This section is from the book "Principles And Practice Of Plumbing", by S. Stevens Hellyer. Also available from Amazon: Principles and practice of plumbing.
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IT may not be without some interest to theorize a little on the cause of the loss of water-seals in traps by syphonage and back-pressure. Trap-syphonage is chiefly caused by the removal of the atmospheric pressure from the pipe-side of the water-seal of a trap by the sucking action of a descending column of water through the pipe on which the trap is branched, or to which it is connected by a branch pipe; and this action is always at the side or rear of the column. Back-pressure is caused by a pressure of air upon the pipe-side of the seal of a trap greater than the atmospheric pressure upon it on the house-side; and this action is always in front of the column; but directly the column has passed the outlet of the trap, or the junction of the branch pipe on which the trap is fixed, the back-pressure is removed, and a sucking or syphonic action commences.
(a) In front of the discharge the air in the pipe is forced downwards with great velocity, as the air out of a pop-gun; and unless a way of escape is made for it by an anti-syphoning pipe, as shown in figs. 112 and 134, between the seal of the trap and the pipe through which the discharge is rushing - on every trapped branch upon the pipe - water will be forced out of the traps, as shown at d, fig. 94a. Where (a) there is no fixture upon the trap, the water forced out of it will partly fall on to the floor, and partly fall back again into the trap; or (b) where a closet-basin, urinal, or lavatory, or such-like fixture is fixed upon the trap, the water, foul or otherwise, will be forced up into the fixture to gravitate back again into the trap directly the back-pressure is removed; and if this were removed suddenly, as sometimes would be the case, then, with the energy gained by the fall, to partly flow out over the weir of the trap, and run away through the branch pipe, and partly to be syphoned out by the sucking action of the piston-like discharge; or (c), in the case of what is called a running-trap, the water would be forced up into the horizontal pipe, and leave the trap in some such cases without a seal. [For this reason I never allow running-traps to be fixed on any of my works.]
(b) The effect behind the discharge is equally disastrous upon the water-seals of traps when fixed upon a stack of pipe without an anti-syphoning pipe. For though the pipe be open to the atmosphere at top and bottom, the motion of a descending column of water through a pipe is so rapid that the air cannot enter the top of the pipe to reach the parts where it is wanted quickly enough to supply the demand, and to prevent a vacuum air rushes into the pipe through the trap or traps fixed upon it, frequently carrying with it enough water to leave the trap or traps without any seal. Or, in other words, the atmospheric pressure having been removed from the interior or outlet of the trap, by the withdrawal of air from the interior of the pipe, the atmospheric pressure upon the inlet of the pipe has pressed its way through the water-seal to fill the void.
2. Trap-ventilation, i.e., an anti-syphoning pipe, not only prevents a disturbance of the seals of the traps in communication with a stack-pipe from back-pressure, by providing a way of escape for the air forced down in front of a column of water passing through the pipe, but it also prevents a disturbance of the seals of the traps at the rear of the column, by giving air to each branch pipe, and freeing the traps from the action of syphonage.
The surplus of air in front of the column is forced up through each branch into the anti-syphoning pipe, to be sucked back again into the stack through the upper branches, to supply the great demand for air at the rear of the column; so that in many cases the supply almost equals the demand. This immediate supply of air from the pipe itself is of great value, for in such contests, especially in high pipes, the seals of many traps would be lost before air could come down through the top of the pipe to prevent a breach - a vacuum.
The air sucked down through the top of the pipe is of great value, though, like Blucher's army upon the field of Waterloo, it may arrive late.
3. The greater the distance between the ends of the stack-pipe - the top and bottom ends - that is, the greater the height of a pipe the greater will be the demand for air in its lower part by the passage through it of a pluglike discharge from some high point - from the fourth or fifth floor of a six or seven-storied house. Therefore when a soil-pipe (or waste-pipe) is of great height, with many branches upon it, it is a great advantage, even in the case where an anti-syphoning pipe is fixed, to increase the bore of the upper part of the pipe - the ventilation-pipe. Supposing a soil-pipe to be 4 in., the ventilation-pipe should be 5 in.; and where a waste-pipe is 3 in. in high buildings, its ventilation-pipe might with advantage be 4 in.; and traps fixed on a 2 in. stack would be benefited by a 2 1/2 in. ventilation-pipe fixed on the top of the 2 in. stack.
4. When the bore of a pipe is only partially filled by a body of water sent into it, the actions both of backpressure and syphonage would be very much less than would be the case with a discharge which quite filled the pipe; for though there might be a great disturbance of the air in the pipe, by the passage of the discharge through it, and though some of the air in the pipe would be entangled in the discharge and be forced downwards in front of it, enough air would escape between the discharge and the uncharged pipe, together with what had been sucked down through the top of the pipe, to prevent a vacuum; that is, sufficient air would be retained in the pipe, together with the current sucked down through the top, to about maintain the normal atmospheric pressure upon the seals of the traps. But even in such cases round-pipe traps with a rounded weir would often be subjected to a little loss of seal by the oscillation of the water in the traps.
 
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