Siphon

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A siphon is a continuous tube that allows liquid to drain from a reservoir through an intermediate point that is higher than the reservoir, the up-slope flow being driven only by barometric pressure without any need for pumping. It is necessary that the final end of the tube be lower than the water surface in the reservoir.

Contents

1 Operation 2 Practical application 3 History 4 Use 5 Biological siphons 6 Bernoulli's equation 6.1 Velocity 6.2 Maximum height 7 Exhibit A: Sample building code regulations regarding back siphonage 8 See also

Operation

Once started, a siphon requires no additional energy to keep the liquid flowing up and out of the reservoir. The siphon works because the ultimate drain point is lower than the reservoir and the flow of liquid out the drain point creates a vacuum in the tube such that liquid is drawn up out of the reservoir.

The maximum height of the intermediate point (the crest) is limited by atmospheric pressure and the density of the liquid. At the high point of the siphon, gravity tends to draw the liquid down in both directions creating a vacuum. Atmospheric pressure on the top surface of the higher reservoir is transmitted through the liquid in the reservoir and up the siphon tube and prevents a vacuum from forming. When the pressure exerted by the weight of the height of the column of liquid equals that of atmospheric pressure, a vacuum will form at the high point and the siphon effect ended. For water at standard pressure, the maximum height is approximately 33 feet (10 m); for mercury it is 30 inches (76 cm).

An analogy to understand siphons is to imagine a long, frictionless train extending from a plain, up a hill and then down the hill into a valley below the plain. So long as part of the train extends into the valley below the plain, it is "intuitively obvious" that the portion of the train sliding into the valley can pull the rest of the train up the hill and into the valley. What is not obvious is what holds the train together when the train is a liquid in a tube. In this analogy, atmospheric pressure holds the train together. Once the force of gravity on the couplings between the cars of the train going up the hill exceeds that of atmospheric pressure, the coupling breaks and the train falls apart. The train analogy is demonstrated in a "siphon-chain model" [1] (http://jedlik.phy.bme.hu/~hartlein/physics.umd.edu/deptinfo/facilities/lecdem/f4-32.htm) where a long chain on a pulley flows between two beakers.

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 and lungs. This is sometimes done with any leak-free hose to siphon gasoline from a motor vehicle's gasoline tank to an external tank. 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 come with a siphon pump to start the siphon process.

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[2] (http://sti.srs.gov/fulltext/tr2000066/tr2000066.html). 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 be "degassed". 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. 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.

Among some physicists there is some dispute as to what causes the siphon to lift liquid from the upper reservoir to the crest of the siphon[3] (http://www.straightdope.com/columns/010105.html). They argue that theoretically, internal molecular cohesion is sufficient to pull the liquid up the intake leg of the siphon to the crest. Furthermore, some argue that theoretically a siphon will operate in a vacuum. In practice atmospheric pressure is required.

The term self-siphon is used in a number of ways. Liquids that are composed of long polymers can "self-siphon"[4] (http://sprott.physics.wisc.edu/demobook/chapter6.htm)[5] (http://www.chem.soton.ac.uk/schools/ks3/docs/poly.pdf) 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[6] (http://www.amazon.com/gp/reader/0471410772/ref=sib_vae_pg_235/102-3250583-7976102?%5Fencoding=UTF8&keywords=siphon&p=S06Z&twc=2&checkSum=Y6wUqKpqAPXfPs8T8qiIRUMfirNkBa1v98gT%2FlP4lLU%3D#reader-page).

"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 inaccurately 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"[7] (http://www.grow.arizona.edu/water/pressure/siphon.shtml). 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.

Practical application

When applying a siphon to any application it is important that the piping be as closely sized to the requirement as possible. 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. Once the vacuum is reduced the siphon effect is 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 repriming 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 preferential 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.

History

It is tolerably certain that Ctesibius was the discoverer of the principle of the siphon[8] (http://www.gutenberg.net/etext99/1hsci10.txt). His student, Hero of Alexandria, wrote extensively about siphons in the treatise, Pneumatica[9] (http://www.history.rochester.edu/steam/hero/index.html).

The siphon was first used as a weapon by the Byzantine Navy, and the most common method of deployment was to emit Greek fire, a formula of burning oil, through a large bronze tube onto enemy ships. Usually the mixture would be stored in heated, pressurized barrels and projected through the tube by some sort of pump while the operators were sheltered behind large iron shields. It is not clear whether these were true siphons or merely pumps that used air pressure to project the Greek fire. "Some apparatus called a 'siphon' (σ ι φ ω ν ) was used." "The siphons were, apparently, flame-projectors, either hand-pumps or reservoirs worked by mechanical force-pumps".[10] (http://print.google.com/print?id=fD6zJao-c4wC&pg=28&lpg=28&dq=siphons&sig=4Jc3An2_JIb1DhMMttuPf4f2xCI)

Use

Bowl siphons are part of flush toilets. Siphon action in the bowl siphon siphons out the contents of the toilet bowl and creates the characteristic toilet "sucking" sound. Some toilets also use a siphon for the actual flush from the storage tank.

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. At no point does the siphon effect come into play; an inverted siphon will work fine in the absence of atmospheric pressure. Liquid flowing in one end simply forces liquid up and out the other end. Engineers must ensure that the flow rate in such a channel is fast enough to keep suspended solids from settling. Otherwise, the inverted siphon tends to act as a debris trap. This is especially important in sewage systems which must be routed under rivers or other deep obstructions.

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. 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 in intermediate high-point and is thus much more difficult to guard against.

Anti-siphon valves[11] (http://www.toiletology.com/anti-sph.shtml) are required in such designs. Building codes often contain specific sections on back siphonage and especially for external faucets. (See Exhibit A.) The reason is that external faucets may be attached to hoses which may be immersed in an external body of water, such as a 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 are also used medically. Hydrocephalus, or excess fluid in the brain, maybe 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[12] (http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=7923233&dopt=Abstract)[13] (http://www.sbaa.org/site/PageServer?pagename=asb_hydrocephalus)[14] (http://www.aans.org/education/journal/neurosurgical/oct99/7-4-9.asp).

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.

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 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.

A siphon bottle 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 siphon bottle is sometimes called a gasogene[15] (http://www.merriam-webster.com/cgi-bin/dictionary?book=Dictionary&va=gasogene) or even more rarely, a siphoid.

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.

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[16] (http://www.physics.purdue.edu/demo/2C/herons_siphon.html)[17] (http://www.physics.purdue.edu/reports/demo/fluids/Mf-7.2.html) 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 Hero's fountain[18] (http://arxiv.org/ftp/physics/papers/0310/0310039.pdf).

Biological siphons

Biologists debate whether the siphon mechanism plays a role in blood circulation [19] (http://www.desc.med.vu.nl/Publications/Thesis/Gisolf/Gisolf_Chap1.pdf). 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[20] (http://jeb.biologists.org/cgi/content/full/207/8/1305). Some have concluded that the siphon mechanism aids blood circulation in giraffes [21] (http://ajpregu.physiology.org/cgi/content/abstract/256/2/R567). Many others dispute this[22] (http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=2890463&dopt=Abstract)[23] (http://ajpregu.physiology.org/cgi/content/abstract/265/4/R715) and experiments show no siphon effects in human circulation[24] (http://ajpregu.physiology.org/cgi/content/abstract/287/4/R911).

The term "siphon" is also used with a number biological objects either because flowing liquids are involved or because the object is shaped like a siphon. In all cases, no actual siphon effect is occurring.

• Mollusks have an organ called a siphon which sucks water in and out for the purpose of filter-feeding.
• Mosquito larvae and other insect larvae (e.g. Tabanidae, Belostomatidae) live in the water and breathe through a so-called siphon which is functionally a snorkel
• Some adult insects which spend considerable time underwater, such as the water scorpion, have an abdominal breathing tube that is also called a siphon.
• A siphon gourd has a long curved neck, shaped like a siphon
• A portion of the human internal carotid artery running through the cavernous sinus is called the carotid siphon because of its shape.

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 +h_B above the surface of the upper reservoir.

Let point C be the drain point of the siphon at height −h_C below the surface of the upper reservoir.

Bernoulli's equation:

<math> {v^2 \over 2}+gy+{P \over \rho}=\mathrm{constant} <math>

<math>v \;<math> = fluid velocity along the streamline

<math>g \;<math> = gravitational acceleration downwards

<math>y \;<math> = elevation in gravity field

<math>P \;<math> = pressure along the streamline

<math>\rho \;<math> = 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 may assume the reservoir to be infinite and the velocity of the surface may be set to zero. Furthermore, the pressure at the surface is atmospheric pressure. Thus:

<math>{0^2 \over 2}+g(0)+{P_\mathrm{atm} \over \rho}=\mathrm{constant} <math> (Equation 1.)

Apply Bernoulli's equation to point A at the start of the siphon tube in the upper reservoir where P = P_A, v = v_A and y = −d

<math>{v_A^2 \over 2}-gd+{P_A \over \rho}=\mathrm{constant} <math> (Equation 2.)

Apply Bernoulli's equation to point B at the intermediate high point of the siphon tube where P = P_B, v = v_B and y = h_B

<math>{v_B^2 \over 2}+gh_B+{P_B \over \rho}=\mathrm{constant} <math> (Equation 3.)

Apply Bernoulli's equation to point C where the siphon empties. Where v = v_C and y = −h_C. Furthermore, the pressure at the exit point is atmospheric pressure. Thus:

<math>{v_C^2 \over 2}-gh_C+{P_\mathrm{atm} \over \rho}=\mathrm{constant} <math> (Equation 4.)

Velocity

As the siphon is a single system, the constant in all four equations are the same. Setting equations 1 and 4 equal to each other gives:

<math>{0^2 \over 2}+g(0)+{P_\mathrm{atm} \over \rho}={v_C^2 \over 2}-gh_C+{P_\mathrm{atm} \over \rho}<math>

Solving for v_C:

Velocity of siphon:

<math>v_C=\sqrt{2gh_C}<math>

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, h_B, does not affect the velocity of the siphon. However, as the siphon is a single system, v_B = v_C 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:

<math>{0^2 \over 2}+g(0)+{P_\mathrm{atm} \over \rho}={v_B^2 \over 2}+gh_B+{P_B \over \rho}<math>

Setting P_B = 0 and solving for v_max:

Maximum velocity of siphon:

<math>v_\mathrm{max}=\sqrt{2\left({P_\mathrm{atm} \over \rho}-gh_B\right)}<math>

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 P_A 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 h_C. Note also that this equation assumes P_C 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:

<math>{0^2 \over 2}+g(0)+{P_\mathrm{atm} \over \rho}={v_B^2 \over 2}+gh_B+{P_B \over \rho} <math>

Maximum height of the intermediate high point occurs when it is so high that the pressure at the intermediate high point is zero. Setting P_B = 0:

<math>{P_\mathrm{atm} \over \rho}={v_B^2 \over 2}+gh_B<math>

Solving for h_B:

General height of siphon:

<math>h_B={P_\mathrm{atm} \over \rho g} - {v_B^2 \over 2g}.<math>

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 v_B = 0:

Maximum height of siphon:

<math>h_B={P_\mathrm{atm} \over \rho g}<math>

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 for water will give 10 metres for water and 0.84 metres for mercury.

Exhibit A: Sample building code regulations regarding back siphonage

From Ontario's building code: [25] (http://www.e-laws.gov.on.ca/DBLaws/Regs/English/970403c_e.htm)

7.6.2.3.Back Siphonage

(1) 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.

(2) 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.

(3) 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.

See also

• Sewer for details of an accident involving a siphon.nl:Sifon

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