• r3

NBS MONOGRAPH 86

Investigation of tlie Hydraulics

of Horizontal Drains in

Plumbing Systems library

JANl 1 1955

\ iSE

..is.

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards is a principal focal point in the Federal Government for

assuring maximum application of the physical and engineering sciences to the advancement of

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and making such tests as may be necessary, particularly for government agencies; cooperation

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technical, and engineering information. The scope of the Bureau's activities is suggested in the following listing of its four Institutes and their organizational units.

Institute for Basic Standards. Electricity. Metrology. Heat. Radiation Physics. Mechanics. Applied Mathematics. Atomic Physics. Physical Chemistry. Laboratory Astrophysics.* Radio Standards Laboratory: Radio Standards Physics; Radio Standards Engineering.** OflBce of Standard Reference Data.

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Materials.

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Physics.

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*NBS Group, Joint Institute for Laboratory Astrophysics at the University of Colorado. Located at Boulder, Colorado.
UNITED STATES DEPARTMENT OF COMMERCE • Luther H. Hodges, Secretary

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

Investigation of the Hydraulics

of Horizontal Drains in Plumbing Systems

Robert S. Wyly

National Bureau of Standards Monograph 86

Issued December 18, 1964

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C., 20402 - Price 35 cents
Library of Congress Catalog Card Number: 64-60067
Contents

Page

1. Introduction 1 2. Symbols and definitions 2

3. General characteristics of hydraulic phenomena. 3

4. Field study 7

4.1. Test methods and apparatus 7

4.2. Results 7

5. Laboratory experiments 8

5.1. Surge flow in initially empty simple

drains 8

a. Hydraulic capacities 8

(1) Test methods and apparatus. 8

(2) Results 9

b. Surge attenuation 10

(1) Test methods and apparatus. 10

(2) Results 17

5.2. Flow in compound drains 21

a. Test methods and apparatus 21

b. Results 22

6. Analysis of experimental results 24

6.1. Surge flow in initially empty simple

drains 24

6.2. Attenuation of discharge rates in long,

initially empty drains 28

6.3. Flow at junction of main and branch in compound drains 29

a. Steady flow in branch and main in a common horizontal plane 30

b. Surge flow in branch, steady flow in main 32

Page

7. Conclusions 34

7.1. Estimating hydraulic capacity 34

7.2. Design of plumbing systems with mini- mum venting 34

7.3. Utilization of field data and of data on

surge attenuation 34

7.4. Effect of surge-duration time, drain slope,

and other factors on hydraulic capacity. 35

7.5. Surge-flow capacities of simple drains 35

7.6. Steady flow capacities of compound

drains 35

7.7. Capacities for surge flow superimposed on steady flow 35

7.8. Need for further investigation 35

7.9. Computation of allowable fixture-unit loads 35

8. References . 35

9. Appendix 36

9.1. Computation of roughness coefficients 36

9.2. Eff'ect of drain length on measured steady

flow capacity 3() 9.3. Determination of K-values for unusual

jet forms . 38

9.4. Terminal velocities in soil and waste

stacks 38

i

iii

Investigation of the Hydraulics of Horizontal Drains

in Plumbing Systems

Robert S. Wyly

Results are reported from an investigation of the hydraulics of flow in experimental

apparatus simulating nominally horizontal simple and branching drains of plumbing systems.

The data are correlated with limited findings in an earher, unpublished XBS study the

results of which have been utilized in current plumbing codes. The need for further re- search is pointed out, particularly in relation to hydraulic performance of drain sj'stems as affected by steep slopes, drain storage volume, energj- losses at stack bases, attenuation

of water depths and discharge rates in long drains, and large drain diameters. Analysis yielded equations useful in estimating hydraulic capacities for surge flow or

for surge flow superimposed on steady flow over a range of conditions. Capacity estimates

for the large drains are substantially greater than formerly assumed. The experimental

findings suggest that through careful design it may be possible to reduce the number of conventional vents extending above plumbing fixtures in small sj-stems such as those in one- and two-family houses. The results, of interest to writers of plumbing codes and

handbooks, have important applications in computation of optimum plumbing loads on

buUding drains and building sewers, in terms of actual plumbing fixtures.

1. Introduction

Knowledge of the hydraulics of nominally

horizontal drains under conditions similar to those

occurring in service in building sanitary drainage

systems is essential to the rational computation

of minimum pipe sizes for such systems. This

paper provides some of this needed information,

partictilarly that concerning the hydrauhcs of sanitary building drains and building sewers. Investigations of some of the factors which affect hydraulic capacities of such drains are reported.

The typical discharge into a drainage system

produced by plumbing fixtm-es is intermittent

in occurrence and variable in magnitude; and

on many occasions there is discharge due to concurrent operation of two or more fixtiu"es. A

method of estimating discharge for design purposes

under these conditions is required in order to compute drainpipe sizes. A method which has

gained widespread acceptance in the United States

has been described in some detail [1, 2].' In early plumbing codes the computation of minimmn sizes of horizontal drains was based

on the assumption of steady, uniform flow. This basis is still employed in some codes, but

many modem codes employ design criteria based on heretofore unpublished experimental data on unsteady or "surge" flow and on flow interference

at drain junctions. These criteria were developed

by the late Dr. R. B. Himter, who was in charge

of plumbing research at the National Bureau of Standards from 1921 to 1943. Hunter's experimental data provided an improved basis for the determination of drain loadings as given by

BMS66, Plumbing Manual [3]. Design requirements for horizontal drains derived from BMS66

have been utihzed by model codes and handbooks [4, 5, 6, 7, 8] and by numerous State and

municipal plvmibtng codes.

' Figures in brackets indicate the literature references on pages 35-36.

Prolonged illness and subsequent death pre- vented Dr. Hunter from preparing a technical

paper on his investigation of flow in horizontal

drains and on the computation of pipe sizes from

the data. Without the information this paper

would have provided it has been diflicult to evaluate, or to make improvements in the procedtires for selecting sizes of horizontal drains

presently based on his data. This was recognized

particularly by the Coordinating Committee for a National Mumbing Code [5]. This committee

made some improvements in the loading tables

originally developed by Hunter [3], but found the

lack of documentation of Hunter's work on

horizontal drains seriously handicapped its re- view of loading tables. Although experience had

indicated that adequately large pipe sizes apparentl}^ resulted from drain design in accordance

with BMS66, the committee realized that since

the time at which Hunter's recommendations were made, there had been some significant changes in

available types and M'drauhc properties of plumbing equipment and in the typical use of this equipment. Furthermore, some members of the

committee felt that drain design in accordance

with BMS66 or with some of the state and

municipal codes actually resulted in pipe sizes

larger than necessary in many systems, and that

the design procedures lacked desirable flexibility.

These considerations by the Coordinating Coinmittee indicated that further research on horizontal drains was needed.

In this paper, data obtained by Hunter and by

the author are reported from laboratory investigations of (1) surge flow introduced into empty

simple drains, (2) attenuation of surges in simple

drains, (3) continuous fuU-section flow in simple

drains under substantially steady, uniform conditions, (4) steady flow in compoimd drains, and

(5) surge flow introduced through a branch drain

1
into the side or top of a main drain carrying steady

flow. In addition to the laboratory data, some of

Hunter's field observations on flow in building

drains are reported.

Code writers and design engineers may find the

equations developed for estimating hydraulic

capacities over a range of conditions useful in

computing permissible plumbing loads on building

drains and building sewers. These equations

should contribute to increased flexibility and

rationaUty in the design of such drains. The

relations should be particularly useful in design

computations in the event that further research

should prove the feasibility of achieving adequate

venting of fixture drains in plumbing systems for houses through maintenance of a continuous air- space above the water surface in horizontal

branches, building drains and building sewers so

as to minimize or eliminate the need for conventional dry vents extending above fixture flood

level rim height.

2. Symbols and Definitions

Insofar as practicable, the terminology used in

this paper is in agreement with American Standard

ASA YlO.2—1958, Letter Symbols for HydrauUcs,

and with American Standard ASA A40.8—1955,

National Plumbing Code. The following ex- planation of terms is given for the convenience of the reader. Definitions marked with an asterisk are not defined in the above standards.

Symbols

:

A cross-sectional area C the Chezy co'efficient of roughness

D diameter

e the base of the natural system of logarithms (numerically, 2.718)

/ the Darcy-Weisbach coefficient of fric- tion

F force

g acceleration of gravity (numerically,

32.2 ft/sec2)

h head

ki Nikuradse roughness magnitude for

drain

Nikuradse roughness magnitude for

stack

K a dimensionless coefficient

L length

Nr Reynolds number

n the Manning coeflScient of roughness

V kinematic viscosity

p pressure

TT-terms (ttj, ir2, ttj, etc.) groups of dimensionless

parameters derived from dimensional

analysis

Q volume rate of flow (discharge rate)

Th hydraulic radius

R ratio of water section to cross section of

drain or stack

p density (mass per unit volume)

5 drain slope

t time

4> functional symbol

6 angle of inclination from the horizontal

(equivalent to S)

V mean velocity

z vertical distance from drain invert to center of gravity of cross section of water stream

Subscripts

:

c confluence of steady flow and surge flow at junction in compound drain system

d drain

i initial conditions

j jet

s stack

sfc steady flow capacity

sg surge

st pertaining to steady flow introduced into

drain entrance as a jet of water of given

cross section at a rate sufficient to equal

the steady flow capacity of the drain

t terminal conditions

1 main drain

2 branch drain

Definitions

:

*Altenuation refers to diminution of depth,

velocity, and/or discharge rate with time or

length.

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 building (house) sewer is that part of the

horizontal piping of a drainge system which

extends from the end of the building drain and

which receives the discharge of the building drain

and conveys it to a public sewer, private sewer, individual sewage-disposal system, or other point

of disposal. I *Capacity is synonomous with hydraulic capacity

or flow capacity (see flow capacity).

The *capacity surge refers to a surge, specifically

described by volume rate of input flow and time

duration, which results in the hydraulic capacity

of the drain being attained.

A *compound drain is a system of connected

conduits in which the main drain is nominally

horizontal, and in which there are one or more

branch drains.

The *crown of a horizontal drain is the topmost

point on a cross section of the bore.

2
A drain is any pipe which carries waste water or water-borne wastes in a building drainage system.

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

which conveys sewage, rain water, or other

hquid 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 drain is the drain from the trap of a

fixture to the junction of that drain with any

other drain pipe.

The *flow capacity or *hydraulic capacity, of a

drain is the maximum volume rate of input

flow which can be received without producing

hydrostatic pressure at the crown of the drain

somewhere along its length.

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

fixtiu'e drains and conducts it to the soil or waste stack or to the building (house) drain.

*Hydraulic capacity, see *jiow capacity.

The term *hydraulic elements, as applied to a given cross section in a horizontal drain, refers to hydraulic radius, depth, mean velocity, discharge

rate, wetted perimeter, and cross-sectional area of water stream.

* Initial area, velocity, or cross section of surge

refers to the surge as it approaches the stack-base

fitting and before it enters a horizontal test drain.

The Hnvert of a horizontal drain is the lowest

point on a cross section of the drain.

The Hoccd attenucUing force as used in this paper

refers to the gravity induced accelerative forces near the ends of a surge of limited length which

tend to "flatten" the surge and hence to inhibit it from fully occupying the cross section of the drain.

A *primary branch (of the building drain) is the

sloping drain extending from the base of a soil or waste stack to its junction with the main building

drain or with another branch thereof.

*Relative capacity is the ratio of the hydraulic

capacity of a simple drain for surge flow to the

capacity of the drain for steady flow. *Relative discharge rate, with reference to a com- pound drain, is the ratio of the rate of discharge

in either the main or a branch drain to the steady

flow capacity of the main.

A *secondary branch (of the building drain) is any

branch of the building drain other than a primary

branch.

A *simple drain is a single conduit without

branches, is used as a drain, is in uniform alinement, and has uniform slope and diameter.

A soil pipe is a pipe which conveys the discharge

of water closets or fixtures having similar functions, with or without the discharge from other

fixtures.

*Steady flow is a type of flow in which the hydraulic

elements at any cross section in the stream are constant with time.

*Steady flow capacity refers to the hydraulic

capacity of a drain in which steady flow is maintained.

*Surge flow refers to a type of flow produced by

discharging water into a drainage sj^stem at a

substantially constant volume rate for a limited

period of time.

*Surge-flow capacity is the hydraulic capacity

associated with a capacity surge. *Time duration of surge is the length of time for which a jet of water was allowed to discharge into a test drain at a substantially constant volume

rate of flow.

* Uniform flow is a type of flow in which the

hydraulic elements are constant from section to section along the stream at any given time.

A vent jnpe (or system) is a pipe (or pipes) installed

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 siphonagc

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

waste, free of fecal matter.

3. General Characteristics of Hydraulic Phenomena

The nature of fluid flow in sanitary drainage

systems is described briefly to acquaint the reader

with the general characteristics of the phenomena

dealt with in these investigations; and to indicate

the basis for methods of computing hydrauhc

capacities of nominally horizontal drains derived

from the experimental data.

The flow at any point in a horizontal drain

serving a number of plumbing fixtures will fluc- tuate with time. The drain is in general only

partially filled or empty, and the stream varies in

depth and velocity. It seems reasonable to consider the flow as comprising either surges introduced into an empty drain, or as comprising a combination of surges superimposed on antecedent

flow. Minimum time duration of surge is associated

with the discharge of a single plumbing fixture

into the drain to which it is connected. If several

fixtures are connected to a horizontal branch,

random overlap of the individual discharges will form composite surges characterized by average

3
volume rates of flow and time durations greater

than in the case for a single fixture. As these

discharges move through the vertical and horizontal members of the drainage system, the

gravitational and frictional forces produce significant changes in the hydraulic characteristics. In

large systems, particularly at considerable dis- tances from the origin of hydraulic loading, the

surges tend to coalesce and to produce a condition

approaching steady flow. However, it is generally

recognized that in most drainage systems, particularly in those of small or moderate size, the flow

is definitely unsteady and nonvmiform, and at times is nonexistent.

In many instances, the velocity at which water

is discharged into a sloping drain of a plumbing

system is greater than can be maintained in that

drain by gravity. This is particularly true for a

bviilding drain at the base of a tall stack. However, the excessive velocity is reduced because

initially frictional forces are large in relation to gravitational forces acting parallel to the invert

of the drain. During this early stage of move- ment through the drain, the surge depth actually

increases. The distance from the drain entrance

at which a maximum surge depth occurs appears

to be influenced by the velocity and cross section

of the stream at entrance; by the diameter, slope,

and roughness of the drain ; and by water already

flowing in the drain when the surge is introduced.

After maximum depth is produced, gravitational

forces become predominant. Subsequently, the

surge depth gradually decreases ana its length

increases. Downstream from the section of maximum depth the hydraulic elements undergo con- tinuous change. For this reason, some attention was given to surge attenuation.

Characteristic behavior of a surge in a simple

drain, observed at the station at which maximum

depth was produced in. a laboratory experiment,

is shown in figures 1 to 3. The drain was vented

by holes along the top of the drain spaced at intervals of approximately 4 ft. This assured

pneumatic pressures near atmospheric and eliminated the necessity for considering possible effects of pneumatic pressures substantially different

from atmospheric. This type of venting produced essentially the same venting effects as are attained in actual building drains by other means. The surge shown in the photographs was in- troduced into the drain at essentially a constant

volume rate for a limited time and at a velocity

in excess of that which could be maintained in the drain at the particular slope used. Three

successive stages are shown in the development of the surge at intervals of a few seconds. In

figure 1, the surge approaches from the right.

Figure 2 shows the existence of fuU-conduit

flow at the observation station as indicated by a

slight spurt of water thrown upward from the

observation hole. The flow at the drain entrance

had been stopped by suddenly closing a control

valve before the maximum depth occurred. The

surge did not fill the drain at other stations along

the length of the drain. Figiu-e 3 shows rapidly

decreasing depth. Subsequent to the time of

maximum depth at any station along the length

of the drain, attenuation of depth at that station

continued until the drain was empty. Observations showed that the hydrauhc capacity of the

drain for surge flow, as indicated by a full section

without hydrostatic pressure at the crown of the

drain, exceeded its steady flow capacity.

The mutual interference of two streams of water which meet at the junction of a compound

drain causes a local increase in water depth near

the junction. If the interference is excessive,

the drain may become full under pressure for some distance upstream and downstream from

the junction. If this happens, low-set fixtures

may be flooded and trap seals may be lost be- cause of excessive pneumatic pressures. Most

building drainage systems exhibit at least one example of a compound drain, particularly below

grade where primary and secondary branches

of the building drain are joined.

Figure 1. Surge approaching observation station from right.

4
Figure 2. Surge fills drain for short distances upstream

and dovmstream from this station.

Figures 4 to 7 show flow interference at the

j miction of a compound drain carrying flow in both the branch and the main. The main drain was vented as described above for the simple

drain. Figures 4 and 5 show a full section

(capacity condition) in the vicinity of the junction, produced by steady flow in the branch and

the main. Measurements showed that the sum

of the two flow rates was less than the steady

flow capacity of the main.

Figures 6 and 7 are the first and last photographs, respectively, in a sequence not shown

completely here. They indicate the development

of a full section at the jimction due to flow interference between surge flow in the branch and

steady flow in the main. The main drain was

not filled either upstream or downstream from

the junction. The hydraulic capacity of the

system for steady flow, as indicated by a full section at the junction and by the absence of

hydrostatic pressure at the crown of the drain, was in general less than the steady flow capacity

of the main alone. The hydraulic capacity of the

system for combined surge and steady flow was

greater than the system capacity for steady flow

in both the branch and the main.

Figure 3. Water depth decreases rapidly after maximum depth is produced.

Figure 4. Elevation view of full-section condition at junction in compound

drain {steady flow in main and in branch)

.

5

738-631 O - 64 - 2
Figure 5. Plan view of condition at junction in compound drain shown in

figure 4-

Figure 6. Elevation view showing surge from branch entering main which is carrying a small steady flow. Main Is not completely filled upstream or downstream from junction.

Figure 7. Continuation of surge in branch soon produces a full section at junction.

6
4. Field Study

4.1. Test methods and Apparatus

Hunter installed gages on the building drains

of several large buildings by tapping the top and

bottom of each drain. Two types of gage were

used. The first was an external glass tube con- nected to the top and the bottom of the drain,

and the second was a simple piezometer tube

connected to the bottom of the drain near the same point as was the first gage, the upper end

being open to the atmosphere. Under conditions

of steady flow, the elevation of the water surface

in the closed gage was the same as that within

the drain, and the elevation of the water surface

in the open gage indicated the sum of the pneumatic and hydrostatic pressures at the drain

invert. The difference between the indications

of the two gages was the penumatic pressure

within the drain.

A modified form of the closed gage was used

for determining maximum water depths in building drains over a period of days. Small water

traps were connected to the gage tube at vertical

intervals of ji in. The elevation of the inlet

connection of the highest trap in which water was

collected indicated the highest elevation, within

% in., reached by the water in the tube.

Observations were made by the use of the gages

both in occupied buildings with normal use of

fixtures and in unoccupied buddings mth manual

test flushing of fixtures. Descriptive information on the buildings in which observations were made

is given in table 1.

Table 1. Buildings investigated in field study of flow in building drains

Building No.Location Type Height Occupancy Drains observed

2

3

4.5

6

7

Washington, D.C

Washington D.C New York, N.Y

New York, N.Y

New York, N.Y New York, N.Y

Office and laboratory.

Office.

Office, storage, and laboratory. Apartment

4-story and basement

6-story and basement...

12-story and basement.

16-story

Hotel-apartment

.

Office 22-story.

Occupied

Unoccupied (new) Occupied

Unoccupied (new)

Unoccupied (new) Occupied

4-in. primary and 6-iQ. secondary

branches.

6-in. branch. Two 5-in. main drains ».

Various primary and secondary

branches.

6-in. and 10-in. primary branches.

6-in. secondary branch" (combined

storm and sanitary).

« One of the 5-in. drains served 51 water closets, 43 wash basins, 19 urinals, and 12 slop sinks. These fixtures were used by 450 resident workers and an

unestimated number of transients. The other 5-in. drain served 52 water closets, 54 wash basins, 18 urinals, 12 slop sinks, being used by 680 resident workers and an unestimated number of transients.

" The 6-in. combined drain served 180 water closets, 75 wash basins, 39 urinals, 22 slop sinks, and 2,500 ft' of storm-drainage area. Fixtures in basement

were drained into a sump which was emptied into the building drain by an ejector. It was estimated that 5,700 resident workers and 3,300 transients had daily

access to the toilets.

4.2. Results

A brief summary of the field observations will be given, since this information was later utilized

in the design of apparatus and in establishing

hydraulic conditions for laboratory experimentation. The results of flushing a single water closet, as observed from gages attached to the drains in the manner described in section 4.1, were as follows:

(1) the water level in open and closed gages rose rapidly to the same height in both, then gradually

receded with fluctuations to approximately the same level in both gages; and (2) the time interval

required for the stream to pass an observation

point varied from two to twelve times the duration

of flow at the fixture. In general, the interval

increased length of drain between the fixture

and the observation point.

The results of flushing a number of water

closets either in rapid succession or simultaneously

were: (1) for moderate rates of flow, the water

levels in the open and th? closed gages rose with

fluctuations to approximately the same elevation

in both and receded as described for the flow

from a single closet, with the exception that time

durations of flow and maximum indicated water

depths were greater; (2) for rates of flow sufficient to fni the drain greater than approximately onefourth the drain diameter at the observation point,

the gages indicated the existence of fluctuating

positive pneumatic pressures the magnitude of

which increased with water depth; and (3) for rates of flow sufficient to produce indicated water

depths in excess of half the drain diameter, large

pneumatic-pressure fluctuations were observed,

indicating that intermittently the crests of surges

of water may have filled the drain at one or more

cross sections and produced excessive pneumatic

pressures. The gages equipped with miniature traps in- dicated that normal use of fixtures during the

periods of observation did not cause the drains to flow full at the stations where the gages were

located.

Flushing of fixtures in buildings, either manually

or through normal use, proved to be an unsatisfactor}^ method of producing hydrauHc loadings

7
for test purposes. Satisfactory methods for measuring volume rates of flow in the drains could not

be developed in the time allotted to the field observations. Under the fluctuating conditions

produced hy sewage flowing in the building

drains of occupied buildings, the gages did not

always give accurate indications of pressures and

water levels because of lag or overthrow of the

gages. Therefore, in some cases the peak pres- sures and water depths actually may have been

either somewhat less or greater than indicated by

the gages. For these and other reasons, the field study was discontinued. Experimentation was

continued in the laboratory, where rates of flow

could be controlled and measured, and where

drain slope, length, and diameter could be varied

in a systematic order.

The field study indicated to Hunter the need

for laboratory study of (1) surge discharge in an

initially empty drain, and (2) surge discharge

superimposed on antecedent flow, such as may

occur at the junction of a primary and a secondary

branch of a building drain.

5. Laboratory Experiments

5.1. Surge Flow in Initially Empty Simple

Drains

a. Hydraulic Capacities

(I) Test Methods and Apparatus

Hunter measured surge-flow capacities in a simple drain approximately 70 ft in length. His

apparatus is shown schematically in figure 8. The

drain was constructed of 5-ft lengths of uncoated

cast-iron soil pipe. Diameters of 3 and 4 in., each at successive slopes of Kg, Ys, and % in. /ft, were used. A longitudinal slot about }i in. wide

and several inches long was cut in the crown of

each length of soil pipe in order to relieve pneumatic pressures and to provide a visual indication

of a full drain.

Water was introduced into the drain through

a long-sweep quarter bend in a vertical plane.

The water entered the quarter bend from a 3-in. pipe equipped with a gate valve for regulating

the rate of discharge and a quick-opening gate

valve for initiating and terminating the flow.

3- IN. SUPPLY LINE

3-IN. QUICK

OPENING GATE

OBSERVATION VALVE

SLOT

Test surges were produced manually by suddenly

openyig the quick-opening valve, allowing the

flow thus produced to discharge into the test drain at a substantially constant volume rate of

flow for a selected interval of time, and then suddenly closing the valve. The cross-sectional form

of the water jet produced is shown schematically

in flgure 9E. For each time interval, repeated

trials were made until a rate of discharge was obtained such that the drain was barely filled for some small part of its length. The interval of

time during which water discharged into the drain was taken as the surge duration, and the corre- sponding discharge rate was taken as the hydraulic capacity. The drain capacity was determined for steady, uniform flow without end re- striction and without hydrostatic pressure at the crown of the drain in order to establish the extent

to which surge-flow capacity exceeded steady

flow capacity. The method used for adjustment

of these values to simulate the condition of long

drains is given in section 9.2 of the appendix.

More recently, the author investigated surge

flow in simple drains approximately 98 ft long over an expanded range of test conditions. This

apparatus is shown schematically in figure 10. The drain materials utilized were methyl methacrylate plastic tubing, galvanized-steel pipe, and

cast-iron soil pipe. In general, drain slopes of

1/16, 1/8, and 1/4 in. /ft were used. Plastic was

used for 4- and 6)2-in., steel for 3- and 4-in., and

cast iron for 3- and 4-in. drains. Holes % in. in diameter were drilled in the crown of the drains

at intervals (4.3 ft for the plastic, 5.0 ft for the

cast-iron, and 5.3 ft for the galvanized-steel drains)

to serve as air vents and as visual indicators of the existence of a fuU-conduit condition without

hydrostatic pressure at the crown line.

Figure 9. Cross-sectional forms of jets. FiGUBE 8. Schematic diagram of test system used by Hunter to study surge flow in initially empty simple

drains.

A. Annular

B. Modified annular

C. Single circular D. Multiple circular E. Crescent

8
4- IN. GATE VALVE

4-IN- SUPPLY LINE FROM CONSTANT-

' HEAD TANK

REMOVABLE INSERT

STACK-BASE FITTING

TEST DRAIN

Figure 10. Schematic diagram of test system used by

author to study surge flow in initially empty simple

drains.

The qmck-opening valve which initiated and

terniinated the surges introduced into the test drains was controlled by a pneumatic system

actuated by a push-button electrical circuit. Surge duration time was measured with an electric stop clock. The clock was started by a microswitch actuated by a small paddle projecting into

the cross section of the drain entrance, and

stopped by another microswitch actuated by the

handle of the quick-opening valve as it approached

the closed position.

Initial velocities and cross sections of the test surges at a level about 2 ft above the center line elevation of the entrance to the test drain were

predetermined by means of the stack simulator

shown in figure 11 for an annular jet form.

Inserts were provided such that jet forms of

either sohd cylindrical or annular shapes could be

produced, as shown in figures 9A to 9D. Control

of velocity and cross section was necessary to produce conditions at the base of the stack similar

to those believed to occur in service [9]. Several

cross-sectional forms of jets were used because

the shape may vary in service depending on the

geometry and dimensions of the installation. The

form shown in figure 9D is an uncommon one, actually comprising two separate jets. This was

necessary in some of the tests on the 6K-in. drain

in order to introduce sufficient water to produce a capacity surge. For each of various predetermined combinations of initial velocity and cross section, successive trials were made to determine the time

duration of surge which caused the drains to flow

full for the smallest possible portion of their

length without producing hydrostatic pressure at the crown. Hydraulic capacities were determined

both for surge flow, and for steady flow in the same drains for purposes of comparison. The determination of capacities for steady flow is ex- plained in some detail in sections 9.1 and 9.2 of the appendix.

Volume rates of flow were measured with a cali- brated orifice meter and a calibrated gate valve.

The orifice meter was calibrated by volumetric

measurement of steady discharge as a function of pressure drop across the orifice. The gate valve was calibrated by volumetric measurement of steady discharge produced by the available head

from a constant head tank as a function of degree

STACK - 4.037" 1.0.

Figure 11. Stack-flow simulator for producing jet of water having annular cross section.

of opening of the valve wheel. The average rate

of flow through the valve at a given degree of

opening was not affected significantly by the time

duration of flow for durations greater than 5 sec.

(2) Results

Characteristic performance of a surge in a simple drain has been described in section 3 and

illustrated in figures 1 to 3. Tables 2 and 3

give experimentally determined drain capacities

for surge flow in initially empty drains, using the

apparatus described in (1) and illustrated in figures 8 to 11. Table 2 gives Hunter's data and

table 3 gives the author's data. The ratio of

initial jet velocity to theoretical stack terminal

velocity was varied over a range. In this ratio, the

terminal velocity is for a cast-iron stack of the same diameter as the drain, computed from

eq (A-7) of section 9.4, assuming a value of ks of 0.00083 ft. Initial jet velocities at the bases

of the test stacks may be computed from table

3 by dividing the column 10 value by the product

of the corresponding column 8 value times the

cross-sectional area of the drain, using dimensionally consistent units. Velocities for the data

in table 2 may be obtained in the same way from

column 4 and column 6 values.

Initial experimental velocities for Hunter's

data ranged from about 2.2 to 5.2 times the maximum that should occur at the bases of multistory

stacks in the field loaded with water-occupied

9
Table 2. Surge capacities of initially empty, sloping,

simple drains

(Data on cast-iron soil pipe obtained under Hunter's direction, using crescent- shaped jet, long-sweep stack-base fitting, and open condition at lower end

of drain)

(1) (2) (3) (4) (5) (6) (V) (8)

XvalflU Ul Rutin nf liatio of L^apac- Ullllal Time capacity Drain i^rain icy area of TTpl Af»i 1" V IKJl OLil diam- slopo lur oLlcalli cion 01 ity * for flow to

eter steady f" A CI 7*0 Q surge Qiirffp flfiw tprmina I capacity

flow Ul uraiii fnr <if"pnfiv flow

in. tn./jt Qptn gpm

• 3. 00 1/16 32.

8

0 042 42 0 6. 22 1. 28

ou 42 0 5 22 1. 28

.042 20 42^0 5122 1^28

.042 20 42.0 5. 22 1.28 042 20 42. 0 5. 22 1.28

055 15 61.

8

4. 55 1 58

. uoo 110 51 8 4 55 1. 58

. uoo 1 1: 10 51 8 4 65 1' 58 076 10 66 8 3. 90 2 04

]075 10 66^8 3^90 2! 04

.075 10 66.8 3. 90 2.04

116 99. 6 3 20 3. 03

116 99 5 3. 20 Z. 03

1 1 fi

. 110 0 99 5 3 20 3 03

1/0 40. 0 0 061 54 5 4 25 1 17 ]061 30 54! 5 4^25 1^17

.064 20 69.3 4.27 1.27

071 15 63 4 4. 00 1. 36 086 10 74 3 3 61 1. 69

124 c0 104 3 06 2 22

1/4 00. ( 0 083 40 72 5 3 68 1 09

!086 30 74.3 d. 61 i!ii .089 20 76.7 3.57 1.15

091 15 77 6 3. 54 1 10 095 10 81 8 3 49 1 23

134 e0 112 2 97 1 68

Q on 1 /I R 1/10 64 1 0 054 40 79 5 3 98 1 24

]054 30 79] 5 3! 98 l!24

.055 20 80.9 3. 90 1.26 068 15 97 0 3 54 1 51 095 10 132 3 03 9 06 149 193 2 44 3 01

i/S 91 2 0 071 30 102 3 48 1 12 075 25 107 3 38 1 17 079 20 111 3 31 1 22 094 10 130 3 06 1 43

110 10 101 2 86 1 66

. lUO c0 2 29 2 27

1/4 1 ou 0 103 30 142 2 93 1 09

!l06 30 146 2^89 l!l2 .109 30 146 2.82 1.12

.108 20 149 2.88 1.15

.109 20 149 2.86 1.15 .109 15 150 2.86 1.15

.110 15 152 2.86 1.17

.125 10 167 2.67 1.29

.126 10 169 2. 67 1.30

.175 5 215 2.21 1.65

.176 5 216 2. 21 1.66

» Values given for steady flow capacity were derived by applying correc- tions in accordance with the rational pipe-flow formula to laboratory measure- ments of apparent steady flow capacities in drains 70 ft long discharging to atmosphere at the lower, open end (see sec. 9.2).

>> Based on area of opening through gate valve which was used to control stream introduced through sweep fitting at drain entrance.

' Values given for surge flow capacity were derived from laboratory data

giving degree of opening of control valve and a calibration curve showing rate

of discharge as a function of degree of opening.

•1 Computed from cq (A-7) and from values in columns 1 , 4, and 6. Equal

stack and drain diameters were assumed. A value of absolute roughness of 0.00083 ft for the stack was used In the computations. This value was de- rived from resistance measurements on cast-iron soil pipe (9].

" Nominal diameter. The laboratory notes do not indicate the e.xact diameter of this drain.

cross sections indicated by the values in column

4 of table 2 assuming stack and drain diameter

to be the same. The initial experimental velocities used in the author's tests reported in table 3 covered a more restricted range from a little less than 0.5 to about 1.3 times theoretical stack

terminal velocity. This range of velocities is

reasonable at the bases of drainage stacks in

service.

Table 3 gives, among other information, the

distances along the drains at which the full- conduit condition was observed. In the case of Hunter's data, shown in table 2, this distance is is not given, but was less than 20 ft from the drain

entrance in all cases. The capacities of the test drains under conditions approaching steady,

uniform flow are given in table 4. Perhaps the most significant observations with

reference to svu:ge flow were

:

1. For a given time duration of surge, actual

surge-flow capacity increased with drain slope

but relative capacity decreased,

2. for a given drain, capacity decreased with

increasing surge-duration time, approaching as a lower limit the steady flow capacity of the drain,

and

3. entrance velocity, initial area and shape of surge cross section, and drain roughness appeared

to have small effect on relative capacity.

Detailed discussion of the experimental re- sults appears in section 6.1.

b. Surge Attenuation

(1) Test Methods and Apparatus

The attenuation of discharge rates of surges was

investigated by Hunter. He fiist utilized a 4-in. drainage stack 10 stories in height with a building

drain extending laterally 40 ft from the base of the

stack. BuUding-drain diameters of 4, 5, and 6

in. at slopes of Ys and ji in. /ft were used. For

the 5-in. drain, a slope of jU in. /ft was also used.

The drains were constructed of 5-ft lengths of cast-iron soil pipe. Single water closets were

discharged into 4-in. branch drains at either the

fourth or the tenth floor. The average rates at which the water closets discharged water into the

branch drains were measured, and the cumulative

discharges from the end of the building drain were measured volumetrically in a collecting tank for three consecutive 5-sec intervals after the water

reached the end of the drain.

At another time, Hunter used the apparatus

shown in figure 12 to measure instantaneous rate

of flow at the discharge end of a horizontal drain

produced by a water closet discharged directly

into the upstream end without the use of an

intervening vertical drain. The 60 radial compartments moved transversely beneath the discharge

end of the drain at a constant angular velocity

adjusted so that the full volume of a single operation of the water closet was discharged from the

end of the drain in one revolution. The approximate instantaneous rate of discharge was computed as a function of time from the measurements

of volume of water caught in successive compartments and of angular velocity. Drain diameters

of 3 and 4 in., and lengths of 0, 1,6, 11,21, and 41

ft at a slope of % in. /ft were used successively.

The drains were constructed of 5-ft lengths of cast-iron soil pipe.

10
Table 3. Surge capacities of initially empty, sloping, simple drains

(Author's data)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

Distance Ratio of Ratio of from Ratio of

initial initial drain capacity Drain Drain Drain Capacity Type of stack- Condition at Form of initial area of Time Capacity velocity entrance for surge diameter slope material for steady base fitting lower end of cross section stream duration for surge to stack to point flow to flow* dram of stream to area of surge flow terminal at which capacity

of drain velocity ^ surge for steady

filled flow drain

in. in.lit gpm stc gpm ft 2.985 1A6 Plastic - 42.1 Long sweep Open Modified 0.30 31.5 50.7 0.85 30.8 1.20

anntilar. 21.2 57.0 .91 30.8 1.35 13.9 63.3 .97 30.8 1.50 9.4 78.6 1.11 26.5 1.87

.37 9.0 Tl.l .86 26.5 1.85 4.7 97.1 .98 22.1 2.31 3.1 116 1. 10 17.7 2. 76

. 46 4.

2

111 . 87 22.

1

2. 64

Single circular- .21 31.5 54.1 1.23 39.7 1.28

22.8 58.7 1.29 35.2 1.39

.34 27.

5

5o. 8 . 77 35.

2

1. 32

19.4 59.1 .79 30.8 1.40

13.4 68.7 .87 30.8 1.63 7.2 83.1 .98 26.5 1.97

5.4 102 1.11 26.5 2. 42

.40 8.

0

84. 6 . 86 26.

5

2. 01

5.

3

107 . 99 26.

5

2. 54 3.6 128 1.10 13.3 3.04

. 50 3.

7

127 . 86 17.

7

3. 02

2.985 1/4 Plastic 90.8 I/ong sweep.— Open Modified .37 25.

1

97.

1

. 98

.98

66.

1

1. 07 annular. 20.5 97.1 66.1 1.07 5.0 116 1.10 30.8 1.28

5. 2 116 1. 10 30.8 1. 28

.46 10.2 111 .87 44.1 1.22

10.

3

111 . 87 44.

1

1. 22

4.0 140 1.00 26.5 1.54

3.9 140 1.00 26.5 1.54

. 53 3.

2

142 . 87 22.

1

1. 56

3.

9

142 . 87 26.

5

1. 56

Single circnlar. .34 18.8 102 1.10 61.7 1. 12

18.8 102 1. 10 61.7 1. 12

.40 14.5 107 .99 57.3 1. 18

14.

2

107 . 99 57.

3

1. 18

5.

3

128 1. 10 35. 2 1. 41 6.0 128 1. 10 35.2 1.41

.50 6. 6 127 . 86 35. 2 1. 40

7.1 127 . 86 37.

4

1.40

3.068 Ml Galv. steel 40.7 Long sweep..- Open Modified an- 0.28 21.4 57.0 0.92 28.1 1.40

nular. 14.2 63.3 .99 25.5 1.56

10.3 78.6 1.12 25.5 1.93

0.35 10.0 77.7 0. 87 25.5 1. 91 4.5 97.1 1.00 20.2 2.39

3.8 116 1. 11 20.

2

2. 85

0.43 3.8 111 0. 88 20.

2

2. 73

Single circu- 0. 20 29.8 54.1 1.24 30.8 1.33

lar. 19.6 58.7 1.30 30.8 1.44

0.33 27.4 55.8 0. 78 28.

1

1. 37

20. 5 59.

1

.80 28.1 1.45

14.0 68.7 .88 28.1 1.69 7.2 83.

1

.99 25.5 2.04

5.5 102 1.12 25.5 2.51

0.38 7.9 84.6 0.87 25.5 2.08

5.5 107 1.00 22.9 2.63

3.6 128 1. 12 20.2 3. 14

0.47 3.4 127 0. 87 20.2 3.12

3.068 H Galv. steel... 84.0 Long sweep... Open Modified an- 0.35 11.7 97.1 1.00 36.0 1. 16 nular. 7.2 116 1.11 33.4 1.38

0.43 8.2 111 0.88 36.0 1.32 3.5 140 1. 01 20.2 L67

0.50 3.6 142 0.88 20.2 1. 69

See footnotes at end of table.

11
Table 3. Surge capacities of initially empty, sloping, simple drains—Continued

(Author's data)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

Distance

Ratio of Ratio of from Ratio of

initial initial drain capacity Drain Drain Drain Capacity Type of stack- Condition at Form of initial area of Time Capacity velocity entrance for surse

(liamctor slope material for steady base fitting lower end of cross section stream duration for surge to stack to point flow to flow « drain of stream to area of surge flow tprnniTi \jXjI I 1 1 1 1 I al0 1 at which capacity

of drain velocity ^ for steady

filled flow drain

in. in.lft gpTn

Single circu- gpm ft 0. 33 12. 9 102 1. 12 36. 0 1 21

lar.

0. 38 10.

7

107 1. 00 33. 4 1 27

5.4 128 1.12 28.1 1.52

0. 47 8.0 127 0. 87 25.5 1.51

2. 913 Ms Uncoated 35. 5 Long sweep Open Modified an- 0. 32 18. 5 50. 3.

3

0 84 22. 9 1. 43

cast Iron nular. 10.8 6 7 .96 20.4 L78

soil pipe.

0. 39 6. 7 77. 7 0 85 17. 9 2. 19 4.5 97.1 .98 15.4 2.74

0. 48 4.

1

111 0. 86 15.

4

3. 13

Single circu- 0. 23 8.

8

68.

7

1. 40 20.

4

1. 94

lar. 5.

6

83.

1

1. 57 15.

4

2. 34

0. 42 5.3 84.6 0. 85 15.4 2. 38

4. 5 107 . 98 15. 4 3. 01

Restricted Modified an- 0. 32 25.

8

46.

9

0. 81 22. 9 1. 32

lar. 18.7 50.7 .84 22.9 1^43 12.6 58. 5 . 92 20. 4 1.65

9. 5 63.3 . 96 20. 4 1. 78

7.

8

78.

6

1. 10 17. 9 2. 21

0. 39 12.8 55.8 0. 70 20.4 1.57

6.

8

77. 7 . 85 17. 9 2. 19

4.

4

97.

1

. 98 15.

4

2. 74

0. 48 3] 0 111 0. 86 10.

4

3 13

Single circu- 0.23 31.8 44.8 1.09 25.4 1.26

lar. 17.2 54.

1

1.22 22.9 1.52

12. 6 58. 7 1. 28 20.

4

1. 65

0. 36 16. 8 55. 8 0. 76 22. 9 1. 57 12.9 59.

1

.79 20.4 1.66

8. 9 68. 7 . 86 20.

4

1.94 5.6 83.1 .97 15.4 2.34

3.9 102 1.09 15.4 2.87

0. 42 30.0 45.4 0.59 25.4 1.28 13.0 55.8 .66 17.9 1.57 5.2 84.6 .85 15.4 2. 38

4.4 107 .98 15. 4 3. 01

0. 53 12.2 56.0 0.52 17.9 1.58 4.9 91. 7 . 70 15. 4 2, 58

2. 913 H Uncoated 73.7 Long sweep. -- Restricted Modified 0. 32 11.4 89.2 1.18 30.4 1.21 cast iron annular

soil pipe.

0. 39 11.9 90.5 0. 93 27.9 1.23 6.6 97.1 .98 20.4 1.32 4.4 116 1. 09 20. 4 1. 57

0. 48 8. 0 94.2 0. 78 27. 9 1. 28

4. 2 111 .86 15.4 1. 51

Single circular 0. 36 18. 0 83.

1

0. 97 32.9 1. 13 8.6 92.3 1.03 25.4 1. 25 6.8 102 1.09 25.4 1.38

0. 42 16 0 84 6 0. 85 32 9 1. 15

9.

1

93! 6 .91 27^9 1. 27 5.5 107 .98 20.4 1.45 3.8 128 1. 09 15.4 1.74

0. 53 7. 2 103 0. 75 22.

9

1. 40

4. 0 127 .85 15.

4

1. 72

3. 978 He Plastic 91.9 Long sweep. .. Open Annular 0. 26 25.4 116 1.00 54.2 1.26 20.9 130 1.07 47.6 1.42 15.4 143 1.13 54.2 1.56

0.30 27.6 115 0. 86 54.2 1.25 14.9 147 1.00 43.2 1.60

14.4 147 1.00 52.0 1.60 8.4 179 1.13 49.8 1.95

12
Table 3. Surge capacities of initially empty, sloping, simple drains—Continued

(Author's data)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

Distance

Ratio of Ratio of from Ratio of

initial initial drain capacity Drain Drain Drain Capacity Type of stack- Condition at Form of initial area of Time Capacity velocity entrance for surge diameter slope material for steady base fitting lower end of cross section stream duration for surge to stack to point flow to flow* drain of stream to area of surge flow terminal at which capacity

of drain velocity •> surge for steady

filled flow drain

in. in.lft gpm sec gpm ft

0. 34 14. 6 145 0. 87 49. 8 1. 58

7.8 182 1.00 41.0 1.98

7.7 182 1.00 45.4 1.98 — 5.

1

218 1. 11 45.4 2. 37

0. 39 8.

3

176 0. 87 45. 4 1. 92

6. 0 220 .99 38.8 2.39

5.3 220 .99 45.4 2.39 3.2 269 1. 12 36.6 2. 93

0. 43 5. 7 210 0. 88 43.2 2. 28

4. 4 260 1. 00 32.

2

2. 83

4.8 260 1.00 36.6 2. 83

3.9 260 1.00 36.6 2.83

Restricted Annular 0. 26 26.

6

116 1. 00 49.8 1. 26

26. 6 116 1. 00 49.

8

1. 26 30.4 116 1.00 49.8 1.26 20.7 130 1.07 47.6 1.42

15.

1

143 1. 13 47.6 1. 56

0. 30 31.2 115 0.86 49.8 1.26

19.9 131 .93 45.4 1.42

14.5 147 1. 00 43.2 1.60

8. 0 179 1. 13 41.

0

1.95

0. 34 15.0 145 0. 87 45.4 1.58

8. 0 182 1. 00 41. 0 1. 98

5.

4

218 1. 11 38.8 2.37

0, 39 9.2 176 0. 87 41.

0

1. 92

6. 0 220 .99 36.6 2.39

4.

1

269 1. 12 32.2 2.93

0. 43 6.5 210 0.88 36.6 2.28

4.

3

260 1. 00 32.2 2. 83

Single circular. 1.0 19.8 137 0.28 41.0 1.49

11. 5 164 .31 27.8 1.78

7.7 189 .34 19.2 2. 06

6.4 210 .36 14.8 2. 28 5.4 241 .39 14.8 2.62

3.

6

291 .44 7.3 3. 17

134 Long sweep Open Annular 0.30 13.0 179 1. 13 58. 4 1.34

13.0 179 1. 13 68.4 1.34

0. 34 12.1 182 1.00 56.3 1. 36

12.

0

182 1.00 56.3 1.36

7! 9 218 1.11 62.0 1.63

0. 39 12.4 176 0. 87 60. 6 1.31 12.2 176 .87 60.6 1. 31 7.1 220 .99 52.0 1.64 6.2 269 1.12 66.3 2. 01

5.

2

269 1. 12 43. 2 2.01

0.43 9.3 210 0.88 66.3 1.67 4.9 260 1.00 46. 4 1.94 3.3 329 1. 15 36.6 2.46K

Y-&-H bend.. Open Annular 0. 26 26.1 151 1. 17 64.2 1. 13

26.

1

161 1. 17 54.

2

1. 13

0.30 32.4 147 1. 00 64.2 1. 10 32.4 147 1.00 64.2 1. 10

17.

1

163 1. 06 47.6 1. 22

17.1 163 1. 06 47.6 1. 22

12 3 179 1. 13 45. 4 1.34

12! 3 179 1.13 45.4 1.34

0.34 31.9 145 0.87 66.3 1.08

20.

5

156 .91 54. 2 1. 16

15^7 164 !93 47.6 1.22

10.7 182 1.00 43. 2 1.36

6.8 218 1. 11 36.6 1.63

0.39 11.5 176 0. 87 38.8 1.31 6.4 220 .99 36.6 1.64 4.8 269 1.12 32.2 2. 01

0.43 7.9 210 0.88 32.2 1.67 4.7 260 1.00 30.0 1. 94 3.5 329 1. 15 27.8 2.46

13
Table 3. Surge capacities of initially empty, sloping, simple drains—Continued

(Author's data)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

Distance

Ratio of Ratio of from Ratio of

initial initial drain capacity Drain Drain Drain Capacity Type of stack- Condition at Form of initial area of Time Capacity velocity entrance for surge diameter slope material for steady base fitting lower end of cross section stream duration for surge to stack to point flow to flow • drain of stream to area of surge flow terminal at which capacity

of drain velocity surge for steady

filled flow drain

in. in.lft ffpro SfC gpm ft H Plastic 195 Long sweep Open Annular 0.34 15. 4 218 1. 11 73. 6 1. 12 9.2 240 1.17 67.2 l] 23

0. 39 16.0 220 0.99 73.8 1. 13 5.0 269 1.12 49.8 1.38

0.43 7.0 260 1. 00 62.0 1.33 3.6 329 1. 16 32. 2 1.69

Single circular. 1. 0 9. 0 230 0.38 27.8 1. 18 4.9 291 .44 14.8 1.49

Restricted Aimular 0. 30 20. 6 209 1. 24 84. 6 1. 07

0. 34 20.5 207 1.08 80.2 1.06

12.4 218 1. 11 71.4 1. 12

7.8 240 1.17 58. 4 1.23

0. 39 22.5 208 0. 96 80.2 1.07

13. 2 220 .99 67. 2 1. 13 5.6 269 1. 12 49.8 1.38

0.43 25.0 210 0.88 82.4 1.08 6.6 260 1.00 49.8 1.33 3.3 329 1.16 32. 2 1.69

Single circular- 1.0 21. 6 210 0. 36 54. 2 1. 08 8.2 241 .39 23.7 1.24 3.6 291 . 44 7.3 1. 49

4. 026 He Qalv. steel. -- 90. 6 Long sweep... Open Annular 0. 25 28.5 116 1. 00 41.2 1.28

23.

1

116 1.00 41.2 1. 28 23.0 130 1.07 41.2 1.44

12.3 143 1. 14 41.2 1.58

0.29 30.2 115 0. 87 41.2 1.27

26. 0 115 .87 41.2 1.27 21.4 131 .94 41.2 1.45

10.5 147 1.01 41.2 1.62

7.5 179 1. 13 41.2 1.98

0. 33 12 6 145 0.87 41.2 1.60 7.6 182 1.00 41.2 2. 01

5.

1

218 1. 11 36. 0 2.41

0. 38 8.6 176 0.87 41.2 1.94

5. 7 220 1. 00 36.

0

2. 43

3.5 269 1. 13 30. 6 2.97

3.5 269 1. 13 30. 6 2. 97

0.42 6.2 210 0.88 41.2 2.32

4.0 260 1.00 30.6 2.87

Single circular. 1.0 23.9 107 0 .24 41.2 1. 18 16.5 137 .28 38. 6 1. 51

12. 5 164 .31 15. 0 1.81

12.

1

164 .31 25.5 1.81 8.5 189 .34 9.7 2.09

9.1 189 .34 15.0 2.09

7.4 210 .36 9.7 2. 32 8 1 210 .36 15.0 2.32

6.1 230 .38 9.7 2. 54 5.5 241 .39 9. 7 2. 66

V* Galv. steel..- 191 Long sweep pe Annular 0. 29 15. 7 209 1. 24 62.2 1.09

0. 33 10.2 218 1. 11 61.7 1. 14

6. 6 240 1. 18 46.6 1.26

0.38 10.8 220 1. 00 67.

0

1. 15 4.7 269 1. 13 41.2 1. 41 3.7 295 1. 19 30.6 1. 54

0. 42 16.3 210 0. 88 62. 2 1.10 4.8 260 1.00 46.5 1.36

Single circular. 1.0 19.0 210 0. 36 57.0 1. 10 9.7 230 .38 46.5 1.20 9.0 241 .39 30.6 1.26

6.9 263 .41 26.6 1.38

5.4 291 .44 25.5 1.62

14
Table 3. Surge capacities of initially empty, sloping, simple drains—Continued

(Author's data)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

Distance Ratio of Ratio of from Ratio of

initial Initial drain capacity Drain Drain Drain Capacity Type of stack- Condition at Form of Initial area of Time Capacity velocity entrance for surge diameter slope TTi otprial tor steady base fitting lower end of cross section stream duration for surge to stack fn nninf tlKJ w

flow » drain of stream to area of surge flow terminal at which capacity

of drain velocity ^ surge for steady

filled flow

drain

in in.lft gpm

Restricted....

sec gpm fi 3.983 Ho Coated cast 89.0 Long sweep... Annular 0.26 20.8 116 1.00 46.2 1.30 iron soil 13.

9

130 1. 07 46.

2

1.46

pipe. 11.9 143 1. 13 42.7 1. 61

0.30 24.2 116 0. 86 46.3 1. 29

16.2 131 .93 46.2 1. 47

11.7 147 1.00 46.2 1. 65

8.

1

179 1. 13 45. 2 2. 01 4.9 209 1.24 36.2 2. 35

0.34 12.4 145 0. 87 46.2 1.63 6.4 182 1.00 35.2 2.04

5.

1

207 1. 08 35. 2 2. 33 4.3 218 1. 11 35.2 2. 45

3.8 240 1. 18 35.2 2.70

0.38 7.2 176 0.87 35.2 19.8 4.9 208 .96 36. 2 2.34

4.4 220 .99 36.2 2. 47 3.4 269 1.12 35.2 3. 02

0. 43 5.

3

210 0. 88 36. 2 2. 36

4.2 260 1.00 35.2 2.92 H Coated cast 188 Long sweep..

Restricted Annular 0. 30 12.1 209 1.24 75.2 1.11 iron soil pipe. 0.34 12.4 207 1.08 75.2 1. 10 9.6 218 1.11 66.2 1. 16

6.

4

240 1. 18 65.

2

1. 28

0.38 13.4 208 0. 96 70.2 1.11

10.

1

220 . 99 65.

2

1. 17 4.6 269 1.12 45.2 1.43

0.43 12.6 210 0.88 75.2 1. 12 5.1 260 1.00 45.2 1.38

6.484 Ml Plastic 342 Long sweep Open Single circu- 0.25 28.6 482 1.10 95.6 1.41

lar. 16.5 574 1.22 78.1 1.68

0.28 25.0 482 1. 01 78.1 1.41 22.0 507 1.04 78.1 1. 48

14.8 573 1. 12 78.

1

1.68

13.8 576 1.12 78.1 1.68

0. 30 35.7 431 0.86 91.2 1.26

19.

5

506 . 95 78.

1

1. 48

19.2 532 .98 78.1 1.56

16.0 553 1.00 78.1 1.62 14.0 577 1.03 78.

1

1.69 14.0 579 1.03 78.1 1.69

12.5 615 1.07 78.1 1.80

11.5 651 1. 10 78.1 1.90

10.4 656 1. 11 73.7 1.92

0.32 26.0 460 0.84 78.1 1.34 21.0 497 .88 78.

1

1.45 19.0 503 .88 78.1 1.47

15.4 561 .94 78.1 1.64

13.

5

584 . 97 78.

1

1. 71 13.7 584 .97 73.7 1.71 11.9 608 .99 73.7 1.78 11.6 625 1.00 75.9 1.83

10.0 664 1.04 73.7 1.94 9.8 684 1.06 75.9 2.00

9.8 690 1.07 75.9 2.02 7.6 727 1.10 64.9 2.13

0.35 26.0 461 0. 79 78.1 1.35

18.4 510 .84 78.

1

1.49

16.4 545 .87 78.

1

1.59

15.5 562 .89 78.1 1.64 13.0 586 .91 73.7 1.71 13.7 586 .91 78.1 1.71 11.5 624 .94 73.7 1.82 9.8 659 .97 75.9 1.93 9.8 689 1.00 75.9 2.02 8.7 690 1.00 69.3 2.02 9.8 692 1.00 75.9 2.02 6.6 754 1.06 60.5 2. 20

15
Table 3.

Surge capacities of initially empty, sloping, simple drains—Continued

(Author's data)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

Distance

Ratio of Ratio of from Ratio of

initial initial drain capacity Drain Drain Drain Capacity Type of stack- Condition at Form of initial area of Time Capacity velocity entrance for surge diameter slope material for steady base fitting lower end of cross section stream duration for surge to stack to point flow to flow • drain of stream to area of surge flow terminal at which capacity

of drain velocity >> surge for steady

flUed flow drain

in. in.lft gpm >ec gpm ft

0. 39 25.5 458 0.70 78.

1

1.34 18.6 610 .74 78.

1

1.49 15.0 659 .79 78.

1

1.64

12.5 594 .82 73.7 1.74 13.7 594 .82 78.1 1.74

13.7 594 .82 78.1 1.74 10.5 658 .87 73.7 1.92 10 0 682 89 73. 7 1 99 8!o 709 !91 69! 3 2^07 8.0 709 .91 69.3 2.07

8 0 717 . 91 69 3 2 10 8.0 720 !91 69! 3 2. 10 8.0 720 .91 69.3 2. 10 7.1 773 .96 64.9 2. 26

5.8 808 .98 60.5 2. 36

6. 484 He Plastic 342 Long sweep... Restricted Single circu- 0. 25 24.8 482 1.10 95.6 1.41

lar. 15.1 574 1.22 78.1 1.68

0.28 29.5 469 0.99 91.2 1.37 13.6 676 1.12 78.1 1.6

0. 30 34.2 431 0.86 91.2 1.26

17.9 632 .98 78.1 1.56

10.1 666 1.11 73.7 1.92

0. 32 20.0 497 0.88 78.1 1.45

11.1 608 .99 73.7 1.78 7.2 727 1.10 62.7 2.13

0. 35 15.6 545 0.87 78.1 1.59 8.5 690 1.00 69.3 2.02 6.2 754 1.06 60.6 2. 20

0. 39 8.8 658 0. 87 69.3 1.92 6.3 773 .96 60.6 2.26 4.9 808 .98 61.7 2. 36

Y-A-Hbend.. Open Single circu- 0. 39 30.6 437 0.68 46.2 1.28

lar. 9^ n zo. u 40 8 1 43 19.8 521 .75 40! 8 1.52 15.3 684 .81 36.4 1.71 16.2 694 .82 32.0 1.74 14.9 604 .82 36.4 1.77 12.2 662 .86 34.2 1.91 10.7 676 .88 34.2 1.97

9.

9

705 . 90 "iA 9 9 Ofi

Multiple 0. 48 18.8 0 561 0.64 64.9 1.64

circular. 10.2 "662 .71 49.5 1.94 9.4 "720 .75 49.5 2. 10 7.5 "804 .80 45.2 2.35 6.9 "871 .84 43.0 2. 55

6.

4

c 911 . 86 40.

8

2 66

0.55 17.8 " 565 0. 55 68.3 1.62 12.0 "665 .61 47.3 1.92

9.1 "726 .65 40.8 2. 12 6.3 "838 .71 27.6 2. 45 6.9 "897 .74 27.6 2.62 6.0 "906 .74 27.6 2.65

0. 61 30.6 "437 0. 43 45.2 1.28

19.8 " 521 .48 43.0 1.52

17.9 " 554 .50 58.3 1.62 15.3 "584 .61 38.6 1.71 14.9 "604 .52 38.6 1.77

12.6 1648 .54 29.8 1.90

12.2 "652 .56 34.2 1.91

10.4 " 664 .56 40.8 1.94

10.7 " 676 .56 34.2 1.97 9.9 " 705 .57 34.2 2.06 8.7 " 754 .60 40.8 2.20

8.6 d 773 .61 27.6 2. 26

7.1 "842 .64 25.4 2. 46 7.0 dSSO .64 27.6 2. 48

6.0 <i888 .66 25.4 2.60

6.2 "915 .67 25.4 2.68 4.9 "925 .67 21.0 2.70

5.2 "1930 .68 25.4 2.72

16
Tablk 3.

Surge capacities of initially empty, sloping, simple drains—Continued

(Author's data)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

Distance

Ratio of Ratio of from Ratio of

initial initial drain capacity Drain Drain Drain Capacity Type of stack- Condition at Form of initial area of Time Capacity velocity entrance for surge diameter slope material for steady base fitting lower end of cross section stream duration for surge to stack to point flow to flow » drain of stream to area of surge terminal at wbich

of drain velocity •> surge for steady

filled flow

drain

in. in.lft Qpm sec gpm /( H Plastic 500 Long sweep... Open Single circular. 0. 32 8. 2 755 1. 13 80. 2 1.51 8.9 769 1. 14 80.2 1.54

0. 35 8. 4 782 1. 08 75.9 1. 56

0.39 8.4 790 0.97 80.2 1.58 8.2 808 . 98 80.

2

1. 62

Restricted Single circular. 0. 30 8.4 738 1.19 78.1 1.48 7.9 753 1, 20 78.

1

1. 51

0.32 8.5 727 1.10 82.4 1.45

7. 6 769 1. 14 73. 7 1. 54

0. 35 8.4 754 1.06 78.

1

1.51

7. 5 782 1.08 69.3 1.56

0.39 7.5 776 0. 96 73.7 1.55 7.0 808 .98 73.7 1.62

e.484 Plastic 500 Y-&-l/8bend. Open Single circular. 0.39 32.0 584 0. 81 71.5 1.17 23.8 604 .82 53.9 1.21 16.4 652 .86 47.3 1.30

12.4 675 .88 43.0 1.35

11.

1

700 .90 38.6 1.40

10.2 720 .91 38.6 1.44

Multiple cir- 0. 48 18.

0

662 0. 71 78.

1

1. 32

cular. 18.0 662 .71 78.1 1.32

12.3 720 .75 64.9 1.44 8.2 804 .80 60.5 1.61 8.3 871 .84 56.1 1.74 8.0 871 .84 56.

1

1.74

5.6 911 .86 34,2 1.82

0. 55 15.

9

655 0. 61 67. 1 1. 31 11.0 655 .61 56.1 1. 31 7.8 726 . 65 38.6 1.45 7.3 838 .71 25.4 1.68

5.3 838 .71 29.8 1.68 7.0 897 .74 34.2 1.79 6.2 906 .74 29.8 1.81

0. 61 29.4 d 594 0.52 67.1 1.19 21.2 0 606 .52 80.2 1.21 18.0 <i 648 .54 51.7 1.30

15. 5 • 664 .55 64.9 1.33

10. 2 0 754 .60 49.5 1.51

10. 5 i 773 .61 38.6 1.55 5.4 "842 .64 25.4 1. 68

5.3 » 842 . 64 16.

7

1. 68

7 5

<i 850 .64 29.8 1.70 6.7 <i 888 .66 27.6 1.78

4.

7

» 915 . 67 25.

4

1. 83

5.8 d 920 .67 25.4 1.84 4.0 0 925 .67 21.0 1.85 5.8 d 930 .68 25.4 1.86

6.484 Plastic.

727 Y-&-1/8 bend. Open TVtultlple cir- 0. 48 14.5 0 871 0.84 73.7 1.20

cular. 13.2 0 911 .86 71.5 1.25

0. 55 18.

9

° 838 0. 71 75.9 1. 15

13. 5 0 897 .74 58.3 1.23

11.4 "906 .74 53.9 1.25

0. 61 18.5 "842 0. 64 75.9 1. 16 21.0 d 850 .64 80.2 1. 17 11.0 d 888 .66 53.9 1.22

13.3 "915 .67 53.9 1.26

11.2 "925 .67 53.9 1.27

10.1 •1930 .68 51.7 1.28

» See table 4.

•> Computed from eq (A-7) and from values in columns 1, 8, and 10. Equal stack and drain diameters were assumed. A value of absolute roughness of 0.00083 ft for the stack was used in the computations (see |91).

" Horizontal-jet supply valve wide open. Flow controlled by vertical-jct supply valve,

d Vertical-jet supply valve wide open. Flow controlled by horizontal-jet supply valve. The author utilized an electrical depth-sensing during the passage of a capacity surge. The

device and a recorder to measure changes in water length of tlic drain was appro.ximately 98 ft. The

depth in a 4 in. plastic drain at a slope of }4-in./ft. sensing element comprised two parallel flat stain17
Table 4. Capacity flow rates and coefficients of roughness for sloping simple drains under conditions approaching steady

uniform flow

(Downstream ends restricted so as to simulate conditions in very long drains completely filled but not under pressure)

(1)

Drain

diameter

(2)

Drain material

(3)

Drain

slope

(4) (5)

Capacity-flow rate

Experi- mentalRationalized »

(6) (7)

Darcy-Weisbach "/"

Experi- mental •> Rationalized o

(8)

Nikuradse

"fc" X 10 *, experi- mental

(9)

Chezy "C"

rationalized

(10)

Manning

'n", rationalized '

in. 2.985

3.068

2. 914

•'3.00

3.978

4. 026

3.983

3.90

6. 484

Plastic 8 (methacrylate).

in.lft

Steel ' (galvanized)

.

Cast iron « (plain).

Cast iron (plain).

Plastic » (methacrylate).

Steel « (galvanized) _

Cast Iron « (bitumen-coated).

Cast iron ' (plain).

Plastic* (methacrylate).

He

gpm

41.6

93.1

39.

35.5

73.6

j 32.1

i 45.6

i 69.8

92.0

192

90.4

191

90.2

186

i 66.8

i 89.0

> 128

340

500

gpm

42.1 90.8

40.7

84.0

35.5

73.7

32.8

46.8

66.7

91.9

195

90.6

191

89.0

188

64.1 91.2

130

342

500

0.0229

.0183

0.0287

.0245

0. 0278

.0259

0.0394

.0391 .0334

0. 0197

.0181

0. 0216

.0195

0. 0206

.0195

0.0338

.0381 .0368

0.0166

.0163

0. 0226

.0193 Averages

0. 0275

.0259 Averages

0. 0278

.0259 Averages

0. 0380

.0374

.0367 Averages

0.0200

.0176 Averages

0. 0216

.0195 Averages

0. 0212

.0191 Averages

0. 0369

.0364

.0361 Averages

0. 0165

.0146 Averages

0.99

.13

ft'/ytec 107

115

/<!/« 0. 00874

.00810

0.56

7.6

4.3

0.00842

0.00972

.00943

6.0

5.3

5.3

96.1 99.7

0.00968

0. 00969

.00934

5.3

2426

16

97.4

82.3

83.1 83.6

0. 00952

0. 0114

.0113 .0112

22

0.46

.73

83.0

114

121

0.0113

0. 00862

.00812

0.60

1.7 1.7

118

109

116

0.00837

0.00901

.00856

1.0

1.7

112

110 116

0. 00878

0. 00892

.00845

1.4

20

3129

113

83.5

84.0

84.5

0.00868

0. 0117

.0116

.0116

27

0.27

.05

84.0

126

133

0.0116

0.00850

.00801

0. 16 130 0.00826

« Computed from the rational pipe-flow equation, using values of "/" given in column 7. Computed from the rational pipe-flow equation, using experimental values of flow rate.

° Computed by adjusting column 6 values in accordance with the rational pipe-flow equation, using experimental values of Reynolds number, column 8 average values of "k," and the relationship between "k," and Reynolds number (see sec. 9.1).

<• Computed by use of chart showing relationship between "k," and Reynolds number (see sec. 9.1).

« Computed from the relationship between "C" and using column 7 values of "/" (see eq (A-3)).

' Computed from the relationship between "n" and "/," using column 7 values of "/" (see eq (A-3)).

8 Drain-pipe materials manufactured about 1958.

•> Nominal diameter. Laboratory notes do not state whether diameter was acutally measured.

' Drain-pipe materials manufactured prior to 1939.

i Estimated from measurements of flow rates in drains 70 ft long without end restrictions, by use of an equation which relates capacity-flow rates In short drains and in long drains (see sec. 9.2). Table 6. Flow from water closet through 4-in. stack and

Table 40 ft of 5-in. building drain 5. Flow from water closet through 4-in. stack and

40 ft of 4-in. building drain

Average flow rate at end Ratio of Flush of drain during indi- max.

cated period Max. recorded

recorded 5-sec rate Slope Height 5-sec rate at end of

of of of dis- drain to drain stack DuraAver- charge at estimated

age 1st 5 2d 5 1st 10 1st 15 end of max. 5-sec tion rate ' sec sec sec sec drain rate at water

closet •

in.lft ft sec gpm gpm gpm gpm gpm gpm H 30 10 31.8 13.5 16.5 15.0 14.0 16.5 0. 389 % 90 10 27.0 12.0 12.0 12.0 10.0 12.0 .333

y* 30 10 30.6 18.0 18.0 18.0 16.5 18.0 .441 90 9.6 31.6 15.0 13.5 14.2 12.2 15.0 .356

Slope

of drain

Height

of stack

Flush Average flow rate at end

of drain during indi- cated period Max.

recorded

5-sec rate

of dis- charge at end of drain

Ratio of max.

recorded

5-sec rate at end of drain to estimated max. 5-sec rate at water

closet •

Duration

Average

rate • 1st 5 sec 2d 5 sec

1st 10 sec

1st 15 sec

in.lft /( sec gpm gpm gpm gpm gpm gpm H 30 9 32.0 18.0 12.0 15.0 14.5 18.0 0.422 90 10 32.4 12.7 15.7 14.2 11.5 15.7 .363

V4H

30 10 30.6 20.0 20.0 20.0 17.0 20.0 .490 90 10 30.0 16,6 15.5 16.0 14.0 16.6 .415 lU 30 9 32.7 21.0 17.2 19.1 16.0 21.0 .482 lU 90 9 32.7 18.0 13.5 15.8 14.0 18.0 .413

• Estimated maximum 5-sec rate at water closet obtained by multiplying

average rate by 1 .33. This factor is based on a review of numerous water closet discharge patterns shown in NBS Reports 1131 and 1633.

« Estimated maximum 5-sec rate at water closet obtained by multiplymg

average rate by 1.33. This factor is based on a review of numerous water

closet discharge patterns shown in NBS Reports 1131 and 1633.

18
Table 7.

Figure 12. Discharge-rate meter.

Flow from water closet through 4-in. stack and

40 ft of 6-in. building drain

Flush Average flow rate at end

of drain during indi- cated period Max.

recorded

Ratio of max.

recorded

5-sec rate Slope Height 5-sec rate at end of

of of of dis- drain to drain stack Dura- Aver- charge at estimated

age 1st 5 2d 5 1st 10 1st 15 end of max. 5-sec tion rate sec sec sec sec drain rate at water

closet »

in.lft

!^H

Vi

ft309030

90

sec98

9

9

gpm

32.0

37.5

31.7

32.7

gpm

18.0

15.0 21.0

16.0

gpm

14.0

15.0 15.0

16.0

gpm

16.0 15.0 18.0

16.0

gpm

14.0

12.2

15.5

13.3

gpm

18.0

15.0 21.0

16.0

0.422

.300

.496 .367

* Estmiated maximum 5-sec rate at water closet obtained by multiplying

average rate by 1.33. This factor is based on a review of numerous water

closet discharge patterns shown in NBS Reports 1131 and 1633.

less-steel probes positioned vertically in a cross

section of the drain. The instrument system was

calibrated bv measuring the current flowing

through the water between the probes over a range of water depth in a plastic vessel. The

water used for calibration was taken from the same source as that used in the test drain . The

salts in the water resulted in sufficient electrical

conducti\'ity to make this method of measuring

depths feasible. The test surge was produced as described in section 5.1a(l) so that the velocity

at the base of the simulated stack was approxi-

—I—I

1—I1 r AT END OF CLOSET BEND -Uq

"I—I—I—I—I—I—

r

21 FT. DOWNSTREAM

16 14 12 10 8

ELAPSED TIME AFTER BEGINNING OF FLOW AT

INDICATED STATION , SECONDS

Figure 13. Rate of discharge from water closet as a function

of time and distance from the fixture.

Discharge rates measured with rate meter at end of a 4-in. drain which was

extended successively to the indicated lengths. Reverse horizontal scale simulates surge profile for left-to-right movement. Table 8. Attenuation of maximum 5-sec discharge rate from single water closet discharged directly into drain

Ratio of esti- Distance Peak rate Estimated mated max.

Drain Drain from water of discharge max. 5-sec 5-sec rate at diameter slope closet to at end of rate at end end of drain end of drain drain » of drain t to max. 5-sec rate at drain

entrance, 1-6

in. in.lft ft gpm gpm

3 Yi 6 36.6 •> 31.

1

0. 99

11 34.5 b 29.3 .93

21 3L7 b 26.9 .86

.41 23.6 ''20.1 .64

3 6 37.5 b 31.9 1.01

11 36.8 bSl.S 0.99

21 26.4 ''22.4 .71

41 17.4 b 14.8 .47

4 Vi 6 36.8 29.6 0.94

11 33.7 29.5 .94

21 36.0 28.8 .92

41 25.3 23.5 .75

4 6 37.1 b31.5 1.00

11 36.9 b31. 4 1.00

21 34.4 b29.2 0.93

41 24.2 b20. 6 .65

• Peak rate at water closet was 37.0 gpm. The data of figure 13, for a 4-in. drain at a slope of 1/4 in. /ft, show that the max. 5-sec rate at the water closet was approx. 85% of the peak rate, or 31.4 gpm.

b Data of figure 13, for the 4-in. drain at slope of 1/4 in. /ft show that the max. 5-sec rate at the end of the drain averaged approx. 85% of the peak rate

at the end of the drain. Accordingly, values identified 6 were obtained by

multiplying the peak rates by 0.85. mately the same as terminal velocity for the same

rate of discharge computed through the use of

eq (44) of NBS Monograph 31 [9] or for the same

cross-sectional area computed through the use of

eq (A-7).

19
(2) Results The data in tables 5, 6, and 7 were obtained

from the 10-story test system. These data relate to attenuation of discharge rate in a simple drain

carrying a small surge, such as the discharge of a

single water closet, which does not fill the drain.

The water discharged from the end of the building

drain for the first 15 sec accounted for 60 to 70

percent of the total discharge. Thereafter, the

flow gradually receded, and was reduced to a

trickle from the end of the drain in about 45 sec

for the 4-in. and in about 60 sec for the 6-in. drain.

The flush duration at the water closets ranged

from 8 to 10 sec. The instantaneous discharge rate from the end

of a 4-in. drain resulting from the flushing of a water closet directly connected to the drain,

measured with the apparatus shown in figure 12

and expressed as a function of time, is shown in figure 13. The purpose of using an abscissa scale

reading from right to left is to create the impression of surge movement from station 1 to 2 to 3, etc. Table 8 gives data on peak discharge rate

for 3- and 4-in. drains.

Data from tables 5, 6, and 7, on the attenuation

of discharge rates from single water closet flushes

in the 10-story system are summarized in table 9. The data in the fourth column indicate the extent

of attenuation of discharge rate in the stack and

40 ft of building drain; and that in the fifth column,

attenuation in the drain only. In order to compare the attenuation data from

the 10-story system with that from the horizontal

drain with a directly connected water closet,

adjustments were made to some of the recorded

data. Maximum 5-sec rates were recorded at the

end of the drain for the 10-story system, while

peak instantaneous rates were recorded for the

other test system. Average rate of discharge at the water closet was recorded for the 10-story

TaBLE 9. Attenuation of maximum 5-sec discharge rate from single water closet with passage through 4-in. soil slack and 40 ft of building drain

Drain

diameter umiii tiiupe neigot of stack

Ratio of max.

recorded 5-sec rate at end

of drain to estimated max. 5-sec rate at water

closet »

Ratio of max.

recorded 5-sec rate at end

of drain to estimated

ITlQX 5-SGC rate i> at drain

entrance, l-{

in. in/ft ft i H 30 0. 39 0.41 H

90 .33 .38 30 .44 .46 90 .36 .41

5 30 .42 .44 90 .36 .42

'A 30 .49 .51 90 .42 .47 Me 30 .48 .50

90 .41 .47

6 H 30 .42 .44 90 .30 .34 M 30 .50 .52 90 .37 .42

» These data are from tables 5, 6, and 7. b Max. 5-sec rate at entrance of building drain estimated by reducing the max. 5-sec rate at the water closet 1.4 percent for each 10 ft of stack height. This reduction factor was derived from data in the third and fourth columns

of this table.

1.0

0.8

0.6 04

0.20

I I I

1 1 STA.I0-I2e PIPE DIA. DOWNSTREAM

J L

25 30

1.0

o.a ae

0.4-

0.2-

0.

1

1 1 STA. 11-141 PIPE DIA. DOWNSTREAM FULL PIPE

20 25 30

ELASPED TIME , MEASURED FROM INSTANT SURGE ENTERED TEST DRAIN , SECONDS

Figure 14. Water depth produced by surge in 4-in. plastic drain, as a function of time and distance from drain entrance. {Measured with electrical depth gage.)

20
system, while instantaneous peak rate was re- corded for the other system. It seems reasonable

to compare the data on the basis of the same type

of peak rate, i.e., attenuation of either instanta- neous peaks or 5-sec peaks. For various reasons

it was decided to make the comparison on the

basis of attentuation of 5-sec peaks. The method

used for estimating maximum 5-sec rates, where

not originally measured, is explained in the foot- notes to tables 5 through 9. Typical data obtained by the author with the

electrical depth gage on the attenuation of water

depth in a plastic drain as a function of time and

position are shown in figure 14. The measured

variables and the test conditions for these data

differ from those for Himter's data in two important ways: first, the data are for water depths

while Hunter's data are for discharge rates; and

second, the data are for capacity surges while

Hunter's data are for surges which did not fill the

drains. The surge from which the data in figure 14 were derived occupied about one-third of the cross- sectional area of the drain entrance and had an

initial velocity of about 16 fps. The time diiration

of the surge at the drain entrance was 6.5 sec and

the discharge rate was 265 gpm, or about 35 percent greater than the steady flow capacity of the

drain. Figure 14 shows that the length of time

for passage of the surge at any given station

increased -with distance downstream. The water

depth increased at first, completely filling the

drain cross section at a distance of 47 ft from the

entrance. Beyond this station, depth decreased

and passage time increased.

Attenuation was inversely related to drain slope,

and directly to drain length according to the data

of tables 8 and 9. The effect of drain diameter was less clearly indicated. For drain lengths of 40 and 41 ft. and diameters of 3, 4, and 5 in., attenuation decreased as diameter increased, other

conditions being the same. However, attenuation

in the 6-in. drain did not conform to this trend.

The possible effect of gravity on discharge rate

of surges through deflection of the surface profile near the unobstructed end of a drain was not

considered in these measurements. It does not seem likely that this would affect comparative

indications appreciably, but might affect actual

values. Hence it should be taken into account

in any further work on attenuation.

The data in tables 8 and 9 were utilized as the

basis for approximate equations for predicting

attenuation of discharge rate as a function of drain length and slope, as explained in section 6.2.

5.2. Flow in Compound Drains

a. Test Methods and Apparatus

Hunter made a preliminary study of the effects of introducing either steady or surge flow through

a branch drain whUe maintaining a steady dis- charge into the entrance of the main drain which

was less than the steady flow capacity of the main.

BRANCH SOIL PIPE FITTING

WATER SUPPLIED FROM 3-IN. LINE

WATER SUPPLIED FROM 2- IN. LINE IN. SOIL PIPE

PLAN VIEW

FiGUBE 15. Schematic diagram of test system used by Hunter to study flow conditions at junction in compound

drain.

STILLING BOX TO

MINIMIZE TURBULENCE

CLOCK

MicRoswrrcH

SUPPLY LINE- FiGUKE 16. Schematic diagram of test system used by

author to study flow conditions at junction in compound

drain. He used a 4-in. diam main drain of cast-iron soil pipe approximately 60 ft in length at slopes of Ke and }g-in./ft. Branch diameter was 4-in., and

lengths were 20 ft and 40 ft. The branch and the

main were in a common nominally horizontal

plane, with the same slope. This apparatus is shown schematically in flgure 15. The author continued Hunter's study over an expanded range of conditions, utilizing the apparatus shown schematically in figure 16. The

main drain was 98 ft in length. Main diameters were 4 and 6}2-in., and slopes were jie, )%, and )i in. /ft. Several different sizes of branch

drain were used. The drains were constructed of transparent methyl methacrylate plastic. The

effective length of the branch drain was either 2 or 4 ft as indicated in the tables of data (see sec. 5.2b).

Two conditions were studied with this apparatus

:

(1) the condition resulting from steady flow in

both main and branch; and (2) the condition re- sulting from surge flow in the branch and steady

flow in the main. In these tests, an arbitrary

steady rate of discharge not sufficient to fill the

main drain was introduced into the upstream end

of the main through a stilling box. After substantially steady, uniform flow was attained

throughout the length of the main, discharge was

introduced through the branch. Adjustments

were made of the flow rate in the branch in order to

just fill the main drain completely at its junction

with the branch. For tests with surge fiow in

the branch, a selected surge duration time was

21
maintained in successive trials to determine

capacity discharge rate for the branch. Sm-ge

flow into the branch was initiated and terminated

by a quick-opening valve in the supply line to the branch drain. Manual opening and closing

of the plunger valve shown in figure 16 was timed

to coincide approximately with push-button operation of the quick-opening valve in order to record

surge duration time at the branch. The surge

duration was recorded by an electric stop clock

controlled by a microswitch actuated by movement

of the plunger shaft. In the tests with steady

flow in the branch, the plunger valve was locked

in a partially open position. For steady flow in

the main drain and either steady or surge flow in a branch in a common horizontal plane, the criterion

of hydraulic capacity was the existence of a full section of minimum length within the main at its junction with the branch.

The author also studied the condition produced

by superimposing surge flow through a vertical

branch on steady flow in a main horizontal drain,

utilizing the apparatus shown in figure 10 as modified by replacing the long-sweep stack-base

fitting with a Y- and Jg-bend fitting with a heel

inlet. Steady flow was introduced into the main

through a short length of 3-in. pipe caulked into

the heel of the base fitting. Surge flow with an

annular cross, section was introduced through a simulated 4-in. stack from the vertical at velocities

approximately equal to stack terminal velocities

computed by a method given in an earlier paper

[9] (see also eqs (A-6) and A-7 of sec. 9.4). A

4-in. main, approximately 98 ft long, was constructed of transparent methyl-methacrylate plastic. Drain slopes of ji and % in. /ft were used.

For a given surge which by itself did not produce

a fuU-conduit condition anywhere along the drain,

steady flow through the heel inlet to the stackbase fitting was increased by increments in successive runs until the superimposition of the surge

produced a full section of minimum length downstream of the stack. This was the criterion of

hydrauUc capacity. The capacity could be described by the volume rates of steady and surge

flow and by the time duration of surge. Venting of the test drains was provided at intervals as described in section 3.

b. Results

A description of flow at the junctions of main

and branch drains was given in section 3 and

illustrated in figures 4 to 7. Hydraulic capacities

of compound drains, measured over a range of

test parameters are given in tables 10, 11, and

12. Table 10 gives data for steady flow in both

main and branch in a common horizontal plane.

Table 11 gives data for flow in the same test system except that surge flow, instead of steady

flow, was introduced through the branch. Table

12 gives data for steady flow in a main and surge

flow through a vertical branch. The data given

for cast-iron drains were obtained by Hunter and

Table 10. Capacity of drain system for steady flow at junction of main and 45° branch

(Main drain and branch In same nominally horizontal plane. Full section at

junction.)

Diameter

of main

Diameter of branch Drain

slope Drain material Length

of branch

Capacity flow rates

Main Branch Total

in. in. in.l/t ft gpm gpm gpm

4 4 Mo Cast iron 20 18.6 41.8 60.4 21.2 44.2 65.4

23.9 41.6 65.4

26.5 38. 4 64. 9 30.0 36.7 66.7 30.9 34.6 66.6 37.2 28.3 65.6 37.8 26.6 64.

1

63.

2

14. 6 67 8 63.6 16! 9 69! 4 76.6 0

77.

1

0

85. 2 0

40 25.6 39.4 65.0

32 6 33 3 66.

9

80^4 o' H Cast iron . ... 20 30.9 37.9 68.8

46.2 24.2 70.4

114 0

114 0

40 31.0 40.

1

71.

1

46.6 28.0 73.6 63.9 13.8 77.7

81.2 7.2 88.4

116 0 116 0

4 3 He Plastic 4 28.4 49.3 77.7 30.0 44.2 74.2 32.6 46.0 77.6 34.9 39. 5 74.4 39.6 35.4 76.0 39.7 32.4 72.

1

44.4 27.8 72.2 48.9 23. 4 72.3

63.6 20. 7 74.3

50.6 16.

1

66. 7 61.6 14.9 76. 6 63.6 12.2 75.8

68.4 11.4 79.8 H Plastic -- 2 39.2 39.0 78.2

39. 8 40. 5 80.3

40.6 39.4 80.0

42.6 39.0 81.6

45.5 33. 7 79.2

48.4 33.0 81.4

48.4 32.2 80.6

50.0 31.8 81.8

74.0 16.

1

90.

1

73.5 15.0 88.5

74.3 16. 2 90. 5

88! 4 8!6 97.0

95.5 6.

1

102 m Plastic 4 94.2 134 228

94.1 137 231 123 109 232

149 86.8 236

172 72.

6

245

193 60!4 253

212 48.5 261 229 42.4 271 243 34.6 278

254 29.6 284 H Plastic - 4 137 110 247

175 84. 0 259 207 63! 0 270 232 62.6 285 253 47.1 300

280 38.5 319 316 31.8 348

4 Me Plastic 2 145 114 259

179 80.2 259

199 64.5 264 219 49.8 269

238 45.2 283

260 34.

1

294 278 29.5 308 H Plastic 2 172 111 283

189 85.

1

274 205 80.6 286 233 74.6 308

22
Table 10. Capacity of drain system for steady flow at junction of main and ^5° branch—Continued

(Main drain and branch in same nominally horizontal plane. Full section at junction.)

Diam- Length Capacity flow rates Diameter eter of Drain Drain material of

of main branch slope branch Mam Branch Total

in. in. in./ft ft gpm gpm gpm

264 50. 7 315

273 46.

1

319 6k 3 Plastic 4 219 63. 6 283

236 45.

1

281

271 30.

1

301 310 22.

6

333 312 22. 6 335

352 14. 8 367

Plastic 2 223 104 327

232 81.1 313

236 73.0 309

243 71.5 315

244 66.1 310

254 67.9 322

263 63.2 326

264 63.0 327

281 61.5 343

292 53.6 346

307 49.0 356

those for plastic drains were obtained by the

author.

The maximum and minimum hmits on the

ranges of discharge used in the tests were determined in some cases by hmitations imposed by

the water-supply or flow-measuring apparatus and

in other cases by inabihty to attain a clear indication that the criterion of hydrauhc capacity had

been satisfied. In most cases of the latter type,

it appeared that hydraulic capacities were actually somewhat greater than indicated by the

equations developed from the data in tables 10,

11, and 12, for which reasonably clear indications

of a capacity condition were attained; but this point was not investigated in a systematic manner.

Table 11. Capacity of drain system for steady flow in main and surge flow in branch

(Main drain and branch in same nominally horizontal plane. Full section

at junction of main and 45° branch.)

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Diam- Diam- Diameter Time

Capacity flow rates

eter

of main

eter of branch Drain

slope Drain

material

of jet at upper end of branchduration

of surge Main Branch Total

in. 4in. 3

in.lft 1/8 Plastic • in. sec

5 gpm

38.9 40.6

49.0

50.0

gpm

84.6

68.4 51.6

41.9

gpm

124

109

10191.9

10 33.6

34.8

43.1

46.0

84.

68. 51

41.

6

16

9

118

10394.7

87.9

15 27.0

31.8

37.6

46.0

84

68

51

41.

8

46

9

112

10089.2

87.9

20 22.9

28.4 34.8

43.3

84

68

51

41

3

16

4

10796.5

86.4

84.7

Table 11. Capacity af drain system for steady flow in main and surge flow in branch—Continued

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Diam- Capacity flow rates Diam- Diam- eter Time

eter eter of Drain Drain of jet at durof branch slope material upper ation main end of of Main Branch Total branch surge

in. in. in.lft in. sec gpm gpm gpm

30 19. 6

SIA ^ 23.4 68.1 -91.5 31.1 .51.6 82.7

38.9 41.9 80.8

Plastic * 2 5 40.2 78.8 119 41.7 79.7 121 46.2 63.5 110

10 34. 5 70 7 35.1 79.3 114 37.6 63.5 101

15 Qn o qU. ^ ou. u

1 in 30.8 79.3 no

35.3 63.2 98.5

20 ^0. u

7a Q to. o 104 25.8 81.4 107 26.2 80.0 106 31.5 62.9 94.4

30 20.1 78.8 98.9

21.6 80.2 102 27.3 63.2 90.5

X las 11^ - - - 5 36.8 116 153

48.4 57.9 106

54.0 39.5 93.5

10 26.2 116 142

40. 9

f^7 Q 98.

8

52.0 39.5 91.5

15 22.0 116 138

35.1 57.9 93.0

48.4 39.5 87.9

20 17.4 129 146 19.0 116 135 19.6 92.8 112 33.0 57.2 90.2

47.

1

40. 0 87.

1

30 11. 0 Hit 140

14.2 116 130

15.6 92.1 108 29.5 57.2 86.7

44.3 40.0 84.3

4 1/16 Cast iron >>. 2 5 16.4 101 117

25. 5 130

38.4 54.4 92.8

54.2 35.2 89.4

10 16.4 103 119

15 16.2 86.7 103 25.5 68.5 94.0

38.4 43.1 81.5

54.2 31.6 85.8

20 16.2 82.0 98.2

25 16.2 76.7 92.9

25.6 51.5 77.0 38.4 39.9 78.3

54.2 26.6 80.8

35 1ft 0 10. z 64 5 70 7 25.5 5L5 77! 0 38.4 37.8 76.2 54.2 23.3 77.5

V^lwt 11 UU 2 10 13.9 99.3 113 20.2 93.6 114

28. 1 89.5 118 30.9 78.

3

109

39. 5 61.7 101 46.8 4L0 87.8

56.3 27.4 83.7

20 13.9 84.5 98.4

20.2 87.9 108

28. 1 80.9 109 30.9 63.0 93.9

39.5 41.9 81.4

46.8 31.2 78.0

56.3 22.9 79.2

23
Table 11. Capacity of drain system for steady flow in main and surge flow in branch—Continued

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Diameter

of main

Diameter of branch Drain

slope Drain

TYl titoriQ 1

Diameter

nf'J Ii pt nt J C 1/ ai/

emFo'f

Time

duration

of surge

Capacity flow rates

Main Branch Total

in. in. in.lft in. sec gpm gpm gpm

30 13.9 78.7 92.6

20.2 70.8 91.0

28.

1

62.

0

90.

1

30.

9

63.

6

84. 6

39. 6 37.

1

76.

6

46.

8

21.

8

68.

6

66.

3

21.

1

77. 4

I/O 1/8 O&st Iron ^ 2 10 16.7 142 169

23.

9

106 130

37.

6

54.

0

91.

6

65. 5 35.

6

91.

1

73. 7 34.

1

108

90. 5 30. 121

20 16.7 100 117 23.9 78.6 102 37.6 37.1 74.7

56. 5 30. 2 86. 7

73. 7 29.

9

104

90. 5 28. 7 119

30 16.7 85.8 102 23.9 60.0 83.9

37.6 34.8 72.4

66.6 26.7 82.2

73. 7 26.

1

99. 8

90. 5 25.

9

116

Cast iron o. 2 S 63.

8

67. 2 111

10 16.4 138 154 26.6 144 170 39.9 65.7 95.6

66. 6 35.

6

91. 1 74.

1

26.

3

100

15 63.

8

34.

9

88. 7

20 16.4 110 126 26.6 64.4 89.9 39.9 43.2 83.

1

55.

6

31.

2

86. 7

74.

1

22.

0

96.

1

25 63.8 32.3 86.1

30 16. 4 77. 0 93. 4 26.5 54.0 79.5 39.9 39.6 79.4

66. 6 27. 4 82. 9

74.

1

18.2 92.

3

40 53.8 26.7 79.6

3 1/16 Plastic 3 5 226 107 332

227 123 360

236 89.6 326

10 208 123 331

213 107 320

221 89.2 310

20 198 123 321

199 107 306

208 89. 5 298

4 1/16 Plastic 4 5 204 109 313

214 87.8 302 236 64.

1

300

10 189 109 298

202 87.8 290

221 64.

1

286

20 165 109 274

181 87.8 269 206 64.1 269

• Branch length 2 ft. « Branch length 40 ft.

i> Branch length 20 ft. ^ Branch length 4 ft.

Hydraulic capacity was affected by velocities in main and branch drains, the ratio of the diameters,

the division of discharge between main and branch.

and other factors. Where surge flow in the branch was involved, time duration of surge also affected

capacity. These and other factors are included

in the equations developed in section 6. Perhaps

the most significant observations were:

1 . A relatively small amount of steady discharge

in a branch drain resulted in a substantial decrease

in system capacity due to mutual interference at the junction of the main and branch, and

2. surge discharge in a branch drain resulted

in an increase in system capacity over that obtained for steady discharge.

Detailed discussion of the results appears in section 6.3.

Table 12. Capacity of plastic drain system for steady flow in main and surge flow in branch

(Main drain Ln nominally horizontal plane; branch, in vertical plane, con- nected to main through Y-&-1/8 bend fitting near upstream end of main. Full section at some distance downstream from junction.)

Initial Distance Capacity flow rates Drain Time area • from branch

slope duration of surge to point at of surge stream which surge Main Branch Total

filled drain

in.lft sec 171.2 n gpm gpm gpm

]^ 5 4.76 23.8 4.6 220 225

4. 23 25.

9

9.8 182 192

4 23 23 g 10 9 182 193

4! 23 23! 8 15!l 182 197 3.71 19.4 27.7 147 175 3.24 21.6 46.8 116 162 2.62 23.8 92.4 76.5 169 2.05 23.8 108 52.0 160

10 4.23 30.3 1.3 182 183 4.23 36.8 1.9 182 184

3. 71 34.6 16.2 147 163 3.24 30.2 34.2 116 150 2.62 28.1 75.7 76.5 162

2. 05 28.1 104 52.0 156

15 3.71 43.4 8.

1

147 165 3.24 34.6 31.

1

116 147 2.62 34.6 69.5 76.5 146

2. 05 32.4 90.4 62.0 142

20 3.71 62.2 5.0 147 152 3.24 43.4 25.8 116 142 2.62 43.4 64.4 76.5 141

2. 05 34.6 88.4 62.0 140

V* 5 5.23 34.6 6.3 260 266 4.76 30.2 14.2 220 234 4.23 21.6 34 8 182 217 2.62 12.8 107 78.6 186

10 4.76 56.6 9.0 220 229 4.23 47.8 27.8 182 210

3. 71 43.4 53.4 147 200 3.24 2L6 73.8 116 190 3.24 21.6 66.2 116 182

15 4.76 60.9 4.5 220 224 4.23 60.9 24.6 182 207

3.71 60.9 51.8 147 199

» Surges were annular in initial cross section. Initial velocities were

approximately in accordance with terminal velocities for a 4-in. stack as computed from eq (A-7) for a value of ;c,=0.00083 ft.

6. Analysis of Experimental Results

6.1. Surge Flow in Initially Empty Simple

Drains

The analysis begins with a consideration of the

forces acting on the water, followed by an application of the principles of dimensional analysis. The

primary object of this analysis is to obtain a

solution which can be used for predicting hydraulic

24
capacities over a range of conditions. Definitions

and symbols used in the analysis are explained in section 2. For steady, uniform gravity flow in a long,

sloping drain of uniform slope and cross section,

the hydraulic elements are constant throughout

the length of the drain, and constant with time at any particular cross section.

On the other hand, for surge flow, the hydraulic

elements vary both with distance along the drain

at any given time and with time at any given cross

section. Therefore, a knowledge of the hydraulics

of steady flow is of limited value in the solution of problems of surge flow. A simple method is desired for predicting

relative capacity, defined as the ratio of surge-flow

capacity to steady flow capacity. This knowledge

is needed for design of plumbing drains in service.

The steady flow capacity of a conduit for full-bore

gravity flow without pressure at the crown can be

determined from established formulas with reasonable accuracy or by direct measurement. Experimental observations have indicated that the

predominant parameters affecting surge-flow

capacity are time duration of surge and drain

slope. The combined effect of roughness and

drain diameter was less clearly indicated.

A consideration of the forces acting on the fluid indicates that relative capacity wUl be greatest

when the local attenuating force is at a maximum,

thus making it possible for the drain to carry a

substantially greater rate of surge flow than steady

flow without creating hydrostatic pressure at the crown of the drain. Local attenuating force is defined in section 2. Since such forces are most

predominant in short-duration surges, relative

capacity should be inversely related to the length

of time that water is allowed to discharge into the

drain. The experimental data confirmed this. The data showed clearly that, for any given

time duration of surge, relative capacity decreased

with increasing drain slope. Although actual

hydraidic capacities increased with slope for both

steady and surge flow, the increase for a given

increase in slope was relatively less for surge flow

than for steady flow. Surface roughness of the drain material introduces a shearing force in opposition to the longitudinal component of gravity which tends to empty the drain. For any given slope, increased

roughness decreases actual drain capacity, both

for surge flow and for steady flow. However, local attenuating force is a significant factor in surge

flow, tending to prevent the drain from filling up. This is not a factor in steady flow. Therefore, a given change in roughness should affect surge-flow

capacity relatively less than steady flow capacity.

Hence, relative capacity for surge flow should in- crease with surface roughness. A slight trend in

this direction was observed in the experimental

data.

Dimensional analysis [10] was used in obtaining

groupings of pertinent variables that satisfy the

qualitative requirements discussed above. The

variables considered in the analysis are in general

those associated with the water stream near the

drain entrance, since no measurements were made

of dynamic quantities as the surge moved through

the test drain between the entrance and the cross section at which the drain was filled. Among the

variables considered are the following: (1) velocity

Va, of the water stream (jet) at the drain entrance; (2) equivalent diameter, Dj, of the jet at the drain entrance; (3) time duration of surge, t; (4) drain slope, 6; (5) drain diameter, Da, (6) drain

length. La, (7) absolute roughness, ka, of drain

material; (8) fluid density, p; (9) fluid viscosity,

v; and (10) acceleration due to gravity, g-, If the

problem is to be analyzed from the standpoint of

relative capacity, another variable must be added

to the list; namely (11) the velocity, Fg,, which,

if multiplied by the cross-sectional area of the

stream at the drain entrance, 0.785Z)f, would

produce a rate of discharge equal to that required

to cause the drain under consideration to flow

barely full without pressure under steady flow

conditions. These variables can be collected into

dimensionless terms as follows: _ Va . _ Vst . _D,

TTl 7=, 172—1=, T^3 —JY

yJDag ^JDag ^tf

^'

7r6=^; ^^^=9 and 7r8=yyJ-^d LJd

Dimensional analysis does not give the functional

relationships which may exist between the indicated terms but it does reduce the number of potentially significant variables to be studied.

The term LajDa can have no effect on the phe- nomenon under consideration so long as none of the discharge reaches the lower end of the drain

before the maximum depth is produced. That is in very long drains LJDdiOr ts, is not a pertinent

variable. This term is significant only when the

drain is so short that the characteristic surface

profile in the region of maximum depth is affected

appreciably by the proximity of the downstream

or outlet end. The analysis will be developed to apply to drains that are quite long, so that tts can

be omitted from consideration. Actually, this omission will lead to the prediction of capacities

tending to include a safety factor when applied to practical conditions where drains may be short,

since short drains tend to have surge capacities

somewhat greater than long ones, other factors

being the same. Experimental data showed no significant effect on relative capacity attributable to ts or ws over

the range of experimentation, hence these parameters will not be included further in the analysis.

The fact that variation in Reynolds number did

25
not affect relative capacity significantly indicates

that the experimentation with surge flow was in

the hydraulically "rough" range where frictional

resistance is independent of Reynolds number.

Therefore, the relationship

and

</>(ti, TTz, 7r4, TTs, 7r7)=0 (1)

follows. It is desired to predict the relative ca- pacity for surge flow, or the relative increase in

hydraulic capacity for surge flow as compared to that for steady flow. For any given cross-sectional area of jet and time duration of surge, the

relative increase in capacity can be represented by

AQ TTi —7r2 Qetc

(2)

Plotting of experimental data on logarithmic paper

showed that this convenient grouping of the variables brought order from the data. Therefore,

the relationship

^sfc

(3)

was utilized in further consideration of the experimental data. That is,

The term AQ/Q^ic, the relative increase in capacity

for surge flow over that for steady flow, will be

looked upon as the dependent variable.

Data for any particular drain at a given slope

showed that AQJQatc was approximately an inverse

linear function of the time duration of surge. This indicated that

(5) Qstc T^i t-yfg The data for different degrees of drain roughness

indicated that AQ/Q^tc increased slightly with

roughness, other factors being the same. Computations based on the experimental data indicated

the relationship between AQ/Q^ic and kJD^ as exhibited by the data cannot be represented

satisfactorily by a simple power function of kJD^.

Since the Reynolds numbers associated with the

relatively high velocities of the surges introduced

into the experimental drains indicate the flow to be within or near the hydraulically rough regime,

it seems reasonable that the roughness effect might

have been related to the roughness coefficients

associated with the "rough" regime. Using values

of ki given in table 4, corresponding values of /, C, or n for the rough regime may be computed from

the usual relationships [11]

J. =2 log ^+1.14 (6)

1 _ Cr _1.18(Z?,)^/«

^ITr VS^ ^^^nr

(7)

The subscript r denotes the rough regime. It was

found that the resistance coefficient was related

to the observed effect of roughness on AQ/Q^tc by

the simple relation

AQ

QbIc

OCTTeOC (8)

By use of eq (7) the roughness effect could have

been expressed equally well in terms of Cr or Ur. Data for any particular drain for different slopes

showed that AQ/Qs,c was approximately an inverse

linear function of the drain slope, or AQ 1 1 Qstc TT: tan 0

(9)

The experimental results of tables 2, 3, and 4

and figures 17, 18, and 19 indicate that the left- hand member of eq (3) is approximately a linear

function of the product of the terms in the righthand member as given by eqs (5), (8), and (9). This provides the basis for a convenient simplification in which the dependent variable is expressed

as a function of the independent variables which

could be computed easily from the experimental

measurements. The curves shown in figures 17,

18, and 19 were computed from this function

expressed as

tan 0 (10)

In eq (10) K is a dimensionless coefficient dependent on the geometry of the jet form. This

simple function of the principal variables may not

be applicable far outside the range of the experimentation. However, the agreement is satisfactory over the practical working range investigated.

The quantities l + A^/^e,c, t, and k, were measured for several values of d and Da, the values

of which are given in tables 2, 3 and 4. Corresponding values of l/V/r (and hence V/i-) were computed from eq (6). From eq (10) values of K

were computed for the various jet forms used. Possibly the explanation of the difference in /^-values

for different jet forms is that the energy losses asso- ciated with the passage of the water through the

stack-base fittings are affected by the jet form.

However, this effect was not incorporated in eq

(10) as a function of other variables, since in a typical plumbing system the flow at the base of the stack tends to approach the annular jet form

which yielded the lowest capacity in the experimentation. Thus the use of the coefficient

derived for the annular jet form should be safe

for design.

With a few exceptions, the data in table 3 are

in satisfactory agreement with eq (10). This is

26
DURATION OF SURGE .SECONDS Figure 17. Comparison of eq(lO) and experimental measurements on drain systems shown in

figures 8 and 10 {surge flow in initially empty 3-in. drains, long-sweep stack-base fitting).

End of drain open End of drain restricted Slope

In./ft O • 1/16

1/8 A A 1/4

(Xumbers adjacent to symbols indicate duplicate values.)

Chart Jet form

(see fig. 9)

l:)rain material

A B Plastic. B C Plastic. C B Steel, galvanized. C Steel, galvanized. E B Cast iron, uncoated. F C Cast iron, uncoated. G E Cast iron, uncoated.

demonstrated in figures 17, 18, and 19. The

curves in these figures represent eq (10), using

values of K as indicated in the follo\ving table

computed from data in tables 3 and 4. The

plotted points in the figures are experimentally

deternained values.

Jet form K

Annular 9. 86 Modified annular 10. 5 Single circular 11. 4

These values of K were determined from the data

where long drains were simulated. Values of K=10.5 for Hunter's crescent jets and K=12.S

for the multiple-circular jets were used in plotting

the curves for these data. The basis for the latter two values is discussed in section 9.3 of the

appendix.

It had been expected that the type of stack-base

fitting used might affect surge-flow capacities,

and hence the value of K. However, the data in table 3 on this effect appear to be inconclusive.

Data on a 4-in. drain show that, for the Y and

% bend, Q/AQsic was of the order of 3 percent less

27
4.0 4.0

10 20 30

10 20 30

10 20 30

DURATION OF SURGE , SECONDS

Figure 18. Comparison of eq{10) and experimental measurements on drain systems shown

in figures 8 and 10 {surge flow in initially empty 4-in. drains, long-sweep stack-base fitting except where otherwise indicated).

End oi drain open End of drain restricted Slope

in./rt O • 1/16

1/8 A 1/4

(Numbers adjacent to symbols indicate duplicate values.)

Chart Jet form

(see fig. 9) Drain material

A A Plastic. B* A Plastic. C C Plastic. D A Steel, galvanized. E C Steel, galvanized. F A Cast iron, coated. G E Cast iron, uncoated.

than for the long sweep. Similar data on the

6K-in. drain show a value of the order of 4 percent

greater. Therefore, no allowance has been made

for the type of stack-base fitting in estimating

surge-flow capacities. The experimental data

with a Y and % bend are too limited in scope to permit a satisfactory evaluation of the effect of type of stack-base fitting.

6.2. Attenuation of Discharge Rates in Long,

Initially Empty Drains

When a surge is introduced into a sloping drain, a maximum depth is produced at some cross sec-

*Y- and 1/8-bend stack-base fitting.

tion, which may or may not be in the vicinity of

the drain entrance. Both the depth and discharge

rate of the surge decrease continuously after it passes the section where maximum depth occurs. A precise, physical evaluation of the phenomenon of surge attenuation might indicate some

effect due to initial entrance velocity, drain roughness, drain diameter, and other factors. The data

summarized in tables 8 and 9 are not believed

adequate for a rigorous evaluation. However,

the data are presented because they are informative and because they were utilized by Hunter in making certain recommendations as to permissible

28
<

CL<o

<

LU

I-

>-H

o<

o

o

liJ o

cr. V)

L.O

<

CC

4.0

3.0

2.0

1

'

'

1 \ A

- _

- 90

1 1 10 20 30

4.0

10 20 30

DURATION OF SURGE, SECONDS

Figure 19. Comparison of eq(lO) and experimental measurements on drain system shown in figure 10 (surge flow in initially empty 6y2-in. plastic drain, long-sweep

stack-base fitting except where otherwise indicated)

.

End of drain open End of drain restricted Slope

in./ft o • 1/16

1/8 A 1/4

(Numbers adjacent to symbols indicate duplicate values.)

Chart Jet form

(see fig. 9) A C

B* C C D

'Y- and 1/8-bend stack-base fitting. loads on secondary branches of long building

drains and building sewers [3]. The data in tables 8 and 9 are somewhat erratic,

but inspection indicates that the predonainant

factors affecting the attenuation of discharge rate between the drain entrance and outlets were (1) the length, L, measured between these two sections, and (2) the slope, S. The empirical

equations

and

(11)

(12)

have been derived from the data, where L is ex- pressed in feet, and S in in./ft. The term

8=

Qu

(13)

is the attenuation factor, where Q„ is the discharge

rate at the upstream cross section, and Qa is the

rate at the downstream cross section. Equation

(12) is proposed as being more reasonable than eq

(11), since it yields a more reasonable result,

5^1.0, for a very long drain than eq (11). The

values for discharge ratio in the right-hand column

of tables 8 and 9 are actually values of 1—5.

Hunter utilized eq (11) with a value of Ki

=0.005 in computing permissible loads on drains

located at considerable distances from the load

origin [3]. An upper-envelope fit to the data of

tables 8 and 9 can be obtained through the use of

eq (12) with a value of K2 of about 50, where 5 is expressed as a function of Lj^S. However, the

data do not provide as conclusive a basis for the

derivation of a design equation as might be

desired. Further work appears to be needed on

this aspect of attenuation.

6.3. Flow of Junction at Main and Branch in

Compound Drains

Two types of flow were considered : steady flow

in both the main and branch, and surge flow in

the branch with steady flow in the main. The

criterion of capacity was the occurrence of a full- section condition at the junction of the main and

the branch similar to that illustrated in figures

4 to 7. In practically all of the experimental determinations of flow capacities at drain junctions, the

combined capacity of the main and the branch was appreciably greater when the branch carried

surge flow and the main steady flow, than when

both carried steady flow. When surges of short duration were discharged

through a branch into a main carrying steady

flow, the unfilled portions of the drains upstream

from their junction appeared to affect the flow

capacity of the system. This effect was not in- vestigated systematically, but the experimental

evidence indicated that system capacity increased

with this "storage" volume.

When siirge flow was superimposed on steady

flow in a nominally horizontal main through a

vertical branch (stack) at a velocity comparable

to terminal velocity in a soil or waste stack under

service conditions, a full section was produced

downstream from the junction, somewhat as shown in figme 2. This was taken as the criterion

of capacity. The data indicated that under these

29
conditions system capacity was roughly in agree- ment with an equation of the same form as that

derived from data on full-section flow at the junction of compound drains \\'ith both the branch

and the main in a common nominally horizontal

plane and with surge flow in the branch and

steady flow in the main.

a. Steady Flow in Branch and Main in a Common

Horizontal Plane

Referring to figure 20, case 1 represents conditions in a horizontal drain system for which a given rate of flow, Q3, is carried in the main

without the addition of any flow from the branch.

The center of gravity of this stream is at a dis- tance 23, above the invert. Case 2 represents

conditions for which the same rate of flow is divided between the branch, Q2, and the main Qi.

Thus,

The system is filled at section a-a without creating

appreciable hydrostatic pressure at the crown of the main in the vicinity of the junction. It is evident that the upstream velocity near the

junction (section a-a) is less and the depth greater

in case 2 than in case 1. It is also evident that, at sufficient distance downstream from section

a-a, the hydraulic elements are the same in the

two cases. In case 2, the average elevation of

section a-a above the invert is i/, or Di/2. The

difference between and i/, Ai, is the result of

the confluence of the two streams at the Y -branch.

The observed effect is intimately related to energy

and momentum changes occurring in the vicinity

of the junction of the two drains.

An analysis of the data was first made on the

thesis that the difference in water depth with

reference to the drain invert at the junction of

the main and the branch and at a section far downstream was caused by the centrifugal force

generated by mutual deflection of streamlines in

the vicinity of the junction. This analysis fol- lowed the approach given in the NBS Monograph

31 [9] regarding interference of flows at the junction of a vertical drain (soil or waste stack) and

a horizontal branch.

However, a precise evaluation of the factors

involved in this complex phenomenon did not seem to be justified on the basis of the data obtained, because several gross simplifying assumptions were necessary in developing the analysis for

practical apphcation and certain constants had

to be determined from the experimental data.

Nevertheless, in reviewing the data in accordance

with the centrifugal force thesis, it was found that

the equation:

(14)

PLAN

-NO BRANCH FLOW

ELEVATION

CASE I.

PLAN

ELEVATION CASE 2.

Figure 20. Diagram illustrating terms used in discussion

of flow interference at junction of main and branch.

Case 1: Elevation of center of gravity of section a-a above invert ="3 = 21, Vl=V3,

Qi=Q3, and

Q2=0. Case 2: Elevation of center of gravity of section a-a above invert ="i'= -^'s^zs,

Qi^O, and

main and branch are full but not under hydrostatic

pressure at junction (sec. a-a).

(14) X=§^' and Y- .^^^L^_ where full-section

2gAz 2gAz

flow is assinned at the main-branch junction as indicated in case 2 of figure 20. An equally

good fit was found by replacing the diameter ratio

function in eq (14) with a more complex function

involving the volume common to the intersestion

of main and branch. This function was also ex- pressed in terms of the diameters but was not a simple power function.

It can be shown by the methods of dimensional

analysis that the variables that are most apparent can be grouped in a form similar to that of eq (14).

Let the appUcable variables be Qi, Q2, Di, D2, S,

and C. In addition, the acceleration of gravity,

g, will be introduced as an experimental constant. One possible grouping of these quantities is

:

Qx Q2 =0. (15)

Ai

It is permissible to introduce ^ in place of S

on the basis of the relationship between S and

Th by the Chezy formula and between and A2

by the geometry of segments of circvdar sections.

Thus, Y_^,_^,A 0 (16)

fitted the data in table 10 reasonably well. In eq

4>

30
which can be placed in an equivalent form

\gAz gAz Di Vi /

The first three variables in eq (17) are identical

in form to those appearing in eq (14) which is in

reasonable agreement with the data of table 10. The fact that the experimental data showed no

apparent consistent effects due to variation in A 2/A and C over the range of the experimentation indicates that these terms can be neglected

in regard to the analysis of these particular data.

Thus on the basis of dimensional analysis it is pernfdssible to utilize the function shown in eq

(14) for application to the data shown in table 10. Equation (14) can be expressed in terms of dis- charge rates, rather than velocities. This can be

done through use of the relationship

q=Ay=-^- (18)

This results in the equation,

Km^gtrz) ^-^^^kdJ ^^^^

or

(Qi)'''(^2)'''=0.0955 iPll^k^, (20)

in which Qi and Q2 are expressed in cubic feet per

second; A, D2, and Ai are in feet; and g is in feet per second per second. The latter equation is in a more convenient form for solution than eq (19).

Equation (20) can be solved to give corresponding

values of Qi and Q2 which caused the compovmd

drains to flow full at their junctions without cre- ating hydrostatic pressure at the crown of the

main, applicable over the range of the experimentation. The solution can be achieved for a drain system for which the steady flow capacity

of the main flowing full is known.

The relationship between vertical distance from

invert to center of gravity of water cross section,

Z3, and water depth for free-surface flow was

determined from King's tabulation of vertical

distance l)elow water surface to center of gravity

of water cross section for circular conduits flowing

partly full [12]. The relationship between total rate of discharge for the drain system {Qi + Q2 in

the terminology of this paper) and water depth

in the main downstream of the junction was

computed from the Manning formula wherein the

hydraulic radius was expressed as a function of water depth. This made it possible to relate rate of discharge, ^1 + Q2, to difference in vertical

distance between center of gravity of water cross section and center of gravity of conduit cross

section, (A2), where As =21 ' —23, or A2=^—23 as shown in figure 20.

Values of A and A were known for the ex- perimental drains. The number of unknowns

in eq (20) was reduced to two through use of the

relationship between A2 and (Qi + Q2) described

above. Curves were computed by assuming

X

o

^ RELATIVE DISCHARGE RATE IN MAIN

Figure 21. Comparison of eq {20) and experimental measurements on plastic drain system shown in figure 16

{for 4-in. main and 3-in. branch, steady flow).

Steady flow capacity Drain slope of main as a simple

drain (see table A-1)

in.lfl gpm

1/16 100

1/8 139

Curves dashed for values of branch discharge in excess of steady flow capacity of branch as a simple drain. X

o

X

M 1 1 1 \ \

1 1 1 1

\ \

\ \

\ \

^ \

\ \

\ \

\ ^

\ \

rS = 1/16

1 1 1 1 1 1 1 ~i 1 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

RELATIVE DISCHARGE RATE IN MAIN

Figure 22. Comparison of eq {20) and experimental measurements on plastic drain system shown in figure 16

(for eji-in. main and 4-in. branch, steady flow)

.

Steady flow capacity Drain slope of main as a simple

drain (see table A-1)

in.lft gpm

1/16 380

1/8 535

Curves dashed for values of branch discharge in excess of steady flow capacity of branch as a simple drain.

31
o

<

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 <^ RELATIVE DISCHARGE RATE IN MAIN

Figure 23. Comparison of eq {20) and experimental measurements on cast-iron drain system shown in figure 15

{for 4-in. main and branch, steady flow).

Steady flow capacity Drain slope of main as a simple

drain (see table 10)

in.lft Qpm

1/16 79 8

1/8 114

numerical values of Az and solving eq (20) for corresponding values of Qi and Q2.

This procedure has been carried out for several

of the experimental drains. Results from some

of the tests are shown in figures 21 to 23. Actual

measurements from table 10 are shown for comparison with the computed curves. In these

figures equal slopes are assumed for main and

branch drains. The ordinates and abscissas are expressed as "relative discharge rates," obtained by

dividing the actual rates by the steady flow capacity of the main determined experimentally.

Therefore, the ordinate and abscissa values

represent factors which, if multiplied by the known

steady flow capacity of the main, give the actual

capacities of the branch and the main, respectively.

This method of representing ordinate and abscissa

values is useful in showing the magnitudes of

permissible flow rate in relation to the steady flow

capacity of the main, over the range of the ex- perimentation. Also it clearly shows that the

relative discharge rate decreases as slope is increased, evidently because of greater energy

losses in the vicinity of the junction.

The computed curves in the figures are dashed

for ordinate values greater than the approximate

steady flow capacities of the branch drains at the

indicated slopes. Rates of steady flow in branch

drains in excess of these limits should never be

permitted to occur in sanitary systems in service.

The agreement between observed values and

values computed from eq (20) is considered satis- factory for drain slopes of 1/16 and 1/8 in. /ft.

However, measurements in a 4-in. drain with 2-,

3-, and 4-in. branches at a slope of 1/4 in. /ft (not

given in table 10) differed erratically from those

computed from eq (20) . This difference may have

been influenced by the excessive turbulence

characteristic of the l/4-in./ft slope. Further

investigation of junction flow at slopes greater

than 1/8 in. /ft is needed.

b. Surge Flow in Branch, Steady Flow in Main

Table 11 gives data obtained for surge flow

discharged through a branch drain into a main

carrying steady flow. The main and the branch

were both nominally horizontal, and were joined

by a 45°-Y-branch fitting as shown in figure 16. System capacity, (Q1+Q2), was somewhat greater

under this condition than under the conditions

described in section 6.3a where steady flow was

carried in both the main and the branch. An

empirical equation was developed from the ex- perimental data which gives hydraulic capacity

for combined surge and steady flow based on

distribution of flow between main and branch,

and on hydraulic capacities for the two separate

types of flow as given by eqs (10) and (20), re- spectively. The equation

Qe=est[l+7(l-e-*«-'^0] (21)

conformed to the experimental findings more

closely than did several others considered. The

terms have the foUowing significance

:

Q2/Qi=ratio of branch discharge to main dis- charge, to be considered as an independent variable,

system capacity for combined surge and

steady flow,

Qs,=system capacity for steady flow in both

branch and main, as given by eq (20),

7=relative increase in capacity for surge flow

of a given time duration over that for steady flow in a simple drain of the same diameter and slope as the main,

as obtained from eq (10), and

^=an experimental constant.

Rates of discharge and surge-duration times apply

to conditions at the entrances to the test drains.

The accuracy of eq (21) should be greatest for very small and very large values of Q2/Q1, since

full-pipe, steady flow in the main is approached

as Q2/Q1 becomes small, and surge flow into the

empty main is approached as Q2/Q1 becomes large.

At intermediate values of Q2/Q1, agreement of eq

(21) with observed capacity depends on the value

of k used. This constant may depend to some

extent on drain length upstream from the mainbranch junction, on drain slope, and possibly on other factors not yet investigated.

Figures 24 and 25 show experimental data from

table 11 for the test system in which both the

main and branch were nominally horizontal. Data

32
X

o<

CD

<

CC

UJ

a:<X

u

CO

UJ>

<

-I

Ld

ir

0.1 02 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 RELATIVE DISCHARGE RATE IN MAIN

FiGUBE 24. Comparison of eq {21) and experimental measurements on plastic drain system shown in figure 16 (for

4-in. main and 3-in. branch on a slope of Vs in. /ft, steady flow in main, surge flow in branch, steady flow capacity of main= 184 gpm based on data of table 4)- O 5-sec surges. A 10-sec surges.

20-sec surges.

1.0

I

0.9 1- <

m 0.8 — ~ 07 -

liJ I-< 0.6 -

^ 0.5 —

OC<X 0.4-

O

cn 0.3

0.2

0.1

T

20 10 t=5 SEC

00 \ \ \

02. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 RELATIVE DISCHARGE RATE IN MAIN

1.0

Figure 25. Comparison of eq (21) and experimental measurements on plastic drain system shown in figure 16

(for 6}'2rin. main and 4-in. branch on a slope of lll6 in. Ift, steady flow in main, surge flow in branch, steady flow

capacity of main — 352 gpm based on data of table 4)- O 5-sec surges. A 10-sec surges.

20-sec surges.

are shown for 5-, 10-, and 20-sec surges in the

branch, with steady flow in the main. For comparison, dashed curves are shown, computed from

eq (21) with a value of ^=0.41. The term 7 is the same as AQ/Qstc in eq (10). Values of 7 were based on an annular jet form and on drain

diameter, slope, and roughness appUcable to the

main in the particular test system under consideration. The solid curve represents eq (21) where

the surge duration time is infinity. In this case, 7 becomes zero according to eq (10), and Qc=Qst

according to eq (21); hence eq (20) for steady

flow in both main and branch is applicable. The

agreement between eq (21) and the data is considered satisfactory. However, more work is needed to establish the limits of the range where

satisfactory agreement can be expected; particularly as to ratio of branch diameter to main

diameter, ratio of branch discharge to main dis- charge, and slope.

Figure 26 shows data from table 12 for combined

X

o

<

OHCD

<

LUO

CC<

X

o

CO

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 RELATIVE DISCHARGE RATE IN MAIN

1.0

Figure 26. Comparison of eq (21) and experimental measurements on drain system comprising a vertical branch and a 4-in. plastic main drain on a slope of 1I&

in.lft (steady flow in main, surge flow in branch, steady flow capacity of main=134 gpm based on data of table 4). O 5-sec surges. A 10-sec surges.

1 5-sec surges. O 20-sec surges.

33
surge and steady flow in the test system described

in section 5.2a, where the main carried steady flow

and the surges were introduced through a stack

(vertical branch) connected to the main with a Y- and )^-bend fitting about 2 ft from the upstream

end of the main. Steady flow was delivered at the upstream end of the main, and surge flow was

delivered through the branch at velocities comparable to terminal velocity in soil or waste stacks

under service conditions as given by eq (A-6).

Pressure conditions were not investigated in the

main immediately upstream from the junction nor within the junction itself. As indicated in section 5.2a, the criterion of capacity was the occurrence of a full section of minimum length

downstream from the junction. The dashed

curves in figure 26 were computed from eq (21),

based on a value of A;=0.22, in a way similar to that described for fig\u"es 24 and 25. System

capacity for steady flow, Qet, as given by the

solid curve, was assumed equal to the steady flow

capacity of the main rather than being computed

from eq (20). Although the agreement between

the data and the computed curves is considered

acceptable, more work is needed on this aspect of

jimction flow. In particular, more information is needed as to what the criterion of hydraulic ca- pacity should be for a system comprising a stack

discharging surge flow into the top of a horizontal

drain carrying steady flow. Preliminary measurements, utilizing the test system in figure 16, showed that for a slope of 1/16

in. /ft increasing upstream storage volume by in- creasing the size of the stilling box resulted in increased system capacity for combined surge and

steady flow, other conditions being the same. Hunter observed capacities for combined flow

which were relatively somewhat greater than the

capacities observed by the author. This difference

may have been caused by the greater upstream

storage volumes associated with his test system,

particularly in the long branch drains. In addition to performing a storage function, such drains

may, under certain conditions, also permit "crest- ing" of high velocity surges and possibly their

subsequent attenuation upstream from the mainbranch junction. In the author's tests on the

system in which both the main. and the branch were horizontal, the branch storage volume was

practically eliminated by making the branches

quite short, and the main storage volume was

limited to that due to 11 lineal ft of main and

approximately 3 ft^ of surface area in the stilling

box. In the test system in which the branch was

vertical, there was no effective upstream storage

volume in either the branch or the main. Under

service conditions where the building drain is connected to one or more branch drains, upstream

storage volume may well be greater than in the

author's tests. The values of ^ in eq (21) derived

from the tests would probably be conservative as apphed to such service conditions, insofar as the

effect of storage volume is concerned. Equation

(21) does not provide for evaluation of storage

volume except empirically through the value

assigned to k.

7. Conclusions

7.1. Estimating Hydraulic Capacity

Methods for estimating hydraulic capacity, as

reflected in eqs (10), (12), (20), and (21), should be

useful as improved criteria for sizing horizontal

drains in sanitary drainage systems for buildings.

Horizontal drains of interest to engineers, plumbing-code writers, and plumbing officials include

fixture drains, horizontal fixture branches, primary and secondary branches of building drains,

and building sewers. The equations are particularly applicable to building drains and building

sewers.

7.2. Design of Plumbing Systems With Minimum Venting

Equations (10), (12), (20), and (21) should be

especially useful in selecting safe economic pipe

sizes for sanitary drainage system designs in which

adequate venting of fixture drains depends on the

existence of a continuous air space or absence of

excessive surge cresting above the mean water

surface in horizontal branches, building drains, or other horizontal drains. Presently, this type of

venting is permitted to a limited degree under the

provisions of some plumbing codes, as for example

under the provisions of paragraph 12.22 Combination Waste and Vent System of ASA A40.8—1955

limited to sinks and floor drains. Guidance in the

design of such systems, as provided in part by eqs

(10), (12), (20), and (21), should make it possible, at least on the basis of hydraulics and pneumatics,

to further minimize the number of vent pipes and

the total quantity of vent piping required in systems where surge flow of relatively short duration is typical such as in one- and two -family

houses. Possibly this approach could result in the

elimination of all conventional vents in the simpler

drainage systems. However, some further re- search on this matter may be needed.

7.3. Utilization of Field Data and of Data on

Surge Attenuation

Attenuation of surge discharge rates in long

drains (see sec. 6.2) may be a significant factor

in the determination of hydrauhc capacities of secondary branches of building drains, and of building sewers. Hunter's data on this phenomenon, given in tables 5 through 9, were utilized in the computation of recommended fixture-unit

loads on secondary branches by the committee

which developed the Plumbing Manual [3]. Hunter's field data from the buildings described in table 1 furnished general information on typical

flow conditions which was later utilized in the

design of experimental apparatus and development

of test procedures.

34
7.4. Effect of Surge-Duration Time, Drain

Slope, and Other Factors on Hydraulic

Capacity

Flow capacities were greatest for short-duration

surge flow and least for steady flow. Actual

capacities increased with drain slope and diameter. Relative capacities decreased with drain

slope. Other factors, including roughness of pipe

material and geometry of fittings, evidently af- fected capacity to some extent, but to a lesser degree than did surge-duration time, drain slope,

and drain diameter.

7.5. Surge- Flow Capacities of Simple Drains

Equation (10) agrees reasonably well with

measured values of surge-flow capacity in a number of simple drains initially empty. The most

significant variables were surge-duration time,

drain diameter, and drain slope. The equation is based on data for drain slopes of Ke, Ys, and

% in. /ft; hence it may not apply to slopes greater

than % in. /ft.

7.6. Steady Flow Capacities of Compound

Drains

Equation (20) is in satisfactory agreement with

measured values of steady flow capacity in several

nominally horizontal compound-drain systems

each of which comprised a main drain and a branch drain intersecting the main at an angle of 45°. The equation predicts a minimum capacity

for the system when a relatively small part of

the flow is carried by the branch, and somewhat

greater capacities when the branch flow is increased

or decreased from this critical value. Evidently eq

(20) is not suitable for application to drain slopes

of 1/4 in. /ft or more.

7.7. Capacities for Surge Flow Superimposed

on Steady Flow

Equation (21), which is an arbitrary combination of eqs (10) and (20), is roughly in agreement

with measured values of flow capacity in compound drains carrying surge flow in the branches

and steady flow in the mains.

7.8. Need for Further Investigation

Adequate safety factors should be used in the

application of the equations to conditions very

much outside the range covered in the experiments reported. Reduction of these safety factors

to a desirable minimum cannot be accomplished

without further information as to the effects, on

hydraulic capacity, of the following factors under

controlled experimental conditions:

1. Partial or complete elimination of conventional venting of horizontal drains,

2. drain storage volume upstream from junctions in compound drains for the case of steady

flow in main and surge flow in branch, eq (21),

3. very small discharge in either main or branch

of compound drains, and correspondingly large

discharge in the other component, eqs (20) and

(21),

4. energy losses at the bottom of drainage

stacks resulting from turbulence and friction in stack-base fittings, eq (10),

5. drain slopes greater than % in. /ft in the case

of compound drains (see particularly eq (20)),

6. hydrodynamic pressures upstream in main

from junction of main and vertical branch, eq

(21),

7. attenuation of depth and discharge rates for surge flow in long drains, eqs (11) and (12), and

8. drain diameters greater than employed in

the experiments reported herein.

7.9. Computation of Allowable Fixture-Unit

Loads

For design purposes it is desirable to express

allowable sanitary loads in terms of plumbing

fixtures (fixture-unit loads) rather than in terms

of hydraulic capacity. This procedure involves

the simultaneous solution of two types of equations—one relating to hydraulic capacity and the

other to probable discharge from mixed groups

of fixtures. The computation of fixture-unit loads for nominally horizontal drains in plumbing systems is an appropriate subject for a later paper. Such

a paper should give in some detail methods by

which the computations may be made on the

basis of hydraulic data such as reported herein,

of data on typical use and discharge of plumbing

fixtures, and of the mathematics of probability.

Acknowledgment is made to a number of

persons at the National Bureau of Standards

who contributed significantly to the success of

the investigation. The late Dr. Roy B. Hunter

left unpublished data in his files on an early study

of some of the problems discussed in this paper.

John L. French made an informative analysis

(unpublished) of Hunter's data, which pointed

out the need for further research and stimulated

the author's interest in the subject. Herbert B.

Banks, Douglas E. Gasterland, Daniel R. Tolliver,

and Carl W. Brumfield gave careful attention to construction of equipment, to making of measurements, and to analysis of data under the direction

of the author. Editorial assistance by Theodora

C. Bailey and constructive technical suggestions

by John L. French, Bradley A. Peavy, Jr., and

Joseph C. Davis contributed notably to the

presentation.

8. References

[1] R. B. Hunter, Methods of estimating loads in plumbing systems, NBS Building Materials and Structures Report BMS 65, 1940.

[2] H. N. Eaton and J. L. French, Fixture-unit ratings

as used in plumbing system design, Housing

Research Paper 15, Housing and Home Finance

Agency, 1951.

35
[3] Plumbing Manual, NBS Building Materials and

Structures Report BMS 66, Report of the Subcommittee on Plumbing of the Central Housirg Committee on Research, Design, and Construction, 1940.

[4] 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.

[5] American standard national plumbing code, ASA

A40.8—1955, American Society of Mechanical

Engineers and American Public Health Association.

[6] V. T. Manas, National plumbing code handbook

(McGraw-Hill Book Co., New York, 1957).

[7] H. E. Babbitt, Plumbing, 3d ed. (McGraw-Hill Book

Co., New York, 1960).

[8] V. T. Manas, National plumbing code illustrated, 3d

ed. (Manas Publications, 1962).

[9] R. S. Wyly and H. N. Eaton, Capacities of stacks in sanitary drainage systems for buildings, NBS

Monograph 31, 1961.

[10] E. Buckingham, Notes on the method of dimensions,

Phil. Mag. V42, No. 251, Nov., 1921.

[11] H. Rouse, Elementary mechanics of fluids (John

• Wiley & Sons, Inc., New York, N.Y., 1946).

[12] H. W. King, Handbook of Hydraulics, 4th ed. (McGraw-Hill Book Co., New York, 1954).

[13] L. F. Moody, Friction factors for pipe flow, A.S.M.E.

Transactions, V66, 1944.

[14] 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).

[15] 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).

[16] F. Sommer, Studies made on vertical drains at 100 mm diameter. Trade School, Bern, Switzerland,

1963.

[17] Sovent, a new vertical stack system, Oderlin and Co. Limited—metal works, Baden, Switzerland, 1961.

[18] H. E. Voegeli, Drainage without vent stacks, Air Conditioning Heating and Ventilating, V60, No. 8, August, 1963.

9. Appendix

9.1. Computation of Roughness Coefficients

Table 4 gives ttie results of computations of

roughness coefficients for the drains used in the

experiments. The method for computation is summarized below.

The capacity flow rate for steady flow was

determined for each drain under conditions which

simulated a very long drain (see sec. 9.2). A

continuous flow at a constant volume rate was

discljarged into the drain entrance. The supply

rate was adjusted carefully so that the hydraulic

gradient, or surface profile, coincided with the crown of the drain downstream from the point at which substantially steady, uniform flow was

attained, this point being somewhat less than 50

drain diameters from the entrance in most cases. The fuU-conduit condition was determined visually

by means of the vent holes in the crown of the

drain.

A value of the Darcy-Weisbach friction factor was computed for each combination of drain slope,

diameter, and material from the relationship

in which dimensionally consistent units are used.

Equation (A-1) was derived from the DarcyWeisbach formula by expressing velocity in terms

of discharge rate and setting hydraulic gradient

equal to the drain slope.

In order to obtain the Nikuradse roughness

magnitude, the Reynolds number,

(A-2)

corresponding to each experimental value of/ was

computed. Values of the roughness magnitude,

kd, were then determined approximately by inspection of the conventional graph showing the rela- tionship between/, Nr, and ka/D [13]. According

to the theory on which this relationship is based,

the roughness magnitude for a given pipe is not

affected by Reynolds number. However, because

of small errors in measurement and possible sys- tematic differences occurring when drain lines were

disassembled and reassembled in changing slope,

the experimental values of ka determined for a given drain as described actually were somewhat

different for the Reynolds numbers associated with

different slopes. Since no predominant trend was

observed, the values of ka obtained for the different

slopes were averaged. For each combination of

drain diameter, material, and slope the graph was

again consulted to obtain a value of / corresponding to this average value of ka, based on the experimental value of Nr. These values of/ are referred

to as "rationalized" values, from which rationalized values of capacity flow rate were computed

through the use of eq (A-1). The word "rationalized" is used here in the sense that the quantities

referred to are in conformance with the DarcyWeisbach formula and the Nikuradse roughness

magnitude concept ("rational" pipe flow theory).

Values of Chezy's C and IManning's n, corre- sponding to the rationalized values of /, were computed from the relationship obtained by

equating the conventional expressions for dis- charge rate as given by Chezy, Darcy-Weisbach,

and Manning, i.e.,

l_1.49(r,)'/«_ C_

^^_3^

V7 V8^ ^ ^I8g

in which the hydraulic radius is expressed in feet

and Th is equal to Dd/4: for a circular drain completely filled.

9.2. Effect of Drain Length on IVIeasured

Steady Flow Capacity

Evidently the steady flow capacities recorded

in Hunter's notes for drains 70 ft long were obtained without end restriction. For comparison

with the author's measurements with end restric- tion, it was necessary to estimate the steady flow

capacities that probably would have been ob36
tained by Hunter had very long drains been used

or simulated by end restriction.

The slope of the free surface of the water flowing at a constant volume rate in a channel or conduit of uniform slope and cross section without

end restriction is greater near the discharge end

than upstream. This makes it difficult to determine steady flow capacity for such a conduit

if the ratio of length to diameter is small. In

attempting to bring the water surface into contact with the crown very close to the end of the

drain under this condition, somewhat too large a discharge rate is likely to be used. Consequently some slight internal hydrostatic pressure

and overflowing occurs farther upstream. Under

this condition there is some uncertainty as to how an experimenter is to decide that the drain

is "full." The end restriction utilized in the new

work consisted of a wood block % in. thick

clamped into place across one side of the discharge

end of the drain. The top of the block was in- clined outward from the vertical by about 5

deg, and the inside edge projected across the bore

of the drain just enough (a maximum of the

order of % in. or a little more) to bring the water

surface up to the crown uniformly along the drain

from the discharge end upstream to the point

at which entrance disturbances had been substantially dissipated.

Experimental data are given in tables A-1 and

A-2 for steady flow capacities with and without

end restriction. Inspection of the values in

table A-1 shows that capacities were less when

long drains were simulated, and the effect of end

restriction was greatest for small slopes. The

relationship is a complex one, and the data re- ported here are not sufficient to yield a fuUy

satisfactory solution of the problem. However,

they provide enough information to develop a rough empirical method for estimating the effect

of slope and drain length on observed values.

The empirical relationship

(A-4)

is in satisfactory agreement with the data in table

A-1. The term Q' represents the measured

capacity for a drain of finite length, L, and unrestricted end; Q represents the capacity for a

drain of great length; and j3 is represented approximately as ^^W^U^lD. (A-5)

Actually, the roughness of the drain material may

affect /S slightly, but this effect was neglected. Insertion of values from table A-1 in eqs (A-4) and

(A-5) yielded the values of c shown in table A-3.

Finally, eq (A-4) was applied to the flow rates recorded by Hunter for drains 70 ft long as indicated in table A-2 in order to make a rough esti- mate of the rates which probably would have been

obtained if very long drains had been simulated.

A value of c=0.21 was used in these computations.

The estimated flow rates are shown in the fifth

column of table A-2. The values thus obtained were then rationalized by the method described in section 9.1. That is, rationalized values of/ were

determined, and rationalized values of steady flow

capacities were computed from eq (A-1). The

results are given in the last column of table A-2.

Table A-1. Steady flow capacities as a function of drain

length

Drain

Diameter and

material

3-in., plastic

3-m., galv. -steel

4-in., plastic

4-in., cast-iron (coated)

6H-in., plasticSlope Length

in.ift

Me

Me

Me

LID

404

404

385

296

296

294

294

178

179

Capacity flow rates

Drains approx.

98 ft long, without end

restriction

gpm

(measured)

45.6

94.3

43.5

100 200

92.8 189

380

535

Very long drains simulated by end

restriction

gpm

(measured)

41.6

93.1

39.8

92.0

192

90.2

186

340

600

gpm

(ration- alized) 42.1 90.8

40.7

91.9

195

9.0

188

342

500

Table A-2. Steady flow capacities for test drains used in Hunter's investigation of surge flow in simple drains

Drain Capacity flow rates

Estimated for very Measured with long drains ends of 70 ft Diameter and drains unre- material Slope Length stricted and Measured Corrected

discharging to rates rates atmosphere corrected rationfor end alized •> eflect »

3-in., cast-iron (uncoated) .

4-in., cast-iron (un- coated)

in./ft MeH

MeH

L/D

280

280

280

215

215

215

gpm

35.6 49.0

72.7

76.1 98.5 137

gpm

32.1 45.6

69.8

66.8 89.0

128

gpm

32.8

46.8

66.7

64.1 91.2

130

» Measured rates corrected for "end eflect" through use of eq (A-4) with a value of c=0.21.

b Corrected rates rationalized by method outlined in section 9.1. Table A-3. Computation of c-values in eq {A-4)

Drain

Diameter and material

3-in., plastic.

3-in., galv.-steel.

4-in., plastic

4-in., cast-iron (coated).

6H-in., plastic

Slope Length

in./ftMeH

Me

He

Vi MsH

Me

!4

L/D

404

404

385

296

294

294

179 179

c-value

0.17

.21

.18

.20

.18

.29

.24

.21 .22

Averages: For Me-in. slope. For Jg-ln. slope.

For M-in. slope. Grand average.

0. 21 .22

.21

.21

37
Equation (A-4) gives the theoretically correct

result, Q' = Q, when LjD becomes very large, and

is in satisfactory agreement with data from experimental drains over a range of LjD from approximately 180 to 400.

9.3. Determination of K-Values for Unusual

Jet Forms

In computing the curves in figures 17 and 18 for

Hunter's crescent jets, (data shown in table 2), a value of ^C=10.5 was used, this being the same

as was determined for the modified annular jets. It was ascertained by inspection that this value

resulted in satisfactory agreement between

Hunter's data and the computed curves. Possibly the value of K=\\A derived for single

circular jets could have been chosen with comparable justification.

As indicated in table 3, surge-flow capacities for the 6}2-in. drain with the multiple-circular jet were determined only with the end of the drain

fully open. Measurements on the same drain

with the single circular jet showed that the value

of /il was reduced about 10 percent by simulating

a long drain through the use of an end restriction.

For this reason, K determined experimentally for the multiple circular jet without end restriction was reduced accordingly to a value of 12.3 for application to long drains.

9.4. Terminal Velocities in Soil and Waste

Stacks

Terminal velocities can be estimated as a

function of water discharge rate (<?«,), stack

diameter, and stack roughness by the method

given in NBS Monograph 31 [9], in which the

equation

was derived. DimensionaUy consistent units must

be used in eq (A-6) . ^

Substitution of the expression - RsD]Vt for

in eq (A-6) gives the relation

V,=Z.2\{R,y'' (A-7)

in which R, is the ratio of the area of the water

section in the stack to the cross section of the

stack where terminal velocity exists. Equation

(A-7) is convenient for estimating terminal

velocities as a function of water cross section,

stack diameter, and stack roughness without

knowing the water discharge rate. Since terminal lengths characteristic of soil and

waste stacks carrying substantial loads range from

less than one branch interval of height for a 3-in. stack to about 2 branch intervals for an 8-in. stack [9], it is not unreasonable to assume near- terminal velocities at the bases of soil and waste

stacks for design purposes.

Equation (A-7) was utilized in the predetermination of cross-sectional areas and velocities of the

surges which were introduced into the experimental drains, and in relating test-surge velocities to computed service terminal velocities, as shown

in tables 2 and 3. In the use of eqs (A-6) and (A-7) it should be

recognized that these equations are based on the

concept of an annular sheet of water flowing down

the wall of a soil or waste stack enclosing a central

air "core," as presented by Dawson and Kalinske

[14, 15] and by Wyly and Eaton [9]. Recent Eiu-opean data [16, 17, 18] suggest that

through the use of specially designed "mixing"

fittings at the junctions of a multi-story stack

with its horizontal branches an air-water mixture can be created which has a velocity and an effec- tive density less than water. This appears to be

desirable from the standpoint of minimizing

pneumatic pressure fluctuations in the horizontal

branches, thus permitting the elimination of some

conventional vent piping. The European data do

not appear to cover the possible effect of the proposed fittings on total load allowable on a stack,

but are limited to a comparison of air flow rates, pressures, and velocities with and without the

special fittings at loads well below the upper

limits normaUy permitted under plumbing codes

in this country. However, this type of construction has not been investigated as it might

relate to American plumbing practice, and hence

has not been considered in the derivation of eqs

(A-6) and (A-7).

38

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