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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS -1963
i
:

_
.
: Burwell Coey Olmap.2960
ili BURWELL
Cont:-670568- 2 .. cc: Moyens, LINAwenuen, SINOT.
Sprawak, NOLLEARI
Young Mammont.e-Meus rer)
.
International Conference on WATER for PEACE
May 33-91.18! ::
APR 13 1967
.
Washingian, o.a BMW
; Original Languages Anglish
: Author', Countrys United States of America
::.... Author's Arrillations aux Mage National Laboratory
Topdo •-. Of the Aaanda
Author's Name: C. c. Jurvell
Co-Author's Name:
CESTI PRICES
· FTÜCT OF LOW COST POWER ON
WATER TRANSMISSION BY PIPELI NE
HC. 13.01: MN 65
:
INTRODUCTION
which new fresh water. Upplies are created to the distribution
ent. It 16 the means. Also, if new fresh wat from the deselting p?
The suoject of water conveyance forms an integral part of any discussion of water resource .
development. It is the means by which new fresh water resources in water-rich regions are made
availuble to water-short areas. Also, if new fresh water supplies are created through desalination
processus, when the desalted water must be transported from the desalting plant to the distribution
reservoir. Again, if desalted water is to be mixed with brackish ground water, then both desalted
and brackien water must be conveyed to the blending station prior to use:
Projections of low cost desalted water are based on low energy (both heat and power) cost esté.
matcs froin nuclear reactors. Such water cost projections, except when associated with a specific
project and site, normally do not include the cost of delivering water to the distribution reser-
voir. In order to compare alternative methods of providing new water supplies, as well as to com-
pare the relative magnitudes of the cost of desalting seawater and of transporting the desalted
water, it is worth while to analyze water conveyance costs and to consider the effect that low cost
power will have on them. This paper attempts to provide such an analysis.
A thorough treatise on the subject of water conveyance would require many volumes and would
consider alternative methods such as tank truck, barge, dracone, rail car, pipeline and canal:
However, except for special cases, only pipeline and canal appear to be economically suitable for
handling large water quantities for long time periods. Where the terrain 18 suitable (level, open,
and easily excavated), water conveyance by canal wili normally be less expensive than by pipeline
if.other factors such as water, purity, leakace and evaporation are unimportant. Because of these
factors of terrai), purity, and water loss, a generalized analysis of conveyance cost by. canal 18
much less valid than a similar treatuent of conveyance cost by pipeline. Hence, the analysis given
here is restricted to a treatment of conveyance cost by pipeline.
and easily excava such as water. Duater' 1088, a generace cost dy pipe
..........
"
.
It should be noted that the total cost of water supply includes factors other than the con-
veyance cost such as impoundment, treatment, etc. These factors are not considered here except to
state their relative magnitudes for comparison in particular examples.
PIPELINE INVESTMENT COST
The pipeline cupital cost data used are taken from a report by F. P. Linaweaver and C. Scott
· Clark (1) as well as from the chapter written by Louis Koenig entitled "The cost of conventional .
Water Supply." (2) The correlation of the pipeline installation cost with pipeline diameter is
similar in both references. The Linaweaver and Clark data were used directly in this report after
: first increasing the costs by 18% to adjust for an estimated construction cost increase from July
: 1962 (the date to which the data were normalized) and January 1967. The data are described by an
.
equation with the ceneral form:
Investment cost, K, 10 mile - 01.29
:.:. :. (1)
where * 18 a constant with the value 2230 and D 18 the inside diameter of the pipeline in inches. :
It should be noted tlat significant deviation in pipeline capital costs from the relationship
given by equation (1) may exist for any specific project due to type of terrain (rock or loose soil),
labor rates for the region, proximity to the pipo "supplier, urban or rural route, etc. For example,
: .... .:: :: :
... DOUTONS DOCUMENT AS WALMALAR
+
HF:
C. C. Durvoll
a corrolation of pipeline estimates cxcluding concral and anginooring expenses made ¿y the Bureaui
· of Rocianation (31 for the southern Californio region in 1965 for pipeline diwater. Sra 90 in.
190.in. would be represenced by the equations
,
.
Kr 228 .86
which i. 30 to 100 crcater than the correlation given by equation (1) for the 90 in. to 190 in. .!
dianctors, rospectively.
The correlation given by equation (1) as well .'
as the Buriec correlation are shown in graphi. .
cal form in Pigure 1. Also shown on Figura 1
.: do the sechtel Corporatior. estimate (4! for
.. the 25 mile 72 in. dicmeter pipeline that will
be constructed to convey 150 Mcd of distilled
seawater from Bolka Chica Island to the Dienor
reservoir for the Metropolitan Water District ..
of Southern California.

.
QUIMRI: CALIFORNIA
.
.
elne CARTA COSTIER MOLE S 1000s)
:*::
*:
i
PALUS.
: K
.
. .
•
-
-
100 go
Equation, (1) correlates investment costs éron
•: about 55' oil, gas and water pipeline projects
: in the U. 6. over the period. 1958 to 1962.
Pipeline diameters varied from 4 to 108 inches,
MWO (DRCNICO
and lengths varied from 1 to 1600 miles. The
correlation is not statistically affected by
the pipeline material (steel, concrete, etc.)
or by the pipeline length of grecter than a
few miles. The capital cost correlation dous
.. not include the cost of right-or-ay or pump-
BR2250 DIY
:ing stations. However, for many large systems, :
richt-of-way costs' are a small fraction 12) or
· pipeline cost. As discussed leter, an allow..
ance for the cost of pumping stations will be
coupled to the cost of pumping power.
LOND FACTOR
200.
50 ....
.
. : DIAMETER 1 . .
For several reasons (increased construction
costs as a function of time in an inflating
economy, strong capital cost scaling. as a
function of size, and minimum obsolescenso of
:: equipment) pipeline systems are normally in-
.. Pig. 1. Pipeline Capital Cost..
stalled with surplus capacity in the early
years of operation. Conversely, desalting sys.
tens are normally considered to be base loaded throughout their lifetime. Direct comparison of water
costs between conveyance and desalting 18 thus complicated, since by design they deliver disserent
quantities of product as a function of time: In order to avoid the present worth analysis required
to compare these two design philosophico, the p:1 peline system vill be assumed to operate at null
derion capacity throu chout its lifetime. This açoumption should not affect the validity of the
anolyais nor the conclusions that will be drawn." Corrections to the assumption of 100% system
load factor due to downtime for maintenance are relatively minor... .
. !
. . PIPELINE OPERATION, MAINTENANCE AND REPAIR (CER) COSTS
marc duta cor pirclinc OMER cocts are Given in reference 2. A correlation of t
pipeline diameters crcater than 30 inches reveals that an allowance in the capital recovery fac
· tor" of 0.18% would provide for these pipeline O&R costs.
.
1::.:.:
..
1
. Reference 2 gives. eteentially the same, correlation and includes data from 450 pipeline . ;
· installations.
"There 16, after all, no inherent reason why a desalting station cannot be constructed with
surplus capacity or, conversely, that a pipeline system should invariably be designed with sur.
*. plus capacity. A present worth analysis of ways to meet system load growth would be desirable
sor decision making in any case, regardless of the method (conveyance or desalting) ultimately
selected,
"no usod here, the capital recovery factor is that percentage of the total installed system
cost which ir returned annually throuchout the life of the system will provide for several cost.
factors including in this study. Interest on the investment, system depreciation, taxes, Insurance,
AMIR costs and interim replacements. A. capital recovery factor of 5% would include allowance for a
her go interest rate with a 50 year lifetime, 0.2%OMAR cost and a 0.15%. Insurance allowance but would
not includo any allowance for profit or taxes.
:
:.
.:-
Slalocos. SWOTA SINUO
040 INCIO
Non to "ruanne” COST DUE TO RUNnnc
anon Cat, cost wanted
PUMPING COGT .
The main operating cost of a water conveyence
... System 16 due to the consumption of power. II .
... power costs decrease dle to the advent of nu-
:; clear encroy, then it will become more econani-
cal to expend more pump power to do a given Job, .
11: by doing so, the pipeline capital cost cas
: be decreased (by decreasing the pipeline dion-
eter). There are, however, other costs 1880- •
ciated with increased power consumption per
unit of water transported that should be recoge
::· nized. Primary among these are the pumping
station capital and operating costs, both of
: which depend upon the horsepower rating of the
station. An examination of pumping etation
... cost data given in reference 2 reveals that . .
for larger station capacities from 20 to 2000
: . Mgd the investment cost is about $120 per in-
. Stalled horsepower.

.
This figure 18 in good agreement with Durec
2Q
004 004 00... : 0
information (3) which indicates an investment
amo station Conta cover IACTOR
... cost of $120 to $90 per hp for stations with
· total pump heads of 140 to 300 feet, respec-
: tively, and for capacities in the range 100 to
. Fig. 2. Pumping Cost Component Due to
· 1000 Mgd (but excluding right-of-way, engineer.
Pumping Station Capital Cost .. .
..'.. ing and general expenses). Pumping station :
capital costs may be included in the pumping
cost by an addition to te cost of power that allows for their rixed costs. The pumping station
capital cost, when considered a part of the cost of puniping power in this way, 18 a function of the
capital recovery factor as shown in Figure '2.'.'.
STENDO
CONTRIBUTION TO. MAT COST OUE TO PUMPING STATION
· ON ANOR COSTs min
A thorouch analysis of pumping station operation and maintenance costs 16 given by J. M. Eyer
15) of the Aureau of Reclamation. In reference. 5 annual pumping station operating costs for medium
to large (100 to 1000 MCD) stations are rolatively independent of pumping station throughput and
delivery towad but depend, as expected, upon whether or not the pumping station is attended and the
.: ";' operator wage rate. Annual pumping station
ORM 0 .67.33* i , ... maintenance costs are primarily a function of
the pumping station horsepower. (the product of
throughput and delivery' head) and the mainten...
ance mechanic wage rate. In order to include
pumping station OM&R costs as an additive to
the energy cost an analysis of the cost data
given in reference 5 was perforred. The re-
sults of the analysis are given in Figure 3
where the cor.tribution to "pumping" cost due
to pumping station OVER costs in mills/kwhr
UNATTENOLO
STATION
is presented as a function of pumping station
capacity for both attended and unattended
stations. The conditions used in the analysis
are also listed on Figure 3. It should be
| STATION OELMERY MEAO . 250
noted that the OVER costs given in Figure 3
OPERATING WAGE KATE • Szoom
are quite sensitive to station throughput in
MECHANIC WAGE NATE Susoma
MICE LEVEL NATO 982 - 1.3
contradiction to data given by Koenic (2)
where pumping station OM&R costs are given as
LLOUD FACTOR
100%
a fixed 1.5 mills/kwhr ($10/np-yr) for station
capacities ranging from 20 to 2000 Mgd.

.'...
.
100
By using Figures 2 & 3 an "effective" cost for
"pumping" in mills/kwhr may be leternined by
adding the allowances for pumping station api..
tal and operating costs to the cost of energy. :
For example, even if power were free at the
power line, the cost of pumping stations to
utilize the power would give an effective"
cost for pumping of 1.4 mille/kwhr for an
unattended pumping station with a capital re-
covery factor of 5% and a 500 Mģd throughput:
.:.
:
. wwwwo. STATION CAPACITY (not
Mg. 3. "Pumping" Cost Component Due :
".. .to Pumping Station OMER Costs, :
.
C. C. Burwell
(0.9 millb/kwhr for capital charges and 0.9 mills/kwhr for OMER costs). Alternatively, if power
cost nt the power line were 5 mills/kwhr, the "erfective cost of pumaring for conveyance would be.
6.4 millb/kwhr. This "effective" cost of power that represents the total cost of puping is used
throughout the analysis section and 16 given the symbol pt with units of mills/kwhr.
This method proves to be a useful way to include the total pumping costs in terms of the cost
of power used for pumping without adjustment of the pipeline capital cost correlation. The method
serves to emphasize the point that the savings in pipeline construction costs that appear to be
PCssible with higher water velocities are offset in part by an increased requirement for pumping
: . stations.
Examples 7. THE :
Pous AND
FROM PIPELINE
CONVEYANCE COST ANALYSIS
In the appendix an expression is derived for the minimum total cost of water conveyance by
pipeline operating with a 100% load factor that incorporates the pipeline capital cost correlation
given by equation (1). In other words the pipeline capital cost correlation is included in the
expression in such a way that the total cost of conveyance givon balances pipeline diameter. (capi.
tal cost) with the pumping requirement (cost of power and pumping stations) to give the pian
total conveyance cost. :
Tie canoral expression derived is:
0.19
0.000314 D# 62
0.0003
-
0.059 px0.21 0.79 0.79
spi " 20.21 20.40 00:39
,
*
.
:::
where: Teót ló i!ie minimum total cost of water conveyance in W1000 gallons/mi18..
.. per 15 tho orrective cost of power for pumping in mille/xwhr and includes the enro cost :
as well as allowances for .pumping station capital and operating costs.
16 as defined in equation (i) for the Liraweaver and Clark data and equais 2230.
r. 16 the capital recovery factor, fraction/year.
16 the pumping station efficiency including allowances for transformer, autor and
pump efficiencies. ..
18 the pipeline capacity in Mid (10 gallons/day).
36 the Hazen-Williams (6) coerficient that corrects for the surface roughness of the
pipo.
18 the net pipeline slope in feet/mile.
If in equation (2) values form, E, and .C of 2230, 0.85 and 120 are used and the coerficients .
are rainded off, the general expression given in equation (2) becomes: . ..
::::
T
.4.2 px0.2 0.8
-- +0.00037 P* 8
::.
.
.
: opt
.
(3
00.4
.
· The first tern on the right hand side of equations (2) and (3) represents the total cost of i
water conveyance by pipeline for systems with no net change in elevation between the pipeline in
take and delivery points. The second term on the right hand side of equation (2) and (3) correcto
the expression for the effect of a net slope in the pipeline. t Equation (3) shows that the water
corivo:yan's cost for pipeline systems with low gradients are a weak function of power costs (a
l'actor oli two decrease in effective power cost reduces water conveyance cost about 13%). . Water
conveyance cost is much more strongly donendent upon pipeline capacity and the capital recovery
fuctor where a factor of 2 decrease represents an increase of 32% and a decrease of 41%, respec..
tively, in water conveyance cost. Equation (3) may be used to consider questions concerning water
cost's from conveyance and desalting systems. ..
Erfect of Low Power Cost Projections on Water Conveyance Costa ..
In the 'u. S. power costs from large publicly financed, nuclear power plants using present
l'echnology will be in the range of 2 to 3 mille/kwbr. Estimates of power costs from future nuclear
.
'In this discussion it is assumed that all gains to the pipeline system' due to water flows
downhill are recovered and utilized to overcome head losses due to pipeline friction or drag.
C. C. Burweli
1
power stations using breeder reuctors are 1 to 2 mills/kwhr. (7) Ir power at these low costs 1.
used for water conveyance, the unit cost or water conveyance will be less than reported in refer-
onces 1 and 2 where power costo of 1 to 2 #xwhr were used. Table 1 comparc. water conveyancc
costs for in 300-milc systein delivering 500 Mcd for both a horizontal system and one with a 1000 ft
As shown in Table 1, a factor of 7.5 decrease in energy cost will be expected to reduce vater
conveyance costs 28% and 39% for the two examplty. The effect of low power costs would, of course,
. be much more striking for a short pipeline with a high lift.
Table 1. Erfect of Power Cost on Water Conveyance Cost
Energy cost
iniu, kuhr
Efective
Pumping Cost
mill. kwhr
Conveyance Cost
Horizontal System
gallons ·
Conveyance' cost
Systa with 1000 ft mir
W1000 gallons
3.4
.: 15.5
16.8
15
16.4 : :21.4
27.4
c - 120,' B = 0.85, 'm* 2230, 1: = 0.05, unattended pumping stations.
Erfect or Low Power Corto .on Ground Water Pumping
Since a ground water pumping system normally concists of a short vertical pipeline, it repro-
sants a bystem that should recoive a Jurco bonerit from low power cost. Table 2 compares ground
water pumping costs for 2 and 15 millo/kwhr cnercy costs. In the table ground water pumping costs
exclusive of power costs are taken from reference 2. The data in Table 2 are for 1:100 xgd system
with a 200 rt urt.
*Ao indicated in Table 2, a decrease in power cost 'sy a factor of 74 would be expected to do.
cross the water cost from ground water systems by about 45% for the example given. ..
.
.
.
. Tablc 2. Erfect of Power Cost'on Cost of Water from Hells
Total cost (2)
Excluding Energy
#1000 callons
Enercy Cost
millb/kwhr
Enervy Cost
$1000 gal
Total Cost
$1000 gal
0.8.1.1
0.8.1.1
:: 2.:"",
15 ...
0.15
1.1
0.95 - 1.25
1.9 - 2.2
.
.
Water Conveyance Distance Relationship to Desalted Water Cost
Cost projections for desalted water vary greatly because of the many facture that affect them .
such as system size, energy cost (state of reactor technology), seawater conversion equipment cost.
(state or evaporator technology), etc. Table 3 gives the water conveyance distance for a horizona'
tal pipeline that would be in competition with desalted water at assumed specific costs and capa...
cities. The water conveyance cost does not include allowances for water impoundment, Intake or ..
treatment. With thc cxccption of water treatment, these costs would be expected to be small.t .
IS water treatment. including softoninc ig required, then the tradeoff conveyance distances, would
be much less than indicuted.
Table 3. Pipeline Conveyance Trade-Off Distances
Assumed Desalted
Water Cost
#1000 callons
Enercy
mille/
. Effective
. Pumping Cost,
P*, mills/kwhr
System
Capacity
Mgd
Pipeline
Trade-off
Distance, miles
*
20
. 100
226 .
20
..¿ :.,:, 3.22 : 1000
237 :::::
120, 1 = 0.85, m - 2230, T 0.05, unattended pumping stations.
C
*Analysis of data contained in reference 2 shows that for large systems and allowance or 0.5 :
#1000 gallons for water reservoir cost: Is adequate to cover cases with wide range of stream low
ability and percont otrcam withdrawal.
..
V
ILL
'.
-
.
!
.
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!
1.'.
.'
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.
.
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L..
UN
1.
WUNDULELII' I.
L.
1
A
1
.
LE.
W
.
... Y
L
C. C. Durvell
Arrect or Conveyance Coste on the Use of Desalted water for Irrization
Ir in te future desalted water is used extensively for irrigation, it is of interest to in-
dicate what iditional cost will be incurred to convey the desalted water from the deslization
plant to the fan arı. In thi, example, only the cost of conveying the main body of water to the
agricultural area l. included. The cost of distributing the irription water to each square food .
of crop land by gan latarılı, souker pipes, sprinklers, etc., must be paid, regardles* of the ..
water source and do not, therefore, « cost uniquely ussociated vith desalted nuor. Table River
the additional cost of moving 1600 Myd of water to an agriculturl region that is either adjacent
to the dewalting plant, or rirty miles distant, and the cost of olevating the voter 1000 funt. for
ao pricultural water application mot of four rent per year, the total output fra e 1000 M da
salting plant would be wond by land vithin the samicircle described by . 16-uile maius fra the
denlting pinat. Consequently, the equinlent conveyance distance for an adjaceat s oubor
mdad vows to about 12 vilu.
-
-
-
-
-
-
dable de conveyance Cost (W1000 gallons) from a 1000 Mind
: Dualting Station to Assumed Agricultural Areas
Adjacent Andon
12 miles
Canter of
Region, 50 wle
Cost for
1000 root urt
0.5
2.1
1.2
c. 120, X. 0.85, . .2230, r -0.05, p. 3.2 mill. mutir,
unattended pumping station.
CONCLUSIONS
The unit cost of water conveyance by pipeline for optimum systone may be reprouented by :
Total Unit Cost, Topt – Ky pro.2 80.%20* + XxPu8, .
where K, and K2 are constants, Q is the pipeline capacity, I is the capital recovery factor, 8, 1.
the pipeline slope, and p* 1. the effective" pumping cost. The "affective pumping cost Includes
the coot of energy plus dlowances for pumping station costs that amount to about 1.5 willkwhr.
Thus, except for systems that require a high water 111t, pipeline water careyance costs are not
strongly affected by power cost. . Based on the results of the study: pipeling conveyance system
will compete with advanced desalting systems producing water at a cost of 10W 1000 gallone at a
1000 Mgd rate for differences in conveyance distance of under 240 miles; the cost of conveying de-
salted water to an adjacent irrigation area will not significantly affect the cost of water for that
uso; the use of doraltod water for irrigation need not be restricted to arable land at sealevel
since the cost for "pumping to olerate water 1000 ft 10ing power conting 2 uulu kwhr. . about
1.341000 gallons.
..
..
.
i
REFERENCES
• 1. . P. Unavenver, Jr., and C. Scott Clark, "Coots of Water Transadosion, " J. Am. W.W. Assoc., (do 2.00h)
2. Loui. Koenig, "he cost of conventional Water Supply," Chapter 11, Principles of Desaid
edited by K. 8. Spiegler, Academic Press, New York-London, 1966.
.................
T. M. Hollearin, U. 8. Dept. Interior, Dur. Reclamation, cout Curve for Pumping Plants from
200 to 1500 cf. in Capacity," and "Cost Estimating curve for Concrete Pipeline. for Mowing
Desalted seawater Inland from the Pacific Ocean," unpublished, March, 1965.
de Bechtel Corporation, "Engineering and Econanic feasibility Study Phase I and II for a combing !
tion Muclear power and Doulting Plant," USAPC, TID-22330, Yol.1, (Dec. 1965).
5. John M.Byer, "Pumping Plant Operation and Maintenance costo," U. 8. Dopt. Interior, dur. ...
Acclamation, May, 1965...
6. Q. 8. Mulaw and Hllen Ensen, Hydraulic Tables, 3rd ed., Willey, New York, (1992). :::
9. Names A. Lane, "Economics of Mclear power, " Ann. Rev. Mich. Bel., 26, 343-378, (1966). : ;
.
.
.
LEGAL NOTICE
.
.
15
:
L
: TV, report we prepared as an account of Coventat sponsored work. Natthar the waited
states, nor the Comainson, nor any person acting on behalf of the Conclusion:
A. Makes may warranty or representation, aprend or implied, 10 respect to the act
racy, completenes, or wafalmec. of the Autoraation contained to the sport, ar that the w.
of my information, apparatus, method, or procura dincloued be the report may not tatring
privately oward richtes or
B. ARNI un ladiuties with respect to the w ol, or far duan routing trou the
un dany tafarlattia, apparatus, method, or procesu diecloud la tale report.
As used in the abov, "pornoa acttags behalf of the Commission" lacludne m a-
.ploy or contractor of the Coniston, or employs of mch contractor, to the action that
Auch neploys or contractor of the Coaniendom, or taploy of much contractor preparar,
diamoamates, or provide acoso to, way Information purnunat bo no employ or contract
with the Commission, or Me employment with much contractor.
m
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m
:..
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..-.
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2
TULON...M
U NAL
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-.-.
--.
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C. f. burwell
APPENDIX
WATER CONVEYANCE COST ANALYSIS
:
Following the annlytical procedure given in reference 1, the total cost of water conveyance
is made up of the charces for capital investment for the pipeline plus the "offective cost of
pumping. (As described in the main report, OMGR costs for the pipeline are included in its capital
charges and all pumping station costs are included in the cost of puning pover). ...
por 100% system capacity factor, the total cost, T, in W1000 gallona/ns1o.so
Bio P#(8+88)
.
..!
respece
where: 1 and 8 are unit conversion constants with values of 2.74 x 10** and 3.24.7.10°
tively,
'x .. pipeline cost in Unile,
s • capital recovery factor, track.on/year,
Q. design capacity in 100 callons/day (Mad),
pw effectivo "pumping" coot in m111c/kwhr,
8. thic head 1008 in 8t/mile duc to slope(s) and drag (sp), and
8 . punipinc erriciency.
The 1'rct torra on the right side of cquation (a) is the water conveyance cost contribution
due to the capital and maintenance costs of the pipeline, and the second terza 18 the contribution
due to puniping cost (including the allowance for pumping station costs).. . :
The head loss due to alope, saj muy be positive or negative and, in the general case, depende
only upon the difference in Slovation in reet between the water source and delivery points ard the.
distance of the pipeline in miles. It is not a function of the pipe diameter or throughput.
The head loss due to drag, Br, may be obtained from the Hazen-Williams expression (5): .. ..
8
21.85 4.86
whor: C is a constant cqual to
C 18 the Hazen-Williams coefficient that corrects for differences in surface roughness for
different pipe materials, linings, etc.
·
Figure Ia shows a graph of pipeline ''ricition loss, Sn, as a function of pipeline diameter
for Q - 1000 Med and C = 120. Figure Io may be used in conjunction with Figure Ia to determine
the drug head, Sr, for values of the variables, C, Q, and D other than those used in Figure Ia.
For example, if one wishes to determine the effect on drag head loss for a pipeline with a value
of Q of 800 instead of 1000 as used in picure Ia, then the parameter Q has a parameter ratio of.
800:1000 or a 8. According to Figure Ib a parameter ratio of 0.8 produces a drag head factor of
0.67. The drab head loss for a Q of 800 Mgd would be the value given in Figure. Ia times the 0.67
factor.
. The above method of parametric data presentation is also used later in the analysis when
Fraphical expressions for optimum pipeline diameter (Figure IIa,b) and total water conveyance cost
(Ficure IV a,b) are developed. The method is used simply to permit the reader to make his own
selection of parametric' values and not be restricted to the fixed set of parameters selected by:
the author.
-
1. The pumping efficiency term should include factors for power transformation, motor erficiency
and pump efficiency; typical values are 0.98, 0.96, and 0.90, respectively, giving a typical valus
overal of 0.85.
ii....
: ...,
Dr.
.
WWW.LV
1. C. Durwell
OANL omg 67-1668M
:

110. DIAMETER

To 120 MO
O 1000 MCOL
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...
10lb des
Seo ORNG HEAD (feelsoroll
13 LEAO FACTO
, HAZEN-WILLIAMS
COEFFKCIENT
100
200
DIAMETER (in)
800
-
::
ALRAMETER RAINO
...
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:
Pipek a friction Loss.
Elleci ol Parameters on Pipeline Friction cornes." ;
ad
..*
.
-
& subs
....
Figure 1. Pipeline friction loss
'If the expressions for K and 8given by equations (1) (see main repor
tuted into Equation (a), the following expression results:
... ambł.29 :D Pås, : bcpne1.85 :
* B * ¢1.85, 4.86
where we first term on the right side of equation (c) 18 the contribution due to pipeline capital
cost and the second and third terns are the contributions to pumping cost due to pipeline slope ..
and friction, respectively. .
If in equation (c) T 18 differentiuted with respect to D while holding everything else con-
'stant and the derivative aq/OD set equal to cero, the following expression for the most economic
diameter under specified conditions is obtained:
. . 10.163 0.465
i d po 103 0.463
Popt 20.153 20.301, 0.163.0.163 . :
where a 18'a new constant that includes the contribution from constants a, b and c
constants' of differentiation..
:
olding van
::.:.:
..:::
:
1...
::...10.163
4.86 oC)
(1.29 & 3
- 54.3
.
"..i': . .:::..
..:::
Migure IIa shows a graph of optimum pipeline diameter as a function or pipeline capacity for
values of P*, Cym, and 1 of 4; 0.85; 120; 2230, and 0.04, respectively. Mgurt In dves the
optimum pipeline diameter factor as a function of ratios in P*, C, , 'm, and 1. Figures IIa and
· IIO may be used in combination to determine Dopt values for any given parameter set...
.
ORNL-OWG 67-1689R

:
200
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- -
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.
. Dopro OPTIMUM DIAMETER (in.)
FOR: C: 120
P4 mills/kwh
E. 0.85
m* 2230
10.04
....
.
....
.
........
20
.
10
1000
:. 5. 3.1002
5.:.
: Q, PIPELINE CAPACITY (mod)
Optimum Pipeline Diameter as o Function of Capacity.

O13
Dopra 20.301. Com
CO.
LE,m,
+ E, m,
OPTIMUM DIAMETER FACTOR
.
.
.
(0)
.0? 0.
.
5. .
:. 1.0
.2
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..
i.
.
..
PARAMETER RATIO
Effect of Porameters on Optimum Pipeline Diameter.
..
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. .
Figure II. Optimun Pipeline Diameter
::.: (page 9, Dwg67-1689R)
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1.L
U
L
1.
ILL..
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...
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C. C. Durvell
si An exprescion for the minimum total cost of water conveyance may be developed by substituting
the expression for optimum uiameter given by equation (a) into equation (c). The result is: ,
b.p* ,' e p«Q.21 0.79 20.79
*opt 2.2120.40.0.39
where e to a new constant that includes the contributions due to constants a, b, c, and a.;
. Cond..29. - 0.059 .
2.(.)
bc
Tic crot tona or the right side of equation (c) gives the contribution to the total cost of
wator conveyance due to a difference in elevation (expressed as ft/mile) between the water inteke.
and discharco points. The praph in Micure VII evaluates this contribution to water cost as a
nunction of P# for a total olevation chance of 1000 feet and I equal to 0.85.
The second term on the right of equation (e) gives the total cost of water for a horizontal
pipeline or a pipeline with no differenco in oleyation between the pipeline intake and discharge
points. Ito value is given in Mpuré Tya as a function of pipeline capaciiy for values of E, 0,
, , and put equal to 0.85, 120, 22.30, 0.04 and 4 respectively. Mguro IVO gives the total water
cost factor as a function of ratios in Z, C, 'm, rand pi. Figures IVa and Ind may be used togeth
i to determine Toomt values for horizontal pipelines for any given parameter set.... ..!
n
--- cqual to 0.85, 120, 3230, 0.04 and I was i
póliter and on the valy. her capecais intake and Lizontaj
@...omg 47-

linooo oma
100s cousas 1.500 waume
.
de
CFFECTIVE PUMPING COST Wills/kwa
..:
....
Mpure III. cost for "pumping to
urt Water 16co Feet
.
1
. .
',,
.
'.
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...
1
::::
::
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r
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A.
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ORNL-DWG 67-1690
.

...
WATER CONVEYANCE COST
($11000 geilons per mile)
R: es 0.059
E = 0.85
. Co 120
m* 2230 ::::
f = 0.04. i i
pas 4 mills/kwh |
..:
:
1000
:.
:
O. PIPELINE CAPACITY (mad)
Water Conveyance Cost for Pipelines with no Net Lift or Fall.

21:
5.0
(m r;0.791
"
20.40
0.39
DAC
m OR
WATER COINVEYANCE COST FACTOR
QORCI
Pov OR
D
2
.
5
.
.. 10.
ARAMETER RA
i
Eifect of Parameters on Conveyonce Cost for Horizontal Pipelines.
:::: Figure Iv. Water Conveyance Cost
END


DATE FILMED
15 / 18 / 167
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1.51



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