EPA-600/2-76-243
November 1976
WASTEWATER FLOW MEASUREMENT IN SEWERS
USING ULTRASOUND
by
R. J. Anderson
Sewerage Commission
City of Milwaukee
Milwaukee, Wisconsin 53201
and
S. S. Bell
W. H. Vander Heyden
W. K. Genthe
Badger Meter, Inc.
Milwaukee, Wisconsin 53223
Project No. 11024 FVQ
Project Officer
Clifford Risley, Jr.
U.S. Environmental Protection Agency
Region V
Chicago, Illinois 60606
MUNICIPAL ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
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FOREWORD
The Environmental Protection Agency was created because of increasing
public and government concern about the dangers of pollution to the
health and welfare of the American people. Noxious air, foul water,
and spoiled land are tragic testimony to the deterioration of our natural
environment. The complexity of that environment and the interplay be-
tween its components require a concentrated and integrated attack on the
problem.
Research and Development is that necessary first step in problem solution
and it involves defining the problems, measuring its impact, and search-
ing for solutions. The Municipal Environmental Research Laboratory de-
velops new and improved technology and systems for the prevention, treat-
ment, and management of wastewater and solid and hazardous waste pollutant
discharges from municipal and community sources, for the preservation and
treatment of public drinking water supplies, and to minimize the adverse
economic, social, health, and aesthetic effects of pollution. This publi-
cation is one of the products of that research; a most vital communications
link between the researcher and the user community.
As part of these activities, the study described herein demonstrated and
evaluated a new technique for measurement of sewage flow utilizing ultra-
sonic measurements of stream depth and velocity.
Francis T. Mayo
Director
Municipal Environmental
Research Laboratory
111
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CONTENTS
Page
Forward
111
Abstract
IV
Figures
VII
Acknowledgments
Sections
I Conclusions ,
II Recommendations 2
III Introduction 4
Purpose and Scope 4
Concepts 5
Objectives ^
Theoretical Approach 7
IV Installation JQ
Site Locations TO
Installation Details 25
V Operation & Evaluation 36
Design Modification 35
General Analysis of Equipment Operation 40
Cambridge Avenue 45
South Shore Treatment Plant 53
College Avenue 58
VI Discussion of Results 60
Allowable Solids Loading & Air Entrainment 60
Level Gauge Installation Criteria 62
Probe Foulling by Debris & Grease 62
Velocity Profiles & Probe Multiplicity 63
Equipment Costs 64
v
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DISCLAIMER
This report has been reviewed by the Municipal Environmental Research
Laboratory, U.S. Environmental Protection Agency, and approved for publication.
Approval does not signify that the contents necessarily reflect the views and
policies of the U.S. Environmental Protection Agency, nor does mention of trade
names or commercial products constitute endorsement or recommendation for use.
11
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FIGURES
No.
1 Ultrasonic Pulse Propagation Path Between
Transceivers 0
o
2 Wave Shape of Ultrasonic Pulse 8
3 Block Diagram of Meter Electronics 10
4 Meter Installation in a Sewer for Measurement
of Wastewater ^Q
5 Meter Electronics Unit 17
6 City of Milwaukee Sewerage System Map 19
7 Location and Configuration of the 60"
Cambridge Avenue Sewer 20
8 Head Diagram, Vicinity of Cambridge Avenue
Meter Installation 21
9 Flow Record, Cambridge Avenue Intercepter,
September-October, 1975 22
-a Flow Recording - 60" Cambridge Ave. Sewer 23
-b Level Recording - 54" Sewer Upstream of
Cambridge Avenue Site 24
10 Location of Meter Installation, South Shore 26
11 Profile of Sewers in the Proximity of South
Shore Plant 27
12 Detail of Manhole and Sewer, College Avenue 28
13 400 kHz Ultrasonic Transceiver 29
14 Multiple Probe Mounting Configuration 29
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ABSTRACT
A new technique for measurement of sewage volume flow utilizing ultra-
sonic measurements of depth and velocity was demonstrated and evaluated.
The new technique, requiring no costly construction for installation, is
usable for open channel or partially full measurements. The flow tech-
nique can accomplish measurement accuracies from 2 to 5% under conditions
of rapidly changing levels, surcharging, and back-up conditions. Two
installations were accomplished on existing sewers in the Milwaukee Sewage
System, one 12h feet and the other 5 feet in diameter. A continuous flow
record was displayed for each meter and performance of the meter instal-
lations was compared with magnetic flow meters at one site and head
velocity relations on the other site. Relationship between average volume
flow, water level, and average velocity along selected horizontal chords
of the sewer cross section were determined. The unit installed on the
5 foot diameter sewers operated for a period in excess of 18 months with-
out failure and has required only routine maintenance. The flow technique
provides accurate measurement over a range of depths from 25% to full depth
in the sewer and from zero to the full flowing velocity of the fluid in the
sewer. No deterioration of ultrasonic transducer probes has been detected
indicating their suitability for use in the sewer environment.
This report was submitted in fulfillment of Project No. 11024 FVQ by the
Milwaukee Sewerage Commission under the sponsorship of the U. S. Environ-
mental Protection Agency. This report covers the period April 1, 1971 to
June 30, 1974, and work was completed as of September 30, 1975.
IV
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FIGURES (cont'd.)
No.
— Page
34 Mag Meter Flow Readings During Transient Tests,
South Shore 56
35 Isovel Diagram, Circular Channel, 1/3 Full 70
36 Isovel Diagram, Circular Channel, 2/3 Full 71
37 Isovel Diagram, Circular Channel, Full 72
38 k-Factors, Rectangular Channel 73
39 Kahl-Scientific Current Meter, Exploded View 74
40 Vertical Velocity Profiles, Jones Island
Influent Channel 75
41 Horizontal Velocity Profile, Jones Island
Influent Channel 75
42 k-Factor Versus Porportion of Depth 77
43 k-Factor Versus Liquid Level 77
44 k-Factor Versus Liquid Level for Various Probe
Chord Levels 77
45 Experimental Versus Theoretical Velocity Data
For a Full Circular Channel 81
46 Circular Channel Geometry
82
47 Normalized Turbulent Velocities Versus
Normalized Laminar Velocities, Full
Circular Channel 83
48 Isovels for Turbulent Flow in a Partially
Filled Pipe 85
49 Experimental Versus Theoretical Velocity Data
For a Partially Filled Circular Channel 86
50 Normalized Turbulent Velocities Versus
Normalized Laminar Velocities, Partially
Filled Circular Channel 88
IX
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CONTENTS (cont'd.)
Page
VII References 55
VIII Appendices 66
Appendix A - Velocity Profile Analysis 67
Experimental k-Factor Analysis 67
Computer Aided Theoretical Analysis 78
Full Circular Channel Analysis 80
Open Circular Channel Analysis 84
Appendix B - Computer Program for Solution
of the Navier-Stokes Equations for Laminar
Flow in a Rectangular Open Channel 89
Appendix C - Derivation Relating Laminar
Chordal Velocity and the 6th Power of
Turbulent Chordal Velocity 93
Appendix D - Summary of Ultrasonic Waste-
water Metering Performance in Installation
in Japan. 98
vi
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SECTION I
CONCLUSIONS
1. Ultrasonic velocity measurement equipment in conjunction with ultra-
sonic level measurement equipment can be utilized for the measure-
ment of sewage volume flow.
2. At a typical cost of $10,000 to $12,000 for a height-velocity system
(including probes, indicator, totalizer and recorder), the equipment
is sufficiently low in cost to achieve general use, can be convenient-
ly installed in new or existing sewers, requires a minimum maintenance,
and is suited for long term operation in the sewer environment.
3. Installation of the equipment does not normally require special
constructions and/or metering pits or vaults.
4. Between 25% of channel depth and surcharged conditions the corre-
lation between the average chordal velocity and the average area
velocity is sufficiently predictable to enable the average chordal
velocity level and area functions to be easily integrated electroni-
cally providing flow information accurate to within approximately 2%.
5. Pulse leading edge detection in the ultrasonic velocity electronics
is more susceptible to fluctuations in solids loading and/or entrained
air densities resulting in fluctuations in velocity measurement than
is peak pulse detection.
6. The velocity measurement portion has a 20 to 1 turn down capability
and with the velocity probes mounted at the 25% level the level measure-
ment portion is limited to a 4 to 1 turn down. This gives the system
an 80 to 1 turn down capability which well exceeded the flow ranges
experienced. System operation is limited to the turbulent flow regime
and flow media which do not contain large quantities of entrained air.
1
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FIGURES (cont'd.)
No. Part
15 Ultrasonic Probe Mounting Configuration,
Cambridge Avenue 32
16 Ultrasonic Probe Mounting Configuration,
College Avenue 33
17 Detailed Plan View, Ultrasonic Probe Mounting
Configuration, College Avenue 34
18 View Looking Upstream, Ultrasonic Probe
Installation, College Avenue 35
19 Basic Unit, Receiver-Transmitter 37
20 Ultrasonic Pulse Packet 37
21 Timing Diagram 37
22 Modified Unit, Receiver-Transmitter 39
23 ATC Performance Test 42
24 Received Signal, Clear Water 47
25 Received Signal, Water With Entrained Air
Bubbles 47
26 Received Signal, Clear Water, Expanded 47
27 Received Signal, Clear Water, Further Expanded 48
28 Received Signal, Water with Entrained Air
Bubbles, Expanded 48
29 Flow and Velocity Output Signals, Cambridge
Avenue 49
30 Area Correction Factor - Circular Pipe 51
31 Measured Chordal Velocities Versus Depth,
Cambridge Avenue 52
32 k-Factor Estimate, Cambridge Avenue 52
33 Measured Transient Flow Profiles, South Shore 55
vin
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the foam surface absorbs the ultrasonic energy, precluding an echo.
The use of a load-length product to estimate the effects of entrained
solids loads in the transmission path length is advised, although most
applications appear to be well below recommended limits of 5,000 m-mg/Jl
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ACKNOWLEDGMENTS
The support and encouragement of Ray D. Leary, Chief Engineer and General
Manager of the Sewerage Commission of the City of Milwaukee is acknowledged
with sincere appreciation.
Design of the velocity probe mounting fixtures, and installation of the
ultrasonic metering equipment was performed by Kenneth Tappendorf of the
Milwaukee Sewerage Commission Staff.
Instrument design modifications, data collection and analysis, velocity
profile calculations and preparation of the final report draft were per-
formed by the Environmental and Electronic Products Group of Badger Meter,
Inc. of Milwaukee. Also acknowledged are the valuable electronic design
efforts of Ray Thornborough, meter modifications and tests by Jack
Bradach, Al Nagy and Henry Horns, and the art work, plots and drawings of
Dennis Wachs and George Zunker, all of the Badger Meter staff.
The support and guidance of William Rosenkranz and Frank Condon of the
Waste Management Division and George Kirkpatrick formerly with the Division,
and of Project Officer Clifford Risley and Ronald Eng of Region V, U.S.
Environmental Protection Agency, are acknowledged with gratitude. Also,
special thanks goes to Mr. Richard Field, Chief, Storm and Combined Sewer
Section, USEPA, for his suggestions and inputs, and thorough manuscript
review.
Also acknowledged are the helpful discussions held with K. Koyanagi,
M. Yamamoto, and K. Tamura of the Tokyo Keiki Company, Ltd. of Tokyo, Japan.
x
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backflows and surcharging. Further, in a sewage system regulated for
minimization of raw sewage discharge into a watershed, control practices
involve sewer gating, pumping and temporary retention in lesser used
interceptors and trunks. These practices generally alter the character-
istics of sewage flow bringing about unsteady flow, high sewage levels
accompanied by zero flow in the conduits used for temporary storage,
high and rapidly changing sewage levels, and occasional surcharging and
backflow conditions. Flow properties of this sort render the perform-
ance of conventional open channel metering structures unsatisfactory and
contribute to the need for a sewer meter designed specifically for the
application.
With these points in mind, two metering sites were selected which were
felt to be typical in that both had downstream conditions which at times
invalidated the assumption of gravity flow. Furthermore, both sites were
partially filled, circular conduits one of which could conceivably be
subject to surcharging.
CONCEPTS
The sewer flow measurement technique utilized in this demonstration was
designed to afford accurate flow measurement while maintaining advantages
of virtually zero head loss, operation under submerged, back flow, or
surcharge conditions, and installation conditions not requiring signifi-
cant construction. Furthermore, the ultrasonic sensors are free of
significant intrusions and accordingly are not subject to fouling,
damage by flow and do not cause flow blockage. The approach taken in-
volved a new technique using integrated ultrasonic measurements of
velocity and level and resulted in a practical, low cost system suited
to wastewater characteristics and the operating environment of the
sewage system. The design of the equipment was specifically adapted to
the application, involves no moving parts, was shown to be suitably
rugged and non-fouling, and easily installed in existing sewers with
manhole access.
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SECTION II
RECOMMENDATIONS
Operation of the flowmeters at their present locations should be con-
tinued for as long as possible to determine what, if anyf deterioration
of the probes might occur.
The effect of entrained air on transmission using probes having crystals
cut for higher frequencies should be investigated.
The method of using ultrasonic velocity and level measuring equipment
should also be developed to operate in relatively smaller line sizes of
6 to 36 inch diameters. Unlike the ultrasonic sewage metering system,
present flume and weir devices have limited rangeability and are in-
operative under surcharge conditions.
Many sources within municipalities, consulting engineering firms and
state and federal pollution control agencies have identified the
need for reliable semi-portable sewage metering equipment particularly
for infiltration and loading studies in combined sewer networks. Con-
sequently, the development of a portable ultrasonic sewage flow monitor-
ing unit is desirable.
Until such time as the interference caused by entrained air is virtu-
ally, if not completely, eliminated, future installations of the ultra-
sonic sewage flow meter should be limited to those sites which do not
immediately follow either pumping or outfalls which contribute a sig-
nificant portion of the total volume at that site. In addition, those
sites where agitation, outfall or pumping have caused the surface to be
foam covered are unsuitable for the level monitoring equipment in that
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Reynolds Numbers for sewer channels of typical cross sectional
configurations. Determine the discharge coefficient associated
with the above relationships and determine the universality of the
discharge coefficient for typical cross section configurations.
5. Provide manual, computer, and automatic techniques for calculat-
ing and displaying average sewage volume flow (rate and quantity).
THEORETICAL APPROACH
The general concept of the unique metering system was advanced earlier.
In the following, the principle of operation of each major element of
the system will be explained. These are the velocity meter, height
gauge and the electronics which combine the velocity and height informa-
tion.
Velocity Meter
As pictured in Figure 1, two ultrasonic transceivers are affixed to the
pipe wall, one upstream from the other. Pulses of ultrasonic energy are
generated by one transceiver and received by the other. These pulses
have the shape of a wave packet as shown in Figure 2 and are generated
as the response of a piezoelectric crystal to a spike of input voltage.
The voltage spike causes a momentary mechanical construction of the
crystal. The crystal then vibrates to rest at its natural frequency
which is in the ultrasonic range, selected for this project to be 400 kHz
The pulse generated thereby propagates through the liquid across the
pipe to the other transceiver. When the pulse reaches the receiving
crystal, it generates an output voltage waveform also shaped much like
that shown in Figure 2. In operation, a received pulse electronically
triggers the generation of another transmitted pulse in a "sing-around"
fashion, creating a self-sustained pulse frequency, f. If electronic
delays are small, the period of this frequency is just the time re-
quired for an ultrasonic pulse to travel through the fluid from trans-
ceiver to transceiver. If the distance across the pipe between the
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SECTION III
INTRODUCTION
PURPOSE AND SCOPE
Wastewater flow measurement with adequate accuracy, rangeability and
reliability is the keystone of wastewater regulation, namely the exercise
of control over sewage quantity, rate of travel and routing in the sewer-
age system. Among other benefits, effective regulation of a combined sew-
age system minimizes outflow of raw sewage during storm conditions. How-
ever, effective regulation requires effective flow measurement, and the
state-of-the art of instrumentation for sewage flow has been decidedly in
arrears of metering technology developed for other applications. Thus
the primary purpose of this demonstration was to advance a practical, low
cost, wide range sewage flow measurement technique for general use in
existing storm, sanitary and combined sewers.
In a sanitary sewer system with minimal ground water infiltration, flow
is reasonably steady and present metering practice requires measurement
of volume flow using a pressure head producing device such as a flume or
a weir. Open channel metering structures of this type are subject to
debris and sedimentation accumulation and importantly, require loss of
pressure head for operation. Present practice for the measurement of
pressure head in these devices corresponds to the use of either bubbler
gauges or float level gauges, either of which are subject to fouling due
to stringy, greasy and sticky entrainments. In any of the metering
structures presently employed for volume flow measurement the devices
are unidirectional and subject to very large errors under conditions
of submergence or nongravitational discharge conditions. In a storm
sewer, or a combined sanitary and storm sewer system, flow is subject
to transients in level and velocity due to rainfall runoff with occasional
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transceivers in Figure 1 is £, and the velocity of sound in the metered
liquid is S, travel time t is given by £/s. For fluid at rest, this
travel time is the same for pulses moving in either direction. However,
if the fluid is in motion, then the travel time tfl for pulses moving
downstream is shortened because their transit is aided by the fluid
motion and,
'd - ~ (1)
S + v cos 0
c
where VG is the average fluid velocity along the transmission path or
chord between the transmitter and receiver, and v cos 0 is the
component of VG in the direction of pulse propagation. Pulses moving
upstream travel more slowly because their transit is opposed by the
fluid motion, thus the upstream travel time, t , is
t - _____i
u ~ -(2)
S - v cos 0
c
Assuming negligible electronic delays, the related sing-around fre-
quencies are the inverses of their respective transit times, or
S + v cos e
f - E
fd I(3)
S - v cos 0
f £
u ~ I(4)
Flow velocity information is provided by the difference between these
frequencies:
A-F f e 2 COS 0 -
At - t - f = v ic.\
d u H c (^>
In any given installation, 0 and I are constants, thus Af is proportional
to the average fluid velocity along the line joining the transceivers.
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In its basic form the metering concept is quite simple. A beam of
ultrasonic energy is directed through the sewage transport media in
such a manner as to permit the determination of the average of the stream
velocities along the beam. (It is shown that with proper placement and
under reasonable conditions this average path velocity is nearly equal to
the average of the stream velocities taken over the entire flow cross
section.) A separate beam of ultrasonic energy is directed down through
the air toward the surface of the sewage transport media and its echo
detected, permitting an accurate determination of the depth. The depth
(which is directly related to the flow cross section) and average
velocity are then functionally combined to yield flow volume per unit
time.
OBJECTIVES
The following five objectives were set for the demonstration before it
began:
1. The key objective of the project is to demonstrate the performance
of new sewage metering equipment which is of sufficiently low cost,
to achieve general use, which can be conveniently installed in
existing sewers, which requires minimal maintenance and is suited
by design to long term operation in the sewer environment.
2. Verify the performance, design, installation and operation of an
ultrasonic sewage meter by equipping and monitoring two existing
sewers in the Milwaukee Sewerage System, one 12 feet in diameter
and the other 5 feet.
3. Compare the performance of the ultrasonic meter, with respect to
flow reproducibility and ease of installation with other metering
devices presently installed in the system, electromagnetic meter-
ing in the case of the 12 foot diameter conduit and float/Kutter
formula metering in the 5 foot channel.
4. Characterize mathematically and by computer solution the relation-
ships between average volume flow, level, chordal velocity, and
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As described in Appendix A (Velocity Profile Analysis) , this average
velocity along the ultrasonic beam crossing the pipe, v , can be related
to the average velocity, v, across the entire flow cross the entire flow
cross sectional area if flow is in either the laminar or turbulent regimes
In practice, the Af of equation (5) is a very small number, too small to
be measured directly with much precision. For example, the velocity of
sound in water is about 1500 meters per second, and in a pipe one meter
in diameter carrying water flowing 2 meters per second, this frequency
difference is:
Af = fd " fu = 563'195 - 561.805 = 1.39 Hz (6)
where 9 is taken as 22°.
For this reason, each sing-around frequency is multiplied by a constant
M which is usually about 100. For M = 100, Af becomes 139 Hz in this
case. In operation, the meter measures Af by counting f for a period
tc, and counting f^ for a like period and subtracting the two counts.
This count difference AN is proportional to Af and is given by
AN = MAf t = M 2 cos 9 - v
Taking t as 2.5 seconds, for the above example,
AN = 100 (1.39) (2.5) = 327.5, (8)
and AN is sufficiently large to be measured easily with good precision.
Electronic Signal Processing - With the probe switch in the position
shown in Figure 3, the upper transceiver is transmitting pulses upstream
and the lower transceiver is receiving ultrasonic pulses from the stream.
The generated sing-around frequency is f if there is zero flow and f if
0 u
there is flow in the direction shown. The frequency multiplier multiplies
11
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Ultrasonic
Transceiver
Pipe Wall
Figure 1. Ultrasonic Pulse Propagation Path
Between Transceivers
2.5 microseconds
Figure 2. Wave Shape of Ultrasonic Pulse
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the manhole to minimize chances of fouling during surcharging. Any
echo time shorter than that expected for a full conduit (such as would
occur during surcharging) is interpreted the same as that received
when the conduit has just reached its 'full' point.
The combined height gauge and velocity meter system is shown in a sketch
(Figure 4) of one of the sewer installations carried out as part of
this demonstration. It is important to understand that although four sets
of velocity transmitter-receiver probes are shown, only one such set is
required in a typical installation. The extra sets were installed as a
means of verifying the validity of using a single transverse velocity
average to represent the average velocity of the entire flow cross section.
(The validity of this procedure is discussed at length in Appendix A.)
Velocity-Height Combination
For a circular conduit, the relationship between depth (d), radius (r)
and flow cross-sectional area (A) is given as
A = Trr2 (y + i- [ sin~1(x) + x /1-X2 1}
^- TT ** J
(9)
where x is given as (d/r-1).
Although the height gauge provides a measurement which is actually pro-
portional to the 'distance-to-product', this can be translated using a
digital electronic scheme to be proportional to the flow cross-sectional
area A. A voltage proportional to this area is then used as the supply
voltage for the binary ladder in the relay memory. The output of the
relay memory is thus proportional to the product of the average trans-
verse velocity v and the flow cross section area A.
13
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N/
' / \
S. V/ if J
^ X o
J / U
/<
OUTPUT
* CONVERTER
^
^ —
PROBE
OUUIT/*»LJ _
5>wi I un f
. Q_ T
•— H— *VJ
U.
L-o |
u A
4
^
TRANSMIT fo FREQUENCY fo. M
RECEIVE * MULTIPLIER
1^
TIMING & 4 QSC
T CONTROL
1
RELAY . UP-DOWN
MEMORY * COUNTER *
1 r
DIGITAL
INTEGRATOR ^
Figure 3. Block Diagram of Meter Electronics
REMOTE
INSTRUMENTATION
Figure 4.
Meter Installation in a
Sewer for Measurement of
Wastewater.
10
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The pipe friction coefficient X is generally between 0.01 and 0.06
so, for a full pipe on a major chord,
0.9023 < k < 0.9577 (17)
depending upon the value of X. k is the constant by which VG must
be multiplied to yield v.
Since a similar equation does not exist for partially full circular
conduits, it was necessary to examine experimentally obtained data
for such conduits to determine the k-factor ranges. The reduction of
this data for partially full circular pipes has indicated that a value
of k of 0.96 is typical over a significant portion of the cross section
when chordal velocity averages are obtained for planes parallel to the
surface plane and between 30% and 70% of depth. (This is presented in
more detail in Appendix A.) The constant k is incorporated into the
scaling electronics along with the scaling multiplier for engineering
units and the cross section area multiplier for calculation of Q.
In general:
Q = Av = Ak VG (18)
These constants are taken into account when the electronics are set
up for a particular installation. The adjustments are made by
appropriate strapping of elements in binary counting chains and are
accomplished by either soldering or not soldering jumpers in the
standard unit.
The applicability of the above k-factor for calculation of Q depends
upon the existence of a fully developed velocity profile of a
reasonably predictable form. The transceiver mounting site should
therefore have 10 to 20 straight diameters upstream and be sufficient-
ly distant from elbows, constrictions, expansions and pumps. When these
15
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the frequency by M. An oscillator generates a clock rate for the timing
and control circuits,these in turn provide various multiples of the clock
rate for controlling the probe switch and resetting the frequency multi-
plier and up-down counter. The probe switch is reversed every t seconds,
c
thereby reversing the roles of the transceivers and alternately generat-
ing f^ and f . During each such cycle, the up-down counter counts up to
Mf^ and then counts back down to Mf . The number remaining in the counter
after such a cycle is the AN defined in equation (7) and is proportional
to Af. The value of AN is stored in the relay memory after each cycle
until it is updated by the next measurement cycle. For t equal to 2.5
seconds, the count stored in the relay memory is updated every five
seconds. In digital binary format in the memory, the count is converted
to an analog output current proportional to flow rate by means of a seven
element ladder circuit in the output converter. The clock rate from the
oscillator is digitally multiplied by the binary number in the relay
memory representing flow rate and sent to an eleven element binary counter
in the digital integrator. Elements of this counter can be "strapped" in
or out of the counting sequence so as to scale the integrator output to
convenient engineering units of quantity, i.e., cubic meters, gallons,
acre, feet, etc. Similarly, binary elements in the frequency multi-
plier and relay memory can be strapped in or out to select the proper
value for M and full-scale respectively.
Height Gauge
Conceptually this unit is much the same as the velocity meter except for
the following: The burst frequency is about ten times lower (40 kHz),
the burst repetition is preset to permit the reception of the echo
from the greatest distance desired (generally the bottom if and when
the channel is empty), differences in the sonic velocity of air are
corrected for by monitoring the air temperature and making an offset
linear correction to the echo time measurement and a single transmitter-
receiver head is used. This transceiver unit is placed several feet up
12
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IJJ i i •_«
Figure 5. Meter Electronics Unit
17
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Average transverse velocity versus average area velocity - For the
case of a circular conduit running full, the flow velocity v at any
point on the logarithmic velocity profile associated with turbulent
flow at a distance x from the axis of the pipe of radius R is
v = v + 2.5 v* In , (10)
max R
and
v* = v A/ — = "friction velocity" (11)
where X = pipe friction coefficient.
Using (11) and integrating,
R
v — I v 2ir x dx = v - 3.75 v* (12)
2 I max
7TR )
v = v dx = v - 2.5 v* (13)
c R I max
0
Therefore:
v (1 + 3.75 A ) = v (14)
8 max
and
v = -=^ (15)
1 + 3.75
Dividing v by v yields:
r-, = k
v 1 + 0.44194
c
14
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SEWERAGE COMMISSION
Mop
and
Active
LOCATIONS
Figure 6 . City of Milwaukee Sewerage System Map
19
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criteria are met, the calibration has been shown to be adequate and
accurate.
Electronic output - the electronic unit pictured in Figure 5 contains
all of the digital signal processing circuitry mounted on individual
plug-in printed circuit cards, as well as the power supplies and data
readout equipment. The level unit provides a 0-10 volt signal pro-
portional to the distance to the surface. This signal is processed in
the velocity electronic unit to provide the voltage V proportional
a
to the fluid cross section area. The flow signal, generated in the
velocity electronic unit is a 4 - 20 mADC output current proportional
to flow rate. The output signal generated by combining the velocity
and area signals is suitable for telemetering and driving remote read-
out equipment. Circular and strip chart recorders, magnetic and
punched paper tape recorders, and remote totalizers can be provided
for this purpose.
16
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VICINITY OF TrtC CAMMlfr4& AVC.
&£ffitTQL u-N.MORRIS E
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SECTION IV
INSTALLATION
SITE LOCATIONS
Two sites were initially selected as representative combined storm-
sanitary sewers. These were the Cambridge Avenue Site located near
the village of Shorewood in the near north metropolitan Milwaukee
area, (see Figure 6) and the South Shore Plant Site on the far south-
southeast side. Later in the demonstration project the College Avenue
Site was selected. This third location was upstream a mile or so from
the South Shore Site and eliminated difficulties experienced due to
abnormally high loadings contributed by a glue factory located next
to the South Shore Treatment Plant. (This is discussed in detail
later in the report.)
Cambridge Avenue
A sketch of the Cambridge Avenue Site was used earlier (Figure 4) as
being typical of a meter installation in an existing sewer (except
that only one set of velocity probes would usually be required). This
location has a 60 inch diameter circular conduit located approximately
30 feet below the surface. (See Figure 7). The metering site is 1202
feet downstream from an existing weir and float type monitor, 542 feet
downstream from the junction with another smaller sewer and about one-
third mile upstream from the junction with an inverted siphon. It is
known that at times of high flow, some back-watering and surcharging
does occur due to the inverted siphon, and hence the validity of the
measurements based on level only would be suspect. Head diagrams for
the vicinity of this site are included as Figure 8. A flow record,
based on the weir and float data located upstream of the ultrasonic
metering site, as well as the 39 inch East Providence Street sewer
18
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MONDAY
NOON
Figure 9a. Flow Recording - 60" Cambridge Ave. Sewer
23
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COMMI55ICK4
PROPOSED
CAMBRI04£ AVC.
ULTRASONIC
StCT. A-A
OCTAIi. Of
Figure 7. Location and Configuration of the 60" Cambridge Avenue Sewer
20
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outfall, is included as Figure 9- Two 7-day charts showing the ultra-
sonic flowmeter recording and flow upstream of the ultrasonic metering
sites are included as Figures 9a and 9b respectively. Naturally these
flow quantities would be somewhat lower than would be expected at the
ultrasonic metering location since they do not include all flows which
reach that site.
South Shore
A survey sketch of the influent channel at the South Shore Plant is
shown in Figure 10. This is a 12.5 foot diameter circular conduit
at the location of the velocity probe installation which is 60 feet
upstream from the plant inlet section. A transition section begins
36 feet downstream. The height gauge transceiver was placed at the
inlet bay so as to be more accessible and better protected in the
event of surcharge. Mag meters are located downstream of the bar screens
which are located immediately downstream from the inlet bay. It was
anticipated that these would be used to assist in evaluating the oper-
ation of the ultrasonic system.
A profile drawing of the sewers in the vicinity of this site is shown
in Figure 11. Note the proximity of the Peter Cooper Corporation (glue
factory) outfall and drop pipe.
College Avenue
A detail of the manhole and sewer at College and Pennsylvania Avenues
is shown in Figure 12. At this location the sewer is a 12 foot diameter
circular conduit. The average dpeth of flow is 3 feet with a maximum
depth of 8 feet noted following a heavy downpour in 1972.
INSTALLATION DETAILS
There are several ways in which the velocity probes can be installed
in a sewer. On steel conduits, they can be clamped on externally.
25
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Precip-
itation
(Inches)
0.30
0.10-
n
,-n
60" Sewer - Cambridge $ Newpojrt Ave.
Data From
7-Day Chart
Flow in 54" Sewer Up$tream of
Providence Ave. Connection (See Fig. 8).
"0" Computed From Depth of Flow
Data From
7-Day Chart
Fig. 9-b
NOTE: The Difference Between the Above
Flow Rate Values Corresponds to the Estimated
Values of the Flow in the.Providence Ave. Connection
2223 2425 26 27 26 » 6 7 8 9 10 II 12
15 16 17 f8 19 2O 21 29 30 I 2 3 4 S
September October
Figure 9. - Comparison of Measurements - Ultrasonic vs Level Only.
22
-------
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Figure 13. 400 kHz Ultrasonic Transceiver
Figure 14. Multiple Probe Mounting Configuration
29
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cn
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Installation diagrams for each of the sites are shown in Figures 15
(Cambridge Avenue), 10 (South Shore) and 16, 17 and 18 (College Avenue)
It should be noted that the two probe sets used at the College Avenue
Site were the top two sets (of six sets) from the South Shore Site.
The height gauge at College Avenue was also obtained from the South
Shore Installation. Note that the level sensor was not positioned
directly over the sewer center line since it was necessary to mount the
sensor in the manhole (see Figure 16). This was judged to be satis-
factory since the flow level is never so low as not to present an
adequate reflective surface directly below the level sensor.
31
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SEWERAGE COMMISSION
MGASURlKjq STATION! - COLLEGE 4
STANDARD MANHOLE.
FRAME < COVE-«.
-SUNOAP.O MJWOLE
COVER
R\M EL 134. ££
O.C.
. QO-STIPS E
3;=_=vJ 4-S1TIP* 3
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f f , . • " rt 2T ^
II FLOW UNC BL.MI.93 L-\'''"
. -
, Ft. jL^ JVSC. PIPE IM33
l ALL ST'L SHAFT
Figure 12. Detail of Manhole and Sewer, College Avenue
28
-------
PLAM
ELEVATION VIEW
A.A
Figure 16. Ultrasonic Probe Mounting Configuration, College Avenue
33
-------
Where block-outs exist they can be installed flush with the inside
surface. Finally, where neither of the first two methods are practi-
cal, they can be affixed to the inside of the conduit. Due to the site
characteristics at all three locations this third technique was selected.
Furthermore, to facilitate the alignment, the transceivers or probes
were housed in hydrodynamic shields mounted on curved plates which were
then affixed to the interior wall of the sewers. Typical fixtures are
shown in Figures 13 and 14. Wires from the transceivers are carried
to a junction box and then to the electronic unit. The spacing between
the transceivers on the pipe is first calculated and then confirmed by
both physical and electronic measurements, taking into account the propa-
gation of the sound pulses through the plastic material encapsulating the
transceiver crystal and through the metered liquid. The path angle
through each medium is governed by the velocity of sound in each medium
according to Snell's law:
Sln 91 _ Sin 92 (19)
Sl " S2
where Q-i and 92 are the path angles in the transceiver
and the liquid respectively
S^ and S2 are the velocities of sound in these
respective media.
From a knowledge of the sewer dimensions and probe spacing, a zero flow
sing-around frequency f is calculated. When the transceivers are
fixed in place, the actual zero flow signal is measured and compared
with the calculated value. If these two agree within 1%, the installation
is judged satisfactory and the output readings correspond to actual flow.
This procedure has been verified in a large number of actual installations.
For most sewer installations in the sizes commonly encountered (1 foot
to 15 feet and larger) Reynolds numbers are well into the turbulent range.
30
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Figure 18. view Looking Upstream, Ultrasonic Probe Installation,
College Avenue
35
-------
or TO
Menu VAUCf
PLAM VIEW
Figure 15. Ultrasonic Probe Mounting Configuration, Cambridge Avenue
32
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))DH
R
X
LEADING
CIW*C
CD6fc
DETECTOR
ASMV
TX
Figure 19. Basic Unit, Receiver-Transmitter
Figure 20. Ultrasonic Pulse Packet
RESET
ASMV OUTPUT
VOLTAGE
SFT
RECEIVER
TRANSMITTER
PULSE TIMING
RX' Tx
i
1
s
RX-TX
FREE RUNNING
RESET TIME
Figure 21. Timing Diagram
37
-------
Figure 17. Detailed Plan View, Ultrasonic Probe Mounting Configuration,
College Avenue
34
-------
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39
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SECTION V
OPERATION & EVALUATION
Early in the operational phase of the demonstration program it be-
came evident that there were significant fluctuations in the received
signal strength, caused by variations in the attenuation character-
istics of the fluid transmission medium. Due to the nature of the
Leading-Edge detection scheme employed in the receiver-transmitter
block of the basic unit (see Figure 19), these random amplitude
variations resulted in random frequency modulations of the upstream
and downstream sing-around frequencies generated by the Astable
Multivibrator (ASMV). Occasionally a transmitted pulse was not re-
ceived at all, and in such a case the ASMV would time-out to its
natural period termination point, injecting a large error in the
sing-around frequency determination.
The difficulties with utilizing Leading-Edge detection can be seen
by examining again the ultrasonic pulse packet as shown in Figure 20.
If the detector level is set so as to detect any voltage excursion
which exceeds level V-j_, then a received pulse is detected at time tlf
as shown. This means that for a fluid with both uniform and constantly
homogeneity each pulse packet will be detected at the same point in
time within the packet. However, should the packet shown be attenuated
by 50% on occasion, the pulse packet would not be detected until time to.
This injects a time error of about 2.5 micro-seconds into the determination
of the sing-around period (see Figure 20). In the installations being
tested this could amount to more than a full scale error in the
determination of channel velocity, depending entirely on the random
nature of the amplitude fluctuations.
36
-------
turbulence to reflect the ultrasonic beam at an angle outside the
reception area of the transducer. Consequently noise spikes occur in
the output signal. Additional damping was externally added to reduce
this problem. Another possible drawback to this single transducer type
of unit is the need for a dead zone of about three feet from the trans-
ducer face in which no echo can be detected. This region is blanked to
allow the transducer sufficient time to damp oscillations remaining
from the transmission burst. A new type of ultrasonic system presently
under development will eliminate this drawback.
Velocity Meter Probes
The ultrasonic beam was measured in a tank of clean water and found to
have a transmission cone having an included angle of approximately 8
degrees. For the Cambridge Avenue site this means good reception with-
in a 3 inch radius about the receiving transducer. Good reception with-
out interference from surface absorbtion or reflection can be obtained
when the probes are submerged at least 2 inches. For the clean water,
an attenuation of approximately 5 db per foot was observed, with the
probes operating at 400 kHZ. This attenuation was independent of trans-
mitter power.
Automatic Trigger Control (ATC) Performance - As discussed earlier, the
electronic portion of the velocity meter was modified to include a cir-
cuit which would automatically insert a phantom trigger should the trans-
mission path be momentarily occluded. The insertion time is based on
that for the last received pulse. A test of the ATC system was made
under a variety of conditions. Transmission in a channel 10 feet wide
was simulated, with a full scale velocity representing 10 feet per second.
The results of the test are summarized in Figure 23. Note that erroneous
velocities of relatively stable appearance are generated when the missed
pulses are symmetrically distributed both upstream and downstream with-
out the ATC operating. When the symmetry is broken by randomly
missing a group of pulses there is incoherence in the output without
41
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The difficulties with triggering the ASMV and transmitter directly
upon detection of a received signal becomes apparent upon examination
of the ASMV function. The timing diagram shown in Figure 21. Note
that the free-running period of the ASMV is so set that it is in a re-
settable mode well before the time range in which a received pulse
might occur, and will reset itself automatically well after the probable
received pulse time range. Since the transmitter is fired upon reset
of the ASMV, the self-starting capability of the entire unit is ensured.
However, should a received pulse packet be so severely attenuated so as
not to be detected, an extremely large time error, and hence frequency
error, is injected into the system, and indeed such errors were observed.
It was thus obvious that an alternative to Leading-Edge detection was
necessary and that some substitute trigger mechanics had to be provided.
Close study and evaluation of the ultrasonic pulse packets being re-
ceived indicated that, although the sewage medium did randomly attenuate
pulse packets in varying amounts, all oscillations within any one packet
were generally attenuated by the same amount. Consequently, it was deter-
mined that detection of the peak of the pulse packet envelope would provide
more stability. Using this scheme, relatively rapid fluctuations in the
envelope would not be detrimental and by adding automatic gain control (AGC)
long time constant changes in amplitude could also be tolerated. The AGC
also ensured that the pulse packet envelope would not have a slipped top
due to over-driven receiver amplifiers. Since the pulse packet envelope
existed for only 1% of the total "listening" period, the AGC had to be
of the "keyed" type, i.e., only the amplitude of the packet envelope
itself would be "checked" to determine any gain correction.
The remaining problem of automatically triggering the transmitter and
resetting the ASMV without undue delay in the event of a missing re-
ceived pulse involved more effort.
38
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the ATC operating. This condition most nearly simulates the actual
sewage channel environment. in all cases, accuracy and coherence are
maintained when the ATC is operational.
_ An evaluation of the effects of suspended
solids on the performance of the velocity measurement was undertaken
both in the laboratory and in the field. Field evaluation was more
qualitative than quantitative in that precise determination of the
variables involved was difficult at best. For comparative purposes a
quantity equal to the product of the solids loading in milligrams per
liter times the ultrasonic transmission path length in meters divided
by 1000 was used. For future reference this product will be called the
Load-Length Product (LLP) . On typical days the LLP ' s were determined
at Cambridge Avenue, South Shore and at Jones Island. These were de-
termined to be 0.192, 0.735 and 1.357. Of interest was the fact that
the ultrasonic transmission at Cambridge Avenue Site was uninterrupted,
at the South Shore Site the transmission was hopelessly occluded and at
Jones Island the transmission was only intermittently blocked. Further-
more, the transmission path length at Jones Island was a full foot
longer. Clearly the LLP was not by itself an adequate indicator of
probable performance capability. Other variables considered were:
particle size, density of particles (number per unit volume) and particle
density (weight per unit volume) . Although an exact theoretical or
experimental treatment which includes all these variables would be
essentially impossible, the following treatment is of such a nature
as to indicate their general effect on the transmission intensity.
Consider a region in which there exists a number of spherical scatterers
arranged in such a manner and with such separation as to preclude ex-
tensive multiple scattering. The incident wave attenuation in this'
region is given by the equation
Xi = Tio exp {~ N
43
-------
In this case an analog scheme was employed in which a ramp voltage
was generated at the time the ASMV entered the "set" mode and the
voltage which existed at the time at which a pulse was received was
held. During the next cycle the ramp voltage was compared to the
value held and if it exceeded that value, caused a surrogate trigger
to be injected. To ensure an adequate capture capability in the
event of a reduction in the sonic velocity, a small delay was in-
serted between the detection of a pulse packet and the triggering
of the transmitter. Additional noise rejection was obtained by blank-
ing the receiver detector during the period for which the ASMV was in
the "set" mode.
The block diagram of the stages in the modified receiver transmitter
block is shown in Figure 22. Laboratory tests of the modified
system under ideal conditions resulted in less than 1% error when 9
out of 10 pulses were absent and there were no detectable effects
when the input signal amplitude varied over the full range allowed by
the receiver gain-control potentiometer.
GENERAL ANALYSIS OF EQUIPMENT OPERATION
In the following sub-sections operational characteristics of physical
elements of the flowmeter system are presented followed by discussions
of environmental factors, such as solids loading and air entrainment,
and their effects on the operation. Finally, specific data obtained
at each site is presented.
The electronic unit used to sense the liquid level was the Bin-Dicator
Level Data LC-520 control with transducer LT-A and temperature
compensator (South Shore installation only). The claimed electronic
accuracy of ± 1% of full scale vyas met or exceeded. However, the re-
sponse of the unit is somewhat faster than desirable, even when operat-
ing in the "Delayed" mode. It is possible to have sufficient surface
40
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relating intensity to scatter site density it is easy to predict total
occlusion at the site. Thus it was discovered that entrainment of verv
small air bubbles was the cause of blocked transmission and not suspended
solids loading.
To complete the study, a laboratory study of the effects on transmission
by various materials was made. The results for several representative
types of materials are presented below. Note particularly the values
of the LLP's.
Occlusion
M . . . Density Length
Material (Milligrams per liter) (Meters) LLP
Rubberized
Horse Hair 19 595
^'^^ 0.305 5.984
Open-Cell
Plastic Foam 20,620 0.0658 1.357
Cotton Toweling 265,150 0.015 3.977
In a separate study performed on return sludge of controlled densities,
the Japanese have determined that the LLP should be less than 5.0 to
ensure operation for this equipment. Note that this figure is bracketed
by the horsehair and cotton toweling LLP's which are probably representative
of the textural quality of part of domestic sewage. From both studies
it would appear that the criteria should be that in the absence of
entrained air, the LLP should not exceed 5.0
Effects_of Entrained Air - Following up on the observation that entrained
air had an enormously deleterious effect on the ultrasonic transmission
quality, a series of experiments were performed in the laboratory. Al-
though not intended to be highly refined or conclusive, the results are
of interest. The 400 kHz probes used in the equipment were placed in
clear water approximately two feet apart and the transmitter probe was
45
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FULL SCALE
1. NO MISSING Rx PULSES.
2. RANDOM PERIODS MISSING 1 OUT OF EVERY 10 Rx
PULSES, ATC 'ON1 (PHANTOM PULSES INSERTED).
3. AS IN 2, EXCEPT ATC 'OFF1 (NO PHANTOM PULSES INS.).
if. RANDOM PERIODS MISSING 9 OUT OF EVERY 10 Rx PULSES
ATC 'OFF'.
5. AS IN **, EXCEPT ATC 'ON1.
6. MISSING 1 OUT OF EVERY 10 Rx PULSES AT ALL
TIMES ATC 'ON'.
7. AS IN 6, EXCEPT ATC 'OFF'.
8. MISSING 9 OUT OF EVERY 10 Rx PULSES AT ALL
TIMES ATC 'OFF1.
9. AS IN 8, EXCEPT ATC 'ON1.
Figure 23. ATC Performance Test
42
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Figure 25.
Received Signal,
Water with Entrained
Air Bubbles
Figure 24.
Received Signal,
Clear Water
I ' . '
Figure 26.
Received Signal,
Clear Water, Expanded
47
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here I is the initial incident wave intensity, N is the number of
io
scatters per unit volume, x is the distance into the region and the
Z and E are defined as the scattering and absorption cross sections
s a
respectively. These cross sections are defined as the ratio of the
power scattered (or absorbed) to the incident intensity.
The initial incident intensity I is given as
T —
io pc
Where A is the amplitude, p is the density of the medium and c is the
propagation velocity in the medium.
One author has indicated that the Z term is proportional to N for
particle sizes large compared with the wave length and to N^ for those
small compared with the wave length. In either event, this yields an
attenuation relationship of the form.
]^
I. ^ exp (KN )
where 2
-------
-------
in diameter with four"sets of probes placed at the 1.0, 1.75, 2.5
and 3.25 foot levels. Probe face-to-face separation are summarized
in the Table below.
Probe Level Separation
Set # (feet) (feet)
1 3.25 4.54
2 2.50 4.88
3 1.75 4.54
4 1.00 3.88
The velocity unit is calibrated for the separation found at both
sets #1 and #3 and for a maximum or full-scale velocity of 5.5 feet
per second. (The estimate is based on slope and typical flow data
supplied by the Milwaukee Sewerage Commission.) Using the unit in
flow rate (Q) mode by integrating the level data as discussed in an
earlier section, the full-scale value is Q = 70 mgd (i.e., a velocity
of 5.5 fps with a level of 5.0 feet).
Of interest is a plot (see Figure 30) of the normalized area of a
circular conduit, versus the depth of flow (normalized to the radius
of the conduit). It was surprising to note that a least-squares fit
of a linear approximation would result in a maximum error of less than
5%. And over the level range of 0.1 < h/r < 1.9, constituting 90% of
the range and over 99% of the occurrences, an error of less than 2.5%
can be realized. For this reason, the Cambridge Avenue unit has been
calibrated using an off-set linear approximation of the latter type.
As a check on the flow profiles anticipated from theoretical and
observed data, the probe sets of this site were strobed manually and
over a period of several minutes average velocity data was obtained
at each of the lower three sets. The level was 3.10 feet during the
test which occurred at 0830 on March 9, 1973. The necessary correction
factors for probe sets #2 and #4, due to the different transmission
50
48
density of air bubbles of resonant size would be reduced. Ultrasonic
transmission in the presence of entrained air at various sonic frequencies
would be a fruitful area for additional investigation.
CAMBRIDGE AVENUE
From the very beginning of the tests, signal levels at this site have
usually been quite strong. In fact, reduction in receiver and/or trans-
mitter strength was clearly indicated. Very little difficulty with
entrained solids or air was experienced, and the addition of the ATC
circuit eliminated any occasional traces. A section of a typical
chart recording at this location is included in Figure 29. The system
at this location has continued to operate with only routine periodic
maintenance for nearly 2 years. Installation diagrams for the site
can be found in Section IV. Note that it is a circular conduit 5 feet
46
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ft
.rri
tit
til
I
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51
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•rtrmtt
; rt" lTTTTtt*"T'11
Figure 31. Measured Chordal Velocities Versus Depth, Cambridge Ave
Figure 32. k-Factor Estimate, Cambridge Avenue
52
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lengths, were applied and the results are plotted in Figure 31. By per-
forming an area integration of VG as shown in Figure 31, an average
velocity v is determined to be 1.15 feet per second yielding a minimum
k-factor of 0.97. Note the close agreement with the value of 0.98
obtained for open circular pipes in turbulent flow. (See Appendix A for
a detailed presentation of the k-factor analysis.)
Using this value of v (1.15 feet per second) a k-factor plot is obtained
and presented as Figure 32. Note again the close similarity to the
k-factor plots for the circular pipes as presented in Appendix A.
Typical velocities observed at this site fall in the range of 1.0 to 2.0
feet per second, and typical levels between 3.0 and 4.0 feet. As such,
typical flow extremes are approximately 8 MGD and 22 MGD. It is im-
portant to note that these flow velocities are only 20% to 40% of those
predicted by use of Manning's equation, indicating that the energy slope
is only a fraction of the channel slope. Retardation of the flow may
be caused by the hydraulic characteristics of an inverted syphon down-
stream from the metering site.
SOUTH SHORE TREATMENT PLANT
As discussed in an earlier section, difficulties were experienced with
the ultrasonic transmission at this site which were not fully under-
stood, until late in the demonstration grant period, to be caused by
entrained air. Installation diagrams for this site can be found in
Section IV. Note that it is a circular conduit 12.5 feet in diameter
with initially six sets of probes installed at the 2.0, 3.75, 5.5, 7.25,
9.0 and 10.75 foot levels. Probe face-to-face separations are summa-
rized in the following table.
53
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Probe Level Separation
Set # (feet) (feet)
1 10.75 8.66
2 9.0 11.57
3 7.25 12.78
4 5.5 12.81
5 3.75 11.74
6 2.0 9.19
The velocity unit was calibrated for the separation found at probe set #6
and for a maximum or full scale velocity of 10 feet per second. Using
the unit in the flow rate (Q) mode by integrating the level data as dis-
cussed in an earlier section, the full-scale value is Q = 795 MGD (i.e.,
a velocity of 10 fps with a level of 12.5 feet). Although the system
did not perform as expected and flow level was low (about 3.0 feet) most
of the time, some evaluation was possible during a period when the glue
factory was not operating and during which the level could be elevated
by temporarily restricting the plant input volume.
As expected, the 2-week shut-down of the Peter Cooper Plant and subsequent
reduction or termination of its contribution to the South Shore Plant in-
fluent resulted in the ultrasonic velocity meter being 100% operational.
This confirmed the suspicion that the occlusion of the ultrasonic signal
was caused in some way by the glue factory effluent. Without doubt, this
is not a typical condition which would be expected at most treatment
plants. During several of these days the input flow at the South Shore
Plant was purposely reduced, backfilling the 12^-foot diameter conduit
to a depth of 6 to 9 feet. Flow control gates were then opened slightly
permitting numerous sets of average chordal velocity readings to be
obtained. This data was then plotted and correlated with the chart
recordings of total plant influent. Although much of the data was ob-
tained during hydraulic transients, graphic interpolation of the results
yields flow values in close agreement with those obtained by alternate
54
-------
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56
-------
means (more specifically the mag meters downstream). Although cali-
bration data for the mag meters was not available, the operating engineer
indicated that they had been recently checked and were as accurate as
could be expected considering the operating conditions. Their proximity
to the ultrasonic unit precluded the need for significant time corrections
due to lag. During the greater part of the morning and early afternoon
of June 6, 1972, the influent flow to the South Shore Treatment Plant was
significantly reduced, backing up the 12h foot diameter conduit to a
depth of 6 feet. Average chordal velocity data at the levels permitted
by probe locations were recorded at depths of 5 feet (1130 hours) and
6 feet (1400 hours). The former exhibited a typically turbulent profile
whereas the latter did not, appearing more laminar. No doubt the
dynamics of the filling conduit contributed to the shape. Figure 33
shows these profiles whereas Figure 34 has the corresponding plant in-
fluent flow data as recorded by mag meters further downstream (follow-
ing coarse screening,. Note that estimates of flow based on these pro-
files yield values of 13.6 MGD at 1130 (versus 14 MGD recorded) and 10.2
MOD at 1400 (versus 11 MGD recorded).
fit approximately 1510 the butterfly valves downstream were partially
opened, resulting in a rapid flow rate increase from about 13 MGD to 70
MGD, followed by a typically exponential decay characteristic. The gates
at the conduit-plant junction permit flow into the plant from the bottom
of the conduit, hence there would be a reduced flow impedance at lower
levels. Although the velocity sensing elements were located approxi-
mately 60 feet upstream, the physical configuration of the gates would
probably result in some dynamic effects being observed even at that
distance.
The butterfly valves were again adjusted at about 1524 increasing the
flow to 93 MGD briefly. Note that the effects of these two adjustments
can be readily observed in both figures. Of course, the extrapolations
are estimates; however, these estimates are based on observed flow
57
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characteristics reported elsewhere (Barnes, et al). For instance, a
reverse slope characteristic such as observed at 1515 is also found in
circular conduits having a large slope and consequent high flow. No
doubt, the shape in this case is due to the gate location, inasmuch as
the profile does tend to stabilize.
Signal strength during the tests was outstanding, a situation due pri-
marily to the fact that the Peter Cooper Glue Factory was not operating
and was not discharging into the conduit.
Flows calculated from the velocity profiles measured by the ultrasonic
meter agreed quite well with those measured by the plant mag meters:
Calculated From
Flow Profiles
Measured Mag Meter
Time Ultrasonically Recording
1515 63 MGD 65 MGD
1520 66 61
1525 82 87
1530 86 70
Again it must be reemphasized that these flow tests were run under transient
conditions caused by backing up the sewer and then emptying it, by means
of positioning the flow control gates at the plant inlet and thus are not
entirely representative of normal flow conditions. Note under these
conditions that flow profiles seem to "pivot" about a point at about 40%
maximum depth, lending additional support to the procedure of locating
a single set of ultrasonic probes at this depth for velocity measurements.
COLLEGE AVENUE
Due to the difficulties encountered at the South Shore Plant and in order
to realize a full-time operating system, the top two probe sets (#1 and #2)
58
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of the South Shore installation were removed and located in a 12 foot
diameter conduit 120 feet below the intersections of College and
Pennsylvania Avenues. The probe sets #1 and #2 were located at levels
of 1.7 and 3.45 feet respectively (inverted from their previous position-
ing). Face-to-face separations of the reinstalled probes are 8.25 and
11.14 feet for the 1.7 and 3.45 foot levels respectively. The calibration
of the unit was not changed and hence its use requires a correction
factor equal to the ratio of the operational length to the calibration
length. Installation diagrams for this site can be found in Section IV.
At this site proper operation of the velocity unit was immediately attain-
ed and continued to the end of the program with no problems of any kind.
Due to the fact that this was a last minute change under a demonstration
grant extension, little additional data was obtained. However, it has
demonstrated conclusively that the highly agitated glue factory effluent,
with its extremely high concentration of entrained air bubbles of
'resonant' size, was solely responsible for the poor performance at the
South Shore Site since the sewage volume passing the College Avenue probes
is the very same as that passing the South Shore probes with the solitary
exception of the glue factory effluent.
59
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SECTION VI
DISCUSSION OF RESULTS
ALLOWABLE SOLIDS LOADING & AIR ENTRAINMENT
Although existing instrumentation was applied in the demonstration for
both the ultrasonic velocity and level measurements, modifications were
required to suit it to the wastewater metering application. In the case
of the velocity measurement, adequate pulse propagation in the presence
of varying entrainments of suspended solids and air bubbles required
added sophistication in the detection circuitry. Automatic gain control
(AGC) was added to provide uniform detected signal amplitudes under con-
ditions of changing received pulse energies. Even with AGC, use of
leading edge pulse detection resulted in unacceptably large errors in
the velocity measurement. So pulse peak detection was used instead by
detecting the received pulse envelope, differentiating, and triggering
on the zero crossing of the derivative.
Infrequent passage of large solids can be expected to (and did) complete-
ly block the transmission of occasional ultrasonic pulses, introducing
another error into the velocity determination. This problem was minim-
ized by automatic insertion of an external trigger pulse substituting
for the missed pulse. The results of these modifications to the de-
tection and signal processing circuitry made it possible to measure waste-
water velocity accurately within the following figure of merit (Lead-
Length Product, or LLP) relating the conduit diameter and solids loading:
(D) x (SS) <_ 5000
where D is sewer diameter in meters and SS is the suspended solids con-
60
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centration in milligrams per liter.
Solids loadings in the Cambridge Avenue and College Avenue sewers were
in the range of 200 milligrams per liter, well below limiting values of
3300 and 1380 milligrams per liter respectively, so no difficulties due
to solids loadings were encountered. In full pipe installations in
Japan (see Appendix D) successful flow measurements are also being made
on return sludge with solids loadings of 10,000 milligrams per liter in
a 0.2 meter line. So for the typical conduit diameters presented in the
following table no operational limitations would be expected for suspended
solids loadings which did not exceed the maximum level specified:
Maximum
Conduit Diameter Suspended Solids
_ (meters) Concentration milligrams per liter
°-2 25,000
°-3 16,700
°-6 8,300
1-° 5,000
i-5 3,300
2 2,500
3 1,700
5 1,000
Entrained air bubbles caused operational problems at the South Shore
installation site because of dissipation of the ultrasonic pulse due to
scattering by the resonant entrained air bubbles. In this installation,
20 to 50% of the sewage flow was due to a single effluent reaching the
sewer from a glue factory at a point about 10 minutes upstream from the
meter site. Air bubbles are generated in this effluent because it
enters the main sewer via a 58.7-foot vertical drop (see Figure 11).
Bubble lifetime in wastewater is longer than in tap water bacause of
bubble adherence to solids particles. There were still enough bubbles
in the sewage after a 10 minute transit time to completely occlude the
61
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ultrasonic transmission. Accordingly, another criterion for meter instal-
lation sites is to "avoid waterfalls". In other words, select probe sites
which are reasonably free of severe upstream agitation. Normal sewer
flows are sufficiently quiescent so as to avoid excessive air entrainment.
No entrained air difficulties were encountered at the Cambridge Avenue or
College Avenue installations.
LEVEL GAUGE INSTALLATION CRITERION
We experienced some temporary difficulties with level gauge performance
at the College Avenue Site due to standing ripples in the sewage surface
which interfered with echo returns. This was alleviated by moving the
level sensor a few feet to a point where the sewage surface was less dis-
turbed, with only random surface turbulence. Inaccuracy due to occasional
missed echos was satisfactorily minimized by electronic damping.
PROBE FOULING BY DEBRIS & GREASE
One of the major design features which was a subject of considerable
conjecture before the installations were made was the possible suscep-
tibility to fouling of the velocity probes by passing debris and grease.
A major result of the program was the demonstration that this did not in
fact occur, arid the meters, once operational, remained in service without
further attention at least for the duration of the demonstration (18
months for the Cambridge Avenue meter) and probably indefinitely. The
velocity probes at the South Shore Site were inspected about a year after
installation, and a quarter inch deposit on the probe face was noted.
However, the systems continue to operate properly even though the sound
pulses must first propagate through the deposited layer. The thickness
of the deposits is apparently limited due to a balance between deposition
rate and erosion rate. In other words, thicker deposits are eroded by
the abrasion of passing solids, and thus build only to tolerable thick-
nesses. The protective housings surrounding the probes were designed
to prevent the accumulation of rags, branches or other debris, and per-
formed successfully. Materials used must be tough and noncorrodible,
62
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stainless steel or plastic.
VELOCITY PROFILES & PROBE MULTIPLICITY
Another major design feature to be demonstrated was the ability to measure
flow accurately with the use of only a single probe set for the velocity
measurement, and a single level transducer. To accomplish this, a usable
relationship between area velocity v& and chordal velocity v had to be
derived and applied. Using extensive flow profile data collected by
Barnes4 and Nikuradse5, the analysis of Appendix A demonstrates that in
subcritical open channel flow, v& and VG are sufficiently close to being
linearly related to enable flow to be measured within 2% over a range of
depths from 35% full to full, using just a single velocity probe set
mounted below the 35% level, and a single level transducer. Because of
the complexity of solution for the Navier-Stokes equations for turbulent
flow, an attempt was made to infer turbulent velpcity provile information
from laminar flow data for various channel shapes. For circular channels
running full or partially filled, an apparent 6th power relationship was
observed between normalized laminar chordal velocities and normalized
turbulent chordal velocities. For rectangular channels, the relationship
appears to be 4th power. The utility of these relationships is the ease
with which average chordal velocities in turbulent flow can be obtained,
as well as the subsequent computations of v^v^ the k-factor, provides
a measure of the accuracy of flow measurement based on an area velocity
inferred from a single chordal velocity.
After the necessary electronic modifications were made for the wastewater
application, and the South Shore test site was abandoned in favor of the
College Avenue Site to avoid the air bubble problem, all equipment per-
formed satisfactorily. Ultrasonic flow measurements checked well with
current meter traversals at Jones Island (2%), and reasonably well with
the transient mag meter readings at the South Shore Site. All equipment
remained in operation at the close of the demonstration project.
63
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EQUIPMENT COSTS
At the time of the demonstration program, equipment costs were approximate-
ly $12,200 for the ultrasonic velocity meter, $1,200 for the ultrasonic
level gauge and about $1,600 for the mounting fixtures, cables and electri-
cal conduits. Total system cost for each site was thus about $15,000
(this included multiple velocity probe sets). Current costs are sig-
nificantly less, being approximately $7,500 for the ultrasonic velocity
meter, $1,000 for the ultrasonic level gauge, and $1,000 for mounting
fixtures, cables and electrical conduits, for a total system cost of
about $9,500 for each site (with a single velocity probe set).
For the large diameters metered (51 and 12'), this cost compares well
with that of other flow metering devices such as venturi and magnetic
meters which require full pipes for operation. It is relatively more
expensive than flumes or weirs. However, the ultrasonic system continues
to measure accurately when the sewer is surcharged, when weirs and flumes
become inoperative. Further simplifications of the ultrasonic circuitry
made possible through more extensive use of integrated circuits have the
promise of further reducing the $9,500 system cost.
64
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SECTION VII
REFERENCES
1. Genthe, W. K., and Yamamoto, M., "A New Ultrasonic Flowmeter for
Flows in Large Conduits and Open Channels", Proceedings of the
Symposium on Flow, AIP, ASME, ISA, NBS, Pittsburgh, Pennsylvania,
May 10-14 (1971).
2. Birger, G. I., "Certain Problems in Calibrating Ultrasonic Flow-
meters", Measurement Techniques, Vol. 10, pp. 872-874, October (1962)
3. Yamamoto, M., Tokyo Keiki Co., Ltd., Tokyo, Japan. Private
Communication, 1969.
4. Barnes, A. H., "Velocity Distribution Factors in a Circular Cross-
Section", u. S. Bureau of Public Roads Contract #CPR-ll-3584,
Colorado State University Engineering Research Center, October (1966),
5. Nikuradse, J., "Untersuchung Uber Die Geschwindigkeitsverteilung in
Turbulenten Stromungen" (1926)
6. Landau, L. D., and Lifschitz, E. M., Fluid Mechanics. Pergamon,
London, p. 120 (1959).
7. Henderson, F. M., Open Channel Flow. Macmillan, New York (1970),
522 pgs.
65
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SECTION VIII
APPENDICES
Page No.
A. Velocity Profile Analysis 67
B. Computer Program for Solution of the Navier-
Stokes Equations for Laminar Flow in a
Rectangular Open Channel 89
C. Derivation Relating Laminar Chordal Velocity
and the 6th Power of Turbulent Chordal Velocity.. 93
D. Summary of Ultrasonic Wastewater Metering
Performance in Installation in Japan 93
66
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APPENDIX A
VELOCITY PROFILE ANALYSIS
Concurrently with the demonstration of the metering equipment, an investi-
gation of velocity profiles was undertaken. This included an examination
of much data for various conduit geometries and another look at the theo-
retical characterization of turbulent flow. The primary objective of the
investigation was to obtain the relationship between the average velocity
in a horizontal plane or chord (VG), the level of that plane or chord (£)
and the average velocity over the entire flow cross section (v ). Although
it was not anticipated as a probable result of the analysis, a means of
predicting the relationships between v^ v&/ and £ by a computer program
would have been desirable and was included as a secondary objective.
Experimental k-factor analysis
Having ultrasonically measured the average chordal velocity v at a chord
level £, it is necessary to relate this to the average area velocity v
This relationship can be mathematically stated as:
v (t) = k(£,v )v U;t)
a C C
where k is the proportionality factor which is a function of both the level
at which VG is determined and the value of the average chordal velocity
itself. In addition, the k-factor would be expected to vary in its
functional dependence on £ and VQ with variations in conduit geometry.
At first glance such functional dependence and interdependences would
appear to present an insurmountable barrier to successful analysis;
however, it was found that there were several saving factors.
67
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Limiting the analysis to turbulent flow, it became evident upon
examining existing data from a variety of sources that the value of
k is nearly independent of both level and average chordal velocity over
a major portion of the depth. Furthermore, it appears to be relatively
independent of conduit geometry. This is reasonable when one considers
the natural asymptote of the process. In extreme turbulence it would
be expected that over a major portion of the cross section the average
chordal velocity, would be nearly equal to the average area velocity,
i.e., k = 1.
Although the Russians and Japanese have published some results of
studies of the k-factor, relatively little work has been done. The
difficulty is principally that of obtaining reliable data in large
conduits during well-developed turbulent flow. Fortunately a great
deal of reliable data was found to have been obtained during an unrelated
study by Professor A. H. Barnes at Colorado State University. The
apparatus used consisted of an 800 ft. long/3 ft. diameter conduit. It
was supplied by a reservoir with a 200 ft. head and had the capability
of variable slope. The velocity data was obtained using propeller meters
mounted on rods which could be rotated in a plane perpendicular to the
conduit axis. From this data cross-sectional plots of isovels were
obtained for several depths and flows. These isovel plots were then
used to obtain velocity profiles in horizontal planes at various levels.
Integrating these profiles and averaging over the chord length and
dividing the resulting value of v into the average area velocity, v
C cl
determined the value of k at that level. In this manner a plot of k as
a function of level was obtained for that particular flow situation. In
each case, a computer generated set of k values for laminar flow in a
pipe filled to the same depth was obtained. Isovel diagrams for pipes
roughly one third and two thirds full as well as for a full pipe are
shown in Figures 35, 36 and 37 respectively, along with the k-factor
plots for each.
68
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In addition to the circular conduits, an isovel diagram of a
partially full rectangular conduit, obtained and published by
Nikuradse, was analyzed and the k-factors obtained. Again, a com-
puter generated k-factor for laminar flow in a similar conduit
at a similar depth was obtained. This is presented as Figure 15.
In an effort to independently ascertain the value of the k-factor
for a typical sewer channel, a readily accessible open rectangular
channel at the Milwaukee Sewerage Commission's Jones Island Treat-
ment Plant was studied. This channel connects the coarse-screen
house and grit chamber area, is 10 feet wide and 8.5 feet deep. A
Gemware magnetic type current meter of the type shown in Figure 39
was utilized in the study. Data was obtained over approximately a
two hour period from 1300 to 1500 hours on September 28, 1972.
During the test period the level remained at 7.06 feet with fluctu-
ations of less than 1%. During the same period the ultrasonic
velocity meter had an average indication of 4.5 ft/sec with fluctu-
ations of ± 6%. Current meter readings were taken at one foot
vertical intervals along the vertical center line, and verticals
2.5, 4.0 and 4.5 feet from that center line. A plot of this data is
presented as Figure 40. A horizontal profile at the 2.5 foot level
(the level at which the ultrasonic velocity probes are located) re-
flecting the values taken over the same averaging period is shown
in Figure 41. Interpolation and integration yield a chordal average
velocity of 4.475 ft./sec. This value calculated from the profiles
measured with the current meter agrees closely with the average re-
corded value from the ultrasonic velocimeter of 4.5 ftyfeec. Without
doubt, the error is less than the inherent measurement errors en-
countered during the test and may not be entirely accurate itself;
however, it would be expected to be of that approximate percentage.
An estimation of the average area velocity, based on the profiles in
Figure 42 of 4.29 ft./sec. indicates that the chordal average velocity
69
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5
u
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U
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•H
Q
IT)
ro
70
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-IX
CN
<1J
c
c
£
U
•H
U
Cn
(d
•H
Q
rH
0)
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O
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CM
C
C
id
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U
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Q
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0)
m
0)
72
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oc
o
to
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m
0)
t>o
74
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Figure 40. Vertical Velocity Profiles, Jones Island Influent Channel.
Figure 41. Horizontal Velocity Profile, Jones Island Influent Channel.
75
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value of 4.475 feet per second is approximately equal to 0.96 times the
area average velocity, i.e., a k-factor of 0.96. This is in close
agreement with values for other open rectangular channels reported by
others. Unfortunately the above experiment could not be repeated at any
of the sites covered by this demonstration grant due to their location.
Having obtained k-factor plots versus depth for circular conduits filled
to various levels, and in turbulent flow, a composite plot of k-factor
versus proportion of depth (0 - bottom, 1.0 = surface) for circular
conduits filled to a depth of 0.77R, 1.61R and 2.OR (full) was made (see
Figure 42). This family of curves is also presented as a plot of
k-factor versus liquid level (0 = empty, 2.OR = full) as Figure 20.
Finally, from this last family, a family of curves (Figure 44) represent-
ing the k-factor versus liquid level as the probe chord level is varied
was obtained. Although it would have been desirable to have had more
data sets, there is a sufficient density of data to indicate the general
trend, i.e., that velocity probes situated to measure the average velocity
along the chord at a depth of 0.7R (35% of maximum) would have measured
an average chordal velocity which was within 1% or 2% of the average area
velocity for all flow levels between 0.7R and 2.0% (full). Some sacri-
fice in the constancy of the k-factor for level fluctuations would be
experienced if the probes were situated at a depth less than 0.7R. (Note
that as probe placement level and level of flow jointly approach O.OR,
the k-factor must asymptotically approach infinity.)
In essence, this means that by their judicious placement, a single
ultrasonic velocity probe set allows sufficiently accurate (1% or 2%)
measurement of the average area velocity for a wide range of levels
provided that turbulent flow conditions exist. This is a result of the
relative constancy of the k-factor over a wide range of depths.
76
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Figure 42. k-Factor Versus Proportion of Depth.
Figure 43. k-Factor Versus Liquid Level
Figure 44. k-Factor Versus Liquid Level for Various Probe Chord Levels.
77
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Computer Aided Theoretical Analysis
A computer program was developed to present the axial velocities
at cross-sectional area grid intersections for irregular shaped
conduits with vertical symmetry in laminar flow. The computer pro-
gram interatively solves the Navier-Stokes equation for laminar
incompressible flow given as
2
V v + k = 0
where v is the axial velocity, k is the product of the gravitational
acceleration (g) and the slope (s) divided by the kinemetic viscosity
(v). The boundary conditions are v = 0 at the walls and, in the
8v
case of an open channel, -r— = 0 at the surface (where h is the
dh
coordinate perpendicular to the surface). (The program, for an open
rectangular channel, is presented in Appendix B.)
In attempting to solve this equation for either full or open (partially
filled) circular channels, some thought was given to an appropriate
coordinate system. The cylindrical system is the obvious choice for
the full circular channel, however, it presents a number of problems
when used for an open circular channel, not the least of which is the
implementation of the surface boundary condition. Additional problems
are encountered in maintaining a more-or-less uniform grid throughout
the cross section. It appeared that the bi-polar (or bi-cylindrical)
coordinate system might be a better choice. And, indeed it did
facilitate the application of the surface boundary condition but made
the wall-surface boundary difficult to define. Furthermore, determin-
ation of the lengths of the grid segments (needed for the interative
technique used in solving Poisson's equation) would have required
either a prohibitively large number of grid points or an integration
subroutine for each segment. A few trial runs proved that inadequate
data accuracy resulted when a grid of reasonable size was selected and
the segment lengths were approximated using standard techniques.
78
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In view of the above difficulties, the cartesian system was again con-
sidered and found to have several features previously not appreciated;
i.e., grid patterns are rectilinear (not curvilinear!), segment lengths
are uniform in any given row or column (except for the last segment in
a row or column) and the segment lengths are not a function of the
coordinates (except at boundaries), data can be easily plotted and other-
wise manipulated and boundaries for various shapes (not just rectangular
or circular) can usually be easily specified mathematically. This last
feature is of further significance when future solutions for channels
with trapezoidal, flat-side circular and other mixed geometries are con-
sidered. Hence, a computer program was written which uses a rectilinear
grid size that can also be varied within the cross section, if desired.
A trial solution for a full circular channel was obtained (using theo-
retically predicted values). Accuracy beyond the third place was obtained,
and is deemed sufficient for the present purposes. Other trial solutions
for full rectangular channels indicate the same, or better, accuracy
when compared to experimental results obtained by others (notably
Leutheusser).
The output consists of the velocity at each grid intersection point
normalized to the velocity at the intersection of the surface and the
vertical centerline. (Geometries not having symmetry about the vertical
axis are not presently being considered.)
Inasmuch as the Navier-Stokes equation describing turbulent flow becomes
far too complex for computer solutions on any but the largest computer
systems, efforts were directed at correlating the laminar and turbulent
data. The results, although incomplete, are encouraging and a corre-
lation of sorts does appear to exist. This is discussed later.
79
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Full Circular Channel Analysis
As indicated above, the velocity profile for the full circular
channel in the laminar region obtained by the computer agreed with
that predicated on the theory. This distribution was compared to
the data obtained by Nikuradse for the full circular channel in
the turbulent region. The velocities along each chord were
normalized to the velocity at the centerline of the chord for both
the laminar and turbulent cases. This data was plotted versus the
fraction of the distance along the chord from the centerline to
the wall. As shown in Figure 45, the theoretical and experimental
laminar data correlate exactly for all chords, and the experimental
turbulent data correlates quite well for all chords considering
the inherent errors involved in extracting data from the small
figure in the Nikuradse paper. The fact that the normalized laminar
chordal velocity distributions are identical for any normalized chord
can be easily shown.
Referring to Figure 46, note that for the observed data to lie on the
same line it would be necessary that the following relationship be
valid.
Indeed, substitution of L/L for r in the theoretically derived
equation for a full circular channel in the laminar region:
2
v = 1-r (with R and v both unity) and the trigonometric formula for
max
22 22 ?
a right triangle from which L = r - (1-d) and L = l-(l-d) shows
c
that the relationship does indeed hold, as expected.
Further study of the chordal velocity distributions for the full cir-
cular channel in the turbulent region, as given in Figure 45, seems to
80
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a
u
U
n
•H
U
o
•H
-p
(D
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indicate that a similar relationship may exist for the turbulent case; if
not exactly, then possibly it would be close enough to assume as exact in
any approximation. Several attempts to approximate the distribution are
shown in Figure 45, including that of Nikuradse (v = r/R)
ever, that the equation
Note how-
VL =Vt
n n
yields a much closer fit.
Figure 47 is a plot of the normalized turbulent velocities versus the
normalized laminar velocities at
the 6th power relationship fits.
normalized laminar velocities at the same L/L ratio. Note how closely
V*f
It would appear that this approximation might provide a good transfor-
mation relationship for converting the laminar data to turbulent values
for this example.
Figure 46. Circular Channel Geometry
82
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r-
^
o>
83
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Open Circular Channel Analysis
Using the computer program at hand, a normalized laminar velocity profile
was obtained for an open circular channel of unit radius and filled to a
depth of 0.766 times the radius. This was then compared, in a manner
similar to that described for the full channel, with a profile presented
by Barnes (Figure 48) of a similar circular channel in turbulent flow.
The Barnes profile was then sectioned in such a fashion as to match the
computer solution grid for the laminar case. The theoretical or experi-
mental laminar normalized chordal velocities (Figure 49) again fall on
essentially the same curve for all chords, with some deviations caused
most probably by computer iteration errors near the boundary (since all
deviations of any amount occur near L/L or for the bottom row or two
C*
of the grid). In addition, the experimental turbulent distributions
indicate a strong correlation with each other for all chords (again some
values for L/LC > 0.8 and for the surface grid and bottom grid are
questionable inasmuch as they were obtained through interpolation from
graphical representations of the raw chordal data). Also, note the good
correlation of the turbulent data to the 6th root of the laminar data
for any given L/L value.
c
The plot of v versus v , obtained using the plots given in Figure 49,
L Li
is presented in Figure 50. It appears that the same relationship holds
here as for the full circular channel. There is, however, one major
difference which is not immediately evident, and this is the marked
difference in the vertical profiles. One possible saving characteristic
is noted and that is that the vertical profiles, when appropriately
normalized, do seem to correlate well.
The apparent correlation between the normalized laminar chordal velocities
and the 6th power of the normalized turbulent chordal velocities would
not at first appear to have any theoretical justification. However, if
one considers the viscosity to be a function of velocity, then such a
84
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86
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direct correlation is not only theoretically possible (see the derivation
in Appendix B) but practically probable. The concept of expressing the
viscosity of a turbulent fluid by a value different than that used when
it is in laminar flow is discussed by Landau and Lifshitz. However, there
remain two unresolved problems. First, the way in which the power in
the relationship is determined is not known. For instance, under similar
flow conditions the relationship between the normalized laminar velocities
and the normalized turbulent velocities for the open rectangular channel
appears to be fourth order, i.d. VL * vt4. Second, the depression of
n n
the maximum flow velocities to levels below the surface are not explained
by such a correlation. Generally, this depression is attributed to
secondary flows. However, there appears to be some validity in attaining
the same result by the use of proper surface boundary conditions. Such
an approach is briefly alluded to by Henderson. Unfortunately, the
continuation of this theoretical investigation is beyond the scope of
this demonstration, although it would seem to be a worthwhile pursuit.
87
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-------
APPENDIX B
COMPUTER PROGRAM FOR SOLUTION
OF THE
NAVIER-STOKES EQUATIONS
FOR
LAMINAR FLOW IN A RECTANGULAR OPEN CHANNEL
A computer program which iteratively solves the Poisson equation
2
V v + k = 0
is presented. A cartesian coordinate system is used with a maximum
grid size of 10 x 10, not including the wall boundaries (bottom and
side). As shown, the program will find the laminar velocities at
grid intersection points normalized to the velocity value at the
center of the surface. Symmetry about the vertical centerline is
assumed. The boundary condition at the surface is
0
surface
For geometries having proper symmetry but irregular sides and/or
bottom, it is necessary to modify the portions labelled: Initial
Data, Row and Column Lengths and Number and Length of Each Row
and Column Segment. This can be done as a data entry or by another
computer program.
Output data is presented in matrix form with the average row velocity
presented first for each row, followed by the centerline velocity and
thence each velocity sequentially to the wall. Vertically rows are
presented from the surface down to the bottom. The average velocity
over the entire area is presented as a single-entry final row.
89
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RECTANGULAR-OPEN
DIMENSION RL(1Q),CL(10),NSEUR(10),NSEGC(10>
DIMENSION RSEGL(10.10),CSEGL(io,10),C(10,lO,5),V(ll,ll>
DIMENSION VH(10»lO)tVC(10)
1 FORMAT(1X,F6.3,4X,10F6.3)
2 FORMAT(1X,F6.3)
3 FORMAT(F6.3)
INITIAL DATA
READ(5,2)DLR
READ(5,2)DLC
NC=10
A = 0.0
8=1.0
EPS=1.0E-10
DO 5 1=1,11
DO 5 J=l,ll
5 V(I,J)=0.0
CK=400.0
ROk AND COLUMN LENGTHS
RI=NC
DR=RI»DLR
RJ = NR
DC=RJ»DLC
DO 10 1=1,NR
10 RL(I)=DR
DO 15 J=1,NC
15 CL(J) = DC
NUMBER AND LENGTH OF bACH ROW AND COLUMN SEGMENT
DO 25 1=1,NR
SEGN = RL( D/DLR
ISEGN=SEGN
TSEGN=ISEGN
K=l
IF«SEGN-TSEGN),LT.0.001) K=Q
NSEGR(I)=ISEGN+K
DO 20 J=l,ISEGN
20 RSEGL(I»J)«DLR
25 IF(K.EO,1) RSEGLU'ISEGNM > = DLR« (SEGN-TSEGN )
DO 35 J=1,NC
SEGN=CL(J)/DLC
ISEGN=SEGN
TSEGN=ISEGN
K = l
IF((SEGN-TSEGN).LT .0.001) K=0
NSEGC(J)=ISEGN*K
DO 30 1=1,ISEGN
30 CSEGL( I ,J)«DLC
35 IF(K.EQ.l) CSEGL(ISEGN*1,J>=DLC«(SEGN-TSEGN)
90
-------
GRID INTERSECTION
C(l,l.l)=A/(CSEGL»CSEGL<1.1»
C(1,1,4)=C<1.1,2)
C(1.1.5)=C(l.l,l)*C(l.l,2)*C(i,i.3)
NT=NSEGC(1)
DO 40 1=2, NT
C( I,1,1)=2.0/(CSEGL< I-1.1>»=C
DO 42 J=2,NT
C(l, J»1>=A/(CSEGL<1, J)»CSEGL(i,j))
C(l. J.2)s2iO/
DO 44 J=2,NT
C( I, J,D=2.0/(CSEGL( 1-1. J)»< CSEGK I , J) *CSEGL ( I -1 , J ) ) )
C(I,J,2)=2.0/(RSEGL )
C(I,J,4)*2.0/(RSEGL(I,J)*(«SEGL(I, J)*RSEGL( I . J-l ) ) )
44 C(!,J,5)=C+C
GRID INTERSECTION VELOCITIES
48 T = V(1, 1)
V(1,1)=((C(1,1,1)*C(1,1,3))*V(2,1)
1 *(C(1.1,2)*C(1.1.4))*V(1.2)*CK)/C(1,1.5)
NT=NSEGC(1)
DO 50 1=2, NT
50 V+C< I, J,3)»V
-------
OUTPUT
62
DO 70 1=1, NR
NT=NSEGR(I )
RNT=NT
SUMP = SUMP«-RNT
SUMBsQ
DO 75 K=1,NT
75 SUMB=SUMB+V< I
AVGB=SUMB/RNT
VC(I )=AVGB
70 WRITE (3.1) AVGB, ( V ( I , J ) , J=l. NT )
AVGA=SUMA/SUMP
WRITE (3,2) AVGA
DO 72 1=1, NR
VK = AVGA/VC(I )
72 WRITE(3,2)VK
STOP
END
92
-------
APPENDIX C
DERIVATION RELATING LAMINAR CHORDAL VELOCITY
AND THE
6TH POWER OF TURBULENT CHORDAL VELOCITY
Af + M Centered at (XQ, YQ/ ZQ)
0 having sides Ax, Ay, Az
and viscosity v
t\
Assume that n = nQ + ^ Aw and v = -^ with uniform p, then the
shear forces are
Af +
Af
n_ -
9n
Ay
2
it
o By
Ay;
2
8v
o 8y'
2
3 Vx
o 3y'
Ay AxAz
2J
The difference in shear forces is Af =
Af =
2
9 v
o 2
v I 8y
x *-
AxAyAz
93
-------
The term
1 lim Af .
A -K> Av is the acceleration term due to viscosity
effects (AV = AxAyAz), and since n= pv=>
xy
2
8 v
x 8v
2 ' 8v
a x
8v
x
3y
Including the similar term for trie z direction shears, yields
V = V
X
8 v 8 v
8v
8v
8z
For the assumption that v ^ v (x), this can be rewritten as
.
v = vV v + —
x x 8V
(V'Vv )
x
Assuming that the viscosity can be expressed in terms of powers
of v , i.e.
x
V = V V
O X
n-1
then
a o _2 n
v = V v
x n x
Assuming gravitational flow, the modified Navier-Stokes equation
would be
V2v
x v
= 0
94
-------
where g is the gravitational constant and oc is the angle of
inclination. Note that the laminar solution is given when n = 1.
The solution at the surface, where the equation would be given as
A2 n
d v
x ng sin**
—— + k = 0 with k = — ,
dy vo
follows.
Assume a width w and v = 0 at y = 0 and y = w. Then
X
n k 2
Vx + "2 Y + C1Y + C2 = °-
Since v = 0 at y = 0, C = 0 and evaluation at y = w yields,
x &
j^
C, = - — w. Thus
n k /
vx = — y (w-y)
w
Normalizing v to v and y to — yields
XX ^
max
v n = y(2-y) with v sin
x x 8
max v
o
(Note that to be dimensionally correct v = v v has an implied
ox r
unit coefficient whose dimension is (sec/ )n.)
m
Hence
1/n
v
X
turb
V
x
lam
This appears to work well for normalized horizontal cross sections of
both circular and rectangular channels running full or open.
95
-------
Air-Water Boundary Conditions
\
I
AIR [ \
— I v
[
WATER \
. Az
+ ~T
o 2
interface plane
*- "z
o 2
The shear at the upper surface is
Af Az
.
air
air
Az
X .
air
32v
x .
air
o
_A_z
2
AxAy
and at the bottom
Af Az
Zo ' -1
water
water
9z
Az_
2
water water) Az
9z " 2 | 2
1 o 9z o
AxAy
Equating the two in the limit as z o yields
1 . air rj water
air __ _ water (at the surface)
96
-------
Assuming that the velocities at the interface are the same yields
the condition that
v v
x . = x (at the surface)
air water
97
-------
APPENDIX D
SUMMARY OF ULTRASONIC WASTEWATER
METERING PERFORMANCE
INSTALLATIONS IN JAPAN
During the sewage metering demonstration program conducted in the United
States, ultrasonic flow measurements were also under way in Japan in
eleven installations in pipes running full, seven in raw sewage and four
on return sludge, made by the Tokyo Keiki Company, Ltd. The following
table describes the performance of these installations:
Suspended Pipe
Metered Solids Diameter
Liquid Concentration and Material
(Milligrams/liter) (Millimeters)
Influent
Influent 70-100
Influent
200
Influent 10,000
Influent 120-130
Influent
4000
900
ductile iron
800
ductile iron
1600
cast iron,
rubber lining
200
steel, vinyl
lining
700
steel, poly-
urethane
lining
500
cast iron,
moltar lining
Approx.
Flow
(Cubic Meters
per Hour)
5000
3000
Remarks
27,000
2m/sec
6000
1000
Some jitter in
flow record prob-
ably due to air
bubbles from pump
operation.
Within 1% of mag
meter
98
-------
Influent
Return
Sludge
170
10,000-
20,000
600
cast iron
300
steel
Return 4400-9300
Sludge
Return
Sludge
Return
Sludge
6500
8500-16,000
300
ductile iron,
cement lining
300
cast iron
200
cast iron
4000 Within + 2.1% of
mag meter
700 Large transmission
fluctuations.
Within _2.1% of
mag meter.
500 Within +1.2% of
mag meter.
1200 Difference with
mag meter - 14%.
250 Unstable operation
In these installations, the ultrasonic velocimeter probes were attached
to the outside of the pipe wall and sound propagation is through the pipe
wall to the liquid. Note that plastic, cement or bituminous linings do
not interfere with proper operation. Tokyo-Keiki has made successful
experimental installations on open channels, ditches and rivers. In
these, level was either controlled by constant level gates or measured
with capacitance or float gages.
99
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/2-76-243
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
"WASTEWATER FLOW MEASUREMENT IN SEWERS USING
ULTRASOUND"
5. REPORT DATE
November 1976 (Issuing Date)
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
R.J. Anderson, S.S. Bell, W.H. Vander Heyden,
W.K. Genthe
8. PERFORMING ORGANIZATION REPORT NO
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Sewerage Commission
City of Milwaukee
Milwaukee, Wisconsin 53201
10. PROGRAM ELEMENT NO.
1BC611
11. CONTRACT/GRANT NO.
11024 FVQ
12. SPONSORING AGENCY NAME AND ADDRESS
Municipal Environmental Research Labortory
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
13. TYPE OF REPORT AND PERIOD COVERED
Final Rppnri- 4/71 to 9/75
. SPONSORING AGENCY CODE
EPA - ORD
15. SUPPLEMENTARY NOTES
P.O. Clifford Risley, Jr.
16. ABSTRACT ~~ ~~ ~~
A new technique for measurement of sewage volume flow utilizing ultrasonic
measurements of depth and velocity was demonstrated and evaluated. The new
technique, requiring no costly construction for installation, is usable
for open channel or partially full measurements. The flow technique can
accomplish measurement accuracies from 2 to 5% under conditions of rapidly
changing levels, surcharging, and back-up conditions. Two installations were
accomplished on existing sewers in the Milwaukee Sewage System, one 12 1/2
feet and the other 5 feet in diameter. A continuous flow record was displayed
for each meter and performance of the meter installations was compared with
magnetic flow meters at one site and head velocity relations on the other site.
Relationship between average volume flow, water level, and average velocity
along selected horizontal chords of the sewer cross section were determined.
The unit installed on the 5 foot diameter sewers operated for a period in excess
of 18 months without failure and has required only routine maintenance. The
flow technique provides accurate measurement over a range of depths from 25%
to full depth in the sewer and from zero to the full flowing velocity of the
fluid in the sewer. No deterioration of ultrasonic transducer probes has
been detected indicating their suitability for use in the sewer environment.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COS AT I Field/Group
Flow, Sewers, Flowmeters, Combined Sewers,
Field Tests, Ultrasonic Frequencies, Flow
Measurement
Ultrasound Flowmeter,
Sewer Environment,
Ultrasonics
13B
3. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report)
UNCLASSIFIED
20. SECURITY CLASS (This page)
UNCLASSIFIED
21. NO. OF PAGES
_ 110
22. PRICE
EPA Form 2220-1 (9-73)
Too"
U. S, GOVERNMENT PRINTING OFFICE: 1978 — 657-060/1515
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