Siphon
A siphon is any of a wide variety of devices that involve the flow of liquids through tubes. In a narrower sense, the word refers particularly to a tube in an inverted "U" shape, which causes a liquid to flow upward, above the surface of a reservoir, with no pump, but powered by the fall of the liquid as it flows down the tube under the pull of gravity, then discharging at a level lower than the surface of the reservoir from which it came.
There are two leading theories about how siphons cause liquid to flow uphill, against gravity, without being pumped, and powered only by gravity. The traditional theory for centuries was that gravity pulling the liquid down on the exit side of the siphon resulted in reduced pressure at the top of the siphon. Then atmospheric pressure was able to push the liquid from the upper reservoir, up into the reduced pressure at the top of the siphon, like in a barometer or drinking straw, and then over. However, it has been demonstrated that siphons can operate in a vacuum and to heights exceeding the barometric height of the liquid. Consequently, the cohesion tension theory of siphon operation has been advocated, where the liquid is pulled over the siphon in a way similar to the chain fountain. It need not be one theory or the other that is correct, but rather both theories may be correct in different circumstances of ambient pressure. The atmospheric pressure with gravity theory cannot explain siphons in vacuum, where there is no significant atmospheric pressure. But the cohesion tension with gravity theory cannot explain gas siphons, siphons working despite bubbles, and the flying droplet siphon, where gases do not exert significant pulling forces, and liquids not in contact cannot exert a cohesive tension force.
All known published theories in modern times recognize Bernoulli's equation as a decent approximation to idealized, friction-free siphon operation.
History
reliefs from 1500 BC depict siphons used to extract liquids from large storage jars.Physical evidence for the use of siphons by Greeks are the Justice cup of Pythagoras in Samos in the 6th century BC and usage by Greek engineers in the 3rd century BC at Pergamon.
Hero of Alexandria wrote extensively about siphons in the treatise Pneumatica.
The Banu Musa brothers of 9th-century Baghdad invented a double-concentric siphon, which they described in their Book of Ingenious Devices. The edition edited by Hill includes an analysis of the double-concentric siphon.
Siphons were studied further in the 17th century, in the context of suction pumps, particularly with an eye to understanding the [|maximum height] of pumps and the apparent vacuum at the top of early barometers. This was initially explained by Galileo Galilei via the theory of Horror vacui , which dates to Aristotle, and which Galileo restated as resintenza del vacuo, but this was subsequently disproved by later workers, notably Evangelista Torricelli and Blaise Pascal – see barometer: history.
Theory
A practical siphon, operating at typical atmospheric pressures and tube heights, works because gravity pulling down on the taller column of liquid leaves reduced pressure at the top of the siphon. This reduced pressure at the top means gravity pulling down on the shorter column of liquid is not sufficient to keep the liquid stationary against the atmospheric pressure pushing it up into the reduced-pressure zone at the top of the siphon. So the liquid flows from the higher-pressure area of the upper reservoir up to the lower-pressure zone at the top of the siphon, over the top, and then, with the help of gravity and a taller column of liquid, down to the higher-pressure zone at the exit.The chain model is a useful but not completely accurate conceptual model of a siphon. The chain model helps to understand how a siphon can cause liquid to flow uphill, powered only by the downward force of gravity. A siphon can sometimes be thought of like a chain hanging over a pulley, with one end of the chain piled on a higher surface than the other. Since the length of chain on the shorter side is lighter than the length of chain on the taller side, the heavier chain on the taller side will move down and pull up the chain on the lighter side. Similar to a siphon, the chain model is obviously just powered by gravity acting on the heavier side, and there is clearly no violation of conservation of energy, because the chain is ultimately just moving from a higher to a lower location, as the liquid does in a siphon.
There are a number of problems with the chain model of a siphon, and understanding these differences helps to explain the actual workings of siphons. First, unlike in the chain model of the siphon, it is not actually the weight on the taller side compared to the shorter side that matters. Rather it is the difference in height from the reservoir surfaces to the top of the siphon, that determines the balance of pressure. For example, if the tube from the upper reservoir to the top of the siphon has a much larger diameter than the taller section of tube from the lower reservoir to the top of the siphon, the shorter upper section of the siphon may have a much larger weight of liquid in it, and yet the lighter volume of liquid in the down tube can pull liquid up the fatter up tube, and the siphon can function normally.
Another difference is that under most practical circumstances, dissolved gases, vapor pressure, and lack of adhesion with tube walls, conspire to render the tensile strength within the liquid ineffective for siphoning. Thus, unlike a chain, which has significant tensile strength, liquids usually have little tensile strength under typical siphon conditions, and therefore the liquid on the rising side cannot be pulled up in the way the chain is pulled up on the rising side.
An occasional misunderstanding of siphons is that they rely on the tensile strength of the liquid to pull the liquid up and over the rise. While water has been found to have a significant tensile strength in some experiments, and siphons in vacuum rely on such cohesion, common siphons can easily be demonstrated to need no liquid tensile strength at all to function. Furthermore, since common siphons operate at positive pressures throughout the siphon, there is no contribution from liquid tensile strength, because the molecules are actually repelling each other in order to resist the pressure, rather than pulling on each other.
To demonstrate, the longer lower leg of a common siphon can be plugged at the bottom and filled almost to the crest with liquid as in the figure, leaving the top and the shorter upper leg completely dry and containing only air. When the plug is removed and the liquid in the longer lower leg is allowed to fall, the liquid in the upper reservoir will then typically sweep the air bubble down and out of the tube. The apparatus will then continue to operate as a normal siphon. As there is no contact between the liquid on either side of the siphon at the beginning of this experiment, there can be no cohesion between the liquid molecules to pull the liquid over the rise. It has been suggested by advocates of the liquid tensile strength theory, that the air start siphon only demonstrates the effect as the siphon starts, but that the situation changes after the bubble is swept out and the siphon achieves steady flow. But a similar effect can be seen in the flying-droplet siphon. The flying-droplet siphon works continuously without liquid tensile strength pulling the liquid up.
The siphon in the video demonstration operated steadily for more than 28 minutes until the upper reservoir was empty. Another simple demonstration that liquid tensile strength is not needed in the siphon is to simply introduce a bubble into the siphon during operation. The bubble can be large enough to entirely disconnect the liquids in the tube before and after the bubble, defeating any liquid tensile strength, and yet if the bubble is not too big, the siphon will continue to operate with little change as it sweeps the bubble out.
Another common misconception about siphons is that because the atmospheric pressure is virtually identical at the entrance and exit, the atmospheric pressure cancels, and therefore atmospheric pressure cannot 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 each tube, 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 does not 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 example of two carts being pushed up opposite sides of a hill. As shown in the diagram, even though the person on the left seems to have his push canceled entirely by the equal and opposite push from the person on the right, the person 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 due to tensile strength – see [|vacuum siphons] – and in these situations the chain model can be instructive. Further, in other settings water transport does occur due to tension, most significantly in transpirational pull in the xylem of vascular plants. 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. But liquid tensile strength in a siphon is possible when the liquid adheres to the tube walls and thereby resists narrowing. Any contamination on the tube walls, such as grease or air bubbles, 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. At liquid level in the top reservoir, the liquid is under atmospheric pressure, and as one goes up the siphon, the hydrostatic pressure decreases, since the weight of atmospheric pressure pushing the water up is counterbalanced by the column of water in the siphon pushing down – 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 tube; this pressure is lower because the tube is longer, 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, while the pressure at the top of the tube from the bottom reservoir is lower, 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. The liquid is under positive pressure 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 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 falls below the intake, allowing air or other surrounding gas to break the siphon, or until the outlet of the siphon equals the level of the reservoir, whichever comes first.
In addition to atmospheric pressure, the density of the liquid, and gravity, the [|maximal height] of the crest in practical siphons is limited by the vapour pressure of the liquid. When the pressure within the liquid drops to below the liquid's vapor pressure, tiny vapor bubbles can begin to form at the high point, and the siphon effect will end. This effect depends on how efficiently the liquid can nucleate bubbles; in the absence of impurities or rough surfaces to act as easy nucleation sites for bubbles, siphons can temporarily exceed their standard maximal height during the extended time it takes bubbles to nucleate. One siphon of degassed water was demonstrated to for an extended period of time and other controlled experiments to. For water at standard atmospheric pressure, the maximal siphon height is approximately ; for mercury it is, which is the definition of standard pressure. This equals the maximal height of a suction pump, which operates by the same principle. The ratio of heights equals the ratio of densities of water and mercury, since the column of water is balancing with the column of air yielding atmospheric pressure, and indeed maximal height is inversely proportional to density of liquid.