Reference

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NBSIR 81-2266

Experimental Investigation of

Transport of Finite Solids in A

76 mm-Diameter Partially-Filled

I Pipe

Bal M. Mahajan

Building Equipment Division

Center for Building Technology

National Engineering Laboratory

U.S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

April 1981 ^ 100

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81-2266

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Prepared for Division of Energy, Building Technology

and Standards

Office of Policy Development and Research

Department of Housing and Urban Development

Washington, DC 20410

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NBSIR 81-2266 vJUN 1 o 1981

EXPERIMENTAL INVESTIGATION OF

TRANSPORT OF FINITE SOLIDS IN A

76 mm-DIAMETER PARTIALLY-FILLED

PIPE

Bal M. Mahajan

Building Equipment Division

Center for Building Technology

National Engineering Laboratory

U.S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

April 1981

Prepared for Division of Energy, Building Technology

and Standards

Office of Policy Development and Research

Department of Housing and Urban Development

Washington, DC 20410

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U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
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PREFACE

This report is one of a group documenting National Bureau of Standards (NBS)

research and analysis efforts in developing water conservation test methods,

models for technical and economic analysis, and strategies for implementation

and acceptance of practices. This work is sponsored by the Department of

Housing and Urban Development/Office of Policy Development and Research,

Division of Energy Building Technology and Standards, under HUD Interagency

Agreement H-48-78.

iii
ABSTRACT

An exploratory experimental investigation of the hydro-transport mechanisms of

finite solids with non-uniform, unsteady and transient water flow introduced

into a pitched-horizontal drain (p-h drain) pipe by discharging a plumbing

fixture was carried out. The purpose of the investigation was to examine the

effects of relevant variables on the velocity attained and the distance traversed by the solid in the p-h drain. The variables selected for the study

include: the water volume used (i.e., the volume of water discharged from the

plumbing fixture into the drain), diameter and length of cylindrical solid,

and diameter and slope of the p-h drain.

This report contains a description of the experimental equipment and

procedures, and a summary of the data acquired during the solid transport

experiment in 7.6 cm diameter drain pipe at a pipe slope of 0.02, 0.04, and

0.06.

The solid dragged on a thin film of water between the solid and drain wall

when relatively small water volumes (Vw _< 1.9 liters or 0.5 gallons) were

used; and the solid moved like a waterborne object when relatively large

water volumes (Vw >^3.8 liters or 1.0 gallons) were used. The solid velocity

and the distance traversed by the solid increased with an increase in the water

volume used, an increase in the drain slope, a decrease in the solid diameter,

and a decrease in the solid length.
TABLE OF CONTENTS

Page

1. INTRODUCTION 1

1.1 Background 1 1.2 Waterborne Waste Transport 2 1.3 Scope 4

1 .4 Purpose of Scope of the Experiment 5

2. EXPERIMENTAL EQUIPMENT AND PROCEDURE 6

2.1 Experimental Equipment 6

2.2 Solid Waste Simulants 6

2.3 Experimental Procedures 7

3. EXPERIMENTAL RESULTS AND DISCUSSION 9

3.1 Visual Observations ' 9

3.2 Solid Velocities 12

3.3 Distance Traversed by the Solids Within the p-h Drain 14

4. CONCLUSIONS 16

5. REFERENCES 17

v
• -V

.

..
1 . INTRODUCTION

1 .1 BACKGROUND

Water shortages experienced during the past several years have brought

increased attention to the need for water conservation. This concern for

water conservation has drawn attention to the large quantities of water used

in water closet (WC) operations and to a variety of means that can curtail this use. It has been estimated that about forty percent of the water used in the

home is used for WC operation, about 95 liters (50 gallons) per person per

day. [1,4] It has also been estimated that a reduction of thirty percent or more in this usage can be realized by replacing the conventional WC's (19 to

26 liters/flush) with the currently available water-saving units (11-13

liters/flush) [3-5 ] , and a reduction of up to 90 percent of this water usage

is possible if the conventional syphonic-f lush water closets are replaced

with innovative systems. [3]

Some researchers and plumbing professionals [5,9], however, have reported

concern about the use of very low-volume WC's, indicating that such a usage

may reduce the wastewater flow in the horizontal drains below that needed for

the transportation of waterborne solid waste, and thus impair the effectiveness

of the drainage system. Relatively little has been done in the United States

to study the waste transport phenomena within the horizontal drains or to

examine the effects of reduced water flows on the transportation of solid

waste.

Cole [5], and Konen and DeYoung [10] studied the effects of low volume [11-13]

liters/flush) water closets on sanitary drainage systems. They reported that

the flow reduction in the drainage system resulting from the use of these units

is not likely to produce any adverse effects. The reported results are not

conclusive, however, because the investigators did not include the waterborne

solids as a part of the wastewater flow through the drainage system. Cole [5]

also determined the flow velocity and flow depth in horizontal drains for different flush volumes. He reported that flush volumes less than 13 liters (3.5

gallons) per flush would substantially reduce the flow depths in the horizontal

drains, which may cause problems for the transportation of solid waste.

Studies to investigate the transportation of solids, flushed from low-volume

water closets, through horizontal drains are under way in some European

countries and in Japan. Some of these studies are cited below.

Swaffield et al. have been studying the transportation of relatively large

solids (maternity pads) at Brunei University, U.K. [9,11]. In their studies,

water closet contents (9 to 10.2 liters of water and a maternity pad) were

flushed into a relatively long (>_ 14 meters) pitched horizontal drain to

investigate the solid transport. From this experimental work, they report

that the transient partially filled pipe flow has three zones. These are:

(1) initial zone, adjacent to the elbow at the horizontal drain entrance where

turning of the flow and the wall impact reduce the solid velocity. The solid

is then accelerated by the momentum of water flowing behind the solid; (2) a second zone, where the fluid friction predominates and the solid decelerates;

1
(3) a final zone, where the solid stops in the pipe as the water leaks past the

solid. The results of their experiments indicate that the velocity of the

solid as well as the distance traveled by the solid increase with an increase

in the flush volume, and an increase in the drain slope. The velocity of the

solid during deceleration correlates with the square root of the ratio L/g,

where L is distance along the pipe and S is the pipe slope. Governing momentum

equations have also been developed but without a mathematical formulation of

all the force terms.

Kamata et al. [12] at the University of Tokyo, Japan, have conducted

experiments to measure the distance traveled by solid waste simulants, flushed

with different water volumes (5, 8, 10 and 12 liters) from water closets within

a horizontal drain. Their experiments were conducted with drain having circular and oval cross-sections. They used the following waste simulants: (1)

four pieces of cylindrical polyvinyl chloride (PVC) sponges (22 mm diameter,

80 mm length); (2) four pieces of toilet paper; (3) both (1) and (2) together;

and (4) single pieces of larger solids such as sanitary napkins and cloth and

paper diapers. Their results indicate that the distance traveled by the solids

in the horizontal drain is increased when: (1) flush volume is increased;

(2) slope of the drain pipe is increased; and (3) cross-sectional area of the

drain is reduced either by using a smaller diameter circular pipe or by using

an oval cross-sectional pipe. They concluded that: (1) the increase in the

distance traveled by solids with increased pipe slope is mainly due to the

increase in flow velocity; and (2) the increase in distance travelled by solids

with a change in pipe cross-section is mainly due to the increase in flow

depth.

Nielsen and Nielsen [13] reported preliminary data acquired for a 3- to 4-year

research program (1979 to 1982) under way at the Danish Building Research

Institute, Horsholm, Denmark. The objective of this research program is to

acquire necessary data to design drainage systems for buildings with water

closets which use only 3 liters (0.8 gallons) of water per flush. The experimental apparatus simulates a 110 mm (4.3 in.) building drain receiving solid

waste from water closets situated on different floors via two soil stacks. One

of the soil stacks carries wastes from three 8-liter water closets situated on three different floors, and the other one from three 3-liter units situated on

three different floors. Natural sponges having cylinderical shapes, 30 mm

diameter by 100 mm length, are being used as solid waste simulants. The preliminary data on the distance traveled in the building drain by the solids

indicate that: solids from 8-liter units traveled farther than those from

3-liter units and solids from units located at higher levels traveled farther

than those of units located at lower levels. When the solid discharged from a unit did not clear the simulated building drain, the unit was flushed again and

again, but without any solids in the bowl, until the solids cleared the building drain. Three-liter units had to be flushed several times before the drain

was cleared.

1 .2 WATERBORNE WASTE TRANSPORT

The primary function of the water utilized for water closet operations is to remove and transport the solid as well as liquid waste through the drainage

2
network without clogging. The waste is transported by the water in two

distinctly separate operations. First, the waste is carried out from the

closet bowl, moved through the trap and fittings, and transferred to the horizontal drain. Second, the waste is transported through the horizonal drain

into the soil stack and through the building drain into the sewer or on-site

treatment facility. This study deals only with the second operation, that is,

the transport of solid waste deposited in the horizontal drain.

Impact with the wall of the turning elbow decelerates the solid flushed from

a WC, and the solid enters the horizontal drain with a speed nearly equal to zero. The solid is then accelerated and transported by the action of the

water entering the drain behind the solid. Therefore only a portion of the

total water consumed per flush (that is, the quantity of water which leaves

the closet bowl behind the solids) is available for transporting the solid

through the horizontal drain. Because, as Swaffield et al. [9] reported,

almost all of the water present in the bowl for the trap seal leaves the bowl

ahead of the solid, and there is a certain minimum quantity of water necessary

for transferring the solid from the closet bowl into the drain. Both of these

quantities of water are dependent upon the geometry of the closet bowl and

bowl-to-drain connections. It follows, therefore, that any reduction in the

total flush volume without changing the closet bowl or bowl-to-drain connections would reduce the amount of water available for transporting the solid

through the horizontal drain.

Horizontal drain is only partially filled; the flow is usually non-uniform and

unsteady. The transportation of solid waste within the horizontal drain is

also dependent upon the rate of flow, that is, both the depth and velocity of

water flowing through the partially filled drain. The flow rates required for

the transportation of solids through the horizontal drain are dependent upon

many other variables, and the information on such flow rates is not readily

available. No information exists concerning the depth of flow, and the generally accepted velocity of about 0.6 m/s (2 ft/s) may not be applicable. This

is so because this value of flow velocity was derived for the transportation

of sediments, such as gravel, through the sewers [14,15]. Most of the solid

waste leaving a water closet has a specific gravity close to one, (0.95 to

1.05).

The flow rate (depth & velocity) in the drain pipe serving a water closet is

dependent upon the discharge rate from the closet bowl, bowl-to-drain connections, horizontal drainpipe variables (i.e., diameter, length, roughness and

slope), and horizontal drain exit conditions. Water discharge rate data, for

a typical conventional water closet, available in the literature [2] show that

the discharge rate gradually rises from zero to peak, may remain constant for

a few seconds, and then gradually falls off to zero. These data suggest that

the flow rate of water behind the solid decrease, with increasing time or distance traversed by the solid. Data reportd by Konen [2] indicate that the discharge rate from a water-saving water closet (12-13 liter/flush) falls to zero after reaching a peak sooner than a conventional unit (19-20 liter/f lush)

Konen' s data suggest that a reduction in the total flush volume would reduce

both the amount and flow rate of water discharged behind the solid, thus

increasing the likelihood of solid deposition in the horizontal drain causing

3
drain blockage. Bishop [16] reported this type of adverse experience when

tanks of conventional water closets were modified to reduce water usage in

the Cabin John area, a suburb of Washington, D.C. Reducing the water used for

water closet operations by modifying the closet tank caused blockage problems

in some of the horizontal drains.

1 .3 SCOPE

To minimize the likelihood of drain clogging with a reduced flow, the pitched

horizontal drain should be properly designed. That is, the selected drain pipe

variables (diameter, length, and slope or pitch) should be such that the water

volume discharged behind the solid can adequately transport the solid waste

through the drain. Theoretical and/or empirical relationships relating the

variables of the drain pipe, water volume used, and the solid waste transport

parameters, however, are almost nonexistent. The hydrodynamics of solid waste

transport through the p-h drain is not completely understood and the exact formulation of the water flow induced forces responsible for motion of the solid

in the drain pipe has not been established. Development of mathematical models

for solid waste transport in p-h drains requires a good understanding of the

transport mechanism.

The objectives of the study program are: (1) to determine the parameters

controlling the transport of solids within the pitched-horizontal drain by

examining the effects of relevant variables on the transportation of solids;

(2) to develop mathematical model (or models) for analyzing the hydraulics of

solid transport within the drain; and (3) to establish design recommendations

for drain pipe diameter, length and slope for the satisfactory transportation

of waste with reduced water usage.

The study program has been divided into four subtasks as follows:

(1) Experimental Investigation . The purposes are to investigate experimentally

the transportation of finite solids through a p-h drain with flows introduced

into the drain by a simulated water closet discharge and to examine the effects

of relevant variables on the transportation of solids; (2) Preliminary Model

Development . The purpose of this subtask is to develop preliminary mathematical models based upon the equations governing the solid motion within the drain

employing principles of fluid dynamics such as force balance, momentum and

energy exchange; (3) Experimental Study Under Simulated Service Conditions and

Refinement of Math Models . Purposes are to conduct experimental investigation

under simulated service conditions to compare the information acquired in subtasks 1 and 2, and validate and refine the mathematical models; and (4) Establishment of p-h Design Recommendations . The purpose is to utilize the information acquired in subtasks 1, 2, and 3 and the available information from

literature and establish design recommendations for pipe diameter, length,

and slope for an effective waste removal from low-volume water closets. The

study reported herein deals only with the first subtask, i.e., the experimental

investigation.

4
1.4 PURPOSE OF SCOPE OF THE EXPERIMENT

The significant solid transport parameters include the velocity (U s ) attained

by the solid, and distance (L g

) through which the solid is transported in the

drain by the water volume used. [9,11,12] It was pointed out earlier the solid

from a WC enters the horizontal drain with a speed nearly equal to zero, and is

transported by the action of the water entering the drain afterwards. Hence,

the experiment has been designed to place solid waste simulants in an empty p-h

drain connected to a simulated water closet which permits control of water discharged behind the solid, introduce flow into the drain behind the solid, measure U s and L s , and examine the effects of relevant variables on U s and L s

.

Variables that may influence U s and Lg include the following: solid variables

(shape, size, specific gravity, surface roughness, amount and distribution);

drain pipe variables (diameter, length, roughness, slope); volume of water

discharged behind the solid, and water discharge rate-time history; fixture-todrain connection variables (type and size of trap, size of down pipe, size and

type of elbows); draine exit conditions (type of drain-to-stack connection,

stack load conditions); and lateral bends in the drain, if any. It was decided,

however, to consider only some of the more important variables in the initial

experimental study. Total water volume discharged behind the solid, and solid

and drain pipe variables, appearing relatively more important than the others,

were selected. Flat ended right circular cylinders with specific gravity equal

to one were selected as solid waste simulants. The solid transport experiments

were conducted with only one solid at a time in a 3-inch (76.2 mm) diameter

drain having a pitch equal to 0.02, 0.04, and 0.06. Thus, the independent

variables selected for the initial experimental work include the following:

volume of water discharged behind the solid; diameter and length of the solid,

coefficient of friction between the solid and pipe; and diameter and slope of

the drain pipe.

This report contains a discussion of the data compiled in the first exploratory

experimental investigations. The report contains a description of the experimental equipment and solids, and a summary of the data on the transport of

cylindrical solids in a 3-inch diameter pitched horizontal drain with different

volumes of water. These data include visual observations and the velocities

attained and distances traversed by solids in the drain at three different

pitches

5
2. EXPERIMENTAL EQUIPMENT AND PROCEDURE

2.1 EXPERIMENTAL EQUIPMENT

The apparatus used in the experiment is shown schematically in figure 1. A

right circular cylindrical tank containing a flush valve and down pipe is

utilized to simulate a water closet. The flush valve is operated by a solenoid

switch. The down pipe is connected to the pitched horizontal drain via a 90

degree elbow followed by a tee. The tee permits insertion of the experimental

solid into the drain. The pipe is transparent to permit visual observation

of the transport phenomenon. The drain pipe is mounted on several stands which

are evenly spaced along the length of the drain. The height of the stands is

adjustable to allow for changes in the pitch of the drain. The exit end of the

drain is open to the atmosphere and the efflux from the drain is caught in a container for proper disposal. All pipes and fittings used to construct the

apparatus are of standard plumbing sizes.

Photocell detectors were utilized to measure velocity of the solids transported

through the p-h drain. A photocell and a light source placed on opposite sides

of the circumference at a cross-section of the pipe constitute a photo detector.

When a solid passes through the pipe cross-section containing the detector,

light to the photocell is interrupted and an electric signal is generated.

The signal from the photocell is fed to an electronic counter (or clock).

This signal can be employed to start a counter, to stop a counter, or to stop

one and start another. The velocity of the solid is computed from the time interval for the passage of the solid between two photodetectors located at a known

distance apart along the length of the pipe. A photograph of two such light

sources-photocell detectors is shown in figure 2.

Four photodetectors, numbered 1 through 4, are located at specific distances

apart, as indicated in figure 1. The signal from detector 1 starts the first

counter, the signal from detector 2 stops the first counter and starts the

second, the signal from detector 3 stops the second counter and starts the

third, and the signal from detector 4 stops the third counter. The logic

circuit is shown schematically in figure 3. This detector-counter system

provides the time period required to determine the solid velocity within the

three sections, i.e., the sections between detectors 1 and 2, 2 and 3, and 3

and 4. As indicated in figure 1, the first section (i.e., section between

detectors 1 and 2) is adjacent to the drain entrance; it begins at a distance

of 0.45 m downstream from the starting position of the solid and is 0.30 m in

length. The second section (i.e., section between detectors 2 and 3) starts

where the first section ends; it is 3.60 m in length and extends over most of

the central part of the p-h drain. The third and last section (i.e., the section between detectors 3 and 4) preceds the drain exit; it starts where the

second section ends and ends at a distance of 0.45 m upstream of the drain

exit; it is 0.30 m in length.

2.2 SOLID WASTE SIMULANTS

Flat ended right circular cylinders were used as test solids in the experiments.

These cylinders were constructed from opaque and rigid plastic tubings. A

6
typical experimental cylinderical solid is shown schematically in figure 4.

One end of the hollow cylinder is completely plugged, and the other end is

only partially plugged with the plug containing a concentric threaded hole.

The partially plugged end of the cylinder is closed with a threaded cap. The

end plugs and threaded cap were made from the same plastic material and were

so constructed that the center of gravity of the closed cylinder concided with

its geometric center. The hollow cylinder with threaded cap allows for desired

changes in the specific gravity of the solids, since the cylinders can be

filled with different materials. The specific gravity of the solid used was adjusted to be equal to 1.0. The coefficient of wet friction between the solid

and the pipe, measured in the laboratory, was equal to 0.6. The aspect ratios

( length/diameter ) of the twenty solids used in the experiment are given in

table 1

Table 1

Aspect Ratio (Length/Diameter) of the Twenty Cylindrical Solids

Length (cm)

1

I 2.5

1 3.8 5.1 6.4 7.6

Diameter (cm) 1.9

1

| 1.33 2.00 2.67 3.33 4.00

2.5 | 1.00 1.50 2.00 2.50 3.00

3.2 | 0.80 1.20 1.60 2.00 2.40

3.8 I 0.67

1 1.00 1 .33 1.67 2.00

2.3 EXPERIMENTAL PROCEDURES

The pitch of the drain pipe was adjusted to the desired value. A solid was inserted through the tee opening and placed on the lower wall of the p-h drain.

The end of the solid facing the elbow was aligned with an indicator line marked

on the outside lower wall of the drain opposite to the tee opening; the indicator line is approximately at the center of the tee (see figure 1). With the

solid at rest in the drain, the light source-photocell detectors were energized

and three gallons (11.35 liters) of water was flushed behind the solid from the

tank. Visual observations and photographs of the solid transport phenomenon

were made.

The passage of the moving solid through the drain cross-section containing the

photo detectors was detected and timed by the detector-counter system. The

experiments were run with the following water volumes 3.0, 2.0, 1.0, 0.5, 0.4,

0.3 and 0.2 gallons (11.35, 7.56, 3.78, 1.90, 1.51, 1.13 and 0.76 liters).

Three test runs were carried with each of the water volumes. When the solid

did not clear the p-h drain, the distance traversed by the solid within the

7
pipe was measured and recorded. The times recorded by the counters were utilized to calculate the average speed of the solid within each section of

the drain (i.e., the drain sections between photo detectors 1 and 2, 2 and 3,

and 3 and 4).

Each of the twenty solids, listed in table 1, were tested with the seven different water volumes mentioned above.

Six of the solids were covered with tight fitting rubber sleeves to change the

coefficient of friction between the solid and the drain pipe wall. The coefficient of wet friction between the sleeved solids and the pipe wall, measured

in the laboratory, was equal to 1.0. The six solids included one 2.3 cm diameter cylinder which was 6.4 cm long, and all five of 1.9 cm diameter cylinders. The full length rubber sleeves were fabricated of 0.3 cm thick flexible

tubing. Hence, in addition to chainging the coefficient of friction, the

sleeves also changed the diameter of the solid. These sleeved solids were

also transported through the drain with various volumes of water with pipe

pitch set at 0.02.

The forgoing experiments were reported with the p-h-drain positioned at two

other pitches (0.04 and 0.06). The experiments with sleeved solids, however, were conducted only with drain pipe pitch set at 0.02 because the results of

the earlier experiments had indicated that once the solid was waterborne and

cleared the drain the friction coefficient between the solid and pipe was not

very important.

8
3. EXPERIMENTAL RESULTS AND DISCUSSION

The results obtained for the transport of simulated solids are summarized in

this section.

3.1 VISUAL OBSERVATIONS

Before discussing the visual observations of the solid transport phenomenon,

it is instructive to describe the flow that ensues when a plumbing fixture,

such as the experimental water-closet simulator, is discharged into an empty

p-h drain. The drain pipe is only partially filled, and the flow is both nonuniform, unsteady and lasts only for a short duration (13 to 60 seconds). Both

the flow rate (i.e., depth and velocity of flow) and flow duration through any

cross-section are primarily dependent upon the volume of water discharged and

the rate at which water leaves the fixture or enters the drain. In general

the flow rate rises rapidly to a peak value and then gradually falls off to zero.

When water was discharged into the drain containing a simulated solid at rest

on its lower wall, the flow through the drain pipe basically displayed the

above-mentioned pattern with the following modification. The solid at rest,

initially, obstructs the water flowing from the upstream direction. The water

is forced to dam up upstream of (behind) the solid, and to leak past the stationary solid streaming through the crescent-shaped space between the solid

and the pipe wall. As a result of this restriction, a "wave" traveling in the

upstream direction of the solid was observed. The depth of water stream behind

(upstream of) the solid rises at a faster rate than that in front (downstream)

of it which causes hydrostatic head difference across the solid. Hence, the

solid at rest in addition to its weight is also subjected to the following

forces in the downstream direction: a pressure force equal to a hydrostatic

head difference across the solid due to unequal stream depth at the opposite

ends of the solid, and a velocity head difference due to unequal water velocities on the two ends of the solid; and a drag force due to the water streaming

past the solid. The flow-induced forces acting on the solid increase with an

increase in water influx.

The solid remains stationary until the sum of forces acting in the downstream

direction overcome the force due to static friction between the solid and the

pipe wall. When this friction force is exceeded, the solid starts to move. This initial interaction between the stationary solid and the water influx to

set the solid into motion was observed for all of the experiments, and it

appeared to be independent of the experimental variables. Once the solid was

set in motion, the phenomenon that followed, however, was greatly dependent

upon the volumes of water discharged and the other experimental variables.

Observations of this phenomenon suggested that the various volumes of water

used in the experiment may be grouped into three ranges. These are: small

volumes (0.10, 0.20, and 0.30 gallons or 0.38, 0.76, and 1.13 liters); intermediate volumes (0.40 and 0.5 gallons or 1.51 and 1.90 liters); and large

volumes (1.00, 2.00, and 3.00 or 3.78, 7,57, and 11.35 liters). Each volume

range revealed the effects of experimental variables on the solid movement to

a different extent. The patterns of solid movement in each volume range were

9
quite similar, but the patterns of the water stream adjacent to the solid were

somewhat different in each range. These observations for the three water

volume ranges are discussed below.

Small Volumes . When small volumes (0.10 to 0.30 gallons or 0.38 to 1.13

liters) of water were discharged into the drain, the effects of the experimental variables on the motion of the solid were very pronounced and visible.

The stationary solid accelerated very slowly, and the acceleration of the

larger diameter solids was slower than that of smaller diameter solids. The

depth of the water stream behind the solid remained below the lower half of

the solid, and the solid apparently dragged on a very thin film of water on

the lower wall of the drain pipe throughout the course of its motion within

the drain. During the motion of the solid, water continued to flow around the

solid, since the speed of water was larger than the speed of the solid.

The solid accelerated to a maximum speed, and apparently continued moving with

this maximum velocity as long as the forces acting on the solid in the downstream direction were sufficient to balance the force due to sliding friction.

The magnitude of the maximum speed attained by the solid with these small water

volumes was less than that of the local watet speed, and the water kept leaking

past the solid. When the water influx behind the solid declined, the forces

acting on the solid in the downstream direction became smaller than the force

due to sliding friction, the solid started to decelerate and slowly came to a stop within the drain pipe with some water still present in the drain behind

the solid. The remaining water then flowed around the stationary solid and

exited the drain. Smaller solids traveled farther than larger solids when

equal volumes of water were discharged, all of the 1.9 cm diameter solids

cleared the drain pipe with 0.30 gallons (1.13 liters) of water, while the 3.8 cm diameter solid traveled only a few centimeters. The solids clearing the

drain exited the pipe while decelerating with a portion of the total water

used exiting the pipe after the solid.

When sleeved solids were transported through the drain having a pitch equal

to 0.02, the effects of the coefficient of friction between the solid and the

pipe wall on solid transport were also observed. The sleeved solids were

slower to be set in motion, and traveled a shorter distance in the drain than

the sleeved solids having an equivalent diameter.

Intermediate Volumes . When intermediate volumes (0.40 and 0.50 gallons or 1.51

and 1.90 liters) of water were used, the effects of the experimental variables

on the motion of the solid, although less pronounced, were very similar to

those observed for the small water volume tests. That is, the acceleration

of larger solids was less than that of smaller solids.

The solid accelerated from rest to a maximum speed, traveled at this maximum

speed for a while, and then decelerated. The acceleration of the solids from

rest to maximum speed was faster than in the previous case with small water

volumes. Also, in this case, most of the solids cleared the drain, while in

the previous case only a few of the solids cleared the drain. The solids which

stopped within the drain in this case included: all of the sleeved solids and

some 1.5 inch (38.1 mm) diameter solids with 0.40 gallons (1.51 liters) of

10
water; and some sleeved solids with 0.50 gallons (1.90 liters) of water. As

before, the solid which cleared the drain pipe exited the drain while decelerating with a portion of the total water used exiting the pipe after the solid.

In situations where the solid stopped within the drain pipe, the portion of the

water remaining in the pipe flowed around the stationary solid and exited the

drain.

The depth of the water stream behind the solid, in some situations, reached

up to about the lower half of the solid for a short while when the solid was accelerating, but for most of the solid's motion within the drain, it stayed

below the lower half of the solid. The solid mostly dragged on a thin film of

water on the lower wall of the drain pipe, as water continued to flow around

the solid.

Figure 5 and 6 show the photographs of a 2.5-cm diameter and 5.1-cm long

cylinder being transported with 0.50 gallons (1.90 liters) of water. In

figure 5, the solid is just leaving photo detector No. 1 and all of the solid

is not visible. A close examination of this photograph reveals that the depth

of water stream upstream of the solid is larger than that in front of it, and

that the depth of the water stream upstream of the solid is almost as deep as the lower half of the solid. In figure 6, the solid is in between photo detector Nos. 3 and 4, and the depth of water stream adjacent to the solid is much

below the lower half of the solid. Also, the depth of the water stream

upstream of the solid is larger than that downstream of the solid.

Large Volumes . When large volumes (1.00, 2.00 and 3.00 gallons or 3.78, 7.57

and 11.35 liters) of water were used, the effects of the experimental variables

on the motion of the solid were not apparent. The solid accelerated quickly to

a maximum speed, and apparently exited the drain with the maximum speed. There

were some exceptions, however; the 1.50-inch (38.1 mm)-diameter solids and all

of the sleeved solids when transported with 1.00 gallons (3.78 liters) of water

exited the drain while decelerating. In all of the tests with large volumes of

water, the solid cleared the drain and a major portion of the water used exited

the pipe after the solid.

The depth of the water stream adjacent to the solid was higher than the lower

half of the solid for most of the solid's motion within the drain. Throughout

the length of the drain pipe stream depth upstream of the solid was larger than

that downstream of the solid. The solid was mostly riding on a thick film of

water, and it was apparently moving with the local velocity of the water stream

as a waterborne object.

Figure 7 shows a photograph of a 2 ,5-cm-diameter and 5.1-cm-long solid being

transported with 1.00 gallon (3.78 liters) of water. In the photograph, the

solid is between photo detectors 1 and 2. A close examination of the photograph shows that the depth of the water stream adjacent to the solid is

slightly higher than the mid height of the solid, and that the depth of water

stream upstream of the solid is larger than that downstream of the solid. The

increased depth of the water stream a short distance upstream of the solid is

the "moving wave” which was traveling in the upstream direction during the

experiment

11
The visual observations indicate that the solid has three phases of motion,

and these three phases of solid motion occur in three different zones of the

drain. The first or initial zone where the solid accelerates from rest to a maximum speed; the second zone, where the solid continues to move at the maximum speed; and the third or final zone, where the solid decelerates from the

maximum attained speed to a stop. The length of each zone as well as the magnitudes of respective accelerations and velocities are dependent upon the water

volume used and the other experimental parameters.

Also, depending upon the water volume available for transporting the solid and

solid variables, the length of a drain may be either longer or shorter than the

combined length of the three zones. For example, with small water volumes most

experimental solids failed to clear the drain, indicating that the length of

the experimental drain was longer than the combined length of the three zones. While with larger water volumes all of the experimental solids cleared the

drain, indicating that the length of the experimental drain was shorter than

the combined length of the three zones, a desired condition for the proper

transport of solids through a p-h drain.

3.2 SOLID VELOCITIES

The velocity of the solids was measured in three different sections of the p-h

drain namely the pipe sections between photodetectors No. 1 and 2, 2 and

3, 3 and 4. The positions of the three sections with respect to the drain

entrance and exit are as indicated in figure 1. The average values of the

solid velocities within each of the respective sections are denoted by U]_, U2 , and U 3

. The velocity represents the solid velocity during the initial stage

of its motion following the acceleration from a state of rest. The velocity U2

and U 3 represent the solid velocity where the solid may be accelerating, moving

with a constant velocity or decelerating.

The velocities attained by various solids with different water volumes are presented in figures 8 through 14. The data presented in these figures represent

the average of three repeated experimental values under the same conditions.

Figures 8 (8-1 through 8-10), 9 (9-1 through 9-15), and 10 (10-1 through 10-15)

show the solid velocity versus water volume discharged into the drain for various

solid lengths and diameters with the pipe slopes equal to 0.02, 0.04, and 0.06

respectively. Each figure is for one of the velocities (Uj_, U 2 or U 3 ) for one drain slope, one solid length and all four solid diameters. For example,

figures 8-1, 8-2, 8-3, 8-4, and 8-5 show solid velocity respectively for 2.5,

3.8, 5.1, 6.4 and 7.6 cm long solids and a drain slope of 0.02. Figures 8-6

through 8-10 show the solid velocity U 3 in a similar manner (the solid velocity

U 2 was not measured for the drain slope of 0.02). Figures 9-1 through 9-5, 9-6

through 9-10, and 9-11 through 9-15, respectively, show velocity , U 2 and U3

at a drain slope of 0.04. Figures 10-1 through 10-5, 10-6 through 10-10, and

10-11 through 10-15 respectively show velocity U]_, U 2 and U 3 at a drain slope

of 0.06.

An examination of figures 8 , 9, and 10 indicates that: (1) the solid velocity

increases with an increase in the water volume used; and ( 2 ) the solid velocity

12
decreases as the solid diameter is increased. The data presented in these

figures also suggest that the incremental increase in the solid velocity with an incremental increase in the water volume used is larger for small water volumes

(Vw 0.5 gallons or 1.9 liters) than that for large water volumes (Vw _> 1.0

gallons or 3.78 liters). This pattern of the effect of incremental change in

the water volume on the solid velocity may be interpretted as follows: when the

depth of the water stream in the drain is relatively small and the solid is

dragging on a very thin film of water between the solid and the pipe wall, a small increase in the amount of water volume used substantially increases the

depth of water stream in the drain and the thickness of the water film between

the solid and the pipe wall and reduces the friction; this pattern of solidwater movements was observed when small water volumes (Vw ^0.5 gallons or 1.9

liters) were used. With large water volumes (Vw _> 1.0 gallons or 3.78 liters)

the depth of the water stream in the drain is relatively large and the solid is

not dragging on a thin film of water but moving as a waterborne object, an increase in the stream depth due to further increase in water volume used has

little or no effect on the friction; and any increase in solid speed is primarily due to an increase in the water speed. This pattern of solidwater movement

was observed when large water volumes were used. This pattern of the solid

velocities dependence upon the water volume used suggests that the depth of the

waterstream in the p-h drain is a significant parameter for solid transport.

Figure 11 shows the velocities Uj, U 2 and U3 of a 2.5 by 5.1 cm (diameter by

length) solid in the drain having a slope of 0.04. An examination of figure 11

indicates that: (1) the magnitude of velocity U]_, in general, is larger than that

of velocity U 3 ; and (2) the magnitude of velocity U 2 is larger than that of velocity

Uj except when very small water volumes are used. These observations indicate

that the solid accelerates to a maximum velocity and then starts to decelerate.

Figure 12-1, 12-2 and 12-3, respectively, show solid velocity Uj_, U 2 and U 3 for

2.5 cm diameter solids and a drain slope of 0.04. An examination of the

figures indicates that: (1) the solid velocity U]_, in general, decreases as the

solid length is increased; and ( 2 ) the effect of the solid length on the solid

velocity U 2 and U 3 does not show a definite trend. It appears that: (1) the

solid length is an important parameter during the initial phase of the solid

motion, when the solid is starting from rest, and ( 2 ) the solid length becomes

less important as a parameter when the solid is moving with a constant speed or accelerating (or decelerating) slowly

Figures 13-1, 13-2 and 13-3, respectively, show velocity U]., U2 and U3 for a 2.5

by 5.1 cm solid for all three p-h drain slopes. An examination of these figures indicates that the solid velocity increases with an increase in the slope

of the p-h drain, particularly when small water volumes (Vw _< 0.5 gallons or

1.9 liters) are used. It also indicates that the solid velocity at a slope

of 0.06 is higher than that at a slope of 0.02 and lower than that at a slope

of 0.04. The solid velocity U 2 at a slope of 0.06 is lower than that at a slope of 0.04, particularly when larger water volumes (_> 1.0 gallons or 3.78

liters) are used. The indication of the existence of an optimum value of the

drain slope requires further examination. The effect of the p-h drain slope on

the velocity of the solids with relatively large water volumes indicates that

the depth of water stream in the partially filled p-h drain is an important

13
parameter for solid transport. For a constant (steady) flow rate through the

drain the flow velocity would increase as the drain slope is increased thereby

causing a decrease in the stream depth. However, the effect of the change of

slope on the flow is very complex, depending on whether the initial flow was supercritical or subcritical, which may lead to a hydraulic jump [17].

Figures 14-1 and 14-2 respectively show velocities Uj and U 2 of two 2.5 by 3.8 cm solids with different surface roughness characteristics and figures 14-3 and

14-4 show similar data for two 2.5 by 6.4 cm solids. One of the two solids

represented in each of these figures is the unsleeved solid, and the coefficient of friction between the solid and the drain pipe wall is approximately

equal to 0.6; the other solid is the sleeved solid, and the coefficient of

friction between this solid and drain pipe wall is approximately equal to 1.

An examination of these figures reveal that the solid surface roughness characteristic does not have a significant effect on the solid velocity. This is so because the velocity of the sleeved solid is lower than that of the unsleeved

solids during some experiments and higher in others. Also, the difference in

the velocities of the sleeved and the unsleeved solids, during most experiments,

was within the normal experimental scatter. Thus, the velocity data confirm the

conclusion reached earlier, that the surface roughness of the solid becomes

insignificant as a parameter once the solid is waterborne and moving.

The effects of the water volume used and the p-h drain slope on the solid

velocity indicated by these data are similar to those indicated by the data of

Swaf field et al. [9], although the two experiments were conducted under different conditions. As reported earlier in the Introduction, Swaf field et al. [9]

used relatively larger solids (maternity pad), and flushed the solid from a water closet along with the water into a relatively long (> 14 m) p-h drain;

and in their experiment, the velocity of the solid increased with an increase in

the water volume and an increase in the drain slope. However, the solid velocities in the experiments reported in this report varied from 0.0 to 8.0 ft/sec

(0 to 2.4 m/s), while in the experiment of reference 9 it varied from 0.0 to

4.0 ft/sec (0 to 1.2 m/s).

3.3 DISTANCES TRAVERSED BY THE SOLIDS WITHIN THE P-H DRAIN

It was noted previously in the discussion of visual observations that all but some sleeved solids cleared the 5 meter long p-h drain with 0.5 gallons (1.9

liters) of water, and all of the solids cleared the p-h drain with water

volumes in excess of 0.5 gallons. Hence, the data on the distance traversed

by the solid within the p-h drain (L s ) are limited. These data are summarized

in figures 15 to 19.

Figures 15-1, 15-2 and 15-3 show L s versus water volumes (Vw ) for 5.1 cm long

solids for a slope of 0.02, 0.04 and 0.06 respectively. Figure 16-1 shows L s versus Vw

for 2.5 by 3.8 cm sleeved and unsleeved solids for a drain slope of

0.02, and figure 17-2 shows Ls versus Vw for 2.5 by 6.4 cm sleeved and

unsleeved solids for a p-h drain slope of 0.2.

14
Figures 17-1 and 17-2 show L s versus solid diameter for 5.1 cm long solids for

all three drain slopes, and for water volumes respectively equal to 0.2 and 0.3

gallons (0.76 and 1.13 liters); and figures 17-3 and 17-4 are similar to

figure 17-1 and 17-2, respectively, for 7.6 cm long solids.

Figures 18-1 and 18-2 show L s versus solid length for 2.5 cm diameter solids,

for all three drain slopes, and for water volumes respectively equal to 0.2 and

0.3 gallons (0.76 and 1.36 liters); and figures 18-3 and 18-4 are similar to

figures 18-1 and 18-2, respectively, for 3.8 cm diameter solids.

Figures 19-1 and 19-2 show L s versus Vw

for all three p-h drain slopes for 2.5

by 5.1 cm solids and a 3.8 by 5.1 cm solid, respectively.

An examination of figures 15 to 19 indicates that the distance traveled by

the solids increases with: (a) an increase in the water volume used, (b) a decrease in the solid diameter, (c) a decrease in the solid length, (d) an increase in the p-h drain slope, and (e) a decrease in the coefficient of

friction between the solid and the drain pipe wall.

The effects of the water volume used and the- p-h drain slope on the distance

travelled by the solids indicated by these data are similar to those indicated

by the data of Swaffield et al. [9] and Kamata et al. [12], although the various experiments were conducted under different conditions. As reported earlier

in the Introduction, the researchers of references 9 and 12 utilized different

solids than used in this experiment, they also flushed the solid along the

water from a water closet into a relatively long p-h drain (14 m or longer)

while in this experiment the solid is placed in the empty p-h drain, which is

relatively short (5 meters).

15
4. CONCLUSIONS

1. The water volumes used for transporting the solids through a 7.6

cm-diameter drain may be grouped into two volume ranges: small volumes,

which are equal to or less than a 0.5 gallon (1.9 liters) of water; and

large volumes, which are equal to or greater than 1.0 gallon (3.78 liters)

of water. A solid drags on a thin film of water between the solid and the

p-h drain wall when small water volumes are used to transport the solid,

while the solid moves as a waterborne body when large water volumes are

used.

2. The velocity attained by a solid increases with an increase in the water

volume. The incremental increase in the solid speed with an incremental

increase in the water volume is larger for small water volume than for

larger water volumes.

3. The solid velocity decreases with an increase in the solid diameter. The

solid velocity also decreases with an increase in the solid length. However, the effects of the solid length on its velocity are more significant

during the initiation of the motion of th'e solid than during the remainder

of its motion within the p-h drain.

4. The solid velocity increases with an increase in the p-h drain slope,

particularly when small water volumes are used. When large water volumes

are used, the solid velocity also increases with an increase in the p-h

drain slope, but as the drain slope is further increased, the solid velocity

decreases indicating the possible existence of an optimum value of the

drain slope. The effects of drain slope on the solid velocity also suggest

that the depth of water stream in the partially filled p-h drain is a significant parameter for the transportation of solids.

5. The distance traveled by the solid within the p-h drain increases with:

(a) an increase in the water volume, (b) a decrease in the solid diameter,

(c) a decrease in the solid length, (d) an increase in the drain slope, and

(e) a decrease in the friction coefficient between the solid and the drain

pipe wall.

Acknowledgement

The author wishes to express his gratitude to Mr. Samuel R. Price for

processing the data, and to Mr. James D. Pollard for assisting in apparatus

assembly and data acquisition.

16
5.

REFERENCES

i

1. Bailey, J.R., et al., "A Study of Flow Reduction and Treatment of Waste

Water from Households," Water Pollution Control Research Series 11050

FKE Cincinnati, Ohio: Advanced Waste Treatment Research Laboratory,

1967.

2. Konen, T.P., "A Review of the Hydraulics of Gravity Drainage, Waste and

Vent Systems," Edward J. Zimmer Memorial Reference Course, Orlando,

Florida, 1977.

3. Fowell, A.J., et al., "Water and Water Related Conservation in Buildings,"

Proceedings of International Symposium on Water Supply and Drainage,

September 1976, NBS Special Publication 533.

4. Sharp, W.E., "Water Conservation with Water Savings Devices," Paper

presented at the New Jersey Conference on Water Conservation, Rutgers

University, New Jersey, 1976.

5. Cole, A.C., "Impact of Home Water Saving Devices on Collection Systems

and Waste Treatment," Proceedings of Conference on Water Conservation

and Sewage Flow Reduction with Water Savings Devices, Pennsylvania State

University, University Park, Pennsylvania, April 1975.

6. Wyly, R.S., et al., "Hydraulics of Gravity Drainage," Proceedings of

International Symposium on Water Supply and Drainage, September 1976,

NBS Special Publication 533.

7. Wertz, R.J., "A Plumbing Manufacturer’s Viewpoint on Water Savings

Devices," Proceedings of the Conference on Water Conservation and Sewage

Flow Reduction with Water Saving Devices, Pennsylvania State University,

University Park, Pennsylvania.

8. Sampler, D.L., "Water Conservation: Prospects and Problems," Proceedings

of National Conference on Water Conservation and Municipal Wastewater

Flow Reduction, Chicago, Illinois, November 1978.

9. Swaffield, J.A., and Marriott, B.S.T., "An Investigation of the Effects of

Reduced Volume W.C. Flush on the Transport of Solids in Above Ground

Drainage Systems," Proceedings of CIB W62 Symposium, Brussels, Belgium,

May 1978.

10.

Konen, T.P., and DeYoung, R., "An Investigation of the Performance and

Effects of Reduced Volume Water Closets on Sanitary Drainage, Sewer, and

Sewage Treatment Plants," Proceedings of the Conference on Water Conservation and Sewage Flow Reduction with Water Savings Devices, April 1975,

Pennsylvania State University, University Park, Pennsylvania.

17
11. Swaffield, J.A., and Wakelin, R.H.M., "A Study of the Interaction of

Drainage System Loading and Reduced Flush W.C. Operation," Proceedings

of the CIB W62 Seminar on Drainage and Water Supply in Buildings, Paris,

France, November 1979.

12. Kamata, M., et. al., "Studies on Flow and Transport of Feces in Horizontal

Waste Pipes," Proceedings of the CIB W62 Semi.ar on Drainage and Water

Supply in Buildings, Paris, France, November 1979.

13. Neilsen, O.J. and Nielsen, V., "Drainage Systems for Buildings with Water

Closets with 3 Liters of Flusing Water," Proceedings of the CIB W62

Seminar on Drainage and Water Supply in Buildings, Paris, France, November

1979.

14. Camp, T.R.,

" Civil Engineering Classics - Outstanding Papers of T.R. Camp."

A.S.C.E. Publication, 1973.

15. Fair, G.M, Geyer, J.C. and Morris, J.C., " Water Supply and Wastewater

Disposal , " John Wiley and Sons, 1956.

16. Bishop, J.W., "Field Experiences in Water Savings Programs of the

Washington Suburban Sanitary Commission," Proceedings of the Conference

on Water Conservation and Sewage Flow Reduction with Water Saving Devices,

April 1975, Pennsylvania State University, University Park, Pennsylvania.

17. Chow, V.T., " Open Channel Hydraulics ," McGraw-Hill Book Company, Inc., 1959.

18
19

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59
NBS-114A irev. 2-bo

U.S. DEPT. OF COMM.

4.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR 2 REPORT NO.

NBSIR 81-2266

. Performing Organ. Report No. 3. Publication Date April 1981

TITLE AND SUBTITLE

Experimental Investigation of Transport of Finite Solids in 76 mm-Diameter

Partially-Filled Pipe

5. AUTHOR(S)

Bal M. Mahajan

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7„ Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

8.

Type of Report & Period Covered

1/79 to 3/80

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Department of Housing and Urban Development

451 7th Street, SW

Washington, D.C. 20410

10.

SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

An exploratory experimental investigation of the hydro-transport mechanisms of finite

solids with non-uniform, unsteady and transient water flow introduced into a pitchedhorizontal drain (p-h drain) pipe by discharging a plumbing fixture was carried out.

The purpose of the investigation was to examine the effects of relevant variables on

the velocity attained and the distance traversed by the solid in the p-h drain. The

variables selected for the study include: the water volume used (i.e., the volume

of water discharged from the plumbing fixture into the drain), diameter and length

of cylindrical solid, and diameter and slope of the p-h drain.

This report contains a description of the experimental equipment and procedures, and

a summary of the data acquired during the solid transport experiment in 7.6 cm diameter

drain pipe at a pipe slope of 0.02, 0.04, and 0.06.

The solid dragged on a thin film of water between the solid and drain wall when

relatively small water volumes (Vw 1.9 liters or 0.5 gallons) were used, and the

solid moved like a waterborne object when relatively large water volumes (Vw £^3.8

liters or 1.0 gallons) were used. The solid velocity and the distance traversed by

the solid increased with an increase in the water volume used, an increase in the

drain slope, a decrease in the solid diameter, and a decrease in the solid length.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) cylindrical; non-uniform; partially-filled; pitched-horizontal drain;

velocity; volume; water.

13. AVAILABILITY

[XX] Unlimited

| | For Official Distribution. Do Not Release to NTIS

j Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

[XX] Order From National Technical Information Service (NTIS), Springfield, VA. 22161

slope; solid;

14. NO. OF

PRINTED PAGES

64

15. Price

$ 8.00

USCOMM-DC 6043-P80

1J)J