United States
Environmental Protection
Agency
Office of Water Enforcement and
Permits Enforcement Division (EN-338)
Washington, DC 20460
September 1981
Water
rxEPA
NPDES
Compliance Flow
Measurement Manual
MCD - 77
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NOTES
To order this publication MCD-77 "NPDES Compliance Flow
Manual", write to:
General Services Administration (8BRC)
Centralized Mailing Lists Services
Building 41, Denver Federal Center
Denver, Colorado 80225
Please indicate the MCD number and title of publication.
Multiple copies may be purchased from:
National Technical Information Service
Springfield, Virginia 22151
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NPDES GOMPLIANCE FLOW MEASUBEMENT MANUAL
U.S. Environmental Protection Agency
September, 1981
by:
David L. Guthrie, P.E.
Office of Water Enforcement: and Permits
Enforcement Division
Compliance Branch
26355
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DISCLAIMER
This manual has been reviewed by the Office of Water Enforcement and
Permits, U.S. Environmental Protection Agency, and approved for publication.
Mention of trade names or commercial products constitutes neither endorsement
nor recommendation for use.
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ACKNOWLEDGEMENT
The author wishes to express his appreciation to the staff of the EPA
Compliance Branch, Enforcement Division, Office of Water Enforcement and
Permits, for their assistance provided in the preparation of this Manual.
Special thanks are owed to Mr. Gary Polvi for his continued support throughout
the project and to Mr. David Rogers for his technical review and assistance in
producing the manual. Mr. Rogers' comments and suggestions proved to be
invaluable.
The author also would like to acknowledge the efforts of the engineering
staff of JRB Associates, Inc. for their technical assistance in preparing some
of the background materials used herein.
iii
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NPDES COMPLIANCE FLOW MEASUREMENT MANUAL
Table of Contents
Disclaimer ii
Acknowledgement iii
Table of Contents iv
List of Illustrations vii
List of Tables ix
Foreword 1
Introduction 3
Basic Methods 10
Weighing the Discharge 10
Volumet ric Methods 11
Sump Pumps 13
Orifice Buckets 15
Weirs 17
Sharp Crested 17
V-Notch 19
Rectangular 22
Cipolletti 27
Other Weirs 30
Submerged Weir Conditions 32
Correcting for Velocity of Approach 34
Weir Inspections 36
Broad Crested 37
iv
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Table of Contents
(Continued)
Page
Flumes 39
Farshall 39
Palme r-Bowlus 48
Pltot Tubes 51
Methods Used To Measure Water Height (Head) 56
Stevens Meters or Drum Recorders 56
Manning Dippers 58
Belfort Liquid Level Recorders 61
Sonics 63
Gauges 65
Scow 65
Bubblers 67
Charts/Calibrations 71
Energy Grade Line Calculations 71
Orifices 76
Nozzles • 79
Venturi Flowtneters 84
Open-Pipe Methods 87
California Pipe Method 87
Purdue Method 90
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Table of Contents
(Continued)
Open Channel Measurements 93
Flow From Vertical Pipes 93
Equations 93
Velocity-Area Method 100
Stream Gauging 105
Current Meters 106
Dilution Methods and T racers Ill
Dilution 112
Slug vs. Constant-Rate Inj ection 112
Exotic Methods 115
Elect romagnetic Flowmeter 115
Acoustic Flowmeters 115
Electrical Methods 119
Summary 120
Appendix
vi
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List of Illustrations
Figure Page
1. Sharp-Crested Weir Nomenclature 18
2. Three Common Types of Sharp-Crested Weirs 20
3. Flow Rates for 60° and 90° V-Notch Weirs 23
4. Discharge Curve for 90° V-Notch Weir 24
5. Suppressed Rectangular Wei r 26
6. Nomograph for Capacity of Rectangular Weir 28
7. Discharge Curve for 10" Rectangular Weir 29
8. Discharge Rate vs. Weir Head for Cipolletti Weir 31
9. Submerged Weir Calculations/Ratios... * 33
10. Typical Suppressed Weir in a Flume Drop 40
11. Configuration for a Standard Parshall Flume 41
12. Parshall Flume Discharge Curves 44
13. Typical Flume Submergence Flow Rate 45
14. Parshall Flumes - Typical Installation and Capacity Curves 46
15. Discharge Curve for a 6" Parshall Flume 47
16. Typical Installation of a Temporary Flume 49
17. Pitot Tube Measures Velocity Head 52
18. Graph for Converting Velocity Head to Velocity 54
19. Horizontal Drum Water-Stage Recorder 57
20. The Manning Dipper™ 59
21. Typical Installation of a Manning Dipper™ 60
22. Belfort Liquid Level Recorder 62
23. System Layout of a Sonic Water Level Meter 64
24. Hook and Staff Gauges 66
vii
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List of Illustrations
(Continued)
Figure Page
25. Typical Installation of a Scow... 68
26. Typical Installation of a Bubbler 69
27. Typical Strip Chart Recorder and Strip Chart. 72
28. Surcharging Sewer Schematic 75
29. Orifice Shapes and Their Coefficients 77
30. Flow Nozzle in Pipe 80
31. Kennison Open Flow Nozzle 83
32. Venturi Meter 85
33. California Pipe Flow Method 89
34. Discharge Rate vs. Flow Depth for California Pipes 91
35. Purdue Method of Measuring Flow from a Horizontal Pipe 92
36. Approximating Flow From Vertical Pipes 94
37. Hydraulic Elements for Circular Sewers. 97
38. Depth Ratio vs. Area Ratio 98
39. Nomograph Based on Manning's Formula 99
40. Determining Mean Velocities 103
41. Assembly Drawing of Price Type AA Current Meter 107
42. Type "A" Crane and Current Meter Assembly 108
43. Ott-Type Horizontal Axis Current Meter 110
44. Constant Rate and Slug Injection Methods 113
45. Typical Magnetic Flow Meter 116
46. Ultrasonic Flowraeter 118
viii
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List of Tables
Table Page
1. Flow Measurement Methods 9
2. Volumetric Formulas 11
3. Values of C for V-Notch Weirs 21
4. Exponents in the Free Discharge Equation for Submerged Weirs 34
5. Calculating Velocity of Approach for a Sharp-Crested Weir 35
6. Advantages and Disadvantages of Parshall Flumes 42
7. Submergence Ration vs Throat Size In Parshall Flumes 42
8. Flume Checklist 50
9. Features of the Belfort Liquid Level Recorder 61
10. Values of n to used with the Manning Equation 96
/
11. Values of K and K for Circular Channels 101
12. Comparison of Merits of the Dilution Method Ill
ix
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FOREWORD
The subject of flow measurement is not new. One of the first to recognize
the relationships between area, velocity, and quantity of flow was Hero of
Alexandria about 150 B.C.! The science of hydraulics evolved during the
Renaissance — Torricelli (1608-1648) developed the concept of velocity head in
the early 1600s. In fact, many of the formulas presented in this manual
have their roots in the 18th and 19th centuries. Several scientists have made
outstanding contributions to the field of hydraulic engineering in this period.
r
/ Flow measurement is now an integral part of the National Pollutant
Discharge Elimination System (NPDES).2 To comply with the permit require-
ments established under NPDES, the wastewater discharger or permittee must
determine the quantity of wastewater generated^"?
Most effluent permit requirements are expressed in terms of mass loadings
instead of pollutant concentrations to enable the regulatory agency to deter-
mine more accurately the permittee's compliance status. Mass loadings are
quantities of pollutants per some unit time. For example, kilograms per day is
a common mass loading expression.
Pollutants vary from the standard indicators of aquatic environmental
quality — pH, temperature, color, odor, suspended solids (SS), biochemical
oxygen demand (BOD), chemical oxygen demand (COD), turbidity, etc. — to some
of the more toxic substances — pesticides such as dieldrin, DDT, and mirex,
heavy metals such as mercury, cadmium and selenium, and carcinogens such as
PCBs and asbestos. The pollutants and limitations specified in NPDES permits
vary from permit to permit, but in most cases they are not expressed in
concentrations except where the flows are extremely variable and usually
small.
-1-
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The Compliance Branch, EPA Office of Water Enforcement and Permits, has
compiled several compliance inspection manuals. They are:
• NPDES Compliance Sampling Inspection Manual, 1979.
• Interim NPDES Compliance Biomonitoring Inspection Manual, October
1979.
• NPDES Compliance Evaluation Inspection Manual, January 1981.
These manuals present the legal considerations and ramifications of
compliance inspections, planning inspections, inspection types, general
information on health and safety, and post inspection activities including
completion of inspection forms. These procedures and discussions will not be
repeated in this Flow Measurement Manual. For more information, please refer
to any of the above manuals.
The NPDES Compliance Sampling Inspection Manual includes a small section
on flow measurement, but its scope is limited. This Flow Measurement Manual is
designed to furnish enough additional information on flow hydraulics to whet
the appetite of the curious investigator and lead him/her in quest of more
detail elsewhere.24
It is anticipated that field surveillance personnel from State and Federal
environmental regulatory agencies will represent those interested in flowrate
measurements for compliance monitoring purposes. This manual is directed
towards meeting the needs of this group of students. To the extent possible,
material is presented with emphasis on practical applications. Theory is
presented only for the purpose of conveying basic concepts; technical
references are cited for those students interested in pursuing the more
theoretical considerations and exploring the field at length.
-2-
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INTRODUCTION
Flow data are needed for two basic reasons. First, as previously
explained, mass loadings are usually specified in NPDES permits. Since the
flow multiplied by the unit concentration (and by the appropriate conversion
factor) is equal to the mass pollutant loading, properly obtaining flow data is
as critical to calculating pollutant loadings as good sampling and analysis
techniques are to ascertaining pollutant concentrations.
Second, the current compliance strategy depends heavily on the submittal
of self-monitoring data by each permit holder. The NPDES inspection, then,
should verify the data collected by the permittee, support any enforcement
action if necessary, and eventually provide a basis for NPDES permit reissuance
or revision.
Collection of Flow Data
Flows are measured in two ways — instantaneous and continuous.
Instantaneous flows must be determined at the time samples are taken for
analysis to calculate the pollutants discharged at a particular instant. In a
continuous flow measurement system, the flows are totalled to obtain a value
for total flow, used to verify NPDES compliance. If the NPDES inspector
desires to obtain an instantaneous flow, he/she must check the device installed
by the permittee and also determine the correct instantaneous flow by using
his/her own measurement technique and/or portable equipment. Such equipment
-3-
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will be discussed later. If the NPDES inspector desires to obtain a value for
total flow, he/she must use a continuous flow measurement system.
A word of caution should be inserted at this point. It is very common for
authors to use ,the term "flowrate" when describing flow. To avoid confusion,
the terms flow and velocity will be used in this text. Flow is the quantity of
fluid per unit time (e.g., gallons per day), whereas velocity is a distance
over unit time (e.g., feet per second).
Flow Measurement Systems
A flow measurement system is required to obtain continuous flow data. It
is constructed so that it has predictable and measureable hydraulic responses
related to the flow of the water or wastewater through it.3 A standard flow
measurement system consists of the following five components:
FLOW-
FLOW DEVICE
V
FLOW SENSOR
DISCHARGE
I
TRANSMITTER
RECORDER
FLOW TOTALIZER
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The primary element in the system is, of course, the flow device by which
the flow can be measured. Flow devices include weirs, flumes, venturi or
orifice meters, magnetic flow meters, among others.
The flow sensor measures the height (or head) of the water or wastewater
over or in the flow device. The flow sensor can be a probe, a float, or a
series of pressure cells, for example.
The flow sensor is connected to the flow recorder by means of a trans-
mitter. The transmitter can include electrical conductors, wires or cables,
etc.
Now that the signal has arrived at the recorder, it is transformed into a
unit of flow by a mechanical, electromechanical, or electronic system. This
system displays the flow per unit time once the flow measurement system has
been initially calibrated. Common displays are strip charts, circular charts,
or inputs into a mini-computerized data file by data elements.
More advanced systems include a flow totalizer attached to the recorder.
Basically, the flow totalizer displays total flow on a real time basis, cal-
culated by taking the integral of the value of the height of water over the
gage over time.
It is important that the NPDES inspector check the permittee's flow
measurement system. Is instantaneous or continuous flow measurement required
in the NPDES permit? If the flow must be measured by a flow measurement system
-5-
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and there is none on-site, then the NPDES inspector should install a temporary
device. This task is difficult and time-consuming and should be avoided if
possible. If a primary flow device has been installed by the permittee, and if
only a reading of instantaneous flow is desired, then only a flow sensor,
transmitter and recorder should be installed. Of course what is required
depends on the conditions stated in the NPDES permit.
A brief discussion should be inserted here about precision and accuracy of
flow measurement systems. Precision and accuracy have distinctly different
meanings. Precision is used to describe data reproducibility, or the ability
to obtain approximately the same data from repeated measurements of the same
quantity. Accuracy is the lack of deviation from a known true value. For
example, if a series of measured flow values are 3.0, 3.1, 2.95, 2.98, and 3.05
million gallons per day (mgd), but the true value is 3.75 mgd, the measurements
are very precise but not accurate. If the measured values are 3.6, 3.8, 3.75,
3.7, 3.85 mgd, they are fairly accurate but not precise.
The accuracy of flow measurement devices varies widely with the device,
its location, the environmental conditions (e.g., is it submerged?) and other
factors such as maintenance and proper calibration. Normally error greater
than +10% is considered unacceptable for NPDES compliance assurance
purposes.^ However, error values of +25% are not uncommon in some cases. In
fact, one EPA region determined that approximately 50 percent of those sampling
stations surveyed had no flow measurement devices of any kind, and it was
frequently necessary to Install temporary flow measurement equipment.4
-6-
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When evaluating a flow measurement system during a compliance inspection,
the inspector must consider four items:
(1) Does the system/device measure the entire flow? — Sometimes the
permittee's flow measuring device is too far upsteam.
(2) Is the permittee's system accurate? — There are two ways to check the
permittee's flow measurement system. First, the inspector can take an
independent flow measurement with other equipment or by another method.
Second, the inspector can check existing equipment to see if it is
properly installed, calibrated, and in good working order.
(3) If the permittee's equipment is found to be inaccurate and the problems
cannot be corrected, should new equipment be installed? — This is a
recommendation that the inspector should include on the Deficiency Notice*
or suggest during the post-inspection debriefing with the permittee.
(4) Does the permittee have a regular calibration and maintenance program for
the flow measurement equipment? — If not, such a program should be
recommended.
Methods/Types of Flow Measurement
There are many methods and types of flow measurement and flow measurement
devices. This manual will not discuss all of them in detail, but it will
present the ones most commonly seen in the field. The most common methods
*The Deficiency Notice (EPA Form 3560-4) is used by the inspector to alert
the permittee to deficiencies in their self-monitoring procedures.
-7-
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are listed in Table 1. They vary in > sophistication from the "throw-the-
pingpong-ball-in-the-stream-method" to radioactive tracer studies. The former
method is a last resort method to be used when nothing else is available, and
the latter method is not recommended because it may have an adverse affect on
the environment..
Three hydraulic situations will be encountered in the field:
• Open channels
• Closed conduits
• Outfalls
Types of flow measurement applications will now be described to measure flows
in each of these situations.
-8-
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TABLE 1
FLOW MEASUREMENT METHODS
1. Weighing the discharge
2. Volumetric discharge measurement
3. Sump pump calibration
4. Orifices
5. Standard weirs
6. Parshall flumes (Venturi flume)
7. Palmer-Bowlus flumes (critical-depth meters)
8. Nozzles (contracted openings)
9. Pitot tubes
10. Water height measurement and calculation methods
11. Venturi meters
12. Open-pipe methods (California and Purdue)
13. Tracers (chemical and radioactive)
14. Current meters
15. Magnetic flowmeters
16. Acoustic flowmeters
17. Electrical methods
18. Salt-velocity and dilution methods
-9-
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BASIC METHODS
There are four basic methods for determining flow — weighing the dis-
charge, volumetric methods, sump pumps, and orifice buckets. They are all
useful but rather primitive. However, they are convenient and fast.
Weighing the Discharge
This procedure is easy and quick. First, a container must be selected in
which to collect the discharge. Its size depends on the relative volume of
discharge. This method should only be used primarily for small flows in the
range of 25 gallons per minute (gpm) or less. Another estimating value to
determine if this method should be used is the container should take more than
two or three seconds to fill. The longer the container takes to fill, generally
•
the more accurate this method will be. A handy container is a standard plastic
or metal bucket.
After the container has been selected, weigh it empty. This weight is
called the TARE WEIGHT. After weighing, collect a quantity of water or waste-
water while using a stopwatch to time how long the container takes to fill.
Then the weight of the full bucket minus the tare weight equals the weight of
the fluid. To convert the fluid's weight to gpd, use the factor 8.347 Ib/gal
water.
Example ; If a bucket takes 5.1 seconds to fill, the tare weight is 1.4
Ibs. , and the total weight is 16 Ibs. , what is the flow?
16 - 1.4 = 14.6 Ibs. water x 0 0/_ ,. — -. — =- = 1.75 gal
8.347 Ibs /gal
-^ — —= 0.343 gal/ sec x 60 sec/min » 20.6 gpm
O • X S6O
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Volumetric Methods
Volumetric flow measurement methods have the advantage of being easy. A
volumetric measurement is simply a measurement of the amount of time it takes to
fill a container. Different types of containers can be used depending on their
availability.
Some of them are listed below with their corresponding volumetric
formulas.
TABLE 2
Container Type
Sphere
Right Cylinder
Rectangular Cylinder
Triangular Cylinder
Elliptical Container
Frustrum of a Cone
V
V
V
V
V
V =
Formula
1/6 TT D3
1/4 TT D2h
HLW
1/2 HBL
TT BDH
(where B is
TT
Cone
V = (1/12) TT D2H
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TABLE 2 (Continued)
Container Type
Parabolic Container
Formula
V= (2/3) HDL
In the above formulas,
D = diameter
h, H = height
L = length
W = width
B = base
For this method to approach accuracy, the minimum filling time should be
about 10 seconds, and the flow should be less than 30 gpm. Fill the container
*•
three times while timing it with a stopwatch, and average the results.
Exanple: It takes 15.2, 15, and 15.8 seconds to fill a bucket with the
dimensions, Dj = 8 in., D2 = 10 in., H = 11 in. What is the flow?
V
V
t
DiD2 + D22)
3.1416
(11) (82
102)
703 in3 x (1 ft3/1728 in3) = 0.41 ft3
15.2 + 15 +15.8 . 15>33
Q = 0.41 ft3/15.33 sec = 0.027 cfs x °-64^
1
cfs
Q » 0.0173 mgd = 0.017 mgd (or even 0.02 mgd)
In this example and in the rest of this manual, 0 is the quantity of water or
the flow.
-12-
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Sump Pumps
Often, the NPDES Inspector will have to calculate flow based on the dis-
charge or overflow from a sump pump. Many pumping stations still discharge raw
or disinfected sewage directly to watercourses, so a method to calculate flow by
using the sump pump is very useful. Because many pumping station discharges
have either underwater (submerged) or inaccessible outfalls, the best method
calculates flow in direct proportion to the kilowatt hours used by the station.
A summary of the sump pump method follows. The entire method, with
corrections by the author, appears as appendix 1.5
If the flow, Q a kwh used*, then the volume pumped per pump cycle is:
Vp = Vs + Qitp
where:
Vp = volume pumped/cycle (gal)
Vs = storage volume of the wet well (gal)
Q! = flow of the influent sewer (gal/sec)
t = time pump runs/cycle (sec)
* a means "is directly proportioned to"
-13-
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The error introduced is the flow into the sump during the pump cycle. To
correct this error, a station constant must be calculated, based on the
station's electrical meter:
/ t
1,000 Vs ( 1 + -
C = — =*-
nKh
where:
C - station constant (gal/kwh)
tf = time required for wet well to fill (sec)
n = number of revolutions made by the meter disc per one pump cycle
Kfo = meter constant (watt-hours/revolution)
Thus the flow can be calculated:
0 = * *—
xavg t
where:
Qavg = average flow for the period (gpm),
C = station constant (gal/kwh),
EC «• kwh reading at the beginning of the period,
E = kwh reading at the end of the period, and
t = elapsed time between observations E*- and E«- (min).
0 1
The meter should be read at an interval greater than one hour.
• If the instantaneous flow is desired, it is equal to the flow of the
influent sewer. To calculate the Q.. (see Appendix I):
-14-
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whe re:
Q^ = flow of the influent sewer (gal/sec)
Vg = storage volume (gal)
tf = time required to fill the sump (sec)
However, three notes of caution should be mentioned:
(1) When both pumps are operating together instead of alternately in stations
with more than one ejector pump, the force main will choke, decreasing the
head loss (!IL) and thus decreasing the efficiency.
(2) Pay attention to meter multipliers (e.g., one notch = 4 kwh).
(3) In pneumatic ejector stations versus pumping stations, the "batch" volume
of discharge will be constant because the pressure vessel discharges under
forced air pressure when full.
Orifice Bucket
The Orifice Bucket technique for measuring wastewater flow is a step up
from the "bucket and stopwatch" technique. It involves the use of an orifice
bucket, which is basically a five gallon bucket modified by cutting holes in the
bottom and plugging the holes with rubber stoppers for calibration. The flow is
a function of the depth of wastewater in the bucket, or Q = + (h), where h is
the hydraulic head.
-15-
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A graduated piezometer tube on the outside is used to read the water levels. A
dispersion device like a screen should be mounted in the bucket to reduce direct
velocity impingement on the orifices. The orifice bucket can be used to
calculate a range of flows from 7 to 100 gpra.
A calibration or rating curve family should first be developed in the
laboratory by removing one of the rubber stoppers and determining the flow rate
through the orifice at different constant heads with a known, variable water
source.^ it should generally look like the following:
gpm
A constant head is required to achieve accuracy with the orifice bucket
method, so it should not be used for variable flow discharges.
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WEIRS
As previously stated, there are three basic types of hydraulic conditions
— closed conduits, open channels, and outfalls. Weirs are a commonly used flow
measurement device and are found in many field situations. They are one of the
three kinds of devices normally employed to measure open channel flow. The
other devices, which will be discussed later, are flumes and meters. Weirs are
the most simple and reliable of the three devices.
Sharp-Crested Weirs
There are two basic categories of weirs — sharp crested and broad-
crested. In each of these two categories, there are many types of weirs.
A sharp-crested weir is a very thin plate, perpendicular to the flow.
Most sharp-crested weirs are less than 0.25 inches thick, and many are about
0.10 inches thick. The weir's top edge is often chamfered towards the
downstream face. Water or wastewater flows over the weir and the flow is
directly proportional to the head or height of water over the weir. A side view
of an ideal sharp-crested weir is shown in Figure 1. From Figure 1, several
important conclusions can be drawn:
• There must be a straight run of water to the weir, usually at least 20
times the total height of the weir head (H).
-17-
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= APPROX. 0.1'
POINT TO
MEASURE
DEPTH, H
20 H
I*-
: 2.S -to 4.OH
or
max
STRAIGHT
INLET RUN
SHARP - CRESTED WEIR
MAPP6
max
disch
level
FIGURE 1
SHARP-CRESTED WEIR NOMENCLATURE
(SIDE VIEW)
-18-
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• The depth of water flow over the weir, or the head, h, must be measured
at a distance approximately 4 times H behind the weir.
• The point where water springs freely over the weir is called the nappe.
• The height of the weir must be at least 2 times the maximum head.
K in Figure 1 is the width of the weir itself. The variable, X, is the
height of the weir to the bottom of the notch, and H is the head over the weir.
This terminology will be used as much as possible from here on. Deviations will
be explained to conform with standard nomenclature.
V-Notch Weirs
The most common kind of sharp crested weir encountered in the field is the
V-notch weir. A standard V-notch weir is shown in Figure 2. Remember, X is
often H, and Hmax is often h^^ Theta (9), the angle of the
notch varies, but the standard angles used are 90°, 60°, and 45°. If a primary
flow measurement device must be installed on-site by the NPDES inspector, the
V-notch weir is a good candidate. A portable adjustable V-notch weir made of
plexiglass with a rubber skirt can be obtained.*
* N.B. Products, 35 Beulah Road, New Britain, PA
-19-
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Max Level
RECTANGULAR WEIR
{CONTRACTED;)
j^mox
I
•
4-'l slope^X^
~HY
CIPOLLETTI WEIR
/ ^max
-I-
TRIANGULAR OR
V-NOTCH WEIR
L at least 3Hmax
X at least
t
X
I
max
FIGURE 2
THREE CCX4MON TYPES OF SHARP-CRESTED WEIRS
-20-
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The formula for the V-notch weir
Q = CH 5/2 - CH 2»5
where: Q » flow (cfs)
C » weir constant
H » head over the weir (ft)
If the notch appears as:
and:
and:
then: Q - 2.5(tan-|-)H5/2
To find the weir constant, C, just use the following table:
TABLE 3
9
22.5°
45°
60°
90°
C
0.497
1.035
1.443
2.50
-21-
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The C for a 90° V-notch weir is 2.5, or the same as the value in the weir
formula, because the tangent of 90°/2 = 45° is 1.0.!
So the NPDES inspector must:
(1) Measure the V-notch angle, 9, or find it from plant records,
(2) Measure the height or head over the weir, H, usually with a measuring
stick,
(3) Then find the instantaneous flow with the above formula for V-notch weirs.
Nomographs and rating curves can also be used to determine flow. On-site, they
are easier and faster to use for rough estimates, especially under adverse
weather conditions. A nomograph is Figure 3, and a rating curve is Figure 4.
An excellent reference which contains families of rating curves may be obtained
o
from the Chicago Pump Company.0
Rectangular Weirs
A standard rectangular sharp-crested weir front view is shown in Figure 2.
There are two types of rectangular weirs — contracted and suppressed. When
approach conditions allow complete contractions at the ends and at the bottom
(the free-fall of the weir head is completely within the notch area), the weir
is called a contracted weir. If a rectangular weir is in a flume or channel so
the sides of the flume are the ends of the weir; there are no side contractions,
-22-
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-4OO
r3OO
•200
T co S
-80
w
r€o ^
r s
-40 z
•3O o
i-20
UJ
rIO
'. Q
:«
•
-4
•
r3
:
r2
:L5
.24
•20
-IS
" *
-w
^
-12
*•
rK>
r8
•5
•4
.
-3
t
•2
•
B
-1
FIGURE 3
FLOW RATES FOR 60° and 90° V-NOTCH WEIRS
-23-
-------
r .
J •
I
SO
100
ISO 200 250 300 350 400
DISCHARGE IN THOUSANDS OF GALLONS PER DAY
480
500
FIGURE 4
-------
and the nappe does not contract from the width of the channel, this second type
of rectangular weir is a called suppressed weir.9 A contracted rectangular
weir is shown as Figure 2, and a suppressed rectangular weir is Figure 5.
The formula for a rectangular weir is:
Q = CLH3/2
whe re:
Q = flow (cfs)
C = weir constant
H = head or height of water over weir (ft)
L = weir length (ft)
However, if the velocity of the water approaching the weir is great
probably because the length of the cross-section over which the flow falls is
large, it is best practice to correct for the approach velocity by using the
equation developed by Francis in 1823;1
Q = 3.33 (L - 0.lnh)h3/2
whe re:
Q = discharge (cfs)
L = weir length (ft)
n = number of end contractions
h = head = H - H, where H = normal head level
-25-
-------
FIGURE 5
SUPPRESSED RECTANGULAR WEIR
-26-
-------
In reality,
Q - 3.33U - 0.1 nH)H3/2
For a suppressed weir (see Figure 5):
n « 0
Thus, Q - 3.33LH3/2
For a contracted weir (see Figure 2):
n - 2
Thus, Q -..3.33(1 - 0.1 (2)H) H3/2
Q •= 3.33(1 - 0.2H) H3/2
In the field, nomographs and rating curves can be used to calculate flows
over rectangular weirs. A nomograph appears in Figure 6; a rating curve is
shown in Figure 7.
Cipolletti Weir
Efforts to compensate for problems with end contractions causing increased
turbulence in the flow over the weir led to the development of the Cipolletti
weir in 1894.^»11 The Cipolletti weir is shown in Figure 2. Its
formula is:
Q - (2)
-27-
-------
L5-
20 J
2.5-j
30-i
ui
4.0| -T
• ac
II
5X54*
I*
ssl 5
10.0-i
8000x45
o 5°°°^
n
c
5 " c
0.2 •
£ OJ02-
-'
200-
2SO-
Mott: oo»«d on Fronei* *«ir formuta at fo<(ew«:
Q * 3.33 LH ^ (for tupprwud OTII
Of
OCIW
0.005-^
Wh«rt:
9000--20
looooT
9000
80CO-J
60C04
5000^
4000-£9
3000-?7
|-6
2000-3T
>4
i £
z looo-t
-Ofl
| 300|TO-7
a
o
UJ
(O
UJ
c.
Uf
UJ
u
ai
u
o
o
5- 0.6 2
3-0.3 2
a 200T
1-0.4
( LH^2 -0.66 H*/2(for ««troct«d
««ir vitk tvo Md cot«traeiiofi*)
0- dlachargt, in cubic ft«t ?«r
L.- I«i«4t1t of Mir, n f««t.
n * w^Ofl IA
FIGURE 6
NOMOGRAPH FOR CAPACITY OF RECTANGULAR WEIRS
-28-
-------
120
180 240 300 360 420 480
DISCHARGE: THOUSANDS OF GALLONS PER DAY
540
600
FIGURE 7
-------
where Z is the ratio of the slope of the modified contraction as follows:
vertical
horizontal
thus, Q =6.36^LH3/2
where,
4:1 (optimum)
H
T
A family of curves has been developed for Cipolletti weirs to ease field
computations. It appears as Figure 8.8
Other Weirs
A variety of other sharp-crested weirs exist. Their formulas can be found
in hydraulic handbooks^, but their field use is extremely rare. They are:
Weir Type
Pictorial (Front Visa)
Inverted Trapezoidal
Poebing
Approximate Exponential
Approximate Linear
Proportional/Sutro
-30-
-------
100,
Length of Weir
9 ft
3 ft
A
50-
-. '-• • !-/////-/ ~S^i
.^y/////-- --
JL.^- '-'.-f=-- --"•"•'-- ^'f/.^Af / / *~frr~_
•-•-•-^--•"-^^.-•rr^/Tv^yy./—'/'?^-''^
/--/^:--
/ /
— 0.5.
.c ft
0.4
O.Gs
/// / //
////// - ,
7//X = /.^^:tAK-a^^^>
o.oile
0-01
0.05 0.1
•1 1 I '.. I
a.5 i.o
i— i i | i i M |
5.0 1C
I . I
50 IOC
Weir Head (feet)
FIGURE 8
DISCHARGE RATE VS WEIR HEAD FOR CIPOLLETTI WEIRS
-31-
-------
Submerged Weir Conditions
A submerged weir is a sharp-crested weir that is completely underwater. A
pictorial and rating curve appears as Figure 9.' Mavis developed a formula in
1949 by which to calculate flow under submerged conditions.?»12 for all
weir types, the formula is (see Figure 9):
Q / 0.40
-^-- 1- 0.45S +
2(.10-10S)
where: Q = Discharge for submerged condition in cfs
Ql = Free discharge (H2 < 0) in cfs
a2
where:
&2 = weir area corresponding to H2
a^ = weir area corresponding to H^
It is interesting to note that tests made more than 230 years before by Foleni
(1717) agreed within +2 to +4% with Mavis1 data!
A Graphical Solution for a submerged weir using Figure 9 assumes the
following:
Ql m discharge at HJ, computed from the equation for the unsubmerged
free discharge*
Thus,
Ql - CHf
-32-
-------
IF
Submerged Weir
10
Q9
0.8
Q7
ae
05
CM
oil
Discharge for submerged
condition in cfs
QfFree discharge (H2^ 0) />7 c/s
n 'Exponent In the free c/iscftarge
f quafion, Q, = CH"
Curves 'are based on fesfs reported
by Vi/lemonfe and Mavis
0.2 0.3 Q4 0.5 O.fa 0.7 0.8 0.9 10
H2 ,/H2\n
FIGURE 9
SUBMERGED WEIR CALCULATIONS/RATIOS
-33-
-------
where:
TABLE
Weir Type
V-notch
Rectangular
Cipolletti
n
5/2 =2.5
3/2 = 1.5
3/2 = 1.5
Example; Determine the discharge of a submerged 90° V-notch weir if
0.9 ft, and H2 = 0. 3 ft.
= 2.50 Hi'
Q! = 2. 5(0. 9)2' 5 = 1.92 cfs
Using curve 3 in Figure 9 to solve the problem.
/H2\n /0 3\2.5 2.5
(-L\ =( U'J ) = (0.333) = 0.
W \ 0- 9 /
064
~ = 0.064, then — =0.972
Q - 0.972Qi = 0.972 x 1.92 «• 1.86 cfs
Correcting for Velocity of Approach
As in the case of rectangular weirs, the velocity of approach can become a
significant factor in the accuracy of the flow measurement. The NPDES inspector
must first remove all trash, slime, and garbage obstructing free-flow over the
weir. If quiesent conditions are not met, and if the velocity, V, is much
greater than 1 fps (measured commonly with a current meter stuck in front of the
weir), it is best to correct for velocity of approach error.
To do this, the most famous hydraulic equation, Darcy's Law or the law of
Continuity, is used:
-34-
-------
i
1
,
'•
J
J
3
3
v
V0.
D.4
.5
.A
.7
.8
.9
.0
.1
.2
.3
.4
.5
.6
.7
.8
.9
i.O
M
t.2
(.3
t. 4
LS
r.6
-
'.B
.9
.0
a a»s
.
.178
.189
.199
1
1.0
1.004
.DOS
.008
.Oil
.014
.018
.022
.1126
.0:»1
.036
.041
.047
.052
.OS9
.005
.072
.079
.087
.094
.102
.110
.119
.128
.137
.146
.155
..165
l.S
1.002
1.004
1.005
1.007
1.009
1.012
1.015
1.017
1.021
1.021
1.028
1.1132
1.035
i.040
1.045
1.049
1.055
LOGO
1.065
1.071
1.077
1.083
l.OKH
1.095
1.100
1.108
1.115
ft
1
2.0
1.002
.003
.004
,000
.007
.009
.011
.013
. Oifi
.018
.021
.024
.027
.an
.034
.038
.042
.046
.050
.054
.059
.063
.OSS
.073
.078
.0»3
.088
1
2.5
1.002
.0112
.003
.004
.006
.007
.009
.011
.013
.015
.017
.019
.022
.025
.027
.030
.03)
.037
.039
044
.047
.051
055
059
003
067
.072
3.0
1.001
.002
.003
.0114
.005
.0.16
.007
.009
.011
.012
.014
.016
.OIK
.021
.023
.026
.023
.031
.034
.at?
.040
.043
.046
.050
.053
.057
.061
1
3.S
.001
.002
.002
.003
.004
.005
.1X16
.OOS
.01)9
.011
.012
.014
.016
.018
.021)
.022
.025
.027
.029
.032
.034
037
.040
043
046
049
.053
:
i
i
i
4.0
1.001
.001
.002
.003
.01)3
.005
.OOS
.007
.008
.009
.Oil
.012
.014
.016
.017
.019
.021
.024
.026
.028
.030
.033
.035
.038
.041
.043
.046
5.0
1.001
.001
.002
.002
.003
.004
.005
.006
.007
.008
.010
.011
.012
.014
.016
.017
.019
.021
.023
.025
.027
.029
.032
.034
.036
.039
.041
TABLE 5
TABLE FOR CALCULATING VELOCITY OF APPROACH
FOR A SHARP-CRESTED WEIR
-35-
-------
Q = VA
where:
Q = flow (cfs)
V = velocity (fps)
A = area (ft^ or square ft)
Modified, Darcy's Law becomes:
va = q/A
where Va is the velocity of approach. From Table 5, enter Va (obtained with
the current meter), and H (measured), and read €. ^ Thus,
Qa * *Q
where:
Qa = flow corrected for Va, cfs.
(E = constant from Table 5.
Q » flow calculated by the appropriate weir formula, cfs.
Weir Inspections
For a sharp-crested weir, NPDES inspectors should note the following
during the inspection:^
• Is the plate perpendicular? Are the sides vertical in the channel?
-36-
-------
• Is the plate thickness about 0.1"? Does it have a 45° chamfer (see
Figure 1)?
• Is P + HT > 2H? Is P + HT «£ 1 ft.?*
• Does the nappe touch the upstream side? Does air circulate freely
underneath on the downstream side?
• Is H measured at about 4Hmax upstream from the weir?
• Is the channel straight and long upstream from the weir?
• Has Va been corrected for?
• Do the sides and bottom of the weir allow leaks? There should be none.
Broad-Crested Weirs
A broad-crested weir, from the side view, is much wider than a sharp-
crested weir. Lateral widths can even exceed 10 feet. There is neither a notch
nor nappe, and the weir shapes are very different. The weir notch is mounted in
a wall too thick for the water to spring past. Broad-crested weirs do not have
many advantages over sharp-crested weirs except they are relatively free from
fouling by suspended solids deposition on their leading edge. Broad-crested
weirs usually extend from bank to bank unlike sharp-crested weirs which have
their "working" section, or the notch, at mid-point in the channel (except in
the case of suppressed sharp-crested weirs which will be discussed later as a
special case) .
is "not less than"
-37-
-------
There are four types of broad-crested weirs, named for their side-view
shapes. They are:
Shapes
• Triangular
• Trapezoidal
V///////A VZ%
• Rectangular
• Irregular
In these cases the flow over the weir is from the left to the right of the
page, in this direction: Q ^
The general broad-crested weir formula is:
Q - CLH3/2
C, or the weir coefficient, can be found in any good hydraulics handbook.^
-38-
-------
FLUMES
Flumes are commonly used to measure water or wastewater flow. They can be
used alone, or in combination with some other flow measurement device (see
Figure 10).° Flumes are usually specially shaped open channel flow sections
installed in canals, laterals, ditches or at the end of unit processes to
measure flows.
Farsball Flumes
The NPDES inspector will often encounter Parshall Flumes, especially if he
is inspecting Publicly-Owned Treatment Works (POTWs). A standard Parshall
flume, originally developed in 1922 and tested in the Arkansas River Valley
between 1926 and 1930,^ is shown in Figure II.3
The Parshall flume uses the venturi principle of flow restriction. It has
the following advantages and disadvantages:"
-39-
-------
FIGURE 10
TYPICAL SUPPRESSED WEIR IN A FLUME DROP
-40-
-------
NOTE: 7.6cm(3in) TO 2.4m (8ft) FLUMES HAVE
ROUNDED APPROACH WINGWALLS
T
FIGURE 11
CONFIGURATION FOR A STANDARD PARSHALL FLUME
-41-
-------
TABLE 6
ADVANTAGES AMD DISADVANTAGES OF PARSHALL FLUMES
ADVANTAGES
1. Can operate with sraall head losses.
2. Insensitive to velocity of approach,
3. Good measurements with considerable
downstream submergence.
4. The discharge velocity is high to
eliminate sediment deposition.
DISADVANTAGES
1. Cannot be used in close-coupled,
combination structures (See Figure
10).
2. More expensive than weirs and
orifices.
3. Requires a solid, watertight
foundation.
4. Requires accurate and careful
worksmanship for satisfactory
construction, installation,
and performance.
Parshall flumes are designed by width of the throat section. A 1.0 in.
\
section can handle 0.01 second-ft (or 80 gpd) to a 50 ft-wide throated flume
which can handle up to 3,000 second-ft (or 1,944 mgd).* The discharge is not
reduced until the submergence ratio, H^,/Ha is greater than or equal to:
TABLE 7
SUBMERGENCE RATIO VS. THROAT SIZE IN
PARSHALL FLUMES
% SUBMERGENCE
50
60
70
80
THROAT
1 -
6 -
1 -
8 -
WIDTH
3 in.
9 in.
8 ft.
50 ft.
*1 second-ft = 450 gpra = 0.648 mgd
-42-
-------
Two regimes of hydraulic conditions may occur for flume flows — free-flow
conditions and submerged-flow conditions. Free-flow conditions should prevail
to obtain accurate flow measurements. When obstructions occur downstream from
the flume, or if the rated flume capacity is less than the actual flow rate,
submerged flow conditions may occur. If downstream obstructions are the cause,
these obstructions should be removed to increase accuracy.
A graphical representation of percent submergence related to percent flow
appears in Figure 12, along with a nomograph to determine free-flow discharge in
3 inch to 8 foot Parshall flumes .9 Use Figure 13 to calculate the flow in a
submerged Parshall flume.9
The flow through Parshall Flumes is easily calculated by means of families
of rating curves for various hydraulic conditions. Figure 14 shows a rating
curve and a picture of a Parshall flume.^»9 Another type of standard
rating curve is shown as Figure 15.°
It is not appropriate for the NPDES inspector to check design tolerances
of a Parshall flume unless they are readily available. However, in an NPDES
inspection, the inspector should see that:^
• longitudinal and lateral axes of the crest floor are level,
• approach flows are uniformly distributed in the upstream convergence
section,
• head measurement devices (to be discussed later) are installed at the
correct location, and
• flow variations are within the range for which the flume is accurate
(see Table 7).
-43-
-------
,100
^r x 100 = Percent submergence
H»
30 40 SO 60
PERCENT OF MAXIMUM 0
IOO
Typical discharge corves (or Parshall Humes with free flow and with submersed conditions.
No reduction
m discharge--,.
Useful range for submerged
flow from 67 to 95 percent.
Discharge begins to /
measurably reduce ,*(
at 67-70 % ,'' \
submergence, _-*' \
*
o «
j 90
U.
uj go
u
OC
u.
7O
U.
0
1- 60
Z
UJ
UJ
"" 40
Z
* 10
0
* 20
4
= 10
0
4
0
Pro
to
cticol upp
r submerc
ir lim
ence =
V
it
95%'
N
s
f*
Nof
\
I
1
!OW-,
\
i
I
0 0 20 SO 40 50 60 70 bO 9O 100
Hb
SUBMERGENCE, ;p , IN PERCENT
Typical discharse reduction caused by submersence in 1 - to 8-foot Parjhalt Humes.
iQO-
80-
~~i— 30,000
60— -
' -
- -
o
S 6
" 5^
DISCHARGE EQUATION
H0-OI«
; —8,000 5
- — 2
: ^-6,000 i
i-5,OOO K
u
7 E-1.000 "•
in
•3,000 §
5-
-I.OOO
-eoo
: i-eoo
-5OO
DISCHARGE
o
0.4 —
.-•
O.6 —
•i !
-3
-II !
-IZ1
_ -zo
•2S
-v.
-3!
HEAD
Ho
Nomograph for free-flow discharge through 3-inch It
8-foot Parshall flumes.
FIGURE 12
PARSHALL FLUME DISCHARGE CURVES
-44-
-------
UPSTREAM HEAD He, FEET
UJ BO
2
o 82
:
••
01 • O
:
,
.
'
.
0 O.Z 0.4 0.6 0.8 l.o 1.2 1.4 1.6 1.8 2.0 Z.2 2.4 2.6 2.8 3.0 5.8 3.4 3.6 3.8 4.0
DISCHARGE, SECOND-FEET
—Diagram for determining rate of submersed flow for a 6-inch Parshall flume,
Soil Conservation Service.)
(Courtesy U.S.
UPSTREAM HEAD Ha, FEET
_ eg to
10 us
TT
--
1
r
,
,,
,
;
/
I.O 1.9
2.0 2.5 3.0 3.5
DISCHARGE, SECOND-FEET
4 S 5.0 5 5 6.0
—Diagram for determining rate of submerged flow for a 9-inch Parshall flume.
Soil Conservation Service.)
(Courtesy U.S.
FIGURE 13
TYPICAL FLUME SUBMERGENCE FLOW RATE
-45-
-------
N
ta
tf>
ui
I 20
o
z
I
0 »
u
X
w
5
^ls'
.-
-- -
i
-
1
7
/
y
^ *
.1 .Z .5 .4 .9
^
i
" ' -£! J_
' -^
^ **"
jf ^
|| J|
Ik
»J
J^"
•"»
/
f
/
/
s
S
/ s
• ' /
^s* ' ^
^ —
?
/
2
/
/
^
' *
^
'
•
- •
•-
V
'
i
-
,
i
-
*-
.
7
i
' f
.-
-•
7
7
^
^ *
\4J<&
3]
fc- !
I A.
-fr--J
^ /
/
^
^
--Z
•
- - (^
^
,y" ^
^ LX* v-
X'x
•"• ^^ *^
/
/ ,
/
/
/
/
' i
' /
/ /
/
> /
/
/
/ /
'_ /
/ /
' / /
. .
'/ S
/
/'
/
1
/
J
„
2
/
I
/
r j
/
> /
/
/
/
;
J
-
•!
:'
'
-'
-
-
"
'
-
-
-
i
i
,
.
//
V
/ ,1
/ /
1 I
/ '
2 .
L /,
7
2
U '^L
m
n » •
-7- 4
K- L
t — 1
r I
?
I'.'.
€ T .• * 1 X 3 4 5 • 7 • t 10 20 JO 40 SO *O7O«0 WO
FREE FLOW CAPACITY-M.6.D.
FIGURE 14
PARSHALL FLUMES
TYPICAL INSTALLATION AND CAPACITY CURVES
-46-
-------
i
DISCHARGE CURVE
6" PARSHALL FLUME
FIGURE 15
-------
Palmer-Bowlus Flumes
A second standard flume Is the Palmer-Bowlus flume. Although not widely
used, there is a chance that the NPDES inspector may encounter this flume in the
field. A Palmer-Bowlus flume consists of a level floor, with or without
constriction, placed in a pipe (commonly at a manhole for easy access) for
approximately the length of the pipe's diameter (see Figure 16).
Palmer-Bowlus flumes have the same advantages as other flume types, but
because they are more simply constructed, they are compact and portable, which a
Parshall flume is not. To obtain accurate readings, the Palmer-Bowlus flume
should be smooth, free of debris, and level. The flume kit usually contains a
bubble level (or bullseye level) to ease leveling the flume in the field.
Figure 16 shows the flume inserted in the sewer and the tire accompanying the
flume inflated to seal the space between the flume and the sewer.
Because there are many varieties of the Palmer-Bowlus flume, a universal
rating curve or equation to describe the flow rate as a function of the hydrau-
lic head does not exist. Manufacturer's calibrated rating curves should be used
to calculate the flow.
For both Parshall and Palmer-Bowlus flumes, a handy inspector's checklist
is shown as Table 8.1-* Again, it is probably impractical in most cases for
the NPDES inspector to verify flume design tolerances in the field, especially
under adverse weather conditions.
-48-
-------
'-Inlet Pipe
Inflatable
Tire
ing
FIGURE 16
TYPICAL INSTALLATION OF A TEMPORARY FLUME
-49-
-------
TABLE 8
FLUME CHECKLIST
1. Is channel upstream of flume free of debris or deposits?
2. Does flow entering flume appear reasonably well distributed
across the channel and free of turbulence, boils or other
distortions?
3. Are cross-sectional velocities at entrance relatively uniform?
4. Is flume clean and free of debris or deposits?
5. Is crest level in all directions?
6* Are all dimensions accurate?
7. Are side walls vertical and smooth?
8. Are sides of throat vertical and parallel?
9. Is head being measured at proper location?
10. Is head measurement zeroed to flume crest?
11. Is flume of proper size to measure range of flows existing?
12. Is flume operating under free-flow conditions over existing
range of flows?
13. Is channel downstream of flume free of debris or deposits?
YES NO REMARKS
-50-
-------
PITOT TUBES
The pitot tube, invented by Henri Pitot in 1732,* is a basic device used
to measure the velocity at a point in a flowing fluid. It is still one of the
most accurate methods of measuring velocity (see Figure 17). Its optimium
accuracy is about +1% of the flow rate. ^ The pitot tube also has the
advantage of being insensitive to flow alignment, if the yaw misalignment is
less than 15°. Its application is in pipes flowing full, usually under
pressure.
Using Bernoulli's equation, the equation for the manometer, and solving
for velocity yields the equation for the Pitot tube:^°
V =
Y^-A
Vs /
whe re:
v • velocity (fps)
g » acceleration of gravity = 32.2 ft/sec^
RX = total pressure (ft)
S0 - specific gravity of mercury = 13.57
S - specific gravity of water » 1.0
-51-
-------
z////// //// / / ///// /////// / /_/./ / / / ///////////// / ////////// ///
•0
H
i
en
to
I
8
H
3
//// i / i i i r i
PITOT-STATIC
TUBE
PITOT TUBE
-------
simplifying:
28
.45 V R'
However, because of the uncertainty in the static pressure measurement
(from the center of the tube to the pipe wall), a corrective coefficient C must
be included:
28.A5C
C must be known or determined by calibration. By substituting the above equation
into Darcy's Law, Q = VA, an expression for the flow results:
A 28.45C
But this exercise is not as difficult as it seems. The graphical solution
in Figure 18 can be employed to relate velocity head to velocity under certain
flow regimes or conditions. Moreover, this discussion will only probably serve
as background information for the NPDES inspector for the following reasons:
(1) Because of high suspended solid loads in most wastewaters, pitot tubes
are impracticable due to fouling.
(2) Because the NPDES inspector will encounter flows generally in open
channels, the pitot tube will not be seen in most field situations.
-53-
-------
25 —
20
15 —
o
cu
oo
"G 10
o
-------
(3) Pitot tubes are difficult to maintain under usual field conditions, so
their use is limited.
-55-
-------
METHODS USED TO MEASURE WATER HEIGHT (HEAD)
There are many methods and types of gauges for measuring water height or
head over a weir or flume or in a sewer. All have different types of applica-
tions, but the NPDES inspector will probably see or use a variety of them in the
field.
Stevens Meters or Drum Recorders
A very common type of water stage recorder is a horizontal drum-type.
This author classifies all such recorders as Stevens meters because that is a
well-known trademark. Other product types are available.
The Stevens* recorder is a versatile, horizontal-drum, graphic recorder
where the clock positions the pen along the drum axis and the gage height
element rotates the drum (see Figure 19). Usually, an 8-day spring-driven clock
is used.^ xhe Stevens meter or recorder is usually installed in a stilling
tube, so that the float can remain level and relatively stable. The NPDES
inspector can easily make a stilling tube from PVC pipe about 1/2 to 1 inch
larger in diameter than the float with several holes drilled in the pipe below
the water line to ease water movement in the tube.
*Leupold and Stevens Instruments, Inc.
-56-
-------
—Horizontal drum water-stage recorder. The time element
records parallel to the axis of the drum. (Cour-
tesy Leupold and Stevens Instruments, Inc.)
FIGURE 19
-57-
-------
On an inspection, the inspector must note:
• Is the stilling well perpendicular to the meter?
• Has trash and debris accumulated inside the meter? (If so, clean it
out).
• Is the float dirty? Is the float perpendicular to the flow and mounted
properly in the stilling well?
• Is the cable slack?
• Has the correct chart paper been used?
• Is there ink in the pen?
• Has the clock been wound?
Of course there are other variations of recorders (e.g., vertical drums,
or gear boxes instead of pulleys), but the same principles apply.
Manning Dippers
The Manning Dipper™ is commonly used for temporary, direct flow
measurements in sewers for a variety of purposes including compliance
monitoring. The Manning Dipper is easy to install, versatile and rugged.1'
The Dipper uses a dipping-probe technique that detects the liquid surface by use
of a thin, corrosion-resistant metal probe lowered on a cable controlled by a
precision motor. The probe continuously tracks the changes in liquid level with
a regulated "dipping" action, normally maintaining its position just above the
liquid's surface (see Figure 20).20 A Dipper installed in a manhole in
conjunction with a Palmer—Bowlus flume is shown in Figure 21.
-58-
-------
FIGURE 20
THE MANNING DIPPER™
-59-
-------
Recorder and
Cable Drive System
With or Without a
Primary Flow
Measuring Device
Such as Weirs or
.Tl umes
Dipper Probe
FIGURE 21
TYPICAL INSTALLATION OF A MANNING "DIPPER"™
© Manning Environmental Corporation, Santa Cruz. Co..
-60-
-------
On an inspection, the NPDES inspector must look for:
• A bad battery (12 VDC),20
• Trash, debris clogging the probe,
• A twisted cable,
• An improperly calibrated Dipper.
The dipper must initially be calibrated by measuring the wastewater level
in the sewer by a rule or gauge, or measuring rod.
Self o rt Liquid^ Levej^ jleco rders
A Belfort Liquid Level Recorder is shown in Figure 22.* Several EPA
Regions use this recorder in their field operations. The advantages and
disadvantages of the Belfort Liquid Level Recorder are shown in Table 9.^
TABLE 9
FEATURES OF THE BELFORT LIQUID LEVEL RECORDER
ADVANTAGES
DISADVANTAGES
• Rugged
• Mechanically simple
• Reliable
• 6 hr to 8 days/chart
revolution
• Can be repaired in the
field
• Stilling well offers an
obstruction to the flow
• Hard to install
• Almost impossible to install
in manholes
*The Belfort Instrument Company, Baltimore, Maryland
-61-
-------
fr
FIGURE 22
BELFORT LIQUID LEVEL RECORDER
-62-
-------
Sonics
Ultrasonic level meters detect and measure the water surface by sonic
waves. The ultrasonic level meter consists of a sonic emitter, a sonic
receiver, and a timer (see Figure 23). Its principle of operation is the same
as that of sonar. High frequency sound waves are regularly emitted by the
meter. The sonic wave travels through air and is reflected by the water surface
to be measured. The reflected sonic wave bounces back and is detected by the
sonic receiver. The traveling time of the sound wave is accurately measured by
a built-in timer within the meter. The traveling time is converted to an elec-
trical signal proportional to the water level, and then it is fed to a recorder.
Ultrasonic level meters are widely adopted to measure liquid levels in the
petroleum or petro-chemical industries and are gaining applications in the field
of wastewater flow measurement. They do not come in contact with the wastewater
being measured. Therefore, their performance is not affected by suspended solid
loads. They are compatible with almost all open channels except gravity sewers
in a manhole. Disadvantages associated with an ultrasonic level meter include:
• inaccurate readings when foams, scums or ice are present in the
channel.
• temperature or humidity variations may cause inaccuracies in the
readings (some sonic level meters have a temperature compensating device
to alleviate these problems to some extent.)
-63-
-------
Signal Conditioner
and Recorder
Digital Display
Analog Display
Instrument
==~Ground
Transmission
Cable (Coaxial)
Sonic Emitter
and Receiver
Cross Section of
Open Channel
Endress + Hauser, Inc., Greenwood, IN.
FIGURE 23
SYSTEM LAYOUT OF A SONIC WATER LEVEL METER
-64-
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Gauges
There are many types of gauges used to measure liquid levels, but the most
common are the hook gauges and staff gauges (see Figure 24).
A hook gauge consists of a hook and a graduated gauge, which is manually
and slowly brought to the water surface before the measurement is taken. Just
as the tip of the hook is first shown on the water surface, take the reading.
Hook gauges are probably the cheapest device for measuring surface elevation.
They are especially useful for installation in the stilling well of flumes or
weirs, but their application is rather limited.
Staff gauges employ the same principles as hook gauges. A staff gauge is
a graduated scale, usually installed vertically at the point where the depth of
the wastewater is to be measured. There are many different types.
The head is read directly and corresponds to the gauge division at which
the liquid surface intersects the gauge. When using a gauge which is installed
directly in the flowing liquid, surges with flow or oscillations in the water
surface can make the accuracy questionable. Use of a stilling well will
substantially reduce or eliminate this difficulty.
Scow
A scow is a floatable block attached to the side of a manhole by a verti-
cally pivoting rod. A wire from the top center of the scow is connected to a
-65-
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HOOK GAUGE
A TYPICAL STAFF GAGE
Gauge
Vernier
Horizontal and
Vertical Levels
Level
Hook
Graduated
Scale
FIGURE 24
HOOK AND STAFF GAUGES
-66-
-------
water level recorder located at the top of the manhole (see Figure 25).
The scow is particularly useful in estimating flows in extremely deep
manholes or manholes subject to wide flow fluctuations. Even surcharging
conditions can occasionally be monitored by a scow attached to a recorder.
However, surcharging conditions can cause the following problems:^
(1) Cable slippage,
(2) Recorder destruction,
(3) Unreliability of the recorder charts, and
(4) Ink spillage.
Bubblers
Figure 26 shows a typical installation of a bubbler system for water level
measurement. A bubbler system consists of an air supply, a bubbler tube, an air
pressure-sensing device and a recorder. The air pressure-sen sing device
measures the air pressure necessary to push the bubble out of the bubbler tube
into the wastewater stream. Usually the bubbler tube is lain as close as
possible to the invert of the pipe. The air pressure thus measured by the
system is proportional to the depth of the flow.
Bubbler systems are frequently used to monitor the water level in a wet
well to control the pumping station which may use multiple pumps or variable
speed pumps. Bubbler systems are rarely used for water level measurements in
gravity sewers due to their shallower depth of flow as compared to wet well
depths.
-67-
-------
%M\ik-
^^^^^v^^^^^^^^^^^^?
•Manhole Cover
///W/tr//w//
Outlet
Pipe
FIGURE 25
TYPICAL INSTALLATION OF A SCOW
-68-
-------
Recorder and
Bubbler Source
Existing
Manhole
Bubbler Tube
jStandard
ISensing Probe
FIGURE 26
TYPICAL INSTALLATION OF A BUBBLER
-69-
-------
Bubblers can be an accurate method for measuring water surface elevations
when they are properly installed and when compatible recorders for the expected
range of flow depths are selected. They are relatively expensive and require a
reliable air supply. If insufficient air pressure is encountered, the bubbler
tubes are likely to be clogged by suspended solids in the wastewater stream.
When a portable air supply is used, frequent inspection and maintenance of the
air supply is an important routine task for obtaining accurate measurements.
Because of these problems, the NPDES inspector will rarely encounter this system
in the field.
-70-
-------
CHARTS AND CALIBRATIONS
When working with charts be sure to (see Figure 27):
• use the correct chart paper;
• initially calibrate the chart to actual conditions;
• label the chart fully;
• recalibrate the chart when it goes off-scale;
• make sure the pen has ink in it.
In calculations:
• make sure to read the graphs carefully;
• do every calculation at least twice.
ENERGY GRADE LINE CALCULATIONS
Surcharging sewers present special complex problems for the NPDES inspec-
tor. A surcharge condition exists when the wastewater height is into the barrel
of the manhole above the form groove in the base concrete. Then not only is the
sewer flowing full, but there is a certain amount of hydraulic pressure forcing
too much wastewater through an inlet not large enough to accomodate the flow,
thus increasing the velocity head.
-71-
-------
Event
Marker
TYPICAL STRIP CHART RECORDER
7
-
0
—
a
TYPICAL RECORDER CHART
FIGURE 27
TYPICAL STRIP CHART RECORDER AND STRIP CHART
-
•
-
-12-
-------
Under these conditions, flows can be calculated occasionally by computing
the energy grade line, or the total energy in any section with reference to some
elevation or datum, as it is often called. The technique is useful for
measuring flows in sewers located directly upstream from pumping stations. The
method's reliability, however, is jeopardized by only periodically measuring the
flow. A constant flow record is impracticable to obtain by this method.1^
Theoretical energy grade line calculations accounting for density, pres-
sure, velocity head, pipe friction, etc. are too difficult in the field. To
obtain a reasonably accurate flow measurement with simplified calculations, a
situation of steady-state hydraulic conditions, no pipe networks nor pipes in
series can be assumed. This method cannot be used to calculate flows in siphons
or through pumps.
The hydraulic situation is shown in Figure 28 (adapted from reference 10).
A key assumption is made that the energy grade line, for all practicable pur-
poses, is parallel to the hydraulic grade line. The datum is taken upstream
from the centerline (£) of the downstream manhole. The method is:
1. Measure the distances Y^ and ¥3 in feet along £ with a plumb line and
measuring tape by subtracting the depth from the land surface to the water
surface from the total depth from the land surface to the invert.
2. Measure or compute X in feet.
-73-
-------
LAND
i
v,
DATUM
— X-
5-t
FIGURE 28
SURCHARGING SEWER SCHEMATIC
-74-
-------
3. Calculate Y2 from the slope(s) of the sewer. Example;
if X = 350 ft and S = 0.001 ft/ft, then
Y2 - (X)(S) - (350)(0.001) = 0.35 ft
4. Calculate the slope of the hydraulic grade line (and the energy grade line
because they are assumed to be parallel) by:
Y + Y - Y
X * * X
5. Substitute Se into the Manning Equation to obtain the velocity
(see page 93 ):
1'486 Hi 1/7
V = R2/3s 1/2
6. Since the pipe is flowing full, the cross-sectional area of the wastewater
is equal to the area of the pipe, so compute the area by simple geometry:
A = IT r2 = ir(—)
4
7. Finally, substitute the velocity and area into Darcy's Equation to obtain
the flow of the surcharging sewer.
Q - VA
This algorithm is accurate enough for NPDES use in the field. It can even be
applied to infiltration/inflow analysis.
-75-
-------
ORIFICES
An orifice is an opening with a closed perimeter of regular form through
which water or wastewater flows (if it flows only partially full, then it is a
weir, and the standard weir formulas are used to calculate flow).^ The first
work with orifices was done by Torricelli about 1640, and this work lead to the
concept of velocity head.1 See Figure 29 for common orifice shapes and
coefficients.1^
Because the orifice works by velocity head, the velocity must be a
function of the force of gravity, or:
(H)
whe re:
V » velocity
g = acceleration of gravity » 32.2 ft/sec2
H « velocity head or height of water over the orifice.
because the expression for head loss, hL, is:
V2
" 28
the theoretical velocity (Vt) becomes:
-76-
-------
T?""—r-»T7»
li
a
c
A
180'
0.541
157J'
0.546
B
135"
0577
112J'
0.606
C
90'
0.632
D
67y
0.684
45*
0.753
221-
0.882
nr
0.924
sr
0949
E
0'
0.966
FIGURE 29
ORIFICE SHAPES AND THEIR COEFFICIENTS
-77-
-------
A constant must be included to relate the theoretical velocity Vt to the
actual velocity V. This constant, the coefficient of contraction, describes the
opening of the orifice. Substituting the above theoretical velocity equation
into Darcy's Law, or Q » VA, and applying C yields the discharge equation for an
orifice:
Q = Ca \/2gH '
where:
Q = flow (cfs)
C = coefficient of contraction
a = orifice area (ft2)
g - acceleration of gravity = 32.2 ft/sec2
H = head (ft)
Example; A 75-mm-diameter orifice type "B" with a - 112.5° has a head of
4.88 inches. What is the flow?
Q -
a =Trr2 = 3.1416 x *™ 0*03937 in
x
2 am
'l/2
. x 1 ft A
12 inJ
*&- [2(32-2) (4*88 in-* irfe)]
C - 0.606 (From Figure 29)
Q = (0.606X0.387X26.19)1/2 - 1.20 cfs
Note; Convert all values to proper units.
-78-
-------
NOZZLES
Experimentation with nozzles started in 1888 by John R. Freeman, who
applied his studies to fire hoses.16 The general equation for a nozzle is
almost identical to that for an orifice.-"*
Ca
where:
a - area of the nozzle,
C = constant for the nozzle, varying per the type of nozzle
g - force of gravity • 32.2 ft/sec^
h « head, ft
The flow nozzle is cheaper than a venturi meter, and it works quite well
in wastewaters with high suspended solid loads. A schematic of a flow circular
nozzle mounted inbetween the flanges of a pipe is shown in Figure 30. Notice
the high pressure and low pressure tap. A manometer is usually connected
inbetween these taps.
If a manometer is connected inbetween the taps, a manometer-derivation of
the nozzle equation must be used to calculate flow. It is:
-79-
-------
HIGH
PRESSURE TAP
' S S SSS SS SS
LOW PRESSURE TAP
ENTRANCE
CONE
L— THROAT
FIGURE 30
FLOW NOZZLE IN PIPE
(SIDE VIEW)
-80-
-------
whe re:
Q = flow (cfs)
C = nozzle constant
A2 = area at the downstream end of the nozzle (ft~)
g = acceleration of gravity = 32.2 ft/sec^
R' = gage difference (ft)
SQ = specific gravity of the manometer liquid
S]^ = specific gravity of the flowing fluid (e.g., water)*
Example:1" Determine the flow through a 6-in-diameter waterline that
contains a 4-in-diameter circular flow nozzle. The mercury-water differential
manometer has a gage difference of 10.0 in. at standard conditions (Author1 s
Note: for NPDES purposes, standard conditions can usually-.be assumed). The
nozzle coefficient is 1.056. What is the flow?
From the data given:
S0 - 13.6
1.0
g = 32.2 ft/sec2
C = 1.056
-81-
-------
Substituting:
Q = (1.056X0.0873) |2(32.2)(0.
Q =2.40 cfs
2
L
[^± - j]
i.o A
1/2
There are two other kinds of nozzles, the Kennison* and the Parabolic.
The Kennison nozzle looks like (also see Figure 31):
H
•L
Its flow is directly proportional to the head, or Q a H. It is used in
pipe diameters from 6 in. to 36 in. and for flows from 0 to 18 mgd (0 to 27.8
cfs). The flow can be calculated by means of the rating curve in Figure 31, or
by one supplied by the manufacturer.
The Parabolic nozzle looks like:
•i
The flow is proportional to the square of the head, or Q a H . The dis-
charge should be read from rating curves supplied by the manufacturer.
The nozzle should be mounted at the end of a long, straight, horizontal
pipe to provide the greatest accuracy. Ten diameters of straight pipe
preceding the nozzle is recommended. °
* The BIF Company
-82-
-------
Kennison Nozzle
0
Installation for Chamber
or Basin Flow
IO" KENNISON
OPEN NOZ7LE
IOO ZOO 300 4OO SOO 6OO
FLOW-GALLONS PER MINUTE
Typical Rating Curve - 10 Inch
Kennison Nozzle (Note Linear Relationship
from 1/10 to Maximum Flow).
FIGURE 31
KENNISON OPEN FLOW NOZZLE
PICTORIAL, INSTALLATION, AND TYPICAL RATING CURVE
-83-
-------
VENTURI FLOWMETERS
The principle of this apparatus was discovered in about 1791 by the
Italian engineer, J.B. Venturi. The principle was first applied in 1887 by
Clemens Herschel in the so-called Venturi meter. 10
A side view of a Venturi meter is shown in Figure 32. 21 However,
most Venturis are mounted horizontally in wastewater flow measurement
applications, so another drawing appears below:
THROAT
FLOW
1
f ».
D A,
±. *
• 1
1 ,4
HIGH PRESSURE
CONNECTION
LOW PRESSURE
CONNECTION
The Venturi formula is:
.10
Q = (1.00 + 0.02) A2 2gH
where:
g
H
flow, cfs
area at the throat,
acceleration of gravity = 32.2 ft/sec2
head, ft « hj - h2 (the pressure heads, ft)
-84-
-------
PIPE
DIAMETER*
(d9)
Converging Section (Inlet)
THROAT
'DIAMETER (
-------
The coefficient (1.00 + 0.02) has two parts:
c - cjc2 - (1.00 +0.02)
cl * Al / ^Al2 - A22 * - 1.0062 to 1.0328
c2 " coefficient of friction •- 0.97 to 0.99
The coefficient, c, should be supplied by the manufacturer of the Venturi. If a
manometer is used, the formula must be modified like the nozzle formula to
include the manometer equation. A Venturi meter should be frequently flushed or
continuously flushed.-*
-86-
-------
OPEN-PIPE METHODS
If there is no flow measurement system and the outfall discharges
unsubmerged above a receiving water, an open-pipe method can be used to
determine flow. There are two main open-pipe methods: The California Pipe
Method and the Purdue Method. A third formula is used for approximating flow
from vertical pipes.
The California Pipe Method
This method was developed by Van Leer in 1922.22 Many of its applica-
tions undoubtably have been for coastal discharges. Four basic criteria must be
satisifed for the method to be valid:
(1) The pipe must be level.
(2) The pipe must discharge partially full.
(3) The pipe must discharge freely into the air.
(4) The velocity of approach must be practically zero.
The equation is based on experimental data, and it is good for pipe
diameters from 3 to 10 inches (0.25 to 0.83 ft.). It cannot be used with corre-
gated metal pipes.
-87-
-------
A support diagram for the California Pipe Method is (see also Figure 33):
The formula for Figure 33, the above drawing, and the California Pipe
Method is:
Q = 8.1
•88 2.48
where:
Q =
discharge, cfs
distance from the inside crown (top) of the pipe to the water
surface measured at the point at which the wastewater discharges
from the pipe, ft.
diameter of the pipe, ft.
-88-
-------
d 1
G-
OP€N END
AT
LEAST
6 d — *
— •—
^M
to
MEASUREMENTS NEEDED FOR
CALIFORNIA PIPE FLOW METHOD
FIGURE 33
CALIFORNIA PIPE FLOW METHOD
-89-
-------
If a/w < 0.5, the formula does not work.
For solution, the NPDES inspector must:
(1) See if the four criteria are met.
(2) Measure a and $ , or obtain ft from the permittee's records.
(3) Determine the flow, either by the equation or by the graphical
solution in Figure 34.
Purdue Method
The Purdue Method is for measuring flow in either partially filled or
completely filled pipes. It is a graphical solution developed at Purdue
University.23
For calculation of flow, see Figure 35.
If d < Q.QjO at the outlet, measure y at x = 0.
If d 2. 0.8J0 at the outlet, measure y at x = 6, 12, or 18 inches from
the end of the pipe.
Always be sure to use the correct graph! In the above two conditions,
d » depth, ft. and ft = d^x or the inside diameter of the pipe.^
-90-
-------
100,000 —
50.000 —
10,000.
5.000-
1,000-
g.
^ 500-
7
100-
50-
&L
/,//
///
-^=^--- [g^OEEEIEIz ///•//-•/-•/'
/ ./• / f / /
x 7 x. /
-fei:£ ///////;/;/! /
M
/ i f / f /--/---£— f -- A- / / -///// /
/////i"/-/ /; 71 '/- / /////- '/
/.//'// /•/-/- /- -/•-/' "A •;/ •/./•////' ;/•':
//////A// /././:• ////•///!/••/
/ / / / / / /- •'// / / / -.-/ ' / :: 7
/ -• / / - • .- // / / ] - / '^
/ / / / / /////// / / /
/ -// /-../ ///.//.-/ / /- 7
?ipe Dlarecer v in.)
-;
36
33
3D
27
-
::
18
j--i
j.Q5
FIGTJRE 34
DISCHARGE RATE VS. FLO/ DEPTH FOR CALIFORNIA PIPES
-91-
-------
I
k~- — ,
- — ,
I
-
"X.
\
0 INCHES
s
\
—
-
~-i — L^__
^
Fs
4-
,
"~~— ~
^\
^-~0-c.
x
\
s
s
\
s
*?
V
-V .-
^
\
\
\
=
\
-
JO 5 20 SO 40 50 40 10 *0 '50 ZOO JOO 400 5»
FLOW.Q. IN GALLONS »£« MtNUU
;-
K:
.
"T
-
1
~;
> :
4
•
.
— v
V
\
B
.
1
!v ,
\
\
V
a
\
S
\
\
10
\
1
__\ . ,
\
V
S
•
-
-,
-.
i
•
-
•
i
K'lZ INCHES
y
\
1\
n
•
\
N
V
\
\t
i
s
\
V
\
'
V
.
V
S
',
!
-
i
!
1
'•
\
;
V
V
\
-
•.
;
«-\o.
'
•N
&
Vi
\-
\
\
SO «0 » M SO tOO 150 200 300 «00 500 600 BOO 1000 2000
FLOW,4. IN GALLONS PERMiNUTE
X- 16
N
1
!
•.
\
s
c
\
\
I*
5
\
•
•
\>^ i
\
\
\
,
-
\-
•.
\ i
g
*v
\
\
^
•
•
- — —
'
\T 1
A*i !
\ <" *
V
\
, \>-
\ s
tO SO 40 50 «0 BO '00 1)0 ZOO 500 40O 400 400 800 (000 20
FLOW, q. IN GALLONS PER MINUTE
FIGDBE 35
PURDUE METHOD OF MEASURING FLOW FROM A HORIZONTAL PIPE
-92-
-------
OPEN CHANNEL MEASUREMENTS
So far, open channel (sewer), and closed-conduit flow measurements have
been discussed. But often the NPDES inspector will be required to measure
streamflow, particularly for hydrodynamic or mathematical modelling
applications. Open channel flow can be calculated by equation or by various
field methods.
Flow From Vertical Pipes
The NPDES inspector may encounter pipes discharging vertically, especially
if flow measurements need to be taken for water and injection wells, aerators,
or groundwater supplies. In this case, use the method shown in Figure 36.^9
Equations
Different equations have been developed to calculate open channel flow.
The most famous of these are the Manning, Chezy, and Kutter equations.? Pbr
years, the Kutter equation has been favored to calculate open channel flow (see
solution nomographs and graphs in Reference 8 for more information), but in the
last twenty-five years, the Manning equation has been more commonly used in
hydraulic engineering.
The Irish engineer, R. Manning, found in 1890, that the Kutter formula did
not agree well with many field measurements. He adopted a more accurate and
simpler formula:
„ 1.486 2/3 .1/2
V = -•—• •• i 3
n
-93-
-------
FIGURE 36
APPROXIMATING FLOW FROM VERTICAL PIPE
Q - (5.68) KD2 H1/2
where: Q = capacity, gpm
D = inside diameter of pipe, in.
H = vertical height of water jets, in.
K = a constant, varying from 0.87 to 0.97
for pipes 2 to 6 in. diameter and
H = 6 to 24 in.
-94-
-------
whe re:
V = velocity, ft/sec or fps
n = roughness coefficient (See Table 10), dimensionless
s = slope, ft/100 ft
r = hydraulic radius = area (A)
wetted perimeter (Pw)
The term, r, is very difficult to solve for mathematically, but its solution is
easy and fast graphically. Graphical solutions for Manning's Equation appear as
Figures 37*0 and 38. A nomograph solution is shown in Figure 39.^5 Also,
see Reference 8 for more graphical solutions to Manning calculations.
Example; Calculate the flow in a 6 in. concrete pipe in good condition,
with a slope of 0.01 and a depth of water equal to 4 in.
F rom Da rcy ' s Law :
Qfull - Vf Atotal
9
/A
TT(— J - IT
1 ft.N2
6 x 12 in.
AT = 0.196 ft2
d 4
Depth Flow Ratio «— = — = 0.67
D 6
From Figure 38, Enter 0.67 on Y-Axis and read on X-Axis, 0.75 » a/A and
from Figure 37, r/R fu^ =1.2.
-95-
-------
VALUES OF n TO BE USED WITH THE MANNING EQUATION
Surface
Uncoated cast-iron pipe
Coated cast-iron pipe
Commercial wrought-iron pipe, black
Commercial wrought-iron pipe, galvanized
Smooth brass and glass pipe
Smooth lockbar and welded "OD" pipe
Riveted and spiral steel pipe
Vitrified sewer pipe
Common clay drainage tile
Glazed brickwork
Brick in cement mortar; brick sewers
Neat cement surfaces
Cement mortar surfaces
Concrete pipe
Wood stave pipe
Plank flumes:
Planed
Unplaned
With battens
Concrete-lined channels
Cement-rubble surface
Dry-rubble surface
Dressed-ashlar surface
Semicircular metal flumes, smooth
Semicircular metal flumes, corrugated
Canals and ditches:
Earth, straight and uniform
Rock cuts, smooth and uniform
Rock cuts, jagged and irregular
Winding sluggish canals
Dredged earth channels
Canals with rough stony beds, weeds on
earth banks
Earth bottom, rubble sides
Natural stream channels:
(1) Clean, straight bank, full stage, no rifts or
deep pools
(2) Same as (1), but some weeds and stones
(3) Winding, some pools and shoals, clean
(4) Same as (3), lower stages, more ineffective
slope and sections
(5) Same as (3), some weeds and stones
(6) Same as (4), stony sections
(7) Sluggish river reaches, rather weedy or with
very deep pools
(8) Very weedy reaches
Best
0.012
0.011
0.012
0.013
0.009
0.010
0.013
f 0.010 1
1 0.011 J
0.011
0.011
0.012
0.010
0.011
0.012
0.010
0.010
0.011
0.012
0.012
0.017
0.025
0.013
0.011
0.0225
0.017
0.025
0.035
0.0225
0.025
0.025
0.028
0.025
0.030
0.033
0.040
0.035
0.045
0.050
0.075
Good
0.013
0.012*
0.013
0.014
0.010
0.011*
0.015*
0.013*
0.012*
0.012
0.013
0.011
0.012
0.013
0.011
0.012*
0.013*
0.015*
0.014*
0.020
0.030
0.014
0.012
0.025
0.020
0.030
0.040
0.025*
0.0275*
0.030
0.030*
0.0275
0.033
0.035
0.045
0.040
0.050
0.060
0.100
Fair
0.014
0.013*
0.014
0.015
0.011
0.013*
0.017*
0.015
0.014*
0.013*
0.015*
0.012
0.013*
0.015*
0.012
0.013
0.014
0.016
0.016*
0.025
0.033
0.015
0.013 •
0.0275
0.0225*
0.033*
0.045
0.0275
0.030
0.035*
0.033*
0.030
0.035
0.040
0.050
0.045
0.055
0.070
0.125
Bad
0.015
0.015
0.017
0.013
0.017
0.017
0.015
0.017
0.013
0.015
0.016
0.013
0.014
0.015
0.018
0.030
0.035
0.017
0.015
0.030
0.025
0.035
0.030
0.033
0.040
0.035
0.033
0.040
0.045
0.055
0.050
0.060
0.080
0.150
•Values commonly used in designing.
TABLE 10
-96-
-------
Q
- I
0 9
-
6
r
o
o
I 0.3
Values of — and —
', n,
1,2 1.4 1.6 1.8 2.0 2.2 2.4 26 2.8 3.0 3.2 "34 3.6
n, /variable with depth
........ n, f constant
—— Independent of n, f
\ Darcy-Wetsbach
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 12 1.3
Hydraulic elements J.
Hydraulic elements for circular sewers
. --. Jl
FIGURE 37
-97-
-------
-'
at
3
C
1.1
0.8
0.6
0.4
0.2
^
-±±
X
Z_
ii
i i i
*\
¥^
0.2
0.4
0.6
0.8
1.0
Cross Section Area Ratio TT
FIGURE 38
DEPTH RATIO VERSUS AREA RATIO
-98-
-------
- 90
:-8U
-70
i
h60
-50
r
:_40
:
•
-
-
r30
!
.
-20
-
.
-
_
o
o>
0>
-10 fc
'- • .C
^ g 0
L *°
^8
^7" °
r .-^
: Q.
r o
^ 5
V
-4
-
-
r3
-2
~ i
:-0.9
: 0.8
- 0.7
90
84
-
-72
-66
-60
-54
-48
-42
-36
-30
-27
"•24
-21 .£
~
' 3
-18 "g
o
O
-15 o
03
E
- 12 o
Q
- 10
-8
-6
-4
0.0002^
:
0.0003-^
0.0004-
0.0005^
0.0006^1
0.0007-
0.0008H
0.0009^
0.001 ^
~.
-.
0.002 -j
4
0.003-^
0.004^
0.005^
0.006^
0.007-;
0.008-:
0.009-=
0.01 ^
-
-
0.02-.
j
0.03 -j
0.04 -j
0.05 -:
0.06^
0.07H
0.08^
0.09 -
0.1 -
-
0.2-
4
0.3^
0.4-
0.5-1
0.6 - :
0.7 --
0.8-
0.9 --
1.0-
:
2.0
x'
;^\
OJ
Q. >C
o ~--
tn-JL
^"
'*5
2 _
. 3'-
5-
6-
8-
10-
15-
20-
FIGURE 39
NOMOGRAPH BASED ON MANNING'S FORMULA, n = 0.013
-99-
-------
So, if Rfuii = 2TTr-2ird/2=ird= 6/12 T = 1.57 ft.
Then, r = 1.2 Rf - 1.2 (1.57) = 1.88 ft.
Using the Manning Equation,
l/2
n
where:
n - 0.013 (From Table 10)
v -^751! (1.88)2/3 (O.oi)1/2
V - (114.3) (1.52) (0.1) = 17.4 ft/sec
Using Darcy's Law, Q - Va
And, 0.75 - -?- so a - 0.75 (0.196) - 0.147 ft2
A
Q - Va =- (17.4 ft/sec) (0.147 ft2)
Q = 2.56 cfs
For circular channels, a modification of the formula is: 10,
K' d8/3 8l/2
Q --
n
where K can be obtained from Table 11.' For rectangular and trapezoidal
f
channels, use K instead of K in the above formula, where K can be obtained also
from Table 11.
Velocity-Area Method
Velocity area methods are extremely easy, but rather time consuming
methods by which to determine streamf low. All of these methods involve using a
current meter to determine the component velocities. Current meters are
discussed in the next section on Stream Gauging.
-100-
-------
Values of K for Circular Ckonnels in the Formula
D =• depth of water d — diameter of channel
D
~d
.0
.1
.2
.3
.4
.5
.6
.7
.8
.9
1.0
.00
4.49
2.96
2.25
1.80
1.470
1.215
1.004
.821
.654
.463
.01
15.02
4.25
2.87
2.20
1.76
1.442
1.192
.984
.804
.637
.02
10.56
4.04
2.79
2.14
1.72
1.415
1.170
.965
.787
.621
.03
8.57
3.86
2.71
2.09
1.69
1.388
1.148
.947
.770
.604
.04
7.38
3.69
2.63
2.05
1.66
1.362
1.126
.928
.753
.588
.05
6.55
3.54
2.5G
2.00
1.62
1.336
1.105
.910
.736
.571
.06
5.95
3.41
2.49
1.96
1.59
1.311
1.084
.891
.720
.553
.07
5.47
3.28
2.42
1.92
1.56
1.286
1.064
.874
.703
.535
.08
5.08
3.17
2.36
1.87
1.53
1.262
1.043
.856
.687
.516
.09
4.76
3.06
2.30
1.84
1.50
1.238
1.023
.838
.670
.496
Values of K' for Circular Channels in the Formula
Q = — dWsW
n
D — depth of water d •= diameter of channel
D
d
.0
.1
.2
.3
.4
.5
.6
.7
.8
.9
1.0
.00
.00907
.0400
.0907
.1561
.232
.311
.388
.453
.494
.4i>»
.01
.00007
-011S
.0148
.0960
.1633
.239
.319
.31)5
.458
.496
.02
.00031
.0142
.0492
.1027
.1705
.247
.327
.402
.463
.497
i
.03
.00074
.01 87
.0537
.1089
.1779
.255
.335
.409
.4(i8
.498
.04
.00138
.0195
.0585
.1153
.1854
.263
.343
.416
.473
.498
.05
.00222
.022.'.
.0634
.1218
.1929
.271
.350
.422
.477
.498
.06
.0032S
.0257
.OfiSfi
.1284
.2005
.279
.358
.429
.481
.496
.07
.00455
.0291
.0738
.1352
.2082
.287
.366
.435
.485
.494
.08
.00004
.0327
.0793
.1420
.2160
.295
.373
.441
.488
.489
i
.09
.00775
.03(10
.0849
.1490
.2238
.303
.380
.447
.491
.483
TABLE 11
-101-
-------
For the following discussion, refer to Figure 40. From Figure 40(b) it
can be seen that the velocity profile in a stream is not uniform; it varies due
to frictional forces found at the sides and bottom of the channel. Thus,
several current measurements are needed to accurately determine streamflow.
There are three different ways to determine streamflow. All can be used
by the NPDES inspector with relative ease. Other methods are discussed full}' in
References 9, 24, and 26.
The three methods are the Six-Tenths Depth Method (Figure 40(c)), the
Two-Point Method (Figure 40(d)), and the Mid-Section Method. Each involves
dividing the stream into equally long (measured from bank to bank in a perpen-
dicular line to streamflow) segments and measuring the flow in each. This is
shown in Figure 40(a). The flows per segment are added to obtain the total
streamflow.
The Six-Tenths-Depth Method is for shallow flows. It requires a measure-
ment at 0.6d from the water surface. Darcy's Law, Q = VA, is used to determine
the streamflow.
The Two-Point Method is for deeper flows than 2 or 3 feet, and it requires
that two readings be taken, at 0.2d and 0.8d from the water surface. The
velocities are averaged as follows:
V
avg
V j^ V
0.2 + 0.8
Then the streamflow is calculated by Darcy's Law, Q = Vavg A.
-102-
-------
view
'o.t
CO
FIGURE 40
DETERMINING MEAN VELOCITIES
-103-
-------
The Mid-Section Method is the preferred method for larger streams with
deeper flows. After the stream has been sectioned as in Figure 40(a), the
following equation is solved for each section:
"0.2 + "o.s
and so on for each section (1,4 - 1*3, etc.), where:
q = streamflow in the section, cfs
L = distance from the inital point, ft.
do = water depth at interval L, ft.
Then the total streamflow is the sum of the flows in each section, or
mathematically:
1-n
QT = /_, q
n=l
The Mid-Section Method can be used for shallower streams by substituting
V + V
—— ^- by V0.6 in the above equation.
-104-
-------
STREAM GAUGING
Stream gauging has been carried out by various governmental agencies since
the mid-nineteenth century.* To measure stream velocity, the NPDES inspector
must use several different pieces of equipment. It is best to prepare a
checklist before going out in the field.
Essential Equipment is:
• Current meter
• Wading rod (to measure depth and set the current meter to a desired
depth).
• Sound box or Earphones (to hear the clicks, one/revolution of the
cups or blades on the current meter).
• Stopwatch (to time the number of clicks/minute).
• Clipboard and forms (on which to record data).
*See References 9, 24, and 26 for extensive detail on this subject.
-105-
-------
This equipment is available from several companies, including:
Weather Measure Corporation
P.O. Box 41257
Sacramento, CA 95841
Kahlsico Scientific
P.O. Box 1166
El Cajon, CA 92022
EPIC, Incorporated
150 Nassau Street
New York, NY 10038
For ease of non-smearing and for making duplicate copies of data, rubber-
ized paper forms are available from the Government Printing Office, Washington,
D.C.4 Order by GSA 07-EPA-5300-1.
Current Meters
There are two popular types of current meters used today—the Price and
the Ott meters. Others are described in Reference 9.
The Price Meter is used extensively by the U.S. Geological Survey. It is
shown schematically in Figure 41 and in action in Figure 42. The Price Current
Meter is similar to an anemometer, and each full revolution of one cup causes a
-106-
-------
M
O
®r
ASSEMBLY
LIST OF PARTS
1. CAP FOR CONTACT CHAMBER
2. CONTACT CHAMBER
3. INSULATING BUSHING FOR CONTACT BINDING POST
4. SINGLE-CONTACT BINDING POST
5. PENTA-CONTACT BINDING POST
6. PENTA GEAR
7. SET SCREWS
8. YOKE
9. HOLE FOR HANGER SCREW
10. TAILPIECE
11. BALANCE WEIGHT
12. SHAFT
13. BUCKET-WHEEL HUB
14. BUCKET-WHEEL HUB NUT
15. RAISING NUT
16. PIVOT BEARING
17. PIVOT
18. PIVOT ADJUSTING NUT
19. KEEPER SCREW FOR PIVOT ADJUSTING NUT
20. BEARING LUG
21. BUCKET WHEEL
FIGURE 41
ASSEMBLY DRAWING OF PRICE TYPE AA CURRENT METER
-------
FIGURE 42
TYPE "A" CRANE AND CURRENT METER ASSEMBLY IN
POSITION ON A BRIDGE
-108-
-------
click to be heard in the attached earphones. The pygmy current meter is a
smaller version of the Price meter for use on shallow streams.
The Ott current meter is one of several propeller-type, horizontal axle
meters in use (see Figure 43). Others include Hoff, Haskell, and "Dumas"
meters.' Ott meters are useful where vertical velocity gradients are a
problem.
Flows can be determined by using the rating tables furnished with the
current meters. Velocity is usually plotted against the number of clicks per
unit time, most commonly per minute.
Maintenance is a problem with most current meters, and lack of it can skew
streamflow results drastically. The most common problems are:^
• Worn pivots,
• Lack of oil (a silicone-type must be used),
• Bent cups, and
• Solids build-up.
The NPDES inspector must carefully check the current meter for these
problems before and after each use. If the meter is used in extremely contam-
inated or salt water, it must be washed off thoroughly with fresh water before
storing.
-109-
-------
FIGURE 43
OTT-TYPE HORIZONTAL AXIS CURRENT METER
-110-
-------
DILUTION METHODS AND TRACERS
Dilution methods for water and wastewater flow are based on the color,
conductivity, or fluorescence of a tracer injected into the waste stream. The
advantages and disadvantages of this flow measurement method are:
TABLE 12
COMPARISON OF MERITS OF THE DILUTION METHOD
ADVANTAGES
DISADVANTAGES
• Method which can be used
where other methods are
inappropriate or impossible.
• Good for measuring large
flows (billions of gallons/
day).
• High accuracy reference
procedure to check devices
in situ (on site).
• Procedure to verify closed
conduit flow measuring
systems.
• Requires special equipment.
• Detailed procedures.
• Time-consuming.
• Costly.
-Ill-
-------
Dilution
There are two methods: a slug-dose can be injected, or the tracer can be
injected continuously. There are merits to each method. Tracers used include
sodium chloride (NaCl)—sometimes called the salt-velocity method or the salt-
dilution method for slug addition'—and lithuim chloride (LiCl). Fluorescent
dyes, like rhodamine B and Pontacyl Brilliant Pink B, have been extensively used
in ocean outfall studies. Submersible pumps with flow-through fluororaeters and
recorders can also be employed to measure flow by this method.
Slug vs. Constant-Rate Injection
A comparison of the mathematical expressions used to calculate flow and
the concentration-time curves for each of the above methods is presented as
-Figure 44. 27
For continuous injection, if q, the constant flow rate of the injected tracer,
is much smaller than the flow, and if the optimum concentration (of the plateau)
is much greater than the background concentration, then the equation can be
simplified to:
C,
C2
But:
• q is a constant injected by perhaps a piston chemical metering pump;
• the tracer must not degrade or sorb onto other particles, and
• the dye must be well-mixed across the section so the following
relationship results:
-112-
-------
UJ
i
t
z
O
O
TIME
CONCENTRATION-TIME CURVE FOR
CONSTANT-RATE INJECTION METHOD.
t
O
z
O
O
TIME
b. CONCENTRATION-TIME CURVE FOR
SLUG-INJECTION METHOD.
v C
1
/oo
(<*'.)
dt
Q •= IS FLOW RATE OF STREAM
q * IS FLOW RATE OF CHEMICAL
Crt-iIS BACKGROUND CONCENTRATION OF
0 STREAM
C1 = IS CONCENTRATION OF CHEMICAL
1
1
INJECTED
CONCENTRATION OF STREAM PLATEAU
Q rIS FLOW RATE OF STREAM
v "=IS VOLUME OF CHEMICAL INJECTED
C =IS BACKGROUND CONCENTRATION OF
,
1
STREAM
lS CONCENTRATION OF CHEMICAL
INJECTED
C-,-=.IS INSTANTANEOUS STREAM
Z- CONCENTRATION
FIGURE 44
CONSTANT RATE AND SLUG INJECTION METHODS
-------
distance
r
For slug injection, the bottom value I (C£ - Co)dt can be determined
graphically by plotting fluorescence over time and integrating between Co and
€2 manually with a planimeter:
t
-------
EXOTIC METHODS
There are three rather exotic methods for measuring flow. They use the
principles of electromagnetic, acoustic, and electrical energy. Usually, they
will neither be seen nor used by the NPDES inspector, but their presence here
completes this manual.
Electromagnetic Flowmeter
An electromagnetic flowmeter, like the one shown in Figure 45, works on
the principle of Faraday's Law, which says that the voltage is directly propor-
tional to the velocity and to the magnetic field strength. This is measured by
electrodes in contact with the water or wastewater. The conductor must be
perpendicular to the electrical field, induced by an electromagnet.
This method is good in pipes with diameters from 2 to 24 inches (0.167 to
2 ft). Its error is ± 1%, and it has no moving parts. A severe disadvantage is
the buildup of solids on the electrodes can cause error. Thus frequent cleaning
of the flowmeter is essential. Vacuum or air entrainment may also cause error.
Acoustic Flowmeters
Acoustic flowmeters operate on the principle that the difference in time
of arrival of two simultaneously created acoustic or sound pulses traveling in
opposite directions through the water can be related to the velocity of
flow.9
-115-
-------
Fisher & Porter
Magnetic Flow Meter
INSULATING
LINER
ELECTRODE
ASSEMBLY
STEEL METER
BODY
MAGNET COILS
POTTING COMPOUND
FIGURE 45
TYPICAL MAGNETIC FLOW METER
-116-
-------
They also make use of the fact that sound waves traveling downstream propagate
at higher velocities than those traveling upstream.* A mathematical solution
and picture of an acoustic flowmeter is Figure 46. There are two generic types
of acoustic or ultrasonic meters available—a Doppler—effeet meter, and a "Delta
traveling-time meter "(Author's terminology). 27
The first type of sonic flow meters operates on the principle of the
Doppler effect. A sonic wave of given frequency is emitted through the flowing
stream. The effect of the moving wastewater on the sound wave results in a
shift of the wave frequency which in turn is detected by the receiver. The
degree of frequency shift is proportional to the flow velocity. A conversion to
flow velocity is done electronically.
The second type of sonic flow meter works on the principle of the differ-
ence in traveling times for two identical sound waves which travel at different
angles. One wave travels along the flow direction, while the other wave travels
against the flow direction. The differential traveling time reveals the flow
velocity. Therefore, this type of sonic meter generally has the sonic emitter
and receiver aligned at an angle which is oblique to the direction of flow. (See
Figure 46).
Ultrasonic flow meters are increasing in their application in flow
measurement in POTWs for both wastewaters and sludges. Sonic flow meters have
been successfully coupled with Venturi tubes for accurate flow measurements.
* BIF Company
-117-
-------
AT = tu-td,
ULTRASONIC FLOWMETER
Q = (v)
V -
AT
2 cos 6
^u " C - VcosG, Ld " C + VcosG
t- traveltime, C = velocity of sound (~ 1088 fps), V = flow velocity, L -
pathlength. The tu and t^ are measured along the diagonal acoustic path.
Sound waves traveling downstream propagate at higher velocities than those
traveling upstream.
FIGURE 46
-118-
-------
Ultrasonic flow meters do not come in direct contact with the flow,
therefore, are less susceptible to the foulings. Sonic flow meters are
sensitive to and compatible with a wide range of flow rates.
Vacuum conditions (which result in gas production) or an entrainment in
the pipes may produce false readings by the sonic flow meter. Sonic flow meters
themselves may be affected by environmental conditions such as high temperature,
rapid temperature fluctuations, or humidity.
Electrical Methods
There are three electrical methods for measuring wastewater flow. A
thorough discussion is beyond the scope of this manual, especially since the
NPDES inspector is unlikely to encounter these in the field. All of their
performances in accurately measuring wastewater flow are hampered by high
suspended solids loads. The methods are:27
• Conductivity cells
• Hot-wire anemometers
• Warm-film anemometers
-119-
-------
SUMMARY
This manual is intended to serve as a guide for the NPDES inspector.
Often he/she will encounter alien flow situations where he/she will be faced
with difficult problems in calculating wastewater flows. As many practical
ideas as possible are incorporated to aid the inspector in these situations.
Example problems are included to highlight important concepts in practicality.
However the manual does not include every detail related to flow measure-
ment. The references should serve to augment the material presented here if
more information is required by the NPDES inspector.
A final word about safety is appropriate at this point. Many field situa-
tions are extremely dangerous, especially concerning:^
• Traffic diversion problems,
• Hazardous and toxic materials,
• Sewer gas buildup and the risk of explosion,
• Theft of equipment kept on-site,
• Deep manholes as safety hazards,
• Noise in confined areas.
-120-
-------
In these flow measurement methods, environmental in situ factors not only
have a tendency to shorten equipment life, reduce measurement accuracy, and
lengthen necessary field time, but they also could potentially jeopardize human
life.
Be careful. Observe standard safety procedures at all times. And above
all, use your common sense!
-121-
-------
FOOTNOTES
1. Morris, H.M. and Wiggert, J.M. Applied Hydraulics in Engineering, 2nd
edition, Ronald Press Co.: New York, 1972. p.8.
2. "NPDES: Revision of Regulations." 44 FR 32854. June 7, 1979.
3. U.S. EPA. NPDES Compliance Sampling Inspection Manual. Office of Water
Enforcement, Enforcement Division, Compliance Branch, Washington, D.C. 1979.
4. Harris, D.J. and Keffer, W.J. Wastewater Sampling Methodologies and Flow
Measurement Techniques. U.S. EPA Region VII Surveillance and Analysis
Division, Kansas City, Missouri. EPA 907/9-74-005. June 1974.
5. Jacobi, J.W. "Pumping Stations as Flowraeters." WPCF Deeds & Data. July,
1975, pp. 1-4.
6. Smoot, C.W. "Orifice Bucket for Measurement of Small Discharges from Wells,"
Water Resources Division Bull., Illinois Water Survey, Champaign, Illinois,
November, 1963.
7. King, H.W. and Brater, E.F. Handbook of Hydraulics, 5th edition, McGraw-Hill
Book Company: New York, 1963.
8. Chicago Pump Company, Hydraulics and Useful Information. FMC (Corp.).
Bulletin 9900, 1973.
9. U.S. Bureau of Reclamation. Water Measurement Manual. 2n(* edition -
Revised Reprint. Denver, Colorado, 1967, Reprinted 1975.
10. Metcalf and Eddy, Inc. Wastewater Engineering; Collection, Treatment,
Disposal. McGraw-Hill Book Company: New York, 1972.
11. Flinn, A.D. and Dyer, C.W.D. "The Cipolletti Trapezoidal Weir", Trans. ASCE.,
Volume 32, 1894.
12. Mauis, F.T. "How to Calculate Flow Over Submerged Thin-Plate Weirs," Eng.
News-Record, July 7, 1949, p. 65.
13. Sponagle, C.E. "A Prototype for Development of Routine Operational Procedures
for the Measurement of Flow in an Open Channel by Sharp-Crested Weir",
NTOTC-OWPO, U.S. EPA, Cincinnati, Ohio, (1979?).
14. Parshall, R.L. "Improving the Distribution of Water to Farmers by Use of the
Parshall Measuring Flume," SCS Bulletin 488, USDA and Colorado Agricultural
Experiment Station, Colorado A & M College, Ft. Collins, Colorado, May, 1945.
15. Sponagle, C.E. "Evaluation of Flow Installations." Part of a Prototype
Training Package on Flow Measurement. NTOTC-OWPO, U.S. EPA, Cincinnati,
Ohio, April 5, 1978.
-122-
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FOOTNOTES
(continued)
16. "Experiments Relating to Hydraulics of Fire Streams," Trans ASCE, Volume 21,
1888. pp. 303-482.
17. U.S. EPA. Inspector's Guide for Evaluation of Municipal Wastewater Treatment
Plants. Municipal Operations Branch- OWPO. EPA/430/9-79-010. Washington,
D.C., April, 1979.
18. Streeter, V.L. and Wylie, E.B. Fluid Mechanics. 7th edition. McGraw-Hill
Book Company: New York, 1979.
19. Guthrie, D.L., Washington, D.R. and Vincenty, C. "Errors in Flow Measurement
and Their Importance in Infiltration/Inflow Analysis." Paper Presented at the
National Bureau of Standards. 1977 Flow Measurement Symposium, Gaithersburg,
Maryland. February 24, 1977.
20. Manning Environmental Corporation, "Portable Dipper Level and Flow
Recorders," Publication DIP - 578. Santa Cruz, California.
21. U.S. EPA. Handbook for Monitoring Industrial Wastewater. Technology
Transfer Publication, Cincinnati, Ohio, 1973.
22. Van Leer, B.R. "The California Pipe Method of Water Measurement." Eng. News
Record, Aug. 3, 1922, and Aug. 21, 1924.
23. Grove, F.W. "Measurement of Pipe Flow by the Coordinate Method," Purdue
Engineering Experiment Station Bulletin 32, 1928.
24. Discharge Measurement Structures. International Institute for Land
Reclamation and Improvement. Publication #20. The Netherlands, 1976.
25. Clark, J.W. and Viesmann, W. Water Supply and Pollution Control.
International Textbook Company, Scranton, Pennsylvania, August, 1970.
26. Orsborn, J.F. amd Watts, F.J. Manual for a Short course on Hydraulics and
Hydrology for Fishery Biologists. U.S. FWS National Fisheries Academy.
Leetown, West Virginia, January, 1979.
27. U.S. EPA. Sewer Flow Measurement; A State-of-the-Art Assessment. MERL-ORD.
Cincinnati, Ohio. (Undated).
28. Turner Designs Company "Fluorometric Facts, Flow Measurements Monograph."
Mountainview, California, 1976.
29. U.S. R»rest Service, Forest Service Handbook, 1963, and U.S. FWS Refuge
Manual, Technical Appendix, 5RM 1, Appendix 1, 1981.
-123-
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APPENDIX
I
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PUMPING STATIONS AS FLOWMETERS5*
Joseph W. Jacob!, Sr.
Jacob! and Toorabs, Inc.
Consulting Engineers
Clarksville, Indiana
In the normal operation of wastewater handling facilities, and especially
when making infiltration/inflow analyses, it is desirable and even necessary to
measure the amount of wastewater handled by a pumping station. Ten State
Standards^ lists flow measurement capability as a requirement for new pumping
stations. State agencies reviewing plans for pumping stations generally inter-
pret this requirement as applying only to the larger stations, and many older or
smaller pumping stations are without any means for measurement.
The author has developed a method by which the flow of any electrically
driven pumping station may be measured with accuracy that will satisfy most
requirements. The method is based on the proposition that the mass volume of
water (wastewater) pumped by any given station is directly proportional to the
consumption of electrical energy in kilowatthours. This means that, for the
duration of time under consideration, for example, 1 hr. or 1 day, the total
through-put of the station in gallons is proportional to the kilowatthours
consumed during that period. The average flow during the period under
consideration may be determined by dividing the total gallons by the time period.
Thus, the kilowatthour meter may be read hourly, daily, or weekly and the
average flow computed for the time interval desired.
im "Recommended Standards for Sewage Works." Great Lakes-Upper
Mississippi River Board of State Sanitary Engineers.
Corrections were made by this author.
A-l
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There remains, of course, the matter of determining the constant of pro-
portionality for a particular station in terms of gallons per kilowatthour. This
constant must be determined experimentally for each pumping station because each
is unique in terms of static head, friction head, pump efficiencies, motor
efficiencies, and station auxiliaries. This paper is devoted largely to an
explanation of the method of determination of station constants. It will show
how a few simple experimental observations may be made on a pumping station and
how, from these, the required station constant may be derived.
For purposes of this explanation, a conventional dry pit pumping station
may be visualized as having two identical electric pumps drawing from a separate
wet well. The pumps are assumed to be equipped with controls that permit one
pump to pump the wet well down and then shut off. On filling up a second time,
the other pump performs the pumping down; the two pumps alternate unless the
water level in the wet well reaches the alarm level and calls for duty from both
pumps. It is also assumed that the station is fitted with other powerconsuming
auxiliaries such as sump pump, dehumidifier, and electric lights.
The influent sewer runs steadily until the water level in the wet well
reached the "pump-on" level. Then the duty pump starts and the water is pumped
down until the water level reaches "pump-off." This is called one pump cycle.
During one pump cycle it is necessary for the pump to pump out the volume stored
in the wet well between pump-on and pump-off plus the flow of the influent sewer.
This may be expressed by an equation:
Vp = Vs + Q±tp (1)
A-2
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in which:
Vp = volume pumped per cycle (gal),'
Vs - storage volume of the wet well,
Qi = flow of the influent sewer (gal/sec), and
tp = time that the pump runs per cycle (sec).
Vs, the storage volume, may be easily determined by measuring the
difference between the pump-on and pump-off levels (drawdown) and multiplying by
the cross-sectional area of the wet well.
Thus, for a circular wet well,
Vs = 0.7854 x D2 x d x 7.48 (2)
in which:
Vs =* storage volume (gal) ,
D = diameter of wet well (ft),
d = the drawdown (ft)
0.7854 - the constant, Tr/4 [from Aclrcle (Tr)(D2/4)]
7.48 = a constant (gal/cu ft).
For a rectangular wet well, the equation would become,
Vs = 1 x w x d x 7.48 (3)
in which:
1 = length of the wet well (ft),
w = width of the wet well (ft)
d = drawdown (ft) , and
7.48 = a constant (gal/cu ft).
A-3
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Knowledge of the storage volume allows one to measure the flow of the
influent sewer. This is done by simply observing the time required to fill the
wet well. As soon as the duty pump shuts off, the stop watch is started and the
wet well starts to refill. When the wet well is full, the next pump will start
and the fill time is recorded.
To calculate the flow of the influent sewer the following equation is
used:
in which:
Qi = flow of the influent sewer (gal/sec) ,
Vs = storage (gal), and
tf - fill time (sec).
Equation 1 still requires one further parameter, cp the pumping time for
one pump cycle. This is the time that one pump requires to pump the wet well
down one time. This time is observed with a stopwatch and recorded.
Now all of the data necessary to compute V0, the volume pumped per
cycle, are available.
The use of electrical energy also should be considered. An electric
watthour meter operates only when power is flowing through it. Ordinarily, it
indicates the amount of electrical energy consumed by a series of dials that
register the cumulative kilowatthours consumed. There is also an aluminum disk
that rotates when power is being used. There may also be a demand scale and
pointer on some meters, but this analysis is not concerned with demand.
A- 4
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The amount of electrical energy through a kilowatthour meter is directly
proportional to the total number of rotations of the aluminum disk. The constant
of proportionality is ordinarily shown on the face of the meter and is designated
Kfo. The dimensions of this constant are watthours per revolution. For
example, if a meter has a K^ of 14.4, 14.4 watthours of electricity are
consumed during on revolution. It would therefore take 1,000/14.4 = 69.44
revolutions to indicate usage of 1 kwh. The ability to measure the use of small
amounts of electrical energy by observing the meter disk makes it possible to
determine the amount of energy used by the lift station for one pump cycle. It
is simply necessary to observe the number of revolutions made by the meter disk
during one pump cycle.
The amount of energy used for one pump cycle is as follows:
n x K,
E, =
1,000
in which:
EI = energy used per pump cycle (kilowatthours),
n = number of revolutions made by meter disk during one pump cycle,
and
Kft = meter constant (watt-hours per revolution).
The factor of interest here is the station constant expressed in gallons
per kilowatthour. When this is known, it is possible to determine flow for any
period for the lift station simply by reading the meter dials on two separate
occasions, subtracting the readings to get the amount of electrical energy used,
and then multiplying this figure by the station constant to get total gallons
through the station. By dividing this result by the time interval between the
two meter readings, the average flow during that interval is obtained.
A-5
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The foregoing may be reduced to a single equation:
Vp = Vs + Q±tp (6)
(repeat Equation 1)
vp = vs + (-|T) tp (7)
(substituting for Q^, Equation 4)
Vp Vs + Ef-
(8)
El ° X Kh
1,000
(dividing by Equation 5)
1,000 Vs (1 +
(simplifying) (9)
in which:
C = station constant (gal/kwh),
Vg = wet well storage volume (gal),
tp = time required to pump down one time (sec),
tf - time required for wet well to fill (sec),
n = number of revolutions of meter disk per pump cycle, and
Kjj = meter constant (watthours per revolution)
A-6
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The above discussion describes the method by which the lift station is
calibrated for one pump. A similar set of observations should be made on the
other pump in the station, and, ordinarily, two identical pumps will exhibit
similar power requirements. A large difference is a warning of trouble somewhere
in the system.
Because the pumps operate alternately, a true averaging takes place and
the two values of the station constant may be averaged to represent the station
under actual alternating pump service. This condition is true for lightly loaded
stations or for dry weather conditions. In wet weather or for overloaded
stations, both pumps may run together. A new station constant must be determined
for this condition. It is done in the same manner as described, except that both
pumps are turned on while the meter readings are taken. As might be expected,
when both pumps are manifolded into a common force line, the station constant
will be lower than with single pumps; that is, there will be fewer gallons pumped
per kilowatthour of electrical energy used. When both pumps operate together,
the force line tends to choke and the total dynamic head loss is greater, leading
to poorer pumping efficiency. When making flow measurements, the researcher will
use either the average constant of two pumps running separately or the constant
determined when both pumps run together, whichever is appropriate to the actual
pumping situation.
Once the constants for the station have been determined, it is reasonable
to assume that they will remain unchanged unless the station is modified in some
way. To determine flow it is necessary to read only the kilowatthour dials (not
the disk) at the beginning and the end of the period desired. The power company
will cooperate in showing the operator how to read these dials. It should be
informed of the purpose of the readings. Sometimes, the meter enclosures will be
A-7
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locked or sealed against vandalism and it may be necessary to ask the power
company for access to the meter. The average flow for the period under
observation many be found from the expression
C(Etl - EtQ) (10)
Qavg 1
in which:
Qavg * average flow for the period,
C « station constant (gal/kwh),
Eto • kilowatthour reading at the beginning of the period,
Etj •* kilowatthour reading at the end of the period, and
t » elapsed time between observations EtQ and Etj
The units of Qa will depend on the units chosen for t. If t is in
minutes, Qavg will be in gallons per minute; if t is in days, Qavg w*^'ke
in gallons per day. Ordinarily, it will not be practicable to read the meter at
an interval shorter than 1 hour because the power consumed will be too small to
produce a reliable reading. If an instantaneous flow is desired, the reader
should refer to Equation 4 and compute the flow of the influent sewer, Q^.
For purposes of measurements for infiltration/inflow analyses, it is
convenient to read the electric meter once a day, recording the time of day.
From each pair of readings, the daily flow may be computed and a trend identified
from dry and wet weather readings.
Attention should be paid to any meter multipliers. These multipliers are
devices attached to the meters by the power company to extend their range and are
A-8
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often tagged on the face of the meter. If a meter has a multiplier, the multi-
plier value must be added to both the K^ and the kilowatthour readings.
The pumping station auxiliaries use about 5 percent of the total energy
consumed by the station, and this component is fairly constant and independent of
the pumping rate. Because the station is calibrated in terms of gross energy
consumed, some error will be introduced by not significantly so. For practical
purposes, it may be neglected.
The method is best illustrated by an example. The following parameters
may be assumed for a lift station such as the one described above:
Diameter of wet well =6.0 ft
Drawdown in wet well = 2.2 ft
Time for wet well to fill =318 sec
Time for wet will to empty = 99 sec (time pump runs/cycle)
Electric meter constant K^ = 14.4 watthours/revolution
Electric meter disk revolutions for one pump to pump
down wet well = 15.34 revolutions
V_ - 0.7854 x D2 x d x 7.48
o
V~ - 0.7854 x (6)2 x 2.2 x 7.48
O
Vs = 465 gal, wet well storage
1,000 Vs
c
nKh
1,000 x 465
15.34 x 14.4
C =2,760 gal/kwh, station constant
A-9
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The above calculation determines the station constant. The station is now
observed on 2 successive days and the following readings taken from the electric
meter dials:
February 25, 1975 11:10 a.m.
67532.0
February 26, 1975, 8:47 a.m.
67553.3
67553.3 - 67532.0 - 21.3 kwh consumed
Time interval = 1,297 min.
0.9007 days
C( V
Q
avg t
2,760 (67553.3 - 67532.0)
Qavg = OTSUU?
Qavg " 65,269 gal/day
Once the technique is learned, it is convenient to prepare a program for
computer or programmable calculator to assist in reduction of data. The reduces
labor and mistakes in calculation and makes the process almost routine so that
the engineer may focus his full attention on the meaning of the results thus
obtained.
Pneumatic ejector stations may also be calibrated by a slightly different
technique. Most pneumatic ejectors used in municipal wastewater service are of
the duplex type, consisting of two pressure vessels, one or more air compressors,
A-10
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and, sometimes, an air storage tank. Essentially, these stations work by
admitting wastewater into one of the pressure vessels and, when it is full,
applying air pressure to exhaust the water. Each time a "pot" discharges, it
discharges a known amount of water, the volume of one pot. The researcher may
determine this volume from the geometry of the pot. To calibrate such a station,
it is simply necessary to relate the amount of electric energy used to the amount
of water discharged. The following example illustrates this readily. An ejector
station has two 75-gal pots. It was observed for a 30-min period, and, during
this time, each pot discharged 16 times. The electric meter disk made 120.85
revolutions during this period, and the meter had K^ of 10.8.
16 + 16 « 32 pot discharges in 30-min test period.
Vp - 32 pots x 75 gal/pot - 2,400 gal discharged in 30-min test
Ei = 120.85 revolutions x 10.8 -watthours x
revolution 1,000 watthours
» 1.305 kwh consumed during 30-min test period
2.400 gal m 1,839 gal/kwh
1.305 kwh station constant
Ejector stations must be carefully .observed to make sure that the pots
fill completely each cycle and do not fire prematurely. Pots that are triggered
by electrode generally will not fire until the liquid level reaches the upper
electrode. Some ejectors are equipped with timers, and error will be introduced
if the pots do not fill completely.
A-11
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As with any experimental technique, this method needs to be applied
judiciously. When a station is overhauled or repaired or the controls adjusted,
the researcher should, recalibrate. Used with discretion, the method provides an
inexpensive way to monitor flows and makes the power companies* records a source
of data for determining historical growth of the flows in the system.
A—12 *U.S. GOVERNMFNT PP.INTINf, OFF If.F : I 9RI-- 3'i I -
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