- For the carbonation device, see soda siphon.
The word siphon (from Ancient Greek: σίφων “pipe, tube”, also spelled syphon) is sometimes used to refer to a wide variety of devices that involve the flow of liquids through tubes – see siphon terminology – but in the narrower sense it refers specifically to a tube in an inverted U shape which causes a liquid to flow uphill, above the surface of the reservoir, without pumps, powered by the fall of the liquid as it flows down the tube under the pull of gravity, and is discharged at a level lower than the surface of the reservoir it came from. Note that while the siphon must touch the liquid in the (upper) reservoir (the surface of the liquid must be above the intake opening), it need not touch the liquid in the lower reservoir and indeed there need not be a lower reservoir – liquid can discharge into mid-air.
In practical siphons, atmospheric pressure pushes the liquid up the tube into the region of reduced pressure at the top of the tube in the same way as a barometer, and indeed the maximum height of a siphon is the same as the height of a barometer, because they operate by the same mechanism. The reduced pressure is caused by liquid falling on the exit side.
When both ends of a siphon are at atmospheric pressure, liquid flows from high to low. However, if the lower end is pressurized, liquid can flow from low to high, as in siphon coffee. While in everyday siphons, atmospheric pressure is the driving mechanism, in specialized circumstances other mechanisms can work – in the laboratory, some siphons have been demonstrated to work in a vacuum – see vacuum siphons – indicating the tensile strength of the liquid is contributing to the operation of siphons at very low pressures. Most familiar siphons have water as a fluid, though mercury is often used in experiments, and other fluids such as organic liquids or even carbon dioxide can be siphoned.
In the 9th century, the Banu Musa brothers 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 (and the recently developed vacuum pumps), particularly with an eye to understanding the maximum height of pumps (and siphons) and the apparent vacuum at the top of early barometers. This was initially explained by Galileo Galilei via the theory of horror vacui ("nature abhors a vacuum"), 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.
Specifically, Pascal demonstrated that siphons work via atmospheric pressure (as Torricelli had advocated), not via horror vacui, via the following experiment. Two beakers of mercury are placed in a large container, at different heights. The beakers are connected with a three-way tube: a regular siphon (U-shaped tube), with an additional tube extending upward from the hook in the tube: one end of the tube goes down into each beaker (as in a normal siphon), while the third end faces upward, and is open to the air. The large container is slowly filled with water (the tube remains open to the air): as water goes into the container, the weight of the water forces the mercury up into the tube (water being denser hence heavier than air) – as the water level increases, the level of mercury rises because the pressure increases – and once the mercury enters the top of the siphon, the mercury flows from the higher beaker to the lower, as in a standard siphon. As the mercury had been open to the air at all time, there was never a vacuum – it was instead the pressure of the water.
There are two main issues in the operation of a siphon:
- why liquid flows from the higher reservoir to the lower reservoir, which is basic; and
- why liquid flows up the siphon, which is subtler.
The first issue is basic: liquid flows from the higher level to the lower level because the lower location has lower potential energy – water flows downhill. This is independent of the particular connection – liquids will also flow from higher to lower if there is a direct path (a canal), or if there is a tube that goes below the reservoirs (an "inverse" siphon), and these do not depend on siphon effect. Note that this is due to different heights (moving in the direction of gravity), not due to differences in atmospheric pressure at different heights (in fact, lower locations will, all else equal, have higher atmospheric pressure, due to a longer column of air above).
The second issue, why liquid flows up, is due primarily to atmospheric pressure (in ordinary siphons), and is the same mechanism as in suction pumps, vacuum pumps, and barometers, and can be replicated in the simple experiment of placing a straw in water, capping the top, and pulling it up (leaving the bottom tip submerged).
A siphon works because gravity pulling down on the taller column of liquid causes reduced pressure at the top of the siphon (formally, hydrostatic pressure). This reduced pressure means gravity pulling down on the shorter column of liquid is not sufficient to keep the liquid stationary so it flows from the upper reservoir, up and over the top of the siphon.
In more detail, one can look at how the hydrostatic pressure varies through the 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.
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 great deal of tensile strength in some experiments (such as with the z-tube), 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, 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 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. Another simple demonstration that liquid tensile strength isn't 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 it, defeating any liquid tensile strength, and yet if the bubble isn't too big, the siphon will continue to operate with little change.
The uphill flow of water in a siphon doesn’t violate the principle of continuity because the mass of water entering the tube and flowing upwards is equal to the mass of water flowing downwards and leaving the tube. A siphon doesn't violate the principle of conservation of energy because the loss of gravitational potential energy as liquid flows from the upper reservoir to the lower reservoir equals the work done in overcoming fluid friction as the liquid flows through the tube. 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 maximum height of the crest 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 maximum height during the extended time it takes bubbles to nucleate. For water at standard atmospheric pressure, the maximum siphon height is approximately 10 m (32 feet); for mercury it is 76 cm (30 inches), which is the definition of standard pressure. This equals the maximum height of a suction pump, which operates by the same principle. The ratio of heights (about 13.6) equals the ratio of densities of water and mercury (at a given temperature), since the column of water (resp. mercury) is balancing with the column of air yielding atmospheric pressure, and indeed maximum height is (neglecting vapor pressure and velocity of liquid) inversely proportional to density of liquid.
Siphon coffee 
While if both ends of a siphon are at atmospheric pressure, liquid flows from high to low, if the bottom end of a siphon is pressurized, liquid can flow from low to high. If pressure is removed from the bottom end, the liquid flow will reverse, illustrating that it is pressure driving the siphon. An everyday illustration of this is the siphon coffee brewer, which works as follows (designs vary; this is a standard design, omitting coffee grounds):
- a glass vessel is filled with water, then corked (so air-tight) with a siphon sticking vertically upwards
- another glass vessel is placed on top, open to the atmosphere – the top vessel is empty, the bottom is filled with water
- the bottom vessel is then heated; as the temperature increases, the vapor pressure of the water increases (it increasingly evaporates); when the water boils the vapor pressure equals atmospheric pressure, and as the temperature increases above boiling the pressure in the bottom vessel then exceeds atmospheric pressure, and pushes the water up the siphon tube into the upper vessel.
- a small amount of still hot water and steam remain in the bottom vessel and are kept heated, with this pressure keeping the water in the upper vessel
- when the heat is removed from the bottom vessel, the vapor pressure decreases, and can no longer support the column of water – gravity (acting on the water) and atmospheric pressure then push the water back into the bottom vessel.
In practice, the top vessel is filled with coffee grounds, and the heat is removed from the bottom vessel when the coffee has finished brewing. What vapor pressure means concretely is that the boiling water converts high-density water (a liquid) into low-density steam (a gas), which thus expands to take up more volume (in other words, the pressure increases). This pressure from the expanding steam then forces the liquid up the siphon; when the steam then condenses down to water the pressure decreases and the liquid flows back down.
Chain analogy 
A simplified but misleading conceptual model of a siphon is that it is 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 chain will move up around the pulley and down towards the lower surface.
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. The first is in practical siphons, the liquid is pushed through the siphon, not pulled. That is, under most practical circumstances, dissolved gases, vapor pressure, and (sometimes) 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.
A related problem is that siphons have a maximum height (for water siphons at standard atmospheric pressure, about 10 meters), as this is the limit to how high atmospheric pressure will push the water, but the chain model has no such limit – or rather is instead limited by how strong the links are (above a certain height, the chain links could not support the weight of the hanging chain and the links would snap), corresponding to tensile strength of the liquid, which is not the cause of maximum height in siphons.
A further problem with the chain model of the siphon is that siphons work by a gradient of hydrostatic pressure within the siphon, not by absolute differences of weight on either side. The weight of liquid on the up side of the siphon can be greater than the liquid on the down side, yet the siphon can still function. For example, if the tube from the upper reservoir to the top of the siphon has a much larger diameter than the 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, yet the siphon can function normally – this is because hydrostatic pressure depends on height (reduces as one goes up a column), but does not depend on diameter of the tube.
Despite these shortcomings, 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.
Practical requirements 
A plain tube can be used as a siphon. An external pump has to be applied to start the liquid flowing and prime the siphon. This can be a human mouth. This is sometimes done with any leak-free hose to siphon gasoline from a motor vehicle's gasoline tank to an external tank. (Siphoning gasoline by mouth often results in the accidental swallowing of gasoline, or aspirating it into the lungs, which can cause death or lung damage.) If the tube is flooded with liquid before part of the tube is raised over the intermediate high point and care is taken to keep the tube flooded while it is being raised, no pump is required. Devices sold as siphons often come with a siphon pump to start the siphon process.
In some applications it can be helpful to use siphon tubing that is not much larger than necessary. Using piping of too great a diameter and then throttling the flow using valves or constrictive piping appears to increase the effect of previously cited concerns over gases or vapor collecting in the crest which serve to break the vacuum. If the vacuum is reduced too much, the siphon effect can be lost. Reducing the size of pipe used closer to requirements appears to reduce this effect and creates a more functional siphon that does not require constant re-priming and restarting. In this respect, where the requirement is to match a flow into a container with a flow out of said container (to maintain a constant level in a pond fed by a stream, for example) it would be preferable to utilize two or three smaller separate parallel pipes that can be started as required rather than attempting to use a single large pipe and attempting to throttle it.
When certain liquids needs to be purified, siphoning can help prevent either the bottom (dregs) or the top (foam and floaties) from being transferred out of one container into a new container. Siphoning is thus useful in the fermentation of wine and beer for this reason, since it can keep unwanted impurities out of the new container.
Self-constructed siphons, made of pipes or tubes, can be used to evacuate water from cellars after floodings. Between the flooded cellar and a deeper place outside a connection is built, using a tube or some pipes. They are filled with water through an intake valve (at the highest end of the construction). When the ends are opened, the water flows through the pipe into the sewer or the river.
Siphoning is common in irrigated fields to transfer a controlled amount of water from a ditch, over the ditch wall, into furrows.
Large siphons may be used in municipal waterworks and industry. Their size requires control via valves at the intake, outlet and crest of the siphon. The siphon may be primed by closing the intake and outlets and filling the siphon at the crest. If intakes and outlets are submerged, a vacuum pump may be applied at the crest to prime the siphon. Alternatively the siphon may be primed by a pump at either the intake or outlet.
Gas in the liquid is a concern in large siphons. The gas tends to accumulate at the crest and if enough accumulates to break the flow of liquid, the siphon stops working. The siphon itself will exacerbate the problem because as the liquid is raised through the siphon, the pressure drops, causing dissolved gases within the liquid to come out of solution. Higher temperature accelerates the release of gas from liquids so maintaining a constant, low temperature helps. The longer the liquid is in the siphon, the more gas is released, so a shorter siphon overall helps. Local high points will trap gas so the intake and outlet legs should have continuous slopes without intermediate high points. The flow of the liquid moves bubbles thus the intake leg can have a shallow slope as the flow will push the gas bubbles to the crest. Conversely, the outlet leg needs to have a steep slope to allow the bubbles to move against the liquid flow; though other designs call for a shallow slope in the outlet leg as well to allow the bubbles to be carried out of the siphon. At the crest the gas can be trapped in a chamber above the crest. The chamber needs to be occasionally primed again with liquid to remove the gas.
Siphon terminology 
Bowl siphon 
Some toilets also use the siphon principle to obtain the actual flush from the cistern. The flush is triggered by a lever or handle that operates a simple diaphragm-like piston pump that lifts enough water to the crest of the siphon to start the flow of water which then completely empties the contents of the cistern into the toilet bowl. The advantage of this system was that no water would leak from the cistern excepting when flushed.
Early urinals incorporated a siphon in the cistern which would flush automatically on a regular cycle because there was a constant trickle of clean water being fed to the cistern by a slightly open valve.
Inverted siphon 
An inverted siphon is not a siphon but a term applied to pipes that must dip below an obstruction to form a "U" shaped flow path. Inverted siphons are commonly called traps for their function in preventing smelly sewer gases from coming back out of drains and sometimes making dense objects like rings and electronic components retrievable after falling into a drain. Liquid flowing in one end simply forces liquid up and out the other end, but solids like sand will accumulate. This is especially important in sewage systems or culverts which must be routed under rivers or other deep obstructions where the better term is "depressed sewer". Large inverted siphons are used to convey water being carried in canals or flumes across valleys, for irrigation or gold mining.
Back siphonage 
Back siphonage is a plumbing term applied to clean water pipes that connect directly into a reservoir without an air gap. As water is delivered to other areas of the plumbing system at a lower level, the siphon effect will tend to siphon water back out of the reservoir. This may result in contamination of the water in the pipes. Back siphonage is not to be confused with backflow.[clarification needed] Back siphonage is a result of liquids at a lower level drawing water from a higher level. Backflow is driven entirely by pressure in the reservoir itself. Backflow cannot occur through an intermediate high-point. Back siphonage can flow through an intermediate high-point and is thus much more difficult to guard against.
Anti-siphon valve 
Building codes often contain specific sections on back siphonage and especially for external faucets. (See sample building code below.) Backflow prevention devices such as anti-siphon valves are required in such designs. The reason is that external faucets may be attached to hoses which may be immersed in an external body of water, such as a garden pond, swimming pool, aquarium or washing machine. Should the pressure within the water supply system fall, the external water may be siphoned back into the drinking water system through the faucet. Another possible contamination point is the water intake in the toilet tank. An anti-siphon valve is also required here to prevent pressure drops in the water supply line from siphoning water out of the toilet tank (which may contain additives such as "toilet blue") and contaminating the water system. Anti-siphon valves function as a one-direction check valve.
Anti-siphon valves are also used medically. Hydrocephalus, or excess fluid in the brain, may be treated with a shunt which drains cerebrospinal fluid from the brain. All shunts have a valve to relieve excess pressure in the brain. The shunt may lead into the abdominal cavity such that the shunt outlet is significantly lower than the shunt intake when the patient is standing. Thus a siphon effect may take place and instead of simply relieving excess pressure, the shunt may act as a siphon, completely draining cerebrospinal fluid from the brain. The valve in the shunt may be designed to prevent this siphon action so that negative pressure on the drain of the shunt does not result in excess drainage. Only excess positive pressure from within the brain should result in drainage.
Note that the anti-siphon valve in medical shunts is preventing excess forward flow of liquid. In plumbing systems, the anti-siphon valve is preventing backflow.
Other anti-siphoning devices 
Along with anti-siphon valves, anti-siphoning devices also exist. The two are unrelated in application. Siphoning can be used to remove fuel from tanks. With the cost of fuel increasing, it has been linked in several countries to the rise in fuel theft. Trucks, with their large fuel tanks, are most vulnerable. The anti-siphon device prevents thieves from inserting a tube into the fuel tank.
Siphon barometer 
A siphon barometer is the term sometimes applied to the simplest of mercury barometers. A continuous U-shaped tube of the same diameter throughout is sealed on one end and filled with mercury. When placed into the upright position, mercury will flow away from the sealed end, forming a partial vacuum, until balanced by atmospheric pressure on the other end. The term "siphon" is used because the same principle of atmospheric pressure acting on a fluid is applied. The difference in height of the fluid between the two arms of the U-shaped tube is the same as the maximum intermediate height of a siphon. When used to measure pressures other than atmospheric pressure, a siphon barometer is sometimes called a siphon gauge and not to be confused with a siphon rain gauge. Siphon pressure gauges are rarely used today.
Siphon bottle 
A siphon bottle (also called a soda syphon or, archaically, a siphoid) is a pressurized bottle with a vent and a valve. Pressure within the bottle drives the liquid up and out a tube. It is a siphon in the sense that pressure drives the liquid through a tube. A special form was the gasogene.
Siphon cup 
A siphon cup is the (hanging) reservoir of paint attached to a spray gun. This is to distinguish it from gravity-fed reservoirs. An archaic use of the term is a cup of oil in which the oil is siphoned out of the cup via a cotton wick or tube to a surface to be lubricated.
Siphon rain gauge 
A siphon rain gauge is a rain gauge that can record rainfall over an extended period. A siphon is used to automatically empty the gauge. It is often simply called a "siphon gauge" and is not to be confused with a siphon pressure gauge.
Heron's siphon 
Heron's siphon is a siphon that works on positive air pressure and at first glance appears to be a perpetual motion machine. In a slightly differently configuration, it is also known as Heron's fountain.
Venturi siphon 
A venturi siphon, also known as an eductor, is essentially a venturi which is designed to greatly speed up the fluid flowing in a pipe such that an inlet port located at the throat of the venturi can be used to siphon another fluid. See pressure head. The low pressure at the throat of the venturi is called a siphon when a second fluid is introduced, or an aspirator when the fluid is air.
Siphonic roof drainage 
Siphonic roof drainage makes use of the siphoning principle to carry water horizontally from multiple roof drains to a single downpipe and to increase flow velocity. Air baffles at the roof drain inlets reduce the injection of air which causes embolisms in siphons. One benefit to this drainage technique is the reduction in required pipe diameter to drain a given roof surface area, up to half the size. Another benefit is the elimination of pipe pitch or gradient required for conventional roof drainage piping.
Siphon spillway 
A siphon spillway in a dam uses the siphon effect to increase the flow rate. A normal spillway flow is pressurized by the height of the reservoir above the spillway whereas a siphon flow rate is governed by the difference in height of the inlet and outlet. (See math section below.)
Sample building code regulations regarding back siphonage 
- 18.104.22.168.Back Siphonage
- Every potable water system that supplies a fixture or tank that is not subject to pressures above atmospheric shall be protected against back-siphonage by a backflow preventer.
- Where a potable water supply is connected to a boiler, tank, cooling jacket, lawn sprinkler system or other device where a non-potable fluid may be under pressure that is above atmospheric or the water outlet may be submerged in the non-potable fluid, the water supply shall be protected against backflow by a backflow preventer.
- Where a hose bibb is installed outside a building, inside a garage, or where there is an identifiable risk of contamination, the potable water system shall be protected against backflow by a backflow preventer.
The term self-siphon is used in a number of ways. Liquids that are composed of long polymers can "self-siphon" and these liquids do not depend on atmospheric pressure. Self-siphoning polymer liquids work the same as the siphon-chain model where the lower part of the chain pulls the rest of the chain up and over the crest. This phenomenon is also called a tubeless siphon.
"Self-siphon" is also often used in sales literature by siphon manufacturers to describe portable siphons that contain a pump. With the pump, no external suction (e.g. from a person's mouth/lungs) is required to start the siphon and thus the product is described as a "self-siphon".
If the upper reservoir is such that the liquid there can rise above the height of the siphon crest, the rising liquid in the reservoir can "self-prime" the siphon and the whole apparatus be described as a "self-siphon". Once primed, such a siphon will continue to operate until the level of the upper reservoir falls below the intake of the siphon. Such self-priming siphons are useful in some rain gauges and dams.
Capillary action can be used in self-priming siphons. In these, water soaks upwards (into a cotton-filled hose) and below the crest to begin the siphon gradually, and as weight is added to the down stream, this kind of siphon will speed up, but it will never be as fast as the same diameter of open hose.
Siphons in nature 
The term "siphon" is used for a number of structures in human and animal anatomy, either because flowing liquids are involved or because the structure is shaped like a siphon, but in which no actual siphon effect is occurring: see Siphon (biology).
Biologists debate whether the siphon mechanism plays a role in blood circulation. It is theorized that veins form a continuous loop with arteries such that blood flowing down veins help siphon blood up the arteries, especially in giraffes and snakes. Some have concluded that the siphon mechanism aids blood circulation in giraffes. Many others dispute this and experiments show no siphon effects in human circulation. Some cite negative pressure in the brain as supporting the role of the siphon effect in the brain.
A number of species are named after siphons because they resemble siphons in whole or in part. Geosiphons are fungi. Siphonal algae, siphonales have tube-like structures. Siphonacanthus are tropical plants of the family Acanthaceae.
In speleology, a siphon or a sump is that part of a cave passage that lies under water and through which cavers have to dive to progress along it.
Explanation using Bernoulli's equation 
Bernoulli's equation may be applied to a siphon to derive the flow rate and maximum height of the siphon.
- Let the surface of the upper reservoir be the reference elevation.
- Let point A be the start point of siphon, immersed within the higher reservoir and at a depth −d below the surface of the upper reservoir.
- Let point B be the intermediate high point on the siphon tube at height +hB above the surface of the upper reservoir.
- Let point C be the drain point of the siphon at height −hC below the surface of the upper reservoir.
- = fluid velocity along the streamline
- = gravitational acceleration downwards
- = elevation in gravity field
- = pressure along the streamline
- = fluid density
Apply Bernoulli's equation to the surface of the upper reservoir. The surface is technically falling as the upper reservoir is being drained. However, for this example we will assume the reservoir to be infinite and the velocity of the surface may be set to zero. Furthermore, the pressure at both the surface and the exit point C is atmospheric pressure. Thus:
- (Equation 1.)
Apply Bernoulli's equation to point A at the start of the siphon tube in the upper reservoir where P = PA, v = vA and y = −d
- (Equation 2.)
Apply Bernoulli's equation to point B at the intermediate high point of the siphon tube where P = PB, v = vB and y = hB
- (Equation 3.)
Apply Bernoulli's equation to point C where the siphon empties. Where v = vC and y = −hC. Furthermore, the pressure at the exit point is atmospheric pressure. Thus:
- (Equation 4.)
As the siphon is a single system, the constant in all four equations is the same. Setting equations 1 and 4 equal to each other gives:
Solving for vC:
- Velocity of siphon:
The velocity of the siphon is thus driven solely by the height difference between the surface of the upper reservoir and the drain point. The height of the intermediate high point, hB, does not affect the velocity of the siphon. However, as the siphon is a single system, vB = vC and the intermediate high point does limit the maximum velocity. The drain point cannot be lowered indefinitely to increase the velocity. Equation 3 will limit the velocity to a positive pressure at the intermediate high point to prevent cavitation. The maximum velocity may be calculated by combining equations 1 and 3:
Setting PB = 0 and solving for vmax:
- Maximum velocity of siphon:
The depth, −d, of the initial entry point of the siphon in the upper reservoir, does not affect the velocity of the siphon. No limit to the depth of the siphon start point is implied by Equation 2 as pressure PA increases with depth d. Both these facts imply the operator of the siphon may bottom skim or top skim the upper reservoir without impacting the siphon's performance.
Note that this equation for the velocity is the same as that of any object falling height hC. Note also that this equation assumes PC is atmospheric pressure. If the end of the siphon is below the surface, the height to the end of the siphon cannot be used; rather the height difference between the reservoirs should be used.
Maximum height 
Setting equations 1 and 3 equal to each other gives:
Maximum height of the intermediate high point occurs when it is so high that the pressure at the intermediate high point is zero; in typical scenarios this will cause the liquid to form bubbles and if the bubbles enlarge to fill the pipe then the siphon will 'break'. Setting PB = 0:
Solving for hB:
- General height of siphon:
This means that the height of the intermediate high point is limited by velocity of the siphon. Faster siphons result in lower heights. Height is maximized when the siphon is very slow and vB = 0:
- Maximum height of siphon:
This is the maximum height that a siphon will work. It is simply when the weight of the column of liquid to the intermediate high point equates to atmospheric pressure. Substituting values will give approximately 10 metres for water and, by definition of standard pressure, 0.76 metres = 760 millimetres for mercury. The ratio of heights (about 13.6) equals the ratio of densities of water and mercury (at a given temperature), since the column of water (resp. mercury) is balancing with the column of air yielding atmospheric pressure.
Vacuum siphons 
|This section requires expansion with: explanation of theory of operation. (December 2012)|
Oxford English Dictionary 
The Oxford English Dictionary (OED) entry on siphon, published in 1911, states that a siphon works by atmospheric pressure. Stephen Hughes of Queensland University of Technology criticised this in a 2010 article which was widely reported in the media. The OED editors stated, "there is continuing debate among scientists as to which view is correct. ... We would expect to reflect this debate in the fully updated entry for siphon, due to be published later this year." Dr. Hughes continued to defend his view of the siphon in a late September post at the Oxford blog. A set of experiments was recently published, seriously questioning Hughes's hypothesis.
See also 
|Wikimedia Commons has media related to: Siphons|
- 1992 Guadalajara explosions for details of an accident involving a siphon.
- Communicating vessels
- Gravity feed
- "Video Demonstration of Siphon in Vacuum".
- Minor, Ralph Smith (1914). "Would a Siphon Flow in a Vacuum! Experimental Answers". School Science and Mathematics. 14,2 (2): 152. doi:10.1111/j.1949-8594.1914.tb16014.x.
- Nokes M C 1948 "Vacuum siphons" School Science Review 29 233
- Siphon Concepts
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