AlHOO PUBLICATIONS

NBSIR 81-2450

Experimental Investigation of

Transport of Discrete Solids With

Surge Flows in A

10.0 CM-Diameter Partially

Filled Pipe

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Building Equipment Division

Washington, DC 20234

October 1 981

Issued January 1982

Division of Energy, Building Technology and Standards

Office of Policy Development and Research

'*QC«MMaMMpartment of Housing and Urban Development

2QQ

jshington, DC 20410

.U56

81-2^50

1981

c. 2

NBSIR 81-2450

EXPERIMENTAL INVESTIGATION OF

TRANSPORT OF DISCRETE SOLIDS WITH

SURGE FLOWS IN A

10.0 CM-DIAMETER PARTIALLY

FILLED PIPE

Bal M. Mahajan

UATlOKAh m>REAt> or gTANDAKDa

ubbast

MAR 4 198?

riO'l OlLc - CX'LLy

no.

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Building Equipment Division

Washington, DC 20234

October 1 981

Issued January 1982

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
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ABSTRACT

This report presents the results of a series of experiments on the transport

of discrete solids with surge flows in a partially filled slightly pitched

horizontal pipe. The experimental apparatus, Instrumentation, and procedures

are described.

The experiments were conducted, using a cylindrical solid in a 10.0-cm (4-in)

diameter pipe. The water surge flows were obtained by discharging different

volumes of water into the pipe from a falling head open container which

simulated a water closet.

For each experiment, flow induced solid velocities and stream depth histories

at various locations along the length of the pipe were measured. The effects

of water volume used, pipe slope, and size of the solid, on the solid velocities were examined. Solid velocities were compared with the maximum water

velocities estimated from the stream depth histories. Also, the distance

traversed by the solids in the pipe were measured for those cases in which the

solids did not clear the pipe.

The solid velocity increased with an Increase in water volume used, a decrease

in the size of the solid, and an Increase in the pipe slope. The solid velocity

in the initial reach of the pipe was less than the maximum water velocity; and

the solid velocity approaches the maximum water velocity as the solid traveled

downstream, except for some experiments with small water volumes.

The distance traversed by the solid increased with an increase in water volume,

a decrease in the size of the solid, and an increase in the pipe slope.

The available data are too few to indicate any definitive conclusion, however,

a comparison of data on solid transport in 7.6-cm (reported in a prior publication) and 10.0-cm pipe suggests that the 7.6-cm pipe may be slightly better for

transport of solids with small water volumes than the 10.0-cm pipe.

iii
PREFACE

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

research and analysis efforts in developing water conservation test methods,

analysis, economics, and strategies for implementation and acceptance. 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.

iv
TABLE OF CONTENTS

Page

ABSTRACT iii

PREFACE iv

ACKNOWLEDGEMENTS 12

1 . Introduction 1

2. Experimental Equipment and Procedures 3

2.1 Equipment 3

2.2 Procedures 4

3. Experimental Results and Discussion

3.1 Visual Observation

3 .2 Maximum Water Velocities In Surge Flows

3.3 Solid Velocities

3.4 Distance Traversed by the Solids Within the Pipe 11

3.5 Comparison of Solid Transport Data In 7.6 and 10.0 cm Diameter Pipes 11

4. Conclusions 12

5. References 13

V

00

"vj

O'

O'
NOMENCLATURE

= portion of the pipe's cross-sectional area occupied by the water, or the

flow cross-sectional area

d = diameter of the solid

D = diameter of the pipe

h = depth of water stream

L = length of the solid

n = the Manning coefficient

= perimeter

p = pressure

q = volume flow rate

R = A/P^ = hydraulic radius

5 = pipe slope sin0

Sf = energy gradient or slope of the energy line

t = time

T = time period (or duration) of the surge flow through a cross-section

(location) of the pipe

Ug = solid velocity

= water velocity

Ujjj = maximum value of water velocity

Vy, = total volume of water used in an experiment

X = x-axis or the axial distance along the length of the pipe

Greek Symbols

6 = pipe slope angle

X = h/D

y = (y'Sf)/n

vi
Subscript

refers to maxlnium value

refers to Instantaneous values

vii
1

/
1 . INTRODUCTION

Need for water conservation has drawn attention to the large quantities of

water used in water closet (WC) operations and to a variety of means to curtail

this use. Water closets consume about 195 liters [50 gallons] per person per

day [1-4]*. This figure represent 40 percent of the total water consumed in a residence. It has been estimated that a reduction of 30 to 50 percent can be

realized by replacing conventional WC's (19-26 liters per flush) with the cur- rently available low-volume water-saving units (11-13 liters per flush), and a reduction of up to 90 percent of this water usage is possible if the

conventional syphonic-f lush WC's are replaced with innovative units [5].

Some researchers and plumbing professionals [5-8] however, have expressed

concern about the use of low-volume WC's. These concerned professionals indicate that the use of low-volume WC's may reduce the wastewater flow in the

horizontal branches of the gravity drainage system below levels necessary for

the transport of waterborne solid waste, impairing the effectiveness of the

drainage system.

To minimize the likelihood of drain clogging with reduced water usage, the

drain pipes serving WC's should be properly designed. That is the selected

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

volume of water used in the WC's operation can adequately transport the solid

waste through the drain. The theoretical and/or empirical relationships among

the water volume used, drain pipe variables, hydraulic parameters of the flow

in the pipe, and solid waste transport, however, are not well established.

The study presented in this report is part of a research program under way to

investigate the transport mechanism of solids in slightly pitched horizontal

drains and to develop the data base and establish correlations needed for

selecting drain pipe design variables for effective solid waste transport with

reduced water usage.

Data acquired earlier, during the exploratory experiments in a 76-ram (3 in)

diameter pipe has been presented in two separate reports [9, 10]. The data of

reference 9 indicated that the surge flow induced solid velocity and the distance traversed by the solid increased with: (a) an increase in the volume of

water used; (b) an increase in the pipe slope; and (c) a decrease in the diameter

and length of the solid.

The data of reference 10 indicated that: (a) the water stream depth at any

given cross-section (or location) of the pipe rose rapidly to a peak value and

then gradually fell off to zero; (b) the peak value of stream depth decreased

with an increase in the distance from the pipe entrance for a given volume of

water used; (c) at a given location the peak value of the stream depth increased

with an increase in the volume of water used, a decrease in the pipe slope and

with the presence of a solid in the pipe; and (d) the flow blockage produced by

* Numbers in brackets indicate references listed at the end of the report.

1
a solid depended upon the size of the solid as well as its velocity relative

to the local flow velocity.

The data acquired during the earlier experiments did not allow for a comparison

of the flow-induced solid velocities (Ug) with the maximum water velocities

The solid velocities were measured in only 2 or 3 locations of the pipe,

and the water depth data were not suitable for estimating the values of Um.

For this experiment the instrumentation was upgraded so that the data gathered

would provide for a comparison of Ug and U^.

The objectives of the experimental study presented in this report were: (a) to

measure the water flow-induced solid velocities at several locations along the

length of the pipe; (b) to examine the effects of water volume used, size of

the solid, and pipe slope on the solid velocity; (c) to estimate maximum velocity of water at various locations along the length of the pipe, and compare

the solid velocity to the maximum water velocity; and (d) to measure the distance traversed by solids in the pipe for those cases in which the solid do

not clear the pipe.

The data and results of the experimental studies will be utilized to validate

and refine the mathematical models that are being developed for predicting the

flow-induced motion of solids in pipes. Considerable work on modeling the

partially filled pipe flows [11,12,13], and motion of the solid in partially

filled pipes [14] has already been completed. The mathematical models along

with these data will provide a basis for establishing design recommendation

for drain pipe diameter, length and slope for an effective waste transport

with low water usage.

2
2. EXPERIMENTAL EQUIPMENT AND PROCEDURE

2.1 EQUIPMENT

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

similar to the apparatus used in the earlier experimental work reported in

references 1 and 2. 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 10.0-cm (4-in) diameter PVC pipe about 5 m (16.4 ft) long which simulates

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

the elbow to permit insertion of the selected solid. The drain pipe is transparent, to facilitate visual observation of the transport phenomena. The pipe

is mounted on several stands, which can be adjusted to establish the desired

pitch or slope of the pipe. The exit end of the drain is about 4.8 m downstream

of the solid starting line. 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 used in the United States.

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 plug on the other end contain

a concentric threaded hole which can be 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 coincide

with its geometric center. The hollow cylinder with threaded cap permitted the

specific gravity of the solids to be adjusted to unity. The length to diameter

ratio of the cylindrical solids used in the experiments is given in table A.

Table A.

Length to Diameter Ratio

Used in

of the Nine Cylindrical Solids

the Experiment

No. 1 2 3 4 5 6 7 8 9

Length (cm) 2.5 2.5 2.5 5.1 5.1 5.1 7.6 7.6 7.6

Diameter (cm) 2.5 3.2 3.8 2.5 3.2 3.8 2.5 3.2 3.8

L/d 1.00 0.80 0.67 2.00 1.60 1.33 3.00 2.40 2.00

Strain gauge pressure transducers are utilized to measure the depth of water in

the tank (i.e., simulated WC) as well as in the pipe. The pressure transducers

are connected to pressure taps, or small holes, situated at the bottom of the

tank and at the lowest point of the pipe cross-section (see figure 1). The

locations of the seven pressure transducers, numbers Pj through Py , used in the

experimental study are shown in figure 1. Pressure transducer P^, located at

the bottom of the tank, measures the water depth history of the water in the

tank when the tank is being flushed. Pressure transducers P2 through Py

,

3
located at specific distances along the length of the pipe measure the water

stream depth histories of the surge flow through the pipe.

The outputs of the pressure transducers are amplified and fed into an A/D

converter of a micro-computer and subsequently recorded on a floppy disk. The

computer is programmed to record the water depth data for each of the seven pres sure transducers at 0.1 second intervals for a total of sixty seconds, starting

with the activation of the flush valve.

Photodetectors, identical to those used in the earlier experimental work [1], are utilized for measuring the velocities of the solids in the pipe. However,

a microcomputer was used for data acquisition instead of the automatic timers

used in the earlier work. Also, the velocity of a solid is measured within six

different sections of the pipe as compared to only three in the previous work.

Seven photodetectors, numbers through Dy , are situated at specific distances

apart along the length of the pipe as indicated in figure 1. When a solid

passes through the pipe cross-section containing the photodetector, the light

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

microcomputer records the time of the generated signals in miliseconds on a floppy disk. The velocity of the solid is computed from the time Interval

required for the solid to pass between two photodetectors located at known

distance apart. The microcomputer is programed to calculate the average

velocity of a solid within six different sections of the pipe: namely the

sections between photodetectors and D2 , D2 and D3 , D3 and D4 , D4 and

D 5 , D5 and D5 , and D5 and Dy.

2 . 2 PROCEDURE

The slope of the pipe was adjusted to the desired value. The data collection

system (i.e., the computer, photodetectors, pressure transducers, amplifiers,

etc.) was activated. The selected volume of water resting in the tank was released by the flush valve into the empty pipe. The depth histories of water

flowing through the pipe cross-sections containing the pressure transducers

was recorded. These data were later used to estimate the maximum velocity of

water in surge flow at each location.

Next, a selected cylindrical solid was inserted through the tee opening, and

placed on the lower wall of the empty pipe with its upstream end aligned with

the solid starting line and its axis aligned with the drain axis as indicated

in figure 1. With the solid at rest in the pipe, the selected volume of water

was flushed from the tank into the pipe. The passage of the solid through the

pipe cross-sections containing the photodetectors was timed by the microcomputer

From these data the average velocity of the solid within various pipe sections

was calculated and stored on a floppy disk along with the solid passage time

data.

Solid transport experiments were conducted with only one solid in the pipe at a time. Each experiment was run twice. The selected variables were: water

volumes equal to 1.0, 1.5, 2.0, 3.0, 4.0, 6.0 and 8.0 liters; pipe slopes equal

to 0.02, 0.04, and 0.06; no solid in the pipe; and with a single cylindrical

solid in the pipe with dimensions shown in table A.

4
3. EXPERIMENTAL RESULTS AND DISCUSSION

3.1 VISUAL OBSERVATIONS

Observations of the surge flow and solid transport phenomenon revealed

information identical to that observed previously during the earlier experimental work [9, 10]. A summary of the observations is presented below.

The water flushed from the tank into the empty pipe streamed through the pipe

unobstructed. The drain pipe was only partially filled and the depth of water

stream was both nonuniform and unsteady. At a given pipe cross-section, stream

depth rose rapidly to a peak value and then gradually fell off to zero. The

peak value of depth decreased as the distance from the drain entrance increased.

When the water from the tank was flushed into the pipe containing a solid, the

flow through the pipe basically displayed the above mentioned patterns with the

following differences. The stationary solid partially blocked the flow, producing "backwater" effects on the flow (figure 3), and forcing the water to rush

through the crescent shaped space between the solid and the pipe wall. The

flow blockage produced by the solid appeared to be a function of the velocity

of the solid relative to the local water velocity, because stationary solids

and/or slow moving solids produced larger "backwater" effects than faster

moving solids.

The stationary solid, in addition to its weight component, is also subjected to

the following water flow Induced forces in the downstream direction: a pressure

force due to the unequal water depth and velocity on the opposite ends of the

solid; and a shear force due to the streaming of water past the solid. In addition, the solid is also subjected to buoyancy force, equal in magnitude to the

weight of water displaced by the solid, acting in an upward direction. These

forces increase with the volume of water flow through the pipe.

When the forces acting on the solid in the downstream direction overcame the

force of friction between the solid and the pipe wall, the solid started to

move and accelerate. The motion of the solid within the pipe was greatly dependent upon the water volume used and the size of the solid. When water volumes

equal to 1.0, 1.5 and 2.0 liters were used, the solid, regardless of its size,

dragged on a thin film of water on the lower wall of the pipe; and when the

water influx behind the solid declined, the solid started to decelerate. The

decelerating solid during some experiments stopped within the pipe with some water still present in the pipe behind the solid. The remaining water then

flowed through the crescent shaped space between the solid and the pipe.

Smaller solids travelled farther in the pipe than the larger solids when equal

volumes of water were used.

When water volumes equal to 3.0, 4.0, 6.0 and 8.0 liters were used, the solid

moved on a thick film of water between the solid and pipe wall; and the solid

accelerated quickly to a maximum or terminal velocity. During all experiments

with these water volumes, the solid cleared the pipe with a major portion of

the water exiting the pipe after the solid.

5
3.2 MAXIMUM WATER VELOCITIES IN SURGE FLOWS

Water velocity, U^, and volume flow rate, q, of steady (uniform as well as gradually varied) water flows through partially filled pipes at any pipe crosssection are related to the depth of water through the hydraulic radius by the

Manning equation [15]

:

r„ = r

2/3 (/Sf)/n (1)

q = A,,R2/3(/s;)/n » A„U„ (2)

where various terms are defined in the nomenclature.

The Manning equation is not directly applicable to surge flows because the

energy gradient, Sj, is variable. Nevertheless, approximate values of instantaneous velocity, Uj-, may be computed from the stream depth history data by

the use of the Manning equation as follows

:

2/3 2/3 2/3 _

= R^ [(/S^)/n]^_ = Rj. ~ ^t ^ (3)

2/3 2/3

(('sp/nlj = V Rt n (4)

where, p = (/S^)/n; and p is the average value of p at a given pipe location

(cross-section; for a given surge flow.

The value of p at any pipe location for a given surge flow may be computed

from the stream depth history data at that location, and the fact that the

total volume of water flushed from the tank passes through the location during

the time period of the surge duration, T, at the location, or

T T

= f qt dt = Z qt At (5)

0 0

or, substituting for q^ from equation (4) and rearranging

U = V /[(d2/4)(D/4)2/3 k] (6) w

T T

where: K = f f(X^) c|)^'^(Xj.) dt = Z f(X^) (]>^'^(X^.) At (7)

0 0

f(X) = 4 A^/d2 = [cos"^(l-2X) - 2(1-2X) /(X-X^)] (8)

(j)(X) = 4R/D = |l-[2(l-2X) /(X-x2)/cos"1(1-2X)]| (9)

and X = h/D (10)

6
During a surge flow the instantaneous water velocity will be maximum when ((((X^-) is maximum, and will be maximum when the quantity [f(Xj_) (|)“''^(Xt)] is maxmum, For flow through circular pipes, t|)(X) initially increases as X is

increased, attains the maximum value when X is about 0.81, and then starts to

decrease as X is further increased. The quantity [f(X) (()^'^(X)] follows a trend similar to that for <j)(X), however, it attains the maximum value when X is about 0.94. For all the experimental surge flows in this study, the measured

values of X (i.e., stream depth divided by the pipe diameter) were less than

0.5. Hence, for these flows the U and q will be maximum when X is maximum.

Equations (3) may be rewritten for the maximum values of water velocity, U^,

in a surge flow as:

Urn = [(4V^/d2) <J,2/3 (x^)] ( 1 /k) ( 11 )

The maximum water velocities in surge flows at different pipe locations, with

no solid in the pipe, were computed numerically from the stream depth history

data utilizing equation (11). The typical results of the computations are presented in figures 4 to 6 as the maximum water velocity versus nondlmensional

axial distance from the solid starting line or the pipe entrance (X/D), Figures

4, 5 and 6 respectively are, for a pipe slope of 0.02, 0.04 and 0.06, and each

figure show data for several water volumes. The values of U^, for a given

water volume, are also plotted as solid lines in figures 17 to 43 along with

the solid velocity data for the purpose of comparison.

An examination of these figures indicates the followings: (1) The maximum water

velocity at a given station increases as the value of increases; (2) Urn, in

general, increases as the S is increased except at pipe location P 3 (i.e, the

pipe cross-section where pressure transducer P3 is situated); (3) U^, in general,

decrease as the distance from location P 2 increases except for location P3 ; (4)

It appears that depending upon the value of and S, the surge flows experience

a "hydraulic drop" or a "hydraulic jump" in the vicinity of location P3 ; and

that the location P 3 which is about 6 pipe diameters downstream of the solid

starting line or about 9 pipe diameters from the elbow is within the transition

zone where the swirls and/or eddies due to the change in the flow direction

cause this odd behavior of the surge flow.

3.3 SOLID VELOCITIES

The velocity of the solid was measured in six different sections of the pipe

The positions of the photodetectors Dj^ through Dy are shown in figure 1, The

average values of the solid velocities within each respective section are denoted by Vel. #1 through Vel. # 6 ; and each velocity is considered to represent the solid velocity at an axial distance equal to the axial distance of

the center of the respective section. Hence, referring to figure 1, the non- dimensional axial distance (X/D) from the solid starting position corresponding

to velocities Vel. #1 to Vel, #6 respectively is about 2.3, 3.8, 5.3, 14,5,

31.8, and 42.2, The solid velocity data is presented in figure 7 to 43.

Figures 7 to 16 show the data as solid velocity versus water volume. Each

figure show only two of the six solid velocities, namely Vel, #1 and Vel. # 6 . Figures 7, 8 , and 9 respectively show the data for 2.5, 5.1 and 7.6 cm long

7
solids for a pipe slope of 0.02. Figures 10, 11, and 12 respectively show the

data for 2.5, 5.1 and 7.6 cm long solids for a pipe slope of 0.04. Figures 13,

14, and 15 respectively show the data for 2.5, 5.1 and 7.6 long solids, for a pipe slope of 0.06. Figure 16 show the data for a 3.5 by 5.1 cm solid for all

three pipe slopes.

Figures 17 to 43 show the data as solid velocity versus X/D (the nondimensional

axial distance from the solid starting line). Each figure show average solid

velocity data for: all three solid diameters; one value of solid length; one value of water volume, and one value of pipe slope. Each of these figures,

also show the maximum water velocities as a line for the surge flow for the

indicated values of water volume (V^) and pipe slope (s) with no solid in the

pipe. The maximum water velocity data are reproduced from figures 4 to 6.

Effects of the experimental variables (i.e., water volume used, size of the

solid, and the pipe slope) on the velocity attained by the solid are similar to

those indicated by the data of earlier experiments conducted in a 7.6-cm.

diameter pipe [9, 10]. A discussion of these effects is presented below.

Variations of solid velocity with water volume used . An examination of these

data, particularly of figures 7 to 15, indicates that the velocity of solid

generally increases with an increase in (i.e., the water volume used). 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 (V^ ^ 3z) than that for large water volumes (V^^

3?,). This pattern of incremental change in the water volume on the solid

velocity may be interpreted 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 solid-water movements was observed when

small water volumes (V^ ^ 3z) were used. With large water volumes (V^ > 3i)

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 velocity is primarily due to an increase in the water velocity. This pattern of solid-water

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

solid velocities dependence on the water volume used suggests that the depth of

water stream in the drain is a significant parameter for solid transport.

Variations of the velocity of solid with its size . An examination of these

data indicates that the velocity attained by the solid generally decreases with

an increase in the size of the solid, that is with an increase in the diameter

and/or length of the solid.

In general, the incremental increase in the solid average velocity with

incremental change in its size is larger for relatively small water volumes

(Vw _< 3)1 ) than that for relatively large water volumes (V^^ > 3)i). It appears

that for small water volumes, since the solid drags on a thin film of water

8
between the pipe and the solid, an increase in the solid size increases the

force of friction significantly; and both the Increase in the friction force

and in the mass of the solid decrease the acceleration of the solid. For large

water volume, since the solid moves as a waterborne object; an increase in the

size of the solid has little or no effect on the friction force; and the

decrease in the acceleration of the solid is primarily due to the Increase in

the mass of the solid.

Variation of solid velocity with the pipe slope . An examination of these data,

particularly of figure 16, indicates that the velocity attained by a solid, in

general, increase with an increase in the pipe slope (S), except with water

volumes equal to 1,0 and 1,5 in the initial reach (length) of the pipe which

represents the transition zone for the surge flow. For those water volumes,

in the initial reach of the pipe the velocity of a solid was minimum for S=

0,02 and maximum for S=0,04, It was observed earlier, in section 3,2, that in

the transition zone the maximum water velocities for S=0,04 were larger than

that for S=0,06, It appears, therefore, that velocity attained by a solid is

strongly dependent upon the maximum value of local water velocity which in turn

is a complex function of S, and axial distance from the pipe inlet.

Variations of solid velocity with the axial distance and its comparison with

the local maximum water velocity . An examination of figures 17 to 43 indicates

the following: Solid velocity first increases with an increase in the axial

distance from the solid starting line, reaches a maximum value and then starts

to decrease as the axial distance is further increased.

The magnitude of solid velocity, Ug, is less than the magnitude of the local

maximum water velocity, Ujjj, throughout the pipe for all experiments at a pipe

slope of 0,02 and for experiments with water volumes less than 2 liters at pipe

slopes of 0,04 and 0,06, For all other experiments at pipe slopes of 0,04 and

0,06, Ug is less than only in the initial reach (initial length) of the pipe,

and Ug approaches Uj„ as the solid travels downstream. For experiments with

water volumes equal to or greater than 2 liters, Ug approaches Uj^ at an axial

distance of about 14,5 and 5 pipes diameters for pipe slopes of 0,04 and 0,06

respectively.

The difference between U^^j and Ug appears to be a function of water volume used,

pipe slope, size of the solid, and the axial distance from the solid starting

line, or

S, d,L, and x] (12)

Ds = - UxlV„, S. d,L, and x] (13)

where, Uj^ is a complex function of the experimental variables and axial

distance from the solid starting line, and has the dimensions of velocity,

3,4 DISTANCE TRAVERSED BY THE SOLID WITHIN THE PIPE

It was noted previously in the discussion of visual observations that only

during experiments with water volumes equal to 1,0, 1,5, and 2,0 liters some of

9
the solids stopped within the pipe. All solids cleared the pipe during experiments with water volume equal to 3.0, 4.0, 6.0, and 8.0 liters. Hence the data

on the distance traversed by the solid within the pipe are limited. These data

are summarized in table 1.

An examination of these data indicates that, in general, the distance traversed

by the solid increases with: an increase in the water volume used; a decrease

in solid diameter and length; and increase in the pipe slope. However, the

number of data points are too small to obtain quantitative relationships.

3.5 COMPARISON OF SOLID TRANSPORT DATA IN 7.6 AND 10.0 CM DIAMETER PIPES

The data on the surge flow induced solid velocities and the distance traversed

by the solid in a 7.6 cm diameter pipe has been reported earlier in reference

9. Similar solid transport data in a 10.0 cm diameter pipe are presented in

this report. These data indicate the following:

1. The effects of the experimental variables (i.e., water volume, pipe slope,

diameter and length of solid) on the solid velocity, and distance traversed

by the solid are similar in both cases.

2. Measured values of average solid velocities at comparable pipe locations in

the 7.6 cm pipe, in general, have a larger magnitude than those in the

10.0 cm pipe; and the difference is dependent upon the other experimental

variables. The difference noted range between zero to about twenty percent.

3. The comparable solids which stopped in the pipe, in general, traversed a longer distance in the 7.6 cm pipe than that in the 10.0 cm pipe. The data

for the distance traversed by the solids in the 7.6 cm pipe is reproduced

and presented in table 2 for comparison.

4. CONCLUSIONS

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

The incremental increase in the average solid velocity with an incremental

increase in the water volume is larger for small water volumes (1-3 liters)

than for large water volumes (3-8 liters).

The average solid velocity decreases with an increase in the size of the solid

(i.e., the diameter and/or length), and it increases with an increase in the

pipe slope.

The average solid velocity at first increases, reaches a maximum value, and

then starts to decrease as the axial distance from the starting reference

increases. The magnitude of solid velocity is less than the maximum water

velocity in the initial reach (initial length) of the pipe. The solid velocity

approaches the maximum water velocity as the axial distance is further increased

(or as the solid travels downstream), except for the experiments with 1.0, 1.5,

and 2.0 liters of water. For these experiments the solid velocity is always

less than the maximum water velocity; and in some cases the solid stopped

within the pipe.

10
The distance traversed by the solid within the pipe increases with an increase

in the water volume used, an increase in pipe slope, and a decrease in the size

of the solid.

The effects of the experimental variables on the solid velocity, and distance

traversed by the solid, and stream depth history are similar to those found

during the earlier experimental work with a 7,6-cm diameter pipe.

Under comparable experimental conditions, the solid velocities in a 7.6-cm pipe

are somewhat larger (0 -> 20 percent) than those in the 10.0-cm pipe. The solid

which stopped within the pipe, in general, traversed a slightly longer distance

in the 7.6-cm pipe than that in the 10.0-cm pipe. The available data are too

few to draw any definitive conclusions, however, these data suggest that smaller

7.6-cm pipe may be slightly better for the transport of solids with small water

volumes than the 10.0-cm pipe.

ACKNOWLEDGMENTS

The author wishes to express his gratitude to Ms. Laura Sampson for her

contribution to data acquisition and data processing, Mr. Michael J. McCall for

his contribution to apparatus assembly, and Mr. Paul A. Kopetka for contributing

to apparatus assembly and data processing.

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. Konen, T.P., "A Review of the Hydraulic 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 Draiange,

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 Municpal Wastewater Flow

Reduction, Chicago, Illinois, November 1978.

9. Mahajan, Bal M. , "Experimental Investigation of Transport of Finite Solids

in a 76 mm - Diameter Partially-Filled Pipe", NBS Report No., NBSIR 81-

2266, April 1981.

10. Mahajan, Bal M. , "Unsteady Water Depth Measurement in a Partially-Filled

7.6 cm Diameter Horizontal Pipe", NBS Report No., NBSIR 81-2249, April

1981.

11. Swaf field, J. A., "Entry Transition Water Surface Profile Prediction in

Supercritical Partially Fitted Pipe Flow", NBS Report No. NBSIR 91-2290,

June 1981.

12
12. Swaf field, J. A., "Prediction of the Hydraulic Jump Location Following a Change of Slope in Partially Filled Drainage Pipe", NBS Report No.

NBSIR 81-2367, May 1981.

13. Swaffield, J. A,, "An Initial Study of the Application of the Numerical

Method of Characteristics to Unsteady Flow Analysis in Partially Filled

Gravity Drainage Sized Pipes", NBS Report No. NBSIR 81-2308, July 1981.

14. Swaffield, J. A., "Dependence of Model Waste Solid Transport Characteristics in Drainage Systems on Solid Geometry, Mass and Pipe System

Parameters", NBS Report No. NBSIR 81-2307, July 1981.

15. Chow, V.T., "Open-Channel Hydraulics," McGraw-Hill Book Company, New York,

1959.

13
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SOLID DIHMETER » * » a . e CM

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1 .a T 1 1 1 ~r B.B H.S B.B 7.S S.B NRTER VOLUME CLD

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Figure 7. Solid velocity #1 and i'/S versus water volume for 2.5 cm long

solids at a pipe slope of 0.02
cu_

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1 1 1 1 1 1 1 i.a a.

a

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,

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la.B

1 iB.B

Figure 8. Solid velocity #1 and //6 versus water volume for 5.1 cm long

solids at a pipe slope of 0.02
SOLID

VEL.

CM/SECD

VEL.

CM/SECI

-B

-B

1.2

l.B

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9

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SLOPE 0.0S

SOLID LEN. - 7.B CM

SOLID DIHMETER s X - 3. a CM

O - S.l CM

d' - S.S CM

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.a x.u a. a h.b b.b 7.b s.b NRTER VOLUME CLD —I 1 IB.B la.B

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O - 0.1 CM

«- S.S CM —T 1 1 1 1 1

1 B.0 s.B B.0 y.B a.

a

xa.e xe.a WRTER VOLUME C L. D

Figure 9 Solid velocity #1 and #6 versus water volume for 7 , 6 cm long

solids at a pipe slope of 0.02
.

CM/SEC)

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VEL.

CK/SECD

(VI cn

03 _

cu

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5K « 3.e CM

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^ « 2 . 5 CM

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! 1 1

1 V.a X.S 9.0 H.S 6.0 7.S 9.0 i0.5 i.6.0 WRTER VULUME CLj

a.Ki -1.;^ u.w UIRTER VOLUME CLD

Figure 10 Solid velocity #1 and #6 versus water volume for 2.5 cm long

solids at a pipe slope of 0.04
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(ri

03 .

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cn

X _

lU

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Figure 11, Solid velocity #1 and #6 versus water volume for 5.1 cm long

solids at a pipe slope of 0.04
SOLID

VEL.

Cli/SECD

SOLID

VEL.

CM/SEC

I

1.8

1.6

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- 2.5 CM

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a

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T 1 10.

S

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10.0

Figure 12. Solid velocity #1 and #6 versus water volume for 7.6 cm long

solids at a pipe slope of 0.04
SOLID

VEL.

CM/SEC

I

SOLID

VEL.

CM/SEC

I

|f.B

.H

.8

1,2

1.6

2JI

2.M

2,8

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O - a.B CM

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1 1 1 1 1 1

1 i.a a. a h.b a. a t.b s.a la.a xe.a WBTER VOLUME CLD

a

Xa

8

a

VEL *B

SLOPE 0.0S

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SOLID DIBMETER i X - a.B CM

O - a.i CM

- a.B CM

x.a —I

1 1 1 1 1 1 a. a H.B a. a 7 .b a. a la.a i.a.a WBTER VOLUME CLD

Figure 13. Solid velocity #1 and #6 versus water volume for 2.5 cm long

solids at a pipe slope of 0.06
SOLID

VEL.

CM/SECO

SOLID

VEL.

CM/SECO

tf.B

.M

.6

1.2

1.6

ZJI

2.H

2.S

3.2

10.0

.H

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1.2

1.6

2.0

2.H

CU_

cri

03

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O a

8

9X

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X

VEL.

SL-OPE 0.0B

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SOLID DIBMETER i

PK - 9 . S CM

O - 0.1 CM

- S . B CM

S..B —I

1 1 1 r- a.a h.b s.b 7.b b.b WRTER VOLUME CLD —I

1 IB.B J.B.0

a.io a.w WRTER VOLUME CLD

Figure 14. Solid velocity #1 and #6 versus water volume for 5.1 cm long

solids at a pipe slope of 0.06
SOLID

VEL.

C

M/SEC 0

SOLID

VEL.

C

M/SEC

D

tf.B

.H

.B

1.2

1.6

2.0

2.S

2.6

3.2

tf.B

.H

.6

1.2

1.6

2JS

2.H

2.B

3.2

,m

a

VEL.

SLOPE 0,06

SOLID LEN . - T-.B CM

SOLID DIBMETER t

5K - a . e CM

Q - 3,1 CM

- a. 5 CM —I

1 1 1 1 1 1

1 x.a a .0 H.a a. a 7 .s a. a la.a le.a WBTER VOLUME CLD

f

f I

.a

9

X

a

JL T i.a

VEL *6

SLOPE 0,06

SOLID LEN. - 7.6 CM

SOLID DIHMETER i X - a. 8 CM

O - a.i CM

- a . s CM —I

1 1 1 r- a.B H.a a. a 7 . a a.

a

WRTER VOLUME CLD —I

1 la.a a.B.a

Figure 15. Solid velocity #1 and #6 versus water volume for 7 . 6 cm long

solids at a pipe slope of 0.06
2.0’T

>-' H

M

U

O

hJw

>

oM

o

oo

0 . 0 --

0.0

+

O o

+ ^

o

t

^ 1 ^ 0.2

+

o

t> 6

t> >

Pipe Slope

> = 0.02

O = 0.04

+ = 0.06

-H • 1 1 1-

0.4 0.6 8.0

WATER VOLUME USED (L)

>>

E-< M

U

o

w

>

Q

I—

I

hJo

c/:

Figure 16. Solid velocity //I and #6 versus water volume used

for a 3.5 by 5.1 cm solid for all three pipe slopes
IU_,

iii

cu

LJ x_

LU oi cn

t ^ cu

WRTER VPL . 1. LITER

SLOPE 0.0S

SOLID LEN. - a. 5 CM

SOLID DIRMETER »

JK - 3.8 CM

O - 3.1 CM

-r - a.s CM

NONDIMENSIONAL DISTANCE, X/D

WRTER VOL. a LITER

SLOPE o.oa

SOLID LEN. - e.S CM

SOLID DIRMETER t

(-J x_

LU oi cn

«s-

(U

—I ia_

LU 4

—Iacn

JK « 3.B CM

9C

v.fl «. liB.a xa.m as.

a

ea.f> aa.a Bs.a —I

NONDIMENSIONAL DISTANCE, X/D

. Solid velocity versus distance from the solid starting line

for 2.5 cm long solids and for V = 1.0 and 2.0 L, at a pipe

slope of 0.02

Figure 17
Solid velocity versus distance from the solid starting line

for 5.1 cm long solids, and for = 3.0 and 4.0 L, at a pipe

slope of 0.02

Figure 18
NOMDIMENSIONAL DISTMCE, X/D

r~^ LJ

LXJ cu cn

es.

t ' cu

LU ^

cu

.

WRTER VOL . S LITERS

SLOPE 0.0E

SOLID LEN. - a. 5 CM

SOLID DIBMETER s X » 3.0 CM

O - 3.1 CM

o

CD

cn

• -r 1 1 1 1 1 1 1 1

1 S.0 i.a.m xs.ca est.es ss.a aai.a ms.ea Hss.a hs.sb

NONDIMENSlONAL DISTANCE, X/D

Figure 19 . Solid velocity versus distance from the solid starting line

for 5.1 cm long solids, and for = 6.0 and 8,0 L, at a pipe

slope of 0,02
SOLID

VEL.

CM/SEC

3

SOLID

VEL.

CM/SEC

3

WRTER VOL . 1 LITER

SLOPE 0.02

SOLID LEN . - S.l CM

SOLID DIRMETER t X - 3 . B CM

O - 3.1 CM

- B.S CM

%.(S

-**1 1 1 1— 1—

J.5.G9 ea.a ss.ia aa.e as.

a

NONDIMENSlONAL DISTANCE, X/D

HB.a HB.a

Figure 20. Solid velocity versus distance from the solid starting line

for 5.1 cm long solids, and for V =1.0 and 2.0 L, at a pipe

slope of 0.02 ^
SOLID

VEL.

CM/SEC)

SOLID

VEL.

C

M/SEC

D

NONDIMENSIONAL DISTANCE, X/D

Figure 21. Solid velocity versus distance from the solid starting

for 5.1 cm long solids, and for = 3.0 and 4.0 L, at

slope of 0.02

line

a pipe
r~\

m r.

LLI «j cn

21

LU>

WRTER VOL. 6 LITER

SLOPE 0.C3E

SOLID LEN. - B.l CM

SOLID DIRMETER >

>K - S.8 CM

O - a.I CM

- a.S CM

CU oi _

CD

CO

T T T T

V.a .a sjB.a iB.m am.m aa.m mm.m NONDIMENS lONAL DISTANCE, X/D

aa.a —I

1 H0.a HS.a

r~^

C_J LU

CO

Q

f—

1

CD

CO

Figure 22. Solid velocity versus distance from the solid starting line

for 5.1 cm long solids, and for = 6.0 and 8.0 L, at a pipe

slope of 0.02
SOLID

VEL.

C

M/SEC D

SOLID

VEL.

Ch/SECD

l.C

i.6

8.H

8,8

9.8

-H

.8

i.8

l.B

8.0

S.H

WHTER VOL. a. LITER

SLOPE 0.02

SOLID LEN. “ 7.6 CM

SOLID DIHMETER s X - 3 .B CM

o 3.1 CM

- 2 .S CM

3K X

.a

X

T

1 B.B ^a.a

1 ea.e —I

es.o

-uaca.sa HB.B HB.B

NONDIMENSlONAL DISTANCE, Z/D

Solid velocity versus distance from the solid starting line

for 7.6 cm long solids and for V„ = 1.0 and 2.0 L, at a pipe

slope of 0.02

Figure 23
Figure 24. Solid velocity versus distance from the solid starting line

for 7.6 cm long solids and for = 3.0 and 4.0 L, at a pipe

slope of 0.02
SOLID

VEL.

C

M/SEC D

SOLID

VEL.

CM/SEC

3

l.a

l.B

2.0

2.H

2.8

3.2

.M

.8

1.2

l.B

2.0

8.M

cu _

01

a>.

«u

WRTER VOL. 6 LITER

BLaPB a. 08

SOLID LEN. “ 7.8 CM

SOLID DIRMETER i X - a . B CM

« a. I CM

o

* *

•

»

» *

-j , 1 1 1 , , , ,

.0 a.o J4B .0 is.0 00.0 ee.o a«.0 os.0 H0.0

NONDIMENSlONAL DISTANCE, X/D

WRTER VOL . B LITERS

SLOPE 0.0S

SOLID LEN. - 7.B CM

SOLID DIRMETER : X »=• 3. a CM

O - 3.1 CM

a% .0

T' 5.0 —T 3.0.0

1

1 XB.Ca E0.0 —, 1

1 B5.0 50.0 55.0

1 H0.O

NONDIMENSIONAL DISTANCE, X/D

—

I

S6.0

Solid velocity versus distance from the solid starting line

for 7.6 cm long solids and for V.= 6.0 and 8.0 L, at a pipe

slope of 0.02

Figure 25

4oh

ex
^_l , , , , ,

1

^ 1 , v.a a. a ia.a is.a ea.a es.a aa.a aa.a hb.b hs.b

NONDIMENSIONAL DISTANCE, X/D

Figure 26. Solid velocity versus distance from the solid starting line

for 2.5 cm long solids, and for = 1.0 and 1.5 L, at a pipe

slope of 0.04
SOLID

VEL.

C

M/SEC

D

(U. m

to.

cxl

WRTER VQl- . e LITER

SLOPE 0»0H

SOLID LEN . — S.S CM

—1 1 as. a M0.0

1.0 —r— s.a

1 1 1—

10.0 1B .0 B0.0

1

1 es , 0 00 - B> HS.0

NONDIMENSIONAL DISTANCE, X/D

LI

LLl cn

IXJ I

ta _

I UJ

WRTER VOL

.

SLOPE 0.0H

SOLID LEN

.

H LITER

e .B CM

l._J

I—

i

_.J CJ

LO

Ri ..I

•.-J

*r

*ii.0 B.0 10.0 1B.0 ea.ia BB.o B0.0 es.0

NONDIMENSIONAL DISTANCE, X/D

T S0.0

1 H6.0

Solid velocity versus distance from the solid starting line

for 2.5 cm long solids, and for = 2.0 and 4.0 L, at a pipe

slope of 0.04

Figure 27

K

a
l'-'. C J 3' _

!JJ ol I LO

/ ~ OJ_

> nl I

U J

I 1 » 1

a

« X

CJ

if)

WRTER VQL . G LITER

SLOPE O.0H

SOLID L.EN . - e.S CM

SOLID DIBMETER s X - 3 . B CM

0-3.1 CM

- S . 5 CM

uTV)

td —

r

B.a —

1

r 1 1 r 1—

xB.a xB.a £!0.a es.u sa.a as.

a

NONDIMENS lONAL DISTANCE, X/D

—1 1 Ho.e MS.

a

Figure 28. Solid velocity versus distance from the solid starting line

for 2.5 cm long solids, and for = 6.0 and 8.0 L, at a pipe

slope of 0.04
a

Ma ^ HP ^*1 I 1 1 1 1 1 1 1 *

1 V.ts a. a a.0.0 is .0 00.0 es.a 00.0 aa.0 H0 .a H0.0

NONDIMENSIONAL DISTANCE, X/D

Figure 29. Solid velocity versus distance from the solid starting line

s^op^o£TM.o^ - pip-
NONDIMENSI ONAL DISTANCE, X/D

Figure 30. Solid velocity versus distance from the solid starting line

for 5.1 cm long solid, and for = 2.0 and 4.0 L, at a pipe

slope of 0.04
SOLID

VEL.

CM/SEC

3

SOLID

VEL.

CM/SEC

3

.4

.8

1.2

1.6

2.B

2.S

E.B

3

2

-B

1.8

1.8

E.0

2.4

Cfl

ca .

cu

O X m

S s r

a,.

WBTER VOL . e LXTER

SLOPE 0 . 0H

SOLZD LEN . “ 5.1 CM

SOLID DIBMETER t

7K - S.e CM

o - a . 1 CM

- a . 5 CM

'W|

—I— S.B

1 3.0.0

1 1 IS.B 00.0 BB.0 80. BB.0 H0.B

0

NONDIMENS lONAL DISTANCE, X/D

HB.0

WRTER VOL . a LITER

SLOPE 0.0H

SOLID LEN. “ 5.1 C^

P_ B.0

I ,

, p 1 1.0.0 iS.B 00.0 05.0 B0.0

NONDIMENSI ONAL DISTANCE, X/D

—1—

8B.0

1 -I H0.0 HS.0

Figure 31. Solid velocity versus distance from the solid starting line

for 5.1 cm long solid, and for = 6.0 and 8,0 L, at a pipe

slope of 0.04
IU_

oi

OD _

oi O 3-_ LU lu cn

a!

I U3 _ LU 4

_JOcn

oa

WRTER VOL. X.G LITER

SLOPE 0.0H

SOLID LEN. - 7.e CM

O

a

X

«.a —r- B.a —I

1 1 1 1 1 1 1 3Lta.a xe.ia ea.e ea.a aa.a as. a sa.a mb. a

NONDIMENSI ONAL DISTANCE, X/D

Figure 32. Solid velocity versus distance from the solid starting line

for 7.6 cm long solids, and for Vw = 1.0 and 1.5 L, at a pipe

slope of 0.04
SOLID

VEL.

C

M/SEC D

SOLID

VEL.

C

M/SEC

D

(U_ m WRTER VOL . 2 LITER

SLOPE 0.0H

1 1 s.e X0.0

1

as.

a

IS.a aa.a es.a aa.a NONDIMENSI ONAL DISTANCE, X/D —I , Ha.a Hs.a

lU —

iri

«scu

oi

(U

to _

.H

WRTER VOL . H LITER

SLOPE 0.0H

SOLID LEN. - 7.6 CM

iS-*i 1 1 1 1 1 ( 1 1

1 "fa. a s.a a.a.B is. a aa.a es.a aa.a as. a hb.b HS.a

NONDIMENS lONAL DISTANCE, X/D

Figure 33. Solid velocity versus distance from the solid starting line

for 7.6 cm long solids, and for = 2.0 and 4.0 L, at a pipe

slope of 0.04
SOLID

VEL.

C

M/SEC

0

SOLID

VEL.

C

M/SEC

D

WRTER VOl_. S LITERS

SLOPE 0.0H

SOLID LEN. - 7.B CM

1

1 1 1 1 1 r 1 1

CS S.B 3.19.0 3.5.0 B0.0 B5.0 50.0 SS.0 H0.0 H5.0

NONDIMENS lONAL DISTANCE, X/D

. Solid velocity versus distance from the solid starting line

for 7.6 cm long solids, and for = 6.0 and 8.0 L, at a pipe

slope of 0.04

Figure 34
(U —

ni

lU

LJ 3-_

LU ai CD

WRTER VQL. 1 LOCTER

SL-OPE 0.06

SOLID LEN. - e.B CM

SOLID DIRMETER t X o a . B CM

O - a. I CM

- a.B CM

«.a

X —

I

1 1 1 1 1 1

1—

1 a.B ajB.m is.a bb.b es.a bb.b aa.a hb.b hb.b

NONDIMENS lONAL DISTANCE, X/D

LJ 3-. lU ol CO

«w>

LU

di |U_

O

CO

WRTER VOL. I.S LITER

SLOPE 0.06

SOLID LEN. - S.5 CM

SOLID DIRMETER I X - a. a CM

o - a. I CM

- a . s CM

I -yvi

—r~ a.B —I

V.B asa.a IB. as.B

a

BB.B ea.B aa.B HB.B HB.B

NONDIMENSIONAL DISTANCE, X/D

Figure 35. Solid velocity versus distance from the solid starting line

for 2.5 cm long solids, and for = 1.0 and 1.5 L, at a pxpe

slope of 0.06
cu —

in

cu

t 3 zr _ LU cu CO

WRTER VaU. S LITER

SLOPE 0.06

SOLID LEN. - e.S CM

SOLID DIHMETER I X - S.S CM

O - 3.1. CM

- S.S CM

NONDIMENS lONAL DISTANCE, X/D

Figure 36. Solid velocity versus distance from the solid starting line

for 2.5 cm long solids, and for = 2.0 and 4.0 L, at a pipe

slope of 0.06
SOLID

VEL.

CM/SECI

SOLID

VEL.

CM/SECD

.H

.8

1.8

1.8

8.8

8.M

8.8

3.8

,h

.8

1.8

1.8

8.8

8.H

lUm WRTER VOL. 6 LITER

SLOPE 0.06

SOLID LEN. - a. 5 CM

SOLID DIRMETER i ^ - 9. a CM

o - a. I CM

1— a.

a

—I

1 .0 i0.O 00.0 00.0 00.0 aa.0 H0.a Hs.a

NONDIMENSI ONAL DISTANCE, X/D

WRTER VOL. a LITER

SLOPE 0.06

SOLID LEN. - a. 5 CM

a.0 10.0 1S.0 00.0 00.0 00.0 oa.0

NONDIMENS I ONAL DISTANCE, X/D

H0.0 HS.0

Figure 37 Solid velocity versus distance from the solid starting

for 2.5 cm long solids, and for = 6.0 and 8.0 L, at

slope of 0.06

line

a pipe
1 1 1 1 B.B 3.B.B iS.B BB.B BB.B

1 1 1 95. a HB.a HS.a

NONDIMENSlONAL DISTANCE, X/D

Figure 38. Solid velocity versus distance from the solid starting line

for 5.1 cm long solid, and for = 1.0 and 1.5 L, at a pipe

slope of 0.06
CU -. i

oi

CJ 3-_

LU (u CO

WRTER VQL. 2 LITER

SLOPE 0.06

SOLID LEN. - S.l CM

SOLID DIAMETER i X > S . B CM

O - a. I CM

'f- - 2.B CM

O

CO

1

«.0 — BB.a

I— B.a 10.

B

10.0 00.0 00.0 00.0 HB.B H0.0

NONDIMENS lONAL DISTANCE, X/D

Figure 39. Solid velocity versus distance from the solid starting line

for 5.1 cm long solid, and for = 2.0 and 4.0 L, at a pipe

slope of 0.06
NONDIMENSIONAL DISTANCE, X/D

Figure 40. Solid velocity versus distance from the solid starting line

for 5.1 cm long solid, and for V =6.0 and 8.0 L, at a pipe

slope of 0.06 ^
SOLID

VEL.

Cli/SECD

SOLID

VEL.

CM/SEC

I

Figure 41. Solid velocity versus distance from the solid starting line

for 7.6 cm long solids, and for = 1.0 and 1.5 L, at a pipe iL slope of 0.06
SOLID

VEL.

CM/SEC

I

SOLID

VEL.

CM/SEC

3

tf.B

.H

.B

i.S

1.6

B.0

S.4

B.8

S.B

if.B

.4

.6

l.B

1.6

E.8

S.H

WBTepi vai_. e uxtbr

SLOPE 0.06

SOLID LEN. - 7.B CM

SOLID DIRMETER i

5K . a.e CM

o - a.i CM

- B.B CM

T r- ,m a.m —I

1 1 1 1 1 1

1 ajB.a aa.a m.b aa.e as.a hs.b hs.b

NONDIMENSlONAL DISTANCE, X/D

WHTeP VOL . H LITem

SLOPE 0.06

SOLID LEN. - 7.6 CM

SOLID DIRMETER I X - a. 6 CM

O - a.l CM

B

,

1

, ,

1 1 1 1

1 .B B.B iB.B 18 . B 8B.B BB.B BB.B BB.B HB.B 48 .

B

NONDIMENS lONAL DISTANCE, X/D

Figure 42. Solid velocity versus distance from the solid starting line

for 7.6 cm long solids, and for s 2.0 and 4.0 L, at a pipe

slope of 0.06
ni

LJ =•_ LU oi LD

z: c,-

OI

__l O

CO

MRTER VOL . B LITER

SLOPE 0.06

SOLID LEN. - 7.B CM

SOLID DIAMETER i X - 3.8 CM

O - a . I CM

o

—I

IB.

a

1 , 1

1 r—

IB. a BB.B BB.B BB.B BB.B

NONDIMENSIONAL DISTANCE, X/D —I

HB.B

1 HB.B

NONDIMENSIONAL DISTANCE, X/D

Figure 43. Solid velocity versus distance from the solid starting line

for 7.6 cm long solids, and for = 6.0 and 8.0 L, at a pipe

slope of 0.06
Table 1. Distance traversed by solids in 10.0 cm pipe (m)

j = 1.0 L = 1.5 L Vw = 2.0 L

i Solid Size Pipe Slope Pipe Slope Pipe Slope

! (cm) 0.02 0.04 0.06 0.02 0.04 0.06 0.02 0.04 0.06

1

' 3.8 by 7.6 0.5 2.1 1.5 nl 4.0 3.6 3.0 c2 c

1 3.8 by 5.1 1.2 3.0 3.0 n c c 4.2 c c

1 3.8 by 2.5 2.2 4.4 3.9 n c c c c c 3.1 by 7.6 1.2 3.3 3.1 n c c 4.2 , c c

I 3.1 by 5.1 1.8 4.2 4.8 n c c c c c

1 3.1 by 2.5 2.2 4.6 4.0 n c c c c c

1 2.5 by 7.6 1.8 4.2 c c c c c c c

i 2.5 by 5.1 2.7 c c c c c c c c

1 2.5 by 2.5 2.7 c c c c c c c c

Table 2. Distance traversed by solids in 7.6 cm pipe

Solid Size

(cm)

Vw= 1-15 L Vw = 1.5 L Vw = 1.9 L

Pipe Slope Pipe Slope Pipe Slope

0.02 0.04 0.06 0.02 0.04 0.06 0.02 0.04 0.06

3.8 by 7.6 n 2.1 4.4 n 4.6 c c c c 3.8 by 5.1 n 2.7 4.2 n c c c c c 3.8 by 2.5 n 4.8 c n c c 3.1 by 7.6 n 2.1 c n 4.5 c c c c 3.1 by 5.1 n 4.0 5.0 n c c c c c 3.1 by 2.5 n 4.8 c n c c 2.5 by 7.6 n 3.3 c n c c c c c 2.5 by 5.1 n c c n c c c c c 2.5 by 2.5 n c c n c c

1. n refers to no data

2. c refers to clear the pipe
NBS»114A (REV. 2-60) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instruction s)

1. PUBLICATION OR

REPORT NO. NBSIR 81-2450

2. Performing Organ. Report No 3. Publication Date January 1982

4. TITLE AND SUBTITLE

EXPERIMENTAL INVESTIGATION OF TRANSPORT OF DISCRETE SOLIDS WITH SURGE FLOWS IN

A 10.0 CM DIAMETER PARTIALLY FILLED 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

8 . Type of Report & Period Covered

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

Dept, of Housing and Urban Development

451 7th Street, SW

Washington, DC 20410

10.

SUPPLEMENTARY NOTES

(^21 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)

This report presents the results of a series of experiments on the transport of discrete solids

with surge flows in a partially filled slightly pitched horizontal pipe. The experimental apparatus,

instrumentation, and procedures are described.

The experiments were conducted using a cylindrical solid in a 10.0-cm (4—in) diameter pipe.

The water surge flows were obtained by discharging different volumes of water into the pipe from a falling head open container which simulated a water closet. For each experiment , flow induced solid velocities and stream depth histories at various

locations along the length of the pipe were measured. The effects of water volume used, pipe slope,

and size of the solid on the solid velocities were exaailned. Solid velocities were compared with

the maximum water velocities estimated from the stream depth histories. Also, the distance traversed

by the solids in the. pipe were measured for those cases in which the solids did not clear the pipe.

The solid velocity Increased with an Increase in water volume used, a decrease in the size of the

solid, and an increase in the pipe slope. The solid velocity in the initial reach of the pipe was less

than the maximum water velocity; and the solid velocity approaches the maximum water velocity as the

solid traveled downstreeun, except for some experiments with small water volumes.

The distance traversed by the solid Increased with an increase in water volume, a decrease in

the size of the solid, and an increase in the pipe slope.

The available data are too few to indicate any definitive conclusion; however, a comparison of

data on solid transport in 7.6-cm (reported in a prior publication) and 10,0-cm pipe suggests that

the 7.6-cm pipe may be slightly better for transport of solids with small water volumes than the

10.0-cm pipe.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) equation; flow; horizontal; motion; partially-filled pipe; slope; solid;

stream-depth; surge; transport; velocity; water

13.

AVAILABILITY

^3] Unlimited

I I For Official Distribution. Do Not Release to NTIS

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

20402.

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

14. NO. OF

PRINTED PAGES

51

15. Price

$9.00

USCOMM-DC 6043-P80
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