under vertical pressure variation), since the weight of atmospheric pressure pushing the water up is counterbalanced by the column of water in the siphon pushing down (until one reaches the maximum height of a barometer/siphon, at which point the liquid cannot be pushed higher) – the hydrostatic pressure at the top of the tube is then lower than atmospheric pressure by an amount proportional to the height of the tube. Doing the same analysis on the tube rising from the lower reservoir yields the pressure at the top of that (vertical) tube; this pressure is lower because the tube is longer (there is more water pushing down), and requires that the lower reservoir is lower than the upper reservoir, or more generally that the discharge outlet simply be lower than the surface of the upper reservoir. Considering now the horizontal tube connecting them, one sees that the pressure at the top of the tube from the top reservoir is higher (since less water is being lifted), while the pressure at the top of the tube from the bottom reservoir is lower (since more water is being lifted), and since liquids move from high pressure to low pressure, the liquid flows across the horizontal tube from the top basin to the bottom basin. Note that the liquid is under positive pressure (compression) throughout the tube, not tension.
Bernoulli's equation is considered in the scientific literature to be a fair approximation to the operation of the siphon. In non-ideal fluids, compressibility, tensile strength and other characteristics of the working fluid (or multiple fluids) complicate Bernoulli's equation.
Once started, a siphon requires no additional energy to keep the liquid flowing up and out of the reservoir. The siphon will draw liquid out of the reservoir until the level 