Hatir

NBS MONOGRAPH 31

Capacities of Stacl(s in

Sanitary Drainage Systems

For Buildings

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act of Congress, March 3, 1901,

as amended by Congress in Public Law 619, 1950. These include the development and maintenance of the

national standards of measurement and the provision of means and methods for making measurements consistent with these standards; the determination of physical constants and properties of materials; the development

of methods and instruments for testing materials, devices, and structures; advisory services to government

agencies on scientific and technical problems; invention and development of devices to serve special needs of the Government; and the development of standard practices, codes, and specifications. The work includes basic and applied research, development, engineering, instrumentation, testing, evaluation, calibration services, and

various consultation and information services. Research projects are also performed for other government

agencies when the work relates to and supplements the basic program of the Bureau or when the Bureau's unique

competence is required. The scope of activities is suggested by the listing of divisions and sections on the inside

of the back cover.

Publications

The results of the Bureau's work take the form of either actual equipment and devices or published papers. These papers appear either in the Bureau's own series of publications or in the journals of professional and

scientific societies. The Bureau itself publishes three periodicals available from the Government Printing Ofiice: The Journal of Research, published in four separate sections, presents complete scientific and technical papers; the Technical News Bulletin presents summary and preliminary reports on work in progress; and Basic Radio

Propagation Predictions provides data for determining the best frequencies to use for radio communications

throughout the world. There are also five series of nonperiodical publications: Monographs, Applied Mathematics Series, Handbooks, Miscellaneous Publications, and Technical Notes. Information on the Bureau's publications can be found in NBS Circular 460, Publications of the National Bureau of Standards ($1.25) and its Supplement ($1.50), available from the Superintendent of Documents,

Government Printing OjEce, Washington 25, D.C.
UNITED STATES DEPARTMENT OF COMMERCE • Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Capacities of Stacks in Sanitary

Drainage Systems for Buildings

Robert S. Wyly and Herbert N. Eaton

National Bureau of Standards Monograph 31

Issued July 3, 1961

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. - Price 35 cents
Contents

Page

1. Introduction 1

1.1. Purpose and scope of paper 1

1.2. General principles of the design of buildingdrainage systems 1

1.3. Definitions 2

1.4. Nomenclature 2

2. Previous research on capacities of drainage and

vent stacks 3

2.1. National Bureau of Standards 3

2.2. Universities 6

3. Test equipment and procedures 8

3.1. Tests on interference of flows at junction of drainage stack and horizontal branches 8

a. Simulated stack—sanitary-tee and long- turn T-Y fittings 8

b. Prototypal stack—sanitary-tee fittings. 8

3.2. Tests on air flow in stack vent and in vent to horizontal branch 9

3.3. Miscellaneous tests 10

a. Distribution of air and water in cross section of 3-in. drainage stack 10

b. Velocity distribution of water in cross section of 3-in. drainage stack 10

c. Vertical distribution of pneumatic pres- sures within 3-in. drainage stack 11

4. Analysis of flow conditions in plumbing stacks 11

4.1. Interference of flows at junction of drainage

stack and horizontal branches 11

a. Simulated stack 14

b. Prototypal stack 15

4.2. Terminal velocities and terminal lengths 16

a. Derivation of equation for terminal

velocities 16

b. Derivation of equation for terminal

lengths 18

4.3. Flow capacities of multistory drainage

stacks 18

4.4. Air flow in drainage systems 19

4.5. Flow capacities of vent stacks 20

5. Test results 20

5.1. Flow capacities at junction of drainage

stack and horizontal branches 20

a. Simulated stack 20

b. Prototypal stack 22

5.2. Air-flow measurements 23

5.3 Miscellaneous measurements 27

a. Distribution of air and water in cross section of drainage stack 27

b. Velocity distribution of water in cross section of drainage stack 28

Page

5. Test results—Continued

5.3 Miscellaneous measurements—Continued

e. Pneumatic pressures within drainage

stack 28

6. Application of results of investigation 30 1 6.1. Permissible simultaneous rates of flow at junction of drainage stack and horizontal , branches 30

6.2. Loads on drainage stacks 32

6.3. Loads on vent stacks 33 I 6.4. Comparison of loads given by plumbing j codes with computed values for drainage

' and vent stacks 36

a. Loading tables for drainage stacks 37 'i b. Loading tables for vent stacks 38

7. Conclusions 38 ' 7.1. Interference of flows at junction of drainage

stack and horizontal branches 38

7.2. Flow capacities of drainage stacks 38

7.3. Air flow in drainage systems 38

7.4. Loading tables 38

7.5. Miscellaneous phenomena 39 ;: a. Distribution of air and water in cross

' section of drainage stack 39 [ b. Velocity distribution of water in cross section of drainage stack 39 : c. Pneumatic pressures within drainage

stack 39 ! 7.6. Need for further research 39

a. Design-flow problems 39 \ b. Flow-capacity problems 39

(1) Flow of air in venting systems 39 I (2) Interference of flows at stack- ' branch junctions 40

(3) Velocity distribution of water, and

air-water distribution in cross 5 section of drainage stack 40

(4) Detergent foam in plumbing sys- tems 40

8. References 40

9. Appendix . 41

9.1. Individual measurements relating to inter- ference of flows at junction of simulated

stack and horizontal branches 41 ^ 9.2. Computation of the absolute roughness, k„ ; for cast-iron soil pipe 41

9.3. Effect of drainage-stack height on permissible loads 41
Capacities of Stacks in Sanitary Drainage Systems for Buildings

Robert S. Wyly and Herbert N. Eaton

Some of the important results obtained in investigations of capacities of plumbing

stacks in test systems at the National Bureau of Standards and elsewhere are discussed. Data are shown from experiments on the flow of water and air in such systems, and

analyses of certain flow phenomena are given. Methods are shown for applying the

results of research in hydraulics and pneumatics to the preparation of loading tables (for drainage and vent stacks) suitable for use in plumbing codes. The need for additional research in further improvement of plumbing codes is discussed.

1. Introduction

1.1. Purpose and Scope of Paper

The lack of an adequate knowledge of the

hydrauhcs and pneumatics of building-drainage

systems is one of the most serious handicaps

under which the writers of plmnbing codes and

design handbooks must work. A budding-drainage system cannot be designd with maximum

economy tmless the minimum sizes of pipes that can be used satisfactorily in its various parts can be computed. This is particularly true of a

multistory system or of a system serving a low

building which covers a large area, since many

such systems are large enough and complex

enough to afford opportimities for appreciable

savings through the apphcation of design methods

based on research.

Attempts have been made to determine by

experiment the capacities of various components

of building-drainage systems. The complexity

of the flow phenomena in such systems makes

it necessary to simphfy test conditions. Unfortunately, this limits the usefulness of the results. Hence, it is not surprising that loading tables in some plumbing codes have been based more on

experience and opinion than on rational analysis

and experiment. It is certain that the factors

of safety used in preparing some loading tables

have been excessively large. This leads directly

to oversizing of pipes.

' The purposes of this paper are:

1. To summarize certain aspects of experimental studies of the hydraulics and pneumatics

of plumbing systems conducted at the National

Bureau of Standards and other laboratories since

1921, with particular emphasis on some of the

results obtained at the National Bureau of

Standards during an investigation of the capacities

I of stacks and horizontal branches;

2. to correlate laboratory data on the flow of

water and air obtained in this and other investigations ; 3. to illustrate the application of research

results to the computation of loads for drainage

and vent stacks; and

4. to compare some of the loadings obtained

from tables in currently used plumbing codes with

loadings computed by methods outlined in this paper.

The most recent laboratory investigation

described in this paper comprised four parts:

1. A study of the flow conditions at the junction

of a drainage stack and its horizontal branches,

using a specially designed flow simulator (simulated stack) with sanitary-tee stack fittings;

2. a study similar to (1), except that long-turn

T-Y stack fittings were used

;

3. a study similar to (1), except that a multistory test system (prototypal stack), rather than

the simulated stack, was used; and

4. a study of miscellaneous items, including air flow in drain and vent pipes; pneumatic pressures

in drainage stacks; air content of the layer of

water flowing on the wall of a stack, and velocities

in this layer. The prototypal stack was used in

this part of the investigation.

1.2. General Principles of the Design of

Building-Drainage Systems

The drainage system of a building requires two

distinct sets of pipes. The first is required to transport the waste water and the water-borne

liquid and solid wastes from the plumbing fixtures to the street sewer, septic tank, or other means of

disposal. The second set of pipes, the vent

system, is required to reduce the intensity of

pneumatic disturbances caused by the intermittent use of the plumbing fixtures. The vent

system, if properly designed, will prevent excessive depletion of the water seals of the fixture

traps. These water seals must be maintained to prevent sewer air from entering the budding.

In order that the drainage and vent systems may

perform their functions in a manner that meets

generally accepted standards of performance and

that will not create health hazards or nuisance

conditions, the foUowrng broad requirements

should be satisfied:

1. The dimensions and arrangement of the

I
various components of the piping systems should

be such that normal peak loads of water and waterborne wastes discharged into the drainage system

may be carried away by gravity without creating

excessive hydrostatic pressures, and that pneumatic-pressure fluctuations in horizontal branches

and fixture drains shall not seriously deplete the

water seals in fixture traps.

2. The design should be such that noise and

vibration due to the flowing water are reduced to a

practical minimum.

3. The various sloping pipes in the drainage

system should be of such diameters and slopes

that self-cleansing velocities will be attained.

4. Adequate, but not excessive, allowance

should be made for the effects of fouling and cor- rosion in the piping systems and for cases where

additional loads may be imposed on the system at some future date.

1.3. Definitions

The following definitions of some of the terms

used in this paper are given in order to avoid confusion or possible misinterpretation of statements

made in the paper. Except for those that are marked with an asterisk, the definitions have been

taken from the American Standard National

Plumbing Code A40.8-1955 [1].^ A branch interval is a length of soil or waste

stack corresponding in general to a story height,

but in no case less than 8 ft within which the

horizontal branches from one floor or story of a

building are connected to the stack.

The building (house) drain is that part of the

lowest piping of a drainage system which receives

the discharge from soil, waste, and other drainage

pipes inside the walls of the building and conveys

it to the building (house) sewer beginning 3 ft outside the building wall. The *drainage stack is the vertical main of a drainage system and may be either a soil or a waste stack.

A drainage system (drainage piping) includes all the piping within public or private premises, which

conveys sewage, rain water, or other liquid wastes

to a legal point of disposal, but does not include

the mains of a public sewer system or private or

public sewage-treatment or disposal plant.

A fixture unit is a quantity in terms of which

the load-producing effects on the plumbing system

of different kinds of plumbing fixtures are expressed on some arbitrarily chosen scale. A horizontal branch is a drain pipe extending

laterally from a soil or waste stack or building

drain, with or without vertical sections or branches,

which receives the discharge from one or more fix- ture drains and conducts it to the soil or waste

stack or to the building (house) drain.

The nrtain vent (referred to as the vent stack in

this paper) is the principal artery of the venting

system, to which vent branches may be connected.

1 Figures in brackets indicate tbe literature references on page 40.

The *piezometric head is the height to which

water would rise in a vertical tube connected at

its lower end to a pipe containing water and open

at its upper end to the atmosphere.

Plumbing fixtures are installed receptacles, devices, or appliances which are supplied with water

or which receive or discharge liquids or liquidborne wastes, with or without discharge into the

drainage system to which they may be directly or

indirectly connected.

A soil pipe is any pipe which conveys the discharge of water closets or fLxtures having similar

functions, with or without the discharge from

other fixtures, to the building drain or building

sewer. A stack is the vertical main of a system of soil, waste, or vent piping.

A stack vent (sometimes called a waste vent or

soil vent) is the extension of a soil or waste stack

above the highest horizontal drain connecting to the stack.

* Terminal length as applied to drainage stacks means the distance through which water discharged into the stack must fall before reaching

terminal velocity.

* Terminal velocity as applied to drainage stacks means the maximum velocity of fall attained by

the water in the pipe, whether or not the cross section of the pipe is filled with water. A trap is a fitting or device so designed and constructed as to provide, when properly vented, a

liquid seal which will prevent the back passage of

air without materially affecting the flow of sewage

or waste water tln:ough it. The trap seal is the maximum vertical depth of

liquid that a trap will retain, measured between

the crown weir and the top of the dip of the trap.

A vent stack is a vertical vent pipe installed primarily for the purpose of providing circulation of

air to and from any part of the drainage system.

(In this paper it is to be understood that the developed length of vent stack may include some

piping in other than a vertical position.)

A vent system is a pipe or pipes instaUed to provide a flow of air to or from a drainage system or

to provide a circulation of air within such system

to protect trap seals from siphonage and back

pressure. A waste pipe is a pipe which conveys only liquid

waste, free of fecal matter.

A wet vent is a vent which receives the discharge

from wastes other than water closets.

1.4. Nomenclature

The following list of letter sjonbols used in the

analyses and equations appearing in this paper

will be useful to the reader. Insofar as possible

the symbols used are in agreement with ASA

standard YlO.2-1958, Letter Symbols for Hydraulics.

General terms:

.A =area of cross section

Z)= diameter

2
force

^= acceleration of gravity

^=head

L=length

jP= pressure

0=volume rate of flow (discharge rate)

ff= radius

P=nias3 density (mass per unit volume)

f=time

F=mean velocity

2= elevation above datum

Subscripts:

l=refers to drainage stack

2=refers to horizontal branch

a=refers to air i=refers to terminal conditions

?;= refers to vent

w=refers to water

Special terms: C6=head-loss coeflicient for bend.

(?£,= head-loss coefficient for flow through

pipe fittings and transitions in cross section

5= function of several variables

A£'= energy loss per unit voliune of water

due to flow resistance

y=Darcy-Weisbach friction coefiicient

i^d= centripetal force required to cause an

elementary mass of water to move

in a curved path

A6=head loss due to bend

Ad=H3'drod}Tiamic-pressure head caused

by deflection of stream

A/= head-loss term in Darcy-Weisbach pipeflow equation resulting from friction

Ai=pneimiatic-pressure head in drainage

stack

A2=piezometric head in horizontal branch

measured with reference to elevation

of stack-branch junction

^3 =height to which water will rise in a vent connecting to a horizontal

branch, measured with reference to elevation of stack-branch junction

A4=pneumatic pressure head in vent con- necting to horizontal branch

A:s=Nikuradse sand-rouglmess magnitude

i«= terminal length (length of fall required

for water in drainage stack to reach

terminal velocity)

X=a dimensionless constant determined by

frictional resistance

Am=mass of elementary volume of water

j'=kinematic viscosity

iV^= Reynolds number, a dimensionless flow

parameter

^i=hydrodyiiamic pressure caused by deflection of stream (corresponding to the head ha)

(/>=functional symbol

rs= ratio of area of cross section of water

stream in a drainage stack to total area of cross section of the stack

-Z?c= radius of curvature of path followed by

stream when deflected

hydraulic radius, the ratio of cross sec- tion of the stream in a drain pipe to

its wetted perimeter

7"= thickness of layer of water flowing on

wall of drainage stack

y«=mean terminal velocity of water flowing on wall of drainage stack

f=deflection coefficient apphcable to head

loss in pipe bend

2. Previous Research on Capacities of Drainage and Vent Stacks

Attempts have been made to obtaua knowledge

of the flow and pressure conditions in stacks and

thus to offer a rational basis for computing stack

loadings. This has been difficult, for not enough

has been known about the conditions in stacks to permit the establishment of a wholly satisfactory

criterion for stack capacity. Hunter at the National Bureau of Standards, Dawson and Kalinske

at the State University of Iowa, and Babbitt at the University of Illinois have done research on

stack capacities.

2.1. National Bureau of Standards

Some of the first clear statements regarding the

nature of flow in drainage stacks and a definition

of stack capacity were reported by Hunter in

1923 [2]. From tests, he found that the character

of flow in a partiaUy filled vertical pipe varied

with the extent to which the pipe was filled. For

low rates of flow, the water was entirely on the

wall of the stack; but as the flow rate was in- creased, the frictional resistance of the air caused

the formation of short slugs of water. Increased

air pressure generated by the slugs caused the

water to be thrown to the wall of the stack either

immediately or after falling for some distance

separated into streamlets in the center of the pipe.

Hunter observed that slug formation occurred in a 3-in. stack when the water-flow rate was in- creased to a value such that the flowing water

occupied ]i to ]i of the cross section of the stack.

A further increase in rate of flow resulted in closely

spaced slugs that did not break up readily.

Hunter believed that intermittent slug formation

is partially responsible for the rapid oscillations

of pressure which occur in plumbmg systems.

Hydrostatic head can develop in a drainage

stack only when it is fOled with water at some

point. In the case of a stack which receives

water at one elevation only, this condition would

first occur at the elevation of water entrance,

where the downward velocity is least. The vertical component of the entrance velocity

depends on the rate of flow by volume, the cross- sectional area of the inlet, and the angle of the

entrance. This points to the capacity of the

3
fitting as a measure of the practical capacity of

the stack. (Hunter was probably thinking here

of one- and two-story stacks.)

Hunter defined fitting capacity as the rate of

flow in gallons per minute at which the water just

begins to build up in the stack above the inlet

branch of the fitting when no water is flowing

down the stack from a higher level. Determinations of fittmg capacity were made

for different type fittings on both 2- and 3-in. stacks with the water introduced at one level. It was observed that the rate of flow that caused

the water to stand above the fitting inlet was

greatly in excess of the rate at which the tendency

to build up first appeared.

Some tests were made with inlets at two levels approximately 11 ft apart. Various rates of flow were introduced into the stack through the inlets. Any backflow into an L-shaped tube set in a side

inlet of the lower fitting was taken to indicate

that the fitting capacity had been exceeded. The

tendency was toward an increase in capacity with

water introduced at two levels instead of one. Hunter's tests indicated that stack capacity may

increase with the number of inlets until the point

is reached when the stack is fiowing full throughout

its length. From this line of reasoning, he con- cluded that the fitting capacities which he had

determined for stacks with inlets at one level only would be less than the capacities of stacks

having inlets at more than one level, and that such

fitting capacities could be safely, but not necessarily economically, utilized as stack capacities for

all heights of stack.

From his tests, Hunter decided that safe values

for stack capacity could be computed from the

equation

Q=kD\ (1)

where Q is expressed in gallons per minute, and

D in inches. He gives the values

A;=22.5 for 45° Y inlets, and

Z:r= 11.25 for sanitary-tee inlets. On the basis of this reasoning and the experimental results with 2- and 3-in. stacks, he gave

a table of stack capacities in BH13 [3] (see table 1). The tests which form the basis of table 1 were made with water introduced through doublebranch fittings at one level only. Hunter reported no quantitative results for the tests in which

water was introduced into the stack at more than one level. An illustration of a case in which the fitting

capacity has been exceeded is shown in figure 1. This photograph was taken in the course of the

most recent investigation of stack capacities at the National Bmeau of Standards. It shows a

3-in. double sanitary tee mth 3-in. side inlets made of transparent plastic material with its inside dimensions closely simulating those of the

Table 1. Practical carrying capacities of stacks *

(Hunter)

Diameter of stack

Practical carrying capacity

Sanitary-tee

fittings Y or Y-andJ^-bend

fittings

in. gpm gpni

2 b 45 bgo

3 !> 100 b200

4 180 360

5 280 560

6 405 810 8 720 1,440

» For water introduced at one elevation only, through double-branch

fittings. b Carrying capacities for the 2- and 3-in. stacks were determined by experi- ment. The values for larger diameters were computed from eq (1).

Figure 1. Flow irito 3-in. stack from two horizontal branches at same level, showing case in which the capacity

of the fitting is exceeded {double sanitary tee fitting)

.

Total flow from branches is approximately 200 gpm. No flow down stack from higher levels.

corresponding metal fitting. Flows of about 100

gpm are entering the fitting from each horizontal

branch, but there is no flow down the stack from

above the branch level. It will be observed that

the water is standing up in the stack somewhat

above the level of the branches. According to Hunter's formula (eq (1), using the value 11.25

for k), the capacity of the fitting is approximately

100 gpm. Therefore, it might be expected that a fiow of 200 gpm would overload the fitting.

4
"With further reference to Hunter's work [3], consideration of the design criterion that no

hydrostatic head raay develop in a drainage

system indicates that carrying capacity for a

given diameter will be less in a horizontal section

of the system than in a vertical section. This

suggests separate consideration of vertical and

horizontal sections.

The fact that an appreciable head of water in

any portion of a drainage system into which

branches discharge tends to impair the efficiency

of the drainage indicates a limiting condition on

which to base computations of permissible capacities. Hunter felt that although an occasional

head of water in certain portions of a drainage

system may not be harmful, the assumption of a condition imder which no head can develop in

any portion of the stack or house drain is certainly a safe procedm-e and apparently the only one

that will permit a general appHcation of test

results. One of the most significant criteria for drainagestack capacity suggested by Hunter is that where

terminal velocity exists, a stack should not be

loaded to such an extent that more than ji to ji of

the cross section of the stack is filled with water. Some such limit is required to prevent the occmrence of serious pneiunatic disturbances associated

with excessive rates of water flow.

It is necessary to have information on velocities

in drainage stacks before computing rates of flow

that will produce a water-occupied cross section

bearing a given ratio to the stack cross section.

Hunter [2, 4] made measurements of terminal

velocities in vertical pipes, on one occasion with

the pipes flowing fidl and on another with them

flo^ving partiafly full. He measm-ed the rate of fall of water columns

in vertical pipes up to 100 ft in height, using

1-, 2-, and 3-in. galvanized steel pipe. His

experimental procedure was as foUows: Gage

holes were tapped in the pipe at intervals of 10

ft. A quick-opening valve was installed at the

bottom of the pipe. With the valve closed, the

pipe was filled with water to the level of the

first gage hole. The valve was then opened

quickly, and the time required for the water to flow out of the pipe was observed. This process was repeated, the pipe being fiUed to the height

of each gage hole successively. To obtain the

terminal velocity for each diameter of pipe, he

plotted the lengths of the falling column as ordinates and the times of descent as abscissas.

This gave a straight line in the region where the

water was falling at terminal velocity, and the

slope of this line gave the terminal velocity.

In order to establish limits within which the

measiu-ed terminal velocities should fie, he computed terminal velocities for smooth and for

very rough pipe over a range of diameters of from

1 to 8 in. These curves, together with the

experimentaUy determined velocities, are shown

in figure 2. The three experimental points fie

15 /

I 1.5 2 3 4 5 6 7 8 9 10 DIflMETEf) OF PIPE , in.

Figure 2. Terminal velocities in vertical pipes flowing full under the force of gravity.

between the two curves, as they shoifld, and, as would be expected, they are closer to the curve

for smooth pipe than to the ciu-ve for very rough

pipe. Because of this satisfactory agreement of

the experimental values with the values given

by the smooth-pipe ciu-ve, Hunter concluded that

the smooth-pipe curve given in figure 2 might

be used to set the upper limit of terminal velocities

for flow out of stacks completely fiUed with water. Hunter [2] also measured velocities in 2- and

3-in. cast-iron stacks flowing partly fuU. He used

a 3-in. stack 45 ft in height, open top and bottom,

and introduced the water through a 45° double-Y

fitting at the top of the stack. The velocities were measured with a pitot tube at the bottom of

the stack. Various heights of fall of from 5 to 45

ft were used. From these tests, he found the ter- minal velocity of fiow in the 3-in. stack to be about

16.8 fps, attained in a height of about 15 ft for a fiow of 100 gpm; and 32.8 fps, attained in a height

of about 45 ft for a flow of 200 gpm.

The tests on a 2-in. stack showed that in a fall of about 20 ft for a flow of 45 gpm, a terminal

velocity of 18.5 fps was attained; and for a flow

of 90 gpm, a terminal velocity of 24 fps was

attained.

Hunter remarks that with flows of 90 gpm in

the 2-in. stack and 200 gpm in the 3-in. stack,

slugs of water completely filling a short length of

the pipe occasionally formed, and the maximum

velocity of these slugs approached the maximum

velocity for a completely filled stack.

Up to this point, the discussion of Hunter's

work has been confined to draiaage stacks. He

also studied problems of venting. It seems appropriate to mention briefly a method which he

proposed for sizing vent stacks [3]. He suggested

that the formula

iy-a) {x-h) =c (2)

5
be used. In this equation, y is the volume rate

of water flow in gallons per minute divided by

7.5 (Hunter at that time having conceived of the

"fixture unit" as a volume rate of discharge equal

to 7.5 gpm); x is the length of vent stack (main

vent) in feet; and a, b, and c are constants. The

curve is asymptotic to the lines y=ci and x—h.

By the use of certain experimental data, Hunter

computed values of a, h, and c. These values are given in table 2 for vent stacks and drainage

stacks of the same diameter.

rate of flow into the stack at any one floor level must be limited. They suggested that if sanitarytee fittings are used, the rate of flow introduced'

within any one branch interval shoidd not exceed

;

one-third of the maximum for the stack; while if | 45° Y connections are used, the flow rate intro-'

duced within any one branch interval should be

limited to one-half of the maximum for the stack.

Table 3 gives the maximum carrying capacities

of drainage stacks suggested by Dawson and

Kalinske.

Table 2. Computed constants for use in venting equation

(Hunter)

Table 3. Maximum carrying capacities of stacks

(Dawson and Kalinske)

Diameter of both drain- Values of constants

age stack and

vent stack a b C

in.3 6 33 5, 780

4 8 27 11,400

5 10 20 20, 280

6 12 16 31, 240

8 16 12 81,040

2.2. Universities

Dawson and Kalinske at the State University

of Iowa prepared two reports on an investigation

of stack capacities [5, 6]. Measurements were re- ported of volume rates of water and air flow,

pneumatic pressures, and maximum water velocities in stacks 3, 4, and 6 in. in diam and approximately 30 ft high. Each stack discharged into a short horizontal drain through a 90° bend.

Various rates of flow Avere introduced through a

horizontal branch near the top of the stack, and

pressures and velocities were measm-ed at several

points down the stack.

From their tests, Dawson and Kalinske con- cluded that where the water attains its maximum

velocity, a drainage stack should not be allowed

to flow more than about one-fourth fuU. They

felt that this criterion is a reasonable choice, since

the velocity in the building drain and building sewer flowing full but not under pressure some

distance from the base of the stack is roughly of

the order of one-fourth of the terminal velocity

in the stack. They had observed in tests that a

stack flowing too full caused considerable noise

and vibration, as well as pneumatic disturbances.

Dawson and Kalinske observed, as did Hunter,

that too great a rate of discharge into a drainage

stack at any one level caused the stack to fill up at that point due to the smaU vertical component of

velocity of the incoming stream. Because of the

pneumatic and hydraulic disturbances which are created by this condition, the}^ concluded that the

Diameter of Carrying

stack capacity

in. gpm

3 90 4 180

5 350

6 560

8 1,200

The carrying capacities given in table 3 differ considerably from those in table 1 for some cases. This difference may be explained partly on the

basis that table 1 really gives Jitting capacities as indicated by a filling up of the stack with water

near the fitting, while table 3 gives stack capacities

computed for a given water-occupied cross section

where terminal velocity exists in the stack some

distance below the fitting. Thus, the two tables are based on different phenomena.

The measurements of terminal velocities made

by Dawson and Kalinske with a pitot tube are shown in table 4. From the velocities given in

Table 4. Terminal velocities in vertical pipes flowing partly

full »

(Dawson and Kalinske)

Diameter t Discharge Thickness Terminal

of stack rate of sheet velocity (measured) (computed) (measured)

in. gpm in. fps

3 45 0. 136 1L5

3 90 .209 15.4

3 135 .281 17.6

3 180 .346 19.5

4 90 .141 16.8

4 135 .189 19.0

4 190 .252 20.4

4 240 .311 21.2

4 300 .382 22.0

6 115 .162 12.3

6 165 .199 14.4

6 220 .221 17.4

6 345 .281 21.7

6 450 .320 25.0

6 560 .379 26.5

6 675 .446 27.5

" Water Introduced at one elevation.

•> Nominal diameters. Thickness of sheet computed on basis of actual diameter of standard-weight steel pipe. 6
Table 5. Terminal velocities in vertical pipes flowing partly

full »

(Hunter)

Diameter <> Discharge Thickness Terminal

of stack rate of sheet velocity (measured) (computed) (measured)

in. gpm in. fps

3 100 0. 219 16.8

3 200 .215 34.2

2 45 .133 18.5 2 90 .215 24.0

• Water introduced at one elevation.

•> Nominal diameter. Thickness of sheet computed on basis of nominal

diameter. No measurements on actual diameters were reported by Hunter

for these tests.

the table, the cross-sectional areas, Ai, of the

sheets of water were computed from the known

values of the flow rates. The thickness, T, of the

sheet in each case was then computed from the

equation

A,=-k{D,-T)T. (3)

The values thus obtained are also given in table 4. The same computations were made from Hunter's

data on terminal velocities in stacks flowing partly

full and the results are given in table 5. Dawson and Kalinske [5] derived the following

expression for terminal velocity, which is expressed

here in the notation of the present paper for

simplicity of comparison with eq (37)

:

32

/

V,^iQ,g/irkD,y'' (4)

40 60 80 100

0. (gpm) /O. , in.

Figure 3. Terminal velocities in vertical pipes flowing

partially filled under the force of gravity.

O, Dawson.- 3-in. stack V, do 4-in. stack A, do 6-in. stack , Hunter... 2-in. stack 9, do 3-in. stack

After analysis of the factors which affect the

friction coefficient A: in eq (4), they concluded [6] that terminal velocities could be computed from

the equation

y,=3.9(2ij" (6)

in which is expressed in feet per second, Qi in

gallons per minute, and Di in inches. The data on measured velocities shown in tables 4 and 5 have been plotted in figure 3. The cm-ve in the

figure has been computed from eq (5). The problem of computing sizes of vent stacks was studied by Dawson and Kalinske, along with

the problem of sizing drainage stacks [6]. They

developed a table of vent-stack sizes based on test data from the 3-, 4-, and 6-in. drainage stacks

described above and on the assumption that the

air flow- carried by the vent stack is proportional

to the product of the terminal water velocity times

the cross-sectional area of the drainage stack not

fifled with water. Babbitt of the University of Illinois pubUshed

the results of stack tests [7]. Much of his work

related to variations of pressure in the stacks with

flow. He gives a discussion of "The useful capacity of 2-, 3-, and 4-in. soil stacks," in which he

discusses the capacity of a soil stack to receive the

discharge from plumbing fixtures. He states that a 4-in. soil stack will probably take all the water

that would be delivered to it in a 5-story building, a 3-in. soil stack will probably take all the water

that would be delivered to it in a 3-story residence,

and a 2-in. pipe is unsuitable to be used as a soil stack. He found from tests on a 4-in. and on a

5-in. drainage stack [8] that the capacities were 200

and 500 gpm, respectively.

Babbitt also made tests [7] to determine the rate

at which one horizontal waste pipe of the same

diameter as the soil stack can discharge water

into the soil stack through a sanitary-tee fitting

without backing up water in the system at the

point of junction. He gives the following values:

"2-in. soil stack, 25 gal per min for 7 seconds;

3-in. soil stack, 50 gal per min for 7 seconds; and

4-in. soil stack, 100 gal per min for 7 seconds."

Based on his test data and on empirical reasoning. Babbitt gives a series of tables for sizing vent

pipes for 3- and 4-in. drainage stacks for various

volume rates of water flow. However, he gives no

venting tables for larger diameters of drainage

stacks.

5840.32—61 2 7
3. Test Equipment and Procedures

3.1. Tests on Interference of Flows at Junction of Drainage Stack and Horizontal

Branches

a. Simulated Stack—Sanitary-Tee and Long-Turn

T-Y Fittings

In the most recent National Bureau of Standards investigation of stack capacities, a simulated

stack was first used which provided greater

flexibility of experimental conditions and better

control of pertinent variables than could be provided by the use of a prototype. Figure 4 shows

this equipment in some detail. To connect the

stack and the horizontal branches, sanitary-tee

stack fittings were used first, followed by long-turn

T-Y fittings.

In this part of the investigation as weU as in

those parts described under sections 3.2 and 3.3,

water was delivered to the test system from a

constant-level supply tank. The rates of dis- charge to the stack and the horizontal branches were measured by means of calibrated orifice meters.

DISTRIBUTION CHAMBER

SIX WATER . INLETS

MANOMETER CONNECTIONS

Figure 4. Simulated stack.

In the simulated stack, the layer of water flowing down the stack was produced at the level of

the stack fitting by installing, in the stack just

above the fitting through which the horizontal

branches discharged, a second piece of pipe,

smaller in diameter than the stack. As can be

seen in figure 4, the stack terminated at its upper

end in a chamber or drum supplied with water

around its circumference through six 1-in. diam

pipes. This construction caused water to discharge through the annular space between the

stack and the inserted pipe, thus forming a moving

blanket of water which simulated the layer that

under service conditions is assumed to be flowing

down the stack from higher floors. The diameter

of the inserted pipe determined the thickness of

the layer, and the volimae rate at which water was

introduced into the drum determined the velocity

of flow.

Numerous tests were made on the simulated

stack with one- and two-branch flow, for pneumatic pressures in the stack from 0.3 to 2.0 in. of

water below atmospheric. Three diameters of

horizontal branches were used on the 3-in. stack

1}^, 2, and 3 in. Data were obtained for waterlayer thicknesses of 0.16, 0.35, and 0.58 in. Thus,

the tests provided nine different combinations of

dimensions for which pressures and rates of flow were measured in the stack and horizontal

branches.

b. Prototypal Stack—Sanitary-Tee Fittings

Because conditions existing in the simulatedstack tests did not exactly correspond to conditions in a typical multistory drainage stack in

service, a part of the investigation was repeated

using a prototypal stack with six branch intervals, a building drain, and a system of ventilating pipes.

The important elements of this system are shown

in flgure 5. In making these tests, the system was arranged

so that the pneumatic pressure in the drainage

stack was transmitted from the stack through a

special connection to the horizontal branch at a

point 4 drain diameters from the stack, as shown

in figure 6. Thus, the pneumatic pressure acting on the water in the horizontal branch was the same as that in the stack, assuming equal aspirating effects at the two branch connections. Measurements with no water flowing in the branch

indicated that the aspii'ating effects at opposite

sides of the fitting did not differ by more than 0.1

in. of water for rates of fiow of up to 100 gpm in

the stack. Therefore, it will be assumed that

the head of water indicated in the sight glass

attached to the horizontal branch showed directly

the difference between the total pressure in the
Figure 5. Prototypal stack.

horizontal branch and that in the stack. This

eliminated the need for actually measuring the

fluctuating pneumatic pressure in the stack. It was possible to obtain relatively steady readings

in most of the tests by the use of this system.

Water was introduced into the stack through a double 3- by 3-in. sanitary-tee fitting (sanitary

cross) 24 ft above the horizontal branch imder

observation. All the water entering this fitting was introduced through one side for flows of up to about 100 gpm. For flows exceeding 100 gpm, the

excess was introduced through the opposite side. For each flow introduced at this point, several

different rates of flow were introduced through

the single branch under observation, this branch

being connected to the stack through one side of a sanitary cross, as shown in figure 6. Branch

diameters of 1}^ and 3 in. were selected for observation. Measurements were made of the rates of

flow in the stack and in the branch, and of the

head of water in the sight glass. Water velocities in the stack at the level of the horizontal

branch were not measiu"ed in these tests but were computed by the method described in section 4.2. of this paper.

1. 3-ln. galvanlzed-steel drainage stack.

2. Horizontal branches with controlled supply of water.

3. Sanitary crosses at 8-ft intervals.

4. 4-in. cast-iron soil-pipe building drain, 50 ft long at a slope of H in. per ft. 6. 4-iii. long-sweep bend.

PIPE CONNECTING HORIZONTAL BRANCHES ON OPPOSITE SIDES OF STACK.

3.2. Tests on Air Flow in Stack Vent and in

Vent to Horizontal Branch

Measurements of air flow in a 3-in. stack vent

and in a 2-in. vent to a 3-in. horizontal branch

were made on the test system shown in figure 5. Figure 7 shows in detail the piping arrangement

at the horizontal branch to which air was delivered

through the 2-in. vent. Measurements were made

of air flow in the vents and of the pressure drop

across the layer of water flowing on the wall of the

stack.

= SIGHT GLASS

Figure 6. Method for equalizing pneumatic pressures in

stack and in horizontal branches.

TOP OF STACK VENT

3 HORIZONTAL BRANCH

Figure 7. Method formeasuring air flow in venting system.
Water was introduced 32 ft above the base of

the stack (except in a few tests in which this

distance was 48 ft) through one side of a 3- by

3-in. sanitary cross, and the flow of air was measured in the stack vent and in the vent to the

horizontal branch shown in figure 7. This branch was at an elevation 24 ft above the base of the

stack. Sanitary crosses were inserted at intervals

of 8 ft in this installation, as shown in figure 5. Before beginning these tests, all the vents were

closed except the stack vent and the vent connecting to the horizontal branch at the 24-ft level. The pneumatic pressure in this horizontal branch

could be controlled at will by the degree of closure

of a valve placed in the vent (see figure 7). The

stack vent was fully open in some of the tests and

completely closed in others. Each horizontal

branch, except the one tlu-ough which the water was introduced, was closed. A device utilizing

the principle of the hot-wire anemometer was used

for measuring the air velocity at the axis of the

vent to the branch and at the axis of the stack

vent. Because the primary element of this device was placed at the axis of the pipes, a correction was applied to the measured values in order to obtain approximately the mean velocities instead

of the velocities at the axis. In making these

corrections, mean velocity was assumed to be 0.8 of the axial velocity, this value being in approximate agreement, for a value of the DarcyWeisbach friction coefficient / of 0.03, with an

equation given by Rouse [9]. The volume rates

of au- flow were computed in accordance with the

formula, Q=AV.

In some of the tests, the difference between the

pneumatic pressure in the horizontal branch and

that in the opposite side of the 3- by 3-in. sanitary

cross to which the horizontal branch was connected was measured when air was flowing in the branch.

The inclined differential manometer used for these

measurements indicated approximately the differ- ence between the pneumatic pressure within the

branch and that in the interior of the stack at the

level of the branch. A small correction was

actually applied, obtained by noting the reading on the manometer when water was introduced into

the stack while preventing the entrance of air into

the branch. The need for this correction probably was the result of a slight difference in the aspirating

effect of the flow of water past the opposite openings of the sanitary cross. The correction varied

from 0.06 in. to 0.09 in. of water, increasing with

rate of water flow in the stack.

3.3. Miscellaneous Tests

a. Distribution of Air and Water in Cross Section of

3-in. Drainage Stack

In order to investigate the distribution of air and water in the cross section of a drainage stack,

the test system shown in flgure 5 was employed.

A volume rate of water flow of 100 gpm was introduced 48 ft above the base of the stack, and s sampling measurements were made just above the j branch at the 16-ft level, approximately 31.5 ft below the point where water was introduced. All ; the vents on the test system were open; hence the

flow conditions should have approximated those : to be expected in service for a flow rate of 100 gpm. | Figure 8 shows the principal parts of the special ; equipment used for sampling the flow in the stack. ; An impact tube of Ke-in. inside diameter, inserted , into the stack with its opening facing directly upward, was used to make a traverse of the diameter.

The impingement of flow onto the tip of the impact

tube forced air and water through the tube and ' delivered it at the base of the transparent cylinder ! shown in the figure. At the beginning of a test, . the transparent cylinder (closed at the upper end) was first filled with water and the reservoir of » water around the base of the cylinder was fflled to the overflow-weir level. As the impact tube

delivered a mixture of air and water at the base | of the cylinder, the air rose to the top and dis- \ placed the water therein until the cylinder contained only air. The water displaced from the

cylinder, plus that delivered by the impact tube, was caught in a graduated measure. Thus, as the quantity of water originally contained by the , inverted transparent cylinder was known, and as | the quantity of water flowing over the weir, and i the time required to displace a given volume of |i water in the cylinder could easily be measured,

it was a simple matter to compute the average

rates at which air and water were delivered to the cylinder.

Figure 8. Method for sampling air-water mixture flowing

in stack.

1. 3-m. drainage stack.

2. Sampling tube.

3. Hose clamp.

4. Circular openings.

6. Petoock and connection to vacuum source.

6. Overflow weir at same elevation as tip of sampling tube.

7. Graduated measuring vessel.

b. Velocity Distribution of Water in Cross Section of

3-in. Drainage Stack

Data on the distribution of water velocity across a diameter of the 3-in. stack shown in figure 5

10
were obtained for water flows of 60, 80, and 100

gpm. These data were taken at the same point

at which the data described under (a) above were

taken.

A static-pressure tube was inserted through the

wall of the stack for the purpose of obtaining the

pneumatic pressure inside the stack, which was

indicated on an inchned manometer. The impact

tube described under (a) above was connected to a single-leg manometer. The impact tube had

been cahbrated hy towing it through still water

at known velocities. By taking the difference

between the readings obtained for the impact

tube and those obtained for the static-pressure

tube and referring to the cahbration curve, corre- sponding velocities were indicated.

c. Vertical Distribution of Pneumatic Pressures within

3-in. Drainage Stack

The effect of rate and vertical distribution of

water flow on pneumatic pressures within a drainage stack was studied experimentally by means

of the test system shown in figure 5. In the first series of tests, water was introduced at one point

32 ft above the base of the stack. In the second

series, water was introduced simultaneously at two points, 32 ft and 16 ft above the base of the

stack. In each of these two series of tests, measurements of pneumatic pressures within the stack were made by means of a small static-pressure

tube inserted through the side of the stack successivel}^ at a number of points distributed vertically.

Data were obtained both ^^vith the venting system

functioning and with all vent pipes except the

stack vent closed by valves. Water-flow rates of

60 and 100 gpm were introduced at the higher

point, and rates of 30 and 60 gpm were introduced

at the lower point. In each case, the flow was

dehvered through one side of a 3- by 3-in. sanitary

cross.

4. Analysis of Flow Conditions in Plumbing Stacks

4.1. Interference of Flows at Junction of

Drainage Stack and Horizontal Branches

The flow from a horizontal branch into a multistory drainage stack will encounter a resistance

when it meets the high-velocity blanket of water

which may simultaneously flow doAvnward on the

waU of the stack. This resistance creates a backpressure (head of water) in the branch as a result

of momentum changes in both the horizontal and

the vertical streams. These changes are caused

by the deflection of one stream by the other (see

fig. 9). If the two flows become sufficiently large,

the backpressm-e becomes excessive and interferes

with the normal operation of the drainage system.

The problem is to estimate the maximum rates of

flow which can occur simultaneously in the stack

and the horizontal branch without creating an

excessive head of water in the branch. The

analysis of the problem can be based on either the

law of conservation of momentum or the law of

conservation of energy. Because of the geometry

of long-turn T-Y stack fittings, the law of conservation of energy is easier to apply in the case of

such fittings than is the momentum law. ActuaUy, the momentum law was used in an earher

paper [10] which reported the results of tests on

the simulated stack using sanitary-tee fittings.

The analysis of the problem made in this paper

begins with an application of the law of conservation of energy.

Figure 10 shows the various terms which wiU be

used in the analysis. The piezometer shown in

this figure is for the purpose of the analysis only.

Figure 9. Hydrodynaniic backpressure in horizontal branch caused by mutual interference of flow in stack and

in one horizontal branch.

11
I STACK

I ARBITRARY DATUM FiGUEE 10. Definition sketch showing symbols used in

analysis of mutual interference of flows at stack-branch

junction.

It shows the peizometric head (the height to which

the water in the branch would rise through a tube

open to the atmosphere at the upper end). This

head may or may not be the same as the height to which water rises in the branch or in a vent pipe

connected thereto when excessive rates of flow occur simultaneously in the stack and horizontal

branch. The extent to which the piezometric

head and the actual water level inside the pipe

differ depends on the pneumatic head in the vent

hi, which may be either positive or negative. Pressures will be expressed in height of water

column through the relationship p=pu,gh. The

analysis will begin by considering the change in

energy of the stream of water flowing in the branch

as it passes from section b-b (mean elevation 22) to section a-a (mean elevation Zi). The mean flux of energy through the upstream

section b-b per unit volume of water flowing in

the branch is

and the flux of energy through the downstream

section a-a at the plane of impact with the flowing

water in the stack is

where Va is the mean velocity and ha the mean

pressure head at the section of impact of the two

streams. From continuity considerations, it appears

reasonable to assume that Va is approximately

equal to V2, and it is convenient to assume that

the effective mean pressure head ha over the

impact section can be represented by the sum of

the pneumatic pressure head, hi, in the stack and a dynamic pressure head, ha, related to the curvilinear flow produced by the deflection of the stack

stream by the branch stream. Thus, it is assumed

that ^0=1^2, and Aa=Ai+Ad. Under these as- sumptions, the flux of energy through section a-a can be expressed as

Pw9 ^^^^+hi+ha+z^-

The difference between the unit flux of energy at

sections b-b and a-a represents the amount of

energy lost by a imit volume of water in passing

from the upstream section to the downstream section. This energy loss is caused by friction in the

horizontal branch and stack fltting and by the

change in direction of flow produced by the fltting,

and may be expressed as

AE=ptog(h2—hi—ha+Z2—Zi)- (6) The energy loss per unit volume of water flowing

through a straight pipe due to friction can be

expressed as

Pwghf,

where hf is the head loss computed from the DarcyWeisbach formula for pipe flow.

The energy loss per unit volume due to the

presence of a bend in a pipe can be expressed as

Ptcghb,

where hb is the head loss due to the bend. In a

long pipe having a bend in an intermediate location, the bend loss is the sum of two components, one of which is due solely to the deflection of the

stream filaments by the bend (the deflection component) and the other of which is due to the velocity disturbance caused by flow around the bend

and which extends a considerable distance downstream of the bend (the tangential component).

In the case under consideration the downstream

section is missing, for all practical purposes.

Therefore, it is reasonable to assume here that

only the deflection component f of the bend-loss

coefficient is effective. This assumption makes it possible to express the head loss between the upstream and downstream sections caused by pipe

friction and by deflection of the stream filaments

by the bend as

, .L(V2)\AV2r

Therefore, the energy loss per unit volume of water

flowing between sections b-b and a-a due to the

two causes may be expressed as

12
Substituting in eq (6), the expression =

A2— 22+^1 (see fig. 10), substituting the right member of eq (8) for AE", and dividing by p^g, the

following equation is obtained:

h2—hi—hd

2g

All the quantities in eq (9) can be measured or estimated approximately except the dynamic head,

hd. The interaction between the layer of water

flowing in the stack and the flow from the branch

is too comphcated to analyze, except in a very

general and approximate way. In making this

analysis, it is assumed that the flow lines in the

layer of water flowing down the stack are changed

from straight hnes to arcs of circles of radius Rc by

the stream from the branch (see fig. 11). Obviously, this is a simplif}'ing assumption that is not

entirely correct, yet it does result in an equation

which agrees fairly well with data obtained by

experiment over a wide range of conditions.

Under this assumption, summing up the centripetal forces which the flow from the branch exerts on all the elementary volumes in the water layer

in the stack subject to deflection (figs. 11a and

lib) resiflts in the expression:

Re R.

(10)

where Am is the mass of the elementarj'' volume

TAsAb. Then, if an average value of Rc for all elementary volumes is assumed,

It follows then that

(11)

(12)

and, substituting this result in eq (9), the following

equation is obtained

Dividing by ^2—^1 and rearranging terms gives

the equation

2T (ViY

2g{h2-hx) Rc 2g{h2~hi) (14)

AU of the quantities in eq (14), except the radius

of curvature of the flow lines, are subject to deter-

» This equation is identical to eq (27) of the earlier paper [10] except for the

Inclusion of the bend-loss coefBcient in eq (9) above. In the earlier paper, which reported results of an experiment using sanitary-tee fittings only, it was assumed that the bend loss due to the geometry of the fitting was

negligible.

Figure 11. Mutual deflection at the confluence of streams

at stack-branch junction.

a and b. Deflection of stream in stack by that in branch,

c and d. Deflection of stream in branch by that in stack.

mination, by measurement or otherwise. The

quantity Rc will now be considered in more detail. Other things being equal, it will be assumed

that Rc is directly proportional to the momentum,

pQiVi, of the layer of water flowing down the

stack, and that Rc is inversely proportional to the

momentum, PWQ2V2, of the water in the branch.

The validity of these and other assumptions made

in evaluating Rc will be determined by the success obtained in ifitting the final equation to the experimental data. Based on the above considerations,

i?c=function (

Pu,QiVi\

\P.Q2V2)'

But Rc must be placed equal to a length times

this function if the equation is to be dimensionally

correct, and the dimension that seems to be most

closely involved with Rc is the diameter, D2, of the

branch. Hence,

where Ai is the cross-sectional area of the water

flowing down the stack at the level of the branch,

and A2 is the cross-sectional area of the stream

in the branch for the branch flowing full. In

order to simplify the analysis, the area Ai will be

replaced by its approximate equivalent tDiT.

The latter expression will give values of area which

are accurate within 10 percent for stacks flowing

not over three-tenths fuU.

Hence,

(16)

13
the constant 4 being absorbed in the coefficient C. Going one step further, it will be assumed

that the function ^ is a simple power function.

This was found by logarithmic plotting of experimental data to be approximately true for the

ratio T'/i?2, and will be assumed to be true for the

two other ratios. Thus,

J or

R. 2g{ho-hi)

[2g{h2-hi)J

(17)

The value of Rc given by eq (17) will now be

substituted in eq (14), writing for simplicity:

2g{h2—hi)

=X and

2g{h2—hi)

Rearrangement and simplification give the

expression

A/

(18)

in which the coefficient C is a constant. There are two quantities, C and a, to be determined from the experimental data. From this

point on, the analysis will be carried out separately

for the simulated stack and the prototypal stack.

a. Simulated Stack

In the case of the simulated stack, the construction of the test equipment was such that water

flowed down the stack in a layer which had, as it approached the level of the horizontal branch

under consideration, a definite known thickness

T and a definite known mean velocity of flow Vi

(see fig. 4).

In the analysis applying to the case in which

sanitary-tee fittings were used, the coefficient f

appearing in eqs (9) and (18) was assumed to be

zero. In other words, the resistance due to the

downward deflection of the horizontal stream produced b}'' the slightly curved passage through the

fitting was neglected.

In connection with the analysis applj-ing to long-turn T-Y fittings, a review of some of the

published data on head losses in pipe bends was

made. Measurements reported by Beij [11] on

90° bends between upstream and downstream

pipes showed that the average deflection losses in

his experiment were only about 37 percent as great as the average bend losses, the latter of

which included both deflection and tangential

losses. If a roughness corresponding to ks=

0.00015 (as given by Rouse [9] for wrought-iron

or steel pipe) is assumed, a bend coefficient of j 0.27 for a radius of curvature of one pipe diameter

is estimated for a 90° bend on the basis of Beij's

results. The radii of curvature of the bends in

the long-turn T-Y fittings used in the experiment ; reported herein were of the order of one pipe i diameter. Various investigators have suggested : specific bend-loss coefficients for use with 45° and

90° bends. The values suggested for 45° bends

vary from 47 to 75 percent of the values suggested

for 90° bends. Based on a bend-loss coefficient

of 0.27 for a 90° bend as indicated above, on a

deflection loss of 37 percent of the total loss due

to a bend in a long pipe line, and on a ratio of

45° bend loss to 90° bend loss of 0.47, a value of

f of 0.047 is computed for the case under consideration herein.

The term

^

in eq (18) was held constant at a

value of 4.0 in the tests. Therefore, this value

will be used in what foUows.

If values of 0.03, 0.00, and 4.0 for /, f, and

L/D2 are inserted in eq (18) as it applies to the case

in which a sanitary-tee fitting is used, the equation

may be placed in the form

r=8.33-C7" (^y" (^J Y^X'-^. (19)

In a similar fashion, if values of 0.03, 0.047,

and 4.0 for/, f, and L/D2 are inserted in eq (18) as it applies to the case in which a long-turn T-Y

fitting is used, the equation may be placed in the

form

(20)

^.33-F

(T/A)(X)

for the sanitary-tee fittings, and

5= 6.00-r

iT/D2){X)

(22)

(23)

Further steps in the analysis will be simplified

by combining several of the terms appearing in

eqs (19) and (20) as follows:

-(^J(0(IJ--

If 5 in eq (21) is substituted in eqs (19) and (20),

the foUowing equations are obtained:

for the long-turn T-Y fittings.

The value of the exponent a can be determined

from experimental data by logarithmic plotting

of values of 5 computed from eqs (22) and (23)

Y

against the variable The slope of the lines X

14
plotted in this way gives the approximate value of

a. The value of the coefficient C" may then be

determined by inserting in eq (21) the values of 5 and a, together with the corresponding values of

X and Y, and solving for C". These determinations are given later in section 5.1. a, for both the

sanitary-tee fittings and the long-turn T-Y

fittings.

b. Prototypal Stack

The analysis of flow interference at a branch

connection on a prototypal stack is made in such

a way that the dimension T is not involved. It is assumed that the djmamic head is caused by

the deflection of the horizontal stream by the

vertical stream, instead of conversely as in the

case of the simulated stack. It is assumed that

the horizontal stream is deflected on an arc of

unknown radius of curvature, Rc. It is reahzed

that part of the deflection of the horizontal stream

is caused by gravity. However, since this effect should be smaU in comparison with the deflection

caused by the interference of the two streams

when there is appreciable flow in the stack, the

effect of gravity on the curvature of the stream

lines will be neglected. The centripetal force,

Fa, required to cause an elementary mass Am

moving at a velocity V to foUow a curved path

of radius of curvature Re will be

Yl

r: (24)

If the elementary volume is taken as a cyHnder

of length AL cut perpendicular to the axis of the

horizontal branch, its mass Am will be

Therefore,

p„|AZ(A)^

It is assumed that the average pressure required

to cause the curvature of the stream fines is equal

to the appHed force divided by one-half the

circumferential area of the elementary cylinder,^ or

2Fa ^ TtDoAL

Thus,

1 (V Y

Vi=2 P'^z or, dividing by p^g,

(ZhI!

2gRo

(25)

2 This particular assumption is not essential to the solution of the problem. The end result would be the same if it were assumed that the pressure is equal

to the force divided by the area of the plane which is limited by the boundaries

of the elementary cylinder and which is bisected by its longitudinal axis. This would yield the expression FdjDi^L. The disappearance of the con2 stant - in the latter case would be taken into account in the values deter- mined experimentally for other constants appearing later in the analysis.

It appears that, in general, Rc will increase

when the momentum per unit volume of water

in the horizontal stream increases and will de- crease when the momentum per unit volume of

water in the vertical stream increases. The

momentum of the water in the vertical stream

which passes through a imit area in unit time is a

function of

A,

, or p^iViY,

and the momentum of the water in the horizontal

stream which passes through a unit area in unit

time is a function of

pMv^y , or p^c{V2y.

Hence,

7? ,Yp^(^2)^ ,/C^2)^

Since Rc must have the dimension of a length,

and since the length which appears to be most

closely associated with Rc is D2, the expression

R. (26)^

will be set up. Substitution in eq (25) of the

expression for Rc given in eq (26) yields the

equation

ha= (27)

If eq (27) is combined with eq (9), the following

equation is obtained relating the various heads

:

26f 2g

4,

(28)

If the function ^ is a simple power function,

if /=0.03, if f =0, and if L/Z)2=4.0 (this value

of LID2 applying to the test equipment used),

the following equation is obtained, after some

rearrangement

:

{V2Y

2g{h2—hi)

=8.33 {V2Y

2g{h2—hi)

C

ViViYl'

UV2YA (29)

Now, if X and Y are introduced in the same way that they were in the development of eqs

(19) and (20), eq (29) can be expressed as

r=8.33-C(^)F. (30)

4 The end result of this analysis would be the same if it were assumed at

this point that the radius of curvature Rc is a function of the relative flux

of energy in the horizontal and vertical streams.

584032—61 a 15
If c

eq (30) can be written as F=8.33 —5F, or

, 8.33-F 0= ^ •

(31)

(32)

The value of the exponent a can be determined

from experimental data by logarithmic plotting

of values of 5 computed from eq (32) against the

variable y- The slope of the lines plotted in this

way indicates the approximate value of a. The

value of the coefficient C may then be determined

by inserting in eq (31) the values of 5 and a, together with the corresponding values of X and

Y, and solving for C. These determinations are given later in section 5.1.b.

4.2. Terminal Velocities and Terminal Lengths

a. Derivation of Equation for Terminal Velocities The following derivation of the equation for

terminal velocities is an approximate one, in

which the water is treated as if it were a rigid

body sliding down the stack instead of a fluid

layer with a radial velocity gradient. A more

nearly correct solution would require a consideration of the turbulent boundary layer which

develops in the pipe. However, because of the

difficulty of obtaining an exact solution, an approximate solution is given in this paper.

The annular layer of water is treated as if it were a rigid body moving down a plane vertical

wall, acted on only by the forces of gravity and

wall friction. The effect of the pneumatic-pressure

gradient within the air core should be considered

in a rigorous solution of the problem; but, since

in a properly vented stack the pneumatic-pressure

gradient should be relatively small, this effect will be neglected in what follows. It is assumed

that the water starts with an initial velocity Vq

downward. The velocity is less than the ter- minal velocity, Vt, which it will attain ultimately

if the length of fall is great enough. The thickness

of the layer decreases with z (the distance measured from the point of water entrance downward

to the point under consideration), becoming

constant when z attains the value of the

tei'minal length.

Since, under the assumptions made above, the

accelerating force is equal to the gravitational

force less the frictional resistance,

Am^—Amg—ToTrDiAL, (33)

where tq is the wall shear per imit area, and the

elementary volume of water is assumed to be

ttDi units wide. But

so dV

PwQi-^ At=p^QigAt —ToTDiAL. (34)

To wiU now be defined by the relation,

To 2

(35)

AL will be replaced by its value, VAt. Equation

(33) then becomes

P^Qi — At==p^Q^gAt -'^D.V'At,

or dV ttX _

(36)

The expression for the terminal velocity, Vt,

will now be obtained by setting dV/dt equal to

zero. This yields the equation

(37)

It can be shown that \ is equal to //4, where / is the dimensionless friction coefficient in the DarcyWeisbach formula for pipe flow. It is a function

of the Reynolds number, Nr=TV/v, approximately, and of the roughness ratio, ks/E^ or ks/T.

It wiU be necessary to modify eq (37) to eliminate the friction coefficient X. To do this, the

foUowing equation given by Keulegan [12] for flow in open channels, based on the Manning

formula, is used:

(38)

where V is the mean velocity in the cross section

and is the shear velocity deflned by the

relation,

^*=VVp^ (39)

The Fin eq (38) is the same as the Vin the other

equations, tq is eliminated between eqs (38) and

(39). If Rn is replaced by T, as can be done

approximately, there results the equation

X=0.0303 (40)

Substituting this value of X in eq (37), there

residts

Tt being written for T to indicate that the value of

T is that corresponding to the terminal velocity.

16
One further change will be made m the expression for terminal velocitj^ by eliminating the

thickness of the sheet of water by means of

the relation between the thickness of the sheet,

the cross-sectional area of the sheet, and the rate

of flow. This relation is given by the approximate

expression

Q^=TD,T,Vt, (42)

or by the more accurate expression

(43)

Equation (42) should be sufficiently accurate for

the relatively small values of Tt which are produced in drainage stacks flowing partly full. If the approximate expression is used, there results

The reason that the Reynolds number is not

a factor in eq (44) is that the relationship (eq

(38)) used to eliminate X is based on the Manning

formula which is most accurate for conditions

imder which X is independent of the Rejmolds

number. A discussion by Rouse [9] indicates

that the Manning formula is most dependable for

intermediate values of relative roughness and

least dependable for low values of the Reynolds

number. Computations based on a cast-iron

stack flowing with a water-occupied cross section

of at least one-fourth of the cross section of the

stack, and with a velocity in accordance with eq

(44) indicate that X is substantially independent

of the Reynolds number for stacks of 4 in. in diam

or larger, and that the error in the use of the

Manning formula over the range of relative

roughness involved ranges from approximately

7 percent for a 4-in. stack to approximately 3

percent for a 12-in. stack. The low order of

magnitude of this error indicates that, in view

of the proposed application of eq (44), the use

of the Manning formula in its development is reasonable.

An appropriate value of ks has been determined

from data on friction losses for flow through new

cast-iron soil pipe tested by Hunter [13J. This

yields the approximate value, Ars =0. 00083 ft. (See appendix, section 9.2., for the derivation of

this value.) Rouse [9] gives the value, A:s =0.00085

ft, for new cast-iron pipe.

Equation (44) can be expressed in convenient

form for computation by substituting the

numerical values of (0.00083 ft) and g (32.2

ft/sec/sec). The foUowing equation (for cast-iron

sofl, pipe) is obtained

y.=i2 (45)

where Vt is expressed in feet per second, Qi is in

cubic feet per second, and Di is in feet.

If Qi is expressed in gallons per minute and Di

in inches, eq (45) becomes

F,=3 (46)

Equation (46) is plotted in figure 12, together

with the experimental data obtained by Hunter

and by Dawson and Kalinske. An average curve having the equation

V, (47)

is dra-\vn through the experimental points.

As would be expected, the experimental points

scatter considerably, for the terminal velocity is very difficult to measure. All the measm-ements

lie above the curve computed from resistance

measurements on cast-iron soil pipe. One possible

explanation for this effect relates to the velocity

distribution in the layer of water. A steep velocity

gradient exists in the layer, the velocity increasing

from zero at the wall to a maximum at the inner

surface of the sheet. The experimenters made

Figure 12. Comparison of measured and computed

terminal velocities.

1. Average experimental curve, Vi=4.4^^^

/Qi\2/S

2. Computed curve, yi=3.0(^ I , based on flow-resistance measure- ments in cast-ii'on soil pipe. O, Dawson 3-in. stack. V, do 4-in. stack. A, do --- 6-in. stack. Hunter 2-in. stack. 0, do 3-in. stack.

17
their observations with pitot tubes with dynamic

openings pointing vertically upward through the

vertical layer. It was impossible to get the

pitot tube very close to the wall where the lowest

velocities existed, and hence, the velocities in this

region were not taken into account in the experimental measurements reported. An indirect indication that the velocities reported hj Dawson

and Kalinske may be too high can be obtained by

inspection of their data [5]. They computed

values of Manning's n of the order of 0.006 from

their experimental measurements. This compares

with values of 0.012 to 0.015 for uncoated cast- iron pipe, and of 0.013 to 0.017 for galvanized

Avi-ought-iron pipe given by Horton [14]. All

known measurements on gravity flow in sloping

pipes of various materials have yielded values of n substantially greater than 0.006. The sur- prisingly low value of n indicated by the data of

Dawson and Kalinske could have been the result

of using velocity values that were too large in

computing n. If the reported velocities are substantially greater than the true velocities, as indicated by the above discussion, the curve computed from eq (46) may be more nearly correct than are the direct measurements.

On the other hand, it is known that a negative

pneumatic-pressure gradient exists for a hmited

distance below a point of water entrance. This

tends to accelerate the water, and, if the acceleration were to be sufficiently great, velocities might

exceed those indicated by eq (46). However, the

data of Dawson and Kalinske [5] on water

velocities as a function of distance below the

point of water entrance indicate that the existence

of a negative pressure gradient in the upper part

of the stack was not a significant factor in connection with terminal velocities. Since eq (46)

is intended for application to well-vented stacks

where the pneumatic gradient is small in relation

to that which existed in the experiments reported

by Dawson and Kalinske, it seems reasonable to neglect the possible effect of the negative pneumatic gradient near points of water entrance on

terminal velocities.

b. Derivation of Equation for Terminal Lengths

The equation for terminal lengths in layer flow

down the walls of vertical stacks is derived by

starting with eq (36), making the necessary trans- formations, and integrating the result to obtain

the expression for the terminal length. It is noted first that

dV^dVdZ^ydV

dt dz dt dz'

(48)

If this substitution is made in eq (36) and the

equation is solved for dz, there results

VdV

'2g (49)

If it is assumed that X is not a function of V, and

eq (37) is made use of,

dz-- {VtY ({vrvdd{yrzA\iy^i /j

g \ l-{y|V^f ) g Ki- rn

where 0=F/F«.

Equation (50) can be integrated directly, with

the result

Lt=z

e 3 g

1 +

loge

V^ \V^)

-tan-i (2 ^+1^

-1

0

. (51)

If the upper limit (F/F< = 1) is substituted,

there is obtained an infinite result, as the denominator of the first term in the brackets becomes zero. This difficulty is avoided by assuming that, when

the velocity has reached a value equal to 0.99

times the true terminal velocity, the terminal

length has been attained for all practical purposes.

Making this substitution for V/Vt in eq (51), and

inserting the limits, there is obtained

Lt=^^ loge 29,700- tan-» 2.98 —^loge 1-1-tan-^ l j>

i,=0.052 {V,)'. (52)

or

Equation (52) is useful for computing the dis- tance through which water on the wall of a drainage stack must fall before it attains a velocity

approximately equal to the terminal velocity.

Figure 13 gives the terminal length as a function

of terminal velocity.

If eq (52) is compared with the equation of free

fall under the influence of gravity, it is found that

the layer of water in the pipe must fall approximately three times as far to attain a given velocity

of fall as a body falling freely under the influence

of gravity. Figure 14 shows terminal length as a

function of stack diameter, for two degrees of

fuUness. These curves were computed from eqs

(46), (52), and (53). They indicate that in most

practical cases the falling water will approach

terminal velocity in a distance of from one to two stories.

4.3. Flow Capacities of Multistory Drainage

Stacks

As indicated in section 2, previous research has

shown the necessity for criteria for limiting the

discharge of water into drainage stacks. The

criterion developed herein is based on limitation

18
TERMINAL VELOCITY , f pS

Figure 13. Terminal length as a function of terminal

velocity.

0 1 2 3 4 5 6 7 STACK DIAMETER , in.

Figure 14. Terminal length as a function of stack diameter.

of the water-occupied cross section to a specified

fraction, Tj, of the cross section of the stack where

terminal velocity exists, as suggested by earlier investigators.

Flow capacity can be expressed in terms of the

stack diameter and the water cross section. This

expression,

Q,=27.8(rsy"(D,y" (53)

is derived by equating the fundamental expression

for velocity, V=Q/A in which

and the expression for terminal velocity given by

eq (46). In eq (53), is the volume rate of

water flow in gpm and Di is the diameter of the

stack in inches. Since this equation is based, in

part, on the approximate expression for Tt given

byeq (42) and since, for a given pipe, the error from

using eq (42) increases with Tt (or r,), it is intended primarily for use where Vs is not greater

than 1/3. However, analysis of eqs (41), (42),

and (43) indicates that, even where the pipe is flowing full, eq (53) should give flow-rate values

only about eight percent less than if eq (43) had

been used in its development. This conclusion is consistent with the finding that fiow-rate values

computed for cast-iron soil pipe from eq (53) for rs=1.0 actually are from five to ten percent less than the values computed for very rough pipes

flowing full at terminal velocity as indicated by

figure 2, based on Hunter's experiments.

4.4. Air Flow in Drainage Systems

The principal cause of air movement in building

drainage systems is the friction developed between

the high-velocity layer of water flowing down the

drainage stack and the core of air which it encloses. The friction thus developed drags air along with the water. Under ideal conditions of

annular flow of water at terminal velocity where

there is a positive pneumatic-pressure gradient in

the direction of flow, it is obvious that, at the air-water boundary, the air velocity may approach,

but cannot exceed, the velocity of the water. However, general considerations indicate that the

velocity gradient in the water section is much

steeper than that in the air core. Thus, it is beheved that the mean velocity of the air core can be greater than the mean velocity of the water

stream. Since available data do not establish

this relationship with acceptable precision, it is assumed here that the mean velocity of the air core cannot be greater than 1.5 times the mean

terminal velocity of the water stream.

The analysis of air flow in a drainage stack

begins by expressing the relation between air flow

and water flow as

Qa~~A tt" Qto~ ~ 'Tt' Qw- (54)

Since Q^o is identical to Qi in eq (53), Qy, will be

replaced by Qi. Next, will be replaced by the

right-hand member of eq (53). This yields the

equation

a=27.8(r,)2/3(l-r,) ^« (d^''I\ (55)

in which Qa is in gpm and D\ is in inches. If :^=1.5, the equation becomes

19
WATER FLOW, qpm Figure 15. Relationship between water- and air-flow rates for anmdar flow at terminal velocity in vertical pipes,

computed from eqs (58) and {66).

1.6

I

I I 1 1

1

1 .4 -

1.2 -

1.0 -

0.8 -

0.90 0.95 1.00 1.05 1. 10 1.15

Figure 16. Factor for computing effect on flow capacity of small variations in stack diameter, based on eq {57).

Q^=Al.l{r,Yi\l-r,){D,Yi\ (56)

Figure 15 has been prepared from eqs (53) and

(56). This figure shows the air flow computed for various flows of water in drainage stacks from 2

to 15 in. in diam. Nominal diameters of stack

have been used in the computations. Figure 16

ma}^ be used in conjunction with figure 15, or with

any flow-capacity equation based on the Manning

formula, to estimate the effect on capacity of

diameters which differ to a slight extent from the

nominal values. If Qisr represents rate of discharge associated with nominal diameter D^^,

and if Q represents rate of discharge associated

with actual diameter D, and if ^J" )

' ^^^^

Q=riQN. (57)

4.5. Flow Capacities of Vent Stacks

In most plumbing codes a loading table for vents

is provided. The purpose of such a table is to give the information necessary to design the vent

stack for the delivery of the amount of air required

for the control of pneumatic pressures at critical points in the drainage system within limits of +1

to —1 in. of water column from atmospheric. If this range of pressure can be maintained, the

effects of pneumatic-pressure fluctuations on the

fixture-trap seals will be negligible. The dimensions of pipes required to deliver given quantities

of air at a pressure drop of 1 in. of water column

can be computed from the Darcy-Weisbach

formula combined with the conventional formula t for expressing losses other than those associated

with flow in long, straight pipes. This can be

expressed asL.=l[2200 ||-5f B.} (58)

In eq (58), is in feet, D„ is in inches, and

is in gallons per minute; and the term 2Cz, is the

algebraic sum of the loss coefficients associated

with the entrance and exit conditions and with

changes in section, direction, etc. A temperature

of 60 °F has been assumed in developing eq (58).

If only the pipe-friction loss is considered, which

may usually be done without serious error in practical situations, the equation

.._/2200\ {D,y

^'^K J ) {Qa?

^^^^

is obtained.

5. Test Results

5.1. Flow Capacities at Junction of Drainage

Stack and Horizontal Branches

a. Simulated Stack

Tables 6 and 7 show the range of conditions investigated by use of the simulated stack shown in

figure 4. The individual values in this series of

measurements are shown in tables A-1 and A-2 of

the appendix.

The experimental data afforded the information

necessary for computing the terms X, Y, and

T/D2 appearing in eqs (19) and (20). Next, the

values of 5 were computed from eqs (22) and (23).

20
Table 6. Range of conditions investigated in study of flow interference at junction of 3-in. simulated stack and horizontal branches, sanitary-tee drainage fittings

1 2 3 4 5 6 7

Ratio of Thiet- stack

ness of Num- Rate of veloc- Branch water ber of flow a ity « to Range of flow Range of head

diam- layer » branches in co_in- rates in each losses in branch

eter on wall flowing stack puted branch (h2-hi)

of stack termilocity

in. in. gpm gpm in.

I. Dl 0. 16 40 1 04 10. U LU 00. ^ £j. D i LU O.

1. 61 .16 1 54 I. 41 13. 1 to 40.

2. 94 to 4. 69

1. 61 .16 1 80 2.08 9. 4 to 26. 5 4. 44 to 6. 00

1.61 .16 1 98 2. 55 8. 8 to 17.

5. 44 to 6. 38

1 61 16 2 40 1 04 1 7 d tn 97 9 0^7 LU 0. ^0 L61 !l6 2 54 L 41 7. 9 to 29.

1. 94 to 4. 56

1.61 .16 2 80 2.08 8. 2 to 20. 6 3. 25 to 5. 54

1. 61 .16 2 98 2. 55 8. 2 to 13. 8 4. 44 to 6. 19

1 61 . oD 56 0 47 9 Q4 tn ^ fiQ 1. 61 .35 1 98 ^82 8. 1 to 23.

2. 88 to 5. 94

1.61 .35 1 137 1. 14 8. 4 to 14.4. 44 to 5. 96

1.61 .35 1 180 1.50 8. 1 to 9. 7 5. 96

1 R1 1. 01 . 00 z OD Q R tn 9J. 9

1. 61 .35 2 98 .82 8, 8 to 24. 8 3. 06 to 5. 94

1.61 .35 2 137 1. 14 9. 4 to 13. 7 4. 44 to 5. 94

1.61 .35 2 180 1.50 9.2 5. 94

1. 61 .58 1 98 0. 40 8. 1 to 29.

2. 07 to 4. 44

1. 61 .58 1 1.58 .64 11. 6 to 20.

4. 06 to 6. 12

1.61 .58 1 203 .82 8.1 to. 13.1 4.44 to 5.94

1.61 .58 1 252 1.02 8. 1 to 14. 5 5. 94 to 7. 94

1.61 .58 2 98 0. 40 10. 6 to 16.

2. 69 to 3. 44

1.61 .58 2 158 .64 11. 0 to 16.4. 44 to 5. 94

1.61 .58 2 203 .82 11.1 5.94

. ID J 1. u-± 30 0 3 12

2. 07 .16 1 54 1.41 20. 8 to 34.3. 37 to 4. 62

2. 07 .16 1 80 2.08 23. 0 to 33.

5. 56 to 7. 12 2.07 .16 1 98 2. 55 19.0 to 24.2 6. 31 to 7. 49

. 16 1 AJ. 10. X LU 00. 0

1 QQ Q flfi 1. yy LU 0. UO

2. 07 .16 2 54 1. 41 30.4 3.93

2. 07 .16 2 80 2.08 15. 8 to 30.

4. 34 to 6. 62

2. 07 .16 2 98 2. 55 19. 2 to 28.

6. 37 to 8. 31

2 07 ^ 56 0 47 ID. 0 l-U 1U. 0 UO LU 0. 2! 07 .35 1 98 ^82 20. 4 to 59. 6 4. 06 to 7. 06 2.07 .35 1 137 1. 14 21. 2 to 32. 3 6. 06 to 7. 81 2.07 .35 1 180 1.50 20. 1 to 21.

7.81 > C\7

jL. U/ . 35 2 OD U. -4/ 17 8 2 19

2. 07 .35 2 98 .82 19. 0 to 28.

3. 81 to 4. 81

2. 07 .35 2 137 1. 14 17. 4 to 24.5. 31 to 6. 69

2. 07 .35 2 180 1. 50 20.5 7.99

2.07 .08 1 98 0.40 23. 8 to 49.

3. 43 to 4. 43

2.07 .58 1 158 .64 24. 3 to 42.

5. 81 to 7. 69

2. 07 . 58 1 203 QO . oZ 15 4 to 95 7

SI fn 7 ft! 0. Oi LU 01 2.07 .58 1 252 1.02 16^ 3 to 17! 8 7. 81

2.07 .58 2 98 0.40 16.9 2. 31

2. 07 . 58 2 203 . OJ 18 6 6 31 2.07 .58 2 252 1.02 17^4 7^81

3.07 .16 1 80 2.08 52. 1 to 128.

4. 46 to 6. 46

3.07 . 16 98 2. 55 66. 0 to 110.

6. 46 to 8. 46

3.07 .35 98 0.82 80. 0 to 81.

4. 46

3.07 .35 137 1. 14 42. 0 to 149.

4. 46 to 8. 46 3.07 .35 180 1.50 49. 0 to 71.

6. 46 to 8. 46

3.07 .58 203 0.82 53. 1 to 92. 7 6. 46 to 8. 46

3. 07 .58 252 1.02 47. 8 to 53.

7. 71 to 8. 46

« Above the stack-branch junction.

The values of 5 thus obtained were plotted

logarithmically against YjX. This gave a series of straight lines with a slope of approximately 3/8.

Next, from this plot, values of 5 were potted logarithmicaUy against [(D2/A)-(A/^] for several

selected values of YjX. Again, this procedure

Table 7. Range of conditions investigated in study of flow

interference at junction of 3-in. simulated stack and

horizontal branches, long-turn T- Y drainage fittings

1 2 3 4 5 6 7

Ratio of Thick- stack

ness of Num- Rate of veloc- Branch water ber of flow 0 ity " to Range of flow Range of head

diam- layer » branches in com- rates in each losses in branch

eter on wall flowing stack puted branch (ft2-/ii) of stack terminal velocity

in. in. gpm gpm in. 1.61 0. 16 1 40 1. 04 26. 8 to 34. 4 3. 64

l."61 .16 1 54 L 41 19. 2 to 50.3. 64 to 8.14 L 61 . 16 1 80 2.08 10. 7 to 50.

3. 64 to 9.14

1.61 . 16 1 98 2. 55 10. 9 to 33.4. 64 to 9.22

1. 61 . 16 2 40 1. 04 25. 0 to 38.

3. 64 to 5. 22 L 61 .16 2 54 1.41 21.' 8 to 53. 6 3. 64 to 8.14

\. 61 . 16 2 80 2. 08 11. 4 to 42. 0 3. 64 to 8.22

1.61 .16 2 98 2. 55 8. 0 to 32.

3. 64 to 8.22

1. 61 . 35 1 56 0 47 26. 6 to 26. 7 3. 39

i. 61 .35 1 98 .82 12. 9 to 44.

3. 39 to 7.72

1. 61 .35 1 137 1. 14 10. 4 to 26. 7 4. 64 to 7.72

1. 61 .35 1 180 1. 50 8. 8 to 16.

5. 59 to 7.72

1 61 . 35 2 56 0 47 25. 4 to 38. 3 3. 39 to 5. 09 L 61 .35 2 98 !82 13! 8 to 44. 9 3. 39 to 7.64

1.61 .35 2 137 1. 14 13. 2 to 29. 7 4. 64 to 7.64

1.61 .35 2 180 L 50 10. 2 to 16.

5. 64 to 7.64

1. 61 . 58 \ 98 0. 40 15. 0 to 53. 5 3. 39 to 7. 64

1! 61 !58 1 158 !64 11' 7 to 29.3 4. 64 to 7.64

\. 61 .58 1 203 .82 11. 9 to 19.2 5. 96 to 7.72 L61 .58 1 252 1.02 10. 3 to 11. 7 7. 59 to 7. 64

1.61 .58 2 98 0.40 14. 5 to 41. 3 3. 39 to 6.14

1. 61 .58 2 158 .64 11. 8 to 29.

4. 64 to 7.64

1. 61 .58 2 203 .82 7. 9 to 18.

4. 64 to 7. 72

1. 61 . 58 2 252 1. 02 11. 7 7. 59 to 7. 64

2. 07 .16 1 54 L 41 39. 7 to 64. 4 4. 29 to 5. 92

2.07 .16 1 80 2. 08 21. 1 to 73.

4. 29 to 9. 36

2. 07 . 16 98 2. 55 21. 0 to 50.

5. 54 to 9. 36

2. 07 . 16 2 54 I. 41 46. 4 to 66. 6 4. 29 to 5. 54

2. 07 .16 2 80 2.08 20. 6 to 75. 6 4. 29 to 9. 12 2 07 . 16 2 98 2. 55 22. 8 to 53. 0 5. 54 to 9. 18

2. 07 .35 1 98 0. 82 25. 1 to 72. 7 4. 29 to 7. 62

2.07 .35 1 137 1.14 21. 8 to 62. 5 5. 54 to 9. 49 2.07 .35 1 180 1.50 22. 4 to 39. 6 7. 49 to 9. 24

2. 07 .35 2 98 0. 82 31. 8 to 48.

4. 29 to 5.54

2. 07 .35 2 137 1. 14 16. 8 to 59.

4. 29 to 9. 18

2. 07 .35 2 180 1.50 14. 8 to 35.

5. 54 to 9. 12

2. 07 .58 1 98 0. 40 48. 3 to 109.

4. 29 to 9.04

2.07 .58 1 158 .64 21.0 to 72.7 4. 29 to 9. 24

2 07 58 203 . 82 18 9 to 49.

5 54 to 9. 24

2.' 07 !58 1 232 !94 19. 3 to 39.

6. 29 to 9.24

2.07 .58 2 158 .64 27.2 4.29

2. 07 .58 2 203 .82 17. 3 to 26. 6 4. 29 to 5. 80

2. 07 .58 2 232 .94 19. 8 to 35.7 6. 29 to 9. 12

3. 07 . 16 1 80 2. 08 96. 4 to 199. 5 5. 61 to 10. 11

3. 07 16 \ 98 2. 55 77. 5 to 165.

5. 61 to 10. 68

3. 07 .16 2 98 2.55 83.5 5. 61

3. 07 .35 1 98 0.82 115. 1 to 117.

5. 61

3. 07 . 35 1

1 Q7 lot 1 14 71(1.11 tntu 1lUl. fil 0u 61 to 10. 81 3.07 .35 1 180 l'50 50. 3 to 111. 9 5! 61 to 10! 81

3. 07 .35 2 180 L 50 54.8 5.61

3. 07 .58 1 158 0.64 94. 0 to 142. 2 5. 61 to 10. 36

3. 07 .58 1 203 .82 64. 6 to 125. 8 5. 61 to 10. 36

3. 07 .58 1 227 .92 54. 5 to 107. 9 5. 61 to 10. 36

" Above the stack-branch junction.

gave a series of straight lines having a slope of

approximately 3/8. Therefore, a value of a=3/8

was adopted. Values of C" were then computed

from eq (21) inserting the value of 3/8 for a. Evidently, the same value of C" applies approxi21
mately whether the flow is from one or from both

branches. Average values of C" = 17.1 for the

sanitary-tee fittings and C" =9.65 for the longturn T-Y fittings were obtained. Hence, the

equations representing flow conditions at the junction of the horizontal and vertical streams of the

simulated stack become, for sanitary-tee fittings,

/ T\5/8 /n„\3/8

F=8.33-17.1 (^^j Y^'^X'i'- (60)

and for long-turn T-Y fittings

F=6.00-9.65 (^^j F3/8;^5/8. (gj)

Equations (60) and (61) can be solved for cor- responding values of X and Y for any selected

value of [{T/p^y-mDiy'^ This was done for

all the conditions investigated in order to determine the agreement between the experimental

data and eqs (60) and (61). Representative curves computed in this way have been drawn in figures

17 and 18. The agreement obtained indicates

that the simplifying assumptions made in the

analysis are justified by the residts obtained.

There are certain restrictions on the application

of eqs (60) and (61). First, the head-loss term

appearing in the denominator of X and F (see eqs

(14) and (18)) represents the head loss between

the stack and a point in the horizontal branch 4

pipe diameters from the stack. Second, the equations are based on a value of /=0.03 for the horizontal branches, and on a value of r=0.047 for the

bend in a long-turn T-Y drainage fitting. Third,

the data on which eqs (60) and (61) are based were

obtained for a 3-in. stack only. Although the

analysis indicates the equations should apply to stack diameters other than 3 in. this has not yet

been demonstrated experimentally.

b. Prototypal Stack

The data on single-branch flow in a prototypal

stack are given in table 8. These data were obtained by use ol the test system shown in figures

5 and 6. The experimental data shown in table 8 provided the information necessary for computing the

terms X and Fin eq (30). Next, values of 8 were computed from eq (32). The values of 5 thus obtained were plotted logarithmically against X/Y.

The data from both diameters of branch plotted

fairly weU along a single line with a slope of approximately 0.7, hence this value was adopted for the exponent a. Then, the values of C were computed from eq (31), inserting the value 0.7 for a. An average value of C=2.48 was obtained in this way. Hence, the equation representing flow

conditions at the junction of the horizontal and

vertical streams of the prototypal stack using

sanitary-tee stack fittings becomes

F=8.33-2.48 Z°-^F°-^ (62) | Equation (62) can be solved for values of X j corresponding to selected values of F. This has

been done and the resulting curve is shown in

figure 19. The experimental data shown in table

8 have been plotted in this figm-e. The agreement

between the curve and the plotted points is satisfactory.

There are certain restrictions on the application ( of eq (62). First, the equation applies oiily when

sanitary-tee stack fittings are used and when the

head-loss term appearing in the denominator of

X and F (see eqs (14) and (18)) represents the

head loss between the stack and a point in the

horizontal branch 4 pipe diameters from the stack.

Second, the equation is based on a value of/=0.03. Third, the data on which eq (62) is based were ji obtained for a 3-in. stack only. Fourth, velocities 1 in the stack just above the branch level are [ assumed to be terminal velocities. )

0 I I I \ \ I I \ 0 2 4 6 8 10 12 14 16

X FiGUEE 17. Representative results of tests on flow interfer- ence at junction of simulated stack and horizontal branches

connected with sanitary-tee fittings {Iji-in. branches).

O. two-branch flow •i B one-branch flow

Y

1 0 1 11 1 y 1 ! 1 1 \ v.-

0 8 r \T=O.I6in.

V \-.»

0 6 \t = 0.35 in. \^

o 0 4

0 2

0 1 1 1 1 1 0 2 4 6 8 10 12 14 16 X Figure 18. Representative results of tests on flow interfer- ence at junction of simulated stack and horizontal branches

connected with long-turn T-Y flttings {3-in. branches).

Ol two-branch flow one-branch flow 22
Table 8. Data on interference of flows at junction of drainage stack and horizontal branches

(3-in. prototypal stack, sanitary-tee drainage fittings, one-branch flow)

X>I allLli Dis- X Ci ilillltJiJ Dis- Vplnm" f V Head

("•Ti Q T" fro \jlltXL V CHJV.1L Jr cliarge loss in Y

eter into in stack i> through branch branch

stack » branch

gpTTi jpS gpm J ps ft i.'ei 150 14.2 2.6 0. 41 0. 12 26.

1

0.02

1.61 150 14.2 6.7 1.05 .20 15.7 .09

1 61 150 14. 2 11. 7

- 1. 84 . 29 10.

8

. 18

1 61 125 13.

2

2. 2 0. 35 . 10 27.

1

. 02

1.61 125 13! 2 2^9 !46 !l2 22! 6 !03

1.61 125 13.2 8.1 1.27 .20 13.5 .12

1 61 125 13.

2

14. 7 2. 31 . 29 9.

3

. 28

1.61 100 12.1 3.2 0.50 .10 22.7 .04

1.61 100 12.1 4.5 .71 .12 18.9 .07

1. 61 100 12,

1

9. 4 1 48 . 18 12.

6

. 19 i!ei 100 12.1 15^8 2! 49 !25 9!l [38

1. 61 75 10.

7

4. 4 0 69 . 10 17. 8 . 07 L61 75 10! 7 6]0 !94 !l2 14^8 ill 1.61 75 10.7 10.5 1.65 .16 11.

1

.26

1.61 58 9.7 5.5 0. 87 .10 14.6 .12

1.61 58 9.7 9.9 1.56 .14 10.4 .27

1. 61 55 9. 5 5 4 0. 85 . 10 14.

0

. 11 L61 55 9! 5 11! 0 l!73 ^14 10! 0 .33

1 fil 60 9. 2 5. 6 0. 88 . 10 13.

1

. 12

1 61 50 9. 2 8. 7 1. 37 . 12 10. 9 . 24

3. 07 150 14.2 24.0 1.04 .19 16.5 .09

3. 07 150 14. 2 39. 3 1. 70 27 11 6 17

3] 07 150 14! 2 64^3 2' 79 !35 8^9 !34

3 07 125 13. 2 29.

0

1. 26 . 19 14. 2 . 13

3! 07 125 13^2 4a 8 2^03 27 10! 0 !24

3. 07 125 13.2 75.1 3.25 .35 7.7 .47

3. 07 100 12.1 .33.9 1.47 .19 12.0 .18

0. U/ 100 12.

1

57.

7

2. 51 . 27 8.

4

. 36

3. 07 75 10.7 39.3 1.70 .19 9.4 .24

3. 07 75 10.7 62.1 2.68 .25 7.1 .45

3.07 59 9.8 45.9 1. 99 .19 7.8 .82

3 07 55 9. 5 48.0 2. 08 . 19 7.

4

. 35

3! 07 55 9^5 64! 0 2.77 !22 6!4 !54

3.07 54 9.4 48.4 2. 10 .19 7.2 .36

3.07 53 9.4 63.0 2.73 .22 6.2 .52

3.07 50 9.2 49.2 2. 18 .19 6.9 .37

3. 07 50 9.2 70.6^ 3. 07 .22 6.0 .60

» Above the stack-branch junction.

b Computed from eq (46) and the measured discharge rates listed in second column.

5.2. Air-Flow Measurements

Data on the flow of air delivered to the stack

vent and to a single horizontal branch 8 ft below

the point of water entry are shown in tables 9

and 10. The test system is shown in figures 5 and 7. Table 9 gives data obtained with the

stack vent fully open, and table 10 with it completely closed. Other conditions were the same

in the two cases. The data for several rates of

water discharge have been taken from table 9 and plotted in figure 20. Also, from the data of table 9, figure 21 has been

prepared, showing approximately the rates of

air flow delivered to the horizontal branch for

various rates of water discharge in the stack for

pneumatic-pressure reductions in the branch of

2.0, 1.0, and 0.5 in. of water. Figure 22 has been prepared from the data in

table 9 for a rate of water discharge of 65 gpm.

584032—61 i

0.7 I

1— 1 1 1 r

0 I I I I I I ^

0 5 10 15 20 25 30

X Figure 19. Results of tests on flow interference at junction

of prototypal stack and horizontal branches connected with

sanitary-tee fittings, one-branch flow. O, l-Vi-in. branch

3-in. branch

-6

I

I

1 1 1 1 1 1 r

0 20 40 60 80 ICQ 120 140 160 180

flIR FLOW DELIVERED TO BRANCH , gpm Figure 20. Air flow delivered to horizontal branch of stack.

3-in. stack and branch, stack vent open, water introduced 8 ft above

branch

.

This figure shows graphically the relations between

air flow in the stack vent, air flow in the vent to the horizontal branch, and pneumatic pressure

in the horizontal branch. The dashed line represents maximum rates of air flow computed from

eq (56) and the uppermost solid curve represents

total air-flow requirements determined experimentally on the test system shown in flgures 5

and 7. Figure 23 has been prepared for several rates

of water discharge showing the total inflow of air for various pneumatic pressures maintained in

the horizontal branch. These data have been

taken from tables 9 and 10 and represent conditions with the stack vent open and conditions

with it closed.

23
Table 9. Air-flow data for 3-in. drainage stack, stack vent open Table 9. Air-flow data for 3-in. drainage stack, stack vent open—Continued

Pressure reduction in horizontal branchAir delivered

to horizontal branch

in. of water gpm

0.60 0

. 73 0

!68 3. 5

. 65 7!o

. 62 13.

9

. 46 27.

8

!28 48. 7 .06 83.

4

.75 0

'. 62 11.

1

. 50 19.

5

!25 59.1

b 1.00 0

i!oo 0

0. 81 0 !75 16.

7

!68 3.

5

' 65 7.0 !56 13.

9

!50 38! 2 !44 27! 8 .26 43! 7 .25 73! 0 .12 83.

4

1.50 0

1.38 0 1.25 17.

4

l!25 3.

5

l!25 7^0 1.18 14 0 1.00 34! 8 1.00 34.8

0. 88 41.

7

'. 75 59! 1 !69 69.

5

.60 80.

0

I25 93.

9

.12 104

2. 00 0

l!50 18.8

1.00 52.1

0. 50 90.

4

I25 118

2. 88 0

0 2. 60 Q 2^50 3.5

2. 38 7.0

2. 38 13.

9

1. 75 41.

7

1. 38 69. 5 i!oo 93.

9

o!i8 125

3.00 0 2.50 17.4

2. 00 45. 2

1. 50 73.

0

1. 00 97.

3

0. 50 125

4. 00 0

3. 00 27.8

2. 50 55.6

2.00 76.5 1.50 93.9

1.00 118

0.60 146

5.00 0 4.00 31.3

3. 00 62.6

2. 00 93.9

1.00 132 0.50 160

Air deUvered

to stack vent

Total air delivered to stack

gpm gpm

207 199

184

184

176

169 146

207

203

191 198

229

184 184

1 7R i ID 176

161

loU 183

175

153

146

181

130 213

1 QQ 1 QQ

199 199

192

1 Cd 10^

ZUo 206 206

91 Q

184 226

169

lou

207 207

207

207 199 184

169

154

123

211 214

213 226

239

248

248

Finally, figure 24 lias been prepared showing

rates of air flow for various rates of water discharge

in a 3-in. stack. The experimental points plotted

in this figure represent data from table 9 for pneumatic pressures in the horizontal branch

approximately 1 in. below atmospheric.

Water flow

in stack »

gpm

100

115

Pressure reduction in

horizontal branch

Air delivered

to horizontal branch

in. of wetter gpm

10. 4 0

9] 6 3.

5

9. 5 7.

0

9.

2

13 9 8^6 0' 7.4 41.7

7.

0

Q

5.

3

69.

5

5.

0

48.

7

4] 0 69.

5

3I0 93! 9

2.

8

97.

1

2.

5

111 2^0 118

l!5 136

1.0 163 1.0 153 0.25 167

11.3 0

9.5 0 5.0 76.4 4.0 90.4 3.0 108

2.5 118 2.0 132

1.6 139

1.0 153

Air deUvered

to stack vent

gpm

184

184

176

176

176

146

115

92.1 69.0

Total air delivered to stack

gpm

184

188

183

190

218

"2I6

212

245 236

» Water introduced 8 ft above level of horizontal branch to which air was

delivered.

>> A value of 0.50 in. was obtained by introducing water 24 ft above hori- zontal branch.

° A value of 1.0 in. was obtained by introducing water 24 ft above hori- zontal branch.

60 80 100 WATER FLOW IN STACK , gpm

Figure 21. Effect of pneumatic pressure and rate of water

flow on air required to vent horizontal branch.

3-in. stack and branch, stack vent open, water introduced 8 ft above branch.

1. Pneumatic pressure in branch=—0.5 in. of water.

2. Pneumatic pressure in branch = —1.0 in. of water.

3. Pneumatic pressure in branch = —2.0 in. of water.

Figure 25 gives a comparison of experimental

data from several sources showing the flow of air

24
required to raaintain a pneumatic pressure within

1-in. water column of atmospheric in a horizontal

branch of a 3-in. drainage stack. In the tests from which these data were obtained, with the

exception of the tests made by Babbitt [7, 8], all the water flow was introduced into the stack

within one branch interval above the horizontal

branch under observation. In general, the data

of Dawson and Kalinske [5] indicate less flow of

air than do the corresponding data of Hunter [3] and of the most recent NBS investigation. Babbitt's measurements, made in regions of positive

pressure, are in fair agreement with somewhat

similar measurements made in the most recent NBS investigation, in regions of negative pressxu-e. Among the factors which may influence air flow

in drainage and vent pipes are the following : type

of fitting through which water is introduced ; type

of fitting to which horizontal branch is connected

;

distance from point of water entrance to horizontal

branch where air flow is measured ; distance from

point of water entrance to base of stack; number

of fittings in stack; roughness of stack and of

budding drain and sewer; and presence or absence

of buUding trap or bends in building drain or sewer. Because all of these factors were not held constant

in tests by different investigators, it is not sur- prising that the results are not in close agreement.

However, in spite of their lack of close agreement,

the data of figure 25 show that the maximum flow

of air delivered to a region of negative pressure or

carried away from a region of positive pressure, in

order to maintain pneumatic pressures within 1.0

in. water column of atmospheric, was usually less than that computed from eq (56).

In figures 22 and 23, the agreement between the

test results and eq (56) is close for pneumatic pres- sures near atmospheric in the horizontal branch.

However, as the pneumatic pressure in the horizontal branch was reduced, the flow of air into

the horizontal branch decreased and the flow of

air into the stack vent increased, as shown in

figure 22. Evidently, there existed a tendency for a certain total air inflow, part of it coming from

the stack vent and part of it from the vent to the

horizontal branch, to approximate the value

computed from eq (56). The data of figures 23

and 24 for combined air flow in stack vent and in

branch vent indicate that eq (56) may be useful

to estimate upper limits for air flow under conditions similar to those in the tests on which these

figures are based.

The curves shown in figure 20 show that, for

pneumatic pressures in the horizontal branch only

slightly below atmospheric, the pressure varies

approximately in a linear fashion with the quantity of air delivered to the branch, the lowest

pressure being obtained when no air is delivered

to the branch.

From figure 21, it is evident that for water flows

up to at least 115 gpm in the 3-in. stack, the air flow required to maintain a given pressure in the

horizontal branch increased with increased water

Table 10. Air-flow data for 3-in. drainage stack, stack

vent closed

w 3>t6r now

PrGssur© rC"

citiction in

liorizoiitftl

Air dpliTTPrDii to horizont&l

brancli

QpTU 171. OJ VdZBT

16 5

nu

15 2 O. 0 14^5 7.0

14.0 13.9 37 5 10 5 41 7

7 C 69 5

O. 1 139

i. V 209

236

24 2 u

23 2 3 5 22^5 7.0 21.4 13.9

45 0 16 4 41 7 12 4 69 5 4 4 139

1. u 237 257

' 156 Q

105 3 5 90 3 7 0

oO. U 13 9 25 2 13 9

24 0 d1 7 55.0

20 5

A^ 7 li.i 69.5

15.5 69.5

7. 4

1 "50 lOi) 6 4 139

J., u 250

0. 50 237

4^ 264

184 u

122 o. 0 110 7.0 85.0 13.9

DO. K) , 18.

0

41. 7 10 8 69 5

2 5 139

1. u 244

\ U. OO 195

{ 211 Q

1 Q7 O. 0 177 7.0

147 13.9

100 61.2 41.7

39.8 69.5

11.8 139

1.0 195

I 0.38 195

« Water introduced 8 ft above level of horizontal branch to which air was

delivered.

1 1 1 MAX. FLOW.eq 56 ^

TOTAL FLOW, 1 + 2

— 1

FLOW INTO STACK VENT

1

FLOW INTO HOR. BRANCH

I ^ o1 0 -1.0 -2.0 -3.0

PNEUMATIC PRESSURE IN BRANCH , INCHES OF WATER

Figure 22. Air flow in stack vent and in branch vent. Rate of water flow in stack, 65 gpm.

25
e

Q. 100 s3 0

li- a 300

aoo

100 gpm

WATER

"1 r

55 gpm

WATER

• o

65 gpm

WATER

37.5 gpm

WATER

0 -I -2 -3 -4 0 -I -2 -3 -4

PNEUMATIC PRESSURE IN HORIZONTAL BRANCH , INCHES OF WATER

Figure 23. Total airflow into venting system. Each ordinate represents the sum of the air-flow rates in the stack vent and in the branch vent. O. stack vent open #, stack vent closed

1, Rates computed from eq (56).

2, Equation (56) values reduced by one third.

flow, but tended to level off at the higher rates. This appears reasonable, since it can be shown by

use of eq (56) that for a stack of 3.07 in. diameter

(the diameter used in the tests), the peak rate of

air flow occurs for a water flow of the order of

120 gpm, and the air flow decreases for greater

rates of water flow. The resistance offered by the flow of water on

the wall of a drainage stack to the entrance of air tlirough a vent or horizontal branch connection

has been observed by Dawson and Kalinske [5]. Certain measurements relating to this phenomenon

were also made in the laboratory investigation re- ported herein (see section 3.2.). These measure- ments are not shown because of some uncertainty

about their accuracy. Since the pressure heads

measured were relatively low, a given error in

measurement would be more significant than if the heads measured had been relatively liigh.

However, it is believed that the measurements

were sufficiently reliable to provide some general

indications. Application of the same line of rea- soning which produced eq (62) leads to an equation having the form

(63)

The exponent a evidently has the same value as

in eq (62).

The mean velocity in the layer flow in the stack

corresponding to any particular volume rate of

water flow was computed from eq (45) (it being

assumed that the water had reached terminal

velocity at the branch level) and the thickness of

the water layer on the wall of the stack was com100 WATER FLOW, gpm

Figure 24. Total air flow into drainage system for a pneumatic pressure of approximately 1 in. below at- mospheric in horizontal branch.

Each ordinate represents the sum of the air-flow rates in the stack vent and in the branch vent. O, measured values from table 9 for a pneumatic pressure of —1.0 in. of water

.

9, average of measured values from table 9 for pneumatic pressures in the range 0 to —2.0 in. of water.

1, Rates computed from eq (56).

2, Equation (56) values reduced by one third.

20 40 60 80 100 20 60 100 140 180 320

240

AIR FLOW INTO BRANCH

STACK VENT OPEN.

0 20 40 60 80 100 120 140 160 180 200

WATER FLOW IN STACK , gpm

Figure 25. Data from several sources showing air flow

required to maintain a pneumatic pressure within 1-in. water column of atmospheric in horizontal branch of S-in. drainage stack, water introduced at one elevation only.

1, Equation (56).

2, Appro.ximate curve based on data of table 9 and figure 21, for pneumatic

pressure of —1.0 in. of water in vented branch 8 ft below point of water

entrance.

3, Appro.ximate curve based on data given by Babbitt for pneumatic pressure

of +1.0 in. of water in vented branch near base of stack. O. Values based on data of tables 9 and 10 for pneumatic pressure of —1.0 in.

of water in vented branch 8 ft below point of water entrance. 9, Data from investigation by Dawson and Kalinske for pneumatic pressure

of —1.0 in. of water in vented branch 8 ft below point of water entrance. Q, Data from investigation by Hunter for pneumatic pressure of —1.0 in. of water in vented branch only slightly below point of water entrance. 26
piited from eq (43). In eq (63) the terms X and

Y have the follo-n-ing significance

:

' X—^ ^^^andr==^^^.

2g{h2—hr) 2g{h—hi)

I

I The terms Vi and V2 represent, respectively, mean

velocities in the water stream in the stack and in

the air stream in the branch. The term {h2 —hi)

represents the difference in pneumatic pressure

between a point inside the air core in the stack

and a point inside the horizontal branch near its junction ^vith the stack.

5.3. Miscellaneous Measurements

a. Distribution of Air and Water in Cross Section of Drainage Stack

The data taken in this portion of the investiga1 tion, in the manner described in section 3. 3. a., appear in table 11. These data show that the

ratio of air to water intercepted by the samplingequipment increased, with distance from the wall

of the stack, to a value which appears to indicate

! that about as much air as water was flowing at the axis of the stack. The relative rate of measured air flow as a function of distance from the

wall of the stack is shown in figure 26. Computations indicate that not more than about

0.82 of the water actually striking the tip of the

impact tube used in these tests was delivered to

, the sampling equipment. This value was computed as follows: First, the cross section of the

drainage stack was divided into imaginary concentric areas, each area (except the one at the

axis which included only one traverse point) in- cluding two points on the impact-tube traverse which were equidistant from the axis. Second,

for each such area the average measured rate of

flow into the impact tube was multiplied by the

ratio of the concentric area served to the cross section of the tube tip. Third, the values obtained

in the second step were added and the sum divided

by the total known rate of water flow in the stack

(in this case 100 gpm).

I On the other hand, for estimating the proportion

. of the air which was intercepted by the impact

, tube, no such direct method is available. However, if it is assumed that the total air flow was

that indicated by eq (56), an estimate of approximately 265 gpm for a water flow of 100 gpm is obtained. Integration of the air-flow values,

shown in the third column of table 11, in a man-

: ner similar to that described above for the water

intercepted indicates that, on the average, only

j about 0.20 of the air carried down the stack at any

given point was actually intercepted by the impact

I tube in these tests. It appears likely that the measured values of air and water flow in table 11 were less than the true values to a degree which depended, among other

things, on the distance from the wall of the stack.

Table 11. Distribution of water and air in cross section of

3-in. drainage stack for a water flow of 100 gpm introduced

at one elevation

Water • Air » Ratio of dis- Ratio " of Distance deUvered to delivered to tance from Ratio b of air flow to from wall measuring measuring wall of stack air flow to air flow at

of stack apparatus apparatus to radius of water flow axis of stack stack

in. cc/min cc/min

0. 096 130.1 15.6 0. 063 0. 120 0. 108 .159 119.4 25.9 . 104 .217 .180

.222 140.4 40.6 . 145 .289 .282 284 130.

0

56.

0

. 185 . 431 . 389 !346 120.2 69.2 .226 .576 .481

.409 117.3 78.2 .267 .666 .543

.472 113. 5 87.2 .307 . 768 .605

.634 113.5 94.7 .348 .834 .657 .784 128.1 119.3 .511 .931 .828 1.034 149.0 133.8 .674 .898 .929

1. 284 161.3 144.0 .837 .893 .999 1.534 156.

1

144.

1

1.00 .923 1.00

» Each value shown is the average of two measurements taken equidistant from opposite walls of the stack.

!> Computed from values given in columns 2 and 3.

= Computed from values given In column 3.

0 0.2 0.4 0.6 0.8 1.0 DISTANCE FROM WALL RELATIVE

TO RADIUS OF STACK

Figure 26. Measured air-flow rate as a function of distance from wall of 3-in. stack

100 gpm water Introduced into stack at one elevation.

The reasons for this include the facts that (1) near the center of the stack the inertia and friction

effects associated with intermittent impingement

of water on the impact tube would have produced

less efficient flow of water to the measuring equipment than near the wall of the stack, and (2) the

conditions causing air to enter the impact tube were such as to prevent all the air intercepted by

the tube tip from being delivered to the measuring

equipment. Although this problem was not investigated experimentally, the assumption that

27
the actual flow of either air or water at any point

in the cross section exceeded the measured value

by a fractional part which is a direct linear function of the distance from the wall of the stack

yields a more reasonable picture of conditions in

the stack than would a consideration of only the

direct measurements reported in table 11. If this

assumption is made, computations indicate that

the ratio of air flow to water flow varied from

approximately 1.0 to 3.7 in the region of the

theoretical "air core," as shown in figure 27, reaching the value 3.7 at the center of the stack.

These computations also indicate that, within

the theoretical region of water flow, the ratio of air flow at any point to the air flow at the axis of the

stack ranged from zero to only about 0.12, instead

of the surprisingly larger values indicated by the

measurements reported in table 11 and shown in figure 26.

b. Velocity Distribution of Water in Cross Section of Drainage Stack

Data taken in this portion of the investigation,

described in section 3.3.b., appear in figure 28. For comparison, the thickness and terminal velocity of the water layer, computed from eqs (43) and

(46), respectively, are also shown in this figure for each rate of water flow. Indirect evidence obtained during the tests in- dicated that some air was entrained in the fallingwater and that droplets and small quantities of

water were thrown toward the center of the stack.

The presence of fittings at 8-ft intervals may have

contributed to this phenomenon. This type of

flow could produce impact pressures within the

theoretical "air core," such as were actually observed in the tests. Thus, the impact pressures

obtained some distance from the wall of the stack

may not accurately indicate water velocities, since

the impact tube was calibrated for water only.

One important point which is suggested by the

data shown in figure 28 is that near the wall of

the stack the velocity gradient is very steep, evidently much steeper than the distribution which

occurs in turbulent flow in pipes full under

pressure.

c. Pneumatic Pressures within Drainage Stack

Data on pneumatic pressures within the test system (shown in fig. 5) for various water flows

both with and without venting, were obtained in

the m_anner described in section 3.3.c. These data

are shown in figures 29 through 32. Data obtained

with the venting system functioning are shown

in figures 30 and 32, and those obtained with the

vents closed are shown in figures 29 and 31. The formula

^1 L{Dd"'^gA

4.0

3.0 -

2.0 -

1.0

THICKNESS OF THEORETICAL

'LAYER"

0.4 0.6 0.8 DISTANCE FROM WALL RELATIVE TO RADIUS OF STACK1.0

Figure 27. Ratio of air-flow to water-flow rates as a function of distance from wall of S-in. stack.

100 gpm water introduced into stack at one elevation. estimated measured

1

1 WATER FLOW 100 gpm

0.1 0.2 0.3 0.4 DISTANCE FROM WALL, in.

0.5

5/2^

(64)

Figure 28. Indicated velocities near wall* of S-in. drainage

stack.

1. Mean terminal velocities computed from eq (46).

2. "Layer" thickness computed from eq {431. 'Indicated velocities in central part of cross section were greater than

those shown in the figure.

is in fair agreement, for pneumatic pressures at points more than one story below the point of water

entrance, with most of the data shown in figure 29. In eq (64) Ah is the difference in pneumatic pres- sure between the base of the stack and any point

28
0 5 10 i5 20 25 30 35 DISTANCE BELOW POINT AT WHICH WATER WAS INTRODUCED,

ft Figure 29. Pneumatic pressures in 3-in. drainage stack {water introduced at fourth branch level, stack open at top hut otherwise not vented) {see fig. 5 for details of test system)

.

Curve number Water flow gpm

175

150 - 125

100

60

Q. -12

ST HORIZONTAL BRANCH LEVEL

_L

0 5 10 15 20 25 30 35 DISTANCE BELOW HIGHEST POINT ON STACK WHERE WATER

WAS INTRODUCED, ft Figure 31. Pneumatic pressures in 3-in. drainage stack {water introduced at second and fourth branch levels, stack open at top but otherwise not vented) {see fig. 5 for details of

test system)

.

Qi flow of water introduced 32 ft above base of stack. O2 flow of water Introduced 16 ft above base of stack. Curve number Q2 gpm gpm

1 _ 60 30

60

100

100

60

30

(id

0 5 10 15 20 25 30 35 DISTANCE BELOW POINT AT WHICH WATER WAS INTRODUCED,

ft Figure 30. Pneumatic pressures in 3-in. drainage stack {water introduced at fourth branch level, stack open at top, fully vented at 8-ft intervals) {see fig. 5 for details of test system)

.

Curve number Water flow gpm

1 175

2 150

3 125

4 100

5 80

6 60

+ 4

1 1 —T—

1 1

+ 2 1ST HORIZONTAL0 ^4IH 39 22 BRANCH LEVEL

-2

-4 .2.

-6

-8

-10

-12 1 1 1 1 1 1 0 4 8 12 15 20 24 2f DISTANCE BELOW HIGHEST POINT ON STACK WHERE WATER

WAS INTRODUCED ft Figure 32. Pneumatic pressures in 3-in. drainage stack {water introduced at second and fourth branch levels, stack open at top, fully vented at 8-ft intervals) {see fig. 5 for

details of test system).

Q\ flow of water introduced 32 ft above base of stack

Qi flow of water introduced 16 ft above base of stack Curve number Q, Q2 gpm gpm

1 60 30

2 60 60

3 100 30 4.._ 100 60

a distance L above the base of the stack, expressed

in head of water. A value of (7=0.038 was computed from the data of figure 29, using dimensionally consistent units in eq (64).

When w^ater was introduced into the test stack

simultaneously at two points at different levels,

the pneumatic pressure approached a minimum

value just below the higher point. The pressure

increased with distance below this point. It

again decreased below and near the lower point of

water entrance, after which it once more increased

with distance below the latter point. The pneumatic pressure for a wide range of water flows

tended to approach atmospheric at a fairly

definite point in the stack when the water was

introduced at one point only and when the system was vented by only the stack vent. The elevation

of the point of atmospheric pressure is affectedby

29
the resistance to flow of air and water offered by

the building drain. For a given rate of water

flow, the change in pneumatic pressure between

two points where air could enter or leave the stack was approximately linear with respect to distance

along the stack, except within the interval approximately one floor level below the point of water

entrance. Within this interval, the linear relation

did not apply, probably because the terminal

velocity was developing here with accompanyingenergy and momentum adjustments in the flow

of air and water. The data of figures 29 and 30, as well as earlier data of a similar nature [5, 7, 8], indicate that the

pneumatic pressure within the stack at any given

point between floor levels tended to conform, over

a fairly wide range, to a power function of the

volume rate of water flow. The maximum value

of the power appeared to be 5/2. This is similar

to the flnding by Babbitt that the pneumatic

pressure in a vented horizontal branch is a power

function of the volume rate of water flow, the

exponent being less than 5/2 and greater than zero, depending on the extent of relief provided by the

venting system.

Data shown in figures 29 to 32 are consistent

with those obtained by earlier investigators [5, 7, 8] in showing that the maximum reduction in pneumatic pressure in a drainage stack occurs below

and near a point of water entrance. Figures 30 and 32 indicate that, even in a multistory drainage stack equipped with a venting

system, pneumatic-pressure changes of appreciable magnitude may develop within the stack

between the various floor levels. However, if pressures within the horizontal branches and

fixture drains can be relieved by venting, this is all that is necessary to avoid siphoning or blowing

the trap seals.

6. Application of Results of Investigation

6.1. Permissible Simultaneous Rates of Flow

at Junction of Drainage Stack and Horizontal Branches

One application of the results of the investigation of interference of flows at the junction between

a multistory drainage stack and a horizontal

branch is to the prediction of the permissible rate

of water flow in the stack or horizontal branch

when the rate in one or the other of these components is known. This application of the results of

tests on the simulated stack may be made by

maldng certain substitutions in eqs (60) and (61)

and rearranging terms. A similar application of

the results reported for the prototypal stack may

be made by starting with eq (62). The appropriate substitutions will now be discussed briefly.

The analysis given in section 4.1. of this paper

defined the quantitites X and Y in terms of the

velocities Vi and Vi, the head difference {h2—hi),

and g, the acceleration of gravity. In eq (42),

the dimension T is expressed approximately in

terms of the discharge rate Qi, the stack diameter

Z>i, and the velocity T^i. The next substitution operation is performed

by setting Vi equal to the terminal velocity given

by eq (44) and expressing V2 in terms of Q2 and

Z>2. Finally, for the purpose of computing flow

capacities, the numerical values of ^=32.2 ft/sec^

and ^s= 0.00083 ft (see section 4. 2. a. of this paper)

are substituted.

It is assumed that Vi is equal to the terminal

velocity Vt, since it was shown in the earlier paper

[10] and in section 4.2. of this paper that the

velocity of flow in a stack under ideal conditions

should nearly reach terminal velocity when the

water has fallen through a distance of one branch

interval below the point of entry.

This procedure of substitution leads to the

equations

(Q2y —5^,-5.1414-10 2^Y''-^l'^Y'" 2g(h2-h){D2y 10.2(^^J {Q.rAksJ

' L2g{h2-k)iD2yA L2gih2-himrj '-'"''^

and

(Q2r __ooi on r /AV^^ A

{h2-h){D2Y '^''^\D2) m'"

[

{Q-2.

2 n 3/8 {h2-hx){D2y

-|3/S r (^,)2

-15/8

based on the results of experiments on the simulated stack using sanitary-tee fittings.

In a similar manner, the equations

/16 {Q2Y 7, , 7, (DA'" _A_ {i\

r (^2)^ Y'r T" (f^7^

' i2gih-k){D2yA l2g{h2-kmn ^""'^

and

Di r (^2)^

"I 'iQir"l{h2-k){D2rj

lih-hKDO'j ^^^^

have been obtained from the results of tests on the

simulated stack using long-turn T-Y stack fittings.

30
Beginning -with eq (60) and making substitutions

similar to those which produced eqs (65) and (66),

the equations

2g{h

mi =5 14-5 42 (^Y'(ly'

.[ mi TT mi T' (69)

and

r 1 r m' i .7..

' L(A2-Ai)(A)d L(/i2-Ai)(A)^J ^

the horizontal branch at a distance of 4 branch

diameters from the stack.

The range in values of branch discharge which

may be computed from eqs (66), (68), and (70)

extends beyond practical limits for the smaller

flows in the stack. As a rough guide to the upper

limits of discharge in the horizontal branches flowing full under no external head, it can be shown by

means of the Darcy-Weisbach formula that the

discharge rate should not exceed approximately

16, 29, and 78 gpm for 1)^-, 2-, and 3-in. branches,

respectively. These values have been computed

for a slope of Yi in. per ft and a value for / of 0.03. The hmits established in this manner are indicated

by horizontal lines across the curves in figures 33

to 36. Greater rates of discharge would cause the

hydraulic gradient in a horizontal branch to exceed

the slope of the branch.

are obtained, based on the results of tests on the

prototj'pal stack using sanitary-tee stack fittings.

In order to compute numerical values of flow

capacities from eqs (66), (68), and (70), it is fli'st necessary to select a value for the term (A2— /ii). It appears that a reasonable value would be a

value that would allow the horizontal branch to flow barely fuU. The selection of such limiting

values will be based on identical pneumaticpressures in a drainage stack at a given elevation

and in a vent connecting to a horizontal branch

at the same elevation. This condition requires

that there be an adequate venting system and

1 that the stack and branches not be overloaded.

Therefore, in the terminology of figure 10, Pi—Pt

(or hi=hi). Since h2—liz^hi, it follows directly

that A2—Ai=/i3. Figure 10 indicates that hz is actually the water depth in the branch. Measurements made on the fittings used in this investigation to connect the stack and the horizontal

branches indicated that, at a distance of 4 branch

diameters from the stack, A3 should not exceed

about 0.75 times the branch diameter for sanitarytee fittings, or about 1.8 times the branch diameter

for long-turn T-Y fittings, if the branches are to flow approximately full but not under a head.

Hence, it wiU be assumed in applying eqs (66),

(68), and (70) that (A2— AO =0.75 A for sanitaryi tee stack fittings, and that (A2— Ai) = 1.8 A for long-turn T-Y stack fittings.

Equations (66), (68), and (70) have been solved

for a 3-in. stack for the three different branch

sizes used in this investigation, and the results are

! shown in figures 33 to 36. In these figures, any

] point on the curves represents a combination of

flow rates which should be the maximum that can

occur simultaneously without causing the head

I difference (A2— Ai) = 1 .8 for long-turn T-Y stack

fittings or 0.75 1)2 for sanitary-tee fittings to be

exceeded. Expressed in another way, the combinations of fiow rates which may be taken from

these curves represent the maximum rates which

can be introduced simultaneously without causing

a head of water to build up in a vent connecting to

100 150 200 FLOW IN STACK ABOVE BRANCH ,gpm

Figure 33. Permissible simultaneous rates of flow computed for junction of 3-in. drainage stack and horizontal branches.

Based on data from 3-in. simulated stack, long-turn T-Y fittings. Solid curves represent eq (68), wherein (A2— fti) = 1.8I>3.

0 20 40 60 80 100 120 FLOW IN STACK ABOVE BRANCH, gpm

Figure 34. Permissible simultaneous rates of flow computed for junction of S-in. drainage stack and horizontal

branches.

Based on data from 3-in. prototypal stack, sanitary-tee fittings. Solid curves represent eq (70), wherein (A2— fti)=0.75X>2.

31
40 60 80 100 120 140 160 FLOW IN STACK ABOVE BRANCH, gpm Figure 35. Effect of type of stack fitting on permissible

simultaneous rates of flow computed for junction of 3-in. drainage stack and horizontal branches.

Based on data from 3-ln. simulated stack. eq (66), sanitary-tee fitting, (/!2— /!i) = 0.75Z>2. eq (68), long-turn T-Y fitting, (hi-hi) = l.%Di.

0 20 40 60 80 100 120 FLOW IN STACK ABOVE BRANCH. gpm Figure 36. Apparent effect of test system on permissible

simultaneous rates of flow at junction of 3-in. drainage

stack and horizontal branches, sanitary-tee fittings.

(/!2-/!l)=0.75X)2.eq (66), from tests on simulated staoli. eq (70), from tests on prototypal stacli.

ligure 35 gives a comparison of carrying capacities using sanitary-tee stack fittings and longturn T-Y fittings, computed from eqs (66) and

(68), respectively, based on tests on the simulated

stack. It is evident that the greater capacities are obtained by the use of the long-turn T-Y

fitting.

Figure 36 gives a comparison of carrying capacities based on tests on the simulated stack and on

the prototypal stack using sanitary-tee stack

fittings, computed from eqs (66) and (70), respectively. The two curves for each diameter of

branch coincide at intermediate capacities, and

do not differ greatly anywhere in the range covered

in figure 36. A slight difference in the curves computed by the two methods is to be expected,

since, in the prototypal stack, appreciable quantities of air were entrained in the water and not all of the water flowed in a layer on the wall of the

stack. Other variables not taken into account in

the investigation reported here may have contributed to the slight difference in results obtained

in the two cases. However, it appears that the

fundamental phenomena are quite similar in the

two cases. The fact which is most evident from figures 33

to 36 is that the occurrence of appreciable discharge

in the stack simultaneously with discharge in the

horizontal branches will reduce the capacities of

the branches. This effect is greatest for the case r in which sanitary-tee fittings are used to connect

the stack and the branches.

6.2. Loads on Drainage Stacks

Figure 37 will be introduced at this point in

order to provide a method for estimating peak

discharge for design purposes. The concepts on which this figure is based are given elsewhere

[15, 16] ; hence, they will not be discussed in detail

here. The design fiow as represented by curve

1 of figure 37 is based on the theory of probability.

It takes into account for each type of fixture the

average time between uses during periods of heavy

use, the length of time required for one typical

operation, the average rate of discharge from the

fixture, and the number of fixtures on the system

under consideration. For fixture-unit loads up

to 4,800, the curve has been computed from tables

of the cumulative binomial probability distri- bution. That portion of the curve beyond 4,800

fixture units has been computed from Poisson's

approximation to the binomial distribution. Curve

2 of figure 37 represents the average discharge

from a system of water closets, each of which

discharges 4 gal of water once in 5 min. The

ordinates of curve 3 were obtained by addition of

the ordinates of curves 1 and 2 for each abscissa

value.

The fiow capacities of drainage stacks given by

Dawson and Kalinske [6] were computed by them

on the assumption that the stacks flowed }i full. It will be observed in figure 38 that their recom- mended values he very close to the computed curve

for rs=/^. The reason for this is that Dawson

and Kalinske assumed higher terminal velocities

in developing their equation for flow capacity than

have been assumed in developing eq (53) of this paper. For comparison, flow capacities derived

from table S05(b)-III of BMS66 [17] and figure 37

32
of this paper are also shown in figure 38, these capacities having been obtained by determining from

curve 1 of figure 37 of this paper the design dis- charges for stacks 6 in. and less in diameter, and by

determining from curve 3 the design discharges for stacks 8 in. and more in diameter.

Figme 39 has been prepared from eq (53) and

cm-ve 1 of figure 37, and shows maximum fixtureunit loadings computed for various diameters of

multistory drainage stacks. The dashed curves

at the right of the figure are based on eq (53) and

curve 3 of figm-e 37. The plotted points were taken directly from certain

loading tables which have been widely used [1, 17,

18].Equation (53) should be apphcable to stacks of

height sufficient to produce terminal velocities and,

therefore, can be looked upon as giving hmiting

flow capacities for tall stacks. In practice, loads on relatively short stacks may be limited by the

capacities of the horizontal branches rather than

by a criterion such as eq (53) . The idea of allowing

for stack height in establishing permissible loads is not new [17]. A simphfied method of making al- lowance for stack height is given in section 9.3. of

the appendix.

Table 12 has been prepared from eq (53) and

figure 37. The values in this table are given in

terms of discharge rates and also in terms of fixture

units, for various diameters and relative filling of

stack. Table 12 gives maximum values for tail stacks. It is not intended for use with one- and

two-story stacks.

6.3. Loads on Vent Stacks

Equations (58) and (59) are useful for computing

lengths and diameters of vent pipes required to carry given rates of air flow. Appropriate values

of the friction coefficient should be used in applying

these equations. For any particular pipe, / is an

inverse function of the RejTiolds number and in- creases with roughness of pipe material relative to diameter. Charts showing this effect [9, 19], considered together with eqs (53) and (56), indicate

that values of / applying to vent stacks will vary

inversely to an appreciable extent with diameter of

drainage stack. However, for a given drainage

stack, neither the particular diameter of vent stack

likely to be used nor the particular rate of air flow

within the range rs=0.15 to 0.40 should have a

significant effect on the value of /. Values of / for use with eqs (58) and (59) are given in table 13. In obtaining these values, a value of 0.0010 ft absolute roughness, twice that

given by Rouse [9] for galvanized steel pipe, has

been assumed. This talses into account, to some

extent, the expected effect of corrosion. Each

value of / shown in table 13 is the average of the

two values obtained from the assumption of two

sizes of vent for a particular size of drainage stack,

in one case the vent and the stack being of the same size and in the other case the diameter cf the

vent being one-half that of the stack.

2 4 6 1000 2 4 6 10000 2 FIXTURE UNITS ON SYSTEM

Figure 37. Design-flow curves for plumbing-drainage

systems.

Curve 1 represents the peak discharge into the drainage system which,

according to the theory of probability, will not be exceeded more than 1 per- cent of the time during periods of heaviest use. Curve 2 represents the average discharge into the drainage system during

periods of heaviest use computed from the discharge characteristics of water

closets. Curve 3 has been obtained by adding the ordinates of curves 1 and 2.

6 8 10 STACK DIAMETER, in. Figure 38. Flow capacities of multistory drainage stacks for terminal water velocity. #, values computed by Dawson and Kalinske. 0> values based on eq (53), on maximum fi,xture-unlt loadings from refer- ence 17, and on design-flow rates ftom curves 1 and 3 of figure 37 (curve 1 for diameters of 6 in. or less; curve 3 for diameters of 8, 10, and 12 in.).

Laboratory experiments on simplified test systems have yielded results indicating that

eq (56) is useful for estimating an upper limit to the total volume rate of air flow into or oat of the

33
4 I \ I I 1 1 I 2 4 6 8 iO 12 14 STACK DIAMETER, in Figure 39. Maximum fixture-unit loadings on multistory

drainage stacks. Curves 1, 2, and 3 are based on eq (53) and on curve 1 of figure 37. Curves 4 and 5 are based on eq (53) and on curve 3 of figure 37. O. values from reference 17. 9, values from references 1 and 18.

system. However, the use of eq (56) to predict

the flow of ah' through a typical vent stack at any

particular point probably would result in an

overestimate of the air demand. There are three reasons for this: (1) Some air is normally delivered to the system through the stack-vent as well as through the vent stack. (2) Kecirculation

of air within the main and branch vents and

drains tends to reduce the quantity of air which

must be moved through the vent stack at any

single point. (3) Some air is ordinarily carried

out of the system through the building drain and

building sewer, thus reducing the quantity of air which must be relieved in areas of positive

pressure near the base of the drainage stack.

Data obtained by Dawson and Kalinske [5] for

3-, 4-, and 6-in. drainage stacks and those of

table 9 of this paper for a 3-in. stack give maximum

air demand, exclusive of air flow through the

stack-vent, of the order of 50 to 75 percent of the

hypothetical maximum. For these reasons, values

computed from eq (56) have been reduced by ji in developing table 14. This is equivalent to the use of eq (55) with the mean velocities of the air core and water stream being the same. The

permissible lengths of vent pipe given in this

table have been computed from eq (59) . Equation

(59) has been used instead of the more accurate

eq (58) because it is simpler to apply and because

the errors resulting from its use are not of serious

importance in most instances with which this

Table 12. Maximum loads on multistory drainage

stacks "

stack diameter

Proportion

of cross section occupied by falling

' water

Water

discharge

rate Equivalent

load

in. gpm Fixture units

3 0. 15 22

3 .20 35.6 21

3 .25 51.6 53

3 .29 66.8 100 3 30 70 110 3 .33 83.

4

160

4 .15 47.5 43

4 .20 76.7 140

4 .25 111 320

4 .29 144 530

4 .30 151 580

4 .33 180 850

5 .15 86.1 ISO

5 .20 139 490

5 .25 202 940

5 .29 261 1400

5 .30 273 1500

5 .33 326 2000 6^ .15 140 500

6 1 .20 226 1100

6 .25 328 2000

6 .29 424 2900

6 .30 444 3100

6 . 33 529 3800

8 .15 301 1800

8 .20 487 3400

8 .25 706 6600

8 .29 913 7600

8 .30 957 7800 8 . 33 1140 9800

10 .15 546 4000

10 .20 883 7200

10 .25 1280 11000

10 .29 1660 15000

10 .30 1730 16000

10 33 2070 19000

12 .15 889 7300

12 .20 1440 13000

12 .25 2080 20000

12 .29 2690 26000

12 .30 2820 27000

12 .33 3360 34000

15 .15 1610 15000

15 .20 2600 25000

15 .25 3770 38000

15 .29 4880 50000

15 .30 5110 53000

15 .33 6100 64000

» Loads'given are upper limits computed for terminal-velocity conditions

in tall stacks, and for conditions under which stack is not overloaded within any single-branch interval as determined by the criterion given in section 9.3. of the appendix.

Table 13. Values of the friction coefficient f for use in computing maximum permissible lengths of vent stacks

Diameter

of drainage

stack

f »

in.3 0. 0367

4 .0330

5 .0307

6 .0286

8 .0260

10 .0242

12 .0230

15 .0214

" Computed by averaging values obtained (for stacks flowing ]4 full in accordance with eqs (53) and (55) wherein ValVw=1.0 in eq (55)) with

I>B=0.5Z)i, and Dv = 1.0Dt. A value of t«=0.001 ft has been assumed, this being twice the value given by Rouse [9] for new galvanized-iron pipe. 34
16-in. vent iggils

14-in. vont

12-in. vent iiiSiS

10-in. vont

8-in. VOTlt iSiisS

1

1

0-in. VOTlt «,

1,

000 775 655 595 590 666

5-in. vent

{ 4-in. vent SiiiSi

1

11

iiiiii

3-m. vent iiiils

2-in. vent

m

Fixture

21 53

100 110 160 -Siiii 190 490 940

1,400 1,

500 2,000 500 1,

100 2,

000 2,

900 3,

100

3,800 1,

800 3,400

5,600 7,600 7,900 9,800 iiiiii 7,

300

13,

000

20,

000

26,

000

27,

000

34,

000 iiiiii

Air

discharge rate & iiiiii IliisS 793 904 984

1,030 1,040 1,060 1,

710

1,960 2,

120 2,

220 2,230

2,280 3,

100

3,530 3,

840 4,

020 4,050 4,

140 Siiiii

Water

discharge rate

qpm

22.0 35.6 61.6 66.8 70.0 83.4 ^^33s§ smis iigesi iiiiii iiiiii

Ii 111

c5

neter

of

drainage

stacli

CO 00 o JO

5

35
Table 15. Equivalent lengths of vent -pipe due to entrance conditions

Equivalent lengths =

age-stack diameter Any

diameter

of vent

1' fin. vent

2-in, vent

2' 2-in. vent

3-in. vent

31 2-in. vent

4-in. vent

5-in. vent6-in. vent8-in. vent

lO-in. vent

12-in. vent14-in. vent

16-in. vent

pipe

if in. diO/TTl ft if if if if if if if Jt

if Jt ft ft 3 40.9 5 7 8 10 4 45.4 8 9 12 13 15

5 48.9 10 13 14 16 21 6 52.5 13 15 18 22 26

8 57.7 19 24 29 38

10 62.1 26 31 41 52

12 65.3 33 43 64 65

15 70.1 47 68 70 77 88

a These values have been computed from the second term of the right-hand member of eq (58). A value of Cl=1.5 and table 13 values of f have been used. A sharp-corner exit into an infinite reservoir has been assumed. The value Cl=1.6 includes the head loss due to a sharp-corner entrance from an infinite reser- voir and the head loss due to acceleration of the air from rest.

Table 16. Factors for computing equivalent lengths of vent stacks due to various fittings and changes in cross section

Factor, 0 » Drainage-stack diameter

VA-in. 2-in. 2M-ia. 3-in. 3Jfin. 4-in. 5-in. 6-in. 8-in. 10-in. 12-in. 14-in. 16-in. vent vent vent vent vent vent vent vent vent vent vent vent vent

in. ft ft ft ft ft ft ft ft ft ft ft ft ft 3 3. 66 4.69 5. 61 6. 96

4 5. 22 6.23 7. 75 8. 96 10.2

5 6.70 8. 33 9.63 10.9 13.7

6 8. 94 10.3 11.7 14.7 17.8

8 12.9 16.2 19.4 25.6

10 17.4 20.9 27.5 34.5

12 22.0 28.9 36.3 43.5

15 31.1 39.0 46.7 61.1 58.4

of/.

' Equivalent length (in feet) is computed from the equation L,=0ClValues of Cl applicable to various fittings and changes in cross section are given in figure 40. The values of 0 given in this table are based on table 13 values

paper is concerned. Dawson and Kalinske [6] give an equation of the same form as eq (59) for use in sizing vent stacks. Strictly speaking,

formulas such as eqs (58) and (59) should be

applied only to the flow of incompressible fluids. However, with very little error, they may be applied

to the case of air flow at a pressure drop of 1 in. of water column. The fixture-unit loads in

table 14 have been derived from eq (53) and

figure 37. The values given in table 14 vary in a reasonable manner with air and water flow. The permissible

lengths of vent computed by one authority [6] are somewhat less than those given in table 14, but

those given by certain other authorities [1, 17, 18]

agree well with table 14. Although eq (59) is sufficiently accurate for use where pipe-friction losses are large in relation to other types of losses, special situations may arise

in which it will be desirable to make allowauce

for losses such as those due to entrance conditions,

changes in cross section and direction of flow,

and presence of fittings. Such an allowance might

be desirable in the case of a relatively short pipe

carrjdng a large rate of flow. Table 15 computed

from eq (58), gives equivalent lengths of pipe

which should be subtracted from the vent lengths

given in table 14 in order to take into account

entrance conditions associated with a sharpcorner entrance from an infinite reservoir.

Approximate allowance for the losses due to various fittings can be made by considering the

resistance offered by a fitting as equivalent to that produced by a certain length of pipe of the same diameter as the fitting. The equivalent

length depends on the loss coefficient for the

fitting, the pipe diameter, and roughness of pipe

material. Figure 40 gives values of Cl applicable

to several types of fittings. Equivalent lengths

may be computed from the values of Cl given in

figure 40 and the values of /3 listed in table 16

where

Le=^CL. (65)

Some handbooks list equivalent lengths of vari- ous fittings directly in feet.

6.4. Comparison of Loads Given by Plumbing

Codes with Computed Values for Drainage

and Vent Stacks

Permissible loadings for multistory drainage

stacks and vent stacks given by three well-known

sources [1, 17, 18] are in fair agreement with

values computed by methods described in some

detail in this paper.

The basic concepts of fluid flow in drainage and

vent stacks discussed by Dawson and Kalinske

[5, 6] are reasonably consistent with those on which

36
C, =0.1 0.5

V

C, -0.2

80RDA ENTRANCE SHARP-CORNER

ENTRANCE SLIGHTLY-ROUNDEDENTRANCE

D d

I

d/D Cl

0.5 0.56

.6 .41 .7 .26

.8 . 13

. 9 .05

d/D Cl

0.5 0.33

.6 .28

.7 .22

.8 . 13 .9 .06

ABRUPT ENLARGEMENT ABRUPT CONTRACTION

STD.TEE, END TO END

V -A C, = 1 .8 STD.TEE, END TO SIDE STD.TEE, SIDE TO END, OR SIDE TO END DIVIDED FLOW

» V V

STD. TEE,

SIDE REDUCTION

'0.4

STD. 90° ELBOW, OR STD. 45 ELBOW

END OF TEE REDUCED 1/2 Cl =0.75

MEDIUM SWEEP ELBOW, OR

END OF TEE REDUCED l/4

Figure 40. Some commonly used head-loss coefficients for flow through pipe fittings and transitions in cross section.

1000

G-in. VENT

4-in. VENT

3 -in. VEN

0 500 1000 1500 2000 2500 3000 3500 4000 LOAD ON SYSTEM , FIXTURE UNITS

FiGUBE 41. Comparison of maximum lengths of vent stacks for 6-in. drainage stack. Curves represent computed values taken from table 14. O, values from references 1 and 18. values from reference 17.

this paper is based, but tKe manner in which the

probability of simultaneous discharge of plumbing

fixtures was taken into account by Dawson and

Kahnske resulted in permissible fLxture-imit loadings which are much less for large diameters than

those obtained from the three other sources mentioned above. In what follows, references 1, 17, and 18 will be referred to as the model codes. The comparison, for maximum loadings on multistory drainage stacks, between values taken

directly from the loading tables of the model codes

and values computed by methods given in this paper was shown in figure 39. Figure 41 shows a

similar comparison of maximum lengths of vent

stacks for a 6-in. drainage stack.

Based on figures 39 and 41, on other figures

(not shown) similar to figure 41 (these being for

drainage-stack diameters other than 6 in.), and

on a detailed study of the loading tables in six municipal plumbing codes selected at random

(three adopted before 1951 and three later), the

following observations have been made

a. Loading Tables for Drainage Stacks

1. Some municipal codes permit as much as

nine times the fixture-unit loadings for drainage

stacks permitted by other mimicipal codes.

2. The two municipal codes agreeing most

closely with the model codes on the matter of

maximum loads permitted on drainage stacks were adopted after 1953. The more liberal of these

gives values agreeing quite well with the sohd

computed curve for rs=)^ in figure 39; and, for

stack diameters of 8, 10, and 12 in., it gives values

greater than do any of the other codes analyzed in

this investigation. Some municipal codes give

fixture-unit values ranging down to as little as of

those computed for rs= }{. 3. In general, the municipal codes adopted since

the Eeport of the Coordinating Committee for a National Plumbing Code was issued (1951) permit

greater loads on multistory drainage stacks than

do the older municipal codes.

4. The model codes give values, for maximum

loadings on multistory stacks of 6-in. diameter and

less, which fall between the values computed for

rs=K and rs='% (solid curves, fig. 39). For larger

diameters, the values given by the model codes

are less than those represented by the solid curve

for rs=yi.

37
b. Loading Tables for Vent Stacks

1. Of the six municipal Codes anatyzed in detail,

two of those adopted before 1951 and one of those

adopted later give maximum lengths of vent stacks

unaffected by diameter of drainage stack or by

different loadings on a given diameter of drainage

stack. Hence, these codes cannot be expected to give values agreeing with those computed by the

method given in this paper in which both stack

diameter and drainage load are taken into account. In some cases, the values given by these codes are

gi-eater, and in some cases less, than the computed

values or values taken from the model codes.

2. Of the three remaining municipal codes analyzed, one gives values for maximum lengths of

vent stacks agreeing fairly well with the computed

values, one gives values for the larger diameters of

drainage stacks and vents which are generally less

than the computed values, and one gives values j which are less than the computed values for most

diameters of drainage stacks and vents.

3. All three of the model codes give values for

maximum lengths of vent stacks which agree fairly

well with the values computed in this paper. Such - deviations as do exist do not appear to follow any 'l consistent trend. Of the three model codes, ' BMS66 [17] gives values agreeing most closely ^ with the computed values. ^ 4. It is evident from a study of the venting

tables of a number of plumbing codes that there

is great diversity in the loading ranges covered.

It is difficult to compare fairly the requirements

of the different codes, since in maldng such a comparison it becomes necessary, in the case of f certain codes, to estimate the maximum lengths

of vents for loadings outside the ranges given in

the tables.

7. Conclusions

7.1. Interference of Flows at Junction of

Drainage Stack and Horizontal Branches

Section 6.1 of this paper gives a method for estimating the maximum permissible rate of flow

in a horizontal branch for any given rate of flow

in a drainage stack (or vice-versa) when the two

flows occur simultaneously. The experimental

work on which the equations are based has been

carried out on 3-in. drainage stacks only. The

application of the method is through the use of

eqs (66), (68), and (70).

The hydrodynamic head created at the junction

of a drainage stack and a horizontal branch when

flow occurs simultaneously in both components

of the system should be limited to a value which

will not cause water to back up into drainage

or vent pipes connecting to the horizontal branch.

This criterion should be taken into account in

computing loads for multistory drainage stacks.

Its importance in relation to other criteria can be determined only through further study and

research.

7.2. Flow Capacities of Drainage Stacks

Flow capacities of multistory drainage stacks

may be computed from eq (53) for various

degrees of filling. Research has indicated that

stacks should not be loaded so heavily that they

flow more than ji to % full at terminal velocity.

Equation (53) is intended as an upper limit to flow capacity where stack height is sufficient to insure that stack capacity wfll not be governed

by the capacities of the horizontal branches or by the capacities of the fittings at the junctions

between the stack and the horizontal branches.

7.3. Air Flow in Drainage Systems

The maximum flow of air which could reasonably

be expected to be carried down a drainage stack

may be computed from eq (56) for various degrees

of filling of the stack. However, for several reasons (see section 6.3), the use of eq (56) will give fiow rates larger than are likely to occur anywhere in a vent stack. Therefore, it has been

assumed in this paper that the maximmn rate

of air flow to be carried by a vent stack wfll be

% of that computed from eq (56).

The vent stack should be so sized that pneumatic

pressures anywhere within it, or within fixtiu"e drains or horizontal branches which it vents, will not differ from atmospheric by an amount great

enough to destroy the water seals in fixture traps.

Equations (58) and (59) may be used to compute

vent-stack diameters or lengths for a pressure

drop of 1-in. water column and for any given

fiow of air. A phenomenon which has not been studied in

much detail is that which governs the mutual

interference of streams of air and water at the

juntion of a drainage stack and a vent pipe.

Although measurements have been made which

show a pressure drop across the layer of water on the wall of the drainage stack, it is not immediately apparent whether this fact is significant

from the practical standpoint. The protection

of trap seals against pneumatic-pressure fluctuations depends generally on the existence of

pneumatic pressures near atmospheric within

horizontal branches and fixture drains, rather

than within the drainage stack itself. Nevertheless, the phenomenon should be recognized in

order to attain a better xmderstanding of the

flow of air and water in building-drainage and

venting systems.

7.4. Loading Tables

Table 12 gives upper limits for loads on tall multistory soil and waste stacks. The values

38
in table 12 were computed from eq (53) and curve

1 of figure 37. A method for computing permissible loads for stacks of low or moderate

height is given in section 9.3 of the appendix.

Table 14 gives maximum permissible length of

vent stacks for soU and waste systems. The

length values in table 14 were computed from

eq (59), wherein is taken as % of the value

computed from eq (56).

7.5. Miscellaneous Phenomena

a. Distribution of Air and Water in Cross Section of Drainage Stack

The assumption of an annular layer of water

flov\"ing down the wall of a drainage stack, and

of a central core of air carried along by the water,

represents an ideal condition which is probably not

fully attained in many practical situations.

However, in spite of this, the concept is useful

in estimating maximum values for air and water

flow in drainage stacks.

b. Velocity Distribution of Water in Cross Section of Drainage Stack

Available data on water velocities in drainage

stacks indicate that the velocity gradient is very

steep close to the wall of the stack, becoming less steep with distance away from the wall. In a

stack having branch connections at each floor

level, droplets and small masses of water may fall at relatively high velocities in the central area of

the cross section of the stack.

c. Pneumatic Pressures within Drainage Stack

The flow of water in a drainage stack may cause pneumatic pressure changes of sufficient magnitude to destroy the water seals of fixture traps not

protected by a venting system. Adequate venting

will prevent the occurrence of excessive pressure

fluctuations within horizontal branches and fixture

drains. Fluctuations of appreciable magnitude

may still develop within the drainage stack between floor levels but these do not affect trap

seals adversely. Least pressures occur immediately below a point of water entrance, and greatest pressures occur near the base of the stack. The

pressure at any point is a function of rate of

discharge, elevation of point of water entrance,

degree of venting, and geometry of the system.

7.6. Need for Further Research

a. Design- Flow Problems

Earlier in this paper it was pointed out that

loading tables for plumbing codes must be based

not only on the flow capacities of the component

parts of the plumbing system but also on the

design flow. The design flow is that rate of flow

which is estimated to occur sufficiently often to cause unsatisfactory performance if not adequately

provided for in the design of the system. For

systems serving more than a very limited number

of fixtures, this requires a systematic method of

computing the maximum rate of simultaneous

dischai'ge from a given group of fixtures which, over

a long period of time, will not be exceeded except

for a specified small fraction of the time during

periods of heavy use. The design flow is often

estimated by a method based on the theory of

probability. Such a method is represented by

curve 1 of figure 37, part of which was developed

earher by Hunter [15]. A discussion of Hunter's

procedure was presented by Eaton and French [16]. For some time it has been known that, for relatively large systems, this method of computing

design flow yields rates appreciably smaller than

those obtained by certain other methods which

have been used. Other factors being equal,

computed pipe sizes would be smaller, and this

is in the interest of economy. Field evidence has

pointed to the possibility that design flows

obtained by Hunter's method may, nevertheless,

be greater than flows actually occurring in systems

of moderate size, such as those in apartment

bufldings. The opinion is sometimes expressed

by plumbing officials and design engineers that

flow estimates obtained by Hunter's method may

be unrealistic for systems, or branches of systems,

comprising a small number of fixtures. In fair- ness to Hunter, it should be remembered that he

pointed out that his method is most applicable to large systems. For these reasons, and because

the data on which some of the computations made

by Hunter were based are now thought to be

obsolete or incomplete, there appears to be a need

for further study of this problem, from both a

theoretical and a practical standpoint, including an

analysis of continuous records of flow in existing

plumbing systems.

A method for estimating the simultaneous flows

likely to be discharged from two separate groups

of plumbing fixtures is needed. This problem

must be solved before the results of hydraulic

studies of flow interference at stack-branch

junctions can be fuUy utihzed by the writers of

plumbing codes.

b. Flow-Capacity Problems

Although much of the difference in loadingtable values in various plumbing codes may be the

result of the different ways in which the designflow problem is treated, at least a part of the

difference in table values is caused by the different

flow capacities assumed. Applications of research

in this field have relied to a considerable extent on extrapolation of data from limited tests. The

use of design criteria based on steady, uniform

flow appears to be inconsistent with the occurrence

of surging flow in some parts of the plumbing

system. Knowledge of flow capacities should be

augmented through careful research on several

problems, as follows;

(1) Flow of Air in Venting Systems

Further investigation of air flow in venting

39
systems is required in order to obtain information on the flow and recirculation of air in complex

venting systems. So far, most investigations

have been made on relatively simple systems, and

the application of the results of such investigations may be unrealistic with respect to more

complex systems. It appears likely that certain

economies in pipe sizing could be effected, if the

proper allowances for recirculation of air and. for height of fall of water in complex venting systems

could be made.

(2) Interference of Flows at Stack-Branch Junctions The investigation of flow interference at stackbranch junctions reported in this paper shows a method that can be used to study the problem.

Numerical results have been obtained for certain

conditions. Data are needed for stacks of several

diameters and for forms of construction not used

in the investigation reported.

(3) Velocity Distribution of Water, and Air-Water Distribution in Cross Section of Drainage Staclc Velocity distribution and air-water distribution

affect the flow of air carried down the drainage

stack, the head of water created in horizontal

branches as a result of mutual interference of

simultaneous flows, and the flow capacity of the

drainage stack. A more complete and accurate

knowledge of velocity distribution and air-water

distribution than that obtained so far is required

before desirable refinements can be introduced

into the analysis of certain flow problems.

(4) Detergent Foam in Plumbing Systems

Another factor which may affect flow capacities

of drainage and vent pipes under certain circumstances is the use of synthetic detergents, which

are now being used in large quantities. Plumbing

inspectors report that foam is sometimes forced

back past trap seals of lower-floor sinks and other

fixtures. They attribute this to the use of synthetic detergents in kitchen and laundry equipment and report that the occurrence is becoming

increasingly commonplace in apartment buildings.

The problem has been recognized in Great Britain, as well as in this country. Wise and Croft [20]

report tests in which they observed that detergent

foam increased pressures at the base of a drainage stack. This phenomenon should be taken

into account in the design of drainage and venting systems in which detergents are likely to be

used in a way that may cause frequent trouble.

It is unhkely that the detergent-foam problem

and its effects on system design can be fully understood until further research is conducted under

controlled conditions.

Aclcnowledgment is made to the Housing and

Home Finance Agency for its support of some

of the experimental work reported herein, and to a number of people who made significant contributions to the success of the investigation, and

to the usefulness of the paper. John L. French,

Anthony L. Lembeck, Otto Hintz, and Douglas

E. Gaasterland of the staff of the National Bureau

of Standards assisted the authors in planning and

conducting the experiments and in compiling and

analyzing data. Miss Theodora C. Bailey, of the

NBS staff, was in charge of editorial work relating

to the preparation of the paper. Vincent T.

Manas, Executive Secretary of the Coordinating

Committee for a National Plumbing Code, gave

technical advice to the authors with reference to planning the investigation.

8. References

[1] American standard national plumbing code, ASA

A40.8-1955, American Society of Mechanical

Engineers, New York, N.Y.

[2] Recommended minimum requirements for plumbing

in dwellings and similar buildings. Final Report of the Subcommittee on Plumbing of the Building

Code Committee, U.S. Department of Commerce,

Elimination of Waste Series, BH2 (1924).

[3] Recommended minimum requirements for plumbing,

Report of the Subcommittee on Plumbing of the

Building Code Committee, U.S. Department of Commerce, Elimination of Waste Series, BH13

(1932).

[4] Roy B. Hunter, Gene E. Golden, and Herbert N.

Eaton, Cross-connections in plumbing systems,

J. Research NBS 20, 479, RP1086 (1938).

[5] F. M. Dawson and A. A. Kalinske, Report on hydraulics and pneumatics of plumbing drainage

systems—I, University of Iowa Studies in Engineering, Bulletin 10 (1937).

[6] F. M. Dawson and A. A. Kalinske, Report on the

hydraulics and pneumatics of the plumbing drain- age system. Technical Bulletin 2 of the National

Association of Master Plumbers of the United

States, Inc. (1939).

[7] Harold E. Babbitt, Tests on the hydraulics and

pneumatics of house plumbing, Engineering Experiment Station Bulletin No. 143, University of

Illinois, Vol. XXI, No. 47 (1924).

[8] Harold E. Babbitt, Tests on the hydraulics and

pneumatics of house plumbing, pt II, Engineering

Experiment Station Bulletin No. 178, University

of lUinois (1928).

[9] Hunter Rouse, Elementary mechanics of fluids, John

Wiley & Sons, Inc., New York, N.Y. (1946).

[10] Robert S. Wyly and Herbert N. Eaton, Capacities of plumbing stacks in buildings, NBS Building

Materials and Structures Report BMS132 (1952).

[11] K. H. Beij, Pressure losses for fluid flow in 90° pipe

bends, J. Research NBS 21, RPlllO (1938).

[12] Garbis H. Keulegan, Laws of turbulent flow in open

channels, J. Research NBS 21, 707, RP1151 (1938).

[13] Roy B. Hunter, unpublished manuscript. National Bureau of Standards.

[14] Robert E. Horton, Some better Kutter's formula

coefficients. Eng. News, Feb. 24, May 4, 1916.

[15] Roy B. Hunter, Methods of estimating loads in plumbing systems, NBS Building Materials and

Structures Report BMS65 (1940).

40
[16] Herbert N. Eaton and John L. French, Fixture unit

ratings as used in plumbing system design, Housing

Research Paper 15, Housing and Home Finance

Agency (1951).

[17] Plumbing manual, NBS Building Materials and

Structures Report BMS66, Report of the Subcommittee on Plumbing of the Central Housing

Committee on Research, Design, and Construction

(1940).

[18] Report of the Coordinating Committee for a National

Plumbing Code, U.S. Department of Commerce and

Housing and Home Finance Agency, Domestic

Commerce Series No. 28 (1951).

[19] Heating ventilating air conditioning guide, Vol. 38, American Society of Heating, Refrigerating, and

Air Conditioning Engineers, New York, N.Y.

(1960).

[20] A.F.E. Wise and J. Croft, Investigation of single- stack drainage for multi-storey flats, paper pre- sented to the Royal Sanitary Institute, London

England (1954).

9. Appendix

9.1. Individual IVIeasurements Relating to

Interference of Flows at Junction of Simulated Stack and Horizontal Branches

Tables 6 and 7 show the range covered by certain

measurements of flow conditions in the simulated

stacls. The individual measurements are hsted

in tables A-1 and A-2. The values of

shown in column 6 of table A-1 and in column 7 of table A-2 were computed by adding to the

observed depths of water above the branch invert

(at a distance of 4 branch diameters from the

stacli) the corrections for elevation listed in table

A-3, and by subtracting the pneumatic-pressure

head in the staclr. This fixed the reference level

for elevation at the intersection of the inner

circumference of the stack and the center line of

the passageway through the fitting.

9.2. Computation of the Absolute Roughness, fes, for Cast-Iron Soil Pipe

This section gives the method by which data on

friction losses in cast-iron Soil pipe have been used

to compute an equivalent value of the absolute

roughness for such pipe. The discussion begins

with the presentation of data on friction losses obtained by Hunter [13]. From a 1948 xmpubhshed paper "Friction losses in short pipes and culverts," by Garbis H. Keulegan,

V8^=4.75-2.5 {IcIR)

+5.75 (l+^,/i2)Mogio {l+R/k;}. (A-1)

As kJR is very small,

V8/f=4.75 +5.75 logio (R/h), (A-2)

approximately.

Next, the data in the last two columns of table

A-4 were plotted, and a curve faired through the

points. The curve was then extended to the

point logio R=0, corresponding to R=l in. This

procedure j^i elded a value of approximately 16.24

for -Jsjf corresponding to logio R=0. The values

i?=1.0 and V8//= 16.24 were substituted in eq

(A-2), from which

logio (^)=2.00,

and

A:s=0.010 in., or 0.00083 ft.

9.3. Effect of Drainage- Stack Height on

Permissible Loads

Many plumbing codes include a table which

gives permissible maximum loads on drainage

stacks, the same limits applying irrespective of

stack height. In practice, code-imposed limitations on the loads for the various horizontal

branches and branch intervals of the stack tend

to govern the loads actually placed on short stacks.

If stack height is not taken into account in computing permissible maximum loads, a set of

values may be obtained which is uneconomical

for tall stacks. Such load limits are particularly

applicable to stacks having only one or two branch

intervals.

There are two extreme conditions which should

govern permissible loads on stacks. The first condition is represented by a stack, of one or two

branch intervals, for which the permissible load

may be governed by the limits for single horizontal

branches. The second condition is represented

by a tall stack having a number of horizontal

branches. A greater total load on a stack of a given diameter is justified under the second condition than under the first. A method which

takes stack height into account in assigning permissible stack loads is especially applicable to stacks having three or more branch intervals and

to systems with relatively small horizontal

branches.

The method of assigning load limits on drainage

stacks according to stack height, which is briefly

outlined below, is similar to the method given in

BMS 66 [17]. The following terminology will be

employed

7i=the number of branch intervals

5=permissible fixture-unit load on a single

horizontal branch of diameter equal to the stack

41
Table A-1. Data on interference of Hows at junction of 3-in. simulated stack and horizontal branches, sanitary-tee drainage

fittings, pneumatic pressure {hi) in stack —0.3 in.^

1 2 3 4 5 6 7 8 9 10 11

Tbickness of Ratio of stack Branch water layer » Rate of velocity » to Number of Head loss in Rate of flow Stack pa- Branch pa- diameter on wall of flow » in computed branches' branch in each rameter rameter Coefficient Test numher

stack stack terminal flowing branch

velocity

1/, T Vt ft 2 —ft 1 X Y Q

gpyji

i. 61 0. 16 40 1. 04 X 2. 57 24.

4

5 6 1. 077 12 95 00

1. 61 . 16 40 1. 04 1 2. 94 32.

3

Arl. Qy 1. 650 11 05 A

1 61 16 40 1. 04 X 3. 12 15.

0

4 fi ^. D 0. 335 24 96 aD

liei !l6 40 l!04 1 3.94 33^2 3.7 lisol 15! 27 8

1.61 .16 40 1.04 2 2. 59 17.4 5.6 0. 543 18.05 10

1 61 . 16 40 1. 04 2 3.06 24.

3

4:. i . 897 15 85 XI

1 61 . 16 40 1. 04 2 3. 25 27.

2

t. 0 1 058 15 13 1X^9

1. 61 . 16 54 1 41 X 2. 94 13.

1

y. u 0. 271 18 03 13

1^61 !l6 54 l!41 1 2! 94 17.2 9.0 !468 14! 34 14

1.61 .16 64 1.41 1 4.69 29.8 5.6 .880 14.36 15

1. 61 .16 54 1. 41 X 4. 69 40.

3

fi 0. D 1. 610 10. 33 16

1 61 16 54 1. 41 2 2. 94 15.

1

9 0 0. 361 16 03 1

7

X f 1 61 . 16 54 1* 41 2 3. 94 24.

9

fi 7 D. / . 732 14 08 1 & ilei !l6 54 l!41 2 l!94 7*9 13.6 ;i5o 17] 65 21

1.61 .16 54 1.41 2 3. 00 15.2 8.8 .358 16. 28 22

1 61 .16 54 1. 41 2 3. 75 24.

0

7 n . 714 13 80 9^Zo

1 61 16 54 1. 41 2 4. 56 29 2 0. 0 . 869 14 19 24

1. 61 !l6 80 2. 08 X 4. 44 9.

4

T ^ 1 iO. X . 093 21. 85 29

1.'61 !l6 80 2! 08 1 4^44 14! 6 13.1 !223 15.' 45 30

1.61 .16 80 2.08 1 5.44 12.4 10.7 .131 21.64 31

1. 61 . 16 80 2. 08 X 6. 00 26.

5

Q 7 y. / . 544 12. 82 32

1 61 . 16 80 2. 08 2 3. 25 8.

2

1 7 Q X (. 0 . 096 17. 71 40

1 61 16 80 2. 08 2 4. 56 13.

0

19 7 Xi. / 172 17. 42 41 ilei lie 80 2'. 08 2 5! 54 20] 6 10.5 !356 14] 65 42

1.61 .16 98 2. 55 1 5.44 8.8 16.0 .066 21.89 48

1 61 16 98 2. 55 X 6. 38 17.

4

10.

0

. 221 15. 11 49

1 61 . 16 98 2 55 2 4. 44 8 2 1 Q R xy. 0 . 070 18. 83 53

1 61 16 98 2 55 2 6. 19 13.

8

14 1 . 143 17. 61 54 l.a 56 0! 47 1 2^94 17^9 2.Z !507 19^99 65

1. 61 .35 56 .47 1 3. 00 17.9 2.2 .497 20.43 66

1 61 . 35 56 47 X 3. 56 32 2 1. y 1. 354 13. 90 68

1 61 35 56 47 X 3 69 32 2 1.

0

1. 306 14 50 69

1 Gl 35 56 . 47 2 1. 62 8. 6 4 1 0 212 19. 81 71 liei !35 56 [47 2 l!94 12] 3 sis ;363 17! 80 72

1.61 .35 66 .47 2 2. 94 20.1 2.3 .639 18. 02 73

1. 61 . 35 56 . 47 2 3. 29 24. 2 2 0 . 828 17. 11 74

1 61 35 98 . 82 X 2. 88 8.

1

7 1 . 106 18. 54 90

1 61 35 98 82 X 3 06 8 1 fi 7 100 19. 71 91

1*61 !35 98 .'82 1 i. 44 13^8 4.6 !l99 18] 95 92

1.61 .35 98 .82 1 4. 56 15.2 4.5 .236 18. 02 93

1 fii i. Ox 98 82 X 5 94 20 6 0. 0 . 332 18 46 Oil 1 61 . 35 98 82 X 5 94 23 4 0.

0

. 429 16. 58 95

1 61 35 98 82 2 3 06 8 8 R 7 D. / . 118 ] 4g 101 l!61 !35 98 !82 2 4; 44 15^0 4.6 !236 17] 72 102

1.61 .35 98 .82 2 5. 94 24.8 3.5 .481 15. 76 103

1 fii

. 9^oO 137 1 14 X 4 44 8 4 y. u . 074 18 37 116

1 61 . 35 137 1 14 X 4. 96 11.

4

R 1 0. X . 122 16. 22 117

1 61 . 35 137 1 14 X 5. 96 13 0 fi 7 . 132 17. 64 118

l!61 !35 137 l!l4 1 5. 96 14^4 6.7 !l62 16] 28 119

1. 61 .35 137 1.14 2 4. 44 9.4 9.0 .093 16. 84 126

X. DX 35 137 1 14 2 5 94 13 7 R Q 0. 0 . 147 16 87 127

1. OX . ou 180 1 60 X 5 96 8 1

11 R Xi. 0 051 18 06 142

X. Dl . OO XoU 1 50 X 5 96 Qy. 7( 11 R Xi . D 073 15 73 143

1.61 .35 180 l!50 2 5. 94 9.2 11.7 ;066 ia33 151 1.61 .58 98 0.40 1 2. 07 8.8 4.3 .174 15.17 152

1 fii X. DX . Oo oayo .in X 2 07 R 1 0. X A Q • 147 16 20 153

1 fii X. DX . 58 Ar\

. X 3 13 1 n xo. u 0 Q /. y 334 15 08 154

1 fii X. DX . Oo 98 40 X 3 13 15 0 z. y 334 15. 08 155

1.61 .58 98 !40 4. 44 27! 6 2.0 !798 12] 75 166

1.61 .68 98 .40 1 4. 44 29.8 2.0 .930 11.83 157

1 fii X. DX . 00 Oft yo 40 2 2 69 10 6 0.

0

194 17 11 166

1 fii X. DX . OO yo 40 2 3 44 16 80 fiD 381 15 13 167

1 fii X. DX . 00 100 64 X 4 00 11 fi Xi. 07 0. / 154 13 35 174

:.6i .58 158 !64 1 4! 69 13.4 5.0 !l78 13] 80 175 1.61 .58 158 .64 1 5. 94 19.4 3.9 .295 13. 05 176

1. 61 .58 158 .64 1 6. 12 20.2 3.8 .310 13. 02 177

1.61 .58 158 .64 2 4. 44 11.0 5.2 .127 16. 24 184

1, 61 .58 158 .64 2 5. 94 16.6 3.9 .216 14. 81 185

1.61 .58 203 .82 1 4. 44 8.1 8.6 .059 14.12 190

1.61 1 .58 203 .82 1 4. 50 8.8 8.5 .080 13.43 I 191 See notes at end of table.

42
Table A—1. Data on interference of Hows at junction of S-in. simulated stack and horizontal branches, sanitary-tee drainage

fittings, pneumatic pressure (hi) in stack —0.3 in.''—Continued

1 2 3 4 5 6 7 8 9 10 11

Branch

diameter

Thickness of water layer • on wall of stack

Rate of flow » in stack

Ratio of stack

velocity ^ to computed

terminal

velocity

Number of branches

flowing

Head loss in branch Rate of flow

in each branch

Stack pa- rameter Branch pa- rameter Coefljcient Test number

T Ft hi—hi Q2 X Y C

in.1.61

1.61

1.61

1.61

1.61

in.

0. 58 .58

.58

.58

.58

gpm

203

203

203 252

252

0.82

.82

.82

1.02

1.02

1

12

11

in.

5. 94

5.94

5. 94

5.94

5. 94

gpm

12.2

13.1

11.1 8.1 9.5

6.5

6.5

6.5

10.0

10.0

0.116

.134 .096

.051

.071

13. 81 13.07

14. 86

14. 44

12.79

192

193

201 206 207

1.61

1. 61 2.07

2.07

2. 07

.58

.58

.16 .16 .16

252

252

40

40

40

1.02

1.02

1.04 1.04 1.04

1

1

1

12

7.94

7.94

3. 12

3. 12 1.99

12.4

14.

5

3o!o

30.0

15.1

7.5

7.5 4.6

4.6

7.3

.090

.123 .487

.487

.193

13.96

12. 37

22.68

22.68

25. 11

208

209

220

221 226

2.07

2. 07

2. 07

2. 07

2. 07

.16

.16 .16

.16

.16

40

54

54

54

54

1.04

1.41

1.41

1.41 1.41

2

1

1

11

3.06

3. 37

3. 37

4. 25 4.62

38.5

20 8 20!8

34.1

34.1

4.7

7.8

7.8

6.2

5.7

.818

.217

.217

.462

.425

17.67

22. 91

22. 91 19.34

21.13

228

232

233 234

235

2. 07

2. 07

2. 07

2. 07

2. 07

.16

.16

.16

.16 .16

54

80

80

80

80

1.41

2. 08

2. 08

2. 08

2. 08

2

1

1

1

1

3.93

5.56

5. 56

6. 81

7. 12

30.4

23 0

23! 0 33.6 33.6

6.7

10.4

10.4 8.5

8.1

.397

.161 .161 .280

.268

19. 66 21.60

21.60

19.62

20. 54

239

246 247

248

249

2. 07

2. 07

2. 07

2. 07

2. 07

.16

.16

.16

.16

.16

80

80

80

98

98

2. 08

2. 08

2.08

2. 55

2. 55

2

22

4.34

5.87 6.62

6.31

6. 37

15.8

25.

1

3o!8

19.0

19.0

13.4 9.9

8.8

13.8

13.7

.097

.181 .242

.097

.096

22.52

21.30

20. 45

22. 12

22. 34

251 252

253

258

259

2. 07

2. 07

2. 07

2.07

2.07

.16

.16

.16

.16 .35

98

9898

9856

2. 55

2. 55

2. 55

2. 55 0.47

7.49

7. 49 6.37

8.31

2. 06

24.2

24 2

19! 2 28.9

15.0

11.6

11.6

13.7

10.5 3.3

.132

.132

.098

.170 .184

21.81

21.81 22.16

21.08

25. 88

260

261 264

265 266

2.07

2. 07 2.07

2.07

2. 07

.35

.35 .35

.35

.35

56

56

56

56

56

.47

.47

.47

.47

.47

2. 06

2.69

2. 81 3.19

3. 25

16.3 28 7

28! 7 40.8

40.8

3.3

2.5

2.4

2.1

2.1

.218

.517

.495

.881 .865

24.21

19. 92 20.87

17.30

17.67

267

268

269

270

273

2.07

2.07

2. 07

2. 07 2.07

.35

.35

.35

.35

.35

569898'

98

98

.47

.82

.82

.82 .82

2. 19

4. 06

4. 06

5. 81

5. 81

17.8

20.

4

22! 2 36.6

36.6

3.1

5.1 5.1 3.5

3.5

.244

.173

.205 .389

.389

24.02 20.15

18. 84

18.11

18.11

274

279 280

281 282

2. 07

2. 07

2. 07

2. 07 2.07

.35

.35

.35 .35

.35

98

98

98

98

137

.82

.82

.82

.82

1. 14

6. 56

7. 06

3. 81 4.81

6. 06

56.0

59. 6

19.0 28.2 21.2

3.1 2.9

5.4 4.3

6.6

.807 .849

.160

.279 .125

14.08

14. 38

19. 98

18. 48

19. 33

283

284

286

287 293

2. 07 2.07

2. 07

2. 07

2. 07

.35

.35

.35

.35

.35

137

137

137

137

137

1. 14

1. 14

1. 14 1.14

1.14

6. 31

7.69

7. 81

5. 31

6. 69

24.4

32.3 30.8

17.4 24.5

6.4

5.2

5.1 7.6

6.0

.159

.229

.205 .096

.151

18. 04 17.66

18. 65

19. 72

19. 09

294

295 296

299

300

2. 07

2. 07

2. 07 2.07

2.07

.35

.35

.35 .58

.58

180

180

180

9898

1.50 1.50

1.50

0. 40

.40

7. 81

7. 81 7.99

3. 43

3. 56

20.1 21.4

20.5

24.3

23.8

8.9

8.9

8.7 2.6

2.5

.087 .099

.089

.291 .269

18. 52 17.65

18.67 18.02

19. 05

307 308

313 316

317

2.07

2. 07 2.07

2. 07

2. 07

.58

.58

.58

.58

.58

98

98

98

158

158

.40

.40

.40

.64

.64

4. 31 4.43

2.31

5.81

5.81

49.1 48.8

16.9 24.3 25.7

2.1 2.0

3.9

4.0

4.0

.944

.907 .209

.172

. 192

12. 28

12. 74

16. 10

17. 05

16.31

319

321 326

334 335

2. 07

2. 07

2. 07

2. 07

2. 07

.58

.58 .68

.58

.58

158

158 203

203 203

.64

.64

.82

.82 .82

7.69 7.69

5. 81

5. 81

7. 81

40.6

42.3

15.4

16.7 24.3

3.0 3.0

6.6

6.6

4.9

.362

.393

.069

.081 .128

15. 00

14.49

17. 77

16. 70

16. 85

336

337 350

351 352 See notes at end of table.

43
Table A-1. Data on interference of Hows at junction of 3-in. simulated stack and horizontal branches, sanitary-tee drainage

fittings, -pneumatic pressure (/ii) in stack —O.Sin.^—Continued

1 2 3 4 5 6 7 8 9 10 11

Thickness of Ratio of stack Branch water layer " Rate of velocity » to Number of - Head loss in Rate of flow Stack pa- Branch pa- diameter on wall of flow » in computed branches branch in each rameter rameter Coefiicient Test number

stack stack terminal flowing branch

velocity

Vi

X>2 T Oi Vt hi—hi O1 X Y 0

in. in. gpm in. gpm

2. 07 0. 58 203 0. 82 1 7. 81 25 7 4 9 0. 143 16. 13 353 2.07 58 203 82 2 6.31 18 6 6 1 .093 16 71 356

2. 07 58 252 1! 02 1 7. 81 16 3 7 6 .057 17. 50 368 2.07 58 252 1. 02 7. 81 17. 8 7 6 .068 16 36 369

2. 07 58 252 1. 02 7. 81 17. 4 7 6 . 065 16 65 374

3.07 16 80 2. 08 1 4. 46 52. 13 0 .213 18. 63 381 3.07 16 80 2. 08 1 4. 46 54. 5 13 0 .233 17 87 382

3.07 16 80 2. 08 1 6.46 105. 3 9. 0 .600 15 08 384

3.07 16 80 2. 08 6. 46 128 0 9 0 .887 12. 54 385

3 07 16 98 2 55 6 46 66 0 13 5 . 236 17. 39 400

a' 07 16 98 2. 55 1 6. 46 68 3 13 5 !253 16 91 401

3. 07 16 98 2. 55 1 8. 46 107. g 10 3 .481 15. 29 402

3.07 16 98 2. 55 1 8. 46 110 3 10 3 .6C3 14 98 403 3.07 35 98 0 82 4. 46 80' 0 4 6 .502 15. 17 410 3 07 35 98 82 4. 46 81. 0 4 6 515 15 01 4U

3! 07 35 137 1! 14 1 4. 46 42 0 9. 0 !l38 16. 94 422

3.07 35 137 1. 14 1 4. 46 42. g 9 0 .144 16. 69 423

3. 07 35 137 1 14 1 6. 46 75. 4 6 2 .308 15 49 424 3.07 35 137 1. 14 6. 46 76! 6 6 2 ..318 15. 29 425 3 07 35 137 1. 14 8. 46 148. 5 4 7 . 912 11. 28 426

3! 07 35 137 1. 14 1 8. 46 149. 0 4 7 !918 11. 25 427

3.07 35 180 1. 50 1 6. 46 49. 0 10 7 .130 15. 55 436

3.07 35 180 1. 50 1 6. 46 49 0 10 7 .130 15. 55 437

3.07 35 180 1. 50 8. 46 70. 2 8 2 .204 15. 41 438

3.07 35 180 1. 50 } 8. 46 71 1 8 2 .209 15. 26 439

3. 07 .58 203 0. 82 6. 46 53 1 5 9 . 153 15. 39 400

3.07 58 203 82 6. 46 60 1 5. 9 .196 13. 95 466

3.07 58 203 82 8 46 84 5 4 5 .295 13. 98 467 3.07 .58 203 82 8 46 92 7 4 5 .355 12. 94 468

3.07 .58 252 1 02 7 71 53 4 7 7 .129 14. 00 479 3.07 .58 252 1 02 8 40 47 8 7 0 .094 16. 76 480

0 Above the stack-branch junction. Note: Missing numbers in the series in column 11 represent data obtained for conditions outside the range over which it is reasonable to expect the analysis

in section 4.1. to apply. All data included in the following categories were omitted:

1. Data in which branch velocity was less than half of that required to produce computed steady flow capacity for a full pipe not under external head.

2. Data in which branch discharge for two-branch flow exceeded the criterion for fitting capacity given in section 2.1, wherein the effective stack diameter was assumed to be the computed air-core diameter.

3. Data in which the horizontal momentum iu ono branch exceeded half the momentum in the stack just above the branch.

Table A-2. Data on interference of Hows at junction of 3-in. simulated stack and horizontal branches, long-turn T-Y

drainage fittings

1 2 3 4 5 6 7 8 9 10 11 12

Ratio of Thickness of Rate of stack veloc- Pneumatic Number of Rate of flow Branch water layer » flow " in ity » to pressure » branches Head loss in each Stack Branch Coefficient Test

diameter on wall of stack computed in stack flowing in branch branch parameter parameter number

stack terminal

velocity T hi A2—fii Oj X Y C

V,

in. in. in. in. gpm

1.61 0. 16 40 1.04 -0.3 1 3.64 26.8 4.0 0. 917 11.98 492

1.61 .16 40 1.04 -.3 1 3.64 34.4 4.0 1.511 8. 77 493

1.61 .16 40 1.04 -.3 2 3.64 25.0 4.0 0. 798 12. 92 529

1. 61 .16 40 1.04 -.3 2 4.64 38.9 3.1 1.516 10. 19 530

1.61 .16 40 1.04 -2.0 2 5.22 38.9 2.8 1.348 n.89 541

1. 61 .16 54 1.41 -0.3 3.64 19.2 7.3 0.471 11.50 556

1.61 .16 54 1.41 -.3 3. 64 20.8 7.3 .553 10. 67 557

1. 61 .16 54 1.41 -.3 4.64 25.4 5.7 .646 11.51 558

1.61 .16 54 1.41 -.3 4.64 28.8 5.7 .831 10.11 559

1.61 .16 54 1.41 -.3 6.14 37.4 4.3 1.059 10. 51 660 See notes at end of table.

44
Table A—2. Data on interference of Hows at junction of 3-in. simulated stack and horizontal branches, long-turn T-Y

drainage fittings—Continued

1 2 3 4 5 6 7 8 9 10 11 12

Branch

di&inet6r

Thickness of water layer » on wall of stackRate of flow » in stack

Ratio of stack velocity " to COinputs d

terminal

velocity

Pneumatic

pressure " in stack

Number of branches

flowing Head loss in branch

Rate of flow

in each Stack

jJCLL Oil 11 C LCI Branch CoeflBcient Test

DunilDer

T h2—hi X Y C

in.1.61 1.61

1.61

1.61 1.61

in.

0. 16 .16

.16 .16

.16

gpm

54

5454

54

54

1.41

1.41

1.41

1.41

1.41

in.-0.3 -.3 -.3

-2.0

-2.0

1

1

1

11

in.

6. 14

8. 14

8. 14

5. 96

6.21

gpm

38.4

49.0

50.0 38.4

37.4

4.3 3.2

3.2

4.4

4.3

1.116

1.371 1.428

1.150 1.047

10. 19

10. 66

10. 37

9.82

10.66

561 562 563

571 572

1.61

1. 61 1.61

1.61 1.61

.16

.16 .16

.16 .16

54

5454

54

54

1.41

1.41 1.41

1.41

1.41

-2.0

-2.0 -0.3 -.3

-.3

1

12

2

2

7.96 8.09

3.64

4.64

6. 14

50.0 49.0 21.8

30.9

42.4

3.3 3.3

7.3 5.7

4.3

1.460

1.380 0.607

.957

1.361

10.07

10. 58

10. 20 9.36

8. 98

573 574

579 580

581

1.61

1.61

1.61

1.61

1.61

.16

.16

.16

.16 .16

54

54

54

80

80

1.41 1.14

1.14

2. 08

2.08

-.3

-2.0

-2.0

-0.3 -.3

2

2

2

8-14 4.84

6.59

3.64

3.64

53.6

30.9 42.4

10.7 10.7

3.2

5.5 4.0

15.9

15.9

1.641 0.917

1.268

0. 146 .146

9. 39 9.84 9.84

11.55

11.55

582

587 588 598

599

1.61

1.61

1.61

1.61 1.61

.16

.16

.16

.16 .16

80

8080

80

80

2. 08

2.08

2. 08

2. 08 2.08

-.3

-.3

-.3

-.3

-.3

4.64 4.64

6. 14

6. 14

8. 14

15.2

15.4 23.6

25.0 35.4

12.5

12.5 9.4

9.4

7.1

.231 .238

.422

.473 .716

11.15

11.03 10.26 9.73

9.50

600

601 602

603 604

1.61

1.61 1.61

1.61

1.61

.16

.16 .16

.16 .16

80

80

80

80

80

2.08

2.08

2.08

2.08

2.08

-.3 -.3

-.3

-2.0

-2.0

\

8. 14

9. 14

9. 14 6.22

6.22

37.6

43.3

50.0 21.2

21.8

7.1 6.3

6.3

9.3

9.3

.807 .954

1.272 0.336

.355

8. 93

8. 76 7.37

11.43

11.16

605 606

607

612

613

1. 61 1.61 1.61

1.61

1.61

.16

.16 .16

.16 .16

8080

80

80

80

2. 08

2.08

2.08 2.08

2.08

-2.0

-2.0

-0.3 -.3

-.3

2

2

2

7.59 7.84

3.64

4. 64

6.14

29.5 30.6

11.4 18.2

27.8

7.6 7.4

15.9

12.5 9.4

.533

.555 .166

.332

.585

10. 51

10. 52 10.98

9. 57

8. 81

614

615

626

627 628

1.61

1.61

1.61 1.61

1.61

.16

.16 .16

.16 .16

80

80

80

80

98

2.08

2.08

2.08

2.08

2. 55

-.3

-2.0

-2.0 -2.0

-0.3

22

22

1

8.14

4.96

6.09

8.22 4.64

42.0

18.2 27.8

42.0

10.9

7.1 11.7

9.5

7.1 18.8

1.007

0.310

.590

.998 1119

7. 90 10.27

8. 73 7.99 11.32

629

634

635

636

646

1.61

1.61

1.61

1.61

1.61

.16

.16

.16

.16

.16

98

98

98

98

98

2.55

2.55 2.55

2. 55

2. 55

-.3 -.3

-.3

-.3

-.3

4.64

6. 14 6.14

8. 14 8.14

11.4

17.2

18.8

26.0 28.0

18.8

14.2

14.2

10.7

10.7

.130 .224

.268

.386

.448

10.92

10.45

9. 70 9.87 9.24

647

648

649

650

651

1. 61

1. 61 1.61

1.61

1.61

.16

.16

.16

.16

.16

98

98

98

98

98

2. 55

2. 55

2. 55 2.55 2.55

-.3

-.3

-2.0

-2.0

-2.0

j

9.14

9. 14

6.09

6.34

7. 96

30.8

33.4

17.2 18.8

26.0

9.5

9.5

14.3

13.7 10.9

.483

.567 .226

.259

.395

9.60

8.89 10.36

10. 03 9.64

652

653 662

663 664

1.61

1.61

1. 61 1.61

1. 61

.16

.16 .16 .16

.16

98

98

9898

98

2.55

2. 55

2. 55

2. 55 2.55

-2.0 -2.0

-2.0

-0.3 -.3

2

2

8.22

9.09

9. 22 3.64

4.64

28.0 33.4

30.8

8.0

13.5

10.6 9.6

9.4

23.9

18.8

.443

.571 .478

.082

.183

9.34

8.84

9. 69

11.27 9.54

665 666

667

672

673

1.61

1.61

1.61

1. 61

1. 61

.16

.16 .16

.16

.16

98

98

9898

98

2.55

2. 55 2.55

2.55

2.55

-.3

-.3

-2.0

-2,0 -2.0

2

22

2

2

6.14 8.14

4.84

6. 22

8. 22

21.0

32.1

13.5 21.0

32.1

14.2

10.7

18.0 14.0

10.6

.334

.589

.175 .330

.583

8. 82

8. 13

9. 96

8. 95 8.22

674

675 680

681 682

1. 61

1. 61

1. 61

1. 61

1. 61

.35

.35

.35

.35

.35

56

56

5656

56

0.47

.47

.47

.47

.47

-0.3 -.3

-.3

-.3

-2.0

1

12

2

2

3.39

3.39

3.39

4.64

4. 96

26.6

26.7 25.4

38.3

25.4

2.0

2.0

2.0

l.i

1.4

.970 .978

.885 1.470

0. 605

11.01

10. 96

11.59

10.33

17. 89

683

684

697 698

701

1.61

1. 61

1. 61

1.61 1.61

.35

.35

.35

.35

.35

56

98

9898

98

.47

.82

.82 .82

.82

-2.0 -0.3 -.3

-.3

-.3

2

1

1

1

1

5.09 3.39

3.39

4.64

4. 64

38.3

12.9

12.9

21.0 21.2

1.3

6.1

6.1 4.4

4.4

1,340

0. 228 .228

.442 .450

11.65 10.80

10.80 9.88

9. 79

702

705 706

707

708 See notes at end of table.

45
Table A-2. Data on interference of Hows at junction of 3-in. simulated stack and horizontal branches, long-turn T-Y

drainage fittings—Continued

1 2 3 4 0 6 7 8

Ratio of Thickness of Rate of stack veloc- Pneumatic N.umher of Rate of flow Branch water layer flow ^ in ity » to pressure " branches Head loss in each diameter on wall of stack computed in stack flowing in branch branch

stack terminal

velocity

X>2 T Vi hi O2 V,

in. in. gpm in. in. gpm

1. 61 0. 35 98 0. 82 —0.3 6. 14 30. 7

1. 61 35 98 . 82 —. 3 6. 14 32.

3

1. 61 35 98 . 82 —. 3 7. 64 40. 2 1.61 35 98 .82 -.3 7. 64 44.

1

1. 61 35 98 .82 -2.0 4. 96 21.0

1. 61 35 98 . 82 —2.0 4. 96 21.

2

1. 61 35 98 .82 —2.

0

6. 22 32.

3

1. 61 35 98 . 82 —2.

0

6.34 30.

7

1. 61 35 98 .82 -2.0 7. 72 40.2

1. 61 35 98 .82 -2.0 7. 72 44.1

1. 61 35 98 . 82 —0.3 2 3.39 13.

8

1. 61 35 98 . 82 —. 3 2 4. 64 23.

6

1. 61 35 98 . 82 —. 3 2 6. 14 34.

4

1.61 35 98 .82 -.3 2 7. 64 44.9

1. 61 35 98 .82 -2.0 2 5. 22 23.5

1. 61 35 98 .82 —2.0 2 6. 34 34.

4

1. 61 35 98 . 82 —2.

0

2 7. 69 44. 9

1. 61 35 137 1. 14 —0.3 4. 64 10. 4

1. 61 35 137 1. 14 -.3 } 4. 64 12.2

1. 61 35 137 1. 14 -.3 6. 14 16.3

1. 61 35 137 1. 14 —. 3 6. 14 19.

2

1. 61 35 137 1. 14 —. 3 1 7. 64 24.

0

1. 61 35 137 1. 14 —. 3 7. 64 26.

7

1.61 35 137 1. 14 -2.0 6. 22 16.3

1. 61 35 137 1. 14 -2.0 6. 22 19.2

1. 61 35 137 1. 14 —2. 0 J 7. 72 24.0

I, 01 .35 137 1. 14 —2.

0

1 7. 72 26.

7

1. 61 35 137 1. 14 —0.

3

2 4. 64 13.

2

1.61 35 137 1.14 -.3 2 6. 14 21.0

1.61 35 137 1. 14 -.3 2 7. 64 29.7

1. 61 35 137 1. 14 —2.0 2 6. 34 21.0

1. 61 35 137 1. 14 —2.0 2 7. 59 29.7

1. 61 35 180 1.50 —0.3 5.64 8.8

1. 61 .35 180 1.50 —.3 5. 64 10. 6

1. 61 35 180 1.50 -.3 6. 64 12.4

1. 61 .35 180 1.50 —.3 | 6. 64 13.3

1, 61 .35 180 1. 50 —.3 1 7. 64 15.

4

1. 61 .35 180 1.50 —.3 7.64 16.

4

1. 61 .35 180 1. 50 —2.0 6. 59 10. 6 1.61 . 35 180 1.50 -2.0 1 5. 72 8.8

1, 61 .35 180 1. 50 —2.0 6. 59 13.3

1. 61 !35 180 1.50 —2.0 1 6. 84 12.

4

1. 61 .35 180 1.50 —2.0 7. 59 16.

4

1.61 .35 180 1. 50 —2 0 7. 72 15.4

1.61 .35 180 1.50 -0.3 2 5. 64 10.2

1. 61 .35 180 1.50 —.3 2 6.64 13.4

1. 61 .35 180 1.50 —.3 2 7. 64 16.7

1. 61 '.35 180 1.50 —2.0 2 5. 72 10.2

1.61 .35 180 1. 50 —2.

0

2 6. 72 13.4 1.61 .35 180 1.50 -2.0 2 7. 59 16.7

1. 61 .58 98 0.40 —0.3 , 3. 39 15.0

1. 61 .58 98 .40 —.3 1 3. 39 15.6

1. 61 .58 98 .40 —.3 4. 64 24. 5 1.61 .58 98 . 40 —.3 4. 64 25.8

1.61 .58 98 .40 .3 6. 14 38.4

1.61 .58 98 .40 —.3 1 6.14 38.9

1.61 .58 98 .40 —.3 I 7.64 49.0

1. 61 .58 98 .40 —.3 7. 64 63.

5

1.61 .58 98 .40 —2.

0

4. 96 24.5

1.61 .58 98 .40 -2.0 5. 09 25.8

1.61 .58 98 .40 -2.0 5. 84 38.4

1.61 .58 98 .40 —2.0 6. 09 38.9

1. 61 .58 98 .40 —2.0 7. 44 63.5

1. 61 .58 40 0 n 7. 59 49 0 1.61 .58 98 !40 -0.3 2 3.39 14! 5

1.61 .58 98 .40 -.3 2 4.64 28.0

1.61 .58 98 .40 -.3 2 6.14 41.3

1.61 .58 98 .40 -2.0 2 6. 34 28.0

1.61 .58 98 .40 -2.0 2 6.09 41.3

1.61 .58 158 .64 -0.3 1 4.64 11.7

Stack parameter Branch

parameter

Coefficient

3.3

3.3

2.7 2.7

4.1

4.1 3.3

3.2

2.7

2.7

6.1 4.4

3.3

2.7 3.9

3.2

2.7

6.5

6.5 6.2

5.2

6.4

6.4

5.2

5.2

8.6

6.5 5.2

6.3

5.3

12.3

12.3

10.4

10.4

9.1 9.1 12.4

12.1

10.6

10.1

9.1 9.0

12.3

10.4

9.1 12.1 10.3

9.1

2.6

2.6

1.9

1.9

1.5

1.5 1.2 1.2

1.8

1.8

1.5

1.5 1.2

1.2 2.6

1.9

1.5 1.7

1.5

5.0

0.714

.790 .983

1. 183 0.413

.421 .780

.691 .973

1.171

0. 261 .553 .896

1.227 0.492

1.235

0. 108

. 149 .201

.279

.351 .434 .199

.276

.347 .429

.175

.334

.537

.323 .640 .064

.093

.108

.124

.144

.164

.093 .063

.125

.105

.165

.143

.126

.170

.085

.124

.171

.309 .334

.601 .667 1.116

1.146

1.461 1.742

0. 563

1.174

1.165

1.789

1.471 0.288

.786

1.292 0.683

1.302

0. 137

9.35

8. 87

9. 02

8.08

10. 61

10. 62

9.01

9. 70

9. 13

8. 19

10.21

8. 90

8. 29

7. 90

10. 12

8. 61

7. 84

11. 67

10. 28

10. 85

9. 47

9. 84

8. 95 11.00

9. 60

9. 95

9. 05

9. 65

8. 77

8. 11

9. 07

8. 05

11.52

9. 97 10.41

9. 86

10.11 9.62

9. 88 11.68

9. 77

10. 72

9. 55 10.22

10. 27

9.79

9. 48

10. 42

9. 91

9. 41

11.62 11.24

10.45

9. 93 8.93

8.79

8. 60

7. 55 11.25

11.01

8.39

8.70

7. 27 8.52

11.97

9. 13 8.15

10. 71

8. 06

10.87 See notes at end of table. 46
Table A—2. Data on interference of flowt at junction of 3-in. simulated stack and horizontal branches, long-turn T-Y

drainage ^i^iwgs—Continued

1 o 3 4 5 6 7 8 9 10 11 12

Branch

diameter

Thickness of water layer = on wall of stackRate of flow » in stack

Ratio of stack Telocity • to computed

terminal

Telocity

Pneumatic

pressure " in stack

Number of branches

flowing Head loss in branch

Rate of flow

in each branchStack parameter Branch

parameter

Coefficient Test number

T 0, V,

hi hz—hi O2 X Y C

in.1.61 1.61

1.61

1.61 1.61

1.61

1.61

1.61

1. 61 1.61

1.61

1.61

1.61

1. 61 1.61

1.61

1.61

1.61

1.61

1. 61

1.61

1.61 1.61

1.61

1.61

1.61 1.61

1.61

1.61

1.61

1.61 1.61

1.61

1.61 1.61

1.61 2.07

2.07

2.07

2.07

2.07 2.07

2.07

2.07

2.07

2.07 2.07

2.07

2.07

2. 07

2.07

2.07

2.07

2. 07

2. 07

2.07

2.07

2.07

2. 07

2.07

2.07

2.07

2.07

2.07

in. 0.58

.58

.58

.58

.58

.58

.58

.58 .58

.58

.58

.58 .58

.58 .58

.58

.58

.58

.58 .58

.58 .58

.58

.58

.58

.58 .58

.58

.58

.58

.58

.58 .58

.58

.58

.58

.16 .16

.16

.16

.16

.16

.16

.16 .16

.16

.16 .16

.16

.16

.16 .16

.16

.16

.16

.16

.16

.16

.16

Ifi

.16

.16

.16

.16 .16

gpm

158

158

158

158

158

158

158

158

158

158

158

158

158

158 158

158 203

203

203

203

203

203 203

203

203

203

203

203

203

203

252 252

252

252

252

252

54

54

54

54

54

54

5454

80

80

80

80

8080

80

80

8080

80

80

80

80

80

fin

80

80

98

98

98

0.64

.64

.64

.64

.64

.64

.64

.64

.64 .64

.64

.64

.64

.64

.64

.64

.82

.82

.82 .82

.82 .82

.82

.82

.82

.82 .82

.82

.82

.82

1.02 1.02

1.02

1.02

1.02

1.02

1.41 1.41

1.41 1.41

1.41

1.41

1.41

1.41 2.08

2. 08

2. 08

2.08

2. 08 2.08

2.08

2. 08

2. 08

2. 08

2.08

2.08

2. 08

2. 08

2. 08

2. 08

2. 08

2.08

2. 55

2. 55

2. 55

in.-0.3 -.3

-.3

-.3

-.3

-2.0

-2.0

-2.0

-2.0

-2.0

-2.0

-0.3 -.3

-.3

-2.0 -2.0

-0.3 -.3

-.3

-.3

-2.0

-2.0

-2.0

-2.0 -0.3 -.3

-.3

-2.0

-2.0

-2.0 -0.3 -.3

-2.0

-2.0

-2.0

-2.0 -0.3 -.3

-.3

-.3

-2.0

-2.0

-0.3 -.3

-.3

-.3

-.3 -.3

-.3

-.3

-.3 -.3

-2.0

-2.0

-2.0

-2.0 -0.3 -.3

-.3 —. 3 -2.0

-2.0

-0.3 -.3

-.3

12

2

2

2

2

1

1

1

1

1

1

12

22

2

2

2

I1

1

12

2

1

1

1

1

1

12

2

1

11

1

1

1

1

1

1

1

1

12

2

2

2

2

2

1

1

1

in. 4.64

6. 14 6.14 7.64

7.64

4.96

5. 09 6.34

6. 34

7.46

7.46 4.64

6. 14

7.64

6.16

7.59

6. 14

6. 14 7.64

7.64

5.96

6. 46

7. 59 7.72 4.64

6.14

7.64

5. 09

6.22

7.72

7.64

7.64

7. 59

7.59

7.64

7.59

4.29

4.29 5.54

5.54

5.92

5.92

4.29

5. 54 4.29

4.29

5.54 5.54

7.54

7.54

9.04

9.04

7.62

7.74

9.24

9.36 4.29

5. 54

7. 54

Q fli

7.62 9.12

5. 54

5.54

7. 54

gpm

13.3 20.4

20.5

25.9

29.3

13.3 11.7

20.4

20.5

25.9

29.3

11.8 19.6

29.0 19.6

29.0

11.9 12.4

17.4

19.2

12.4

11.9 19.2

17.4

7.9

12.5

18.4

7.9 12.5 18.4

10.3 11.7

10.3

11.7

11.7

11.7

39.7

41.3

62.5 64.4

62.5 64.4 46.4

66.6

21.1

23.8

29.7

33.7

53.3

55.0

72.8

73.1 55.0 53.3 72.8

73.1 20.6

34.2

57.0

75 6

57.0

75.6

21.0 23.8

35.5

5.0 3.8

3.8

3.0

3.0

4.7

4.6 3.7

3.7

3.1

3.1 5.0 3.8

3.0

3.8

3.1 6.3

6.3

5.0

5.0

6.4

5.9

5.1 5.0 8.3

6.3

5.0

7.5 6.2

5.0

7.7 7.7

7.8

7.8

7.7

7.8 6.2

6.2

4.8

4.8

4.5

4.5

6.2 4.8

13.5

13.5

10.5

10.5

7.7

7.7

6.4

6.4

7.6

7.5

6.3

6.2

13.5

10.5

7. 70

6. 4

7.6

6.4

15.7

15.7

11.5

0.177

.315

.318 .408

.522

.166

.125

.305 .308

.418

.535 .140

.291 .612

.290

.515 .107

.116

.184 .224

.120

.102

.226 .182

.063

.118

.206

.057 .117

.204

.065

.083

.065 .084

.083

.084

.620

.671 1.190 1.264

1.114

1.183

0.847

1.351

0. 175

.223

.269

.346

.636

.677

.990

.998

.670

.620 .968

.964 .167

.356

.727

1. 067

0. 720

1. 058 0.134

.173

.282

9.81

9. 19 9.15

9.41 8.40

10. 50 11.95

9. 51 9.47

9. 17

8. 18

10.80

9. 51

8. 48

9. 54

8.42 10.44

10. 10 9.64

8.89

9. 80

10. 99

8. 83

9. 74

10. 80

10. 04

9. 21 11.86

10. 17 9.31

11.12

10. 08

11.05

10. 01

10. 08

10. 01 11.91

11. 45

9. 78

9.42

10.62

10. 24 10.15 9.02 12.68

11.49

12.46

11.18 10.24

9.92

9. 08

9. 03

10. 04

10.54

9. 32

9.42

12. 92 11.04

9. 57

8. 69

9. 69

8. 78 12.84

11.61 11.49

804

805 806

807

808

811 812

813 814

815

816

818

819

820

823

824

829 830

831 832

837

838 839

840

842

843

844

846

847 848

855 856

863 864

867

870

891 892 893

894

900

901 906

907

914

915 916

917 918

919

920

921 926

927 928

929

930

931 932

933

936

937 940

941 942 See notes at end of table.

47
Table A-2. Data on interference of Hows at junction of 3-in. simulated stack and horizontal branches, long-turn T-Y

drainage fittings—Continued

1 2 3 4 5 6 7 8 9 10 11 12

Branch

diameter

Thickness of water layer " on wall of stack

Rate of flow " in stack

Ratio of stack velocity " to computed

terminal

velocity

Pneumatic

pressure > in stack

Number of branches

flowing Head loss in branch

Rate of flow

in each branch

Stack parameter Branch

parameter

CoefBcient Test number

T 0, Vi

V,

fti hi—hi X Y C

in.2.07

2. 07 2.07

2.07

2. 07

in. 0.16

.16 .16

.16

. 16

gpm

98

98

98

98

98

2. 55

2. 55

2. 55

2. 65

2. 55

in.-0.3 -.3

-.3

-2.0

—2.

0

1

1

1

1

1

in.

7. 54

9.04

9.04

7.74

7. 74

gpm

38.9

48.3

50.9

35.5

38.

9

11.6 9.6

9.6 11.2

11.

2

0.339

.436

.484

.275

. 330

10.62

10. 64

10. 14

11.81

10. 92

943

944

945 950

951

2.07

2. 07

2. 07

2. 07

2. 07

.16

.16

.16

.16

. 16

98

9898

98

98

2. 55 2.55

2.55

2.55

2. 55

-2.0 -2.0

-0.3 -.3 —. 3

1

12

22

9.30

9. 36

5. 54

7.64

9. 04

48.3

60.9 22.8

38.9

53.0

9.4

9.3

16.7

11.5

9.

6

.423

.467 .158

.339

. 625

10.97

10. 63

12. 02 10.62

9. 77

952

953

955 956

967

2. 07

2. 07 2.07

2. 07

2. 07

.16 .16

.16

.35

. 35

98

98

98

98

98

2. 55

2. 55

2. 55

0. 82

, 82

-2.0

-2.0

-2.0

-0.3 —. 3

2

2

2

6.74

7. 62

9. 18

4. 29

4. 29

22.8 38.9

63.0

25.1

30. 8

16.2

11.4 9.5 4.8

4.

8

.163 .336

.517 .248

. 373

12. 47

10. 74

9. 93

12. 86

10. 78

958

969

960

985

986

2. 07

2. 07

2. 07

2. 07

2. 07

.35

.35 .35

.35

. 35

9898

98

98

98

.82

.82

.82 .82

. 82

-.3

-.3

-.3

-.3

—2.

0

5. 54

5. 64 7.64

7.64

5. 92

38.0

50.2

66.4

72.7

60.

2

3.7

3.7

2.7

2.7

3.

5

.440

.768

.987

1.183

0. 719

11. 75

8. 98

9. 49

8. 52

9. 68

987

988

989 990

995

2. 07

2. 07

2. 07

2. 07

2. 07

.35 .35

.35

.35

. 35

98

98

98

98

98

.82

.82

.82

.82

. 82

-2.0

-2.0

-2.0 -0.3 —. 3

5. 99

7. 62

7. 62

4. 29

5. 54

38.0

66.4

72.7

31.8

48.

8

3.4

2.7

2.7

4.8

Si 7

.407

.977

1. 171 0.398

. 726

12.78

9. 01

8. 63

10. 48

9. 24

996

997 998

1001 1002

2. 07

2. 07

2. 07

2. 07

2. 07

.35 .35

.35

.35

. 35

137

137

137 137

137

1.14

1. 14

1. 14

1. 14

1. 14

-.3

-.3

-.3

-.3 —. 3

\

6.64 5.54

7.54

7. 54

9. 04

21.8 30.8

36.4

46.3

50. 2

7.2

7.2

5.3

5.3

4.

4

.145

.289

.297

.480

. 471

12.35

9. 30

11. 15

9. 01

10. 18

1011

1012

1013 1014 1015

2. 07

2. 07

2. 07

2. 07

2. 07

.35

.35

.35

.35

.3^

137

137

137

137

137

1. 14

1. 14

1. 14

1. 14

1. 14

-.3

-2.0

-2.0

-2.0

—2. 0

\

9. 04

7. 74

7. 74

9. 24

9. 49

62.5 36.4

46.3 62.6

60.

2

4.4

. 5.2

6.2 4.3

4.

2

.729

.289

.468 .714

. 448

8. 23

11. 46

9. 27

8. 44

10. 73

1016

1021 1022

1023 1024

2. 07 2.07

2.07

2. 07

2. 07

.35

.35 .35

.35

. 35

137 137

137

137 137

1.14

1.14

1. 14

1.14

1. 14

-0.3 -.3 -.3

-.3

—2.

0

2

2

22

2

4. 29

5. 54 7.64

9. 04

7. 66

16.8 26.0

44.0

59.8

44. 0

9.3 7.2

6.3 4.4

5.

3

.111 .206 .433

.668

. 43,3

11.70

10. 71

9. 44

8. 61

9. 45

1025

1026

1027

1028

1031

2. 07

2. 07 2.07

2.07

2, 07

.35

.35

.35

.35

. 35

137

180

180

180

180

1. 14 1.50

1.50

1.50

1. 50

-2.0

-0.3 -.3

-.3 —. 3

2 9. 18 7.54

7. 54

9. 04

9. 04

59.8 22.4

29.6 30.4

39.

6

4.4

9.2

9.2

7.7

7.

7

.658

.112

.196

.173

. 293

8. 76

11.78

9. 42

11.11

8. 93

1032

1037

1038 1039

1040

2.07 2.07

2.07

2.07

2. 07

.35

.35 .35

.35

, 35

180

180

180

180

180

1.50

1. 50

1. 50

1. 50

1. 50

-2.0

-2.0

-2.0

-2.0

—0.3

\

2

7.49

7.74

9. 18

9. 24

6. 64

29.6

22.4 39.6

30.4

14.

8

9.2

8.9

7.6

7.6

12. 5

.197 .109

.288

.169

. 067

9. 35

12. 09

9. 07

11. 37

11. 90

1045

1046

1047

1048

1049

2. 07 2.07 2.07

2. 07

2. 07

.35

.35

.35

.35

. 58

180

180

180

18098

1. 50 1.50

1.50

1. 50

0. 40

-.3

-.3

-2.0

-2.0

—0.

3

2

22

2

1

7.54 9.04

7. 55

9. 12

4. 29

26.0 36.7

26.0 36.7

48.

3

9.2

7.7

9.2

7.6

2.

1

.151 .238

.151 .236

. 918

10. 46

9.74

10. 47

9. 83

8. 51

1050

1051 1053

1054

1055

2.07 2.07

2.07

2.07

2.07

.58 .58

.58 .68

.58

98

98

9898

98

.40

.40

.40

.40

.40

-.3 -.3

-.3

-.3

-.3

4. 29

6. 54

5. 54

7. 54

7. 64

48.3

64.0

66.4

86.2 91.9

2.1

1.6

1.6

1.2

1.2

.918

1.248

1. 343

1.663

1.891

8. 51 8.32

7.93

8.27

7. 47

1056

1057 1058

1059 1060

2.07

2.07

2.07

2.07

2.07

.58

.58

.58

.68

.68

98

98

98

98

158

.40

.40 .40

.40 .64

-.3

-.3

-2.0

-2.0

-0.3

9. 04

9. 04

6. 05

6. 05

4. 29

101.6

109.2 64.0

66.4

21.0

1.0

1.0

1.5

1.5

5.4

1.927

2. 227

1.143 1.230

0. 174

8. 23

7. 22

9. 29

8. 88

10.03

1061 1062

1065

1066

1079 See notes at end of table.

48
Table A-2. Data on interference of Hows at junction of 3-in. simulated stack and horizontal branches, long-turn T-Y

drainage fittings—Continued

1 2 3 4 6 6 7 g 9 10 11 12

iiatlO 01 Thickness of Rate of Stack veloc- PDeumatic Number of Eate of flow Branch water layer » flow » in ity a to pressure a branches Head loss in each Stack Branch CoefiBcient Test diameter on wall of stack computed in stack flowing in branch branch parameter parameter number

stack terminal

velocity

71* T Vi

y t hi h%—h\ Y 0

in. in. gpm in. in.

2. 07 0.58 158 0. 64 -0.3 4. 29 23 8 5 4 0. 223 9.06 1080

2. 07 .58 158 . 64 3 6 54 31 8 4 2 . 308 9. 27 1081

2. 07 .58 158 ! 64 3

r

5 54 35 5 4 2 . 384 8. 42 1082

2. 07 .58 158 . 64 3

r- 7 54 53 9 3 1 . 650 7. 98 1083

2^07 .58 158 !64 3 1

7.* 64 55! 6 sil ".690 7. 76 1084

2. 07 .58 158 . 64 3 9 04 71.

0

2.

6

,941 7. 36 1085

2. 07 .58 158 '. 64 3

r 9 04 72 7 2.

6

7. 17 1086

2.07 .58 158 . 64 -2.0 r- 5 80 31 8 4 0 . 294 9. 73 1089 2 07 .58 158 64 -2.0 r

0. oD 35 5 4 0 363 8. 94 1090 2.07 .58 158 !64 -2.0 X 7. 62 53! 9 s'l !644 8! 08 1091

2. 07 .58 158 . 64 -2.0 7 62 55 5 3.

1

. 682 7. 85 1092

2. 07 .58 158 . 64 -2.0 r 9 24 71 0 2 6 .921 7. 56 1093

2. 07 .58 158 64 -2.0

i 9 24 72 7 2 5 . 966 7. 36 1094

2. 07 .58 158 ! 64 -0.3 4 29 27 2 6.

4

. 291 8 10 1095

2.07 . 58 203 i82 3 1 5! 54 18*. 9 olo !l09 10! 37 1105

2. 07 .58 203 . 82 3 5 54 23 0 6.

9

.161 8. 87 1106

2. 07 .58 203 . 82 3 7. 54 32.

6

5.

1

[238 9. 17 1107

2. 07 .58 203 . 82 3

r

7 54 38 0 5.

1

[323 8. 05 1108

2 07 .58 203

* g2 3

r" 9 04 44 6 4.

2

. 370 8 60 1109

2107 . 58 203 !82 3 1 9! 04 49! 5 4^2 !458 i. 73 1110

2. 07 .53 203 . 82 -2.0 7 62 32 6 5.

0

.235 9. 27 1115

2. 07 .58 203 ] 82 -2.0 r

7. 62 38.

0

5.

0

[320 8. 14 1116

2. 07 .58 203 82 -2.0 r 9 18 44.

5

4.

2

.364 8. 64 1117

2 07 .58 203 82 -2.0 9 24 49 5 4 2 . 448 7. 91 1118

2107 , 58 203 182 -0.3 2 4! 29 1713 8^9 ills 8! 56 1119

2. 07 .58 203 . 82 3 0£1 5 54 26 6 6.

9

. 216 7. 88 1120

2. 07 .58 203 . 82 -2 0 2 5 **0 26 6 6.

6

. 206 8^26 1124

2. 07 .58 232 . 94 -0 3 6 29 19.

3

8.

0

. 100 9. 82 1129

2 07 .85 232 . 94 3

r 6 29 22 0 8.

0

.130 8. 86 1130

2! 07 . 58 232 !94 3 \ 7! 54 25." 3 6] 6 !l43 9! 64 1131

2. 07 .58 232 . 94 3 7 54 29.

6

6.

6

. 196 8. 40 1132

2. 07 .58 232 . 94 3

r

9 04 34.

4

5.

5

. 221 8. 96 1133

2. 07 .58 232 . 94 3 9 04 39 9 5.

5

'. 297 7. 91 1134

2. 07 .58 232 94 -2 0

r

6 24 22 0 8 0 !l31 8. 78 1137

2! 07 . 58 232 '.9i _2 0 1 e! 61 19] 3 7! 6 !095 10! 33 1138

2. 07 .58 232 -2.0 /. OD 29 6 6.

8

. 201 8. 19 1139

2. 07 .58 232 . 94 -2.0 r 7 62 25 3 6.

6

. 142 9! 64 1140

2. 07 .58 232 94 -2 0

r 9 12 39 9 5.

5

'. 295 7. 98 1141

2. 07 .58 232 -2 0 9 24 34 4 5 4 ! 216 9. 17 1142

2! 07 . 58 232 .94 -0 3 2 6!29 19! 8 8!o !l05 9! 62 1144

2. 07 .58 232 . 94 3 z 7 54 26.

6

6.

6

.158 9. 16 1145

2. 07 .58 232 94 3

0 9 04 35 7 5 5 . 238 S. 69 1146

2. 07 .58 232 94 2 0 0 6 42 19 8 7.

8

!l03 9. 83 1148

2 07 .58 232 QA . v1 -2 0 2 7. 42 OR R ZO. D 6 8

*161 9. 01 1149

2107 . 00 232 .94 -2 0 2 9.12 35.7 5^5 !236 8! 77 1150

3 07 .16 80 0 nil us -0 3 0. Di 96 4 10 3 . 580 9. 81 1163

3 07 .16 80 2 08 3 5 61 108 3 10.

3

. 731 8. 74 1164

3 07 .16 80 ^. Vo 3

:[ 7 36 134 9 7.

9

. 865 9! 48 1165

3 07 .16 80 3

j- / . OD 140 8 7 9 . 942 9! 04 1166

07 .16 80 2. 08 3 8. 86 170]4 a 5 l!l47 9! 05 1167

3 07 .16 80 2. 08 3 8. 86 1 7R K 1 /D. 0 6 5 1. 230 8. 66 1168

3 07 .16 80 0 AQ ^. UfS 3 in n 198 8 5 7 1. 368 8. 78 1169

3 07 .16 80 ^. Uo 3 10 11 199 5 5. 7 1. 377 8. 74 1170

3. 07 .16 80 Z, Uo -2 0 7 1

R

/. XD 140 8 8.

1

0. 969 g] 75 1173

3! 07 .16 80 2.08 -2 0 7.44 134! 9 7] 8 !856 9! 60 1174

3 07 .16 98 2. 55 -0 3 5. 61 77 5 15 6 0. 375 9. 30 1181

3. 07 .16 98 2 55 3 j 0. Dl 79 9 15. 5 .398 9! 06 1182

3 07 .16 98 2. 55 3

|-

1" 7* QR . OD 108 7 11. 8 . 662 9' 16 1183

3 07 .16 98 0 Ke;

iJ. 00 3

7 QR 111 2 11 8 . 688 8 96 1184

3! 07 .16 98 2. 55 3 8. 86 134! 1 9! 8 !710 9! 16 1185

3 07 .16 98 3

Q QR 138 2 9.

8

. 764 8. 88 1186

0. u/ .16 98 2. 55 3

1 fl QR lU. oD 161 2 8 4 . 877 9. 03 1187

0. u/ .16 98 2. 55 3 10. 36 165 1 8 4 . 920 8. 80 1188

0. u/ .16 98 2. 55 -2 0 7. 31 111 2 11 9 . 692 8. 89 1191

3. 07 .16 98 2. 55 -2 0 J 7. 44 108*. 7 11! 7 !566 9! 27 1192

3.07 .16 98 2. 55 -2 0 9. 06 134.1 9.6 .694 9. 39 1193 3.07 .16 98 2. 55 -2 0 9. 06 138.2 9.6 .738 9. 11 1194

3. 07 .16 98 2. 55 -2 0 10.56 165.1 8.2 .903 9. 00 1195

3. 07 .16 98 2. 55 -2 0 10. 68 161.2 8.1 .851 9. 36 1196 S.07 .16 98 2. 55 -0 3 2 5. 61 83.5 15.6 .435 8. 70 1197

See notes at end of table. 49
3 of

er a of

35

35

35

35

35

35

35

35

35

35

3535

35

3535

35

3535

35

35

35

35

3535

35

35

35

3535

35

35

58

5858

58

58

5858

5858

58

58

58

58

58

58

58

58

58

58

58

58

58

58

58

6858

58

5858

58

:-bra mbe:

y. i brar

brar

3 con

'erence of flows at junction of S-in. simulated stack and horizontal branches, long-turn T-Y

drainage fittings—Continued

4 5 6 7 8 9 10 11 12

Ratio of stack veloc- Pneumatic Number of Rate of flow

ity " to pressure " " branches Head loss In each Stack Branch Coefficient Test computed In stack flowing in branch branch parameter parameter number

terminal

velocity

y 1 hi Aj—fti Q2 X Y C

Vt

in. in. gpm

0. 82 —0.

3

1 5. 61 115.

1

3. 7 0. 826 9. 60 1203

. 82 —.3 1 5. 61 117. 2 3. 7 . 857 9. 42 1204

1. 14 —. 3 5. 61 71.

1

7.

1

.315 9. 96 1219

1. 14 —. 3 \ 5. 61 77.4 7.

1

.374 9. 25 1220

1. 14 -.3 1 7. 36 97.9 5.4 .456 10. 03 1221

1. 14 —. 3 1 7.36 104.

1

5. 4 . 515 9. 47 1222

1. 14 -.3 1 8. 86 124. 3 4. 5 . 610 9. 81 1223

1. 14 —. 3 8. 86 134. 0 4. 5 . 709 9. 10 1224

1. 14 —.3 I 10. 3fi 155. 3 3.9 .814 9. 34 1225

1. 14 -.3 1 10. 36 161.0 3.9 .875 8. 98 1226

1. 14 —2.0 1 7. 31 104.

1

5. 5 .519 9. 40 1229

1. 14 —2.0 1 7. 56 97. 9 5.3 . 444 10. 32 1230

1. 14 —2.0 9. 06 134. 0 4. 4 . 693 9. 34 1231

1. 14 —2 0 \ 9. 31 124. 3 4. 3 . 581 10. 37 1232 1.14 -2.0 1 10. 81 155.3 3.7 .781 9.81 1233

1. 14 -2. 0 1 10.81 161. 0 3. 7 .839 9. 44 1234 1.50 —0. 3 1 5, 61 50. 3 12,3 . 158 9. 44 1248

1. 50 -. 3 5. 61 56.

1

12.3 . 196 8. 64 1249

1. 50 — 3 \ 7. 36 66. 4 9.4 . 210 9. 96 1250

1.50 -.3 1 7. 36 74. 5 9.4 .264 9. 05 1251

1. SO —. 3 1 8.86 81. 4 7. 8 . 262 10. 20 1252

1. 50 —. 3 1 8. 86 89. 5 7. 8 . 316 9. 41 1263

1. 50 -.3 10. 36 99. 2 6. 7 . 332 10. 16 1254

1. 50 — 3 J in. 36 111. 9 6, 7 .423 9. 13 1255

1. 50 -2.0 1 7. 56 74.5 9.2 .257 9. 31 1268

1.50 —2.0 1 7. 68 66.4 9.0 . 201 10. 41 1259

1. 50 —2.0 1 9. 06 89. 5 7. 6 .309 9. 63 1260

1. 50 -2.0 9. 31 81. 4 7. 4 . 249 10. 74 1261

1. 50 —2 0 ][ 10. 56 99. 2 6. 6 .326 10. 36 1262 1.50 -2.0 1 10.81 111.9 6.4 .405 9. 56 1263

1. 50 -0. 3 5. 61 54. 8 12.3 . 187 8.80 1264

0. 64 -.3 1 5. 61 94. 0 4.

1

.551 7. 94 1282

. 64 —. 3 5. 61 104. 7 4.

1

. 684 7. 14 1283

. 64 —. 3 \ 7. 36 119. 7 3.2 . 681 8. 48 1284 .64 -.3 1 7. 36 128.1 3.2 .780 7. 91 1285

.64 -.3 1 8. 86 137. 8 2. 6 . 750 9. 07 1286

. 64 —. 3 1 8. 86 138.

1

2.

6

. 753 9. 05 1287

. 64 -.3 10.36 141. 8 2. 2 . 679 10. 52 1288

. 64 — 3 J 10. 36 142. 2 2. 2 . 683 10. 49 1289 .82 -.3 1 5.61 64. 6 6.8 .260 8. 10 1294

0. 82 —.3 1 5. 61 64.6 6.8 . 260 8. 10 1295

.82 —. 3 1 7. 36 85.6 5. 2 .348 8. 47 1296

.82 -. 3 7. 36 85. 6 5. 2 .348 8. 47 1297

. 82 —. 3 \ 8 86 108.

4

4.3 .464 8.37 1298 .82 -.3 1 8. 86 108.4 4.3 .464 8. 37 1299

.82 -.3 1 10. 36 125. 8 3. 7 .534 8. 64 1300 .82 —. 3 1 10. 36 125. 8 3. 7 .534 8. 64 1301 .92 -.3 5. 61 54. 5 8. 6 . 185 8. 10 1306 92 — 3 J 5. 61 54. 5 8. 6 . 185 8. 10 1307 !92 -.3 1 7. 36 72! 8 6.5 .252 8. 46 1308

.92 —.3 1 7. 36 72. 8 6. 5 . 252 8. 46 1309 .92 -.3 1 8.86 90.6 5.4 .324 8. 63 1310 .92 -.3 1 8. 86 90.6 5. 4 .324 8. 53 1311 .92 -.3 10. 36 107.9 4. 6 .393 8. 65 1312 .92 -.3 I 10. 30 107.9 4.6 .,393 8. 65 1313

.92 -1.6 6. 43 54.5 7.5 .162 9. 33 1314 .92 -1.6 7. 18 72.8 6.7 .258 8. 24 1315

.92 -1.6 8. 93 90.6 5.4 .322 8. 61 1316 .92 -1.8 6. 01 54.5 8.0 .173 8. 70 1317 .92 -1.8 7. 36 72.8 6.5 .252 8. 46 1318 .92 -1.8 9.11 90.6 5.3 .315 8. 79 1319

3 in column 12 represent data obtained for conditions outside the range over which it is reasonable to expect the analysis ded in the following categories were omitted:

ras less than half of that required to produce computed steady flow capacity for a full pipe not under external head,

for two-branch flow exceeded the criterion for fitting capacity given in section 2.1., wherein the effective stack diameter e diameter. mentum in one branch exceeded half the momentum in the stack just above the branch.
/=perinissible fixture-unit load within any

single branch interval

^'^permissible maximum load on stack, in

fixture units

For stacks having only one branch interval,

/,„.i,=5(„=i, = 1.55. (A-3)

For stacks having two or more branch intervals,

Table A-4. Hunter''s data'^ on friction losses for new castiron, soil pipe Uowing full

and

(A-5)

2 2 4

'

Table A-5 shows the steps involved in computing by use of eq (A-5) permissible stack loads

relative to permissible single-branch loads for pipe of the same diameter as the stack, or relative

to permissible loads for stacks having one branch

interval.

The concepts described above will now be

applied to the development of loading tables for

soil and waste stacks of various heights. Table

A-6 gives permissible loads for horizontal branches

(B) and for single-interval loads on one-story

stacks of the same diameter (/n=i). The values

of B given in the table are based on Hunter's

research on capacities of horizontal drains. These

values were used later bv plumbing code writers

For diameters greater than 3 m., the smgleinterval loads in table A-6 are about one-tMrd

as large as those obtained by appMng the fitting

capacities for double sanitary-tee fittings (given

in table 1) to curve 1 of figure 37. Table A-7, giving permissible loads for soil and waste stacks ha\dng one or two branch

intervals, has been computed from eqs (A-3) and

(A-5) and from the values given in table A-6.

Table A-8 gives permissible loads for stacks of

various heights, computed from eq (A-5) and

from the values given in table A-6. Load limits

for tall stacks have been taken from table 12 for stacks with 7/24 (0.29) of their cross sections

occupied by water falling at terminal velocity.

Table A-3. Elevation corrections to observed values of head loss through branches, simulated-stack tests

Branch

diameter

Elevation correction "

Sanitarytee fitting Long-turn T-Y fitting

in. in. in. 1.61 -0. 36 -1-1.34

2.07 -.49 -f-1.74 3.07 -.84 +2. 06

• Correction takes into account the foUowmg factors:

1. Shifting of reference level from invert to center of pipe section;

2. Change In elevation of center line of pipe due to H-inch-per-foot slope toward stack over a developed length of 4 branch diameters;

3. Change in elevation of passageway through fitting due to geometry of

fitting at junction between branch and stack.

Nominal

diameter Actualdiameter

f 8/f —

V8/f logioR

tTl, 2 2.'o6 0. 0301 266 16.30 0. 0128 3 2. 90 .0258 310 17. 60 .161

4 3.93 .0243 329 18. 15 .293

5 4. 85 .0250 320 17. 90 .385

» Reference 13.

Table A-5. Computation of permissible stack loads

relative to permissible single-branch loads for pipe of same

diameter as stack, or relative to permissible loads for stacks having one branch interval

Number of Relative loads branch 771 intervals, n

y

IIB S„IB S„ISi

1 L5 L5 1.5 1.5 1.0 2 1.0 2.0 0. 75 1.5 1.0 3 0. 833 2.5 .625 1.875 1. 25 4 .75 3.0 .562 2. 25 L5

5 .70 3.5 .525 2. 625 1.75 6 .667 4.0 .50 3.0 2.0

7 .643 4.5 .482 3.375 2. 25 8 .625 5.0 .469 3. 75 2.5

9 .611 5.5 .458 4. 125 2. 75

10 .600 6.0 .45 4.5 3.0

12 .583 7.0 .437 5. 25 3.5

15 .567 8.5 .425 6. 375 4. 25

Table A-6. Load limits for horizontal branches and

single-interval stacks

Pipe

diameter

Load limits

Horizontal branchSingle- interval stack

in. ,u.^

2

12 20

3 (soil) »20 »30

3 (waste) 32 48

4 160 240

5 360 540

6 620 930 8 1,400 2, 100

10 2, 500 3, 750

12 3. 900 5, 850

15 7, 000 10, 500

a Not more than two water closets.

Table A-7. Maximum loads for soil and waste stacks having one or two branch intervals

Diameter Maximum

of stack load on

stack

in. f.u. iVi 2 m 4 2 8 2^ 20

3 (soU) B30

3 (waste) 48

4 240

5 540

6 930

8 2, 100

10 3, 750

12 5, 850

15 10, 500

» Not more than two water closets within each branch interval. 51
Table A-8. Maximum loads for multistory soil and waste stacks

Number of branch Intervals Load

Diameter limit

of stack 3 4 5 6 i! 10 12 15 for tall stack A B A B A B A B A B A B A B A B

in. f.u. f.u. f.u. f.u. f.u. f.u. f.u. f.u. f.u. f.u. f.u. f.u. f.u. f.u. f.u. f.u. f.u. 2 3 9 10

8 24 7 28 28

3 (soil) b 12 "36 bll 0 44 b 10 "50 b 10 "60 " 102 3 (waste) 20 60 18 72 17 85 16 96 102

4 100 300 90 360 84 420 80 480 530

5 225 675 205 820 190 950 180 1,080 170 1,360 1, 400 6 385 1,155 350 1,400 325 1,625 310 1,860 290 2, 320 280 2,800 2^900 8 875 2,625 785 3,140 735 3,675 700 4,200 655 5,240 630 6,300 612 7,350 7,600

10 1,560 4,680 1,405 5,620 1,310 6, 550 1,250 7,500 1,170 9, 360 1,125 11,250 1,095 13, 100 15,000 12 2, 435 7,305 2, 195 8,780 2, 045 10, 225 1,950 11, 700 1,825 14, 600 1,755 17, 550 1,705 20, 500 1, 655 24, 800 26, 000 15 4,375 13, 125 3,935 15, 740 3,675 18, 375 3, 500 21, 000 3,280 26, 240 3,150 31, 500 3,060 36, 700 2,975 44, 600 50, 000

Note.—Colunms headed A=Maxlmum load within any one branch interval; columns headed B=Maximum load on stack. "These limits are applicable only when the maximum load within any one branch interval is not greater than N (^"1~^)> where JV= permissible load on a stack of one or two branch intervals; and n=number of branch intervals on the stack under consideration.

b Not more than two water closets.

" Not more than six water closets. Washington, D.C., November 25, 1960.

52

U.S. GOVERNMENT PRINTING OFFICE: 1961

[

i

1*

I

I
THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C., and

Boulder, Colorado, is suggested in the following listing of the divisions and sections engaged in technical work.

In general, each section carries out specialized research, development, and engineering in the field indicated by

its title. A brief description of the activities, and of the resultant publications, appears on the inside of the

front cover. WASHINGTON, D.C.

Electricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurements.

Dielectrics. Metrology. Photometry and Colorimetrj'. Refractometry. Photographic Research. Length. Engineering

Metrology. Mass and Scale. Volumetrj' and Densimetry.

Heat. Temperature Ph}-sics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-Ray. Radioactivity. Radiation Theory. High Energy Radiation. Radiological

Equipment. Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Pure Substances. Spectrochemistry. Solution Chemistry. Analytical

Cheniistry. Inorganic Chemistry.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion Controls. Organic and Fibrous Materials. Rubber. Textiles. Paper. Leather. Testing and Specifications. Polymer

Structure. Plastics. Dental Research.

Metallurgy. Thermal Metallurgy. Chemical Metallurgy. Mechanical Metallurgy. Corrosion. Metal

Physics. Electrodeposition.

Mineral Products. Engineering Ceramics. Glass. Refractories. Enameled Metals. Crystal Growth. Physical Properties. Constitution and Microstructure. Building Research. Structural Engineering. Fire Research. Mechanical Systems. Organic Building

Materials. Codes and Safety Standards. Heat Transfer. Inorganic Building Materials. Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics. Data Processing Systems. Components and Techniques. Digital Circuitry. Digital Systems. Analog

Systems. Applications Engineering.

Atomic Physics. Spectroscopy. Radiometry. Solid State Physics. Electron Physics. Atomic Physics.

Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical

Instruments. Basic Instrumentation.

Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemistry. Molecular Spectroscopy.

Molecular Kinetics. Mass Spectrometry. Molecular Structure and Radiation Chemistry.

• Office of Weights and Measures. BOULDER, COLO.

Cryogenic Engineering. Cryogenic Equipment. Cryogenic Processes. Properties of Materials. Gas Liquefaction. Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere

Research. Prediction Services. Sun-Earth Relationships. Field Engineering. Radio Warning Service. Radio Propagation Engineering. Data Reduction Instrumentation. Radio Noise. Tropospheric Measurements. Tropospheric Analysis. Propagation-Terram Effects. Radio-Meteorology . Lower Atmosphere

Physics.

Radio Standards. High Frequency Electrical Standards. Radio Broadcast Service. Radio and Microwave

Materials. Atomic Frequency and Time Interval Standards. Electronic Calibration Center. Millimeter- Wave Research. Microwave Circuit Standards. Radio Systems. High Frequency and Very High Frequency Research. Modulation Research. Antenna

Research. Navigation Systems. Space Telecommunications.

Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. Ionosphere and Exosphere

Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.