EPA-R2-73-138
FEBRUARY 1973 Environmental Protection Technology Series
The Feasibility of Flow Smoothing
Stations in Municipal Sewage Systems
Office of Research and Monitoring
U.S. Environmental Protection Agency
Washington, D.C. 20460
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and
Monitoring, Environmental Protection Agency, have
been grouped into five series. These five broad
categories were established to facilitate further
development and application of environmental
technology. Elimination of traditional grouping
was consciously planned to foster technology
transfer and a maximum interface in related
fields. The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
U. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ENVIRONMENTAL
PROTECTION TECHNOLOGY series. This series
describes research performed to develop and
demonstrate instrumentation, equipment and
methodology to repair or prevent environmental
degradation from point and non-point sources of
pollution. This work provides the new or improved
technology required for the control and treatment
of pollution sources to meet environmental quality
standards.
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EPA-R2-73-138
February 1973
THE FEASIBILITY OF FLOW SMOOTHING STATIONS
IN MUNICIPAL SEWAGE SYSTEMS
by
C. N. Click
Project No. 11010 FDI
Contract No. 14-12-935
Project Officer
Harry E. Bostian
U.S. Environmental Protection Agency
National Environmental Research Center
Cincinnati, Ohio 45268
Prepared for
OFFICE OF RESEARCH AND MONITORING
U. S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402
Price $1.25 domestic postpaid or $1.00 GPO Bookstore
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EPA Review Notice
This report has been reviewed by the Environmental
Protection Agency and approved for publication.
Approval does not signify that the contents nec-
essarily reflect the views and policies of the
Environmental Protection Agency, nor does mention
of trade names or commercial products constitute
endorsement or recommendation for use.
ii
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ABSTRACT
Flow smoothing in sanitary sewers was studied to determine under what
conditions the resulting higher flow capacities can be economically ob-
tained. Conservative assumptions were made in this preliminary design
and economics study to provide a severe test for the cost effectiveness
of the concept. In many situations, flow smoothing is an attractive
alternative when compared to relief pipe installation. Circumstances
which favor flow smoothing are high interest rates, high peak-to-average
flow ratios, low pipe slopes, small diameters, and low design depths of
flow. Flow smoothing is strongly favored where earthen construction can
be utilized.
This report was submitted by Research Triangle Institute, Research
Triangle Park, N. C., in fulfillment of Contract Number 14-12-935,
Project Number 11010 FBI under the sponsorship of the Office of
Research and Monitoring, Environmental Protection Agency.
111
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CONTENTS
Section
I Conclusions
II Recommendations
III Introduction
IV Methods of Calculation
V Discussion
VI Additional Studies
VII Acknowledgements
VIII References
IX Nomenclature
X Appendices
Page
1
3
5
7
21
37
41
43
45
49
v
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FIGURES
1 Representative Typical and Square Wave Model
Sewage Flow Hydrographs 8
2 Half-Section Through Paved Earthen Basin 14
3 Construction Costs for Basins 16
4 Construction Costs for Raw Sewage Pumping
Stations To Be Used with Equalization Basins 17
5 Installed Costs for Floating Aerators 18
6 Installed Costs for Equipment (30-percent BOD Removal) 20
7 Installed Costs for Equipment (10-percent BOD Removal) 21
8 Construction Costs for Pipelines 22
9 Pump Operating and Maintenance Cost Relationships 23
10 Aerator Operating and Maintenance Cost Relationships 25
11 Effect of Velocity 31
12 Effect of Pipe Diameter 31
13 Effect of Peak to Average Flow Ratio 32
14 Effect of Pipe Capacity 33
15 Effect of Interest Rate 34
16 Effect of BOD Removal 34
17 Effect of Equipment Life 35
VI
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TABLES
Base Values of Design and Operating
Variables 29
Effect of Construction Type 29
vii
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I. CONCLUSIONS
The following conclusions were drawn from this feasibility study of flow
smoothing in municipal sanitary sewage systems.
1. Flow smoothing in sanitary systems may offer an economically attrac-
tive alternative to relief sewers in systems needing additional capacity.
2. Flow smoothing is attractive in most circumstances if outfall pipe
length exceeds about 3 miles. For inexpensive basin construction, flow
smoothing can be attractive if outfall pipe lengths exceed about 0.5 mile.
3. Flow smoothing is favored by increasing peak-to-average flow ratios
and interest rates and by decreasing slopes, construction costs, pipe
diameters, and design depth of flow.
4. Capacity increase by flow smoothing will result in a proportionate
capacity increase in all downstream piping and equipment.
The conservative nature of the assumptions made in the analysis must be
emphasized. Field experience should show an even wider potential range
for application of flow smoothing than indicated above.
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II. RECOMMENDATIONS
1. Full-scale demonstrations of flow smoothing stations should be under-
taken to identify and solve technical problems and to provide more
accurate design and cost data. The desirability of locating smoothing
stations at various locations in existing systems should be considered,
i.e., in the collection system and at treatment plants, wherever over-
loads may occur. Demonstrations would provide evidence to justify
flow equalization for new sewerage systems and for upgrading existing
systems.
2. Further feasibility studies should be made to consider additional
possibilities for flow-equalization and to evaluate their economic
attractiveness. Studies are needed to analyze sewer systems with
multiple junctions and multiple smoothing stations and to identify and
evaluate alternatives for smoothing at the treatment plant. The effects
on both hydraulics and concentrations need to be examined. Computer
modeling studies are recommended because these would permit examination
of a greater number of alternatives than would be practical with experi-
mental investigations. Broader investigation is needed to better
determine the long range optimum applications for flow equalization.
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III. INTRODUCTION
It is common knowledge that the flow in municipal sewage systems varies
from day to night, being at its highest during the early daylight hours
when there is increased demand for water and at its lowest in the middle
of the night. Sewage systems are usually designed with sufficient
capacity to carry the peak flows. Since these peak flows only occur for
a fraction of the time, the sewage system operates at less than its
design capacity during the remaining periods. As population grows and
more load is placed on the normal municipal sewage system, the point
will inevitably be reached at which the peak sewage flows exceed the
design capacity of the sewage system and additional capacity is needed.
One possible way to provide this additional capacity is to install flow
smoothing basins at key locations within the sewage system. These
basins would store sewage flow during the periods of high delivery and
release sewage into the downstream piping at more nearly constant rates.
The basin function would thus be to provide for better usage of existing
sewage piping during the off-peak hours by releasing sewage which has
been stored during the high demand period.
The purpose of this study has been to assess the feasibility of flow
smoothing compared to the installation of additional piping as a method
of increasing the capacity of existing sewage systems.
Toward this end, capital and operating costs have been estimated for flow
smoothing basins of several different types and for a range of design
conditions. These costs have been compared with capital and operating
costs for the installation of additional piping to predict the most
economical policy in given circumstances. During the study, design vari-
ables and economic parameters have been assumed to range over the sets
of values indicated in the following tabulation:
1. Basin types:
a. Concrete with a pump station.
b. Earthen with a pump station.
c. Concrete with no pump station.
d. Earthen with no pump station.
2. Pipe diameter from 8 inches to 30 inches.
3. Pipe slopes as calculated to correspond to assumed velocities
of 2, 2.5, 3, and 3.5 ft/sec.
4. Flow capacity (Y), expressed as a fraction of the capacity of
a completely filled pipe, of 0.7, 0.8, and 0.86.
5. Peak-to-average flow ratios: 1,5, 1.75, 2.0, 2.5, 3.5.
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"&
6. Equipment lifetime: pipes, 50 years; basins, 30 years ; in-
stalled equipment, 10, 20, and 30 years.
7. Interest rates; 4, 6, and 8 percent.
8. Basin aeration equipment designed for assumed BOD removals of
10 and 30 percent. (Based on activated sludge process to provide
adequate aeration and mixing - 10 and 30 percent removals are not
expected without sludge return.)
The general procedure for performing the calculations is the following:
For a particular combination of assumed inputs selected from the tabula-
tion above, evaluate (1) the size of the storage basin required, (2) the
capital cost of the basin plus its auxiliary equipment, (3) the operat-
ing and maintenance costs of the basin, (4) the total operating cost of
the basin including amortized debt service, (5) the capital cost per mile
for additonal piping equivalent to that currently existing, (6) operating
and maintenance costs per mile of the additional piping, (7) total
operating costs per mile of the additional piping including amortized
debt service, (8) the break-even length (BEL) or the length of additional
piping that could be installed for the same total operating cost as the
smoothing basin.
The BEL, in practical terms, is a measure of basin cost expressed in
units of equivalent miles of pipe. Thus a high value for BEL, in general,
reflects a more costly storage basin in a particular physical installa-
tion. If the length of additional piping required exceeds BEL, a
smoothing basin is favored; otherwise, additional piping is favored.
Although practice might differ depending on local circumstance, for
simplicity in this analysis it has been assumed that additional piping
will be the same diameter as existing piping. However, final BEL values
are on a unit capacity basis for both basin and pipe. This tends to
diminish the effect of a fixed pipe diameter choice. Final calculations
for an actual cost comparison should be tailored to the individual case.
Detailed methods of calculation used in this present project are presented
in the following section.
*
Although it may seem that basins would outlast pipes, pipes are de-
signed for longer periods to avoid costly excavation for replacement.
The design lifetimes chosen are similar to those suggested in Fair and
Geyer [4], page 117, for sewers and treatment works.
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IV. METHODS OF CALCULATION
The detailed formulae and correlations that have been used in this study-
are listed in this section.
Estimation of Peak-to-Average Flow Ratio
Correlations for the determination of the peak-to-average flow ratio in
municipal sewage systems have been reported by Gifft [1], Harmon [2],
Johnson [3], Fair and Geyer [4], Babbitt and Baumann [5], and Geyer and
Lentz [6]. For this study the following equation, based on Gifft's
results, is recommended for estimation of the peak-to-average flow ratio,
QP/QA, versus population for residential districts:
QP/QA = X = 2.2(1/P)°-08° (1)
where QP/QA = X = the ratio of the peak flow to the average flow for
the max-day
P = the contributing population, thousands.
Estimation of Required Storage Basin Capacity
In order to compute the storage volume required to smooth a particular
fluctuating flow, it is necessary to know or to be able to approximate
some of the characteristics of the flow hydrograph. In Figure 1 is
shown a typical sewage flow hydrograph for 1 day. The storage volume
required to smooth this hydrograph is proportional to the portion of the
shaded area above QA on the figure, and is labeled V.
In general, detailed hydrographs of streams to be smoothed may not be
available. In such circumstances it is desirable to have available a
technique for approximating the characteristics of the hydrograph nec-
essary for the estimation of the storage volume required for smoothing.
Formulae for this purpose have been developed as a part of this study
from a set of hydrographs representing the flow to the Durham New Hope
Waste Treatment Plant.
One technique which was tried and subsequently discarded was to approxi-
mate the area above the average line with an oblique triangle whose base
coincided with the average line (see Figure 1A). The required storage
volume would then be estimated by the area of the triangle, (l/2)bh,
where h = QP - QA and b represented the duration for which the flow
exceeded QA. The method was discarded because daily variations in the
value of b were difficult to generalize.
Another more valuable technique for the approximation of the storage
volume required is to assume that the hydrograph is reasonably represented
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o
0600
0600
(A) Representative Typical Sewage Flow Hydrograph for 1 Day.
(Triangle Approximation Superimposed on Hydrograph for
Determining VT.)
0600
0600
(B) Square Wave Model Hydrograph for 1 Day.
FIGURE 1. Representative Typical and Square Wave Model
Sewage Flow Hydrographs.
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by a square wave, as in Figure IB, with the flow varying instantaneously
between its peak and minimum values. For a hydrograph with this wave
form, the storage volume required for smoothing can be obtained provided
the maximum, average, and minimum flows, as well as the pulse time, can be
estimated in terms of the nature of the flow. This can be done as fol-
lows: The literature [1,7] indicates that for sanitary flows the
average-to-minimum flow ratio can be assumed identical to the peak-to-
average ratio. Thus the relationship X = QA/QM = QP/QA is assumed. By
the definition of the average, a material balance provides
QA
and thus
= QA - QM = X - 1
QP - QM X2 - 1 '
VS, the square-wave estimate of the storage requirement, can be calcu
lated from
VS = h
or
(3)
Since QP/QA = X and we have assumed X = QA/QM, the above equation reduces to
VS = QA(X - X ~
or
X2 - 1
= YQF ^-) . C4)
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In Table 7, Appendix B, the results of the analysis of actual hydrographs
are presented. Storage volumes required to smooth the actual flows have
been estimated by planimeter (VD), by the triangular approximation (VT),
and by the square-wave approximation (VS). The most conservative approxi-
mations (i.e., those assured of predicting sufficient storage volumes)
are those resulting from the utilization of the square wave. Therefore,
the square-wave estimates have been used in subsequent calculations.
Note that the installation of a smoothing basin of volume VS will cause
the flow downstream of the basin to be constant at QA rather than to
fluctuate between the maximum QP and the minimum QM. This means that
the downstream pipe is now operating at less than its design capacity,
QP. As a consequence of the introduction of the smoothing basin, the
downstream pipe is now capable of handling a higher flow—that is, X
times its present average flow, QA. This higher flow must also be
smoothed. To do so requires a storage volume to smooth a fluctuating
flow that has an average equal to the design capacity. This volume can
be caluclated using the previous formula and assumptions, but with an
average flow equal to the previous peak flow. If we designate the new
conditions with primes, use the same value and definition of X for the
new case and assume that the average-to-minimum flow ratio is equal to
X for both cases,
QA' = QP = YQF
QP' = XQA' = XQP = XYQF
XX X
Now, let the smoothing volume required for maximum utilization be VM.
Using Equation (3) for the new conditions,
(YQF
VM = (XYQF - YQF)
= YQF(X -
(XYQF
X ~ X
X - 1
or
VM = YQF
(6)
10
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Equation (6) provides the storage that would be needed if one were to
use all the additional capacity resulting from smoothing, assuming that
the new flow exhibits the same wave form and peak-to-average ratio as
the existing flow. Note that VM is simply VS multiplied by X. This
result can also be deduced directly from the next to last equation on page 9
QA will be the only quantity changed for the new case; its value will
be increased by the factor X resulting in the same increase in the
required smoothing volume.
Cost Estimation for Concrete Basins
Construction assumptions for concrete basins were the following:
1. A constant total variation of 15 feet between minimum and maximum
levels.
2. A minimum level of 1 foot above the bottom with additional sump
provision under each aerator as required by aerator size.
3. A minimum freeboard above the liquid surface of 3 feet for open
stations and of 1 1/2 feet in excess of the exposed height of
aerators for enclosed stations.
4. Minimum thickness of reinforced concrete of 1 foot for all sections
including roofs for enclosed stations.
5. Three feet of additional excavation on all sides of excavations
for erecting concrete forms.
6. Stations to be installed at a pipe depth of 3 feet with the maximum
liquid level of the station at the invert (bottom inside) of the
downstream pipe. Pipe installations deeper than 3 feet may be
common, however a variation in pipe depth should have a negligible
effect on BEL. For example, a 6-foot sewer depth would require
increasing the excavation depth from 19 to 22 feet. The percentage
increase in excavation costs may be about 14 percent but this would
represent a maximum of 5 percent of the total basin cost. Consider-
ing the conservativeness of other assumptions, variation of pipe
depth snould have little effect on the attractiveness of flow
smoothing.
Costs were developed for several representative volumes with and without
provision for concrete covers. The procedure was to assume a square of
side L such that the product of the 15-foot variable depth and the area
(1,2) equaled the chosen useful volume. Covers were assumed to be equal
in area to L . The concrete height, h', was set equal to 15 + (1 + aerator
clearance), feet [11]- Thus the required amount of concrete was V ,
cone
11
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Vconc = [4L(1)h<
for open construction; and
V - [4L(l)h' + 2L (l)](^y), cu yds
cone H
for enclosed construction.
Excavation costs were developed by allowing for an excavation of suitable
length to allow for wall thickness and backfill, H(H = L + 2 + 6), ft,
and of sufficient height to include wall thickness, sump allowance, and
freeboard, h(h = h' +2+2+3), ft,
h = h1 + 7 .
Thus the excavation volume was
V = «,2h (•£=), cu yds.
excav 27
Land areas were determined by assuming that a 10-foot clearance would be
required around the excavation and, in addition, that a 50-percent in-
crease in area would be required to supply an access road. Thus for
concrete stations the land area was calculated by
a .
land 43,560 ' acres-
The costs determined by summing concrete, excavation, and land costs
were increased by 20 percent for engineering and contingencies. Cost
calculations for concrete smoothing basins are summarized in Table 8,
Appendix B.
12
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Cost Estimation for Earthen Basins
Construction assumptions for earthen basins were
1. A minimum dike width of 8 feet.
2. Inside slopes of 1:3 to the upper waterline and 1:1 below that.
3. An outside slope of 1:2.
4. A minimum freeboard of 3 feet.
5. A minimum waterline of 1 foot.
6. A maximum water level change of 15 feet.
7. A water surface area at the midline, between maximum and minimum
water levels, equal to that of a square such that the volume gen-
erated by translating the square 15 feet vertically equals the
desired basin volume.
8. An above-grade dike rise limited to using the excavated earth.
9. A maximum water level that coincides with the invert of the down-
stream side of the pipe, (Upstream pipe depth is essentially the same.)
For earthen basins an excavated volume, paved area, and total land
requirement were calculated. Figure 2 shows a cross section of a
typical earthen basin. Combining the 1:1 slope of the side walls (below)
the waterline) with the 15-foot level variation, 1-foot minimum water
level, and the assumption that the mid-waterline (1 + 15/2, feet from
the bottom) had a side L = /V/15 ft, the various areas and volumes can
be found as follows. The bottom area (A£) equals [L - 8.5 (1/1)2]2, ft2.
The wetted and paved side areas (adjusted to pave the aerator sump
walls) equal 4[(L - 1/2~(18)], where the "4" provides for the four sides
and L is the width at the mid-waterline; hence, (L - 1) is the mid-
width of a side including an additional 1 foot of depth for the minimum
water level. The radical corrects for the pyramidal shape, and the (18)
represents the wall height adjusted to include the sump area.
The volume of earth excavated was calculated from the formula for the
volume of a truncated pyramid whose upper and lower base areas were AI
and A£,
= [L + 7.5 () 2]2
[L - 8.5 (^) 2]2
13
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WATER LEVEL
IEXiSTING
GRADE
7
M!D
WATER LINE
MINIMUM
WATER LEVEL
AERATOR SUMP
PAVEMENT
LINING
FIGURE 2. Half-Section Through Paved Earthen Basin.
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and whose height (h) equaled the sum of the minimum water level plus the
15-foot maximum water level variation plus 2 feet sump allowance. The
volume of the pyramid was increased by the product of the upper water
level area (AI) and the 3-foot thickness of the cut to the pipe. The
volume of the excavation (VEX) was thus
h + (A) (3 ft)
The land area required was calculated by starting at the upper waterline
(pipe invert) with [L = 7.5(1/1)2] and extending this line in both direc-
tions for the run required to achieve the necessary dike rise at the
specified slope (but including the minimum dike width of 8 feet). The
result was about (L + 90) feet for a 3-foot cut below grade plus a 3-foot
minimum dike height above grade. A 15-foot wide buffer strip was assumed
necessary beyond the dike, and thus the final area was (L + 120)2, ft2.
Table 9, Appendix B, summarizes these calculations and the costs assigned
to earthen basin construction.
Figure 3 shows the relationship of total basin construction costs versus
live volume for enclosed concrete and open paved earthen stations.
Capital Costs of Auxiliary Equipment—Pumps and Aerators
The installed costs of pumping stations [8] (Figure 4) have been used in
the present studies. They are probably on the high or "safe" side, since
they include items for which costs have been allowed in smoothing station
construction—that is, excavation, wet well construction, electrical and
piping connections, fencing, and close-out. Finally, above-grade package
plants are only 60 percent of the cost of below-grade package plants and
could reduce pumping costs still further.
Installed costs of aerators as obtained from vendors [11,16,17,18] are
shown in Figure 5. The Aqua Jet data were used in this analysis; these
data were the most conservative and complete. Aerators were sized to pro-
vide aeration equivalent to that which would remove 10 and 30 percent of
an assumed 200 mg/£ average BOD level, assuming 1.3 Ib of oxygen per Ib
of BOD and a transfer rate of 2.5 Ib oxygen per hp-hr. These levels of
BOD removal may not actually be obtained without an activated sludge, but
the aeration provided should be sufficient to prevent septicity. In order
to provide sufficient mixing and aeration for different basin residence
times, the horsepower calculations should be based on 30-percent BOD re-
duction for long average residence times (6 hr) and 10-percent reduction
for short average residence times (2 hr). This method of sizing aerators
for equalization basins, based on common aeration and mixing situations,
is believed conservative. It is consistent with recommendations in Chapter
3 of the EPA Upgrading Manual (21). The method could be refined when data
from actual applications are available. In this study, the aeration
capacity was sized to handle the maximum flow through the storage volume
and standby units were included.
15
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1000
CVMC,ENCLOSED CONCRETE
CVMC-PRIME, PAVED EARTHEN
BASIN VOLUME, MG
Figure 3. Construction Costs for Basins.
16
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10,000
< 1,000
O
O
CO
o
o
CJ
D
a:
t-
-------
O)
00
O
o
tn
tr
UJ
<
o
in
o
o
Q
UJ
MIXING EQUIP CO.(REF 16)
AQUA JET (REFII)
ASHBROOK(REF
REX CHAINBELT (REF. 17)
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
AERATOR HORSE POWER ,H.R
FIGURE 5. Installed Costs for Floating Aerators.
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The calculations used to determine aerator sizes and costs are summarized
in Table 10 in Appendix B. Table 8 includes operating and maintenance
costs (0-M) for aerators and is developed for flow ratios (Q/V) of 4 and
2 and for BOD removal bases of 30 and 10 percent.
Graphs of installed equipment costs versus storage volume were developed
with the parameter (Q/V) identical to (QP/VM) ; see Figures 6 and 7. Re-
ferring to the figures, specific curves show the costs of aerators alone
and the sum of aerator and pump costs for a given basin size.
Capital Cost of Sewer Pipes
The installed costs of sewer pipes (CP) were based on the costs given in
a recent EPA/Taf t Research Center Internal Memo [8] . Recent local costs
for pipes seem to conform well with this reference; see Figure 8. The
equation of the curve in Figure 8, CP = 1540.7(0 + 2. 0436) !• 37949, was
used to compute CP for cost calculations in this report.
Operating and Maintenance Costs
Pumps. Two relationships were used for pump operating and maintenance
costs (PUOM) . The first was taken from Reference 8; the second was
developed from local data. Both relationships are compared in Figure 9.
Local costs were based on Ic/kwh for power, a nominal head (TDK) of
40 feet, and an overall efficiency of 40 percent [19]. Power require-
ments are 0.025 hp/gpm, and power costs are 0.310/1000 gal.
In Durham, pump stations require 4.75 hours of routine maintenance labor
per month plus an allowance for about one mechanical seal replacement
per year regardless of flow [9], Present (1971) rates for maintenance
labor plus overhead result in an estimated cost of $50/month per urban
station. This cost was converted to pump labor cost in c/1000 gallons
by assuming various station flows. PUOM was obtained by summing the
values for pump labor with the 0.31C/1000 gal. charge for power and
plotted in Figure 9 as PUOMLoc- Conservating In-ln straight line equa-
tions of the curves are
(~\ O £
=2.1 (QP)~ ' (7)
PUOMLOC = 0.75 (OP)"' (8)
The more conservative Equation (7) was used for values tabulated in this
report. QP is used as the variable, because this will be the maximum
downstream average flow after smoothing.
Aerators. Aerator operating and maintenance costs (AEOM) were estimated
from Reference 10, assuming Q/V of 4, an intermediate value; power at
IC/kwh; and motor efficiency at 90 percent. Aerator power for 30-percent
19
-------
1000
o
o
A I0°
to
z
00
o
o
I-
z
LU
Q.
5
o
10
..0
0/V=8 CVME-
I
0/V=4 CVME-30
?
Q/M--2 CVME-30
0/V=8 CVME-30-PRIME -»•
O.I
0/V = 4 CVME-30-PRIME
0/V=2 CVME-30-PRIME
1.0
10
BASIN VOLUME, MG
Figure 6. Installed Costs for Equipment (30-Percent BOD Removal)
20
-------
1000
o>
z
o 100
o
o
in
CO
O
u
z
LU
2
a.
ID
o
UJ
10
1.0
Q/V=8 CVME-
Q/V =4 CVME-IO
Q/V=8 CVME-IO-PRIME
Q/V = 4 CVMC-IO-PRIME
Q/V = 2 CVMC-IO-PRIME
O.I
10
100
BASIN VOLUME, MG
Figure 7. Installed Costs for Equipment (10-Percent BOD Removal)
21
-------
1000
o
LU
Q
O
O
O
en
o
o
o
cc
h-
o
0
100
10
1.0
1.37949
= 1540.7(0+2.0436)
1.0
10 100
INSIDE PIPE DIAMETER, INCHES
Figure 8. Construction Costs for Pipelines.
22
-------
5
4
£!
z
PUOM =2.1 (OP)
OSW
-0.26
NJ
CO
o
o
o
5"
o
1.0
0.8
0.6
0.5
0.4
0.3
PUOM = 0.75 (OP)
LOG
rO.26
0.2
0.2 0.3 0.4 0.6 0.8 1.0 2 3 4 6 8 10
FLOW, OP, MGD
20 30
Figure 9. Pump Operating and Maintenance Cost Relationships.
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BOD removal is 10.8 hp/MGD, and power cost is 0.216C/1000 gal. Aerator
maintenance labor, estimated from Reference 10, is
Annual
Item Hours
(a) Motor overhaul 5
(b) Lint removal 13
(c) Lubrication 1
(d) Painting 2
(e) ^Miscellaneous, __4_
e.g., "jamming" 25
Labor
Rate
High
Low
High-Low
High
High
Occurrence
3—5 years
weekly
semiannual
annual
irregular
For city labor plus overhead at $10.00/hr, the labor costs are 0.69
-------
N3
Ln
AEOM-30 = 0.36(QP)
O O
-0.20
AEOM-IO=0.23(QP)
0.03
0.
0.2 0.3 0.4 0.6 0.8 1.0 2
FLOW, OR MGD
8 10
20 30
Figure 10. Aerator Operating and Maintenance Cost Relationships,
-------
Total Costs, Including Amortized Capital
Basins Including Auxiliary Equipment. The total cost per unit of new
capacity, TACC, is given by Equation (11):
TACC = (DARC + DARE)/TQI + DVOM (11)
where DARC and DARE, the daily debt service requirements for basin capac-
ity and equipment, are determined by capital costs and the capital
recovery factors,
TUPP - (CVMC)(VMCRF) ,
DARC - • jg^ , ?/day
Division of DARC and DARE by the daily flow capacity increase, TQI, pro-
vides costs per unit of new sewage transport capacity in c/1000 gallons.
An example calculation of a capital recovery factor (erf) for 1=6 per-
cent and LIFC = 30 years (basins) is
VMCRE -
(1 + I) - 1 (1.06) - 1
The second term on the right side of Equation (11), DVOM, represents the
daily cost of basin operation and maintenance and is the sum of pump and
aerator 0-M costs,
DVOM = PUOM + AEOM .
M£es_. The total cost for pipes per unit of capacity, TACPS is given bv
Equation (12):
26
-------
TACP = H- DPOM
DARP is the daily debt service requirement for relief pipe and is deter-
mined by pipe capital cost (CP) and the pipe erf (PRF),
, $/day_mlie.
The pipe capital costs, CP, were calculated from the equation given in
Reference 8: CP = 1540.7(D + 2.0436)1-37949, $/mile. The pipe erf was
caclulated as
- 0.06344 .
(1 + I) - 1 (1.06) - 1
The term for pipe operation and maintenance, DPOM, represents the daily
charges for cleaning and repairing a mile of sewer pipe,
DPOM = - , $/day-mile .
Division of DARP and DPOM by QA provides TACP as the cost of pipe per
unit of sewage transported per mile in units of c/1000 gal.-mile.
BEL Calculation
The quantities TACC and TACP are divided to obtain BEL. The unit
capacity basis of TACC and TACP tends to counteract the assumption
that new pipe will be the same diameter as the original.
27
-------
V. DISCUSSION
The effects of design and economic variables on the cost of smoothing
basins for municipal sewage systems are summarized in this section. We
continue to express basin cost in equivalent miles of pipe (BEL). Recall
that low values for BEL favor the installation of smoothing basins; other-
wise, additional piping is favored.
The trends exemplified in the tables and figures in this section have
been developed by considering variation of the individual design param-
eters about some arbitrarily chosen base design. Unless otherwise
indicated, the basic design is that indicated in Table 1.
TABLE 1
Base Values of Design and Operating Variables
Pipe diameter 12 in.
Interest rate 6%
Design pipe capacity 80% of full
Peak-to-average flow ratio 2.0
Slope to give velocity of 2,5 ft/sec
BOD removal 30%
Construction A, concrete with pumps
The Effect of Type of Construction. The effect of the type of construc-
tion in basin costs is summarized in Table 2.
TABLE 2
Effect of Construction Type
Basin Type BEL, miles
A, Concrete with pumps 2.358
B, Earthen with pumps 1.561
C, Concrete without pumps 1.437
D, Earthen without pumps 0.640
29
-------
As might be expected, the cost depends rather strongly upon the elaborate-
ness of the construction involved.
The Effects of Pumping Costs. The preceding results were obtained with
the SWRI-OSW pump operating cost correlation [8]. If the local correla-
tion is used, the above values for BEL can be reduced by about 25 percent.
The Effect of Slope. The effect of slope, hence flow velocity, on BEL is
shown in Figure 11. The BEL values increase rather markedly as pipe
slope or velocities increase. This means that flow smoothing is most
attractive in areas where sewer line slopes are low.
The Effect of Pipe Diameter. The effect of pipe diameter on BEL is
illustrated in Figure 12. The BEL increases with pipe diameter but not
so dramatically as with velocity. The larger pipe diameter implies a
larger flow together with a larger and more expensive basin. On the
other hand, there is a slight increase in the unit cost of pipe as one
goes to the larger sizes. The net result, as indicated, is an increase
in BEL.
The Effect of Peak-to-Average Flow Ratio. The effect of the peak-to-
average flow ratio is illustrated in Figure 13. Note that as the flow
ratio increases, the BEL drops off rather dramatically. For a given
pipe diameter, increasing the peak-to-average flow ratio implies reduc-
ing the average flow since the peak is fixed by the assumed pipe diameter.
Such a change would require a basin of only moderate size increase (see
Equation 4) but would provide high potential benefits from smoothing.
Thus the basin costs would be lower per incremental unit of benefit as
reflected in the reduced values of BEL.
The Effect of Pipe Capacity. The effect of pipe capacity expressed as
the fraction of its capacity when flowing full is illustrated in Figure 14.
With an increased pipe capacity the pipe is used more effectively, BEL's
are higher, and smoothing is less attractive.
The Effect of Interest Rate. The effect of interest rate on the BEL is
shown in Figure 15. Note that this plot is for Type D rather than Type A
construction. The decreased values of BEL corresponding to higher
interest rates result from the fact that pipe costs are almost entirely
composed of debt service whereas basin costs include substantial amounts
for operating and maintenance. Thus increased cost of debt service tends
to favor basin construction, as is indicated by the lower values of BEL.
The Effect of Aeration. Increasing aeration by choosing the 30 percent
basis rather than the 15 percent basis increased the BEL from 1.7 to 2.0
miles as illustrated in Figure 16. The velocity for this comparison was
assumed to be 2 ft/sec rather than the basic 2.5 ft/sec.
The Effect of Equipment Life. The effect of equipment life on BEL is
illustrated in Figure 17. Note that the velocity has been assumed at
30
-------
3.0
UJ
m
2.0
3.0
UJ
OD
2.0
2.5
3.0
3.5
VELOCITY, FT/SEC
FIGURE 11. Effect of Velocity.
2.0
I
8 12 16 20 24
PIPE DIAMETER, IN.
FIGURE 12. Effect of Pipe Diameter.
28 30
31
-------
3.0
UJ
CD 2.0
,0
1.0
2.0
3.0
3.6
PEAK TO AVERAGE FLOW RATIO
FIGURE 13. Effect of Peak to Average Flow Ratio.
32
-------
LJ
CO
2 .1
2.0
1.9
I .8
I .7
.8
.9
PIPE CAPACITY-FRACTION OF FULL
FIGURE 14. Effect of Pipe Capacity.
33
-------
m
1.0
.9
'8
.7
.6
.5
TYPE D CONSTRUCTION
4
6
Vs3.5 FT/SEC
FT/SEC
INTEREST RATE , %
FIGURE 15. Effect of Interest Rate.
8
2.0
1.9
1.8
1.7
1.6
1.5
V= 2 FT/SEC
10%
30%
BOD REMOVAL,%
FIGURE 16. Effect of BOD Removal,
34
-------
CD
2.5
2.4
2.3
2.2
2.1
2.0
V=2FT/SEC
10
20
30
EQUIPMENT LIFE , YRS
FIGURE 17. Effect of Equipment Life.
35
-------
2 ft/sec rather than the basic 2.5 ft/sec. Since equipment life affects
only the basin cost the decrease in BEL with longer equipment life is
what would be expected.
Additional graphical and tabular presentation of the computed results
are included in the Appendices. In general, the procedure for utilizing,
this information in a particular circumstance is to use the tabular data
to ascertain the BEL values corresponding to the set of design and eco-
nomic parameters then applicable. If the additional outfall line require-
ment should exceed the BEL, smoothing basin construction should be given
serious consideration. The methods outlined in this report can serve
as a basis for making further cost comparisons tailored to the require-
ments of the individual case.
36
-------
VI. ADDITIONAL STUDIES
Population Increase
To this point the procedure has been to balance estimated basin costs
against estimated costs of additional pipe to get the break-even length
(BEL),^assuming in both cases that the incremental capacity is suffi-
cient to satisfy immediate demand. In general, the additional capacity
obtained by smoothing basins will only equal that obtained by relief
pipe when the peak-to-average flow ratio is 2. The question arises as
to what conclusions can be drawn concerning basins versus relief pipes
when the peak-to-average flow ratio is other than 2.
An additional pipe of identical construction will double the existing
capacity; installation of a smoothing station will increase existing
capacity by a factor X. Consequently, basins provide greater capacity
when X exceeds 2, and additional piping provides greater capacity when
X is less than 2.
If the demand for sewage capacity is assumed to grow at the annual rate
Z, then the time (6) during which a capacity increase by the factor X
will remain adequate is given by the solution to
X = (1 + Z)
or
In X
p In (1 + Z) '
years
Designating as 8p the adequacy time for pipe and as 9^ the adequacy time
for basins, it follows that for X = 2, OVM = 9p and the cost analysis
via the BEL is on relatively firm ground. Even for this case, it is
necessary to assume that significant refinancing costs will not be in-
curred due to the life of some basin component being less than the
maturation time of the original financing. For cases involving very
small values of Z such that 6VM and 8p > 50 years, adequacy times exceed
assumed equipment life and need not be considered. For the cases where
X * 2 and Z is not small, some adjustment should be made to reflect the
fact that the two alternatives are not equal lived.
Such an adjustment is simple to calculate if one assumes that Z is con-
stant for the maximum life of 50 years. In this case, an adjustment can
be made by computing the number of replacements necessary during the 50-
year lifetime. Thus, if NRP and NRC are, respectively, the number of
replacements required for pipes and pipes + basins:
37
-------
NRP = ~, (13)
and
VM
Equation (13) is just the number of times an equal-sized pipe would have
to be replaced in 50 years due to a constant growth in demand. Equation (14)
assumes an initial time, OVM> during which a basin will provide adequate
capacity and allows for additional future capacity by using equal-sized
pipes in conjunction with more basins. NRC must be applied to the total
costs of replacements of pipes + basins. The adjusted costs reflecting
differing "times of adequacy" can be calculated by multiplying the total
costs of each alternative by the appropriate number of replacements re-
quired during the base period. If ATACC and ATACP represent the adjusted
costs:
ATACC = NRC (TACC + TACP) ,
ATACP = NRP (TACP) .
These equations represent the total costs after NRC or NRP replacements
have been made. The least expensive alternative should be chosen.
For practical applications, large values of Z cannot be assumed to re-
main constant for very long.
An example of the effect of Z on the "time of adequacy" is listed below.
VM P' VM p'
Z, years Z, years
percent (X = 2) percent (X = 2)
1 70 5 15
2 36 6 12
3 24 7 10—11
4 18 8 9
38
-------
Local regions tributary to a sewer system can be expected to grow faster
when young and to reach a "saturation" condition as they grow older.
Many city districts even show reduced populations after "maturity" [5].
Thus one would expect fewer replacements to be required than Equations (13)
and (14) indicate.
Downstream Effects
It was assumed that the newly obtained capacity would apply to all the
downstream units in the sewage system except the treatment plant. Thus if
an existing downstream pumping station was operating at design capacity
before flow smoothing, the capacity was assumed to be increased in pro-
portion to that provided by smoothing. Of course, pumping station
operating and maintenance costs will increase for increased flows.
If sewer tributaries feeding a trunk line are out of phase with the main
flow such that the peaks in the tributary flow fill the valleys in the
main flow, then an inherent smoothing will occur. Should this be the case,
one would need to consider the hydrograph of the combined flow to evaluate
the potential benefits of further smoothing.
39
-------
VII. ACKNOWLEDGEMENT S
The investigators at Research Triangle Institute would like to express
their special appreciation to the personnel of the Triangle Region
cities for their fine cooperation in obtaining the records, maps, site
access, and calibrations useful to this study.
Other agencies that were especially helpful to the investigators
include the North Carolina Board of Air and Water Resources and the
Research Triangle Regional Planning Commission.
Finally appreciation is expressed to the Office of Research and
Monitoring of the Environmental Protection Agency for their financial
support under Project No. 11010 FBI, Contract No. 14-12-935 and
especially to Mr. C. L. Swanson and Dr. H. E. Bostian of EPA for their
support and encouragement.
41
-------
VIII. REFERENCES
1. Gifft, H. M.: "Estimating Variations in Domestic Sewage Flows,"
Water Works and Sewerage, May 1945.
2. Harmon, G. W.: "Forecasting Sewage Discharge at Toledo Under Dry-
Weather Conditions." Engineering News Record, 8£, June 27, 1918.
3. Johnson, C. F.: "Relation Between Average and Extreme Flow Rates,"
Engineering News Record, 90, October 8, 1942.
4. Fair, G. M., and J. C. Geyer: "Water Supply and Waste-Water Disposal,"
John Wiley and Sons, Inc., New York, New York, 1965.
5. Babbitt, H. E., and E. R. Baumann: "Sewerage and Sewage Treatment,"
Eighth Edition, John Wiley and Sons, Inc., New York, New York,
1958.
6. Geyer, J. C., and J. J. Lentz: "An Evaluation of the Problems of
Sanitary Sewer System Design," Department of Sanitary Engineer-
ing and Water Resources, The John Hopkins University, Baltimore,
Maryland, September, 1964.
7. "Design and Construction of Sanitary and Storm Sewers," Water Pol-
lution Control Federation Manual of Practice, No. 9, Washington,
D.C., 1969.
8. Internal Memo—AWTRL—from Robert Smith to Dr. William N. Fitch,
"Cost-Effectiveness Task Force—Economics of Consolidating
Sewage Treatment Plants by Means of Interceptor Sewers and
Force Mains," March 10, 1971.
9. Private Communication: Mr. Otha Hursey, Superintendent of Mainte-
nance, Department of Water Resources, City of Durham, North
Carolina.
10. Private Communication: Mr. Tom Alspaugh, Superintendent of Water
and Waste Treatment, Cone Mills, Inc., Greensboro, North Carolina.
11. Catalog Price List—Aqua-Aerobic Systems, Inc. 6306 North Alpine
Road, Rockford, Illinois. Plus personal conversation with
Mr. D. Crocker of Aqua-Aerobic Systems„ Inc.
12. Personal Conversation: Mr. J. Goodman, Director of Utilities, City
of Raleigh, North Carolina.
13. "Recommended Standards for Sewage Works," Health Education Service,
Albany, New York.
43
-------
14. Personal Conversations: Professor J. Lamb III, Environmental
Sciences and Engineering Department, School of Public Health,
University of North Carolina, Chapel Hill, North Carolina.
15. Private Communication: Mr. Harold Spaeder, Sales Representative
for Smith & Loveless, Inc., P. 0. Box 4476, Charlotte, North
Carolina.
16. Private Communication: Mr. Gary Morse of Robert E. Mason Co.,
Sales Representative for Mixing Equipment Co., 1726 North
Graham Street, Charlotte, North Carolina.
17. Private Communication: Mr. Charles Grimes of Rex Chainbelt, Inc.,
4610 West Greenfield Avenue, Milwaukee, Wisconsin.
18. Private Communication: Mr. S. V. Tench, Sales Representative for
Ashbrook Corp., P. 0. Box 11730, Atlanta, Georgia.
19. Personal Conversations: Mr. Richard N. Edwards, President, Aerobic
Control Corp. ,5705 New Chapel Hill Road, Raleigh, North Carolina.
20. McJunkin, F. E., and P. A. Vesilind: "Practical Hydraulics for the
Public Works Engineer—Part II." Public Works Magazine, October
1968.
21. Process Design Manual for Upgrading Existing Wastewater Treatment
Plants. U. S. Environmental Protection Agency Technology Transfer.
Program No. 17090 GNQ. October, 1971.
44
-------
IX. NOMENCLATURE
o
A = pipe cross-sectional area, ft .
AEOM = see PUOM.
AEOM-10,AEOM-30
= respectively, daily equivalent of the annual cost of opera-
tion and maintenance of aerators for 10- and 30-percent BOD
removal.
b = a fictitious time or duration for which flows exceed the
daily average flow, defined by a square-wave hydrograph
above the minimum flow, day/day.
BEL = a fictitious pipe length whose unit cost for sewage trans-
port is just equal to the unit cost of sewage transport by
smoothing basins, miles.
C = coefficient of friction in the Chezy formula.
CP = the capital cost of pipe, $1000/mile.
CP1,CP2,CPN,CPT
= respectively, the total capital cost of pipe segments 1, 2,
and "N", and of pipe, $1000/segment.
crc = capital recovery charge, equals the product of the capital
cost of an item and the capital recovery factor, erf, $.
1(1 + 1)1
erf = general capital recovery factor, erf = /-i ./, T-\n _ i •
CV,CVM = respectively, the capital cost of volumes to achieve partial
and maximum smoothing.
CVMC,CVME,CVMC-PRIME,CVME-PRIME
= respectively, the capital costs of concrete basins alone,
of basin aerators and pumps, of earthen basins alone, and
of basin aerators alone.
CVME-30,CVME-30-PRIME
= respectively, the capital cost of basin aerators and pumps,
and of basin aerators alone; in both cases the aerators are
sized to remove 30 percent of the basin influent BOD.
D = the inside diameter of any pipe, inches.
d = the depth of the wetted section in a partially filled pipe,
inches.
d/D = the "standard", or design, depth of flow for a sewer.
45
-------
DARC,DARE = respectively, the daily equivalent of the annualized capital
recovery charge for basin capacity and for equipment, $.
DARP,DPOM = respectively, the daily equivalent of the annualized capital
recovery charge for pipe and of the annual cost of pipe op-
eration and maintenance.
DVOM = daily equivalent of the annual cost of basin capacity opera-
tion and maintenance on a flow basis (DVOM = PUOM + AEOM),
C/1000 gal.
EQI = the estimated flow capacity increase obtained in a pipe by
partial flow smoothing, MGD.
I = interest rate, percent.
LIFC,LIFE,LIFP
= respectively, the assumed component lives of basins, equip-
ment, and pipes.
n = Mannings roughness factor assumed to vary with the depth of
flow but to equal 0.013 for QF.
NRC,NRP = respectively, the number of replacements of pipes plus basins
and of pipes during a 50-year planning period for a constant
growth rate Z.
P = contributing population in thousands.
PRF = see VMERF.
PUOM,AEOM = respectively, daily equivalent of the annual cost of opera-
tion and maintenance for pumps and for aerators.
Q = the flow capacity in any pipe running at partially full depth
d, MGD.
QA,QM,QP = respectively, the assumed average, minimum, and peak flow
capacities of a pipe, MGD.
QA1,QA2,QAN = respectively, the original average design flow capacities for
pipe segments 1, 2, and N, MGD.
QA18, QP18, etc.
= respectively, the assumed average and design peak flow capaci-
ties of 18-inch lines, etc., MGD.
QF - the nominal flow capacity in any pipe running full at atmos-
pheric pressure, MGD.
46
-------
QNP,QMP = respectively, the new partially and maximally smoothed flow
capacities of pipes, MGD. (QMP = QP = YQF).
R = hydraulic radius equal to D/4 for circular channels.
S = the slope of the hydraulic grade line, ft/ft.
TACC = total annualized cost for capacity via smoothing, C/1000 gal.
TACP = total annualized cost for capacity via relief pipe,
C/1000 gal.-mile.
TQI = the theoretical capacity increase available in a pipe by flow
smoothing.
U = Manning velocity for open-channel flow.
V = the storage volume required to smooth the original average
design flow in a pipe, MG.
VM = the maximum storage volume required to use the maximum flow
capacity of a pipe, MG.
VMERF,VMCRF,PRF
= respectively, the capital recovery factors for equipment,
for basins, and for pipes.
VS,VT = respectively, a square-wave and a triangular approximation
of the volume of storage required for smoothing,
X = the assumed or actual ratio of peak-to-average flow.
Y = Q/QF = the design capacity of a pipe defined as the ratio of
its capacity, QP, at the design depth to its capacity when
full, OF.
Z = growth rate of demand for sewage capacity.
n = recovery period, in years, assumed equal to the life of the
component (LIFE, LIFP, LIFC).
6 ,6 = respectively, the time-of-adequacy of pipes and of smoothing
^ basins, assuming growth rate Z.
47
-------
X. APPENDICES
Page
A. BEL-Value Graphs and Tables 51
Figure 18: Break Even Length Versus Pipe Diameter
for Case A (6-percent interest and 50-
30-30 component lives) 53
Figure 19: Break Even Length Versus Pipe Diameter
for Case B (6-percent interest and 50-
30-30 component lives) 54
Figure 20: Break Even Length Versus Pipe Diameter
for Case C (6-percent interest and 50-
30-30 component lives) 55
Figure 21: Break Even Length Versus Pipe Diameter
for Case D (6-percent interest and SO-
SO-SO component lives) 56
Figure 22: Break Even Length Versus Pipe Diameter
for Case A with Aeration for 10-percent
BOD Removal (6-percent interest and SO-
SO-SO component lives) 57
Figure 23: Break Even Length Versus Pipe Diameter
for Case D (4-percent interest, 30-per-
cent BOD Removal, and 50-30-30 component
lives) 58
Figure 24: Break Even Length Versus Pipe Diameter
for Case D (8-percent interest, 30-per-
cent BOD removal, and 50-30-30 component
lives) 59
Figure 25: Break Even Length Versus Pipe Diameter
for Case A for 20-Year Equipment Life
(6-percent interest and 30-percent BOD
removal) 60
Figure 26: Break Even Length Versus Pipe Diameter
for Case A for 10-Year Equipment Life
(6-percent interest and 30-percent BOD
removal) ......... 61
Tables 3-6: Computed BEL Values for Various Condi-
tions 62
B. Size and Cost Tables 79
Table 7: Various Estimates of Required Storage
Volume (V) to Smooth the Diurnal Varia-
tions in the Design Flow for the New
Hope Plant . 80
Table 8: Calculations for the Cost of Concrete
Smoothing Basins ...... 81
Table 9: Calculations for the Cost of Earthen
Smoothing Basins ..... 82
Table 10: Calculations for Size and Cost of Aera-
tors and Aerator 0-M Costs 83
C. BEL Computer Program ..... 85
49
-------
APPENDIX A
BEL-Value Graphs and Tables
51
-------
As before, the type of basin construction is designated as follows:
Case A: Concrete with a pump station.
Case B: Earthen with a pump station.
Case C: Concrete with no pump station.
Case D: Earthen with no pump station.
52
-------
UJ
_l
2
UJ
CD
I
UJ
UJ
>
UJ
EC
m
6.0
5.0
4.0
3.0
2.0 t
0.5
Y = 0.8
V= 2.0ft/sec
8 12 16 20 24 28 32
PIPE DIAMETER (D), INCHES
8 12 16 20 24 28 32
PIPE DIAMETER (D), INCHES
FIGURE 18. Break Even Length Versus Pipe Diameter for Case A
(6-percent interest and 50-30-3& component lives).
-------
Ul
-p-
to
UJ
UJ
CD
UJ
_J
•z.
UJ
UJ
UJ
a:
m
6.0
5.0
0.5 <
8 12 16 20 24 28 32
PIPE DIAMETER (D), INCHES
6.0
5.0
4.0
3.0
2.0
1.0
0.5
(1!)
CASE B
Y = 0.8
V=3.5ft/sec
X=l.5
,1.75
8 12 16 20 24 28 32
PIPE DIAMETER (D), INCHES
FIGURE 19. Break Even Length Versus Pipe Diameter for Case B
(6-percent interest and 50-30-30 component lives).
-------
CO
UJ
«J
UJ
X
h-
UJ
2
UJ
UJ
K
m
6.0
5.0
4.0
3.0
2.0
0.5
(I)
CASE C
Y= 0.8
V = 2.Oft/sec
X=l.5
3.5-
8 12 16 20 24 28 32
PIPE DIAMETER (D), INCHES
8 12 16 20 24 28 32
PIPE DIAMETER (D),INCHES
FIGURE 20. Break Even Length Versus Pipe Diameter for Case C
(6-percent interest and 50-30-30 component lives).
-------
(f)
UJ
UJ
m
Ul
_J
z
UJ
Ul
Ul
a:
ao
2.0
8 12 16 20 24 28 32
PIPE DIAMETER (D), INCHES
UJ
~ 2.0
UJ
CD
X
I-
0
z
Ul
Ul
>
Ul
UJ
o:
m
Y = 0.8
V= 3.5ft/sec
12
20
24
28
32
PIPE DIAMETER (D), INCHES
FIGURE 21. Break Even Length Versus Pipe Diameter for Case D
(6-percent interest and 50-30-30 component lives).
56
-------
6.0
CO
UJ
LU
m
X
o
UJ
_J
2
UJ
UJ
UJ
cc
m
Y=0.8
V = 2.0 ft/sec
Y = 0.8
V =3.0 ft/sec
0.5
8 12 16 20 24 28 32
PIPE DIAMETER (D), INCHES
8 12 16 20 24 28 32
PIPE DIAMETER (D) , INCHES
FIGURE 22. Break Even Length Versus Pipe Diameter for Case A with
Aeration for 10-percent BOD Removal (6-percent interest
and 50-30-30 component lives).
-------
CO
UJ
_J
UJ
m
X
o
UJ
_J
z
UJ
UJ
UJ
QC.
m
Y= 0.8
V= 2.0 ft/sec
0.0
8 12 16 20 24 28 32
PIPE DIAMETER (D), INCHES
2.0
CO
UJ
UJ
m
UJ
_1
2
UJ
UJ
g 0.0
m e
(ID
CASE D
Y =0.8
V= 3.5 ft/sec
12 16 20 24 28 32
PIPE DIAMETER (D), INCHES
FIGURE 23. Break Even Length Versus Pipe Diameter for Case D
(4-percent interest, 30-percent BOD removal, and
50-30-30 component lives).
58
-------
^ 2.0
.0
UJ
m
x
i-
o
2
UJ
_l
2
UJ
UJ
< 0.0
UJ Q
cc °
m
(I)
CASE D
Y= 0.8
V= 2.0 ft/sec
\2 16 20 24 28 -52
PIPE DIAMETER (D), INCHES
Y =0.8
V= 3.5 ft/sec
24
28 32
PIPE DIAMETER (D), INCHES
FIGURE 24. Break Even Length versus Pipe Diameter for
Case D (8-percent interest, 30-percent BOD
removal, and 50-30-30 component lives).
59
-------
CD
LJ
UJ
m
z:
h-
UJ
_J
UJ
>
UJ
UJ
cc
CD
7.0
6.0
5.0
4.0
3.0
2.0
S.O
0.5
8 12 16 20 24 28 32
8 12 16 20 24 28 32
PIPE DIAMETER (D), INCHES
PIPE DIAMETER (D), INCHES
FIGURE 25. Break Even Length Versus Pipe Diameter for Case A for
20-Year Equipment Life (6-percent interest and 30-
percent BOD removal).
-------
Cf-
en
UJ
UJ
CD
UJ
UJ
UJ
o:
m
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.5
Y = 0.8
V = 2.0 ft/sec
8 12 16 20 24 28 32
PIPE DIAMETER (D), INCHES
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.5
7
(II)
CASE A
Y= 0.8
V= 3.5 ft/sec.
«OY=I
^1.75
2.0
.2.5
3.5
8 12 16 20 24 28 32
PIPE DIAMETER (D), INCHES
FIGURE 26. Break Even Length Versus Pipe Diameter for Case A for 10-Year
Equipment Life (6-percent interest and 30-percent BOD removal).
-------
Notes for Tables 3 through 6, Appendix A
1. CVMC implies the use of a capital cost relationship for a "maximum"
smoothing volume constructed of reinforced concrete.
2. CVMC-PRIME implies the use of a capital cost relationship for a
similar smoothing volume constructed of paved earth.
3. CVME implies the use of the capital costs of built-up pumping sta-
tions in addition to floating aerators designed to remove 30 percent
of the feed BOD.
4. CVME-PRIME implies the use of capital costs for floating aerators
designed to remove 30 percent of the feed BOD (but omits the capital
costs of pump stations).
5. PVOM ^ 0 implies that the pump station 0-M costs were derived from
the relationship PUOM = 0.75(1/QOP)°-26.
6. AEOM-30 implies that the aerator 0-M costs were derived from an 0-M
relationship for 30-percent removal of BOD.
7. CVME-10 and AEOM-10 imply, respectively, the capital and operating
costs for aeration equipment designed to remove 10 percent of the
feed BOD. The "cases"—a, b, c, and d—are consistent as given
(see Section III, Introduction); and therefore, in Table 7, the
"A USED CVME-10 WITH AEOM-10" means costs for concrete tanks with
built-up pumping stations but aeration for 10-percent BOD removal.
62
-------
TABLE 3
CASE A. CVMC WITH CV^E. PyOM NOT EQUAL ZERO. USED AEOM30
INTRST LIFP LIFC LIFE VMAX VMIN RFVMC
•60000E -1 .50000E 2 .30000E 2 .30000E 2 .35000E i .20000E 1 .72652E ~l
RFVME
.72652E -1
RFP
.63445E -1
Y = .70
BEL MILES, D = 8 INCHES
Y = .80
Y = . 86
.0033 .0052 -0075 .Ol02
2~25
.50
.00
.0033 .0052 .0075 .Oj02
.0033 .0052 .0075 .Ol02
X
1.50 2.339 2.769 3.l78 3.573 2.587 3.063 3.5l7 3.954 2.733 3.236 3.716 4.i77
-? rr -* Q..Q r, - c f. ri A •? D n -too rt n-T -» ~x Q f r-\ ~f A A "Z fl A ft o ^o7 o KO"Z o QOn T r>/\4
1.'75 I."8i8 2.'l56 2.478 2
788
2* 00 l
~
'515 l"798 2
1*556 1
,50 .806
2'0i3 2'387 2*744 3'088
1>79 l'992 2^292 2.381
lll59 1.377 1
.948 1.127 1
068 2~329
790 2*016
585 1.786
.298 1.463 1.051 1.250 1.440 1.623
l'452 l|724 l'985 2^235
1.285 1.527 1.758 1.981
2-127 2 523 2 900 3 264
1-774 2*106 2*423 2 729
1*535 l'823 2*099 2*364
l'.359 1°.614 1.859 2.095
1.112 1.322 1.523 1.717
,_Lt-' A»C.'1-' i • ' w v^ i.^-^x X»*--'V JL,'IU J-.v^-1-* J.,J-J.t- o..^'*-«— A • ^ ^ w ^.»>^'
.958 1.104 1.244 .894 1.063 1.225 1.381 .945 1.124 1.296 1.461
BEL MILES, D = 12 INCHES
Y = .70
Y = .80
Y = . 86
.0019 .0030 .0044 .0060
1.50 2.740
1.75 2.142
00
3.50
1.791
25 1 552
1 375
1.127
959
,50
,00
3 .247 3 .732 4.199
2.542 2.924 3.293
2.127 2.449 2.759
1.844 2.124 2.394
1.635 1.884 2.124
1.341 1.546 1.744
1.142 1.316 1.485
.0019 .0030 .0044 .0060
3.033 3.596 4.133 4.$50
2.373 2.817 3.241 3.650
1.985 2.358 2.716 3.060
1.720 2.045 2.356 2.6.56
1.525 1.814 2.090 2.3.57
1.251 1.488 1.716 1.935
1.064 1.267 1.461 1.649
.8019 .0030 .0044 .0060
3.205 3.800
2.508 2.976
2.-099 2.494
1.820 2.163
1.613 1.919
1.323 1.575
1.126 1.341
4.368 4.915
3.427 3.860
2.872 3.236
2.492 2.C1CI
2.211 2.493
1.815 2.048
1.546 1.745
-------
CASE A. CVMC
1NTRST
.60000E -1
TABLE 3 (cont.)
PVOM NOT EQUAL ZERO. USED AEOM30
LIFP
.50000E 2
RFVME RFP
.72652E -1 .63445E -1
LIFC
.30000E 2
LIFE
.30000E 2
VMAX
.350QOE 1
VMIN
. 2 0 0 0 0 E 1
RFVMC
.72652E -1
Y = .70
BEL MILES, D = 16 INCHES
Y = .80
Y = . 86
.0013 .0021 .0030 .0041
.0013 .0021 .0030 .0041
1.50
1.75
2.00
2.25
2 50
3.' 00
3.50
3
2
1
1
1
1
1
.017
.366
983
"721
.526
'. 253
."067
3.578
2.811
2.357
2.047
1.816
1.492
1.271
4
3
2
2
2
1
1
.115
.236
.716
.359
. 094
.721
. 466
4
3
3
2
2
1
1
.632
.646
.061
.660
362
.942
.655
3
2
2
1
1
1
1
.341
. 623
199
.909
694
!391
.185
3
3
2
2
2
1
1
.964
.116
.615
.271
016
.656
.411
4
3
3
2
2
1
1
.560
.588
.012
.617
324
.911
.628
5.J33
4.043
3.396
2.952
2 622
2.J56
1.938
.6013 .0021 .0030 .0041
3 .-531 4.190 4.820 5.427
2.773 3.295 3.795 4.276
2.326 2.766 3.187 3.593
2.019 2.402 2.769 3.123
1.792 2 133 2.459 2 774
1.472 1.753 2.022 2.282
1.254 1.494 1.724 1.946
Y = .70
BEL MILES, D = 20 INCHES
Y = .80
Y = . 86
.0010 .0015 -0022 -0030
.0010 .0015 .0022 .0030
1.50 3.227 3.831 4.408
1.75 2.538 3.017 3.475
2.00 2.130 2.534 2.921
2.25 1.851 2.202 2.540
,50
,00
50
1.643
1 350
1.151
956 2.256
608 1.856
4.
3.
3.
2.
2.
2.
1.
964
917
294
865
546
095
787
3.
2.
2.
2.
1.
1.
1.
576
815
363
054
624
499
278
4
3
2
2
2
1
1
.245
.346
.812
. 445
.172
.786
.523
4 .
3.
3.
2.
2.
2.
1.
886
855
241
819
505
061
758
5
4
3
3
2
2
1
.502
.345
.6.55
.180
.827
.327
985
.0010 ..0015 .0022 .0030
3r780 4.489 5.166 5.818
2.977 3.539 4.077 4.596
2.500 2.975 3.429 3.868
2.173 2.587 2.983 3.366
1.930 2.298 2.651 2.992
1.587 1.891 2.182 2.463
1.353 1.612 1.661 2.102
-------
TABLE 3 (cont.)
CASE A. CVMC WITH CVME. PVOM NOT EQUAL ZERO. USED AEOM30
INTRST
.60000E -1
RFVME
.72652E -1
LIFP
•50000E 2
RFP
.63445E -1
LIFC
•30000E 2
LIFE
-30000E 2
VMAX
.35000E i
VMlN RFVMC
1 -72652E -l
Y = .70
BEL MILES, D = 24 INCHES
Y = .80
Y = .86
Ln
.0008 .0012 -0017 .0024 .0008 .0012 -00l7 .D024
X
1.50 3.398 4.035 4.645 5.232
1 75 2 678 3 l84 3 669 4 137
'678 3*088 3*.483
330 2*.687 3'032
2,388 2.696
1.966 2.220
2.00
2,25 l'957 2
2.50 1.738 2
150
07l
t)70
3.00 1.430 1.704
5.802
4 5_9i
3'967
983 3.367
1.930 2.299 2^653 2.994
1.588 1.892 2.184 2.467
3.766 4.473 5,
2 970 3.533 4,
2 497 2 972 3
2'.586 2'
.8008 .0012 .0017 .0024
3-.-9S2 4.730 5.446 6.136
3 142 3 737 4.307 4.857
2*642 3*145 3*627
2*298
2.042
2.433
,681 2.*C03
2.808 3
2 737 3.157 3,
563
169
2.312 2.611
o.uu l . •»«Ju J. . ' vi i l . ?o
-------
CASE A. CVMC KITH CVME.
INTRST
.60000E -1
RFVME
.72652E -1
LIFP
.50000E 2
RFP
.63445E -1
TABLE 3 (cont.)
PVOM NOT EQUAL ZERO. USED AEOM30
LIFC LIFE VMAX VMIN RFVMC
•30000E 2 -30000E 2 .35000E 1 .20000E 1 .72652E -1
Y = .70
BEL MILES, D = 30 INCHES
Y = .80
Y = .86
.0006 .0009 .0013 .0018
1.50 3 .605 4 .284 4.934
1. 75 2 .849 3 .389 3.907
2.'00 2."398 2.855 3.293
2*25 2*087 2 486 2.868
2>0 l."855 2 .'210 2.551
3 00 1.527 1.821 2.102
5.561
4.407
716
238
881
374
3.50 1.303 1.554 1.795 2.028
.3006 .0009 .0013 .0018
4.227 5.025 5.789 6.525
3.344 3.980 4.589 5.177
2.816 3.354 3.869 4.367
2.452 2 922 3.372 3.807
2.181 2J599 3.000 3.388
1 697 2.023 2.336 2.639 1.796 2.142 2.473 2.794
.0006 .0009 .0013 .0018
3.997 4.751 5.473 6.J68
3 161 3.761 4.337 4.692
2.661 3.169 3.656 4.£26
2 317 2 760 3 186 3.596
2 060 2.455 2.834 3.200
1.448 1.727 1.995 2.254
1.533 1.829 2.112 2.386
-------
TABLE 4
CASE B. CVMC-PRIME WITH CVME. PVOM NOT EQUAL ZERO'.' USED AEOM3Q.
*X VMIN
1 '. 2 0 0 0 0 E 1
INTRST
-60000E -1
RFVME
-72652E -1
LIFP
•5000QE 2
RFP
.63445E -1
Y = .70
LIFC LI
•30000E 2 -30000E
BEL MILES, D
Y =
S
x
1.50
1.75
2 00
2°25
2.50
3.00
3.50
.0033
1 .774
1 316
l"064
"899
'.762
.624
.521
2
1
1
1
0052
.074
.541
.246
054
.917
.732
.612
.0075
2.357
1 754
1.419
1.201
1.046
.835
.698
.
2
1
1
1
1
0102
.628
957
[585
1342
.169
.935
.782
.0033
1.947
1 446
l"l69
989
.860
.686
.573
!FE V
2 .350QOE
= 8 INCHES
.80
S
.0052
2.277
1 694
l'37l
1.160
1.010
.806
.674
.
2
1
1
1
1
0075
.590
929
"562
.323
.152
.921
.770
• 0102
2.989
2 154
l'Z45
1 479
1.288
1.030
.862
RFVMC
•72652E -1
Y = .86
.8033 .0052 .0075 .Ol02
2-049 2.396 2.726 3.042
1,522 1 783 2 03l 2 268
l'23l l'443 1^645 1.839
l]04l 1*222 1.394 1.559
.906 1*064 1.214 1.358
.723 .850 .971 1.086
,604 .710 .812 .909
Y = .70
BEL MILES. D = 12 INCHES
Y = . 80
Y = .86
.0019 .0030 .0044 .0060
X
1.50 1.991 2.335 2.662 2.975
1.75 1.485 1.745 1.992 2.229
2.00 1.204 1.416 1.618 1.812
2,25 1.021 1.201 1.374 1.539
2.50 .889 1.048 1.198 1.343
3.00 .712 .839 .961 1.078
3.50 .596 .703 .805 .903
.0019 .0030 .0044 .0060
2.190 2.570 2.931 3.278
1.635 1.922 2.195 2.457
1.327 1.561 1.785 2.000
1.125 1.325 1.516 1.699
.981 1.156 1.323 1.484
.785 .926 1.061 1.J91
.657 .776 .889 .998
.6019 .0030 .0044 .0060
2.306 2.707 3.089 3.454
1.723 2.026 2.314 2.591
1.-399 1.646 1.883 2.110
I.1186 1.398 1.599 1.793
1.034 1.219 1.396 1.566
.828 .978 1.120 1.257
.694 .819 .939 1.054
-------
TABLE 4 (cont.)
CASE B. CVMC-PRIME WITH CVME. PVOM NOT EQUAL ZERO. USED AEOM30.
INTRST LIFP LIFC LIFE VMAX VMIN RFVMC
.60000E -1 .50000E 2 .30000E 2 .30000E 2 .35000E 1 .20000E 1 .72652E -1
RFVME
.72652E -1
RFP
.63445E -1
Y - . 70
BEL MILES, D = 16 INCHES
Y = .80
Y - . 86
OO
.0013 .0021 .0030 .0041
.0013 .0021 .0030 .0041
1.535 1.757 1.971
1.765 2.080 2^380 2.6.69
X
1.50 2.136 2.512 2.869 3.212 2.353 2.769 3.164 3.?44
1.75 1.600 1.885 2.156 2.417
2.00 1.301
2.25
2.50
105 1
305
140
1 .495 1.678
1.307 1.467
3.00 .774 .915 1.050 1.180
3.50 .649 .767 .881 .991
1.436 1.695 1.941 2.*79
1.221 1.441 1.653 1.856
1.066 1.259 1.445 1.624
.855 1.012 1.162 1.306
.717 .849 .975 1.Q97
.8013 .0021 .0030 .0041
2 -. 4 8 0
1.861
1.515
1.288
1.125
.903
.757
2.919
2.194
.788
.522
.330
. 069
.897
3.337 3.738
2.512 2.817
2.049 2.301
1.745 1.960
1.526 1.715
1.227 1.381
1.031 1.160
BEL MILES, D = 20 INCHES
Y - .70
Y = .80
Y = . 86
.0010 .0015 .0022 .0030
X
1.50 2.247 2.647 3.028 3.394
1.75 1.689 1.993 2.284 2.564
2.00 1.377 1.627 1.866 2.097
2.25 1.172 1.386 1.591 1.788
2.50 1.024 1.212 1.392 1.566
3.00 .823 .975 1.121 1.262
3.50 .691 .819 .942 1.061
.0010 .0015 .0022 .0030
2.478 2.921 3.343 3.749
1.865 2.202 2.524 2.835
1.521 1.799 2.064 2.320
1.295 1.533 1.760 1 .980
1.132 1.341 1.541 1.735
.911 1.080 1.242 1.399
.765 .908 1.045 1.177
.0010 .0015 .0022 .0030
2.613 3.081 3.527 3.956
1.968 2.324 2.665 2.994
1.606 1.899 2.180 2.451
1.368 1.619 1 . o 6 C ? . 0 9 3
1.196 1.417 1.629 1.604
.962 1.142 1.313 1.480
.808 .960 1.105 1.246
-------
TABLE 4 (cont.)
CASE B. CVMC-PRIME WITH CVME. PVOM NOT EQUAL ZERO. USED AEOM30.
INTRST LIFP LIFC LIFE VMAX VMlN
.60000E "I -50000E 2 -30000E 2 -30000E 2 -35000E 1 -20000E 1
RFVME RFP
.72652E -1 .63445E -1
RFVMC
•72652E -i
Y = .70
BEL MILES, D = 24 INCHES
Y = .80
Y = . 86
ON
vo
.0008 .0012 .0017 .0024
.0008 .0012 .0017 .0024
1.50
1.75
2 00
2*25
2.50
3.00
3.50
2
1
1
1
1
337
762
439
'227
.073
. 864
.726
2.757
2 083
1*704
1 '. 4 5 3
1.273
1.026
. 863
3.158
2 390
1.957
1.671
1.464
1.181
. 994
3.544
2.685
2 ' 20l
l'.88l
1.649
1.332
1.122
2.
1.
1 .
1.
1.
.
580
947
592
357
188
958
805
3.045
2 303
1*885
1 609
1.410
1.138
.957
3
2
2
1
1
1
1
.489
*644
*167
.851
. 623
.311
.104
3.917
2 972
2'439
2"085
1.529
1.478
1.246
.0006 .0012 .0017 .0024
2.722 3.214 3.684 4.137
2, 056 2 432 2.793 3 i4i
'681 1*992 2*290 2*578
1.681 1
1.434 1
1.256 1
1.012 1
701 1.957 2.205
491 1.717 1.935
203 1.387 1.565
.851 1.013 1.168 1.319
BEL MILES, D = 28 INCHES
Y = .70
Y = .80
Y = . 86
.0006 .0010 . 0014 .0019
X
1.50 2.414 2.851 3.270 3.673
1.75 1.825 2.160 2.481 2.791
2.00 1.494 1.770 2.036 2.293
2.25 1 . 275 1 .512 1.741
2.50 1.117 1.326 1
.528
,962
,723
3.00 .900 1.071 1.235 1.394
3.50 .758 .902 1.040 1.175
.0006 .0010 .0014 .0019
2.666 3.152 3.616 4.063
2.018 2.391 2.748 3.092
1.653 1.961 2.257 2.943
1.412 1.677 1.931 2.177
1.237 1.471 1.695 1.913
.999 1.188 1.371 1.549
.841 1.001 1.156 1 .307
.8006 .0010 .0014 .0019
2.815 3.328 3.819 4.292
2.132 2.526 2.904 3.269
1.747 2.073 2.386 2.689
1.493 1.773 2.043 ^.304
1.308 1.556 1.794 2.024
1.056 1.258 1.452 1.640
.890 1.060 1.224 1.384
-------
TABLE A (cont.)
CASE B. CVMC-PRIME WITH CVME . PVO* NOT EQUAL ZERO. USED AEOM30.
I NTRST
.60000E -1
RFVME
.72652E -1
L
.50000E
.63445E
IFP
2
RFF
-1
L
.30000E
IFC
2
L
. 30000E
IFE
2
VMAX
.350QOE 1
VM
-20000E
IN
1
RFVMC
.72652E -1
Y = . 70
BEL MILES, D - 30 INCHES
Y = .80
Y = . 86
.0006 .0009 .0013 .0018
.0006 . 0009 .0013 .0018
1.50 2 449 2.694 3.320 3.731 2.706 3.200 3.673 4.J30
2.051 2.431 2.795 3.J47
1.681 1.996 2.298 2.590
1.437 1.707 1.968 2.220
1.260 1.499 1.728 1.951
1.016 1.212 1.399 1.381
.857 1.022 1.180 1.3.35
1.75 1.854 2.196 2.523 2.840
2.00 1.518 1.801 2.073 2.335
2 25 1 297 1.540 1.773 2.000
2.'50 1.136 1.351 1.557 1.757
3.00 917 1.091 1 .259 1.422
3.50 .772 .920 1.062 1.200
.8006 .0009 .0013 .0018
2;857 3.380 3.881 4.363
2.167 2.569 2.955 3.328
1.777 2.111 2.431 2.741
1.519 1.806 2.082 2.350
1.333 1.586 1.829 2.066
1.077 1.283 1.482 1.675
.907 1.082 1.250 1.414
-------
CASE c. CVMC WITH CVME-PRIME.
TABLE 5
PVOM - e . . USED
INTRST
•60000E -l
LIFP
•50000E 2
LIFC
•30000E 2
LIFE
•30000E 2
VMAX
.35000E l
VMIN RFVMC
•20000E i .72652E ~i
RFVME
-72652E -1
RFP
.63445E -1
BEL MILES, D = 8 INCHES
Y = .70
Y = . 80
Y = . 86
5 a b
.0033 -0052 .0075 -Oi02 -0033 -0052 -0075 .Oi02 .6033 .0052 .0075 .Oi02
X
1.
1.
2.
2.
2.
3.
3.
50
75
00
25
50
00
50
1 359
1 lOl
941
'828
"743
.619
.533
1
1
1
.583
290
'l06
.976
. 876
.731
.630
1
1
1
1
1
.800
473
266
.lie
.005
.840
.724
2
1
1
1
1
.012
650
>21
.256
.130
.946
.816
1.488 1.739 1.982 2.218
1 2lO 1 421 1 625 1.824
1 036 1.221 1 399 1.572
.913 1.078 1.237 1.391
.819 .968 l!ll2 1.252
.684 .809 .931 1.049
.589 .698 .803 .?05
1.564 1.831 2.089
'
1-274 i
1 !• 0 9 2 1 '
^963 1°
498 i
2 8 8 1
138 l
1
.865 1.023
.722 .855
.622 .738
2.339
7i5 i 926
478 l ] 6 6 2
307 1^
176 1
1.
.984
.849
,324
,110
.958
BEL MILES, D = 12 INCHES
Y = .70
Y = .80
Y = . 86
.0019 .0030 .0044 .0060
.0019 .0030 .0044 .0060
.6019 .0030 .0044 .0060
1.50 1.533 1.612 2.082 2.343 1.694 2.005 2.306 2.599 1.789 2.119 2.439 2.750
1.75 1.263 1.498 1.725 1,
2.00 1.090 1.295 1 . 493 1
2.25 .965 1.148 1.325 l
2.50
3.00
945
685
496
869 1.035 1.194 1.349
.728 .868 1.003 1.134
3.50 .629 .750 .867 .980
1.398
1.208
1.071
.964
.809
. 699
1.660
1.437
1.275
1.149
.965
.834
1
1
1
1
1
.914
.658
.472
.328
.115
.964
2.160
1.873
1.663
1.501
1.261
1.091
1
1
1
1
.478
.278
.133
.021
.856
.740
1
1
1
1
1
.756
.521
.349
.217
.022
.883
2
1
1
1
1
1
.025
.756
.559
.406
.181
.022
2.286
1.984
1.742
1.590
1.336
1.156
-------
CASE c. CVMC WITH CVME-PRIME.
TABLE 5 (cont.)
PVOH = 0.. USED AEOM30.
INTRST
.60000E -1
RFVME
.72652E -1
L
.50000E
.63445E
IFP
2
RFP
-1
L
.30000E
IFC
2
L
•30000E
IFE
2
VMAX
.35000E
1
VM
?20000E
IN
1
RFVMC
.72652E -1
BEL MILES, D = 16 INCHES
Y = .80
Y = .86
.0013 .0021 .0030 .0041
.0013 .0021 .0030 .0041
1.50
1.75
2.00
2.25
2.50
3.00
3.50
1
1
1
1
.684
398
.211
075
.970
815
.705
2
1.
1,
1,
1.
.003
.666
.446
.284
,159
,974
843
2
1
1
1
1
1
.311
.925
.672
.486
.341
.128
.976
2
2
1
1
1
1
1
.611
.177
.892
.682
.519
.278
.106
1
1
1
1
1
1.868 2.224 2.568 2.903
1.552 1.852 2.142 2.123
608 1.861 2.5:06
873
6.92
.907 1.085 1.256 1.423
.784 .938 1.087 1.232
1.346 1
1.196 1.429 1.654 1
1.079 1.290 1.494 1
.8013 .0021 .0030 .0041
1*976 2.354 2.720 3.076
1.643 1.962 2.269 2.568
1x426 1.704 1.972 2.233
1.267 1.514 1.754 1.986
1.143 1.367 1.584 1.794
.961 1.150 1.332 1.510
.831 .995 1.153 1.307
Y = .70
BEL MILES,'D = 20 INCHES
Y = .80
Y = .86
.0010 .0015 .0022 .0030
1.50 1.814 2
1.75 1.512 1
2.00 1.313 1,
2.25 1.167 1
,50
00
.165 2.565 2.835
.807 2.092 2.370
.570 1.820 2.062
.397 1.619 1.835
1.054 1.261 1.462 1.657
1.061 1.231 1.395
3.50
.886
767
.919 1.065 1.208
.0010 .0015 .0022 .0030
.987 1
,406
,183
.027
.804
.630
,372 1
016 2.409 2.788 3.
682 2.012 2.331 2.6.41
461 1.749 2.027 2.298
299 1.556 1.804 2.045
173 1.406 1.
1.
.948
.556
.854 1.024 1.188 1.3.47
.8010 .0015 .0022 .0030
2.136 2.552 2.955 3.348
1.782 2.132 2.471 2.801
1.549 1.855 2.150 2.438
1.377 1.650 1.913 2.170
1.244 1.490 1.729 1.960
1.047 1.254 1.455 1.651
.906 1.086 1.260 1.429
-------
TABLE 5 (cont.}
CASE c. CVMC WITH CVME-PRIME. PVOM = o.. USED AEOMSO.
INTRST LIFP LIFC LIFE VMAX
.60000E -1 .50000E 2 .30000E 2 .30000E 2 .35000E i
RFVME RFP
.72652E -1 .63445E -1
VMIN RFVMC
•20000E i .72652E -l
BEL MILES, D = 24 INCHES
Y = . 70
Y = .60
Y = .86
.0006 -0012 -0017 .0024
.0008 .0012 -0017 .0024
X
1.50
1.75
2 00
2.25
2.50
3.00
3.50
1
1
1
1
1
. 928
6iO
'400
"246
".125
, 947
'820
2
1
1
1
1
1
.307
.929
'.678
[493
'.349
. 136
.983
2
2
1
1
1
1
1
.673
.236
946
.732
.565
.318
.141
3
2
2
1
1
1
1
.029
536
^207
.965
.776
.495
.295
2.
1.
1.
1.
1.
1.
146
794
560
388
254
056
914
2.569
2.149
1 870
1.665
1.504
1.266
1.097
2
2
2
1
1
1
1
.979
.'493
170
>32
.746
.470
.273
3.378
2 528
2 462
2 192
1.981
1.668
1.445
.0008 .0012 .0017 .0024
2.275 2.724 3.160 3.583
1 902 2 279 2 645 3 OOl
l'654 l'984 2^303
1.472 1.766 2.050 2.326
1.330 1^596 1.853 2.102
1.120 1.343 1.560 1.770
.969 1.163 1.351 1.533
BEL MILES, D = 28 INCHES
Y = .70
Y = .80
Y = .86
.0006 .0010 .0014 .0019
.50 2.
75 1
.030 2.433
698 2. 036
2.00 1.478 1.773
2.25 1.315 1.578
2.50 1.188 1.426
3.00 1.000 1.201
3.50 .866 1.040
2
2
2
1
1
1
.823
.364
.058
.832
.656
.394
3
2
2
2
1
1
.203
.682
.336
.080
.88-0
.583
2
1
1
1
1
1
1.208 1.371
.0006 .0010 .0014 .0019
2.262 2.713 3.149 3.574
1.893 2.271 2.637 2.994
1.648 1.977 2.296 2.607
1.466 1.760 2.045 2.321
1.325 1.591 1.848 2.098
1.116 1.340 1.556 1.767
.966 1.160 1.348 1.530
.0006 .0010 .0014 .0019
2.399 2.878 3.341 3.793
2.008 2,
1.748 2,
1.556 1,
1.406 1,
410
098
868
688
2.799 3.178
<:.*37 2.767
2.170 2.46"
1.961 2.227
1.184 1.422 1.652 1.875
1.025 1.231 1.430 1.624
-------
TABLE 5 (cont.)
CASE c. CVMC WITH CVME-PRIME. PVOM - o.. USED AEOMSO.
INTRST
•60000E -1
RFVME
.72652E -1
L
.50000E
.63445E
irp
2
RFP
-1
L
.30000E
IFC
2
L
.30000E
IFE
2
VMAX
.35000E 1
VMlN RFVMC
•20000E 1 .72652E -1
Y = .70
BEL MILES, D = 30 INCHES
Y = .80
Y = .86
.0006 .0009 . 0013 . 0018
1.50 2.078 2.492
1.75 1.739 2.086
2.00 1.513 1.816
2.25 1.347 1.617
2.50 1 .217 1.461
3.00 1 025 1.231
3.50 .887 1.066
2.892 3.283
2.422 2.750
2.109 2.395
1.878 2.132
1.697 1.927
1.429 1.623
1.238 1.406
.0006 .0009 .0013 .0018
2.316 2.779 3.228 3.665
1.939 2.327 2.704 3.070
1.688 2.027 2.354 2.6.74
1.503 1.804 2.096 2.381
1.358 1.631 1.895 2.152
1.1^3 1.373 1.596 1.812
.990 1.189 1.382 1.569
.9006 .0009 .0013 .0018
2v457 2.949 3.426 3.891
2.-057 2.470 2.870 3.259
1.791 2.151 2.499 2.838
1.594 1.915 2.225 2.527
1.441 1.731 2.011 2.284
1.213 1.457 1.694 1.924
1.051 1.262 1.467 1.666
-------
TABLE 6
CASE D. CVMC-PRIME WITH CVME-PRIME. PVOM = o. USEO AEOM3o.
INTRST LIFP L1FC LIFE
.60000E -1 .50000E 2 .30000E 2 -30000E 2
RFVME RFP
.72652E -1 .63445E -1
VMIN RFVMC
•35000E i V20000E i .72652E ~i
Y = .70
BEL MILES, D = 8 INCHES
Y = .80
Y = .86
o o o
.0033 .0052 .0075 .Ol02 -0033 .0052 -0075 .OJ02 .0033 .0052 .0075 .Ol02
i.50
1.75
2.00
2^25
2.50
3.00
3.50
.794
599
"489
"417
!365
294
^48
.688
.675
.554
.474
.416
.337
. 284
.979
.748
.617
.529
.465
.377
.319
1.067
.820
678
.582
.513
.417
.353
.848 .953 1.055 1.J53 '.880 .992
643 .728 8lO .689 ,669 759
527 .599 '669 .?37 ,549 '626
450 513 575 .$35 .469 '5Z7
^395 !45l [506 .360 .412 !472
.319 .366 .412 .156 .333 .383
.269 .309 .348 .386 .281 .324
1.099 1.203
,846 .930
[700 '.772
'602 *665
.531 .587
.432 .479
.366 .406
Y = .70
BEL MILES, D = 12 INCHES
Y = .80
Y = . 86
.0019 .0030 .0044 .0060
X
1.50 .784 .900 1.011 1.120
1.75 .607 .701 .792 .880
2.00 .504 .584 .662 .738
2.25 .435 .505 .574 .641
2.50 .384 .447 .509 .569
3.00 .313 .366 .417 .467
3.50 .266 .311 .355 .398
.0019 .0030 .0044 .0060
.850 .980 1.105 1.226
.661 .766 .868 .967
.550 .640 .728 .813
.475 .555 .632 .7.07
.420 .491 .560 .628
.344 .403 .460 .317
.292 .343 .392 .441
.0019 .0030 .0044 .0060
.890 1.027 1.160 1.289
.693 .804 .913 1.018
.578 .673 .766 .857
.499 .584 .666 .745
.442 .518 .591 .663
.362 .425 .486 .546
.307 .361 .414 .466
-------
TABLE 6 (cont.)
CASE D. CVMC-PRIME WITH CVME-PRIME. PVOM = 0. USEP AEOM30.
INTRST
.60000E -1
RFVME
.72652E -1
L
• 50000E
.63445E
IFP
2
RFP
-1
L
.30000E
IFC
2
L
.30000E
IFE
2
VMAX
.35000E 1
VM
v20000E
IN
1
RFVMC
•72652E -1
Y = .70
BEL MILES, D ='16 INCHES
Y = .80
Y = . 86
crs
.0013 .0021 .0030 .0041
X
1.50 .804 .936 1.065 1.191
1.75 .632 .740 .845 .948
2.00 .530 .623 .714 .802
2.25 .460 .542 .622 .700
2.50 .409 .482 .554 .624
3.00 .336 .397 -.457 .516
3.'50 .286 .339 .391 .442
,0013 .0021 .0030 .0041
.880 1.029 1.173 1.314
.694 .816 .934 1.Q49
.584 ,688 .790 .689
.508 .600 .689 .Z77
.451 .534 .614 .$94
.371 .440 .508 .574
.317 .376 .434 .491
,8013 .0021 .0030 .0041
-.925 1.083 1.237 1.386
.731 .860 .986 1.109
.615 .726 .834 .940
.535 .634 .729 .823
-.476 .564 .650 .735
.392 .466 .538 .608
.335 .398 .460 .521
Y = .70
BEL MILES, D = 20 INCHES
Y = .80
Y = .86
.0010 .0015 .0022 .0030
X
1.50 .833 .981 1.125 1.265
1.75 .662 .783 .901 1.017
2.00 .559 .663 .765 .865
2.25 .488 .580 .670 .758
2.50 .435 .517 .598 .678
3.00 359 .428 .496 .562
3l50 ^307 .366 .425 .483
,0010 .0015 .0022 .0030
. 918 1. 084 1 . 245 1.403
.732 .868 1.000 1.J30
.619 .736 .851 .963
.541 .644 .746 .845
.482 .575 .666 .756
.399 .477 .553 .628
.341 .408 .474 .539
.0010 .0015 .0022 .0030
.969 1.145 1.317 1.485
.773 .918 1.059 1.198
.655 .779 .901 1.021
.572 .683 .791 .897
.510 .610 .707 .803
.422 .505 .587 .667
.361 .433 .504 .573
-------
TABLE 6 (cont.)
CASE D. CVMC-PRIME WITH CVME-PR1ME. PVOM = 0. USED AEOM30.
RFVME
.72652E -1
VMAX
VMlN
INTRST LIFP LIFC LIFE
.60000E -1 .50000E 2 -30000E 2 -30000E 2 .350QOE j. .20000E 1
RFP
.63445E -1
RFVMC
•72652E -1
Y = .70
BEL MILES, D = 21" INCHES
Y = .80
Y = .86
.0008 .0012 -0017 .0024
X
1.50 .867 1.028 1.186 1.341
1 75 694 .827 .956 1.084
2*00 589 .703 .815 .926
2~25 516 .617 .716 .814
2\5Q !460 .552 .641 .729
3.00 .382 .458 .533 .607
3.50 .327 .393 .458 .522
•0008 .0012 -0017 .0024
.960 1.141 1.319 1.193
770 .920 1.066 l.glO
655 .784 .910 1.034
574 688 '800 .910
]513 '.616 '.717 !fl!6
.425 .512 .596 .680
.365 .439 .513 .585
.0008 .0012 .0017 .0024
1-.015 1.208 1.397 1.584
.816 975 1.131 1.285
-694 831 966 1 099
'608 '730 .850 .968
J544 .'654 |76l !s68
.451 .544 .634 .724
.387 .467 .545 .623
Y = .70
BEL MILES, D = 28 INCHES
Y = .80
Y = .86
.0006 .0010 .0014 .0019
X
1.50 .903 1.077 1.248 1.416
1.75 .727 .870 1.011 1.150
2.00 .619 .743 .865 .985
2.25 .543 .653 .761 .868
2.50 .486 .585 ;683 .779
3.00 .404 .487 .569 .650
3.50 .347 .419 .489 .560
.0006 .0010 .0014 .0019
1.003 1.199 1.392 1.582
.809 .971 1.130 1.287
.690 .830 .968 1.104
.606 .731 .853 .?74
.543 .655 .765 .874
.452 .546 .638 .730
.388 .469 .550 .629
.0006 .0010 .0014 .0019
1;062 1.272 1.478 1.681
.858 1.031 1.201 1.369
.882 1.0*; 1 175
.037
.931
.778
.733
.644 .777
.577 .696
-.480 .580
.412 .500
.907 1
.814
.680
.585
.671
-------
TABLE 6 (cont.)
CASE D. CVMC-PRIME WITH CVME-PRIME. PVOM = (j. USEB AEOM30-.-
INTRST LIFP LIFC LIFE VMAX VMlN RFVMC
.60000E -1 .50000E 2 .30000E 2 .30000E 2 .350QOE 1 ;20000E 1 .72652E -1
RFVME
.72652E -1
RFP
.63445E -1
Y = .70
BEL MILES, D = 30 INCHES
Y = . 80
Y = . 66
00
.0006 .0009 .0013 .0018 .0006 .0009 .0013 .0018 .6006 .0009 .0013 .0018
1.50 .921 1.102 1.279 1.453
1.75 .743 .892 1.038 1.183
2.00 .634 .763 .889 1.014
2.25 .557 .671 .783 .894
2.50 .499 .602 .763 .803
3.00 415 .501 .5B6 .671
3.50 .356 .431 .565 .578
1.025 1.228 1.428 1.626
.829 .997 1.162 1.326
.708 .853 .996 1.138
.622 .751 .879 1.005
.558 .674 .789 .903
.464 .562 .659 .155
.399 .484 .568 .651
1.086 1.304 1.518 1.729
.880 1.059 1.236 1.411
.752 .907 1.060 1.212
.661 .799 .935 1.070
.593 .717 .840 .962
.494 .599 .702 .805
.425 .515 .605 .694
-------
APPENDIX B
Size and Cost Tables
79
-------
Table 7.
Various Estimates of Required Storage Volume (V) to Smooth the
Diurnal Variations in the Design Flow for the New Hope Plantl
Observed Data
By Graphical Estimation
Date
5 Jam
6 Jan
7 Jan
Oo 8 Jan
0 9 Jan
23 Jan
1967
26 Jan
27 Jan
29 Jan
30 Jan
8 Feb
10 Feb
1971
1967
1967
1967
1967
1967
1967
Avg.
1971
1971
1971
1971
1971
19713
Avg.
Average
QA
MG D
1.89
1.88
1.81
1.63
1.59
1.60
1.73
1.58
2.12
1.92
1.87
1.84
2.40
1.96
Peak
QP
MG D
2.75
2.90
2.90
2.60
2.20
2.10
2.57
2.20
3.05
3.10
3.05
2.70
3.60
2.95
Minimum
QM
MG D
0.75
1.00
0.80
0.90
1.00
1.00
0.91
0.80
1.00
0.80
0.80
1.00
1.15
0.93
Time Flow
Ab ove Avg .
t
hours
14.7
13.6
12.3
12.6
15.6
14.0
13.8
15.0
11.0
11.1
10.0
12.3
14.0
12.2
Calculated Quantities
By Planimeter
QA'
MGD
1.96
1.86
1.86
1.65
1.67
1.57
1.76
1.63
2.08
1.94
1.95
1.88
2.59
2.02
Direct
Estimate2
VD
MG
0.204
0.250
0.228
0.186
0.146
0.141
0.192
0.174
0.305
0.351
0.295
0.183
0.380
0.281
X =
QP/ QA
Dimension-
less
1.43
1.54
1.60
1.60
1.39
1.30
1.48
1.46
1.44
1.61
1.63
1.47
1.50
1.52
h =
QP- QA
MGD
0.86
1.02
1.19
0.97
0.61
0.50
0.86
0.62
0.93
1.18
1.18
0.86
1.20
0.995
Triangle "Square-wave"
VT = fcbh '
MG
0.263
0.289
0.278
0.256
0.199
0.146
0.2385
0.194
0.212
0.270
0.246
0.220
0.350
0.249
VS =
X- 1 1
xynx + i'x
MG
0.335
0.357
0.372
0.372
0.302
0.258
0.333
0.330
0.322
0.375
0.380
0.333
0.335
0.346
"Square-wave"
Max
VM =
X - 1
YQF(x + i}
MG
0.479
0.550
0.595
0.595
0.420
0.335
0.496
0.482
0.464
0.604
0.620
0.489
0.502
0.527
Durham's New Hope Plant (18-inch influent line with QF = 3.0 MGD). Y assumed « 0.86 for d/D = 0.80.
The direct estimate was made by averaging two to four planimeter determinations. The volume VD was measured from the planimeter
avg. line QA'.
The "design flow" for the 18-inch line was preseumably exceeded. The "maximum" storage volume VM calculation is shown for comparison.
-------
TABLE 8
Calculations for the Cost of Concrete Smoothing Basins
(1)
(1)
(2)
(3) (4)
(5)
(6)
(7)
(8)
(A) (B)
(9)
(10) (11)
(12) (13)
CONCRETE QUANTITY REQUIRED
Volume
MG
(V)
0.1
0.2
0.4
0.8
1.6
3.2
(14)
A'
Volume Surface
area,
depth of
15 ft
2
cu ft ft
(V) (A)
13,340 890
26,680 1,776
53,360 3,550
106,700 7,100
213,400 14,200
426,900 28,440
Square Bottom or Free-
side top edge
, board,
length 1 ft thick 1 ft +
aerator
Total side
height
w/o sump
Four sides
1 ft thick
clearance
ft cu yd
ft
(L) (l)(A)/27
29.8 32.9
42.1 65.8
59.6 131.6
84.2 263.2
119.2 526.4
168.5 1,052.8
(15) (16) (17)
LAND AREA
=(1'+10)2(1.5)
CONCRETE
Five
sides
at
3
3
4
4
5
5
(18)
COSTS
Six
sides
at
ft
(h)
18
18
19
19
20
20
(19)
EXCAV
COSTS
Excav
at
$3/cu yd
cu yd
4L(l)h/27
79.4
112.1
167.6
236.7
352.8
498.6
(20)
LAND
COSTS
Land
at
$10K/acre
Sump allow.
under
aerators
each, total,
cu yd cu yd
3 6
3 6
4 12
4 12
7 21
7 42
(21)
I
Five
sides
Five
sides
Six l'=L+2+6
sides h'<=h+2+sump allow+3
h'=h+4+3
cu yd
(4)+(7)+(8b)
120
184
312
510
900
1,580
(22)
COSTS
Six
sides
VEX=1
cu yd
(4)+(4)+
(7)+(8b) (I1)
150 38
250 50
445 68
775 92
1,430 128
2,630 177
(23)
COSTS W.
Five
sides
'2h'/27
(h') (VEX)
25 1,340
25 2,300
26 4,450
26 8,100
27 16,400
27 31,300
(24)
20% E&C
Six
sides
$90/cu yd $90/cu yd
ft
(I1 +10)
48
60
78
102
138
187
ft acres $
(I'+IO)
2,300 0.
3,600 0.
6,080 0.
10,400 0.
19,000 0.
35,000 1.
A $90x(9)
080 10,380
124 16,280
209 27,290
357 45,350
655 79,760
20 140,260
$
$90»(10)
13,380
22,200
39,100
69,000
127,100
235,000
$
$3x(13)
4,000
6,900
13,300
24,300
49,200
94,000
$
$10Kx(16)
800
1,240
2,090
3,570
6,550
12,000
$
(17) + (19) + (20;
15,180
24,420
42,680
73,220
135,510
246,260
$
1 (18)+(19)+(
18,180
30,340
54,490
96,870
182,850
341,000
$1000
20) 1.2x(21)
18,216
29,304
51,216
87,864
162,612
295,512
$1000
1.2x(22)
21,816
36,408
65,388
116,244
219,420
409,200
(1)
For 15 feet of vertical level change.
81
-------
TABLE 9
Calculations for the Cost of Earthen Smoothing Basins
(1)
(1)
(7)
(2)
(3)
(4)
(5)
(6)
Volume
MG
(V)
0.1
0.2
0.4
0.8
1.6
3.2
Volume
cu ft
(V)
13,340
26,680
53,360
106,700
213,400
426,900
Cross-Sectional
Surface Area
(depth of
15 ft)
ft2
(A)=V'/15
890
1,776
3,550
7,100
14,200
28,400
Square Side
Length at
Mid Line
ft
(L)WV'/15
29.8
42.1
59.6
84.2
119.2
168.5
PAVING
Bottom
Area
sq yd
[L-8.5(i)2]2/9
19
70
200
500
1,160
2,530
QUANTITY REQUIRED
Wetted
Side Area
Includes Sump
4F(L-l>/2xl81
9
327
466
691
943
1,338
1,900
Total
Paved
Area
sq yd
(4)+(5)
350
540
890
1,440
2,500
4,400
(8)
(9)
(10)
(11)
(12)
(13)
COST S3'4'5
EXCAVATION
Earth Removed
and Placed as
Diking
cu yd
VEX2
840
1,540
2,960
5,740
11,250
22,300
LAND
(L+91)2
43,560
acres
0.33
0.41
0.53
0.70
0.99
1.54
AREA
(L+120)2
43,560
With 30-ft
Buffer
acres
0.52
0.61
0.76
0.96
1.32
1.93
PAVING
$8/yd2
$8(6)
2,800
4,300
7,100
11,500
20,000
35,000
EXCAV
$3/cu yd
$3(7)
2,500
4,600
8,900
17,200
34,000
67,000
LAND
$6000/acre
6K$(9)
3,100
3,700
4,600
5,800
7,900
11,600
TOTAL
COSTS
With E&C
1971 $
10,000
15,000
24,700
41,400
74,300
136,000
For 15 feet of vertical level change.
(2) 1 /—
VEX j(Al + A2+,/A]A2)h+ (3ft)A1) , where A^ ^ equal, respectively, the area of the water
surface at the max level and the area of the paved bottom.
1969 Chapel Hill Bid for street pavement replacement
(4)
(5)
R. Smith, Cincinnati estimated excavation for small operations, 1967 (large basins could justify
use of large equipment at significantly lower cost).
Author's estimate for undeveloped residential-to-rural land in the Triangle Cities area.
82
-------
TABLE 10. Calculations for Size and Cost of Aerators and Aerator 0-M Costs
Useful
Basin
Volume
MG
0.1
0.2
0.4
0.8
1.6
3.2
0.1
0.2
0.4
0.8
1.6
3.2
0.1
0.2
0.4
0.8
1.6
3.2
0.1
0.2
0.4
0.8
1.6
3.2
Max.
Flow
MGD
(Q/V-4)
0.4
0.8
1.6
3.2
6.4
12.8
(Q/V-2)
0.2
0.4
0.8
1.6
3.2
6.4
(Q/V-4)
0.4
0.8
1.6
3.2
6.4
12.8
(Q/V-2)
0.2
0.4
0,8
1.6
3.2
6.4
BOD Oxygen Oxygen
Load Required Req'd
(1.3 Load)
Ib/hr Ib/hr Ib/hr
28
56
112
225
450
900
14
18
56
112
225
450
28
56
112
225
450
900
14
18
56
112
225
450
37
73
146
290
580
1160
19
37
73
146
290
580
37
73
146
290
580
1160
19
37
73
146
290
580
(30% Rem)
11
22
44
90
180
350
(307. Rem)
5
11
22
44
90
180
(10X Rem)
3.7
7.3
14.6
29
58
116
(10% Rem)
1.9
3.7
7.3
14.6
29
58
Aerat .
hp
Req'd
hp
4.4
8.8
17.6
35
70
140
2.2
4.4
8.8
17.6
35
70
1.5
2.9
5.8
12
23
47
0.8
1.5
2.9
5.8
12
23
Aerators Req'd
Op
No.
1
2
2
3
3
3
1
1
2
2
3
3
1
1
1
2
3
2
1
1
1
1
2
3
Spare2
No.
1
\
h
h
h
h
i
l
»5
h
h
h
i
i
i
h
h
%
i
i
1
1
h
h
Power
Each
hp
5
5
10
15
25
50
5
5
5
10
15
25
5
5
7.5
7.5
7.5
25
5
5
5
7.5
7.5
7.5
Aerator Costs
(1971) Installed
Each,
$1000
2.75
2.75
4.1
4.6
6.8
11.5
2.75
2.75
2.75
4.1
4.6
6.8
2.75
2.75
3.2
3.2
3.2
6.8
2.75
2.75
2.75
3.2
3.2
3.2
Total, f
$1000 <
5.5
6.875
10.25
16.1
23.8
40.25
5.5
5.5
6.875
10.25
16.1
23.8
5.5
5.5
6.4
8.0
11.2
17.0
5.5
5.5
5.5
6.4
8.0
11.2
Aerator
Operating
and
lalntenance
:/1000 gal.
0.33
0.31
0.29
0.27
0.25
0.23
0.36
0.33
0.31
0.29
0.27
0.25
0.16
0.14
0.13
0.115
0.10
0.09
0.18
0.16
0.14
0.13
0.115
0.10
'''Operating costs based on lc/kwh for power; 0-M smoothed to fit equations (9) and (10).
Installations requiring only one aerator were assumed to need a complete standby unit, but
multiple-unit stations were assumed to have adequate protection with only a spare motor
and frame costed at one-half unit price (per Reference 10).
From Reference 11.
83
-------
APPENDIX C
BEL Computer Program
85
-------
REAL INTRST, I.IFP, LIFC, LIFE
DIMENSION BELL<15.7,2>. KW(2), ITEXT(20)
DIMENSION A(3,,10)
DIMENSION DOVRD(10),DD(12)»SS(10),XX(10),VV<107
2 FORMATU6I5)
5 FORMAT(8F10,0)
11 FORMAT(1H-,10X2H N , 11X1HD , 11X1HY/1X3E12.5>
12 FORMAT(//16X1HS,10X2HQF.9X3HQOP,8X4HPVOM,8X4HAEOM,8X4HDVOM/5X6E12.
15)
13 FORMAT(/18X4HREL1,&X4HBEL2.8X4HTACC,8X4HTACP,6X6HDARCTQ,6X:>HDARETQ
l,9X3HTCI,9X3HQOP;9X3HQOA/lOX9El2.5//l8X4HCVMf:,8X4HCVMC,9X3HVMI , 8X
24HDPOM,6X6HDARPOO,6X6HDPOMQO,llXlHX,lOX2HCP.9X3HCVM/10X9El2.5//16X
36HCVMTQI.7X5HCPQOA/10X2E12.5)
14 FORMAT(/6X6HINTRST,8X4HLIFP,8X4HLIFC,8X4HLIFE,8X4HVMAX*8X4HVMIN,
1 7X5HRFVMC/7E12.5//7X5HRFVME-9X3HRFP/2E12.5)
15 FORMAT
18 FCRMATdXFS^,1 (-7F6.3.3X) )
32 FORMAT(lXF5.2.1(5F6.4 )
20 FORMATdH-/////)
22 FORMATt//)
28 FORMAT<20A4>
1 CALL AMAKE(A)
READ 5, XN
READ 2»NUMY,NUMD,NUMV,NUMX
READ 5, (DO.RD(I),I=1,NUMY)
READ 5,(XX(L),L=1,NUMX)
READ 5, (VV(K)»K=1,NUMV)
READ 5.(DD(J) ,J = J,NUMD)
VMIN = VV(1)
VMAX = VV(NUMV)
4 READ 5, INTRST* LIFP. LIFC, LIFE
IF( INTRST) 3,1,6
6 READ 2, ISS
RFVMC = RECOVR(INTRST,LIFC)
RFVME = RECOVR
-------
DO 100 K=liNUMV
S = <<48./D)*«<2./3.)«XN«VV(K)/1.486)»»2
SS(K) = S
OF = 3.2E-2*(D»M8./3. )»SQRT(S> )
OOP = Y»QF
C PVOM =<1.61/QOPa«.26257)*ANUMBR
C AEOM = .216 + 357./(QQP»1000 . )
AEOMlO = .14/QOP*».157
AEOM30 = 0.3/QOP»« .104
PVOM =(.75/QQP*».264)«ANUMBR
AEOM = AEOM30*FLQAT( IAEOM/30) * A£OMlQ»FLOAT (1Q/ I AEOM )
DVOM = PVOM » AEQM
IF(ISS) 97,97,96
96 PRINT 12,S,QF,OOP,PVOM,AEOM,DVOM
97 IS = IS-t-1
IX r o
DO 99 L=1,NUMX
IX = IX + 1
X = XX(L)
QCA = QOP/X
VMl = QOPMX-1 • )/(X + l. )
V - VMI
C
•C
C
C
C
C
C
C
VM V
QOAV = OOA/V
CVMC = (IW=1)
CVME - ( IW=2)
CVMC-PRIME = ( IW = 3
CVME-PRIME = ( IW = 4
2 VALUES OF KW PER
CVME OR CVME-PRIME
I W - K W ( 1 )
CVMC - COSTFtV/
)
)
CASE
,
IW, A)
ONE FOR CVMC OR CVMC-PRIME, THE OTHER FOR
IW = KW(2)
VX = VM«CQOP/VM/2. )
CVME - COSTFUX, IW, A)
DARPQO = DARP/QOA*l.E-3
DPOM =- 4000. /364.
DPOMQO = 4./(364.»QOA)
TACP = DARPQO + DPOMQO
TQI - OOP - QOA
DARCTQ CVMC«1QQO.»RFVMC/(3640.«TQI)
DARETQ = CVME«10QO.«RFVME/(3640 .«TQI )
TACC = DARCTQ+DARETQ + DVOM
CVM = CVMC + CVME
CVMTQI = CVM/TQI
CPQOA = CP/QOA
BEL1 = CVMTQI/CPQOA«1.E3
BEL2= TACC/TACP
BELLt IS, IX,1 ) *• BEL1
BELL(IS, IX,2) t BEL2
IF(ISS) 99,99.98
98 PRINT 13,BEL1.BEL2,TACC,TACP,DARCTQ,DARETQ,TQIjQOP,QOA,CVME,CVMC,
1VMI,DPOM,DARPQO,DPOMQO,X,CP,CVM,CVMTQI,CPQOA
99 CONTINUE
100 CONTINUE
ID = D + 0.5
87
-------
C SUPPRESS BEL-1 ENTIRELY.
C DO 24 MV=1,2
MV = 2
NV = -MV
IF(MOD(J,2) >33.34. ,33
33 PRINT 20
PRINT 14!lNTRST,UIFP.LIFC,LIFE,VMAX,VMIN,RFVMC;RFVME.RFP
34 PRINT 22
PRINT 17,NV,ID.(DOvRD(II),Il=l,3),((SS(KK),KK=t,4),MM=l,3)
DO 21 LL=1,NUMX
L = NUMX + 1 - LL
X = XX(L)
IX = L
31 PRINT 18, X, (BELL(IS.IX.MV),IS=1,12)
21 CONTINUE
19 CONTINUE
GO TO 4
3 CALL EXIT
STOP
END
1
REQUIRED SUBPROGRAMS!
$ST
COSTF
$PR
RECOVR
AMAKE
SE
$F
STORAGE
VV
DOVRD
BELL
I I
BEL2
CVM
TOI
DARPQO
IW
VMI
DVOM
AEOM10
SlTl
IS
ANUMBR
NCASES
ISS
K
NUMV
LIFE
END COMP
ASS
R
R
R
R
R
R
R
R
R
R
R
P
R
R
R
R
R
t?
R
R
EXIT
FLOAT
JXE
SON
$A
$/
$)F
IGNMENTS:
00034
00106
00514
02464
02471
02475
02503
02512
02516
02523
02527
02543
02551
02564
02574
02600
02604
02610
02615
02621
MOD
SORT
SFL
SAQ
$)
IX
SI
XX
A
LL
NV
BEL1
TACC
TACP
CVME
QOAV
QOA
AEQM
OOP
S
DARP
IAEOM
RFP
VMAX
L
NUMD
LIFC
RATION
R 00046
R 00144
R 02457
R 02465
R 02472
R 02476
R 02504
R 02513
R 02517
R 02524
R 02532
R 02544
R 02557
R 02566
R 02575
R 02601
R 02605
R 02611
R 02616
R 02622
SS
ITEXT
MM
MV
CPQOA
DARETQ
DPOMQO
VX
VM
X
PVOM
$1T2
R
CP
I AN
RFVME
VMIN
I
NUMY
LIFP
R 00060
R 00170
R 02460
R 02466
R 02473
R 02477
R 02505
R 02514
R 02520
R 02525
R 02535
R 02545
R 02561
R 02572
R 02576
R 02602
R 02606
R 02613
R 02617
R 02623
DD
KW
KK
ID
CVMTOI
DARCTQ
DPOM
CVMC
V
IX
AEOM30
OF
Y
D
NC
RFVMC
J
NUMX
XN
INTRST
00074
00172
02462
02470
02474
02502
02510
02515
02521
02525
02543
02550
02562
02573
02577
02603
02607
02614
02620
02624
88
-------
SUBROUTINE AMAKE(D)
C
DIMENSION 8(3,10).Add,3), YdO), C(3,3), D(3;iO)
IW = 1
103 READ 1, MANY
IF(MANY) 101,101,102
102 DO 2 1=1,MANY
READ 3, X,Z
Y( I ) - ALOGIO(Z)
A( I ,1) = 1.
A( I ,2) = ALOGIO(X)
A( 1,3) = A( I ,2)»»2
C PRINT 13, I,X,Z»Y(I),(A + A(K,I)»A(K,J)
5 C(J,I ) = C(I , J)
EPS = l.OE-15
CALL GJR(C,N,EPS,MSING)
14 FORMAT(/3E12.5)
GO TO (7,6) , MSING
6 PRINT 8, IW, MSING
8 FORMAT(/1X22HSINQULAR MATRIX. IW =,I3,10H. MSING =,13)
GO TO 100
101 RETURN
7 DO 9 1=1,3
DO 9 J = 1, MANY
B( I , J) = 0.
C (ATRAN*A) INVERSE » ATRAN
DO 9 K = 1,3
9 6(1,J) = B( I , J) + C( I , K)«A'< J,K)
15 FORMATC/10E12.5)
C » Y
DO 10 I = 1,3.
D( I , IW) = 0.
DO 10 K = l.MANY
10 D(I, IW) = D( I, IW) + 8(1,K)»Y(K)
DO 20 1=1,MANY
SS = 0.
DO 19 J=l,3
19 SS = SS * A( I , J)«D(J, IW)
SD = Y(I) - SS
20 CONTINUE
89
-------
100
IW = IW+1
GO TO 103
END
REQUIRED SUBPROGRAMS:
$H
$E
SI
{AO
$X
$/
$XA
SRC
$PR
$F
ALOGlQ
STORAGE ASSIGNMENTS:
GJR
$)F
SON
C
SD
EPS
$1T3
J
MANY
END COMPILATION
R 00025
R 00700
R 00705
R 00711
R 00716
R 00725
V
SS
$116
S.II2
Z
IW
R 00037
R 00701
R 00706
R 00712
R 00722
R 00727
A
MSjNG
$1T5
K
X
R 00075
R 00702
R 00707
R 00713
R 00725
B
N
S1T4
S1T1
I
R 00133
R 00703
R 00710
R 00715
R 00724
90
-------
1
REQUIRED SUBPROGRAMS!
$XE $XA ALOG10
STORAGE ASSIGNMENTS:
$1T4 R 00053 $113 R 00055 $1T2 R 00056 S1T1 R 00057
COST R 00060 VLQG R 00061 COSTF R 00062
END COMPILATION
91
-------
REQUIRED SUBPROGRAMS!
SXE
STORAGE ASSIGNMENTS:
$1T1 R 00024 Z
END COMPILATION
R 00026
RECOVR R 00027
92
-------
COLUMN WITH THE KTH COLUMN
SUBROUTINE GJR(A,N,EPS,MS ING)
INTEGER P.Q
DIMENSION A( 3. 3) , B(25>,C<25>.P(25>,Q(25>
MSING = 1
DO 10 K=1,N
DETERMINATION OF THE PIVOT ELEMENT
PIVOT=0.
DO 20 I=K,N
DO 20 J = K,N
IF ( ABS(A(I,J»- ABS(PIVOTM20,20,30
30 PIVOT=A(I,J)
P(K)=I
Q(K)=J
20 CONTINUE
IF ( ABS(PIVQT>-EPS)40,40,50
EXCHANGE OF THE PIVOTAL ROW WITH THE KTH ROW
50 IF(P(K)-K)60,80,60
60 DO 70 J=1,N
L=P(K)
Z=A(L,J)
A(L,J)=A(K,J)
70 A(K,J)=Z
EXCHANGE OF THE PIVOTAL
80 IF(Q(K)-K)85,90,85
85 DO 100 1=1.N
L=Q(K)
Z=A(I,L)
At I ,L)=A( I ,K)
100 At I ,K)=Z
90 CONTINUE
JORDAN STEP
DO 110 J=1,N
IF(J-K)130,120,130
120 B(J)=1./P1VOT
C(J)=l.
GO TO 140
130 B
-------
151 RETURN
40 PRINT 45, P(K),Q(K),PIVOT.EPS
MSING 2
45 FORMAT(/16H SINGULAR MAJRIX3H 1=13,3H J=I3,7H PIVOT=El6.8,
1 5H EPS=,E16.8, 2H KOUNT: ,137)
RETURN
END
REQUIRED SUBPROGRAMS!
$)F
$/
ARS
$E
$ON
$1
$AQ
$H
$PR
STORAGE ASSIGNMENTS:
C
M
$1T3
I
END COMPILATION
R 00045
R 01060
R 01065
R 01071
B
$1T4
S1T2
PIVOT
R 00076
R 01062
R 01066
R 01073
Q
Z
$1T1
K
R 00127
R OJ063
R 01067
R 01074
P
L
J
R 00160
R 01064
R 01070
94
«J.S. GOVERNMENT PRINTING OFFICE:1973 514.153,
-------
SELECTED WATER
RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
1. Report No,
w
"'" "THE FEASIBILITY OF FLOW SMOOTHING STATIONS IN
MUNICIPAL SEWAGE SYSTEMS"
Click, C. N.
Research Triangle Institute
Research Triangle Park, N. C.
J2. S' ssorir, Organ' if ion
S. t* rfottti-,••;; Org&i-
Report fto.
11010 FDI
14-12-935
Type .' Repi .. and
Period Cfi"fred
U.S. Environmental Protection Agency, Environmental Protection Technology Series
Report EPA-R2-73-138. February 1973.
..IS.
Flow smoothing in sanitary sewers was studied to determine under what conditions
the resulting higher flow capacities can be economically obtained. Conservative
assumptions were made in this preliminary design and economics study to provide
a severe test for the cost effectiveness of the concept. In many situations,
flow smoothing is an attractive alternative when compared to relief pipe instal-
lation. Circumstances which favor flow smoothing are high interest rates, high
peak-to-average flow ratios, low pipe slopes, small diameters, and low design
depths of flow. Flow smoothing is strongly favored where earthen construction
can be utilized.
I/a. Descriptors *Surge Tanks, *Sewers, ^Economic Feasibility, *Domestic Wastes,
Waste Water (Pollution), Municipal Wastes, Sewage, Sanitary Engineering, Water
Pollution Control, Feasibility Studies, Cost Comparisons, Estimated Benefits,
Design Criteria, Hydraulic Conduits, Sewerage
1/b. Identifiers *Flow Smoothing, Flow Equalization
05 D
13 Security C/ass
'R».po >
.0. St. .tity C. s.
2] No. of
Send To:
WATER RESOURCES SCIENTIFIC INFORMATION CENTER
US DEPARTMENT OF THE INTERIOR
WASHINGTON D C 2O24O
Dr. H. E. Bostian
Environmental Protection Agency
------- |