Reference

Ainos aia?43

iMBSIR 81-2249

Unsteady Water Depth

Measurement in A Partially Filled

7.6 cm Diameter Horizontal 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

-QC

100

. U56

81-2249

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

NBSIR 81-2249

UNSTEADY WATER DEPTH

MEASUREMENT IN A PARTIALLY FILLED

7.6 cm DIAMETER HORIZONTAL PIPE

RATIONAL RUKIUO

OV STANDARDS

LiajlAHT

JUN l o 1981

no-f acc. - acioo

. uSU>

% I R?l

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

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
*. e „«*

J ' * ; * v
ABSTRACT

A research program to investigate the wastewater solid transport in pitched

horizontal drains is under way. The objective of the program is to develop

data base and establish correlations for selecting drain pipe diameter, length,

and slope for effective solid waste transport with reduced water usage.

The purposes of this portion of the research program were: (1) to measure the

stream depth histories of unsteady, nonuniform, partially filled pipe flow

that ensues when water from a plumbing fixture is discharged into the drain;

and (2) to examine the effects of the presence of a cylindrical solids and

other relevant variables on the stream depth. The variables selected for the

study include: the water volume discharged from the fixture into the drain;

the drain slope, and the diameter and length of cylindrical solids.

This report contains a description of the experimental apparatus, instrumentation and procedures; and a summary of the stream depth data acquired from

experiments in a 7.6 cm diameter drain.

The depth of water stream at any given cross-section of the drain rises rapidly

to a peak value and then gradually falls to zero. The peak value of stream

depth at a pipe cross-section decreases as the distance from the drain entrance

increases. At a given pipe cross-section the peak value of stream depth

increases with an increase in the water volume used, a decrease in the pipe

slope, and with the presence of a solid in the drain. The variations in the

diameter of the solid influence the stream depth history more than the variation

in its length.

iii
PREFACE

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

ressearch and analysis efforts in development of water conservation test methods,

models for technical and economic analysis, and strategies for implementation

and acceptance of practices. This work is sponsored by the Division of Energy,

Building Technology and Standards of the Office of Policy Development and

Research, of the Department of Housing and Urban Development, under Interagency

Agreement H48-78.
TABLE OF CONTENTS 4 Page

1. INTRODUCTION 1

2. EXPERIMENTAL EQUIPMENT AND PROCEDURES 2

2.1 Equipment 2 2.2 Experimental Procedures 5

3. EXPERIMENTAL RESULTS AND DISCUSSION 7

3.1 Visual Observation 7 3.2 Water Stream Depth Data 8

4. CONCLUSION 11

5. REFERENCES 12

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1. INTRODUCTION

The purpose of this report is to discuss the depth measurement of transient

water flow in horizontal branches of gravity drainage systems. Experimental

apparatus, instrumentation and procedures employed for measuring water depth

in unsteady partially-filled horizontal drains are described. A summary of

results obtained from initial experiments is presented.

The requirements for water conservation as a national priority have emerged

due to the recognition of the limited availability of water resources. Technological advances to effect significant savings of water usage in buildings

depend on low volume or water-saving plumbing fixtures. In the routine operation of gravity drainage plumbing systems, reductions in the quantity of

water may result in inadequate transport of wastes after their entry into the

drainage system.

Water closet (WC) operations use about 40 percent of the total water used in

residences [1 - 2]. It has been estimated that a reduction of 30 percent or more in this consumption' can be realized by replacing the conventional water

closets (20-26 liters/flush) with water saving or low volume units (10-13

liters/ flush) [2-4]. Some researchers and plumbing professionals [1 ~7*],

however, have expressed concern about the use of low-volume water closets.

These concerned professionals indicate that the use of low-volume water

closets may reduce the wastewater flow in the horizontal branches (i.e., pitchedhorizontal drains or p-h drains) of the drainage systems below levels necessary

for the transportation of solid waste and impair the effectiveness of gravity

drainage systems.

To minimize the likelihood of drain clogging with reduced wastewater flows, p-h

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

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

used in the plumbing fixture operation, Vw , can adequately transport the solid

wastes through the p-h drain. The theoretical and/or empirical relationships

among Vw , variables of the drain pipe, the hydraulic parameters of the wastewater flow in the drain, and effective solid waste transportation, however, are not well established. Hence, research programs to investigate the transient

partially filled pipe flow transportation of solid wastes through the

horizontal branches (p-h drains) of gravity drainage systems are needed.

Pipeline transportation of solids, both slurries (i.e., small mass elements

or particles in suspension) and capsules (i.e., finite solids), with steady

full bore (flowing full) liquid flows has been investigated by many researchers

[tf - 12]. In these studies of pipeline transport of solids, the flow of the

carrier liquid is controlled by pumps. The transportation of solids through

the gravity drainage system pipeline as compared to the full bore pumped system

is quite different, although in both cases solids are transported by a flowing

liquid. The major differences include: the flow of water through the drainage

system is controlled by the gravity field; the p-h drain is only partially

filled; the flow is non-uniform, and transient; the depth of the water stream

1
is variable and strongly influences the transportation of solids. The hydraulic

parameters of flow (i.e., flow rate y, velocity U, and depth h) and the duration of flow through a p-h drain are dependent upon the volume of water discharged, and the fixture and drain variables. The problem is further complicated

because the flow parameters are not known and methods for predicting the flow

parameter histories along the length of the drain as a function of Vw and other

relevent variables are not yet fully developed. Also, standard instrumentation

is not available for measuring unsteady parameters of water flow and motion of

the waterborne solid without disturbing the flow field.

Kamata et al. [13] utilizing the two-point Laxe-Wondrof f finite difference

scheme for numerical integration of unsteady equations of flow in open channels

obtained approximate values of local hydraulic parameters of transient flow

introduced into horizontal drains by the flushing of a WC. They assumed that

the volume flow rate history of water influx into the drain pipe, due to the

flushing of WC, is equivalent to a triangular surge of relatively short duration (10-20 sec.). Based on the assumed triangular surge influx and the

Manning formula, they assigned certain values to the hydraulic parameters of

flow (i.e., y , U, and h) at a drain cross-section near the drain inlet, and

proceeded to calculate the corresponding values of flow parameters at various

locations (drain cross-sections) along the length of the drain pipe. They also

compared the flow parameter histories thus obtained with the experimentally

measured histories and claimed a "good enough" agreement between the two,

although, because of the experimental techniques utilized, their measured flow

parameters represented only approximate values.

They used the following techniques to measure the flow parameter histories at

various cross-sections along the length of a horizontal drain. They attached

a horizontal pipe of certain length to the outlet of a WC; flushed the wc into

the pipe which was discharging freely into an open tank containing a pressure

transducer; and measured the unsteady flow rate of the efflux and the stream

depth at the exit end of the pipe. They then considered that the flow rate

and stream depth histories thus measured represented the local values for flow

in a long drain pipe at a drain cross-section whose distance from the drain

entrance was equal to the length of the relatively short pipe used in the measurement. To obtain the flow parameter histories at various locations along

the length of a horizontal drain, they repeated the above-mentioned experiment

with pipes of different lengths. The flow parameters thus obtained, however, are not true representatives of the local values at various cross-sections of

a long h-drain because these measurements do not account for the effects of

hydraulic elements of the flow downstream of the stipulated location of

measurement

.

Relatively few investigations have been undertaken to measure the unsteady

depth of water stream in partially filled horizontal drains as a function of

Vw and other relevant variables. The study presented in this report is from

a research program underway to investigate the transport mechanism of solids

in horizontal drains, and to develop the data base and establish correlations

needed for selecting drain pipe variables for effective solid waste transport

with reduced water usage.

2
The objectives of this portion of the research program were: (1) to develop

instrumentation for measuring the unsteady depth of water stream in partially

filled horizontal drains without disturbing the flow field; (2) to measure

the stream depth histories at various locations along the length of the drain

pipe for different values of water volume discharged into the drain from a plumbing fixture; and (3) to examine the effects of drain slope (or pitch) and

the presence of a solid and its size on the stream depth.

3
2. EXPERIMENTAL EQUIPMENT AND PROCEDURES

2.1 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 by a 90-degree elbow to a 7.6-cm diameter

pitched horizontal drain. At the drain inlet, a tee is provided adjacent to

the elbow to permit insertion of the selected solid. An indicator line is

marked on the outside lower wall of the tee-section opposite to the opening;

the indicator line is approximately at the center of the tee-section. Both

the tee and the pipe are transparent, to facilitate visual observation of the

flow field and solid transport phenomena. The pipe drain is secured to stands

which are evenly spaced along the length of the drain; these stands can be

adjusted to establish the pitch of the drain. The exit end of the drain is

5.1 m downstream of the indicator line and is open to the atmosphere. The

efflux from the drain is caught in a container for proper disposal. All pipes

and fittings used to construct the apparatus are standard plumbing sizes used

in the U.S.

Hollow right circular cylinders with flat ends were used as experimental

solids. These cylinders were constructed from opaque and rigid plastic tubing.

One end of the hollow cylinder is completely plugged; the other end is only

partially plugged with a plug containing a concentric hole. The partially

plugged end is closed with a threaded cap (figure 2). The end plugs and

threaded caps were made from the same plastic material and were so constructed

that the center of gravity of the closed cylinder coincided with its geometric

center. The hollow cylinder with threaded cap permits desired changes in the

specific gravity of the solids used in the experiments, since the cylinders

can be filled with any material. For these experiments, the specific gravity

of the solids was made equal to one. The length to diameter ratios of the

cylindrical solids used in the experiments are given in table 1.

Table 1. Length to Diameter Ratios of the Cylindrical

Solids Used in the Experiment

Length/Diameter

Length - cm 1 2.5 3.8 5.0 6.3 7.6

I Diameter - cm | | | I I I 1.9 I 1.33 2.00 2.67 3.33 4.00

2.5 j 1.00 1.50 2.00 2.50 3.00

3.2 I 0.80 1.20 1.60 2.00 2.40

3.8 1 0.67 1.00 1.03 1.67 2.00

4
The water level depth is measured at a pipe cross-section by electrical

conducting pins (point electrodes) inserted in the pipe wall at prescribed

circumferential distances (figure 3). The discrete locations of the pins

provide incremental stepwise signals when the water level contacts the pins.

The level signal remains unchanged over the small spacing distance between the

pins until another point of contact is made. The pins are peripherally located

at 1 cm spacing along the circumference starting from the pipe invert; the pin

spacing arrangement from the invert is staggered by 0.5 cm so that pins on opposite sides of the pipe wall provide peripheral resolution of water depth

of 0.5 cm.

At each station (cross-section), the water level detector consists of 18 pins.

The pins are installed flush with the inside wall surface so they do not interfere with waterborne solids. The water flowing through the pipe wets the pins

to complete the electric circuit by passing the current through the water to

the common pin; the signal current in the circuit feeds a summing operational

amplifier (SOA) that produces a voltage proportional to the number of wetted

pins. The voltage output signal from the SOA is fed to a strip chart recorder

and/or to a floppy disk of a microcomputer where the water depth-time history

is recorded. The logic circuit is shown schematically in figure A. Four such

water level detectors are used along the length of the drain pipe. The detectors numbered 1 through A are situated at distances respectively of 0.6, 0.9,

A. 5 and A. 8 meters downstream of the indicator line in the tee-section.

2.2 EXPERIMENTAL PROCEDURES

The slope of the drain pipe was adjusted to the desired value. The water level

detectors were energized and the selected volume of water was flushed into the

empty drain. Ihe flow of water through each cross-section containing the pins was detected and water stream depth history was recorded on a floppy disk of a microcomputer programmed to record the resolved vertical depth at every tenth

of a second during the flow duration. These data were later used to plot the

stream depth history profiles and maximum water depths, as a function of the

selected experimental variables. For tests of solid transport, and for

examining the effects of a solid on the water flow entering the drain, and

subsequently on the stream depth history profiles at the four selected cross- sections of the drain, a solid was placed in the empty drain. The selected

solid was inserted through the tee opening, and placed on the lower wall of

the drain pipe with its upstream end aligned with the indicator line marked on the outer wall of the tee-section, and its axis aligned with the drain axis.

With the solid at rest in the drain, the selected volume of water was flushed

from the tank into the drain. The interaction between the stationary solid a id

the incoming water flow was observed. The water stream depth histories at the

four drain cross-sections containing the detectors are recorded.

5
Each experiment with the selected test variables was run three times. The

selected test variables were: water volumes equal to 11.4, 7.6, 3.8, 1.9, 1.5

and 1.1 liters (3, 2, 1, 0.5, 0.4, 0.3 gallons); drain pipe slopes (defined as sign 9, see figure 1). equal to 0.04 and 0.06; and single cylindrical solids

with dimensions shown in table 1.

6
3. EXPERIMENTAL RESULTS AND DISCUSSION

3.1 VISUAL OBSERVATIONS

Before discussing the water flow in a horizontal drain serving a plumbing

fixture such as the experimental water closet simulation (or the tank) , it is

instructive to describe the characteristics of the water flow leaving the fixture or entering the drain. The water leaves the tank at an unsteady volume

rate of flow, and for a given fixture the efflux rate-history is primarily

dependent upon the total volume of water dispensed from the fixture. In general the efflux rate rises rapidly from zero to a peak value as the valve is

opened, and then gradually falls off to zero as the tank is emptied.

The water discharged from the tank into the empty horizontal drain enters the

drain via the turning elbow and streams through the pipe unobstructed. The

drain pipe is only partially filled, and the depth of water stream is both

nonuniform and unsteady. The water depth history at any cross-section of the

drain is dependent on the water influx rate history. Water depth history profile is similar to that of the influx rate history. That is, the stream depth

in general rises rapidly to a peak value and then gradually falls off to zero. The peak value of the water depth for a given value of water discharged

decreases as the distance from the drain entrance increases.

When the water from the tank is discharged into the horizontal drain containing

the selected cylindrical solid on its lower wall, it encounters the stationary

solid. The stationary solid blocks the flow resulting in a short-term buildup

of some water behind (upstream of) the solid and passing of some water around

the solid through the crescent-shaped space between the solid and the pipe

wall. The depth of water stream behind the solid rises at a faster rate than

that in front (downstream) of it, which causes a hydrostatic head difference

across the solid. The stationary solid, in addition to its weight component,

is also subjected to the following forces in the downstream direction: a pressure force due to the unequal liquid depth and velocity on the two faces

of the cylinder; and shear force due to the streaming of liquid past the solid.

The flow induced forces acting on the solid increase with the increase of water

influx to the drain. The solid remains stationary until the sum of forces acting in the downstream direction overcomes the force due to static friction

between the solid and pipe wall. When this friction force is exceeded the

solid starts to move, and accelerates until a balance of forces develops. If

the resultant of forces acts off the center of gravity, a net moment occurs which may tilt the solid relative to the axis of the pipe.

The motion of the solid within the drain is dependent upon the volume of water

used and the size of the solid. When water volumes equal to or greater than

1.9 liters were used, the test solid, regardless of its size, cleared the

drain, and a portion of the water exited the drain after the solid. When

water volumes less than 1.9 liters were used, some solids did not clear the

drain; a solid, depending on its size traversed a certain distance and stopped

within the drain while a portion of the water was still flowing through the

drain.

7
The interaction of the solid with the incoming water flow modifies the stream

depth histories along the length of the drain. As a result of water buildup

behind the solid, the peak values of water depth at a drain cross-section adjacent to the upstream end of the solid are higher than the peak values of stream

depth in the absence of a solid, for the same volume of water discharged. This

effect of the solid on the water stream depth is very pronounced and visible

during the early stages of duration of the flow and the motion of the solid.

During the later stages of the flow duration, as the solid moves downstream

picking up speed, the effect becomes less and less noticeable, disappearing

completely as the solid leaves the drain. Hence, the stream depth histories in

the upstream sections of the drain, where the solid is moving slowly, are modified to a greater extent than those in the downstream sections of the drain.

The water stream depth histories, however, display the same basic patterns;

that is, the depth rises rapidly to a peak value and then gradually falls off

to zero; and for a given water volume the peak value of water depth decreases

as the distance from the drain entrance increases.

3.2 WATER STREAM DEPTH DATA

The depth of water stream was measured at four cross-sections or stations

along the length of the drain; these are numbered 1 through 4 in the downstream direction (figure 1). The stream depth at each station was recorded on the floppy disk of a microcomputer. These data were taken at every tenth of a second of the flow duration starting with the activation of the flush valve.

The data are presented in figures 5 through 48. The values presented in these

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

Figures 5 through 28 show stream depth histories as nondimens ional stream

depth (i.e., the ratio of stream depth to drain pipe diameter) versus elapsed

time, measured from the instant the flush valve was actuated. Figures 5 through 16 show the stream-depth histories at the four measuring stations for one value of water volume used, Vw , drain slope S, and with or without a solid

in the drain. Figures 17 to 24 show the stream depth histories at measuring

stations 1 and 3 for two values of Vw , one value of S, and with or without a solid in the drain. Figures 25 to 28 show the stream depth histories at measuring stations 1 and 3 for two values of S, one value Vw , and with or without

a solid in the drain.

An examination of these figures indicates that all of the stream depth-history

profiles display the same general pattern; each profile indicates that the

stream depth rises rapidly to a peak value and then gradually falls off to zero. The peak value of the stream depth is highest at the first station and

it decreases as the distance from the drain entrance is increased which implies

that the average flow velocity is increasing. The elapsed times for the stream

front to reach a station and for the stream depth to attain the peak value

increase as the distance of the station from the drain entrance increases. At

a given station the peak value of stream depth increases with an increase in

Vw , a decrease in S, and with the presence of a solid.

8
Figure 29 shows the peak value of nondimensional stream depth versus water

volume used (Vw) at measuring stations 1 and 3 for a drain slope (S) equal to

0.04, and with no solid, a 2.5 by 5.1 cm (diameter by length) solid, and a 3.8

by 5.1 cm solid in the drain. Figure 30 shows data similar to those of figure

29, for a drain slope of 0.04, and with no solid, a 2.5 by 6.4 cm solid, and a 3.8 by 6.4 cm solid in the drain. These data indicate that the peak value of

stream depth increases with the increase of Vw ; and for a given Vw the peak

value of the stream depth at a station is higher when a solid is in the drain

than when no solid is present.

Figures 31 to 32 show the peak value of nondimensional stream depth versus Vw , for S equal to 0.04 and 0.06, with or without a solid in the drain. Each fig- ure shows data at two measuring stations; figure 31 shows data at stations 1 and 3, and figure 32 represents data at stations 3 and 4. These data show

that, in general, peak values at S equal to 0.06 are lower than those for S equal to 0.04.

Figures 33 to 40 show the variations of the peak values of nondimensional

stream depth with the variation of solid-diameter to pipe-diameter ratios

(i.e., non-dimensional solid diameter). Each figure shows data at two measuring stations, and for three different values of Vw , one value of solid length

and pipe slope. These data indicate that the peak value of stream depth at

each of the measuring stations increases with an increase in Vw

.

These data also indicate that the variations of the peak value of stream depth

with the variations of the solid diameter display different patterns at different pipe locations for the same values of other experimental variables, and

different patterns at the same station for different values of other experimental variables. Hence these data suggest that the peak value of stream depth,

and consequently the stream depth history, in addition to the experimental

variable (i. e., Vw , S, solid diameter and length) is also dependent upon the

velocity of the solid relative to the velocity of water flow. In the upstream

section of the drain (i.e., in the vicinity of measuring stations 1 and 2),

the solid is still accelerating and moving with a velocity slower than the

flow velocity; in the downstream section of the drain (i.e., in the vicinity

of measuring stations 3 and 4), depending on the value of Vw , the solid may

be moving with a velocity very close to the flow velocity and accelerating,

moving at a constant speed, or decelerating. A stationary solid produces a greater flow blockage than a moving solid, a slow moving solid produces more

flow blockage than a fast moving solid, and a solid moving with a speed equal

to the flow speed probably produces no flow blockage.

These data indicate that for Vw equal to 1.9 liters, peak value of the stream

depth generally increases with an increase in the solid diameter; and for Vw equal to 3.8 and 7.6 liters, the peak value of stream depth first increases

with an increase in the solid diameter and then decreases with a further

increase in the solid diameter. These indications suggest the existence of a critical solid diameter for a given set of other experimental variables; and a solid with a diameter larger than the critical diameter moves faster than a solid of smaller diameter than the critical diameter. It also suggests that

the solid with diameter larger than the critical diameter starts to move with

9
less water buildup behind the solid than those with diameters smaller than the

critical diameter. A possible interpretation of this phenomenon is as follows.

Various forces acting on the solid increase in magnitude as the diameter of

the solid is increased for the same values of the variables (Vw , S and solid

length). Obviously volume and/or weight, cross-sectional area and surface area of a solid increase with an increase in the diameter. Therefore, for a given set of water flow conditions (i.e., stream depth and flow velocity) the areas of surfaces of solid-water interface increases with an increase in the

solid diameter. An increase of the solid-water contact surface perpendicular

to the flow direction (i.e., cross-sectional area of the solid) increases the

flow induced pressure force Fpj and an increase in the solid-water contact sur- face parallel to the flow (i.e., peripheral or surface area) increases the flow

induced shear force F^: The volume of water displaced by the solid is also

increased resulting in an increase of the buoyancy force F^. Also, because of

the increase in the weight of the solid, the force of static friction between

the solid and pipe wall increases with an increase in the diameter of the

solid.

If the sum of incremental- increases in the flow induced forces due to an increase in the diameter solid is smaller than or equal to the incremental

increase in the friction force, then the water buildup behind the solid needed

to set the solid in motion increases with an increase in the solid diameter;

this appears to be the case for solids with diameters less than or equal to

the critical diameter. If the sum of the incremental increases in the flow

induced forces is greater than the increase in the force of f 'iction, then the

water build up behind the solid needed to set the solid in motion decreases

with an increase in the solid diameter; this appears to be the case for solids

with diameters larger than the critical diameter.

Figures 41 to 48 show the variations of the peak value of the non-dimensional

stream depth with the variations of solid length to pipe diameter ratio (i.e.,

non-dimensional solid length). Each figure shows data at two measuring stations and for three different values of Vw , and for one value of solid diameter

and pipe slope. An examination of the figures indicates the followings. (1)

At measuring stations 1 and 2 peak value of stream depth increases with an increase in the length of the solid; and the variations of the peak value of

stream depth decrease with an increase in Vw and S, and with a decrease in the

solid diameter. (2) At measuring stations 3 and 4 the peak value of stream

depth is not appreciably effected by the variations in the length of the solid.

It appears that the effects of the length of the solid on the stream depth are dependent upon the state of the motion of the solid. At measuring stations 1 and 2, the solid is accelerating and moving with a speed much less than the

local speed of water, and at the measuring stations 3 and 4 the solid is moving

at a speed very close to local speed of water stream.

10
4. CONCLUSIONS

The point electrode method provides a satisfying method to measure the stream

depth history of nonuniform, unsteady, transient, partially filled pipe flows

containing finite solids as flow constituents, without disturbing the flow.

The depth of water stream at any given drain cross-section rises rapidly to a peak value and then gradually falls off to zero. The peak value of the stream

depth for a given value of water volume decreases as the distance from the

drain entrance increases which implies that the flow velocity is increasing.

The elapsed times for the stream front to reach a station and for the stream

depth to attain the peak value increase as the distance from the drain entrance

is increased.

At a given drain cross-section the peak value of stream depth increases with an increase in the volume of water used, a decrease in pipe slope, and with the

presence of a solid in the drain.

The peak value of the stream depth first increases with an increase in the

solid diameter and then decreases with a further increase in the solid diameter, suggesting the existence of a critical solid diameter for a given set of

other experimental variables (i.e., water volume, pipe slope and perhaps the

pipe diameter). The effects of the length of solid on the stream depth are dependent upon the solid velocity relative to the velocity of the water stream.

The peak value of stream depth and/or the stream depth history are strongly

influenced by the presence of a solid in the drain and by the velocity of the

solid relative to the water stream.

ACKNOWLEDGMENT

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

the data; to Mr. Paul A. Kopetka for contributing to the apparatus assembly and

data processing; to Dr. Richard A. Grot and Mr. Lynn A. Shuman for contributing

to the development of water level detectors; and Mr. James D. Pollard for

assembling the apparatus.

11
REFERENCES

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. 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.

3. Sharp, W. E., "Water Conservation with Water Saving Devices," paper

presented at the New Jersey Conference on Water Conservation, Rutgers

University, New Jersey, 1976.

4. 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 Saving Devices, Pennsylvania State

University, University Park, Pennsylvania, April 1975.

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

International Symposium on Water Supply and Drainage, September 1976, NBS

Special Publication 533.

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

of National Conference on Water Conservation and Municipal Wastewater Flow

Reduction, Chicago, Illinois, November 1978.

7. 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.

8. Grovier, G. W., and Aziz, K, "The Flow of Complex Mixtures in Pipes " Van

Nostrand Reinhold Company, New York, 1972.

9. Yokogowa, A., et al, "Behaviours of Capsules in Hydraulic Capsule

Pipeline," Proceedings of Fifth International Conference on the Hydraulic

Transport of Solids in Pipes, May 1978 (BHRA Fluid Engineering).

10. Kruyer, J., Redberger, P. J. and Ellis, H. S., "Pipeline Flow of Capsule,

Part 9," J. Fluid Mechanics, Vol. 30, Part 3 (1967).

11. Gray, E. C., Nelson, P.a. and Armstrong, W. P., "Flow Properties of

Suspensions with High Solids Concentration," AICHE Journal, Vol. 15, No. G,

1969.

12. Kruyer, J., and Grag, V. K., "Pressure and Couette Flow in a Capsule—Pipe

System," Proceedings of the Second International Conference on the Hydrotransport of Solids in Pipe, September 1972 (BHRA - Fluid Engineering).

12
13. Kamata, M., Matso, J., and Tsukagoshi, M., "Studies on Flow and Transport

of Feces in Horizontal Wastes Pipes", Proc. CIB W62 , Seminar on Drainage

and Water Supply in Buildings, Paris, France, November 1979.

13
14

Figure

1.

Schematic

of

experimental

apparatus
I

15

Figure

2.

Schematic

of

a

typical

experimental

solid
Figure 3. Photograph of a water level detector

l

lj

I

16
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17

Figure

4.

Logic

circuit

for

water

level

detector
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18

Figure

5.

Stream

depth

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at

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four

Figure

6.

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depth

histories

at

the

four

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for

V

w

=

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for

V

w

=

3.8

L,

S

=

0.04,

and

for

no

solid

in

the

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and

for

no

solid

in

the

drain.
19

Figure

7.

Stream

depth

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at

the

four

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Figure

8.

Stream

depth

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at

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four

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stations

for Vw=

11.4

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0.04,

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for

stations

for Vw=

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0.04

anda

no

solid

in

the

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by

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cm

solid

in

the

drain.
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Figure

11.

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Figure

12.

Stream

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at

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for

V

w

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w

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=

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for

no

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in

the

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0.06,

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for

no

solid

in

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drain.
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22

Figure

13.

Stream

depth

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at

the

four

Figure

14.

Stream

depth

histories

at

the

four

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stations

for

V

w

=

11.4

L,

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stations

for

V

w

=

1.9

L,

S

=

0.06,

and

for

no

solid

in

the

S

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24

Figure

17.

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at

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Figure

18.

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at

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equal

to

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26.

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at

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1

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at

drain

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stations

1

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33.

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Figure

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NBS-114A irev. 2-6C

>

U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publication Date BIBLIOGRAPHIC DATA

REPORT NO.

SHEET (See instructions) NBSIR 81-2249 April 1981

4. TITLE AND SUBTITLE

UNSTEADY WATER DEPTH MEASUREMENT IN A PARTIALLY FILLED 7 . 6 cm DIAMETER

HORIZONTAL PIPE

5. AUTHOR(S)

Bal M. Mahajan

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No. H-48-78

I. Type of Report & Period Covered

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

I I 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) A research program to investigate the wastewater

solid transport in horizontal drains is under way. The objective of the program is to

develop data base and establish correlations for selecting drain pipe diameter, length,

and slope for an effective solid waste transport with reduced water usage.

The purposes of this portion of the research program, which is presented here, were:

(1) to measure the stream depth histories of unsteady, non-uniform transient, partiallyfilled pipe flow that ensues when water from a plumbing fixture is discharged into the

drain, and (2) to examine the effects of the presence of a cylindrical solid and other

relevant variables on the stream depth. The variables selected for the study include:

the water volume discharged from the fixture into the drain, drain slope, and the

diameter and length of cylindrical solids.

The report contains a description of the experimental apparatus, instrumentation and

procedures, and a summary of the stream depth data acquired from experiments in a 7.6 cm diameter drain.

The depth of water stream at any given cross-section of the drain rises rapidly to a peak value and then gradually falls off to zero. The peak value of stream depth at a pipe cross-section decreases as the distance from the drain entrance increases. At a given drain cross-section, the peak value of stream depth increases with an increase in

the water volume used, a decrease in the pipe slope, and with the presence of a solid in

the drain. The .variations, in the solid diameter influence the steam depth history more

Chan tne variation in its length.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) Diameter; drain; flow; history; horizontal; length; partially-filled; pipe; slope;

stream-depth; unsteady; volume; water.

13.

availability

[X~| Unlimited

Qj For Official Distribution. Do Not Release to NTIS

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

20402.

fv~| Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

54

15. Price$8.00

USCOMM-DC 6043-P80

V