The program of research on building materials and structures, carried on by the

National Bureau of Standards, was undertaken with the assistance of the Central Housing Committee, an informal organization of governmental agencies concerned with

housing construction and finance, which is cooperating in the investigations through a subcommittee of principal technical assistants.

CENTRAL HOUSING COMMITTEE

SUBCOMMITTEE ON TECHNICAL RESEARCH

Walter Junge, Chairman. Arthur C. Shire, Vice Chairman.

Federal Housing Administration. United States HousingAuthority.

Sterling R. March, Secretary

Albert G. Bear, George E. Knox,

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Agency). Forest Service (Agriculture).

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Farm Security Administration (Agri- Construction Division (War),

culture).

CHAIRMEN OF SECTIONS

Specifications Materials Maintenance

Carroll W. Chamberlain Elsmere J. Walters John H. Schaefer

Mechanical Equipment Methods and Practices

Robert K. Thulman

NATIONAL BUREAU OF STANDARDS

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Mechanics and Sound

Phaon H. Bates, Gustav E. F. Lundell,

Clay and Silicate Products. Chemistry.

HoBART C. Dickinson, Addams S. McAllister,

Heat and Power. Codes and Specifications.

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Organic and Fibrous Materials. Metallurgy.

The Forest Products Laboratory of the United States Department of Agriculture is cooperating with both committees on investigations of wood constructions.

[For list of BMS publications and how to purchase, see cover page III.]
UNITED STATES DEPARTMENT OF COMMERCE • Harry L. Hopkins, Secretary

NATIONAL BUREAU OF STANDARDS • Lyman J. Briggs, Director

BUILDING MATERIALS

and STRUCTURES

REPORT BMS28

Backflow Prevention

in Over-Rim Water Supplies

by GENE E, GOLDEN Ufld ROY B. HUNTER

ISSUED AUGUST 24, 1939

The National Bureau of Standards is a fact-finding organization;

it does not "approve" any particular material or method of construction. The technical findings in this series of reports are to be construed accordingly.

UNITED STATES GOVERNMENT

FOR SALE BY THE SUPERINTENDENT OF

PRINTING

DOCUME NTS,

OFFICE • WASHINGTON • 1939

WASHINGTON, D. C. • PRICE 10 CENTS
Foreword

During the greater part of the past 18 years an experimental study of problems

relating to the functions and performance of the water-distributing pipes, the plumbing

fixtures and fittings, the drain pipes, and the vent pipes of the plumbing systems of

buildings has been in progress at the National Bureau of Standards. These investigations are being made to determine the proper sizes, arrangement, and connections of water supply, drain, and vent pipes for the satisfactory and safe or sanitary operation

of the plumbing fixtures and for effective drainage from the building. Where the conclusions from these studies have been accepted and applied in plumbing regulations and

practices, better sanitary and drainage conditions and lower cost of construction through

simplification of piping layouts have resulted. This program has been continued during

the past two years with particular reference to low-cost housing.

The determination of practical and effective means of preventing the contamination

of the potable water supply of a building by backflow from plumbing fixtures or drains

is one of the important problems studied in the investigations reported in Bureau

Research Paper RP1086. This report relates to a particular problem of prevention of

backflow; namely, the prevention of backflow from over-rim supply fixtures, such as

lavatories. The study, which is a continuation of the Bureau's work on backflow in

plumbing systems, was instituted by the Bureau and carried to completion by the

Plumbing Fixture Manufacturers' Research Associateship, whose sponsors are the

Vitreous China Plumbing Fixtures Association, Sanitary Cast Iron Enameled Ware

Association, Sanitary Brass Institute, and National Brass Association.

The principles demonstrated and the data furnished make possible the specification

of safe air gaps in plumbing codes throughout the country in a simple and rational manner which, in its turn, should make for uniformity of regulation and simplicity of

design and construction. A suggested form of specification is included, which is in

agreement with the report of the American Standards Association's Subcommittee on

Air Gaps, in the formulation of which the authors had the privilege of assisting.

Lyman J. Briggs, Director.

(II)
Backflow Prevention in Over-rim

by GENE E. GOLDEN dud ROY B.

Water Supplies

HUNTER

CONTENTS

Page

Foreword ii List of symbols r 1

I. Introduction 2

II. Previous work on the subject 2

III. Purpose and scope of the investigation _ _ 3 IV. Outline of the problem 3

1. Definition of safe and critical air gaps 3

2. Statement of the general problem- - 4

3. Factors affecting the critical air gap _ 4

4. Discussion of the factors 4

(a) Magnitude of the vacuum

pressure 4

(b) Air backflow capacity of faucets 4

(c) Dimensions and shape of the

faucet spout 5

(d) Position of the faucet spout

with respect to nearby fix- ture walls : 5

(e) Temperature of the water in the fixture 5

(f) Atmospheric conditions 5

(g) Physical characteristics of the

liquid in the fixture 5

IV Outline of the problem—Continued. ^'^^^

5. Statement of the specific problem

and method of approach 6 ^. Experimental procedure 6

1. Experimental apparatus 6

2. Devices tested 6

(a) Orifices 6

(b) Tubes 6

(c) Faucets 8

3. Determination of equivalent diameters of tubes and faucets 8

4. Measurement of critical air gaps 11

5. Effect of water temperature on criti- cal air gaps 12

6. Effect of adjacent walls 12

7. Eff'ect of different liquids on the

critical air gap 12 VI. Analysis of experimental data 12

1. Empirical equation for the critical air gap for tubes 12

2. Application of air-gap equation to faucets 14

3. Effect of adjacent walls 14

VII. Practical application of results 15

VIII. Conclusions 16 IX. References ; 17

ABST

This report describes the methods used and the

results obtained in the investigation of the prevention

of backflow from plumbing fixtures with over-rim sup- ply by means of air gaps between the supply opening

and the highest possible liquid level in the fixture. The previous work is discussed and the data necessary

for a complete understanding of the subject are pre- sented. The treatment has been developed from the

point of view of the construction of the supply fitting as well as its location with respect to the fixture. Finally, recommendations are offered in a form suitable

for use in field inspection.

List of Symbols

A/i = Critical air gap, when there is no wall eff'ect. A^' = Critical air gap, when there is a wall effect. i?=Safe air gap.

(i= Actual internal diameter. de= Equivalent internal diameter.

Di = Actual external diameter,

/la = Atmospheric pressure in feet of air column.

''^oq = Atmospheric pressure in feet of air column at 65° F and 50-percent humidity.

Pa = Density of atmospheric air. Pa = Absolute atmospheric pressure. Pr = Absolute pressure in evacuated tank or system. Pc = Absolute pressure in evacuated tank corre- sponding to the critical-pressure ratio, r^. r = pressure ratio, PrjPa- = Volume of the evacuated tank.

3 = Acceleration of gravity.

<o=Time in seconds for pressure in tank to rise from

zero to Pr-

< = Time in seconds for pressure in tank to rise from some initial pressure to Pr.

\t = Time in seconds for pressure in tank to rise from

zero to initial pressure.

A; = Ratio of the specific heat at constant volume to that at constant pressure. T= Effective wall thickness = (Di-d,)/2.

[1]
I. INTRODUCTION

Under our present standards of living,

plumbing is considered an essential and integral

part of practically every building where a supply of water is available. Hence the program

of research on building materials and struc- tures includes a project on plumbmg.^

One of the problems included in the project

is that of the structural requirements for plumbing necessary to prevent the pollution of the drinking-water supply by the flow of impure

water into it through backflow connections ^ between the piping system that carries the

potable water supply and any piping system or plumbing equipment that may carry or contain impure or nonpotable water, for example,

plumbing drains and plumbing fixtures. This

report deals with one particular phase of the

problem; namely, the structural requirements

necessary to insure against backflow through

faucets and other valves similarly installed.

The general problem of backflow connections has

been treated more fully in a previous paper [1].^ It is common knowledge that the pressure in many building water-distributing pipes is fre- quently reduced below atmospheric pressure,

as indicated by the failure of water to flow from

a faucet or other supply valve when it is opened. These reductions in pressure may be

produced in many ways, such as an excessive use of water in the building or its vicinity, the

drawdown produced by fire-fighting apparatus,

shut-off of the city or building water supply,

breaks in street water mains, or in the building

supply system. Reduction in pressure from

these causes may be sufficient to allow a vacuum

to form in the building water pipes in any upfeed water-supply system.

If a faucet spout or similar water-supply

opening dips below the surface of the water in a plumbing fixture or other open vessel, water

will be siphoned back through the valve whenever it is open or leaking, and the water pres1 BMSl, Research on Building Materials and Structures for Use in Low-Cost Rousing. Price 10 cents. See cover page III.

" It recently was recommended at a meeting of the American Standards

Association Subcommittee on Air Gaps, January 20, 1939. to discontinue

the use of the word "cross-connection" in reference to plumbing systems and to substitute for it "backflow connections." This is to avoid any

possibility of conflict with the water-works usage of the term "cross-con- nection," signifying a continuous enclosed connection between two

water supplies, one of which is nonpotable.

' Figures in brackets indicate the literature references at the end of this paper.

sure in the supply system at the level of the

water surface in the fixture system is below

atmospheric pressure. It is also well known

that water may be lifted vertically across an air gap into a faucet by the atmospheric pressure

in conjunction with a vacuum in the watersupply line, as illustrated in figure 1, in which

an evacuated tank represents an evacuated

water-supply line, the glass tube a faucet spout

and the glass jar a plumbing fixture. Similarly,

water may be lifted through partially enclosed

supply passages; for example, through the jet

passage of a water closet and the flush pipe

from a flushing valve.

II. PREVIOUS WORK ON THE SUBJECT

In addition to the paper [1] previously re- ferred to, the experimental work of Zinkil [2] of the Crane Co., Chicago, 111., and that of Dawson

and Kalinske at the University of Wisconsin

[3] and the University of Iowa [4] are of particular interest in connection with the lifting of

water across an air gap, as shown in figure 1. Zinkil's data for round tubes, ranging from

0.128 to 0.807 inch in internal diameter cover

the following conditions: (1) the tube set vertically over a water surface, (2) the tube set vertically with an adjacent vertical wall ex- tending past the tube and touching the tube

wall, and (3) the end of the tube set at an angle

with the water surface. He also investigated

the effects of elongated, or oval, tube openings.

The data are remarkably consistent, and from

them Zinkil drew the following conclusions:

(1) increasing the intensity of the vacuum

above 15 inches of mercury caused no appreciable increase in the critical air gap (the maximum vertical distance across which water can

be lifted), (2) the critical gap will be practically the same for an elongated opening as for a circular opening of the same cross-sectional

area, (3) when the spout opening is set at an

angle not in excess of 30° from the horizontal,

the critical air gap for this arrangement will be

equal to the critical air gap for the same opening set horizontally, provided the gap for the

included opening is taken as the average

distance of the opening from the water surface.

The published work of Dawson and Kalinske

[3, 4] contain no experimental data and hence

provide no material for independent analysis.
Figure l.~Backflow across air gap.

It is noteworthy, however, that theh conchisions agree substantially with those of Zinkil.

Neither Zinkil nor Dawson and Kaluiske

published any experimental data that defi- nitely apply to passages, such as those formed

by the interior of commercial faucets or defi- nitely connect the conclusions in regard to tubes

with any designated or readily measurable

dimension of a faucet. Nor did they give

complete information regarding the effects of the external diameter of tubes and faucets on

the critical air gap.

III. PURPOSE AND SCOPE OF THE

INVESTIGATION

The experiments reported in this paper were made to complete the data required to connect

the existuig data for tubes with the backflow

characteristics and dimensions of faucets and

other supply openings and to verify the conclusions previously drawn in regard to the critical air gap for faucets. The ultimate purpose is to enable a safe air gap to be specified in terms of some readily measurable dimension of the faucet

itself.

IV. OUTLINE OF THE PROBLEM

1. Definition of Safe and Critical Air

Gaps

Water can be lifted across a vertical air gap

into the water-supply lines by atmospheric

pressure, as illustrated in figure 1, when a

partial vacuum exists in the supplj' system.

[3]
The critical air gap, Ah, will be defined as the

minimum vertical distance across which backflow cannot be started by the effects of atmospheric pressure in combination with the vacu- um in the tank. A safe air gap is any gap

greater than the critical air gap, and the question of the proper margin of safety to be

added to the critical air gap will be taken up

in the discussion which follows the development of the formulas governing the air gap.

2. Statement of the General Problem

The ultimate purpose of this investigation

is to determine the critical air gap, Ah, for supply openings in terms of the various factors

which have an appreciable effect on it, and to reduce the resulting relation to a form such

that the safe air gap can be determined readily

in any particular case.

3. Factors Affecting the Critical Air

Gap

The factors which conceivably may influence

the critical air gap are

(a) Magnitude of the vacuum pressure in

the supply system,

(b) Air backflow capacity of faucets,

(c) Dimensions and shape of the faucet

spout,

(d) Position of the faucet spout with respect

to nearby fixture walls,

(e) Temperature of the water in the fixture,

(f) Atmospheric conditions, and

(g) Physical characteristics of the liquid in the fixture.

4. Discussion of the Factors

As has been indicated, this paper is supplementary to the paper. Cross-connections in

Plumbing Systems [1], in which more detailed

demonstrations of some of the points in the

ensuing discussion are presented. Hence, the

results and conclusions given in that paper will be utilized in. the present problem insofar as they are applicable and will be elaborated only

to the extent necessary to make their application

clear.

(a) Magnitude of the Vacuum Pressure

It has been demonstrated [1] that if air flows

from the atmosphere through an opening into an evacuated system, the velocity of the air increases with decrease in the system pressure

until some critical-pressure ratio is reached, after which any further decrease in the system pres- sure causes no sensible increase in the velocity of the air. The air velocity existing in the opening

at this critical vacuum may be called the critical velocity and is equal to the velocity of sound in

air under the conditions existing in the opening.

As pressure waves for this type of flow can

travel no faster than sound in air, it is obvious

that the effect of any decrease in the system

pressure below the critical cannot be felt upstream of the opening. This maximum backflow of air is attained at vacuum pressures of approximately half an atmosphere, and hence

protection against a vacuum of 15 inches of mercury will protect any system from backflow

when exposed to any possible vacuum.

(6) Air Backflow Capacity of Faucets The capacity of a tube or faucet for the

backflow of air obviously afl'ects the critical air gap through the velocity of the air flowing into

the end of the tube or faucet above the water

surface. There are two resulting effects that

exert an influence on the height through which

water can be lifted to the tube or faucet opening:

(1) If air is to flow into the opening, there must

be a reduction in pressure below atmospheric

pressure there, and this reduction causes the

level of the water below the opening to rise somewhat; (2) the flow of air over the surface of the water toward the opening exerts a frictional

drag on the water, so that a surface current is set up, moving radially inward to a point

directly below the opening, tending to pile up

the water at this point still further. Now, if the

velocity of the air is great enough, and if the

water surface is sufficiently close to the faucet

opening, some of this water will be carried

vertically upward into the opening and back

into the system (see figs. 1 and 5). Obviously,

the greater the velocity of backflow of air, the

greater is the height through which the water

can be lifted; that is, the greater is the critical air gap.

[4]
If we are dealing with the backflow of air through cylindrical tubes, the problem of ex- pressing the backflow of air is relatively simple,

since the quantity (or velocity) of flow can be

expressed in terms of the internal diameter of

the tube and other factors that have a smaller

effect. However, with faucets the problem is not so simple. The passageway in a faucet is not a simple cylindrical passage of uniform

diameter, but is a curved irregular passage

with abrupt changes in section. Furthermore,

the most restricted cross section, which may

be expected to control the backflow, is not

easily accessible to measurement and may vary

greatly in different types of faucets.

Under these circumstances, the logical method

of procedure appears to be to measure the air backflow capacity of the wide-open faucet when

a pressure reduction of at least 15 inches of mercury exists between the free atmosphere

and the system to which the faucet is attached.

This air backflow capacity can then be ex- pressed by assigning to the faucet an "equivalent diameter" equal to the diameter of some

simple standard form of opening through

which the same quantity of air will flow under

the same pressure drop.

This was the procedure adopted in [1] for the measurement of air backflow capacity, and

the reference standard adopted was a series of sharp-edged thin-plate oriflces. The same ref- erence standard will be used for faucets. The details of determining the equivalent diameters of

faucets will be given in section V-3 of the paper.

(c) Dimensions and Shape of the Faucet

Spout

The critical air gap will depend on the di- mensions and shape of the faucet spout. As

already noted in section II, Zinkil demonstrated

I that (1) the critical air gap for an elongated

spout is the same as that for a circular spout

of the same cross-sectional area, and that (2) for spout openings set at an angle up to 30° to the water surface, the mean air gap equals

that for an opening of the same area parallel

to the water surface.

It is obvious, that as elongation and inclination of the spout are carried beyond the limits

of Zinkil's work, the effect will be to decrease

the critical air gap, and hence no further consideration need be given these factors. However, the thickness of the wall at the end of the

spout may be expected to increase the critical air gap as the wall thickness increases, and

therefore it seemed desirable to supplement

Zinkil's work by determining the eft'ect of wall

thickness on the air gap.

(d) Position of the Faucet Spout with Respect

to Nearby Fixture Walls

The efi^ect of position of the faucet spout

with respect to nearby fixture walls was also studied by Zinkil. Using tubes, he determined

(1) the effect on the critical air gap of a wall

tangent to the outside of the tube and, (2) the

distance from the inside edge of the tube at wliich the effect of the wall on the critical air gap becomes negligible. However, he published no data on the effect of two nearby waUs

or on the eft'ect of walls at intermediate distances

from the tube. Hence it was decided to determine the effect of these conditions on the

critical air gap.

(e) Temperature of the Water in the Fixture

It has been commonly assumed previously

that the temperature of the water in the fixture

has a negligible effect on the critical air gap.

It seemed desirable to verify this assumption.

(/) Atmospheric Conditions

It has also been assumed heretofore that

variations in atmospheric conditions have no

appreciable effect on the critical air gap. This

is not strictly true, as the analysis in section

IV-3-a of reference [1] leads to an equation

containing a term representing the height of a

hypothetical air colunui, ha, and attention is called there to the fact that ha varies with

temperature and humidity. The efl'ect of these factors on the air gap may be expected

to be comparatively small. However, the

quantitative effect of variation in ha will be

mvestigated later on in this paper.

(g) Characteristics of the Liquid in the Fixture

It seemed desirable to determine the effect on the critical air gap of various liquids in the

fixture in order to insure that due consideration
be given to the liquid characteristics density,

viscosity, and surface tension..

5. Statement of the Specific Problem and

Method of Approach

The specific problem now is to determine the

critical air gap for faucets, when the pressure

reduction across them is at least 15 inches of

mercury (critical vacuum), in terms of their air backflow capacity (determined by their equivalent diameters), their spout dimensions (outside

diameters), their position with respect to nearby

fixture walls, and atmospheric conditions.

The method of approach to the problem was

to find first a convenient empirical form of a modification of the general equation for tubes

as given in the earlier paper [1]:

A/i/c? =function (d/Di, djha), (1) where

Ah =the critical air gap,

d=the internal diameter of the tube,

Z>i = the external diameter of the tube,

ha=the height of a hypothetical air column

of uniform density exerting at its base a pressure equal to that of the

atmosphere.*

which takes into account the effects of the

external diameter of the tubes and of atmospheric conditions. A systematic series of experiments to determine the effects of the various

factors was made on tubes rather than on

faucets, because it was simpler to make up a

series of tubes of various internal and external

diameters to cover the desired range of conditions than to obtain a suitable series of faucets.

Actually, since the internal spout diameter

of a faucet is meaningless in this connection, as explained earlier, eq 1 was written in the form

A/i,/(/, =function {de/Di, de/ha), (2) where de is the equivalent diameter of a sharpedged thin-plate orifice, having the same air backflow capacity as the faucet.

* ha=Palpa, wheFP Pa IS the barometric pressure in pounds per square

foot, and pa is the density of the air at pressure Pa in pounds mass per cubic foot. Now, since pa varies directly with Pa, the ratio Palpa will remain constant unless the value of pa is changed independently of Pa by changes in temperature and humidity from the assumed values. Figure 3 shows the variation of A a with temperature for dry and moist

air. The data on which figure 3 is based may be obtained from the Smithsonian Physical Tables or from the Handbook of Chemistry and

Physics, Chemical Rubber Publishing Co., Cleveland, Ohio.

Following this, the critical air gaps and

equivalent diameters were measured experimentally for the faucets, and the resulting

values were substituted in the empirical equation obtained for the tubes to ascertain whether

the same equation applied with reasonable ac- curacy to the faucets. This was found to be

the case. Finally, data were obtained on the effect of

adjacent walls on the critical air gaps for a representative tube and it was assumed that

the effect on faucets would be quantitatively

the same.

V. EXPERIMENTAL PROCEDURE

1. Experimental Apparatus

The apparatus used in all of the tests consisted of two interconnected 318-gallon tanks

which could be used singly or together, a vacuum pump for evacuating the tanks, and a mercury manometer for measuring the pressure

in the tanks. For determining the air-flow

characterictics of the thin-plate orifices used as

reference standards, and of the tubes and

faucets, each device in turn was connected to the evacuated tank, and the rate of rise of pressure in the tank was measured.

For measuring the critical air gaps for the

tubes and faucets, a 12-inch glass jar 6 inches

deep was used to represent the flooded fixture. See figure 5.

2. Devices Tested

(a) Orifices

For use as a reference standard; that is, as a

basis for assigning equivalent diameters to tubes

and faucets, a series of thin-plate orifices was

constructed and tested to determine their air- flow characteristics. The orifice diameters used were Ke, Vi, Ya, %, K, and % inch, and in no

instance did the thickness of orifice plate exceed

one-half the diameter of the orifice.

(6) Tubes

The dimensions of the tubes tested are given

in table 1. The tubes used consisted of two

[6]
12 3 4 5 6

? 9 (? s

1

6 9 iO li

Figure 2. —Tubes and faucets used.

groups of four, each group having a given nominal internal diameter, 0.25 and 0.50 inch,

respectively, but having the external diameter

varied within each group to give a series of

values of the ratio of internal to external

diameter. There are also three additional

sharp-edged tubes, making eleven in all. See

figure 2.

Tabi.e 1. —Tubes for air-gap determination

Tube Number d d/Di D2 Li Li Pipe

thread

1

in.

0. 125

in.

0. 125

in. 1.00in. .625in.

0. 50

in.

1. 50 Vs

2 . 125

. 125

. 160 0. 78 .625 .50 1. 50 H

3 . 250 .50 .625 .50 1. 50 Vs

4 . 125 . 500 . 25 .625 .50 1. 50 Vs

5 .250 .250 1.00 .625 1. 56 2. 56 H

6 . 375 .375 1.00 .625 1. 50 3. 81 H

7 . 600 .500 1.00 1.000 1.60 5. 00 Vi

8 . 500 . 666 0. 75 1.000 0. 00 5. 00 M

9 . 600 1.000 .50 1. 000 .00 5. 00 M

10 . 500 2. 000 .25 1.000 C) 5. 00 H

11 0. 625 0. 625 1.00 1.000 1.50 6.31 K

158566°—39-

' 2-iiioh plate soldered on end of tube.

[7]
Viewed from another angle, it is apparent

that the five sharp-edged tubes form a geometrically similar series, and the three remaining

pairs, having equal diameter ratios, form similar series from which results for tubes of intermediate diameters can be obtained by virtue

of the principle of dynamical similarity. See

figiu'e 6. Siich an arrangement allows investigation of the effects of variation in internal and

external diameter with a miTiimum number of tubes.

(c) Faucets A group of 10 faucets, as illustrated in figure 2 and described in table 6, was used in the

investigation.

3. Determination of Equivalent Diameters

OF Tubes and Faucets

The following equation was developed m the

earlier publication [1] for expressing the air backflow characteristics of orifices and other

devices in terms of the rate of change of pres- sure in the evacuated tank to which the devices were attached.

P _

Pr ri-^ I 2k /PcY'T. /^A—

(3)

where

C=the coefficient of discharge of the

device;

A; = the ratio of the specific heat of the

air at constant volume to that at constant pressure: in this case k

may be taken equal to 1 .4

Pa =atmospheric pressure

Fc =pressure in the evacuated tank corre- sponding to the critical-pressure

ratio, Vc] rf= diameter of the device being tested;

.9 =acceleration of gravity;

/i.a= height of a hypothetical atmosphere

of uniform density, pa, exerting the

pressure. Pa, at its base;

volume of the evacuated tank;

r=Pr/Pa, where Pr is the absolute pres- sure in the tank;

io=time in seconds for the pressure in the

tank to rise from zero to P^

When one of the orifices is mounted on an

evacuated tank of volume, Vr, and measure- ments of time, tank pressure, and atmospheric

temperature and humidity are taken, as air is allowed to flow through the orifice into the

tank, the necessary data are obtained to plot

d'^-y/gha Vr

to against r. The proper value of ha can be obtained from figure 3. Table 2 contains the data for three representative sharp-edged plate orifices. The values of

r from table 2, when plotted against ^

.

give the curve of figure 4. This curve, using a

self-consistent system of units, may be ex- pressed for values of r less than 0.6 as

= 0.5^-^0. (4)

Table 2. -Representative data for thin-plate orifices

[Ur = 42..5 cubic feet]

to = t+At .U

Orifice 8. rf = 0.0416 foot (0.50 inch); thicl5ness=0.250

inch.

sec sec 0.0 5.1 5.1 0. 199 0. 10 5.0 5.

10..394 .20

10.0 5.15.

.588 ..30 15.2 5.

20. 3 .791 .40

20.4 5.

25. 5 .994 .50

25.4 5.

30.5 1. 189 .60 31.2 5. 1 36.3 1.415 .70 38.0 5. 1 43. 1 1. 680 .80

46.0 5. 1 51. 1 1.991 .90

100.0 5.

105. 1 4.096 1.00

Orificey. rf=0.0416foot (0.500 inch); thickness=0.125

inch.

0.0 5.0 ,5.0 0. 196 0. 10 5.0 5.0 10.0 .390 .20

10.0 .5.0 1.5.0 .,585 .30

15, 2 5.0 20.2 .787 .40

20.2 .5.0 25. 2 .982 .50

26. 0 .5.0 31.0 1.216 .60

32. 2 5.0 37.2 1. 450 .70 39.8 .5.0 44.8 1.746 .80 49.0 .5.0 .54.0 2. 104 .90

g.'i.O ,5.0 100.0 3.897 1.00

Oiificc 12. d=0.020Sfoot, (0.25 inch) ; thicl<oe,ss=0.12S inch.

0.0 20. 5 20.5 0. 200 0. 10 20.0 20. 5 40.9 .399 .20

41.0 20.5 61. 5 .599 .30

61.8 20. 5 82.3 .802 .40

82.2 20. 5 102.7 1.000 .50

103.2 20.5 123.7 1. 205 .60

126.0 20.5 146. 5 1.427 .70 152.4 20. 5 172.9 1.685 .80

186. 0 20.5 206. 5 2. 012 .90 300.0 20.5 320. 5 3. 121 1.00

1

[8]
33

Equation 4 is based on an atmospheric temperature of 65° F and a relative humidity of 50

percent, which represent the laboratory conditions during the tests. This gives a reasonable

working curve for domestic applications and

may be used with fair accuracy for any determination of de in which the atmospheric conditions are not known. However, if the atmospheric conditions vary appreciably from those

stated above, the appropriate value of ha can

be obtained from figure 3, mterpolatiiig, if necessary, for the existmg humidity.

In this iavestigation the capacity for backflow of air through any device, such as a tube

or faucet, in terms of the diameter of an orifice geometrically similar to the reference orifices, was determined in the following manner. The

device was mounted on the evacuated tank

and measurements taken in the same way as

for the orifices. If the curve of figure 4 is now

entered for any value of r<C0.6, for which is known, a value of d can be determined. This

value of d may be called the "equivalent diameter", de, of the tube or faucet and represents

the diameter of an orifice geometrically similar

to the reference orifices which has an air backflow capacity equal to that of the device.

Table 3.

Representative data for tubes

t At y

d. T

Tube 1.—

'r=42.6 cubic feet

sec. sec. sec. in. 0.0 93.

93.0.200 0. 1175 0. 10 91.8 93.

184. 9 .400 . 1178 .20

191.6 93.

284.7 .600 . 1165 .30 280.6 93.

373.7 .800 . 1173 .40 374.4 93.1 467.5 1.000 . 1173 .50

Average 0.117

Tube 5.— P'r=42.5 cubic feet

0.0 22.6 22.6 0.200 0. 2382 0. 10 22.4 22.6 45.0 .400 .2388 .20 45.0 22.6 67. 6 .600 .2386 .30

67.1 22.6 89.7 .800 .2392 .40

90.0 22.6 112.6 1.000 .2386 .50

0.239

Tube 10.— Vr=88.8 cubic feet

0.0 11.6 11.6 0. 200 0. 4724 0.10

12.0 11.6 23.6 .400 .4724 .20 24.0 11.6 35.6 .600 .4724 .30

36.0 11.6 47.6 .800 .4724 .40

47.2 11.6 48.8 1.000 . 4724 .50

0.472

[9]
2.4

2.2

2.0

1.8

CJ

1.4

1.2

1.0

.2

0.0

SQUARE EDGED ORIFICES SYMBOL DIAMETER THICKNESS

0 0500 INCH 0.250 INCH O500 INCH 0.125 INCH

o 0250 INCH 0.125 INCH

? /

/

/

/

/ /

V /

] /

/

/ /

// y/

// /

0.0 .8 1.0

Figure \.—Pressure ratio, PrIPa, plotted against '^-j^-hfor orifice plate.

d, orifice diameter; g, acceleiation of gravity; ha, atmospheric pressure in feet of air; W, volume of tlie evacuated system; and (o. time of flow for pressure in evacuated system to rise from 0 to pressure at time In. Representative data for three tubes and three

faucets are given in tables 3 and 4, respectively.

This procedure was followed for all of the

tubes, and the average values of de, each determined from several readings, are tabulated in table 5. The same procedure, when applied to the faucets shown in figure 2, gave the values of

de tabulated in table 6.

[10]
Figure 5.

Backflow across air gap

into tube.

Table 4.

Representative data for faucets

[l'r=42.5 cubic feet]

Faucet number ( At

V,

d. r

sec sec sec in.

( 0.0 9.6 9.6 0.200 0. 3654 0. 10 9.7 9.6 19.3 .400 .3647 . 20

1 \ 19.1 9.6 28.7 .600 .3661 .30 28.8 9.6 38.4 .800 .3654 .40

[ 38.3 9.6 47.9 1.000 .3660 .50 Average .366

f 0.0 9.5 9.5 0.200 0. 3675 0. 10 9.3 9.5 18.8 .400 .3695 .20

3 18.7 9.5 28 2 .600 .3695 .30

28.

9.5 37.6 .800 .3695 .40 37.5 9.5 42.0 1.000 .3695 .50 Average . 0. 369

f 0.0 13.9 13.9 0.200 0. 302 0. 10 14.0 13.9 27.9 . 400 .302 .20

9 \ 28.5 13. 9 42.4 .600 .302 .30 42.0 13.9 55.9 .800 .302 .40

[ 56.1 13.9 70.0 1.000 .302 .50 Average .302

Table 5.Equivalent diameters and critical air gaps

for tubes

Tube number d Di d. Ah d,/Di

in. in. in. in. in.

1 0. 125 0. 125 0.117 0. 239 0. 939

2 .125 . 160 . 116 .244 .724

3 . 125 .250 . 116 .257 .463

4 . 125 .500 . 116 .277 . 232

5 .250 .250 . 239 .412 .955

6 .376 .375 .358 .589 .955

7 .500 .500 .481 .789 .962

8 .500 . 666 .478 .811 . 719

9 .500 1.000 .477 .843 . 477

10 . 500 2. 000 . 472 . 910 .236

11 . 625 .625 .583 .935 .932

Table 6.Equivalent diameters and critical air gaps

for faucets

Faucet number d d. Ah' measured

in. in. in. in.

1 0.512 0. 695 0. 366 0. 625

2 __ .500 .628 .321 .543

3 .587 .950 .369 .657

4 .460 .640 .368 .620

6 .485 .640 .360 .619

6 .600 .775 .395 .656

7 __ .600 .775 .390 .656

8 - ____ .400 .613 .314 .539

9 .542 .986 .302 .578

10 .375 .586 .286 .531

» For faucets 5, 6, 8, 9, 10—read with plain rule, precision about 1/64 inch =0.015 inch, appro.xiraately.

4. Measurement of Critical Air Gaps

In order to measure the critical air gaps of the tubes and faucets each was mounted in

turn on the vacuum tank directly above the

glass jar, as illustrated in figure 5, in which tube

8 is shown during the process of backflow. The

micrometer point gage used for measuring the

gap is shown mounted on the tube.

The average of several determinations of the

critical air gap for 11 of the tubes is tabulated

as Ah in table 5. The critical gaps were determined in the following manner: Starting with. the water surface within the distance Ah of the

end of the tube, a vacuum in excess of 15 inches

of mercury was applied and maintained. As

the air gap approached its maximum value the

flow became intermittent, and small waves ap-

[11]
peared on the water surface. When this oc- curred, the valve was closed and the surface

allowed to become quiet, then the quick-acting

valve was opened slowly and backflow allowed

to resume. This was done several times for each determination; and the first gap reached,

across which no visible amount of water could

be drawn after slowly closing and reopening

the valve, was called the critical air gap.

The measurement of the critical air gap for the faucets proceeded along the same lines, the

faucet being wide open when the air gap was

created. It was not feasible to mount the

micrometer gage on faucets 5, 6, 8, 9, and 10,

and hence the critical air gap was measured for these faucets by means of a scale reading in

sixty-fourths of an inch. The average of several readings on each faucet is tabulated mader

A/i in table 6.

5. Effect of Water Temperature on Critical Air Gaps

In order to determine the effect on the critical air gap of variations in the temperature of the

water in the fixture, a series of air-gap measurements was made for tube 8 with water temperatures between 40° and 196° F. No measurable effect of water temperature on the

critical air gap was found.

Table 7.

Effect of nearby walls on critical air gaps

-X

Case 1 Touching one wall

Case 2 Moving away from one wall

X y A/i' A% X y Aft' A% X y Aft' A%

in. in. in. in. in. in. in. in. in. oo oo 0.817 0.0 oo oo 0. 817 0.0 oo oo 0.817 0.0

0. 25 0.25 1. 259 54.0 oo 0. 25 .968 18. 5 0. 25 0. 25 1.259 54.0

.50 .25 1. 132 38.5 .50 .980 20.0 .75 .75 1.094 34.0

.75 . 25 1.062 30.0 oo .75 1.079 32.0 1. 25 1. 25 1. 155 44.0

1.75 .25 0. 970 18.7 CO 1. 25 0.897 9.8 1.75 1.75 1.066 35.0

4. 75 .25 .968 18.5 oo 1.75 .844 3.3 2. 25 2. 25 0. 827 1. 2

Case 3 Moving away from two walls

6. Effect of Adjacent Walls

The effect of one or two nearby walls was

determined for one tube, No. 9, by placing it at various positions with respect to two walls at

right angles to each other and measuring the

critical air gap. These data are presented in

table 7, in which Ah' is the critical air gap when

influenced by nearby walls and A% is the per- centage increase over the critical air gap Ah.

7. Effect of Different Liquids on the

Critical Air Gap

The effect on the critical air gap was determined for dust-covered water, soapy water,

sugar solution, lubricating oil, and gasoline.

The results are tabulated in table 8.

Table 8.

Effect of different liquids on critical air gaps

as determined for pure water, with tube 6

Liquid

Water

Water covered with sawdust Water covered with aluminum powder Water covered with cork dust Soap solution Soapy water Sugar solution Lubricating oil (SAE 30) Gasoline

Difference

in Ah from

that for pure water

0. 000 +. 002 +. 004 +. 001 +. 019 +. 018 -.025

+. 010 +. 049

Change in

Aft compared with

that for pure water

Percent

0.0 +.4 +.8

+.2

+3.3

+3.2

-4.7 +1.8 +8.7

VI. ANALYSIS OF EXPERIMENTAL

DATA

1. Empirical Equation for the Critical Air

Gap for Tubes

In order to get a consistent expression for the critical air gap, the data given in table 5

for the series of tubes wUl be considered.

Plotting Ah versus dejDi from table 5 on logarithmic paper, as shown in figure 6, results in

two parallel straight lines through the points

for the tubes having internal diameters of

0.125 inch and 0.500 inch. Because the sharpedged tubes may be considered geometrically

similar, it is permissible to draw lines through

the points obtained for the tubes 0.250, 0.375,

and 0.625 inch in diameter parallel to those

through the points for the tubes having internal

diameters of 0.125 inch and 0.500 inch. These

lines represent the curves which would be

[12]
0.10.1

o TUBES NO. 1.2,3.4

" "6

• " " 7.8.9.10

" " 11

1.0 EFFECTIVE TUBE DIAMETER EXTERNAL TUBE DIAMETER Figure 6.

Diameter ratio, dJDi^ plotted against Ah for tubes.

d„ "equivalent diameter" of tubes; Di, e.xternal diameter of tube spout; and A/i, critical air gap.

found from a series of tubes of the same in- ternal diameter as the sharp-edged tubes.

This family of curves gives a series of similar

expressions which may be expressed approximately by

Ah^c(^y'\ (5)

in which the coefficient C varies with de. Equation 5 includes the effect of the external

diameter, Dj, on the critical air gap, whereas

the effect of atmospheric conditions is hidden

in the coefficient C and must be brought out in

explicit form by a further consideration of the

general eq 3. In table 9 are listed the values of Cfound from

figure 5 for each of the five measured values of the average effective diameter of the tubes

Table 9.

Air-gap coefficients for tubes

Internal di- ameter, d

Average ef- fective di- ameter, d.

CoeflBcient, C

in. in. in.

0. 125 0. 116 0.236

.250 .240 .411 .375 .358 .585

.500 .477 .786

.625 . 583 .929

Over at least a limited range of values of the

variables de/Di and de/ha, eq 3 can be expressed

as Ah=c{djD,ridjKr, (6) de where c, x, and y are constants, and x has

already been found approximately equal to -0.1.

[13]
Comparing eq 6 with eq 5, it is obvious that

C=cdMelKy, (7a) or C=[cl{KYW'-\ (7b)

where c/ihaY is a numerical constant for given

atmospheric conditions.

Upon plotting logarithmically the values of

C from table 9 against the corresponding aver- age values of de for each size of tube as given in

table 5, it is found that the results can be repre- sented closely, for the tubes larger than 0.125

inch, by the empirical equation

(7=1.50rfr, (8) where C and de are in inches, so that ?/= —0.1. Equation 7b shows that the numerical factor

is proportional to I /ha"; i. e., to ha^°-\ Hence

by designatmg by ha^ the value of ha for which

the value 1.50 was obtained, the effect of varying ha may be made explicit by writing

(7=1.50(^~"j dr, (9)

or since under the conditions of test, ha^ =28,300 feet,

C=0.538h+'HJ'',

in which C and de are in inches and /*„ is in feet. Equation 6 by substitution becomes

/d 2\-o.i ~=0.5S8h+'-'(^J , (10)

which is the general formula for the critical air gap for tubes, in which it is understood that

all quantities are in inches except ha, which is in feet. The variation in value of (Aa)° ' for a considerable range in atmospheric temperature is given in table 10, and it is obvious that its effect on eq 10 will be small; hence, if the average

value is used, eq 10 may be simplified, for practical purposes, to read

or AA = 1.50c?,"«A°S (12)

for dimensions in inches.

The data for the tubes are plotted in figure 7 with Ah/de versus D-^jdi. It should be noted that

for the tubes smaller than 0.250-inch diameter

there is an increase in the measured air gap of

7.5 percent over eq 12. It is probable that the

increase is due to the larger proportional effect on the air gap for small tubes of the ripples on

the water surface caused by the intermittent

backflow of water which occurs as the critical value is approached.

Table 10.

Effect of temperature on ha

Temperature Relative humidity Ac

Deviation

in "1 from value

at 65° F

"F Percent Feet {Feet) «-i Percent

32 50 26, 300 2. 767 -0.fi 65 50 28, 300 2.787 .0 100 50 30, 600 2.808 +.7

2. Application of Air-Gap Equation to

Faucets

It is now possible to compare the performance

of the faucets with that of the tubes by plotting

the experimental results for the faucets from

table 6 in figure 7. It can be seen that the

faucet data are in fair agreement with the

equation found for the tubes, deviations being

small and on the safe side. From this it may

be concluded that eq 11 or 12 can be used for determining the critical air gap for faucets with

fair accuracy and complete safety.

3. Effect of Adjacent Walls

Consideration of table 7 shows that the criti- cal air gap does not vary in a uniform manner

as the tube is moved away from the wall or

walls. This is due to the fact that when the

tube is at a small distance from the walls; e. g., 0.75 inch in cases 2 and 3, the small waves

caused by the intermittent backflow, as the

limiting value of the critical air gap is approached, are reflected from the nearby walls

and tend to increase the height of the waves

under the tube spout. This is made apparent

by a considerable increase in the agitation of the water surface with accompanying increase

in noise as small particles of water are drawn

up from the higher wave crests. As a conse-

[14]
o-TUBES

/:i-FAUCETS

1.0 6 7 8 9 10 D, 20 30 40 50 60 80 100

FiGDRE 7.Ah/d, plotted against d, '-/Di for tubes and faucets.

(I,, equivalent diameter; Du external spout diameter; and AA, critical air gap.

quence, it seems that the most practical way of taking account of the presence of nearby walls

is arbitrarily to increase the critical air gap,

Ah, for no walls as follows:

Position of spout with

respect to nearby walls

1 wall \x<3d,

\x>3d,

{X and y<^4dc

X or y<^4d,

X and y'^idf

Upper limit of critical air gap 1.3Ah. l.OAh.

l.SAh.

l.SAh.

l.OA/i.

Values of x and y, as indicated in table 7.

VII. PRACTICAL APPLICATION OF

RESULTS

It is now possible to express the critical aii- gap for a faucet in terms of its tip dimensions

and equivalent diameter. The quantitative

effect of nearby walls has also been demonstrated.

It is obvious that eq 12 is not in a form suit- able for use in field inspection. However, for practical purposes it may be simplified by

writing it iu the following form:

or

Ah=l.50d°-'{d,+2Ty-' (13)

Ah=l.50de'\l-\-ay' (14)

where

T=Di—de—eSective wall thickness and

2 a =21'

de

Table 11 has been prepared to show the per- centage increase in Ah for various values of a

as the ratio of effective wall thickness to equivalent diameter increases.

Table 11.

Effect of the ratio of effective wall thickness to equivalent diameter on critical air gap

a=2T Increase

d. in Ah

Percent

0 1.0 0.0

0.

1.010 1.0 .2 1.018 1.8 .3 1.027 2.7

.4 1.034 3.4

.5 1. 041 4.1

.6 1.048 4.8

.7 1.054 5.4

.8 1. Of.l 6.

.9 l.Ofifi 6.6

1.0 1.072 7.2

1.25 1.084 8.4

1. iiO 1.096 9.6

2.00 1. 116 11.6

3. 00 1. 149 14.9

It is evident on inspection of the table that

the percentage increase in Ah is slight as the

wall thickness increases, and if reference is made to a faucet of representative dimensions,

No. 10, table 6, a simple computation will show that the wall thickness could be increased

by more than half an inch before the critical air gap would increase 10 percent. This being

true, it is possible to conclude that, if a suitable

amount is added to the critical air gap to form

the safe air gap, consideration of the effect of

wall thickness can be safely omitted in the vast majority of cases. However, if it is desired to calculate the effect of wall thickness on the

critical air gap, this may be accomplished by means of table 11. If the factor in parentheses

is assumed equal to 1, eq 14 becomes

A/i=1.50</"» (15)

It is obvious that when de is less than 1 inch,

which is usually the case for plumbing fix- tures, AA will be greater than LbOd^. For

[15]
small values of de, such as 0.125 inch, the value

of Ah =2de is closely approached for thinwalled spouts. Hence, for use in field inspection, it seems that a safe limit will be H=2de,

where H represents the required air gap and

is the vertical distance between the horizontal

plane of the rim of the fixture and a horizontal plane through the center of the faucet

spout.

It is evident in table 8 that the changes

caused in Ah by variation in the physical characteristics of the liquid in the fixture are negligible, when compared to the margin of safety

listed in conclusion 10. Hence, it is reasonable

to conclude that for practical installation purposes no additional allowance need be made for liquids other than water. The necessity for laboratory determinations

of de may be avoided by using, instead of de, the

diameter of the smallest clear passage in the

faucet. This dimension, which is called the

"effective diameter" in the report of the

American Standards Association Sub Committee on Air Gaps, January 20, 1939, will be

slightly larger than de and hence will introduce

a small additional factor of safety.

Practical considerations of construction and

inspection make it desirable to set a minimum

limit to the value of the safe air gap in practice.

This is a purely arbitrary value that must be

based on practical experience and supported by

the consensus of opinion. It has been recom- mended to the American Standards Association

by its committee on air gaps that this lower

limit be set at 1 inch. To date there has been no criticism of this value, and for the purpose of

this paper it will be accepted. If this be done,

it immediately becomes apparent that if the

required air gap, H, be specified as equal to

2de, with H never less than 1 inch, a factor of safety is introduced which is of reasonable

magnitude. Furthermore, this factor of safety

is sufficient to take care of nearly all variations

in the wall thickness of the faucet spout or of any increase in Ah above 2de in the smalldiameter openings.

VIII. CONCLUSIONS

1. A working value of the equivalent diameter, de, of a faucet (i. e., the diameter of the

reference orifice which has an air backflow

capacity equal to that of the faucet) may be

obtained by using the diameter of the smallest

clear passage between the faucet spout and its tailpiece.

2. Within commercial limits of variation the

elongation of faucet spouts and their angle of inclination to the water surface has no effect on the mean value of the critical air gap.

3. The critical air gap may be determined

for any faucet when there is no wall effect by means of the relation

^=0.538/t„"'(4VA)-°-\. (10)

in which

A/i=the critical air gap in inches

Aa =atmospheric pressure in feet of air de=the equivalent diameter in inches

Z)i =the external diameter in inches

4. Normal variations in atmospheric conditions may be expected to introduce an effect in eq 10 of less than 1 percent.

5. Commercial variations in the effective

wall thickness for faucets, (Di-dg)/^, may be

expected to introduce an effect in eq 10 that is less than 10 percent.

6. Equation 10, rewritten in the approximate

form A/!,= 1.50 de°-^, is sufficiently accurate for most purposes.

7. Practical considerations of construction

and inspection require that a minimum value

be set for the required air gap; it is suggested

that the minimum value be 1 inch.

8. The foregoing conclusions allow the state- ment that safety may be attained economically,

when there are no walls closer than Ade, by

specifying the air gap as not less than 2de.

9. Safety may be obtained when there is a

wall effect by specifying that: If one or two

walls extending above the rim of the fixture or

vessel are within the horizontal distance four

times de measured from the nearest internal

[16]
wall of the spout, the air gap shall be not less than Sdg. 10. For purposes of regulation and inspection,

safe air gaps for lavatory faucets and other

faucets which have no nearby walls closer than

4ide may be specified as follows:

Minimum

additional margin of Bequiren

safety, from air eq 15 gap 1

(Inches) (Indies) Diameter of smallest clear passage be- tween spout and tailpiece

up to and including inch 0. 20 1 from inch to and including %

inch .34 l]4 from ji inch to and including 1 inch_ . 50 2 greater than 1 inch (') (2)

1 Increasingly greater than 0.50 Inch.

> Two times effective diameter inches.

11. Variations in the characteristics of the

liquid in the fixture may be expected to cause an increase in Ah wliich is considerably less than the margin of safety listed in conclusion 10.

Acknowledgment is made to G. H. Keulegan

of the National Hydraulic Laboratory staff for

helpful suggestions in outhning the experimental procedure followed in the investigation;

and to H. N. Eaton, Chief of the Hydraulic

Section of the National Bureau of Standards

for a critical reading of the paper and valuable

suggestions as to the form of presentation of

results.

IX. REFERENCES

[1] R. B. Hunter, G. E. Golden, and H. N. Eaton,

Cross-connections in Plumbing Systems, .1. Research NBS 20, 479 (1938) RP1086.

[2] R. H. Zinkil, Safe air gaps to prevent back-siphonage. Read before the 1936 Annual Meeting of the American Society Sanitary Engineering.

Published in Valve World.

[3] F. M. Dawson and A. A. Kalinske, Cross-connections in Plumbing and Water Supply Systems.

Joint publication of Wisconsin State Board of Health and the University of Wisconsin.

[4] F. M. Dawson and A. A. Kalinske, Report on Plumbing Cross-connections and Back-siphonage

Research, Technical Bulletin No. 1, National

Association of Master Plumbers of the United

States, Inc.

Washington, May 23, 1939.

o

[17]

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