4

Naticnai Bur&au of Standards (7

Library, N. W. BIdg.

AUG 1 9 1952

Self-Siphonage of Fixture Traps

United States Department of Commerce

National Bureau of Standards

Building Materials and Structures Report 126
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UNITED STATES DEPARTMENT OF COMMERCE • Charles Sawyer, Secretary NATIONAL BUREAU OF STANDARDS > E. U. Condon, Director

Self-Siphonage of Fixture Traps

John L. French and Herbert N. Eaton

Building Materials and Structures Report 126

Issued October 15, 1951

For sale by the Superintendent of Documents, V, S, Government Printing Office, Washington 25, D. C.

Price 20 cents

Foreword

This report on the self-siphonage of plumbing fixture traps is the last of a

series of three reports giving the results of an investigation of the problems

involved in the proper venting of single plum.bing fixtures or relatively small

groups of such fixtures in dwellings. The first report, BMS118, Stack venting

of plumbing fixtures, was published in January 1950; and the second is BMS119,

Wet venting of plumbing fixtures, issued in December 1950. The investigation,

the results of which are presented in these three reports, was first undertaken

for the National Housing Agency in connection with the Veterans Emergency

Housing Program of that Agency and was continued and completed under the

Housing Research Program, of the Office of the Adm.inistrator, Housing and

Hom.e Finance Agency, as part of the research program of that Agency under

its statutory authority.

Self-siphonage is the reduction in the water seal of a fixture trap by the

discharge from the fixture to which the trap is connected. The purpose of the

trap is to interpose between the sewer and the interior of the building a water

seal that will prevent sewer air from passing back into the building and causing

offensive odors there. This water seal is normally from 2 to 4 inches in depth

and is sufficient to prevent the passage of sewer air into the building under

any ordinary conditions. However, if, through self-siphonage or any other

cause, part of the water seal in the trap is lost, then the pressure fluctuations

in the drainage system, of the building, which occur as the result of the discharge

of the fixtures on the system, may be great enough to bubble sewer air back

through the trap seal. At present it is customary to control self-siphonage by limiting the

unvented length of drain connected to the fixture. However, this investigation

has shown that other factors than the length of fixture drain afl^ect self-siphonage. Among these are the diameter of the trap and the depth of trap seal,

the diameter and slope of the fixture drain, the type of vent fitting used, and

the rate of discharge of the fixture. This investigation has shown to what

extent these other factors affect trap-seal losses, and the paper gives the neces- sary information to take them into account properly in the design of the system.

The paper also shows the importance of standardizing fixture traps and

the hydraulic characteristics of plumbing fixtures, such as lavatories, sinks,

and trays.

E. U. Condon, Director.

m
Contents

Page

Foreword m

1. Introduction 1 2. Nature of the phenomenon 1 3. Statement of the problem I 3

4. Previous consideration of the problem 3

5. Preliminary considerations 4

5.1. Typical system in which self-siphonage may occur 4

5.2. Action of trap 4

a. No refill of trap 4

b. Refill of trap 5

5.3. Trap-seal loss 6

5.4. Comparison of critical trap-seal loss with 1-inch trap-seal reduction and 1-inch remaining trap seal 7

6. Analysis of the problem 11

6.1. General considerations 11

6.2. Derivation of the applicable dimensionless variables 12

a. Trap-seal loss . 12

b. Orifice outlet and down pipe 12

c. Fixture trap 13

d. Fixture drain 14

e. Vent or stack fitting 14

6.3. Effect of density of the air and the water 15

6.4. Summary : 15

7. Experimental investigation 15

7.1. Description of the test system 15

7.2. Test procedure 16

7.3. "No-trail" discharge tests 16

7.4. Lavatory tests 19

a. Effect of diameter of lavatory drain 22

b. Effect of size of lavatory 22

c. Effect of vertical distance from fixture to trap 23

d. Trap dimensions 23

(1) Effect of internal diameter of trap 23

(2) Effect of depth of trap seal 24

(3) Relative effects of diameter of trap and depth of trap seal 24

e. Effect of plugged overflow ; 24

f. Effect of type of vent fitting 24

g. Effect of rate of fixture discharge 25

7.5. Tests on other fixtures 26

a. Sinks 26

b. Bathtubs 26

c. Water closets 27

d. Miscellaneous fixtures 28

8. Conclusions 28

9. Considerations regarding the self-siphonage problem 29

10. Importance of economy in the use of water 31

11. References 31

rv
r

Self-Siphonage of Fixture Traps

John L. French and Herbert N. Eaton

This paper describes the methods used and the results obtained in an experimental

investigation of the self-siphonage of fixture traps in plumbing systems. Self-siphonage is the reduction in depth of the water seal in the trap by flow from the fixture that discharges

through the trap. The different factors that aff'ect self-siphonage are determined, and

methods for reducing the ill eS'ects of self-siphonage are suggested. Finally, recommendations and conclusions in a form suitable for use by code-writing authorities are presented.

1. Introduction

The flow of sewer gas from the plumbing

drainage system into a dweUing is commonly

accepted as being undesirable, and under unusual

circumstances poisonous gases might conceivably

be introduced into the building in this way. To

prevent such occurrences, traps containing a

liquid seal are almost universally installed on

plumbing fixtures. Under certain circumstances

the discharge of a fixture may, after it has ceased,

leave the water level in the trap lower than its normal level, which is at the level of the trap weir

(see fig. 1). The process whereby a reduction in

the level of the trap seal is caused by the discharge

of the fixture to which the trap is connected

(notably in the case of the lavatory) is commonly

known as selj-siphonage. The phenomenon of

self-siphonage should be clearly distinguished

from siphonage. The latter phenomenon also may reduce the depth of seal in a fixture trap, but

in this case the phenomenon i ! due to the dis- charge of other fixtures on the system, this dis- charge resulting in transient local pressure reductions that siphon water out of the trap attached to the fixture in question.

It has long been known that the trap-seal

losses caused by self-siphonage are frequently more severe with long unvented lengths of fixture

drains than with short ones, and plumbing codes

commonly place a limit on the distance between

the fixture trap and its protecting vent. However, there has been little uniformity in these code

requirements, and the need for an experimental

investigation of the self-siphonage of plumbing

fixtures that would afford a sound basis for establishing code requirements in this respect has been

apparent. For this reason the Housing and

Home Finance Agency, at the suggestion of the

Uniform Plumbing Code Committee, sponsored a

research program at this Bureau which consisted,

among other things, of an investigation of the

process of self-siphonage. The purpose of this report is to present the results of this investigation.

In analyzing some portions of the experimental

data use has been made of the principles of dimensional analysis. This has made it possible to

bring order out of a great mass of observational

data taken in the course of the investigation and

has provided a means of predicting approximately

what amount of self-siphonage will occur under

conditions not actually tested. This would have

been impossible had this mathematical tool not

been used. Thus, certain sections of the paper

have been written for the engineer, not for the

practical plumber. It is believed, nevertheless,

that the conclusions resulting from this investigation are stated in sufficiently detailed form to enable the practical man to use them with ease.

TRAP WEIR NORMAL WATER-SEAL LEVEL

Figure 1. Definition sketch of trap. z=remaining trap

seal, h =trap seal loss, and t — depth of trap seal.

2. Nature of the Phenomenon

The phenomenon of self-siphonage, while very

common in plumbing systems, is an extremely

complicated flow problem, and hence it does not

lend itself to analytical treatment. The only

reasonable method of approach seems to be to obtain empirical results by experiment and then

to generalize the results as far as possible by

theoretical means. A system typical in all respects of those that are considered in this report is sho^vn in figure 2, The system consists of a lavatory, an outlet orifice, a down pipe, a trap, a fixture drain, and a

1
vent fitting and waste pipe. Just below the outlet

orifice there is an overflow opening into the down

pipe thi'ough which overflow water can discharge or air can aspirate into the down pipe.

When a flat-bottomed or round-bottomed fix- ture, such as a sink, bathtub, or lavatory discharges its contents, the rate of discharge is rela- tively high at first, decreasing slowly as the depth

of water in the fixtiu"e decreases, until suddenly a sharp faU almost down to zero flow occurs. The

beginning of this sharp fall is marked by the formation of a vortex, which persists imtil the fixture

is empty, except for the minute flow from the film

of water remaining on the surface of the fixture at the end of the discharge. The flow that occurs

after the vortex forms is called the trail discharge.

The final minute flow from the film on the surface

of the fixture is called j^^m _;^ow or film discharge.

The sequence of flows described above is fllustrated in figure 3, which shows the discharge curve obtained in the laboratory for a bathtub.

When a fixture discharges through a P-trap,

such as is shown in figure 1, as the flow nears its end, the inertia of the water moving in the trap

tends to carry the water out of the trap into the

drain. This effect will be the more pronounced

the more abruptly the flow ceases and the greater

the rate of flow just prior to its cessation. The

result is to decrease the remaining trap seal at the end of the flow. A second way in which the trap seal may be

reduced at the end of the discharge from the

fixture is through a reduction in pressiu*e in the

drain due to the moving water in the drain filling

the cross section of the drain at one or more

points and thus producing a pressure reduction

upstream toward the trap when the flow from the

fixture ceases. This has the effect of pulling the

-LAVATORY

VOLUME WHEN FILLED TO OVERFLOW= 1.40 GALLONS

TRAPCONNECTION FOR MANOMETER

20

.16

£.12

FiGUEE 2. Self-siphonage test system. —I -| 1 1 1 1 1 r \ 1 1 1 1 r

Approximate re gion

of trail discharge^

20 40 60 80 100 120 140 Time « seconds Figure 3. Discharge curve for bathtub.

160 180 200

2
water out of the trap and leaving the trap with a reduced seal. There is still a third way in which trap-seal re- ductions due to self-si phonage can occur. The

water flowing through the trap ordinarily carries

with it bubbles of air. This air comes from the

fixture that is discharging. First, air is entrained

by the water passing the overflow outlet just

below the fixture; and second, when the vortex

forms in the fixture, air is carried down through

this vortex with the flowing water. The air coming from these two sources is carried through the

trap in the form of bubbles by the discharge.

These bubbles tend to drag the water with them as they pass upward through the outlet leg of the

FiGUEE 4. Effect of trapped air in drain.

trap and hence constitute another means of re- ducing the trap seal at the end of the flow. Another way in which air may be drawn through

the trap is the following. If the flow from the fix- ture ends abruptly, the water level in the inlet leg

of the trap may be pulled down to the level of the

dip of the trap, and air may then pass into the

outlet leg of the trap, rising through the water

in the form of bubbles. We have obtained motion

pictmes of this phenomenon occurring in a trans- parent plastic trap.

However, there are several ways in which a

trap-seal reduction due to any of the abovementioned causes may be prevented or may be

partly or wholly compensated by refill of the trap.

The gradual diminution of flow that occurs in

trail and film discharge tends to replenish the trap

seal. Secondly, when the flow from the fixture

ceases, the cross section of the drain may be completely filled with water along its entire length or

at short intervals along its length (see fig. 4), and

water tends to slough off the ends of the slugs of water. Some of this water will flow back up the

I drain, and it is possible that water from the slug

furthest upstream may reach the trap and partly

] or wholly refill it. Again, it has been observed

[ in systems built of transparent plastic material

I that, at the end of the flow, waves may be reflected

' from the vent fitting and that, if the drain is

I sufficiently short and is not laid at too great a

slope, these waves will reach and replenish the

trap seal.

3. Statement of the Problem

The function of the water seal in fixture traps

is, as has already been stated, to prevent sewer

gases from entering the dwelling in objectionable

amounts, and any reduction in trap seal due to self-siphonage may impair the ability of the trap

to perform its function properly. The specific

problem of this investigation was to determine

the factors that affect self-siphonage and, more

particularly, to establish limits on drain lengths,

slopes, and diameters, and other pertinent variables that would insure that excessive trap-seal

losses due to self-siphonage would not occur. In this connection, it may be pointed out that

the trap-seal losses observed in tests of wet and

stack-vented systems under certain conditions

are due in part to the self-siphonage process. For

example, if a wet-vented fixture is discharged

simultaneously with a fixture draining into its wet vent, the resulting seal loss of the wet-vented

fixture will be due in part to self-siphonage as defined above. However, the problems of stack

venting and wet venting have been treated in

earlier papers [1, 2],^ and in this paper the system

will be considered to be backvented.

The terms remaining trap seal, trap-seal loss, and depth of trap seal will be used frequently in

this paper, and for convenience they have been

defined in figure 1.

4. Previous Consideration of the

Problem

Only a limited amoimt of data on the self- siphonage of plumbing-fixture traps has been published. Tests on the siphonage of fixture traps were made as early as 1880 [3], but no record of

investigations of self-siphonage at such an early

date has been found. Perhaps the most sys- tematic investigation of the subject was made by

Hunter in 1924 [4]. From tests made with lavatories. Hunter concluded that the diameter of the

outlet orifice of the fixture had a marked influence on the amount of self-siphonage that resulted,

with the larger outlet orifices yielding the greater

trap-seal losses. Hunter inferred correctly that this effect of the

size of outlet was due to its influence on the rate

of discharge from the fijxture. He also made a few tests on the effect of depth of trap seal on the

self-siphonage process, and his test results lead to the conclusion that, while increased depth of seal gave increased trap-seal losses, the remaining depth

of seal—which is the important quantity—was also increased. This conclusion agrees with results of

the investigation reported in this paper. Hunter's

data also indicated that an increase in the slope

of the fixtme drain from ji to ji inch per foot, or an increase in the length of the fixtiu-e drain,

caused increased trap-seal losses.

' Figures in brackets indicate the literature references at the end of this paper.
Hunter [4, p. 140] concluded from tests on lavatories, kitchen sinks, laundry trays, and bathtubs

. . . the following table summarizes the results of the experiments, giving what are believed to be safe maximum lengths for nominally horizontal unvented

wastes from fixtures connected to a stack or vented

branch at points where they are free from detri- mental aspirating or back-pressure effects. It is understood that they refer to self-siphonage only. Possible increase in self-siphonage due to fouling has been taken into account.

Lengths of nominally horizontal unvented waste 'pipes believed

to he safe against self-siphonage

Plain P-traps nominal depth

full seal

Safe length of waste pipes for

Wash basin

with fall not

greater than

^4 inch to 1 foot or less than H inch

to 1 foot

Wide-bottomed fixtures with fall of

Yi inch

to 1 foot

54 inch

to 1 foot

Inches

2 Feet

4

6

8

Feet

4

68

Feet

812

16 3

4

These lengths are from the center of the trap to stack or larger vented branch waste and would permit one 90° elbow in the waste at a distance not greater

than 18 inches from the inlet arm of the trap. Elbows

in other positions should be counted as equivalent

lengths of pipe.

In this connection, it may be noted that the

Subcommittee on Plumbing of the Building Code

Committee in their report [4] did not utilize Hunter's results in the form of the above table,

but merely limited the unvented length of fixture

drain to 5 feet for all fixtures. Dawson and Kalinske [5] have reported a series

of tests on the relative merits as regards self- siphonage of P traps and deep-seal traps, but it was not their purpose to determine permissible

unvented lengths of fixture drains, and none were

reported.

Babbitt [6, 7] made investigations in 1924 and

1928 of the factors that affect self-siphonage of

plumbing fixtures, but his test procedme was not

such as to yield any information on permissible

unvented lengths of fixtiu'e drains.

5. Preliminary Considerations

The analysis of data on trap-seal losses is quite

difficult because of the many variables that affect these losses and because of the complicated flow

phenomena involved. However, we can predict

certain relations that should exist by utilizing the

methods of dimensional analysis and available

knowledge of the physics of the problem.

5.1. Typical System in Which Self-Siphonage

May Occur

A system typical of those which we shall consider

in this paper is shown in figure 2. The system

consists of a lavatory, an outlet orifice, a down

pipe, a trap, a fixture drain, a vent fitting, and a vent and drain pipe. Just below the outlet orifice there is an overflow opening into the down pipe,

through which overflow water can discharge or air can aspirate into the down pipe.

When we discuss the flow phenomena in the

system, it will be convenient to consider the system

in four separate parts: (1) The fixture outlet orifice and down pipe, (2) the trap, (3) the fixture drain,

and (4) the vent fitting and waste and vent pipe.

It is conceivable that any one of these four parts

of the system might be the controlling factor in

determining what the flow out of the fixture wfll be for a given depth of water in the fixture. If part of the trap seal is removed owing to a

pressure reduction in the drain that puUs the

water out of the trap or to the inertia of the

water column in the trap at the end of the dis- charge from the fixture, refill can occur in two

ways. First, if the fixture has a flat bottom, a

substantial amount of trail discharge will occur. That is, after the fixture has discharged nearly

all of its contents at a relatively high rate of flow, a sudden reduction in the rate of flow will occur, as has been explained earlier in this paper, and the

last fraction of an inch of depth of water in the

fixture will flow out at a small and gradually

diminishing rate. This flow will be too small to decrease the trap seal further as it passes through

the trap, and it will likewise be too small to cause

pressure reductions in the drain, so that it will tend to refill the trap to its completely full state. Second, refill may occur from water in the

drain if (a) the water level in the drain is higher

than the crest of the trap weir, (b) if waves

reflected from the vent fitting move back up the

drain and overflow the trap weir, and (c) if water

sloughs off from the upstream end of a slug of

water filling the cross section of the drain and

flows back over the crest of the trap weir.

5.2. Action of Trap

The authors have never seen in the literature a

detailed discussion of the action of a P-trap, which

is the type considered in this paper, so they wiU

next consider this question in some detail. The

immediate discussion will relate to the case in

which no refiU of the trap occurs.

a. No Refill of Trap

Figure 5, A, illustrates the situation that exists when the trap is filled to its normal level; that is, to the level of the crest of the trap weir with the

air pressure the same above the water level in

both legs of the trap. It is assumed that there

is no flow from the fixture to which the trap is attached. Now if pressure fluctuations in the

drain lead to a momentary or persisting pressure

excess in the drain over the atmospheric pressure

existing in the down pipe, then we shall have the

situation shown in flgure 5, B. The water level wiU faU in the outlet leg and rise in the inlet leg

4
of the trap until equilibrium has been attained.

We have the following relation between the

diflference in water levels thus produced and the

excess pressure in the fixture drain

:

Ap = pgAh, (1)

where

p = the density of the water in the trap,

Ap=the excess pressure in the drain,

fir=the acceleration of gravity,

Ah— the difference in water levels in the two

legs of the trap.

Now, if the pressures on the two sides of the

water seal equalize, there will be no loss from the

trap (except possibly a small loss due to the over03

O

P

1

A B C FiGUEE 5. Effect on trap seal of excess pressure in drain.

shooting of the column of water due to its inertia,

particularly if the pressure changes suddenly) , see

figure 5, C.

In an actual system, however, the pressure in

the drain will fluctuate above and below the

atmospheric pressure in the down pipe, so that

sometimes there will be a pressure reduction in

the draia. Under these conditions the water level in the inlet leg of the trap will be pulled down

below the level of the trap weir, possibly as far as is shown in figure 6, B, while water wUl flow

out of the outlet leg over the trap weir and will

thus be lost. If a succession of such pressure

reductions takes place, the losses wiU, of course, not be additive, but will correspond to the largest

pressure reduction that has occurred.

Figure 6, B, shows the condition that exists

when the pressm-e reduction in the drain is just

sufiicient to pull the water level in the inlet leg

of the trap down to the level of the dip of the trap,

but obviously the pressure reduction may be only

sufficient to puU the water level in the inlet leg

down to some intermediate position, or it may be

so great that air will be sucked through the water

seal at the bottom of the trap. The case shown

Figure 6. Effect on trap seal of reduced pressure in drain.

in figure 6, B, is a special one that will receive

consideration later in this report.

After a pressure reduction in the drain, when the

water levels in the two legs of the trap again

equalize, the condition will be as shown in figure

6, C. The magnitude of the loss thus produced,

whether it be caused by the discharge of other

fixtures or by the discharge of the fixture on this drain (i. e., from self-siphonage) , should not be

permitted to exceed a certain amount, which may

be different for different traps, if we are to prevent

the passage of sewer gas in objectionable quantities back through the trap into the building under

conditions of fluctuating pressures in the drain.

Once a particular trap-seal loss, or a particular

remaining depth of trap seal, has become generally accepted as the maximum or minimum that

should be permitted, then the system should be

designed so that this loss will not be exceeded

under any but very infrequently occurring circumstances. Building drainage systems are ordinarily designed so that pneumatic pressure fluctuations

in the fixture drains wfll not exceed about ±1

inch head of water. Obviously, if there is a

one-half inch depth of water in the trap, measured

upward from the dip of the trap, the trap seal wiU just be adequate to prevent sewer gas from

being forced back through the seal into the down

pipe and thence into the building when the air pressure in the drain is 1-inch head of water above

atmospheric pressure. If the trap seal is reduced

so greatly that an air passage exists below the dip

of the trap, then gases in the drainage system can

pass back freely into the building whenever

pressures in excess of atmospheric pressure

exist in the drain.

b. Refill of Trap

In the self-siphonage process there are two

ways in which the trap seal may be replenished

after the discharge of the fixture connected to the

trap in question has ceased. These consist of

the refill of the trap by the trail discharge of the

fixtm'e and the refill of the trap by water flowing

back from the fixture drain into the trap.

At first thought, it might seem that the flow taking place through a trap ordinarily consists of

954486—51 2 0
water only. However, this is not the case, as has aheady been pointed out. In most instances,

air is carried with the water also. We have observed this phenomenon in a transparent trap and

fixture drain connected to a lavatory, and these

observations indicated that air entered the trap

in three ways. First, air was entrained by the

water as it passed the overflow outlet just below

the lavatory, and this air was carried through

the trap in the form of bubbles.

Second, as the water siu-face in the lavatory

continued to recede, a vortex formed in the lavatory, and in this way additional air was carried

through the trap into the drain with the water. Third, near the end of the discharge of the

lavatory, with its attendant rapid decrease in

the rate of flow through the lavatory outlet orifice,

water was flowing out of the trap more rapidly

than it entered, owing primarily to the inertia of

the water in the trap and drain. Hence the water

surface in the inlet leg of the trap receded to such an extent that in many instances air bubbled past

the dip of the trap and entered the outlet leg of

the trap. This latter manner in which air enters or passes through a trap is especially noticeable

when a large pressure reduction occm*s in the flx- ture drain near the end of the discharge period.

Now if the rate of flow in the drain and the

diameter of the drain are not sufficient to close

off the passageway in the inlet branch of the stack

fitting, tills air can pass off to the vent or stack

and exerts no particular effect on the nature of

the fiow in the drain.

However, if the flow is sufficiently great to

close off the passageway just referred to, then the

air in the drain becomes trapped between the solid mass of water in the vent fitting and the water in the trap and causes changes in the nature of the

fiow in the drain. This in turn affects the pressures in the drain and hence on the outlet end of

the trap when the discharge from the fixture

ceases. The following is typical of the phenomena that were observed when air entered the drain in the

first manner described above. The entrained air from tiie overflow outlet entered the drain in the

form of bubbles, which rose to the top of the drain

at some indefinite point along it. If the quantity

of air that coUected in this way was sufficiently

large, the drain, which was flowing full from the

trap weir to this point, flowed only partly fuU

from this point on to the vent fitting. As the

volume of entrained air diminished near the end

of the lavatory discharge, the water frequently

rose to the top of the drain along one or more portions of its length, filling the entire cross section

of the drain (see fig. 4). Thus one or more plugs

of water formed in the drain near the end of the

period of discharge from the lavatory.

As the fiow from the lavatory trailed off, the

velocity of these plugs of water toward the vent

fitting decreased, owing to the adverse head of

water in the trap, which tended to slow them down

and at the same time the lengths of the plugs of

water diminished, owing to the sloughing off of

water at their upstream and downstream ends.

If one of these plugs was sufficiently near the

trap when this sloughing off occurred, some of the

water that sloughed off from the upstream end of

the plug flowed backward up the drain and

partly or entirely refilled the trap. When the

plug was further down the drain, this temporary

backflow of water in the drain did not reach the

trap, ard hence no refill from this cause occurred.

Under test conditions that were as nearly alike as it was possible to make them, the plugs of water

that formed as described above varied greatly in

size and location, and hence their effect on the

remainmg trap seal varied greatly. Thus it is apparent that there is no single definite flow condition in the drain corresponding to the discharge

of the lavatory, so that considerable variation in

trap-seal loss must be expected, even when the

conditions are as nearly alike as it is possible to make them.

It was observed also, when the fixture drain was

short, that refill entered the trap from the drain

because of waves refiected from the vent fitting.

Another way in which partial or complete refill of a trap can occur is encountered when a bathtub

trap and drain connect to a wet vent. This

phenomenon has been described elsewhere [2] and will not be discussed here.

With regard to the refill of the trap by trail discharge, it is weU known that with fixtures having relatively flat bottoms, such as a sink, a laundry tray, or a bathtub, the trail discharge

lasts longer and the fflm discharge is more pronoimced than it is with a round-bottomed fixtm"e,

such as a lavatory, and hence there is a greater

tendency m the former case for refiU of the trap

to occur. The characteristics of the discharge curve for a bathtub—a fiat-bottomed fixture—are shown in

figure 3. The tub had initially a 10-inch depth

of water in it. As the water surface lowered, the

rate of flow gradually fell off, until suddenly a sharp fall almost down to zero occurred. The

beginning of this sharp fall is marked by the for- mation of a vortex that persists until the tub is empty, except for the minute rate of flow from the

film of water remaining on the surface of the tub

at the end of the discharge.

^ 5.3. Trap-SearLoss

There are various ways of expressing the "trapseal loss" or the "limiting trap-seal loss." By

"limiting trap-seal loss" we mean that trap-seal

loss that is arbitrarily selected by general agree- ment as being the maximum that can be permitted

if we are to have assurance that sewer air wiU

not pass through the trap seal back into the in- terior of the building.

If we are analyzing the problem from the standpoint of dimensional analysis, we shoifld naturally

6
express this loss as the ratio of the trap-seal loss,

h, to the original depth of water in the trap (measured from the dip of the trap) that is, as hjt. It is common practice in plumbing codes to

restrict the depth of trap seal, t, to values between

2 and 4 inches, and traps are made with different

values of t. For example, the traps used in tlais investigation had the dimensions given in table 1.

Table 1. Dimensions of traps used in this investigation

Trap t d, t/d, See fig- ure

Inches Inches

lJ4-inch adjustable oast brass 2. 00 1. 188 1.68 7 IM-inch drawn brass tubing. __ 3. 188 1. 125 2. 83 8 IM-inch cast brass 1.75 1.25 1.40 9 IH-inoh drawn brass tubing 3. 563 1.375 2.59 10

IJ/^-inch cast brass _ 2. 25 1.50 1.50 11

Obviously, the value of h/t may vary from zero

to unity. Wlien this ratio has reached the value

zero, it denotes zero trap-seal loss. When it has

reached the value unity, this means that the

water has been removed from both legs of the trap

down to the dip of the trap and that minute

changes of pressure in the proper direction will

suffice to force sewer gas into the building. One

investigator [4, p. 137] has proposed that a value

of 1 /2 be used as the value of h/t to constitute the

dividing line between satisfactory and unsatisfactory performance of the trap.

However, there are two other common methods

of establishing the limiting trap-seal loss, either of

which has a more practical significance than the one just discussed. The first is to base the limiting

trap-seal loss on a fixed remaining depth of trap

seal. This is probably the most logical criterion to

use, since the ability of the trap to prevent the

passage of sewer gas back into the building depends on the remaining trap seal. A value of

1 inch for this limiting value of the trap seal is quite commonly used.

The other method of establishing the limiting

trap-seal loss is to define it as a fixed reduction in

trap seal, regardless of the initial depth of seal. This is a simple and safe definition to use and has

other advantages, but for large depths of trap seal

it is excessively safe and is not as logical as the

defrnition given in the preceding paragraph.

A fourth method of defining the limiting trapseal loss is offered here for the first time, as far as the authors know, see figure 6. Figure 6, A,

shows the conditions in the trap when the trap-seal

level is at the crest of the trap weir. This is the

normal initial condition. Now assume that a pres- sure reduction in the drain or other condition

causes the water level in the inlet leg to fall imtil

it just reaches the dip of the trap as shown in

figm-e 6, B. The water thus displaced flows over

the trap weir and down the drain, and thus is not

available to refill the trap when the pressures on

the two sides of the trap seal equalize. Now

assume that the pressures do equalize, and the

levels in the two legs again are the same. This

condition is shown in figure 6, C. We propose the

name, "critical trap-seal loss," for this condition.

The critical trap-seal loss is the maximum loss that can occur in the trap, unless the pressure

reduction in the drain becomes and remains for an

appreciable length of time so excessive that air is sucked from the inlet leg of the trap through the

water seal into the drain, and in this process

carries with it some of the water in the trap by

what may be called a pumping process. Thus the critical trap-seal loss corresponds to a

natural maximum loss that can occur for any

P-trap and hence suggests itself as a natural

criterion to adopt. However, the occurrence of

the critical trap-seal loss for a particular trap might

conceivably result in a remaining trap seal of less than 1 inch, which fact has a real significance if we

design the system so that the pressure reductions

in the drain do not exceed 2 inches. Thus, if thi?

critical trap-seal loss were adopted as the borderline between satisfactory and unsatisfactory per- formance, we would have to examine the dimensions of each trap used to see whether the critical trap-seal loss for that particular trap would leave

a remaining trap seal of less than 1 inch. This

question is discussed in section 5.5.

5,4. Comparison of Critical Trap-Seal Loss

With 1-Inch Trap-Seal Reduction and

1-Inch Remaining Trap Seal

The traps investigated are shown in figures 7, 8,

9, 10, and 11. Because of the desirability of

making certain simplifications in the computations, these traps will be divided into two groups.

The first group includes the l)^-inch adjustable

cast-brass trap shown in figure 7, the l}^-inch

drawn-brass- tubing trap shown in figure 8, the

l}^-inch cast-brass trap shown in figm-e 9, and the

l}^-inch drawn-brass-tubing trap shown in figure

10. The other trap, the l}{-inch cast-brass trap

shown in figure 11, will be considered in another manner. The basis for dividing these traps into the above

groups is: with the first group of four traps, the

radius of curvature of the U-bend is nearly the same as the radius of the outlet bend. By making

the assumption that these two radii are equal, a

considerable simplification in the computations

results, as will appear in the analysis to be given.

The fifth trap, which is considered separately, has

a very small radius of curvature of the outlet bend

and a fairly large radius of curvature for the

U-bend. It will be assumed m the computations

relating to this trap that the outlet leg is cylindrical from the downstream end of the U-bend to the level of the trap weir. It then becomes

necessary to compute the volume of water in the

U-bend of the trap from the upstream end of the

U-bend to the level of the dip of the trap. This is a somewhat tedious process. The following applies to the foiu- traps shown

in figures 7 to 10, inclusive, see figure 12: 7
8
Figure 9. 1%-inch cast-brass trap.

9
FiGUBE 11. IVi-inch cast-brass trap.

FiGUBB 12. Trap for theoretical discussion. The initial volume of water in the trap is Va+V,+ V,+ Va+V,.

The volume of water lost when the water level in

the inlet leg is drawn down to the level of the dip

of the trap is Va-\-Vi,. Then, when the pressure

again equalizes, the final volume of water in the

trap is the same as it was after the volume Va+ Vj, was lost, or is V,+ Va+Ve =2Vr+V,-\-Vc.

But we have assumed that Vb=Ve. Hence

Then

Va is the volume of water contained in the

cylindrical portion of the outlet leg of the trap,

and hence the height of the cylinder occupied with

the volume Vf is half the height of the cylindrical

portion of the leg.

Iji-inch adjustable trap {see Jig. 7). The height

of the cylindrical portion of the outlet leg is t—Tu—ro, where r„ is the radius of curvature of the

the lower bend, and Vo is the radius of curvature of the upper bend (see fig. 12). Hence for this trap

we have for the height in question: 2 —^%2 —/'2 = ^K2 inch or 0.969 inch. Then /tc=^}^2-^2 +K =0.985

inch.

I'ji-inch brass tubing trap (seeJig. 8). t—ru—ro=

3%6-'K6-iK6=lK6 inches=1.437 inches. Then

Ac= 1.437/2 +1X6 = 1.53 inches.

lYi inch cast-brass trap (see Jig. 9).

l%-i%2-i}^2 =% inch=0.875 mch.

{%)n + ')i2 =^%2 inch= 0.782.

l}i inch drawn brass trap (see fig. 10). t—r^

t —Tu- Then h,=

.0 9/ ] -0/16 — 25/ - /32- inches= 1.697 inches.

Then /i,= 1.697/2 +2^^2 = lV64inches= 1.641 inches.

PA inch cast brass trap {see Jig. 11).

10
In computing the critical trap-seal loss for this trap, it was assumed that the outlet leg is cylindrical from the downstream end of the U-bend to the level of the trap weir. Then (see fig. 12),

and the volume of water lost when the level in the

inlet leg is drawn down to the level of the dip of the

trap is Va-Wi.

The volume of water, Fs, lost from the U-bend was computed by an approximate process and was

found to be, for this particular trap, equal to the

volume of a torus having a central angle of about

30°. That is, for this particular trap, the volume

would be (30/360) (27r2i?r^ 2) =0.0833X2X9.88X

1.313X0.75^=1.215 cubic inches. See figure 12 for the notation used in the last equation.

As the radius of the trap tube is 0.75 inch, this

corresponds to a water column 0.69 inch long in the

cylindrical portion of the tube. The water level is then at a distance of 1.07 inches above the dip of

the trap, and the critical trap-seal loss is 1.18

inches.

6. Analysis of the Problem

6.1. General Considerations

The discussion in earlier sections of this paper of

the phenomenon of trap-seal losses due to self- siphonage has made it clear that we are concerned

with an extremely complicated problem, one which

defies analytical treatment. Not only are there

many variables on which trap-seal losses depend,

but in addition we are not interested in what happens in the trap when a steady state of flow has

been established, but rather in what occurs under

transient conditions, that is, when the discharge

from the fixture ceases. When a physical problem is too difficult for

analytical treatment, one resource is to utilize dimensional analysis to establish the particular

dimensionless variables that may affect the result

and then indicate that there exists a functional

relation between them:

4>[-Kl, 7r2, -TTs, ... 7r„_i] =0, (2)

, where the tt's are different dimensionless quantities

j built up from the pertinent physical quantities,

and</)[ . . . ] =0 denotes that a functional relation

i exists between them. The experiments are then

iplanned to develop this functional relation [8, 9,

110].

j However, the system with which we are dealing

in this investigation was too complicated to permit

la single functional relation to be developed that

iwould include all of the dimensionless variables

Ithat were involved under different conditions.

iThis can perhaps be appreciated by a more detailed

jconsideration of the system, see figure 2.

I We see that when the fixture discharges into

jjthe continuous waste and vent, the water flows

successively through these parts of the system:

(1) Outlet orifice and down pipe, (2) trap, (3) drain, and (4) vent fitting. It will be assumed

that the diameter of the continuous waste and

vent is adequate to carry the flow properly, and

of course it is vented. Hence it should have no

measurable effect on the trap-seal losses. We

shall also assume for simplicity that the diameter

of the down pipe is the same as that of the outlet

orifice. Now the flow out of the fixture may possibly be

determined by any one of the four portions of the

system outlined above. In other words, any one

of the four portions of the system may be the

"critical" part. Furthermore, each portion of the

system will give rise to a characteristic Froude

number, since the acceleration of gravity is the

impelling physical force that produces the flow. But for any given set of conditions only one of

these Froude numbers will be involved, since the

Froude number characteristic of that portion of

the system that is critical under the given conditions is the pertinent one. However, there is no

simple way of establishing a functional relationship that, under a given set of conditions, will bring in one characteristic of one part of the

system and exclude others, while, under a differ- ent set of conditions, will bring into play a different

Froude number and exclude the others.

Furthermore another somewhat similar complication was found in the fact that, under certain

conditions the slope, S, of the drain was involved

to the first power, while under other conditions it was involved to the one-half power.

Again, the form of the fixture played an important part in determining the magnitude of the

trap-seal losses. A flat-bottomed fixture produced

a long;-continuing trail discharge that tended to replenish the trap and so reduce or completely

prevent trap-seal losses. On the other hand, a

deep, narrow fixture that caused very little trail discharge tended to produce large trap-seal losses because of the slight degree to which the water

lost from the trap was replenished in this way.

Under these conditions, the results obtained were

valid only for the particular shape and size of the

fixture used.

In view of the complications of the problem, it seemed that the only goal that was feasible to set was that of determining what combinations of

dimensionless variables, under given conditions,

would bring order out of the data and to show

that these particular variables had a rational

basis. The development of these variables and

their rational basis will be presented shortly.

In fact, as so often happens, some of these

variables had been found by cut-and-try methods

before their rational basis had been shown. This was due to the fact that heavy pressure was placed

upon us to get practical results at the earliest

possible date to be used in preparing certain sections of the Uniform Plumbing Code [1 1] . Because

of this pressure, it was only when the results were

11
being written up finally that time could be taken

to make an adequate analysis of the problem. As

a result, the tests were not designed to get the

maximum amount of information from them.

However, the practical results that were desired were obtained sooner in this way than if time

had been taken to make a preliminary analysis.

A little consideration of the transient aspects of

the problem is required next in order to justify the

establishment of the characteristic dimensionless

numbers for the different parts of the system under

assumptions of steady flow, whereas the trap-seal

loss occurs only because of the cessation of the

flow. Fundamentally, the trap-seal loss is due to the rate of flow through the system at the moment

when the flow may be said to cease. However,

"the mom.ent when the flow may be said to cease"

is a rather vague concept, as can be seen from

figure 3. Practically, we might take this point as that at which the vortex begins or that at which

the vortex flow ceases and film flow begins.

"When the flow ceases, the trap-seal loss that

results is prim.arily due to the inertia of the water,

except as other factors, such as the resistance to flow offered by the drain and the occurrence of

trail discharge, are concerned.

This rate of flow, Q, may depend on any of the

characteristics of the system: diameter and shape

of the outlet orifice; length and diameter of the

down pipe ; diameter and shape of trap ; diameter,

length, slope, and roughness of the fixture drain;

and size and shape of vent fitting. The trap-seal

loss, then depends on all of these quantities, since

it is a function of Q, and it also depends on some

additional quantities that do not affect Q at all, or not measurably, such as the depth of trap seal

and the trail discharge.

It is a simple matter to include the depth of

trap seal in the list of physical quantities and to use it in forming a dimensionless variable, but it

is not so simple to include the effect of trail discharge, since the latter may affect the trap-seal

loss through the rate at which it decreases to zero. Hence we recognize the trail discharge as one quantity with which we cannot operate

formally, and we specify that the trap-seal losses that are found with a particular shape and size of fixture apply only when that fixture, or a fixture

similar to it in size and shape, is used.

6.2. Derivation of the Applicable Dimensionless Variables

We can treat the system as a whole in doing

this, simply listing all of the physical and geometrical factors that we believe may affect the

trap-seal loss and then using the method of di- mensional analysis to form the corresponding

dimensionless variables, each of which must then

be considered in turn, so that we may determine

from our knowledge of the physics of the problem

which of them may be omitted from consideration

as having no appreciable effect on the phenomenon

in which we are interested.

However, it will probably be clearer if we consider the individual parts of the system in doing

this, discussing each of the dimensionless variables

that apply to that part of the system before passing on to the next part of the system.

a. Trap-Seal Loss

It has already been pointed out that the trapseal loss should be introduced as a dimensionless

ratio if we use the method of dimensional analysis,

and the logical form of this ratio is hjt, where h

is the trap-seal loss (it could equally well be taken

as the remaining trap seal if we chose), and t is the initial depth of trap seal, that is, the vertical

distance from the level of the trap wen- to the

level of the dip of the trap.

b. Orifice Outlet and Down Pipe

The volume rate of fiow out of the lavatory or other fixture, which is the fundamental quantity

that affects trap-seal loss, depends on the geometry

of the outlet orifice and down pipe, on the rate of

air entrainment from the overflow outlet, and on

the head of water from the water surface in the

fixture to the lowest section of the down pipe.

This head will not be exactly equal to the vertical

height of the water column between these two

levels because (1) the pressure at the bottom sec- tion of the down pipe will not be atmospheric

under most conditions of flow, whUe the pressure on the surface of the water in the flxture is at- mospheric, and (2) the entrained air in the column

of water under consideration will cause the density

of the mixture of air and water in this pipe to

differ from that of the water alone.

These effects are too complicated to analyze for our present purpose, but we can write down the

principal dimensionless variable, that is, the one

that has the greatest effect on the outflow and

hence on the trap-seal loss. The general equation for flow from an orifice is Q=CA^2^, (3) where

Q=the volume rate of flow

(7= an empirical dimensionless coefficient

^=:the cross-sectional area of the oriflce gr=the acceleration of gravity

jH'=the vertical distance from the water i surface in the fixture to the lowest ' section of the down pipe, corrected for \ any deviation from atmospheric pres- !' sure that may exist at the latter section.

^ For our present piu-pose, it will be more con- ' venient to characterize the area of the orifice opening by its diameter, do, than by its area, A.

Hence eq 3 can be written

12
The left member of eq 4 is dimensionless and, in

fact, is the particular form of dimensionless

variable that we call the Froude number, since it involves the force of gravitation through the

acceleration g. Thus the Froude number that

applies to the outlet orifice and down pipe is Q|do'^/^.

As the down pipe is short and is vertical, we

need not consider the effect of friction on the flow

in this part of the system. Note that, for simplicity, we have assumed that the diameter of the

down pipe is the same as that of the outlet orifice.

c. Fixture Trap

In considering the flow through the fixtm-e trap, we are led to the conclusion that the following

quantities are the principal ones that may affect the trap-seal loss: (?= volume rate of flow

gr= acceleration of gravity

rf«= diameter of the trap

^= depth of trap seal /«= effective friction and bend loss coefficient

that is characteristic of the trap.

Other dimensions of the trap are involved, but

probably to a much less degree than the diameter

of the trap and the depth of trap seal. These

other dimensions will be ignored, and it will be

recognized that the results obtained with any

particular trap are valid only for that size and

shape of trap.

ft is in the form of the Darcy-Weisbach dimensionless friction coefficient and includes both the

loss due to surface friction and the bend loss, the

latter being assumed to be distributed uniformly

over the developed length of the trap.

Hence we have n=5 physical quantities involved

in flow through the trap: Q, g, dt,t, and ft- These

quantities can be expressed in terms of i=2

physical dimensions—length and time—and ac- cording to the theory of dimensions, they will

combine into n—i=3 independent dimensionless

variables.

The first of these variables is a Froude number,

which is present because, as has already been

pointed out, the force of gravity is the pre- dominating physical force involved in the phe- nomenon of flow through traps. While the given

combination of quantities, Q, g, dt, and t, is adequate to form this dimensionless Froude number, the theory of dimensions affords no assurance

that the above is the exact combination that

should be used, as regards the way in which dt and t enter the nimaber. All that the theory of

dimensions tells us in regard to these lengths is that they must enter in such a combination as

to have the dimensions of (length)^''^.

However, by drawing on our knowledge of the

physics of the phenomenon, we can at least get a

suggestion as to the form of the Froude number

that is characteristic of the trap.

We note that the ratio, Q/di^, is proportional to the mean velocity, Vt, of the flow thi-ough the trap,

assuming that the outlet leg of the trap is flowing

full. We also note that is a velocity, and more specificaUy, it is proportional to the velocity

of free fall that would be attained by the water in

falling through the distance t. Thus the dimensionless variable, Q|di^^|gi, may be looked upon as the ratio of two velocities, one tending to empty

the trap and the other tending to keep it filled. Thus we find that there is a rational basis for this

particular form of the variable, and we should

expect, therefore, that there might be found some

relation between the trap-seal loss and this ratio

when the trap is the controUing factor m the flow

phenomena in the system.

As a matter of pure expediency, a change was made in this Froude number by replacing t by U, in plotting the results of certain tests, since it was

found that this appeared to yield less scatter of the

observed points than did the use of the quantity t. The relation between t and ty is

U=t-\-dtl2,

as can be seen from figure 1. The variable tjdt takes into account the relative

proportions of the trap but is not sufficient to specify the shape of the trap. Two quantities that

obviously should be added to the list of significant

quantities if we were studying the effect of changes

in the shape of the trap are the radius of curvature*

of the U-bend at the bottom of the trap and the

radius of curvature of the bend at the outlet end.

Even the addition of these variables does not suffice to permit an analysis to be made of the effect of changes in the shape of an actual trap, because

there are other minor differences between the traps

used, as can be seen from figures 7 to 11, inclusive.

Neither were the variations made in the test conditions sufficient to permit an analysis of the effect of varying the dimensions of the traps to be made,

nor was this the purpose of the tests. The quantity /(, as has already been stated, is a dimensionless friction factor analogous to the

Darcy-Weisbach friction factor,/, which is defined

by the equation

This equation represents the friction head loss,

H, in a straight full pipe of length I and diameter d

when a fiuid is flowing through the pipe with the

average velocity v. If the pipe is curved, there

will be another loss of head, av^/2g, where the

coefficient a will vary with the geometry of the cm-vatm-e. If we add these two losses, we have

the result

954486—51 3
We can replace the quantity in the parenthesis by

a single coefficient /< in applying the equation to

fixture traps.

It was not feasible to investigate the effect of

variations in the coefficient nor would such aa

investigation have proved fruitful if carried out,

since other and probably far more important factors that affect the trap-seal losses were present,

and since it is of more practical importance to standardize traps than to make exhaustive tests to determine the best possible proportions. Hence

the quantity will be left out of consideration in the analysis of the data.

d. Fixture Drain

The physical quantities that affect flow through

the fixtm-e drain are ()= volume rate of flow

(/= acceleration of gravity

Z=length of the drain

ci?2= diameter of the drain

*S'= slope of the drain

/d=friction factor applying to the drain.

Considerations of dimensional analysis yield

the following four dimensionless variables

There is no question as to the form of the

Froude number, ()/c?2^V!7^2, in coimection with the

drain, since the only other length than ^2 that

could enter tliis variable is the length of the drain

/, and it is hardly conceivable that this length

would be involved in this particular variable.

The variable, l/ch, is always present in pipe-flow

problems, and so it would be expected that it would

be involved here.

However, a study of the data brought out the

fact that if we plot Qjd2^^[gd2 against lld2, we

obtained a separate curve for each value of the

slope S, while if, for some of the tests, we plotted

this Froude number against Slld2 the curves, for the most part, coalesced into a single curve; while,

for other tests, plotting the Froude number

against S^'Hld2 made the points coalesce into a

single curve. In no instance did the points form

a clean-cut curve, but rather they came nearer

to combining to form a definite curve by plotting

against one or the other of the two variables mentioned than if plotted against some other power of

S. This fact led to a further investigation of the

problem.

We start with the following Chezy formula for flow in open channels, which is the case we have

when the drain is flowing only partly full

v=C^d2S,

where 2;=the velocity of flow in the drain

C=a constant

rf2=the diameter of the drain

(S^the slope of the drain.

(7)

We can modify this equation to make it dimensionally correct by inserting g, the acceleration of

gravity, and at the same time we multiply v by

the cross-sectional area A of the stream in the

drain in order to obtain the volume rate of flow Q :

(8) We further modify the equation by replacing A

by some constant multiplied by the diameter

squared and absorbing all the constants in a new

constant C"

Q=C"d2'^gd2S. (9)

This leads us to the product of two dimensionless

numbers, the first of which is the Froude number

previously obtained by the methods of dimensional analysis, ^?/c?2^-\'^, and \IS^'^. If we start with the Darcy-Weisbach formula

for friction loss in pipes flowing full,

do 2,

(5)

we arrive at the same result. By this process of reasoning, combined with

what the theory of dimensions told us, we arrive at the variables.

Q I d2^^gd2S d2

S, and fd

For reasons that will be explained shortly, we

shall not retain the friction factor /d, so that we

are concerned merely with the three variables re- maining. These are not in exactly the form in

which we were led by empirical methods to plot

the data, but we can modify these variables to obtain the form actually used, owing to the fact

that it is permissible to combine the pertinent

dimensionless variables as we wish. Hence we can multiply Q/d2^-^gd2S by S^'^ to obtain Q/d2^-/gd2,

and likewise we can multiply Z/o?2 by either S^''^ or by to obtain S^'Hjdi or Slld2, thus having finally one or the other of the two following groups of

dimensionless variables

Q SI

or

d2^^gd2 d2

Q S''H

d2^^Jgd2 do

S.

This merely shows that there is a rational basis for the use of the groups of variables listed above,

although these variables were originally selected

for plotting the data by purely empirical means.

e. Vent or Stack Fitting

Two forms of vent or stack fittings are com- monly used in installations such as we discuss in

tliis paper—the long-turn fitting and the short14
turn fitting. Furthermore there will be variations

in each of these two fittings in that for a given

vent or stack diameter the drain diameter, and

hence the diameter of the side inlet of the branch

fitting, may be equal to or less than the vent or stack diameter. Hence flow through the side

inlet of the branch fitting will lead to at least the

following dimensionless variables:

Q

d^ — . {->

adn, is \ t'

plus other length ratios that specify the shape of

the fitting. It will be noticed that the variable, Qld^-^gd-i, is identical with the Froude number which characterizes flow in the fixture drain, and hence no new

Froude number is added thereby to the two

already listed. The other variables all have an

effect on trap-seal losses, but it was not feasible to investigate the effects of each separately, nor was

this contemplated within the scope of this investigation. Hence the data were treated separately

for the long-turn and the short-turn fittings, the

only two used in this investigation.

6.3. Effect of the Density of the Air and

the Water

The ratio of the density of the atmospheric air to that of water wUl obviously affect trap-seal

losses. However, if this ratio is constant, or very

nearly so, these two physical quantities can be

ignored, and their effect will be absorbed in the

errors of the observed results. Changes in air density at a given locality will be appreciable but will have very little effect on

the trap-seal losses, since air is only about one- thousandth as dense as water. Changes with

altitude will also be appreciable but will have little effect for the same reason. Water, if unmixed with air bubbles, will have a

density which, for the purposes of this invesitgation, can be considered constant. However, it was observed in many of the tests of lavatory self- siphonage in which transparent plastic traps and

drains were used that, during the discharge of the

fixtiu-e, air was aspirated from the overflow con- nection above the trap mto the water flowing

through the trap and drain. In addition, a vortex

usually formed in the fixture near the end of its period of discharge, with consequent flow of air into the system. For these reasons the effective

density of the air-water mixture flowing through

the traps and drains of plumbing fixtures is not

constant but varies with the type of fixture and

also to some extent, at least, during the period of

discharge of the fixture.

6.4. Summary

Summarizing, we may list the dimensionless

variables with which we may be concerned in

dealing with the problem of self-siphonage as

follows:

h Q t Q Q SH

t' d,'^/gt d! do^^gU d^^-^gdl d^

S,

in which a may take on a value of either unity or

one-half.

We express the fact that there is some functional

relation between these variables by writing:

function

Q Q Q

gd2 d2 d^^4g^ )

dt do^^/gH di'-yjgd:

7. Experimental Investigation

7.1. Description of the Test System

In this investigation the tests were made, for the most part, with standard plumbing fixtures

connected to complete drainage systems, as shown

in figures 13 and 14. The building sewers of these

systems were connected to an 8-inch-diameter

street sewer, in which the flow could be varied up

to 300 gallons per minute and which could be made

to flow completely or partially filled at will. In

these systems the stacks and some of the fixture

drains were made of transparent methacrylate

plastic tubing and fittings. However, the trans- parent parts of the system were used primarily to enable us to see the flow phenomena that occurred

in connection with self-siphonage, and the final test results were obtained with the conventional

metal pipes and fittings. StiU another system

the one shown in figure 15—was used to study

systematically the effect of the volume rate of

flow through the fixture trap and drain as well as lengths, shape, and diameter of drain and type of

INCH DIAMETER STACK

li--INeH DIAMETER WET VENT AND FIXTURE DRAINS

SATHTUB

l^-INCH DIAmETER HORIZONTAL BRANCH

8-INCH DIAMETER STREET SEWER

3-INCH DIAMETER TRANSPARENT TUBING

4-INCH DIAMETER FIBER CONDUIT

lO'-O" -o

70'- 0"- FiGURE 13. Wet-vented test system.

15
vent fitting on the trap-seal reduction. This last system was a more severe test of the ability of fixture traps to resist self-siphonage than the other

two systems, in which actual plumbing fixtures were attached to the system and discharged. This

is due to the fact that some traU discharge oc- curred when actual fixtures were used, and this

trail discharge tended to replace any water lost from the trap as a result of the main part of the

discharge. When the system shown in figure 15 was used, there was virtually no trail discharge.

Figure 14. Stack-vented test system.

3-FEET OF GLOSS TUBING SiME SIZE as OBOIN

MEASURING TANK

Figure 15. Arrangement of apparatus for "no-trail" discharge tests.

7.2. Test Procedure

In the self-siphonage tests the fixture was filled and then was allowed to drain either by pulling

the plug from the outlet orifice or, in the case of

the water closet, by operating the flush valve.

With the lavatories, bathtubs, and sinks, trap-seal

losses were measured by means of a small water

manometer connected to the trap through the

clean-out, and in the case of water closets by

simply measuring down to the water surface from

a horizontal reference plane.

7.3. "No-trail" Discharge Tests

In the usual discbarge of a fixture we have, at the end of the discharge, a condition that is called

"trail discharge" and described in section 2. As

the discharge from the fixture nears its end, the

rate of discharge decreases rapidly (see fig. 3)

owing to the formation of a vortex over the outlet

orifice. In addition, an appreciable amount of

water adheres to the inner sm-face of the fixtures,

and this slowly drains out of the fixture after the

vortex has ceased.

In order to simplify the initial study of the

phenomenon of self-siphonage by eliminating some

of the complications due to this trail discharge, an investigation of the efl^ects of rate of discharge,

and of the length, slope, and diameter of the fix- ture drain, in particular, on self-siphonage, a number of tests were made with the system shown in

figure 15 in which trail discharge was prevented

from occurring. These tests will be referred to as "no-trail" discharge tests. In these tests trail dis- charge was prevented, or reduced to a minimum,

by producing a constant flow through the supply

pipe and then stopping this flow abruptly by means

of a quick-closing valve.

The traps used in this part of the investigation

are shown in figure 16. They included a 2-inch

cast-steel trap having a depth of trap seal of 1%

inches, a l}^-inch drawn-brass- tubing trap having

a depth of trap seal of 2}^ inches, a l}^-inch cast- brass trap having a depth of trap seal of 2% inches,

and a l)^-inch cast-brass trap having a depth of

trap seal of 2 inches. Thus all of the traps used

in these tests were relatively shallow traps.

The results obtained in these tests are given in

figure 17 for long-turn vent fittings and in figures

18 and 19 for straight-tee fittings. The results are plotted in the form of dimensionless variables,

since in this way a number of individual curves

for different slopes are brought together into a

single curve. The utility of such a curve can be

shown in the following manner. Suppose we want to compute the maximum

permissible unvented length of 2-inch drain on a

}^-inch-per-foot slope for a fixture having an

average rate of discharge of 13.2 gallons per

miuute and having little or no trail discharge.

This last-mentioned condition is a very severe one and restricts sharply the permissible unvented

length of drain. We shall assume that a long-turn

vent fitting will be used to connect the fixture drain

to the vent and that the trap shown in figure 16, A

(2-inch cast steel) is to be used with the fixture. Then c?«=1.99 inches, t=1.75 inches, c^2=2.07

inches, and ^i =2.78 inches. The corresponding

values in feet are 0?^= 0.166, fi =0.232, and d2=

0.1725. The slope is foot per foot. The aver- age rate of discharge is ()= 0.0294 cubic foot per

second. All quantities are reduced to foot-second

units before they are substituted in the variables

in figure 17.

16
2- INCH CAST STEEL TRAP

7"

|i-INCH CAST BRASS TRAP

CM

l-|-(NOMINAL 1^) DRAWN BRASS TUBING TRAP

'of. \

1 -<£-

16

l^-INCH CAST BRASS TRAP

Figure 16. Traps used in this investigation.

1.0

0.8

1^0.6

0.4

0.2

1

Ai "*^2-inch diameter drain on

1/4 inch-per-foot slope

a O

i 0

\. 0

0 12 3 4 Si/dj

Figure 17. Curves for computing maximum permissible unvented lengths of fixture drains.

0 SI Belation between — and t- for ft/< = 0.5. Long-turn vent fitting.

0.8

0.6

0.4

ft- R

r 0 c 0

Symbol S

d, d2

t ti Figure Nominal Actual Nominal Actual

In.lft. In. In. In. In. In. In. A H, y^.'A-- 2 1.99 2 2.07 1.75 2.78 16, A M 2 1.99 2 2. 07 1.75 2. 78 16, A 0 H, 'A, 'A m 1.54 IH 1.61 2. 38 3.18 16, C • H --- 1.54 IH 1.61 2. 38 3. 18 16, C

H, Vi, H \Vi 1.38 IM 1.38 2. 50 3. 19 16, B

34--- VA 1. 38 1.38 2. 50 3. 19 16, B

0 12 3 4 Si/da

Figure 18. Curves for computing maximum permissible unvented lengths of fixture drains. 0 SI Belation between — and 3- for ft/£=0.5. d2'^/gd2 Slopes of fixture drain H, H> ?4 inch per foot.

Straight tee vent fitting.

Symbol

d, d2

i ti Figure Nominal Actual Nominal Actual

In. In. In. In. In. In. A 2 1.99 2 2.07 1.75 2.78 16, A

0 1.54 VA 1.61 2. 38 3. 18 16, C m 1.38 IK 1.38 2.50 3. 19 16, B 17
Substituting the above values of Q, d„ U, and the

value of g (32.2 feet per second per second in the

quantity Qldt-\]gtx, we obtain the value 0.39. Entering figure 17 with this value of the ordinate, we read

the corresponding value of the abscissa, Sl/d2=l .56. From this last expression we have

l=l.5Q c?2/-S'=1.56X0. 1725X24=6.46 feet.

Another result that can be obtained from the same curve is the following: If we assume that

the ciu-ve is asymptotic to the value, Q|dc^[gtl =

0.3, we can compute a limiting value of Q, below

—

A

>: -ISO a —

Q

s

\

0 12 3 4 S£/d2

Figure 19. Curves for computivg tnaximum permissible unvented lengths of fixture drains.

Belation between —~= and 3- for ft/<=0.5. Straight tee vent fitting.

Slopes of fixture drain li, H, li, ¥* inch per foot.

Symbol

d, d2

t h Figure Nominal Actual Nominal Actual

In. In. In. In. In. In. A 2 1.99 2 2.07 1. 75 2. 78 16, A

0 Vi 1. 54 m 1.61 2. 38 3. 18 16, C

I'i 1.38 1.38 2. 50

51

3. 19 16, B

which the trap-seal loss will never exceed A/<=0.5, no matter how long the drain may be. Substituting the values of dt, ti, and g in Qld^-^jgti, and

solving the following for Q,

Q =OMt'-^[gh, we obtain Q=0.0226 cubic foot per second, or

10.15 gallons per minute.

If a straight tee is used instead of a long-turn

T-Y, we use the curves in figure 18 or 19 to make

computations similar to those given above.

The straight-tee vent fitting used in part of these

tests was the conventional malleable-iron straight

tee, and it was used merely because it represented one limiting condition for the vent fitting, that is, completely free efflux of water from the drain was

permitted without any possible interference from

an upper lip, such as would occur with a long-turn

drainage fitting and to a lesser extent with a shortturn drainage fitting. It would be expected that

test results for the short-turn fitting would lie

somewhere between those obtained from the longturn fitting and the straight tee; and, as will be

shown later, they are identical, for all practical

purposes, with those obtained with the straight tee. The curves in figures 18 and 19 are plotted from

the same data, but in figure 18 the ordinates are based on the Froude number that applies to the

fixture drain, Old2^-\lgd2. In figure 19 the ordinates are based on tlie^ Froude number that applies

to the trap, Qjdi^^gt. It is interesting to note

that in figure 18, the curves for the three traps

coincide for large values of Sljdi, while in figure

19 they coincide for small values of Slld2. This

appears to mean that the trap exerts a controlling

influence on permissible values of Slld2 when Q

is large, and the drain diameter similarly influ- ences permissible values of Slld2 when Q is low.

Either of these two figures can be used to coro.pute

maximum permissible imvented lengths of drain

when a straight tee is used.

The advantage of the dimensionless plots given

in figures 17, 18, and 19 is that a m.eans is thus

given in compact form for computing the maximum perm.issible unvented length of drain for different flows from the fixture, different trap-seal

depths and trap diameters, and different lengths,

diameters, and slopes of drain. To furnish the same information in form for immediate use would require a considerable number of tables or

figures. It should be remembered that the computations

discussed above are for no-trail discharge and

hence are somewhat conservative if applied to the practical cases in which more or less trail discharge does occur. The factor of safety thus

introduced is offset to some unknown extent by

the fact that the computations are for clean drains.

Another instance of the utility of these three

figures is afforded by the curves shown in figure 20. These curves were computed with the aid of figure

19 for two cases, in both of which it is assumed

that a straight tee vent fitting is used. The first case assumes: 2-inch cast-steel trap (fig. 16,A),

di—2 inches, ^=1.75 inches, ^i =2.78 inches, ^2 =

2.07 inches, 5'=/2 inch per foot. The second

assum.es l}2-inch cast-brass trap (fig. 16, C),

di^lYi inches, i=2.38 inches, ii =3.18 inches,

(/2=-161 inches, 8=}^ inch per foot. Successive

values of the rate of flow Q were chosen, and values

of Q/di^-^gti were computed for the first trap.

Then, by the use of the highest curve in figure 19

(corresponding to the trap used), corresponding

values of Sl/d2 were read. Then, since the values

of S, di, and Sljd^ were Imown, it was possible to compute values of I, the maxim.um permissible

unvented length of drain. Similar computations were m.ade for the second trap, and the results were plotted in figure 20. In making the computations described above,

it is necessary to express S in inches per inch or

feet per foot, and to express the lengths, dt, h, and

c?2 in the same length units, inches, feet, centimeters, or whatever may be convenient.

18
30

E

a.o>S 20

o

H-o• 10 o

IT

1 1 1 1 1 1 1 i 1 I I r 1 - 1 "I—

2-inch cast steel trap

. lA ..--u u .

. ^ 1 -^-incn casi orass irop

_ . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10 12 14 16 Length of drain , feet Figure 20. Curves giving maximum permissible unvented

lengths of drain for two traps when there is no trail dis- charge from the fixture to which the trap is attached. The curves in figure 20 show that below certain

values of Q the n).axim.um permissible length of

drain is quite long, becoming infinite below some

fairly definite value of Q. Hence we can make I as long as we wish by making c?2 or c^, large enough.

7.4. Lavatory Tests

The lavatory tests were made, for the most part, on the single-story stack and wet-vented systems

shown in figures 13 and 14. Except for a rela- tively small number of tests made with the trans- parent plastic traps and drains, conventional

metal lavatory traps, fixture drains, vent fittings,

and horizontal branches were used in order that

there might be no possibility of the relatively

smooth plastic surfaces affecting the test results

adversely.

The basic piu-pose of the investigation was to determine the physical and geometrical factors

that affect self-siphonage and, more specifically, to determine the maximum unvented lengths of

lavatory drain that might be installed without

resulting excessive trap-seal losses. The tests were made by installing a lavatory with a given

trap and with a given length, slope, and diameter

of fixture drain, and then observing the trap-seal

loss caused by discharging the lavatory. The

amount of trap-seal loss was measured by means

of a glass manometer tube connected to the

lower bend of the trap. In the tests, the lavatory was filled to the overflow outlet. The data in table 1 show the effect of filling the lavatory to different depths. It was felt that this information

would be useful, since in ordinary service the

lavatory is filled to the overflow only rarely.

The data indicate that the trap-seal loss will be

approximately the same if the lavatory is filled to any depth of more than 3 inches and discharged.

Table 1. Effect of depth to which lavatory is filled on self- siphonage of its trap

Trap-seal loss Depth of water in lavatory Maximum

of 6 test runs

Average

of 5 test runs

Lavatory filled to overflow .._ Water surface 1 inch below overflow.. Water surface 2 inches below o verflowInches

1.75

1.75

0. 00

Inches

0. 69

.85 .00

Inchesm

2H

For this reason, the use of a full lavatory in the

self-siphonage tests cannot be considered an excessive test load and one that would not be likely

to occur in normal service.

The data obtained in one series of self-siphonage

tests of a lavatory are shown in figure 21 in order

to show the extent of the scatter typical of such

data. In these tests a iK-inch cast-brass trap

having a depth of trap seal of 2 inches was used

with a iM-inch fixture drain, and a short-turn vent

fitting was used. The rate of flow from the lavatory varied between an average of 10.6 to 10.9

gallons per minute in the tests. In plotting the

data shown in this figure and in all subsequent

plotting of data obtained from tests on actual

fixtures, we have used the nominal diameter rather

than the slightly larger true diameter of the fixture

drain. The drain slopes used were K and K inch

per foot. Each point plotted represents the max- imum observed trap-seal loss obtained in 10

consecutive tests made under identical conditions.

2.0

1.5 -

o

0)

</)

Ia.a

1.0 -

§ 0.5 -

"1 1 1 1 11 1 r Depth of trap seal ^ O A

Figure 21. Results of tests of lavatory self-siphonage.

1 J4-inch-diameter trap. Short-turn vent fitting. Average rate of flow from

fixture 10.9 gpm. Trap used is shown in figure 16, B.

Symbol Slope of drain, S

System used

In.lft. O fFigure 13. Lavatory trap, drain, and vent fitting • Vi \ of metal. Remainder of system plastic. H /Same as above except wet vent, tub di'ain, and M \ horizontal branch were also of metal. A M /Figure 2. Partial system, only to continuous waste

\ and vent.

The scatter sho^^Tl by the data in figm-e 21 is characteristic of most of the data obtained on lav19
atory self-siphonage. It will be appreciated from

the discussion earlier in this paper of the action

of traps when subjected to conditions that cause

self-siphonage that considerable scatter is to be

expected, and the only surprising thing is that it

is so small.

Trial plotting of the data, using first the variable,

8^/(^2, and then S^'Hld2, showed that for the tests shown in figure 21 the variable, S^'Hld2, brought

better order out of the data than did the other

variable.

An average curve was passed through the points

plotted in figure 21 and has a shape that is characteristic of tests on lavatory self-siphonage. When

a critical value of S^'Hjd^ is reached, loss of trap

seal commences abruptly and increases very

rapidly at first, then more slowly, and finally approaches asymptotically the value corresponding

to the depth of trap seal for the trap used.

Thus the value of the quantity, S^'H/d2, at the

point where the reduction in trap seal commences

might serve as a basis for determining the maximum permissible unvented length of drain. Or, if a trap-seal reduction of 1 inch, for example, is settled on as the line of demarcation between satis- factory and unsatisfactory seal loss, we select the

value of S^'Hjdz corresponding to this. Similarly,

for a remaining trap seal of 1 inch, or whatever

may be chosen.

The maximum trap-seal losses obtained in the

tests just discussed, as well as in three other series

of tests, are shown in figure 22, with the actual

data not plotted. The curve in figure 22, B, is identical with the curve in figure 21 for the test with the short-tmn fitting. The curve in figure

22, A, is for the same trap and drain but with a

long-turn fitting used instead of the short-turn.

Figure 22, C and D, show the results obtained

with a modification of the drawn-brass tubing trap

shown in figure 10. A portion of the cylindrical

parts of the two legs was removed, shortening the

depth of trap seal to 2.5 inches, thus changing the

trap from a deep trap to one with a medium depth

of seal. The curve in figure 22, C, represents the

results obtained with this trap when a long-turn

fitting was used, while the curve in figure 22, D,

represents the results obtained with a short-turn

fitting. It will be noted that the abscissas are values of the variable, Sljd^, for this trap, in contrast with the variable, S''H/d2, which was used in

plotting the results for the other trap tested. The

only reason for selecting the former variable to use

in plotting the results for this trap was the fact

that this procedure brought better order out of the

data than did the use of the other variable.

The fact that a short-turn fitting will permit the use of longer unvented lengths of drains than will the use of a long-turn fitting is brought out clearly

by a comparison of the curves in figure 22, A and

B. Of course the reason that a short-turn fitting is better than the long-turn fitting in this respect is that there is less tendency for the flow in the drain

to close off the passageway through a short-turn

2.0 p1.5 -

1.0

S

0.5

-Orlginol surface of Irap seal

2.0

Original surface of trap seal

Figure 22. Tests of lavatory self-siphonage for four traps.

0=10.9 gpm. S=M and }i inch per foot. di=l^Aa inches.

t = 2 inches. d2=l}4 inches. iM-inch oast-brass trap. See figure 16, B.

13 and 14. Long-turn vent fitting. Systems used shown in figures

0=10.6 to 10.9 gpm.

34 inch per foot. (/i=15<6 inches.

Z = 2 inches. di=\}4, inches.

IJi-hich cast-brass trap. See figure 16, B. Systems used shown in figures 2 and 13. Short-turn vent fitting.

0=13.1 to 13.5 gpm.

'S'=M, 14, % inch per foot. d!=l?i inches. <=2.5 inches. d2=l}4 inches.

13^-inch drawn-brass tubing trap. See figure 10. Systems used shown in figures 2 and 14. The trap used was modified so that the depth of trap seal was 2.5 inches instead of SHs inches, as shown la figure 10. Long-turn vent

fitting. D

0=13.1 to 13.2 gpm. S=M, H, K inch per foot. di—1% inches. t=2.5 inches. di=l}>i inches.

13--^-inch drawn-brass tubing trap. See figure 10. Systems used are shown

in figures 2 and 13. This trap was modified as stated under figure 22, C.

Short-turn fitting.

fitting than through a long-turn fitting, thus pro- ducing pressure reductions in the drain.

The two traps selected for the tests were chosen

after preliminary tests had shown that they gave

larger trap-seal losses than other representative

P-traps of the same diameters which were on hand.

Therefore, other traps of this same general type

should give results that are not worse than those

reported here. While it is quite possible that traps

exist that would give worse results than those

shown here, it is not believed that their use is sufficiently widespread to warrant basing code

requirements on their performance. As will be

pointed out later in this paper, the method of deter20
mining maximum permissible unvented lengths of

drains by tests on traps possessing the worst self- siphonage characteristics is a wasteful and uneconomical procedure, in that for the most part, or

at least a large part, of the installations, the maximum permissible lengths of drain thus determined

will be unnecessarily short. However, until more

uniformity in the design of traps is achieved, or

until code-writing authorities are willing to complicate their codes slightly by basing maximum

permissible unvented lengths of drain on the actual

trap dimensions and on the particular fixture being

served, we have no obvious alternative to the

method proposed.

As has already been pointed out, each plotted

point in figure 21 represents the maximum trapseal loss obtained in 10 consecutive tests under

identical conditions. Hence the average curve drawn through the points represents a trap-seal

loss for a given value of S^'Hjdi or Sljdz that will occur on the average only once in each 10 times

the fixture is filled to the overflow. Thus it will

be seen that there is a considerable factor of safety

introduced in this manner.

In computing drain lengths from the curves in

figure 22, it should be remembered that S must be

expressed in inches per inch or in feet per foot,

not in inches per foot. Likewise, I and should

be expressed in the same units, either both in

inches or both in feet. Table 2 summarizes the results shown in figure

22 for a remaining trap seal of 1 inch, rather than

for a trap-seal loss of 1 inch. This is the criterion

first suggested in reference [4]. However, it is an

easy matter for any one to prepare from figure 22

a similar table for any other desired criterion, such

as a trap-seal loss of 1 inch.

Table 2. Permissible values of S^P l/di or Sl/difor lavatory drains for a remaining trap seal of 1 inch

Trap and drain diameter 0 Vent fitting Maximuta

permissible values of Smidi or Slldi

Inches V4 Qpm

10.9

10.9

13.5 13.2

Long-turn Smid2=2.6

Smid2=6.2

Sl/d2=1.0 Slld2=1.2 M - Short-turn. m — Long-turn

iy2 Short-turn

The following problem illustrates the use of

table 2. Assume a l^-inch trap and lavatory

drain, the slope of the drain to be }^ inch per foot. A short-turn vent fitting will be used. How long

is it permissible to make the drain without a vent?

From table 2 we find that the equation to be

used is S"H/d2=&.2. 8=% in./ft=)^4 inch per

inch, and c?2=lM inches, actual diameter. Then

5'i/2=o.204,andZ=6.2(i2/5'^''=6.2X1.25XV24 =38

inches.

Similarly, we find for the same conditions,

except that a long-turn fitting is to be used:

Z=2.6(^2/5'^/'=2.6X 1.25X V24= 16.0 inches.

The above lengths are for an average discharge

rate from the lavatory of 10.9 gallons per minute.

Similarly, if we wish to compute the maximum

permissible unvented length of lavatory drain for a Ij^-inch trap and drain, on a slope of ]^-inch per

foot, using a long-turn vent fitting, we use the

formtda

Slld2=l.Q

Z= 1.0X1.25X24 =30 inches,

or, if a short-turn fitting is used,

Slld2=l.2,

whence /=36 inches. These figures are for an

average rate of discharge from the lavatory of

13.5 gallons per minute.

Table 3 summarizes the above results for slopes

of Yi inch per foot and }^ inch per foot. In this

table it has been assumed that the permissible

length of drain is such as to leave a remaining

trap seal of 1 inch. Inasmuch as the venting

system is ordinarily designed so that the positive or negative pressures in the system do not exceed

1 inch of water, the use of a remaining trap seal of 1 inch as a design criterion provides a safety

factor of 2, since a pressure 2 inches of water in excess of atmospheric pressure in the drain will be required to force sewer gas through the trap

into the building. It has been argued in the

past that such a safety factor is necessary to provide, among other things, for corrosion and fouling

of fixture drains, which Hunter [4] has reported

will cause increased trap-seal losses. It is believed

that the safety factor thus provided is ample to take care of the possible increased trap-seal losses caused by corrosion or fouling.

Table 3. Maximum "permissible unvented lengths of drain

for a remaining trap-seal of 1 inch

Diameter of drain and

trap

<? Fitting Slope

of drain

Length

of drain

Slope

of drain

Length

of drain

Inches \H

IM

VAlA—

Gpm

10.9

10.9

13.6

13.5

Long-turn

Short-turn Long-turn

Short-turn

In.lft.A

A

A

A

Inches

17.6

42

33

39.5

In.lft.M

H

K

14

Inches

25

59

66

79

The conclusions in table 3 as to the maximum

permissible unvented length of lavatory drains are based, as has been stated, on the assumption that

the line of demarcation between satisfactory and

unsatisfactory trap performance is a remaining

trap seal of 1 inch. As has been noted previously,

this criterion contains a safety factor to provide,

among other things, for the possibility that positive

pressures in the stack may be caused by the dis- charge of fixtures above the lavatory in question.

However, in the majority of installations in service,

in which the lavatory is the topmost fixture on the

system, it is obvious that the trap wUl not be

required to resist positive pressures of any magni21
tude. Therefore, it appears reasonable in this case, or in any installation in which the venting system

is loaded considerably under capacity, to permit

greater trap-seal reductions than those used in

obtaining the permissible values of S^'Hjdi and Slldi

given in table 2. Reference to figure 22 will show that, if a remaining trap seal of inch is assumed to be adequate

for lavatories on the top floor, the permissible unvented lengths of drains for installations of this

nature can be increased over the values listed ia

table 2. To facilitate determining the maximum

permissible unvented lengths of lavatory drains for

this situation, assuming a minimum remaining

trap seal of }{ inch, the values given in table 4

have been read from the curves in figure 22. In

the judgment of the authors, these permissible

values of S^'H/d^ and Sl/d2 may be used safely in all cases in which the venting system is loaded to

less than half its capacity. The capacities of vents

in terms of fixture units may be obtained from a previous publication of this Bureau [12]. Table 4. Permissible values of S^'H/di and Sl/d2 for

lavatory drains on the top floor of a bvilding, assuming a remaining trap seal of inch

Trap and drain diameter

Inches —

IKVA

IM-- —

Gpm

10. 9 10.9

13.5

13.2

Vent fitting

Long-turn.

Short-turn Long-turn.

Short-turn

Maximum per- missible value ot S»Hld2 or Slld2

S"2?/d2=3. 0 SI 2^2=6.6

Sl/di =1.16

Slld2 =1.58 A number of tests other than those already

discussed were carried out to investigate the efi^ect of other factors that have an influence on selfsi phonage. These will be discussed in the following sections.

a. Effect of Diameter of Lavatory Drain

In practice the drain is sometimes made one nominal size larger than the trap. For this reason, among others, tests were made to determine the effect of changing the drain diameter

when a given trap is used. In figure 23 are given

data for the iK-inch tubing trap shown in figure

10 (depth of trap seal, 3%6 inches; trap diameter,

1% inches) connected to a l}{-inch drain and with

a IK by iK-inch short-turn vent fitting. The tests were made with the wet-vented system shown in

figure 13, with the exception that the horizontal

branch was 2 inches in diameter. The system was

constructed of conventional metal pipe and fit- tings, with the exception of the 3-inch stack,

which was made of transparent plastic pipe.

Each plotted point represents the average of ten

test runs made under identical conditions. The

average rate of flow from the lavatory was 11.5

gallons per minute.

Similar tests were made with the lavatory drain

increased to IK inches in diameter with a rate of

Figure 23. Effect on trap-seal losses of diameter of lavatory drain.

IH-inch fixture drain. O M-inch-per-foot slope. • J-fj-inch-per-foot slope. V/i-iach fixture drain. M-inch-per-foot slope. H-inch-per-foot slope

flow of 11.4 gallons per minute from the lavatory,

and no trap-seal loss was observed in any of the

tests, even when the length of drain was in- creased to as much as 104 inches on a )4-inch slope

(Slld2=lA5) and to a drain length of 93 inches on

a }^-inch slope {Sl/d2=2.58).

It is obvious that, for a given rate of flow, decreasing the diameter of the lavatory drain, will cause increased trap-seal losses. Or, stated dif- ferently, a lavatory installation in which the drain

is larger than the trap will be subject to smaller

trap-seal losses than a sim.ilar installation with the same trap but with the drain the sam.e diameter

as the trap.

b. Effect of Size of Lavatory

It seem.s reasonable to believe that the am.ount

of trail discharge from, a lavatory will bear some

relation to the area and shape of its bottom surface.

For this reason soro.e of the tests were made with

two different sizes of lavatories. With the l}^-inch

trap and drain, trap-seal losses were found to be

practically the same whether the 18' by 20-inch or the 20- by 24-inch lavatory was used.

However, for the iK-inch trap and drain this was not the case. Tests m.ade on the wet-vented

system shown in figure 13 indicated that the

smaller lavatory gave appreciably larger trap-seal

losses than did the larger lavatory. As an illustra- tion, tests made with the 20 by 24-inch lavatory

gave an average trap-seal reduction of 0.075 inch

for a drain 123 inches long on a K-inch-per-foot

slope, while tests on the 18 by 20-inch lavatory

gave an average trap-seal loss of 1.86 inches for a drain 23 inches shorter and on the same slope. The

22
above test results are for a long-turn vent fitting

and tlie l)<-inch tubing trap. It would be ex- pected that a similar situation would hold for the

short-turn vent fitting, back-vented or stackvented lavatories, and for other types of traps.

c. Effect of Vertical Distance From Fixture to Trap

No tests were made during this investigation to determine the effect on the trap-seal losses of

varying the vertical distance between the lavatory

and the trap. However, in an earlier unpublished

report [13], tests were reported in which this dimension was varied from 6 to 12 inches. These

test results indicated that the effect of such

variation is negligible.

d. Trap Dimensions

The principal dimensions of a trap which would

be expected to affect self-siphonage are (1) the

internal diameter, (2) the depth of the trap seal,

and (3) the radii of curvature of the trap bends.

No attempt was made to investigate these factors

systematically, but sufficient tests were made to

infer the effect of the first two factors. (1) Effect of Internal Diameter of Trap. The data

in figures 24 and 25 are for three traps sho"s\Ti in

figures 7, 8, and 9. The trap diameters were i > 1%6, and \}i inches, and the drains used were all

1]{ inches nominal diameter (1.38 inches actual).

No definite conclusions can be drawn as to the

superiority of either the 1}^ inch or the iKe-inch

trap over the other. However, the iK-inch diameter trap shows a distinct superiority over the

others, whether we use as our criterion the length

of drain at which trap-seal losses begin, a remaining trap-seal of 1 inch, or a trap-seal loss of 1 inch.

It seems highly improbable that the superiority

of the trap with the largest diameter can be due

either to the depth of the trap seal or to the radius

of cxirvature of the U-bend. Hence the result is attributed to the relatively large trap diameter.

The results shown in figm-es 24 and 25 are summarized in table 5. The italicized values in the

table indicate the trap that allowed the longest

drain to be used for the given criterion. Table 5. Effect of trap diameter on trap-seal losses

Trap in

figure Trap

diameter

Depth

of trap

seal

Inches

V/i

Inches

2

IM

Radius

U- bend

Inches m

1H2

Fitting

fShort-tum

I--. -do

I Long-turn

l--._do (Short-turn

).._-do ____

1 Long-turn

I. ...do _ Short-turn

•^...-do iLong-tum

Slope drain

in.lft.M

H

H

Length of drain

for

Start

of

loss

Inches 49

30

30

13.5 50.5 30

50.5

15.5 62

47. S

1-inch

seal

re- duction

Inches

53

4136

26

55

4152

2470H

64.5

1-inch

re- maining

seal

Inches

53

4136

26

64.5

66

57.5 40

67.5

51.5

62.6

4

3

-

2

-

Slope - ^ inch per foot

Original surface of trap-seol-

« 4 -

I o. ^ 3

-

2 -

I -

0

Slope - inch per foot

Original surface of trap-seal

0 10 20 30 40 50 60 70 80 90

Length of drain , inches Figure 24. Effect of diameter of trap used with long-turn

vent fitting. • Trap sho-nm in figure 7. (ii=ljf6 inches. O Trap shown in figure 8. d(=l^i inches. # Trap shown in figure 9. d(= 1)4 inches.

Slope- \ inch per foot

Original surface of trap-sealH 3 -

2

-

1

0

Slope- ^ inch per foot

Original surfoce of trap-seal

20 40 60 80

Length of drain, inches Figure 25. Effect of diameter of trap used with short-turn

vent fitting. • Trap shown in figure 7. di=l^.i6 inches. O Trap shown in figure 8. di=llri inches. # Trap shown in figure 9. di=lli inches. The italicized values in the table indicate the

particular trap and other conditions that yield

the longest permissible unvented length of drain.

It will be noted that, "with one exception, regardless

23
of the criterion used, the trap having the largest

internal diameter is the best of the three. This

is a rather surprising result, since it might have

been expected that the trap with the largest

depth of seal would have given the longest permissible lengths of drain for a remaining trap

seal of 1 inch. This seems to indicate that the

diameter of the trap has more to do with the

losses due to self-siphonage than does the depth

of trap seal.

(21 Effect of Depth of Trap Seal. It would be

anticipated that traps with deep seals should

permit longer unvented lengths of drain to be

used than traps with shallow seals, provided we

use as our criterion a given remaining trap seal. The same conclusion is drawn if we consider the curves in figures 17 and 19. The ordinates of

these curves are values of Q/dt^-Jgti, from which we

see that the greater the depth of trap seal t (and

hence ti, which is equal to i+c?2/2) the smaller is the value of this dimensionless variable, and hence

the larger the corresponding value of Sl/d2, and

thus the longer the permissible imvented length

of drain.

The effect of depth of trap seal was further

investigated by conducting tests with the l^-inch-

(nominal) -diameter-tubing trap shown in figure

10, first with the trap shown in the figure with a depth of seal of 3%^ inches, and then with it cut

down to give a depth of trap seal of 2)^ inches.

The installation consisted of an 18- by 20-inch

lavatory connected to a stack-vented single- story

system. The data were somewhat erratic but

did show two things clearly: (1) that the deeper

seal left a larger remaining trap seal after dis- charge of the fixture than did the smaller seal. For the seal depth of 3%6 inches, the maximum

permissible unvented length of drain is given by

the relation, Sl/d2~1.8, while for the seal depth

of 2}i inches it is given by the relation, Sl/d2=1.19,

(2) the effect of increased depth of trap seal is more pronounced with the short-turn vent fitting

than with the long-turn fitting.

(3) Relative Effects of Diameter of Trap and

Depth of Trap Seal. At first thought it may

seem surprising that the diameter of the trap has

a much greater effect on the trap-seal loss, from

the standpoint of self-siphonage, than does the

depth of the trap seal. However, this fact might

have been predicted from inspection of the variable, Qldt^-yjgt, which is significant in regard to the

trap-seal loss. In this variable the diameter of

the trap, dt, enters as the square, while the depth

of trap seal enters only as the square root and

hence must have a much smaller effect than the

trap diameter.

A consideration of the physics of the problem,

as discussed in section 6.2, c, may make our conclusion seem somewhat more plausible. In that

Section it was pointed out that the dimensionless

variable, QJdi^i/gi, might be looked upon as the

ratio of two velocities, one of which tends to empty the trap of its water seal, and the other of

which tends to keep the trap filled. The first velocity is the average velocity of flow through

the trap and is proportional to 0/dt^. The second

is the velocity of free fall for a body falling through

a height equal_to the depth of trap seal and is proportional to -y/gt. Now a small reduction in dt in- creases the average velocity of flow through the

trap considerably and thus has a tendency to produce a considerable increase in trap-seal loss. On the other hand, a small decrease in t produces

only a smaU decrease in the velocity of free fall and thus tends to have only a slight effect on the

trap-seal loss. As a result of the tests, the following conclusions

appear to be warranted in regard to the effect on

trap-seal losses of changes in diameter of trap

and depth of trap seal:

1 . Trap-seal losses that are due to self-siphonage are sensitive to changes in the internal diameter

of the trap, and, under certain circumstances at

least, will overshadow relatively large variations

in depth of trap seal. The tests have shown that,

in regard to the l^-inch trap, a relatively small

decrease in internal diameter below Iji inches re- sults in a marked increase in trap-seal losses.

2. Permissible unvented lengths of fixture drains

are increased appreciably by increasing the seal

depth from 2 to 3 inches, or higher, but primarily

only because greater trap-seal losses are thus

permissible.

The above discussion of the results of tests obviously offers an opportunity for the more effi- cient design of fixture traps.

e. EfiEect of Plugged Overflow

In a number of the tests the efi'ect of plugging

the overflow of the lavatory was studied in order

to determine what might be the effect of pre- venting the aspiration of air through the overflow. Typical results are shown in figure 26.

Comparison of these results with the data of

figure 22, C, will show that the effect is to increase

the trap-seal losses greatly. That this effect is due to preventing air from aspirating through the

overflow was made obvious by tests in which a transparent trap was used. Appreciable amounts

of air could be seen coming from the overflow

when the latter was not closed off, and trap-seal

losses were relatively small. When the overflow was closed off, this air no longer mixed with the

flowing water, and the -trap-seal losses increased

considerably.

f. Effect of Type of Vent Fitting

It will be recalled that the lavatory test data

presented earlier in this paper have all indicated

that the use of a short-turn vent fitting yields

smaller trap-seal losses than does a long-turn vent

fitting under the same conditions of discharge.

Advantage should be taken of this fact in writing

24
" 3.0

o 2.0

£ 1.0 -

3.0 Si/dg

Figure 26. Effect of plugged lavatory overflow on

self-siphonage. Each point is tlie maximum of 10 consecutive readings. Long-turn vent

fitting used. Same trap used in both series of tests, except that 1 inch was

cut of! leg of trap, reducing the depth of trap seal by this amount, before the

tests that yielded the curve in figure 22, C, were run.

plumbing-cocle requirements regarding self- siphonage.

As has been stated previously, a straight-tee

vent fitting was used on some of the no-traU dis- charge tests. Inasmuch as the relatively long

depressed upper lip of the long-turn fitting has

been shown to cause substantially greater losses than the straight-tee fitting, it might be expected

that the small upper lip of the short-turn vent

fitting would also yield greater trap-seal losses than the straight-tee fitting. However, tests made with both Iji- and iK-inch diameter lavatory

drains [13] indicated that there was no significant

difference between the two fittings in this respect,

and it may be concluded that no improvement in

self-siphonage characteristics would be obtained

by increasing the radius of ciu-vature of the upper

lip of the short-turn vent fitting. It is weU known that the long-turn vent fitting

is more effective in introducing water from a

horizontal branch into a stack than is the shortturn fitting, because the former turns the water

downward more than does the latter. On the

other hand, the short-turn fitting has better self- siphonage characteristics than does the long-tmn

fitting.

Thus the characteristics of these two fittings are contradictory in these two respects. It is possible that the advantages of the two fittings

could be combined in a new type of fitting in which the lower half of the cross section followed

the form of the long-turn fitting, while the upper

half foUowed the form of the straight tee fitting.

g. Effect of Rate of Fixture Discharge

From the data presented in this paper, it is obvious that the rate of fixture discharge has a marked effect on the trap-seal losses caused by

self-siphonage. See figures 17, 18, 19, and 20. Thus from the standpoint of self-siphonage it is advantageous to have as low a rate of fixture

discharge as is feasible. For example, figure 20

shows that with the l}^-inch cast-brass trap and

l}^-inch drain, if the fixture flow is not greater

than about 9 gallons per minute, the permissible

unvented length of drain can be made almost in- definitely long. Similarly, for the 2-inch steel trap and drain, if the rate of flow from the fixture

does not exceed about 20 gallons per minute, the same is true. Any one who is familiar with the

design of plumbing systems will recognize immediately the financial savings that could result

from the utilization of this fact. In recent years the customary size of outlet

orifice of the lavatory has been increased from

1)8 to 1/4 inches. This has resulted in an increase

in the rate of flow from the fixture. In 1924

Hunter [4] concluded from a series of laboratory

experunents that the average rate of flow from a lavatory was 7.5 gaUons per minute. Hunter did

not record the dimensions of the orifices on the

lavatories he tested, but tests made in this investigation have sho^vn that this rate of discharge is closely approximated by making the diameter of

the outlet orifice Iji inches. However, we have

found that the lavatories having a diameter of

outlet orifice of l}i inches have an average rate of

discharge of about 10 gallons per minute when

the iK-inch trap and drain are used and about

13.2 gallons per minute when the l}2-inch trap

and drain are used. Because of this it is not

surprising that the permissible unvented lengths

of drains found in this investigation are in some

cases less than those found by Hunter [4]. Test data showing the self-siphonage produced

in a fixture trap when the outlet orifice of the

lavatory is 1}$ inches and when it is 1% inches are shown in figure 27. In both cases the trap and

drain diameters were Iji inches. The relatively

small reduction in diameter of the outlet orifice results in an increase in the permissible unvented

length of drain of approximately 100 percent.

These facts are significant, and they immediately raise the question of whether the decreased

2.0 -

1.5 -

.0 -

0.5 -

"1—I—1—I—1—

r

-Depth of trap - seal o

om Fig. 22, A - meter of outlet

orifice = l'/4 inches Diometer of outlet"

o"rifice = 1 '/g inches10

Figure 27. Effect on self-siphonage of diameter of outlet

orifice of lavatory.

25
time of emptying the fixtm*e caused by increasing

the diameter of the outlet orifice outweighs the

decreased permissible unvented length of drain

and hence the increased cost of the installation.

Certainly in the case of low-cost housing it does

not.

7.5. Tests on Other Fixtures

The great majority of the tests made in this

investigation were made with lavatories. However, other plumbing fixtures are also subject to trap-seal losses due to self-siphonage, and a few

tests were made with kitchen sinks, bathtubs, and

water closets. The test data on these fixtures were limited in scope, and no attempt was made

to investigate systematically the self-siphonage of

these fixtures. Nevertheless, the test data for

sinks, bathtubs, and water closets are believed to be sufficiently extensive to indicate, in a qualitative manner at least, the relative self-siphonage

effects on these fixtures.

a. Sinks

A limited number of tests were made on sinks

and combination fixtures with drains Iji inches

in diameter and 8 and 10 feet in length on slopes

of %, and % inch per foot. These data for a 16

by 24-inch sink are shown in table 6. The l}^-inch

cast-brass trap shown in figure 28 was used in

these tests. Similar tests were made on the sink

compartment of the combination fixture, and the

resulting trap-seal losses were in all cases smaller

than those recorded in table 6.

Table 6. Trap-seal losses for a 16- by 24-inch kitchen sink

Type of strainer

Rate of

dis- charge Type of vent

fitting

Trap-seal losses—inches

Drain length 8 feet Drain length 10 feet

slope

}-2-in. slope

H-in.

slope U-in.slope slope H-in.

slope

Flat Gpm16.5 23.2

23. 2

Long-turn 0.75 .380

1. 00

.75

0

.62

0 Basket ' Do

do

Short-term

0

0 0.12.50

0

0

1 In these tests the basket strainer was removed from the sink.

Figures 29 and 30 show unpublished data

obtained by Hunter on the self-siphonage of sinks.

All of the data in these figures were obtained

with drain slopes of % inch per foot, except as noted. In the plotting of the data m these figures,

is the slope of the drain in mches per inch, I is the length of the drain, from the trap weir to the

vent fitting in inches, and d2 is the nominal

diameter of the drain in inches.

If a remaining trap seal of 1 inch is adopted as the dividing line between satisfactory and unsatisfactory operation, the data in table 6 and

figures 29 and 30 indicate that a value of Sl/d2 of

approximately 10. for the long-turn vent fitting

and 1.4 for the short-turn vent fitting would

serve adequately for the ordinary types of kitchen

FiGUBE 28. lYi-inch cast-brass trap.

2.5 M I I I

I

I I I I

I

I I I I

I

I I I I {

I I I I I

I I

Figure 29. Hunter's data on the self-siphonage of sink

traps.

Long-turn, vent fitting. # 2-inch-diameter trap and drain. O IJ^

inch-diameter trap and drain.

sinks and combination fixtures tested here with 1^2- and 2-inch diameter drains.

b. Bathtubs

Tests were made with a conventional type of

bathtub 5 feet long connected to a l^-inchdiameter drain and trap. The tests were made

with drains 17 and 25 feet long on slopes of K,

and % inch per foot. In no case was any trapseal loss noted. While these tests on one bathtub

with a single type of trap cannot be considered

exhaustive by any means, they do indicate that

self-siphonage of bathtub traps is not a serious

problem and that the permissible value of Sl/d2

indicated earlier in this paper for commonly-used

kitchen sinks and combination fixtures would

provide ample safety for bathtub traps, insofar as self-siphonage is concerned.

26
2.5

2.0

oi

'.5

S 1.0 E

E

B. 0.5

I I I I II I I

^-inch s\ope^

I I I I I ^-fi I ^ I'j) I I I I I I I I I I I I 0 0.5 1.0 1.5 2.0 2.5

Figure 30. Hunter's data on the self-siphonage of sink

traps.

Short-turn vent fitting. # 2-inch-diameter trap and drain. O 13^-inch- diameter trap and drain.

c. Water Closets

In'the preceding sections of this paper the self- siphonage of fixture traps has been viewed in the

hght of an undesirable phenomenon, and various

methods of controlling or eliminating it have

been proposed. However, ia the case of a water

closet, self-siphonage of the fixture is, in general,

necessary for its proper operation. Hunter [14]

summarizes the characteristics of an effective

water closet flush as follows: "A quick priming

of the siphon; a continuous siphon action for

sufficient time to clear the bowl of its contents

and carry them through the trapway; and a breaking of the siphon action before the flow

ceases, in order to refill the trap."

The siphon action occurring in the water closet

trap is "self-siphonage" in the commonly ac- cepted meaning of the term, since it is caused by

the discharge of the particular fixture connected

to the trap in question, and it differs in no way

from the self-siphonage of a lavatory, for example,

except that in the case of the water closet the

fixture trap is designed so that self-siphonage

occurs during each flush of the fixture, no matter

how short the drain is made, while for the lavatory, siphon action in the trap is not necessary

for its proper operation and will not occur unless

the drain is sufficiently long or on a sufficiently

high slope, or unless one of the other variables

previously mentioned as affectmg self-siphonage

brings it about.

As has been pointed out previously, the ill effects of self-siphonage may be overcome by

increasing the volume and duration of trail dis- charge to the trap after the self-siphonage process

has ceased. This fact is utilized in the design of

water closets, and, for then- proper operation,

the duration and rate of discharge from the flush- ing device (flush valve or flush tank) must be

such that sufficient water drains into the fixture

from the flush valve or tank after the breaking

of the siphon action in the trap to fill the latter. As Hunter has pointed out [14], the characteristic operation of conventional water-closet supply devices, if properly adjusted for volume and

time, controls the rate of supply in a manner that

meets this flushing requirement admirably. It

is thus apparent that the self-siphonage process,

far from being detrimental to the safe operation

of a water closet, is necessary for its proper

functioning; and specific means, consisting of an

adequate amount and duration of trail discharge,

have been provided by the commonly used flush- ing devices to overcome the usual ill effects of

self-siphonage. Under these circumstances it would not be expected that the remaining trap

seal in a water closet would be affected appreciably by an increase in the length or the slope

of the fixture drain.

In table 7 are given self-siphonage test results

obtained from the water closet set-up of figure 31. These tests were made with a 3-inch diameter

drain, and the average rates of discharge were

26.1 gallons per minute with the flush tank and

30.0 gallons per minute with the flush valve.

From the data in table 7 it is apparent that the

trail discharge that normally refifls the trap after

the necessary self-siphonage process incident to the flushing action is suflicient also to prevent

tx

Figure 31. Setup for self-siphonage tests of water closets.

27
any appreciable trap-seal losses due to the in- creased slope or length of fixture drain.

Based on the data in table 7, there does not

appear to be any need of limiting the unvented

length of water closet drains on the score of self- siphonage.

Table 7. Trap-seal losses of water closets

Flushing device

Trap-seal losses

Length of drain,

5 feet Length of drain, 20 feet Length of drain,

25 feet

J^-inch slope

'-^-inch slope

J^-inch slope M-inoh

slope

54-inch slope}^-inch

slope

Flush tank with refill pipe in ._ _ Flush tank with refill pipe out Flush valve

Inches

0

.38

Inches

0

.38

Inches

0

.50

Inches

0

.75

Inches

0

.38

Inches

0

.38

d. Miscellaneous Fixtures

In the foregoing sections of this^^reportj^selfsiphonage data on the usual fixtures used in resi- dential installations have been presented, and conclusions regarding the permissible unvented lengths

of fixture drains for these fixtures have been given.

However, there are many other types of fixtures

used in restaurant kitchens, hospitals, and in vari- ous industrial applications that do not closely

resemble those commonly found in residential installations. As has been indicated previously, the

permissible unvented length of drain for such fix- tures, as well as those already discussed, will depend on the rate of discharge, the length, slope,

and diameter of the drain, the trap dimensions,

the type of vent fitting, and the trail discharge

characteristics of the fixture. Inasmuch as the data in figures 17 to 19 were

obtained under conditions of minimum trail dis- charge, the curves given in these figures may, for

any type of fixture, be used to determine a safe

unvented length of fixture drain. In this connection it may be pointed out that, while the use of

figures 17 to 19 will yield safe values of the un- vented length of fixture drain, it will also, for many

fixtures, result in uneconomical designs, owing to the fact that the fixture drains will be limited to shorter lengths than is necessary for any fixture

that has an appreciable trail discharge.

8. Conclusions

The following conclusions are believed warranted by the data presented

1. Many variables affect the self-siphonage

process. Among these are the discharge from the

fixture; the length, diameter, and slope of the fix- ture drain; the type of vent fitting; the dimensions

of the trap, particularly the depth of trap seal and

the internal diameter of the trap; and the amount

and duration of the trail discharge from the fixture.

2. In general, the trap-seal loss produced by the

discharge of a lavatory will be about the same maximum amount if the lavatory is filled to any

depth more than 3 inches.

3. Increasing the diameter of the outlet orifice of a lavatory from 1% inches to 1% inches increases

the trap-seal loss greatly, frequently more than

100 percent, owing to the increased discharge rate.

4. Flat-bottomed fixtures cause smaller trapseal losses than do round-bottomed fixtures, owing

to the greater trail discharge from the former.

5. With a IJ^nch fixture trap and drain, an 18- by 20-inch lavatory gave greater trap-seal losses than did a 20- by 24-inch lavatory, presumably

owing to the greater trail discharge of the latter. When a 1^4-inch trap and drain were used, no particular difference was noted in the trap-seal losses caused by these two lavatories.

6. The elimination of the overflow in lavatories

will increase the trap-seal losses substantially, see

figure 26.

7. The effect on trap-seal losses of varying the

vertical distance from the fixture to the trap from

6 to 12 inches appears to be negligible.

8. For a given rate of discharge from a lavatory,

decreasing the diameter of the drain will increase

trap-seal losses.

9. An increase in slope or a decrease in diameter

of the fixture drain will tend to cause increased

losses due to self-siphonage, and these two dimensions are fully as important as the length of fixture

drain in causing self-siphonage.

10. Tmp-seal losses are usually much greater

when a long-turn vent fitting is used than ^hen a

short-turn or a straight-tee fitting is used. No

significant difference between the behavior of

short-turn and straight-tee fittings in this respect was observed. Thus, since it is known that a

long-turn fitting is more effective in introducing

water from a horizontal branch into the stack

than is either the short-turn or straight-tee fitting,

the characteristics of these fittings are contradictory in these respects. The fitting that is most

advantageous from the standpoint of introducing

the water into the stack is the least advantageous

from the standpoint of self-siphonage.

11. The permissible values of S^'Hjd^ and Sljd^

given in table 2, which are based on a remaining

trap seal of 1 inch, are adequate for lavatory in- stallations throughout the plumbing system.

12. The permissible values of S^'^Ljdi and Sljdi

given in table 4, based on a remaining trap seal

of }2 inch, are adequate for lavatory installations on the top floor or at other locations in the drainage system where the venting system is sufficiently

imderloaded or otherwise designed so that negative

pressm-es either do not occur or are negligible in magnitude.

13. The permissible values of S^'Hjd-i and Slld-i in tables 2 and 4 can be increased appreciably by

proper choice of the lavatory trap and lavatory.

14. With short-turn vent fittings and with

long-tm-n vent fittings when used with drains on

a slope of Yi inch per foot and less, a trap-seal loss of more than half the depth of trap seal will not

28
be obtained if the drain is so designed that the

value of Q/di^-yjgdi is less than about 0.5, see figure

18.

15. Trap-seal losses are increased if the internal

diameter of a P-trap is less than that of the fixtiu-e drain. Thus, if we are to prevent excessive trapseal losses for a P-trap due to self-siphonage, we

should use a trap having a fanly large internal

diameter. Furthermore, siphonage of the trap

due to pressure reductions caused by the discharge

of other fixtures on the system can be rendered

less harmful by using a trap with a large depth of

seal. While increasing the depth of seal may lead

to greater trap-seal losses, it also results in a

greater remaining trap seal than if a trap with a

shallow seal were used.

16. If a remaining trap seal of 1 inch is adopted

as the dividing line between satisfactory and unsatisfactory operation, the relation, 81/(12=1 -0, when a long-turn vent fitting is used, and the relation, Slldi=\A, when a short-tm-n vent fitting is used, will give satisfactory maximum permissible

unvented lengths of fixture drains for ordinary

types of sinks and combination fixtures for lYi- and 2-inch diameter traps and drauis, see table 6

and figm-es 29 and 30.

17. From limited data on bathtubs it is con- cluded that the permissible values of Slld2 given

for sinks can be applied with at least equal

safety to bathtubs. It is believed that more

extensive data on the self-siphonage characteristics of bathtub traps will indicate that self- siphonage of this fixture is not serious under any

commonly used method of installation, and that

the permissible values of Slld2 suggested here can

be increased with ample safety.

18. The test results on the self-siphonage of

water closets have indicated that the unvented

length of drain for these fixtures need not be

limited because of self-siphonage.

19. Permissible unvented lengths of drains for

fixtures for which specific data are lacking can

be obtained from figures 17 to 19, inclusive. The

permissible unvented lengths of drain obtained

in this manner will be safe, but, for most fixtures,

and especially for those with appreciable trail discharge, the data in figures 17 to 19 will yield

drain lengths considerably shorter than those that

might be used with complete safety.

20. Standardization of the dimensions of fixture

! traps, and especially of lavatory traps, with

\\ regard to internal diameter and depth of trap

seal is highly desirable. Minor restrictions on

these dimensions can lead to substantially in- creased unvented lengths of fixture drains.

21. Standardization of the hydraulic characteristics of fixtures is desirable, at least for lava1 tories, sinks, and combination fixtures. Subj stantiaUy increased permissible unvented lengths

\ of fixture drains can be obtained for a moderate

I decrease in the discharge rates of the fixtures.

I 22. Increase in depth of trap seal above the

j 2-inch minimum commonly permitted by codes

will make it possible to increase appreciably the

maximum permissible unvented lengths of fixture

drains.

23. It is practically impossible to duplicate

results in self-siphonage tests owing to the fact

that conditions in the fixture drain are rarely

twice alike, even when the tests are conducted

xmder the most carefully controlled conditions.

All that can be expected is that the range of

values obtained in a series of tests under conditions that are as nearly identical as it is possible

to make them can be repeated approximately.

9. Considerations Regarding the

Self- Siphonage Problem

Most plumbing codes provide protection against

trap-seal losses due to fixture self-siphonage solely

by limiting the length of the unvented portion of

the fixture drain; that is, they limit the distance

between the trap weir and the vent fitting. The

data presented in this paper show clearly that

there are several other variables involved that exert an equally important effect on the trap- seal losses due to self-siphonage.

The rate of discharge from the fixture, the slope

and diameter of the fixture drain, the type of vent

fitting, and the dimensions of the trap have been

shown to be of primary importance likewise. The

rate of discharge from such fixtures as lavatories

and sinks is controlled in large measiu-e by the

diameter and other physical characteristics of the

outlet orifice, and, in the case of the lavatory, self- siphonage is so sensitive to outlet orifice conditions that appreciable differences in trap-seal losses may sometimes be observed with fixtures of the same manufacture and model number, these fix- tures being identical in every respect except for

small differences in the bevel provided on the

outlet orifice to accommodate the rubber stopper.

An increase in the slope of the fixture drain or a decrease in its diameter wiU cause increased

trap-seal losses due to self-siphonage, and these

two dimensions are fully as important in controlling

self-siphonage as the length of the drain.

The permissible unvented length of drain is affected to an important degree by the type of

vent fitting connecting the drain to the contin- uous waste and vent or to the stack, and under

certain conditions the permissible unvented length

of drain for the short-tm-n fitting may be more

than twice that for the long-turn fitting.

The data presented have shown that the trapseal losses due to self-siphonage are very sensiiive

to small variations in the internal diameter of the

trap, and that a relatively small decrease in trap

diameter may cause a substantial increase in

trap-seal losses. Although trap-seal losses due to

self-siphonage, and consequently permissible un- vented lengths of fixture di-ains, are not as sensitive to changes in depth of trap seal as to changes

in trap diameter, it has been shown nevertheless

that substantial increases in depth of trap seal

29
above the 2-inch minimum commonly permitted,

by codes will provide an appreciably increased

permissible unvented length of drain through the

fact that such an increase in trap-seal depth makes

possible an increased permissible seal loss. In like manner, lavatories, as well as other fixtiu"es, are made in a variety of sizes and forms.

Tests on the 18- by 20-inch lavatory have shown

it to have, under certain conditions, worse self- siphonage characteristics than the 20- by 24- inch

lavatory, owing undoubtedly to its smaller surface area and consequently shorter period of trail discharge.

Under these conditions it is not surprising that

current plumbing codes show a lack of uniformity

as regards permissible unvented lengths of fixture

drains, for, in view of the above discussion, it obviously could not be expected that tests made

in one place would yield results as to the permissible unvented lengths of fixture drains that would

be comparable with test results obtained at another place, unless care were taken to insure

that the traps, fixtures, vent fittings, and other

variables entering the problem had been properly

considered.

Because of the many variables connected with

the problem of self-siphonage, and in view of their

effect on permissible unvented lengths of fixture

di'ains, it is obviously impossible, with the present

wide diversity in the design of lavoratories (and

other fixtures) and traps, and with the present

lack of uniformity in the use of the two types of

vent fittings, to establish a single and simple limit on the permissible unvented length of drain which

will be equally safe and equally economical for all installations. Until such time as installation procedure and the hydraulic characteristics of fixtures

and traps are standardized, plumbing codes must

either provide rather complicated requirements

regarding self-siphonage, by permitting different

unvented lengths of drain for different types of

lavoratories (and other fixtui'es), traps, and vent

fittings, or they may provide a single, simple

restriction on unvented lengths of fixture drains,

which is unduly conservative for the majority of

the installations and in many instances uneconomical.

In the analysis of the results of this investigation a relatively large safe+y factor has been

introduced. This was accomplished in four ways.

First, a remaining trap-seal requirement of 1 inch was adopted, which means that after the trap has

been siphoned, it will be able to resist pressure

fluctuations in the drainage system twice as large

as those for which the venting system is ordinarily

designed. Second, in applying the remaining

trap-seal requirement, the least remaining trap

seal observed in 10 identical tests was used. Thhd,

with special reference to the lavoratory tests, the

traps selected for use in this investigation were

those which gave the worst results of all the traps

that were on hand for the investigation. And

finally the tests were made by filling the lavatories

to their overfiows.

The result is that the recommendations made in

this paper as to the maximum permissible un- vented lengths of drain are, in our judgment, ex- tremely conservative and may be used with complete safety by code-writing authorities. As a consequence, it is not necessary to adhere rigidly to the exact values suggested for these lengths.

In connection with this question of safety factor

involved in the recommendations made here, it may be pointed out that approximately 25 years

ago, when a minimum remaining trap seal of 1 inch was first suggested, allowance was made for

the effect of fouling of the fixture drains. The

Uniform Plumbing Code Committee did the same

thing, yet this fact seems to have been forgotten.

It is true that we do not as yet have any reliable

data as to the effect on self-siphonage of fouling of

the fixture drain, and so we cannot set any upper

limit to this effect. On the other hand, the dangers of an occasional loss of trap seal have been

greatly exaggerated. The odor of sewer gas (or

probably it would be better to say sewer air) may

be oft'ensive, but according to public health authorities, the sewer air is not dangerous or detrimental

to the health unless present in great concentration

or continuously over a considerable period of time, a condition that is unlikely to occur in a building

as the result of a lost trap seal, except perhaps in

the case of a fioor drain. Probably the function

of the water seal is actually more to prevent the

development of a nuisance condition than to protect the health, contrary to what many believe.

The purpose of this investigation has been twofold. The first and most irrportant object was to determine the factors that affect fixture self- siphonage and to suggest rreans of minimizing the

ill effects of this phenomenon. The second purpose of the paper was to suggest permissible

unvented lengths of fixture drains based on the

experip" ental work of the investigation. The

latter objective, as has been seen, involved the

adoption of a rr.inimum requirement for the

rerraining trap seal. The point of view adopted in this paper with

regard to the relationship between remaining trap

seal and permissible unvented length of fixture

drain is the one commonly held at present. That

is to say, since the publication in 1924 of Recommended Minimum Requirements for Plumbing

in Dwellings and Similar Buildings [3], it has

been considered good practice to require a minimum remaining trap seal of 1 inch after self- siphonage has occurred. Although the authors

in interpreting the test data have adhered to this criterion of good practice (except as noted in the

paper for underloaded venting systems), they wish

to point out nevertheless that this requirement is entirely arbitrary, and in their considered judgment it will eventually be reduced. The authors,

in considering this question of what constitutes a reasonable requirement for remaining trap seals,

have been handicapped because the problem is not such that it can be investigated by experimental means or by any simple analysis.

30
In view of the fact that the principal factors

influencing the establishment of a reasonable

requirerrent for remaining trap seals are the

magnitude and frequency of the pressure fluctuations in the drainage system, considered together

with the frequency and magnitude of trap-seal

losses and their duration, it is apparent that the

problem may be attacked in either of two ways.

First, the problem, is am enable to solution through

extensive and systematic field investigations, and

secondly the problem may be attacked through

probability considerations, together with a limited

field investigation. The latter method would

require an investigation of the probability of a

positive pressure equal in magnitude to twice the

remaining trap seal occurring at the same time

as the rem aining trap seal in question.

In view of the magnitude of the analysis and

field investigation required to establish a rational

requirement as to remaining trap-seals, the writers

had no alternative but to interpret the experimental data on the basis of requiring a 1-inch

remaining trap-seal in accordance with com- monly accepted good practice, and to defer for the present their inv^estigation of this important

aspect of the self-siphonage phenomenon. It is hoped that it will be possible to consider this latter phase of the self-siphonage problem in a

future paper.

Industry can play an important part in reducing

the cost of plumbing, if it can be persuaded to

|, adopt standard designs for fixtures that will impose

1

1 smaller demand and drainage loads on the system.

||1 And if, in addition industry can be induced to standardize fixture traps, adopting a design or

designs that are less subject to self-siphonage than

many of the traps in use today, very decided modifications can be made in plumbing codes to allow

" for this, with resultant economies in the construction of plumbing systems.

Suggestions have been made in this paper which

make it possible for definite improvements from

i the standpoint of self-siphonage to be made in the

design of fittings, fixtures, and traps. The authors

1 hope that these suggestions will ultimately make

it possible to improve the design of the items

; mentioned.

10. Importance of Economy in the

Use of Water

One other matter might be mentioned here.

I The increasing number of instances of water

; shortage make it imperative that all possible econi omies in the use of water be given prompt consideration. Hence immediate consideration should

j be given to possibilities of reducing the use of

water in plumbing fixtures. There are two ways

j in which such economies can be achieved, first,

• by reducing the amount of water involved in each

j use of a fixture; and second, by changing the

j! habits of the public as regards the use of plumbing

j fixtures. It would seem obvious that the second

way suggested can be made effective only by a concerted process of education extending over a long period of years. The first way proposed is largely in the hands

of the plumbing industry, and this, too, would

involve an uphill fight, since the convenience of

the public is in conflict with the attainment of

economy. The water closet is one fixture, however,

in which economy of operation might be achieved

without encountering resistance from the public,

since the amount of water used per flush is automatically controlled. If a water closet and flushing

device should be designed to operate effectively

with one gallon of water less per flush than is now

required, the savings might be estimated conservatively at 20 gallons per day per household.

In a large city such a saving would be very considerable.

That there is a real possibility of reducing the

amount of water used in each flush of a toilet bowl was shown some years ago by Camp [15]. He

demonstrated that som.e water closets, at least,

could be flushed properly with 3 gallons of water,

whereas 4 or more gallons is generally used today.

Acknowledgment is made to the Housing and

Home Finance Agency for its support of the inv^es- tigation reported in this paper. The authors also wish to express their appreciation of the cooperation of. the m.emibers of the Uniform Plumbing Code

Committee, and especially that of the Chairman,

Vincent T. Manas, in formulating the problem in- vestigated and in offering practical suggestions.

The authors also express their appreciation for the many valuable suggestions made by Edward

Monteath, who acted as Industrial Adviser to the

Bureau in connection with the investigation. The

experimental work was carried out by Robert S. Wyly, Marion II . Brockman, Anthony L. Lerabeck, Victor Brame, Jr., Richard J. O'Brien, and

Edward J. Norcome, and the authors are indebted

to them for their careful and thorough work.

11. References

[11 John L. French, Stack venting of plumbing fixtures, NBS Building Materials and Structures Report

BMS118 (1950).

[2] John L. French, Herbert N. Eaton, and Robert S. Wyly, Wet Venting of plumbing fixtures, NBS

Building Materials and Structures Report BMS119

(1950).

[3] A. E. Hansen, Plumbing fixture traps; a historical and

engineering research on vented and unvented traps. (1921).

[4] Recommended minimum requirements for plumbing

in dwellings and similar buildings. Elimination of Waste Series, BH2 National Bureau of Standards

(1924).

[5] F. M. Dawson and A. A. Kalinske, Report on the hydraulics and pneumatics of the plumbing drain- age system; Technical Bulletin No. 2, National

Association of Master Plumbers (1939).

[6] Harold E. Babbitt, Tests on the hydraulics and

pneumatics of house plumbing. Engineering Experiment Station Bulletin No. 143, University of Illinois (1924).

31
[7] Harold E. Babbitt, Tests on the hydraulics and

pneumatics of house plumbing, Part II; Engineering

Experiment Station Bulletin No. 178, University of

Illinois (1928).

[8] Edgar Buckingham, Model experiments and the form of empirical equations. Transactions American

Society of Mechanical Engineers, vol. 37, page 263

(1915).

[9] P. W. Bridgman, Dimensional analysis, Yale Univ.

Press, New Haven, Conn. (1931).

[10] Garrett BirkholT, Hydrodynamics, Princeton University Press for University of Cincinnati (1950).

[11] Report of the Uniform Plumbing Code Committee,

U. S. Government Printing Office, July 1949.

[12] Plumbing Manual, NBS Building Materials and

Structures Report BMS66 (1940).

[13] Investigation of the self-siphonage of lavatory traps. Report VI/6- 6651.60, National Bureau of Standards (unpublished). Issued to the Public Housing

Authority (1945).

[14] Roy B. Hunter, Methods of estimating loads in plumbing svstems; NBS Building Materials and

Structures Report BMS65 (1940).

[15j Thomas R. Camp, The hydraulics of water closet bowls and flushmg devices: Massachusetts State Association of Master Plumbers and the Massachusetts Institute of Technology (1936).

Washington, January 10, 1951.

o

32
BUILDTNG MATERIALS AND STRUCTURES REPORTS

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[Continued from cover page ii] Structural Properties of Two Brick-Concrete-Block Wall Constructions and a Concrete-Block Wall Construction Sponsored by the National Concrete Masonry

Association 15^

Plastic Calking Materials 15^ Performance Test of Floor Coverings for Use in Low-Cost Housing: Part 1 15^

Stability of Sheathing Papers as Determined by Accelerated Aging * Structural Properties of Wood-Frame Wall, Partition, Floor, and Roof Constructions With "Red Stripe" Lath Sponsored by The Weston Paper and Manufacturing Co 10^

Structural Properties of "Palisade Homes" Constructions for Walls, Partitions, and

Floors, Sponsored by Palisade Homes * Structural Properties of Two "Dunstone" Wall Constructions Sponsored by the W. E. Dunn Manufacturing Co 10^

Structural Properties of a Wall Construction of "Pfeifer Units" Sponsored by the Wisconsin Units Co 10^

Structural Properties of a Wall Construction of "Knap Concrete Wall Units" Sponsored by Knap America, Inc * Effect of Heating and Cooling on the Permeability of Masonry Walls * Structural Properties of Wood-Frame Wall and Partition Construction with "Celotex"

Insulating Boards Sponsored by The Celotex Coiporation 15f5 Performance Test of Floor Coverings for Use in Low-Cost Housing: Part 2 15^ Surface Treatment of Steel Prior to Painting 10^ Air Infiltration Through Windows * Structural Properties of "Scot-Bilt" Prefabricated Sheet-Steel Constructions for Walls, Floors, and Roofs Sponsored by The Globe-Wernicke Co * Structural Properties of Prefabricated Wood-Frame Constructions for Walls, Partitions, and Floors Sponsored by American Houses, Inc 20fJ Structural Properties of "Precision-Built" Frame Wall and Partition Constructions

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Metallic Roofing for Low-Cost House Construction 20^

Stability of Fiber Building Boards as Determined by Accelerated Aging 10^

Structural Properties of "Tilecrete Type A" Floor Construction Sponsored by the

Tilecrete Co 10^

Effect of Ceiling Insulation Upon Summer Comfort 15^

Structural Properties of a Masonry Wall Construction of "Munlock Dry Wall Brick"

Sponsored by the Munlock Engineering Co lOfS Effect of Soot on the Rating of an Oil-Fired Heating Boiler 10^

Effects of Wetting and Drying on the Permeability of Masonry Walls 100 A Survey of Humidities in Residences 10^ Roofing in the United States—Results of a Questionnaire * Strength of Soft-Soldered Joints in Copper Tubing 10^

Properties of Adhesives for Floor Coverings 15^

Strength, Absorption, and Resistance to Laboratory Freezing and Thawing of Building

Bricks Produced in the United States 30(i Structural Properties of Two Nonreinforced Monolithic Concrete Wall Constructions. _ lOjS Structural Properties of a Precast Joist Concrete Floor Construction Sponsored by

the Portland Cement Association 150 Moisture Condensation in Building Walls 150

Solar Heating of Various Surfaces 100 Methods of Estimating Loads in Plumbing Systems 150 Plumbing Manual 350

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Water-Distributing Systems for Buildings 200 Performance Test of Floor Coverings for Use in Low-Cost Housing: Part 4 150

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[List continued on cover page iv]
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[Continued from cover page iii] BMS82 Water Permeability of Walls Built of Masonry Units 250 BMS83 Strength of Sleeve Joints in Copper Tubing Made With Various Lead-Base Solders 15^ BMS84 Survey of Roofing Matciials in the South Central States : 15^ BMS85 Dimensional Changes of Floor Coverings With Changes in Relative Humidity and

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"Knap Concrete-Unit" WaUs 150 BMS95 Tests of Cement-Water Paints and Other Waterproofings for Unit-Masonry WaJs 250 BMS96 Properties of a Porous Concrete of Cement and Uniform-Sized Gravel 100 BMS97 Experimental Dry-Wall Construction With Fiber Insulating Board 100 BMS98 Physical Properties of Terrazzo Aggregates 150 BMS99 Structural and Heat-Transfer Properties of "Multiple Box-Girder Plywood Panels" for Walls, Floors, and Roofs 150 BMSlOO Relative Slipperiness of Floor and Deck Surfaces 100 BMSlOl Strength and Resistance to Corrosion of Ties for Cavity Walls 100 BMS102 Painting Steel _ 100 BMS103 Measurements of Heat Losses From Slab Floors 150 BMS104 Structural Properties of Prefabricated Plywood Lightweight Constructions for Walls,

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BMSllO Paints for Exterior Masonry Walls 150 BMSlll Performance of a Coal-Fired Boiler Converted to Oil 150 BMS112 Properties of Some Lightweight-Aggregate Concretes With and Without an Air- entraining Admixture 100 BMS113 Fire Resistance of Structural Clay Tile Partitions 150 BMS114 Temperature in a Test Bungalow With Some Radiant and Jacketed Space Heaters 250 BMS115 A Study of a Baseboard Convector Heating System in a Test Bungalow 150 BMSllO Preparation and Revision of Building Codes 150 BMS117 Fire Resistance of Walls of Lightweight Aggregate Concrete Masonry Units 200 BMS118 Stack Ventmg of Plumbing Fixtures 150 BMS119 Wet Venting of Plumbing Fixtures 200 BMS120 Fire Resistance of Walls of Gravel-Aggregate Concrete Masonry Units 150 BMS121 Investigation of Failures of White-Coat Plasters 250 BMS122 Physical Properties of Some Samples of Asbestos-Cement Siding 150 BMS123 Fire Tests of Wood-Framed Walls and Partitions With Asbestos-Cement Facings 150 BMS124 Fire Tests of Steel Columns Protected With Siliceous Aggregate Concrete 150 BMS125 Stone Exposure Test Wall 300

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