ity. 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.
Although siphons can exceed the barometric height of the liquid in special circumstances, e.g. when the liquid is degassed and the tube is clean and smooth, in general the practical maximum height can be found as follows.
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 pressure along the streamline being always greater than zero.
- Maximum height of siphon:
This is the maximum height that a siphon will work. Substituting values will give approximately 10 metres for water and, by definition of standard pressure, 0.76 metres (760 mm or 30 in) for mercury. The ratio of heights (about 13.6) equals the ratio of densities of water and mercury (at a given temperature). Note that as long as this condition is satisfied (pressure greater than zero), the flow at the output of the siphon is still only governed by the height difference between the source surface and the outlet. Volume of fluid in the apparatus is not relevant as long as the pressure head remains above zero in every section. Because pressure drops when velocity is increased, a static siphon (or manometer) can have a slightly higher height than a flowing siphon.
|This section requires expansion with: explanation of theory of operation. (December 2012)|
Experiments have shown that siphons can operate in a vacuum, via cohesion and tensile strength between molecules, provided that the liquids are pure and degassed and surfaces are very clean.
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 criticized 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. The 2015 definition by the OED is:
A tube used to convey liquid upwards from a reservoir and then down to a lower level of its own accord. Once the liquid has been forced into the tube, typically by suction or immersion, flow continues unaided.
The Encyclopædia Britannica currently describes a siphon as:
Siphon, also spelled syphon, instrument, usually in the form of a tube bent to form two legs of unequal length, for conveying liquid over the edge of a vessel and delivering it at a lower level. Siphons may be of any size. The action depends upon the influence of gravity (not, as sometimes thought, on the difference in atmospheric pressure; 