D R A F T LU r H P.U. Report No. RES 1I (a) INTERNATIONAL BANK FOR RECONSTRUCTbON AND DEVELOPMENT INTERNATIONAL DEVELOPMENT ASSOCIATION Eniergy., Water and Telecommunications Department RESEARCH WORKING PAPER SERIES DESIGNI OF LOW-COST WATIM D:STRIB3UT=ON SYSTZ;n$ Central Projects Staff Energy, Water and Telecommunications Department This paper is one of a series i ssued bv the Eneray, Water and Telecommunications Department for tha information and guidance of Bank staff working in the pcwar, wa:er and -wastas. and tlec=uale acucaz -c ec- tors. It may not be published or cuoted as represe-nt-ing the views of the Bank Group, and the Bank Group does not accept responsibiity for its accuracy or comoLateness. WATER DISTRIBUTION SYSTEMS FOR DEVELOPING COUNTRIES Abstract Designers of water distribution systems have not had available simple analytical tools with which to test the effect on syste-ia costs of various design assumptions. In consequence, secondary distribution networks have often been designed by rule of thumb without a full appreciation of the effects of the designer's decisions. The effects of the resulting overdesign can be very serious, particularly where service to the urban poor is concerned and levels of affordability are low. This paper presents the results of rigorous analyses of secondary distribution systems for several urban areas in developing countries; from these analyses, simple mathematical models are developed which permit prediction of total pipe length, average diameter and network cost given decisions on variables such as per capita usage and spacing of public standpipes or house connections. ExampA.es are given of the application of these equations to typical design problems. This is an interim report on an onaoing research project; comments and suggestions for further studyr are welcome. Prepared by: Donald T. Lauria, Peter J. Kolsky, Paul V. Hebert (consultants), and Richard N. Middleton (World Bank) Copyright 1979 The In rr-o ,- r f^r r.econstructir 1c31a H ST,;, t.W. WASHINGTON, D. C. 20433, U.S.A. January 1979 0 WATER DISTRIBUTION SYSTEMS FOR DEVELOPING COUNTRIES C O N T E N T S Page No. Summary ....................................................... 1 General Project Description .................................... 1 Study Areas ........................................ ...... 3 City M .................................................... 3 City WA ..........................................3......... 3 City LA .................................................. 4 City WP ..................................................... 4 City SP .......................................... ........4 Pipe Cost Functions .................................. !.......... 5 Alternative Network Designs ..................................... 6 Model Formulation and Calibration ............................... 10 Pipe Length ............................................... 10 Pipe Diameter ............................................. 11 Velocity ............ ........................... ...12 Model Verification .................. ..13 Costs ..................................................... 15 Applications to Design ......................................... 17 Pipe Size/Service Level Relationships ....................... 17 "Basic Needs" Network .................................... 17 Pipe Standardization ......................................18 Standpipe Network .........................................18 Upgrading to House Connections ............................. 18 Budget Constraints ........................................20 Intermittent Supply .......................................20 Public vs. Private Storage .................................22 Table 1 Alternative Designs, Study Zone ME1 ME2 WA LA WP2 SP1 SP2 Figure 1 Original Pipe Length Model 2 Isodiameter Curves Symols C Cost (1976/77 US$) Haz2en Williams C. L Leagth, meters (m) (1 ft. - 0.3048 m) D Pipe 'inside diameter, mil1imetars ( ) V Velocity, Lmeters/second (m/s) i Area, hectares (ha) (1 acre - 0.405 ha) I Liters (I US gallo; - 3.79 1) Q Average per capita consumption, in liters/capita/day (LCD) H Head of water, meters (0.70 psi = I meter head) F Peak factor (maximum flow as proportion of average flow) N Number of "distribution devices", i.e., number of standpipes, number of yard connections or number of 1muses supplied N.;B,, -nat the numoer of metered connections @-hen multiple connections are given to multi-storey properti es). WATER"DISTRIBUTION SYSTEMS FOR DEVELOPING COUNTRIES Suzmmary 1. In designing urban water supply projects, engineers naturally place most emphasis on the major system components - dams and other source works, transmission systems, treatment plants, and primary distribution facilities. Far less attention is focussed on the secondary distribution system, which actually delivers the water to the consumers; and in many cases these networks are designed without any rigorous analysis of requirements. 2. This may not lead to significant overdesign in the developed world, where pipe sizes may 'be largely determined by the need to provide adequate fire protection. The financial impact of overdesign is also less noticeable in these countries, where water charges account for only a small part of disposable incomes. Neither of these conditions, however, applies in the developing world. The explosive growth of cities in developing countries has led to large slums and fringe areas which have no access to safe water supply. To provide for their basic needs without overtaxing the limited resources of the country it is essential to design systems that minimize costs. 3. In September, 1975, the World Bank commissioned a study of means to improve design of distribution systems to serve the urban poor. This report describes the general scope of the study; the derivation of system cost functions in various countries; the design and costing of a number of secondary networks to provide a range of levels of service; the mathematical models that have been developed to fit these alternative designs; verification of these models; and the conclusions that can be drawn. Examples are given of the practical application of the models to actual design decision. 4. The work herein permits prediction of network length, average pipe diameter and total cost, given data such as the population to be served, the Population density (or service area), the assumed daily per capita con- sumption, and local data oin pipe and -other costs. This prediction can be done by means of simple mathematical relationships between the variables in question; computers or other sophisticated means of analysis are not required. -These models do not provide a detailed design of the system, but permit designers to examine quickly the Dverall effect of changes in the variables over which they have control. General Project Description 5. This project is concerned with the design of secondary distribution systems to serve slurL, squatter or urban fringe areas. At this stage, it does not deal with areas with an uneven population distribution or with a mix of service levels, nor with areas where fire protection is required. Upstream and downsstream effects -- water supply facilities up to and inclu- ding the primary distribution network, and waste disposal -- are ignored. The study areas in this project were reasonably level, which may make the findings herein inapplicable to regions with irregular topography. It is assumed that there is no existing water distribution network in the area, or that its effect can be ignorred without significant .error; if this is not true, the study area has to be subdivided into smaller- areas bounded by pipes of the existing network. 6. The designer of a water supply system generally has tq accept certain inputs as beyond his cuntrol; the population to be served; the rate at which that population is increasing; and the area occupied by the population. Variables over which the designer has control are; the accessibility of water to consumers (e.g. the spacing of public standpipes or the proportion of house connections), which in turn affects the quantity of water to be supplied per person; the minimum allowable pressures in the network; and the measures to be take.n to improve system reliability (e.g., the extent of -looping or the number of valves). These are usually known as "decision variables". 7. There is a growing body of opinion that the community to be served should be included ,i dete;niniLng appropriate v4lues-for the decision variables. This has been the case in rural water programs in a number of countries for several years: engineers or "promote-s" explain the available options and their costs and the villagers then decide what level of service they can afford. T"he same practice seems likel7 to be employed increasingly in urban areas occupied by the poor, where community participation in system design may be very desirable in order to reduce costs and to avoid abuse of the system once completed. However, urban water supply designers have not been accustomed to approach the problem in this way; too often design decisions have been made on the basis of "accepted practice", which is almost invariably a synonym for "overdesign" when considering the needs of poor neighborhoods. 8. A major problem for designers is that they have not had available any means of quickly assessing the effect of changes in the decision variables. The designer could not, therefore, without a complex analysis, answer such basic questions as "if standpipe spacing is reduced from 100 meters to 50 meters, so there are not so many people using each outlet and they do not have to carry water so far, how much extra will this cost?" This project set about analyzing such basic questions and developing simple methods of analysis. 9. Preliminary field work was done in late 1975 in. Latin America. This provided guidance for planning more extensive field work and analysis which was carried out during 1976-78 in five different cities. Qity ME is located in the Middle East, City WA is in West Africa, City LA is in L4tin America, City W4P is in the Western Pacific, and City SP is in the South Pacific. 1/ 10. In each study the procedure was essentially the same. Cost data were obtained and cost functions calculated, relating installed pipe cost to pipe diameter. A series of alternative network designs was then prepared, using various levels of ser%-ice (public hydrants at 100 meter or 50 meter 1/ For reasons of confidentiality, these citi es are not identified in this report. Eowever, all data presented are believed to represent the actual situations in these cities. spacings; house connections), per capita consumptions, and residual pressures. These networks were optimized, taking account of the cost functions appropriate to each area; leading to a set of optimal pipe diameters, pipe lengths and system costs for each assumed set of decision variables. Regression analyses were then employed to express the optimal results for some of the cities in terms of simple mathematical models. Results from the remaining cities were then used to verify the regression models. This report describes the various procedures employed and the conclusions that can be drawn from the study, and it also gives some examples of the possible application of its findings. Study Areas City ME 11. The city population was 135,000 in 1975. The annual growth rate is estimated at 6 to 7 percent annually, equally divided between migration and natural increase. The city obtained its 'fater supply from a small public network (serving about 3,000 houses), several private distribution systems, and about 200 private wells. About half the houses in the city have water connections, the rest being served by standpipes or vendors. There is no sewer system. Work is in hand on the planning and construction of extensions to both the water and sewer systems. 12. Study Zone ME1 is the heart of the old city, the area where most migrants initially settle. It has an area of about 29 ha and a, population of about 1Q,000 (equivalent to about 350 persons/ha). The houses are 4 to 6 storeys high, often interconnected. The streets are rarndom and winding, and only a few can accommodate vehicles. The terrain is flat. In due course the area will be completely surrounded with primary water distribution mains. 13. Study Zone ME2 is in a newer, less dense region with area of about 40 ha and population of about 4,000 (equivalent to 100 persons/ha). The streets are wider, the houses lower and often detached. City WA 14. Total city population is between 180,000 and 200, QQO, grqwing at 6 to 7 percent annually. The average density is about 70 persons/ha. About one- third to one-half of the population are squatters living in peripheral shanty- towns. The non-squatter population obtains its water supply from a municipal system in reasonably good condition. About 35 to 40 percent have house con- nections and draw an average of 70 lcd. The remainder obtain water from vendors or public standpipes, using on average about 7 lcd. This very low usage is explained by the inadequacy of standpipes; each has a service area of about 35 ha, with a population of about 2,000. 15. Study Zone WA is an area of about 185 ha which is to be restructured as part of an urban upgrading program. Its population after upgrading will be about 22,200 (120 persons/ha). (The analysis described in this paper deals with the situation after uipgrading; it therefore provides guidance on appro- priate design for the upgrading works). 0 -3- City LA 16. This city is located less than 30 miles from the state capital, which has a significant impact on its social and economic conditions. The present population is about 20,000, but the population of the 14.5 ha region selected for study is only 2,200. The terrain is hilly, with a maximum variation in ground elevation for the study zone of about 70 or 80 m. The houses are detached and of fairly substantial construction. The study zone obtains partial water service from an existing but inadequate distribution network. City WP 17. The population of this capital city is several millions, with enormous migratioti from rural areas. The migrants have formed extensive slum and squatter areas on the fringes. One of the largest of these has an area of 180 ha, and adjacent to it is another sl-um with area of appr6ximately 40 ha. Study Zone TP1 with area of about 4.5 ha and population of 3700 (population density = 820/ha) was selected from the larger squatter neighborhood for study purposes, and a s.econd Study Zone rWP2 (area and pQpulation about 22 ha and 18,000 tespectively; approximately the eame density as WPI) was selected fram the smaller neighborhood. Tne housing in both WPl and WP2 is single storey of: poor quality. Both areas will be incorporated into a sites and services project of the World Bank. The proposed street plan is extremely regular, and differences in ground elevation are slight. City SP 18. The population of this city is over 2 million and the annual growth 0 rate is about 4%. Much of the population lives in temporary housing of poor quality, with. inadequate water supply and other services. Study Zone SP1 has an area of about 30 ha and population of about 11,000 (density = 370/ha), but Zone SP2 has an area and population of 10 ha and 10,000, respect:ively, with higlh density of 1000/ha. The terrain in both areas is generally flat. 19. The characteristics of these eight sturdy zones in five cities are summarized below. These zones. represent a wide range of street patterns and housing types and are fairly representative of the different conditions that are likely to be found in developing countries around the world. Zone Area Population Houses Population Density Housing Density (ha) (1000's) (persons/ha) (houses/ha) iYEl 29.0 10.0 1480. 350 50 ME2 40.0 4.0 785 100 20 WA 185.0 22.2 3000 120 15 LA 14.5 2.2 430 150 30 WP1 4.5 3.7 540 820 . 120 WP2 22.0 18.0 2640 820 120 SP1 30.0 11.0 1650 370 50 SP2 10.0 10.0 1470 1000 150 * IPipe Cost Functions 20. Cost functions for pipe lines may be power functions such as: L =kDa or fixed charge functions such as: C/L = k + aD where C is pipe cost (1976-77$), L is pipe length in meters, D is pipe diameter in mm, and k and a are parameters. Bid data were analyzed to determine the most appropriate function for each study area. 21. In City ME, data were available from four bids in 1976 for (a) supply of polyvinyl chloride (PVC) pipes and fittings to the nearest port, and (b) transportation to the city, excavation of trenches, installation and testing, trench backfilling and road reinstatement. Regression analysis gave a power function for supply costs of C/L = 0.0062 D1 5 , with R2 = 0.99. For trans- portation, excavation, laying, etc., both power and fixed charge functions were investigated; the former gave a slightly better fit (R2 of 0.742 compared to 0.692), but the latter was more logical (trenching costs are relatively unaf- fected by pipe diameter at small sizes) and so was adopted. 22. The overall relationship for furnishing and installing PVC pipe is GC/L = 6.35 + 0.133 D + 0.0062 D1.57. For diameters less than 150 mm, approxi- mately the same results are obtained from C/L = 5 + 0.24 D. For these small diameters it is interesting to note that about 20 percent of the cost is for supply, 30 percent in transportation and installation, and 50 percent in trenching, backfilling and resurfacing. 23. In addition to pipe costs, data were obtained on other components of the complete system. House connections cost about $100, including a meter. The cost of public standpipes ranges between $200 and $L,000, depending on design. Roof tanks for private houses cost between $110 and $130 for 250 to 500 1 sizes, and about $370 to $420 for 800 to lS000 1 sizes, exclusive of installation. 24. Cost data for City WA were not as complete as for City ME and did not permit supply and installation to be separately analyzed. For various bids, the "best fit" function for furnishing and- installing PVC water mains was: C/L - 0.20 D. This function applies to pipes with diameters in the range of 10 to 150 mm. 25. For City LA, a large sample of construction cost data for PVC pipe with diameters up to 160 mm was analyzed. The following power function was obtained from the regression analysis for furnishix.g and installing water lines: C/L = 0.0093 D1-58. 26. For City WP, 1976 and 1977 bid data were available for furnishing and installing locally manufactured asbestos cement (AC) pipe with diameters in the fD range of 50 to 300 mm. The best regression equation was found to be: C/L = 0.021 D1.36. -5- 27. For City SP, data were available Lrom three bidders of water mains in slum areas. The bids for 25 and 50 mm diameter pipes apply.to galvanized iron and cover both supply and installation; bids for 100 mm diameters were for PVC pipe. Additional dazta for furnishing and installing galvanized pipe in City SP but outside squatter areas were also available. By pooling all data, the best regression equation was found to be C/L = 0.0524 D1.04.. 28 . A summary of the cost functions for furnishing and installing water pipe (including appurtenances) in the five cities of thi.s study are presented in the table below. Also shown for comparison purposes are the costs per meter -of length of pipe with 100 mm diameter. All costs are in 1976-77 US$. City Pipe Cost/Lenath R2 C/L for = 100 (US$/m) ME PVC 5 - 0.24 D 0.7 .2,9 WA PVC 0.20 D 18 0.7 20 LA PVC 0.0093 D >0.9 13 rzqp AC 0.021 D1.36 >0.9 11 SP Mixed 0.0524 D >0.9 6 Alternative Network Designs 29. The work of generating alternative network designs began. with Zone ME1. It was decided to investigate three levels of service accessibility: standpipes with 100 m service radius; standpipes with 50 m service radius; and individual house or courtyard cortnections. A standpipe with a 100 meter radius service area serves 3.14 ha; 9.2 are therefore required for the 29 ha of Zone MEl. Similarly 36.9 are required to reduce the service radius to 50 meters. Finally, 1475 distribution devices are required if individual connections are given, one for each house. These values for the number of standpipes are of course theoretical; in practice, the street and path layout will have a con- siderable influence on the actual number of stanBpipes needed and the corre- sponding equivalent service radius. During field work preferred locations were identified for each standpipe. 30. The equation for calculating the theoretical number of standposts N to serve a region with area A ha assuming each standpost has a service radius of R meters is 2 N = (l0,000/I).(A/R ) which can be rearranged to solve for R. The resulting approximate expression is R = 56.4JA/N 31. In the case of the other study zones, alternative P=mbers of standposts were selected varying from wide spacings where the equivalent serv,ice radius Lrom the equation in paragraph 30 was as large as 240 m to courtyard connections -0- where the equivalent values for R were as small as 5 mO A tabulation of the standpost spacings for all eight study zones is shown below. No. of Approx. Persons Study Zone Standposts Radius(m) per Standpost (N) (R) ME1 9 100 1100 33 50 300 1475 8 7 ME2 11 100 360 43 50 90 785 13 5 WA 10 240 2200 17 185 1300 31 135 700 LA 15 50 670 WPl 10 35 400 540 5 7 WP2 13 60 1380 48 30 375 2640 6 7 SP1 9 100 1220 30 50 370 1646 10 7 SP2 16 45 625 38 25 260 1470 5 7 32. In addition to different standpost spacings, alternative design flows were investigated for each study.zone. In the case of Zone ME1 which was the first city to be studied, average per capita flows of 20, 50 and 100 lcd were assumed for standposts, and average flows of 50 and 100 lcd were assumed for courtyard connections. In all cases, the flows actually used for network design were three times the average; i.e., a peaking factor of 3 was assumed. While it is recognized that the actual average demands from standposts are never likely' to be as large as S50 or 100 lcc,' atid that peak fa'ctors will vary widely depending on the characte'ristics of the study area, these values were chosen to provide a very wide range of design conditions for the study herein. It will be seen later that the mathematical models derived from these studies allow the selection of both Q and F. A tabulation of the average design flows for the eight study regions that were assumed for standposts and courtyard taps are as follows: -7- Average Design Flows (lcd) Study Zone - Standnosts Courtyard 20, 50, 100 50, 100 M}E2 20, 50, 100 50, 100 TWA 10, 20, 30, 40, 50,. 100 -- LA - 50, 100 wX1 25, 50, 100 100 WP2. 12.5, 25, 50,100 i 100 SP1 25, 50, 100 100 SP2 25, 50, 100 100 33. For all study zones, the assumption was made that a water main of the pri- mary distribuition network in the city passed nearby, to which the secondary net- works of concern in this study could be connected. 1/ At the single point of connection between primary and secondary grids, the avzailable pressure was generally-assumed to be 25 m. It was then assumed tnat the minimlTm allowable pressure in the secondary network was 15 m, thus allowing a head loss of 10 m across the grid. In some cases, additional minimum pressures were also assumed, 20 m being most common. In the case of Cit7y LA, the hilly terrain made it necessary to design for a large head loss of 30 m across the network. Where standposts were used Lor water distribution, minim'um pressures occurred at the standposts, but with courtyard taps, minimum pressures were at internal points within the grids. 34. During the field workh,.suitable pipe layouts to serve each assumed design condition were identifiet>, and corresponding pipe lengths and elevations determined. For standpipe supplies the networks were branched; for house/court- yard connections, however, where. a pipe is needed on almost every street, they were looped. 35. A total of 72 alternative network designs for the eight 'study zones were prepared during this investigation. The aumber of altaeratives for each city are shown below City MEl ME2 WA. LA rP1 WP2 SP1 SP2 Alternatives 10 10 24 Z 4 8 7 7 1/ Some work was also done assuming entire study zones were surrounded by primary .g-.ids thereby providing multiple connections for the secondary networks. It is not reported herein. -8- 36. All pipe flow calculations were done using the Hazen Williams formula with. a value for Hazen Williams constant C of 100. The actual C value of the network will'of course, depe'nd on the pipe material used, its age, and the configuration of pipes, fittings and house connections. It should be noted, however, that the calculated values for pipe diameter are relatively insensitive to C; since D is proportional to C-0-38, a change in C of 20 will result in a change in pipe diameter of less than 10 percent. 37. Given the assumed design condiltions, the pipe layout and the pipe cost function, the next task was to select pipe diameters such that the network was optimal.; that is, such that it met the design criteria at minimum cost. For branched networks, this can be done using linear programming techniques that have been fully described in the literature. The one selected for this study 1/ assumes that each pipe between two nodes consists of several links of dif- ferent diameters, and then determines the optimal length of each link. It should be noted that this program may design any one pipe length between nodes to include sections of some diameters which may be so short that in practice they wquld be ignored. The, network does not, therefore, correspond exactly to the net- work which would be constructed. However, this is not a significant drawback in the present study, which in order to aid overall planning concentrates on average pipe diameter, the distribution of pipe sizes and overall network costs. 38. Optimal design of looped networks is more difficult, sinca pipe flows are not known in advance and simple linear programming techniques cannot be used. Instead, a simulation algorithm 2/ was used, which indicates node pressures for selected pipe sizes. Successive adjustments to the network are made until all pressure criteria are just satisfied. A separate computer program was used to calculate the resulting network cost. There is no assurance that such a trial and error procedure identifies an optimal solution; on the other hand, repeated iterations lead to designs that are almost certainly near-optimal. 39. The results of the network designs are shown in Table 1. The first four columns of this table contain data on the alternative design conditions for each study zone. The next two columns describe the principal characteristics of the resulting networks for each alternative. Pipe length L is simply the total length of pipe in each grid in meters. Mean pipe diameter D is a weighted average based on length. The equation used to calculate D for each network is D =L DJEL. where L. = length of any link i in the network and D. = diameter of link i. The last column C is the cost of furnishing and installing all of the pipe in the network; valugs irn this column are based on the cost equations presented in paragraph 28. To obtain total network cost CT, it necessary to add the cost of distributicn devices Cs to pipe cost Cp. Cs for each alternative is N times the unit price for the type of distribution device being considered. Public stand- posts were found to vary in unit cost between $200 and $1000, and individual yard faucets ranged from about $50 to $100. 1/ See Robinson, R. B. and Austin, T. A.: "Cost Optimization of Rural Water Systems", J. Hydraulics Div., A.S.C.E., HY 8 pp 1119-1134, August 1976. 2/ See Epp, R. and Fowler, A. G.: "Efficient Code for Steady-State Flows in Networks", J. Hydraulics Div., A.S.C.E., HY 1 pp 43-56, January 1970. Model Formulation and Calibration' 40. The data in Table 1 were divided into two sets, with results for Cities HEl, ME2 and WA in one set, and results for the remaining cities in the other. The first set of data comprising res!-lts from 44 alternative designs wer.e used to develop and calibrate mathematical models for predicting total network pipe length L and mean pipe diameter D based on the decision variables in the first four collmns of Table 1 together with study zone area A and.population P. The second set of data comprising results from the remaining 28 alternative network designs was used for verifying the models for L and D. 41. Based on the first set of data, predictive models were developed using linear regression techniques. For both length and mean diameter, the proposed models were of the form B B B Y = Bo BlX2B 2 ...X n where Y is the dependent vatiable (either L or D) and the X's are the independent variables. The task in regressiorn analysis is to assign numerical values to the B's, which can be done using numerical techniques once the model is linearized by taking the logarithmic transform of both sides. Pipe Length 42. Intuitively, the length of pipe L in a seccndary network is likely to be dependent on the area served A and the number or spacing, N or R, of distribution W devices to be. supplied; per capita flow, Q, and available headloss, H, will affect average pipe size but not total length. It is expected that street geometry and necwork type (looped or branched) would also have an effect. 43. The data for the 44 alternative designs in zones ME1, ME2 and WiA actually include networks with only 9 different total pipe lengths., as shown in Table 1. All 9 alternatives including both branched and looped grids were pooled to form a single data sample, and the Lollowing model was proposed for relating L, N and A. BX, L/A= B (N/A)l From least squares regression analysis, it was found that Bo = 90 and B = 0.4, which permits the above equation to be written as follows 0 0.4 0.6 L = 90 N A the R- for which exceeds 0.9. This model plots as a straight line on loga- rithmic graph paper and is shown in. Figure 1 together with. the 9 data points upon which it is based. 44. As can be seen from the ahove equation, L is relatively insensitive to N; doubling the numher of standpipes, which is equivalent to halving the numb.er -10 of persons served per standpipe, increases network length.by only 30 percent. 1/ Alternatively, access to service may be.expressed in terms of t'Le maximum distance that water has to be carried, R. This can be done by substituting the expression for N in paragraph 30 into the above equation to obtain L-= 2267 A . Hence, cutting maximum walking distance in half requires an increase in network length of 74 percent. Pipe Diameter 45. As would be expected, other things being equal, average pipe diameter D increases with per capita flow but falls with increasing headloss across the system or increasing number of distribution devices (since each pipe then carries a smaller proportion of total demand). Regression analyses were carried out using the data sample. for the 44 alternatives in zones MEl, ME2 and WA to express these relationships in mathematical terms. Considering only the branched net- works, the relationship was found to be: 2. 0.N020 0.23 0.10 0.38 H-0.23 P270 N P A (FQ) H, where F = peaking factor (i.e., the ratio of peak-to-average flow), and the other symbols are as previously defined. If both branched and looped networks are included, the relationship alters only very slightly, and becomes: - 0.17 0.22 0.10 0.38 -0.23 D=2.57 N 1 p A (FQ) HR 46. Althoughl-all the variables in the equatiocs above are statistically significant, the model can be simplified further, to 0.21 0.39 D =2.93 (P/N) (FQ) thereby relating average pipe diameter solely to the number of persons per standpipe and to per capita flow. The resulting loss of accuracy is small under normal conditions. 2/ l/ Some caution is necessary in applying this reasoning to systems with house connects.ons. Once it is decided that house connections will be provided to anyone who applies, it is necessary to lay mains in virtually every street. L is then dependent on the total number of houses in the area, not, for example, on the number that are expected to connect within a given period of time. 2/ In the regression analysis, the values of R fall from 0.99 to 0.90. In a typical example (A = 100, Q = 50, F = 3, H = 10, N = 60, P = 15,000) the equation in paragraph 46 gives D = 66 mm, and for those in paragraph 45, D = 68 mm. In practical terms, these are identical. -11- 47. It is evident that D is relatively insensitive to both P/N and FQ. However, the range of these values in secondary systems may be considerable. FQ may increase tenfold if house connections are provided instead of standpipes - (peak consumption increasing from 30 lcd to 300 lcd); D would correspondingly increase by a factor of about 2.45. Changes in P/N will usually be much larger than those in FQ: typically from 7 to 10 persons per house connection to several hundreds or even thousands per standpipe. For a 50-fold increase (from P/N = 10 to P/N = 500), D would irncrease by a factor of about 2.27. 48. The equations above provide a means of estimating the average diameter of optimally designed secondary networks. They do not, however, indicate the distribution of pipe sizes making up that network. Frequency analysis of the results for the branched systems in Study Zone WA and for the looped systems in Study Zones L'E and ME2 showed that the pipe diameters are approximately log-normally distributed. The standard deviation, S, is about 0.35 to 0.40 times D for branched systems and 0.5 to 0.6 times D for looped systems. The distribution of pipe sizes in a secondary network can therefore be predicted as: 20% of total 60% of total 20% of total length has length has length has- diameter equal diameter diameter equal or less than between or greater than Branched Systems 0.65 D 0.65 D and 1.35 D 1.35 D Looped Systems O..45 D 0.45 D and 1.55 D 1. S5 D Velocity,, 49. Design standards for distribution systems frequently specify maximum acceptable flow velocities. In fact, velocity is not a particularly useful design parameter, except in particular cases; for example, where undersized valves are used (chrough which the velocity may be several times that in the network and where seats may be damaged if pipe'ine velocities are not limited) or where there are problems with scale and corrosion. Nevertheless, an analysis of velocity distribution was made during two of the looped (house connections) systems for City ME and six of the branched systems for City WA. . / 50. The regression analysis led to the following. relati onship for the weighted average velocity, V (in m/s) 1/ --0531 -0-34 0.22 V = 8.6 A N (FQ) The average optimal velocity of the sample was 0.64 m/s, wLth individual values varying between 0.40 and 1.04 m/s. 1/ Mean veloci-ty V in a distribution network is derined as follows V = Z L.V./IL. where V. = velocity in pipe i and L. length of pipe i -12- 51. The variation in velocity was found to follow approximately a log- normal distribution, with a standard deviation of about 0.3 to 0.35 times the average. About 60 percent of all velocities would therefore be predicted to fall in the range 0.67 V to 1.33 V, with 20 percent above and 20 percent below this range. In the models, therefore, 80 percent of velocities would be below 1.33 x 0.64 = 0.85 m/s; this value is considerably lower than those usually specified as maxima, suggesting that velocity is not an appropriate criterion in design of this type of network. Model Verification 52. Having developed the predictive models for pipe length and mean, diameter shown in paragraphs 43, 45 and 46 using data from the 44 alternative designs for cities ME and WA, work was done to verify these equations using data from the remaining 28 cases. Verification consisted of comparing the actual L and D values in Table 1 for cities LA, WP and SP with predicted values of L and D obtained from the regression equations. 53. The first model to be verified was the one for pipe length in paragraph 43. A comparison of predicted values from this equation with the observed values in Table 1 is shown below. The percent error was calculated as follows % Error =(Observed Length - Predicted Length)100 Observed Length where the numerator is an absolute value always greater than zero. No. Stand- Area Observed Predicted City posts (ha) Length Length Error (N) (A) (m) (m) (%) BRANCHED NETWORKS WP2 13 22 1880 1604 14.7 WP2 48 22 3082 2705 12.2 WP1 10 4.5 715 607 15.1 SP1 9 30 1790 1668 6.8 SP1 30 30 2974 2700 9.3 SP2 16 10 1382 1086 21.4 SP2 38 10 1952 1535 21.4 LA 15 14.5 1604 1323 17.5 LOOPED NETWORKS WP2 2640 22 8839 13,450 52.1 WP1 540 4.5 1905 2748 44.2 SP1 1646 30 9868 13,399 35.8 SP2 1470 10 5583 6624 18.6 54. From the above table, it is seen that the regression equation in paragraph. 43 consistently underestimated pipe length for branched networks and consistently overestimated the length of looped networks. While the errors for -13- branched systems are not enormous, they are clearly unacceptable for looped networks. These results suggest the necessity for two pipe length equations, one for branched systems and another for looped. The apparent failure of a single equation for both types of networks seems to be due to a lack of consideration of street configuration. In the case of branched networks, the more streets in a given area, the better the chances for shortening pipe length since many alternative routes are available. In the case of looped networks, however, an increase in the number of streets.. has the opposite effect of lengthening the network. Hence, unless street pattern is taken into account, it seems unlikely that a single equation can apply to both types of systems. 55. The data for the entire set of branched networks in all eight study zones were pooled and used for developing a revised length model. The resulting equation is L =82 N0 55 0.49 and the associated R2 = 0.90. 56. Similarly, data for the entire set of looped designs were pooled from which the following length model was developed L = 105 N032 A063 The R2 value for this equation is 0.97. 57. The predictive models in paragraphs 55 and 56 are calibrated but not verified. To improve confidence in using them, it would be necessary to perform verification work with additional study areas similar to- that described herein. 58. The equations for predicting mean pipe diameter in paragraphs 45 and 46 were verified by comparing their predicted values with observations in Table 1 for network designs in Study Zones LA, rVP and SP. Although paragraph. 45 includes -two equations for D, only the second which 'applies to both branched and looped networks was verified; it is referred to as Eq. 45 in the following table. Eq. 46, on the other hand is the expression for D in paragraph 46. No. Avg. Observed Predicted D (=) Stand- Flow D City posts (lcd) (mm) Eq. 45 Eq. 46 (N) (Q) WP2 48 25 63 48 56 48 50- 83 62 73 48 100 109 80 95 13 25 68 59 70 13 50 85 77 91 13 100 111 100 118 2640 100 52 39 41 -14- . WP1 10 25 40 37 55 10 50 52 49 72 * 10 1QQ 70 63 94- 540 100 35 32 41 SP1 9 25 71 59 68 9 50 92 76 89 9 100 118 99 116 30 25 53 47 53 30 50 69 62 69 30 100 90 81 90 SP2 16 25 65 47 59 16 50 86 61 77 16 100 110 79 100 38 25 50 41 49 38 50 65 52 64 38 100 84 68 83 LA 15 50 40 35 59 15 100 54 46 77 59. While the agreement between predicted and observed mean diameters above is not exact, it appears satisfactory. Consequently, the equations for D in paragraphs 45 and 46 are considered to be verified and valid for use in pre- dicting mean network pipe diameters. Costs 60. The total cost of a secondary system is very dependent on the cost of the distribution devices; standposts and house connections may represent as much as or even more than-50 percent of the total expense. Consider, for example, the data in Table 1 for Study Zone ME1. For the system with 33 stand- posts, piping cost is in the range of $44-$63,000, but at $1000 each, public standposts would cost $33,000. Piping for a looped network in this zone is shown in Table 1 to cost between $142/160,000, but at $100 each, house connections would cost. $147,000. Thus the cost of distribution devices cannot be overlooked and, in fact, the optimal design of these units merits as much attention as that given to network piping. 61. At the outset of this report, one of the stated objectives was to develop mathematical tools that will enable designers to predict the cost consequences of selecting alternative standards for the decision variables under their control. Using the pipe length and mean diameter models from paragraphs 45, 46, 55 and 56, such tools can now be presented. In paragraph 20, pipe cost functions are shown to be of the power or fixed charge type; consider the fixed charge expression C/L k + aD, which can be rewritten as follows C= (L)(k + aD) -15- If one of the equations for predicting total network pipe length shown in paraaraphs 55 and 56 is substituted for L, and one of the equations for pre- dicting mean diameter shown in paragraphs 45 and 46 i s substituted for D, the resulting expression is a mod.el for predicting total ;netwozk pipe coat, which is denoted C 1/ Using, for example, L for branched networks from paragraph 55 and the expression for D from paragraph 46, the model for total pipe cost is 0.55 0.49 0.21 0.39 C = 82N A [k + a(2.93)(P/N) (FQ) p Other expressions for C can be similarly developed. A model.for predicting the piping cost of loopDd networks, for example, is obtained using L from paragraph 56 and, say, D from paragraph 45 105 N .32 0.63k + a(2.57) N017 p0.22 A0.10 0 38 -0.23 p 62. In the case of a power cost function, it is not strictly true that total pipe cost is equal to total length multiplied by the unit cost of the aver9age diame.ter .plipe unles.s the exmonent of D in the- power function 'is 1. However, the error is small for the values of the exponent usually encountered in practice. For illustrative purposes, the power cost function C/L= kDa is used it the remainder of this report. Inserting L and D from paragraphs 55 and 46, respectively, the expression for total pipe cost in branched systems is C = 82 k(2.93)aa 0.49 p0.21a (FQ)0.39a 0.;5-0.21a p Other expressions for C cani be similarly developed by substituting the appro- priate equations for L Lnd D frommparagraphs 45, 46, 55 and 56 into the power cost function. 63. As observed, in paragraph 60, the cost of standposts and house connections (denoted C ) cannot be ignored and must be added to pipe costs C to obtain total system cost (denoted CT); i.e., T P s C is simply the unit cost of public standpipes or house connections S multiplied by the number of de-vices N. Hence, adding SN to the pipe cost equations above results in expressions for total system construction costs. 1/ This can be demonstrated as follows. The cost of the ith pipe is L.(a + kD.); hence, total piping cost C = ELi (a + kD.) -which can be rewritten C = aLL. + kL.D.. From Ehe definition of D in paragraph 39, EL.D. = DZL., wRich can be inserted to obtain C = aZL. = KDL. = LL. (a + kD) 3Hence 1 total pipe cost is the product of total length and thelunit cost of average diameter pipe. -16- Applications to Design 64. Thi-s section includes some numerical examples of the application of the equations described above to .typical design decisions. It does not attempt to cover all the possible applications, but illustrates how these equations can guide engineers when confronted with common problems. The calculations have all been done using a pocket calculator; no special computing techniques were used. The following basic data are assumed to apply to all the examples: A = 100 ha P = 30,000 people Pipe Cost Function C/L 0.2D0 9 Standpipe Cost = $500 House Connection Cost = $100 Pipe Size/Service Level Relationships 65. From the equation in paragraph 46, D = 2.93 (P/N) (FQ) the trade-off between average per capita flow for a peaking factor of 3 and level of service can be determined for any assumed mean pipe diameter. A family of iso-diameter lines for mean diameters of 25, 50, 75 and 100 mm is shown in Figure 2. From this it can be seen that 25 mm average diameter pipe is satis- factory for a house connection system with 5 persons per connection and 35 lcd; at 10 persons per connection it will supply low a consump.ion to be satisfactory. It is also too small to provide a satisfactory supply through standpipes. A network with an average diameter of 50 mm,. on the other hand, will provide 150 lcd average flow through house connections (given 8 consumers/connection) or 20 lcd through standpipes, each serving 350 people. Clearly, this will meet the majority of situations, and average pipe sizes will not usually need to be larger than 50 mm. This in turn implies that 80 percent of total pipe length in branched networks need not exceed 68 mm in diameter (see paragraph 48). "Basic Needs" Network 66. The designer might initially decide to investigate the minimum service that could be provided to meet the basic needs of the population. This might be to supply 15 lcd at a peak factor of 2, service radius up to 250 m, and up to 1,000 persons/standpipe. The service radius condition implies that 2 N = (10,000/r)(100/250 ) = 5 (from paragraph 30), whereas the limitation on the number of persons/standpipe implies N = 30. C Clearly the latter condition governs, and R = 56.4 \100/30 = 103 m (from para- graph 30). The total length of the network can then be estimated (paragraph 55) as : L = 82 30 = 5080 meters. The average pipe size (paragraph 46) would be: D = 2.93 (1,000)0.21 (2 x 15)0.39 47 mm -17- The unit cost of this average size pipe would be 0.2 x 47 $6.4/m, and hence the network cost would be 6.4 x 5080 = $32,500 (paragraph 62). Adding the cost of 30 standpipes C$15,000) gives a total cost of about $47,500. Pipe Standardization 67. If the. distribution network is extensive and has to be broken down into a large number of homogenous subzones', it may be impractical or too expensive to design each subzone in detail. In these circumstances, one approach would A be to use as standard a slightly larger pipe than the calculated l0, with reasonable confidence that -it will meet, the design criteria. In the example shown, D = 47 mm. From paragraph 48, 80 percent of the network corresponding to this D would have a diameter equal to or less than 1.35 x 47 = 63 mm, which is a commercially available size. If the entire network were laid as 63 mm pipe, (with the exception of connections to the primary network, which would have to be larger) the cost would be $42,300, an increase of about 30 percent on pipe costs. Whether the extra cost of about $10,000 is justified by standardizacion benefits or lower engineering costs -is for the designers to judge. StandsiDe Network 68. The models can be used to examine the effects of changing the various decision variables. For example, one could consider designing for a rather better level of service than the 'basic needs" defined in paragraph 66 above: Q = 25 lcd at a peak factor of 3, and with 500 persons/standpipe. Repeating the calculations in paragraph 66 with these new values, it is found that: N = 60 1 = 7440 m D = 58 mm C = $57,500 p Cs = $30,000 CT = $87,500 Hence, improving service to this level would increase cost by about 80 percent, increasing per capita costs from $1.58 to $2.92. Again, whether this is justified must be left to the judgment of the designer. Upgrading to House Connections 69. In time, many squatter neighborhoods develop to the point where individual house connections can be afforded by the residents. It is the.refore desirable to ensure that the network initially installed to ser-vme standpipes is compatible with the network later required to serve house or courtyard connections. In this example, assume that house connections may become feasible in 5 years, and that the average per capita flow at that time is expected to be 100 lcd with a peak factor of 3. At 10 persons/connection, a1lowance must be made for up to 3,000 house connections. The corresponding network length that will be required for -18- such house service (from paragraph 56) is 0.32 0.63 L 105 x 3,Q00 xOO = 24,800 m The average diameter (from paragraph 46) is =2.93100.21(3 100)0.39 44 Thus, the "ultimate" distribution network that will be required 5 years hence to provide 100 lcd average flow through house connections must include pipe with an average diameter of about 44 mm. The task for the present, then, is to design a standpost network with this same average pipe size so that the two networks will be compatible, thus avoiding the need to discard or replace large sections of the standpost network as the upgrading takes place. In paragraph 66, it was shown that the "basic needs" network has approximately this same average diameter, although its total length is of course much shorter than that required for house connections. Hence it appears that if this "basic needs" system is constructed now (with 30 standposts and average design flow of 15 lcd), the two networks will be compatible. 70. While it may be desirable to ensure compatibility between the initial network, laid to serve standpipes, and the later extensions to serve house connections, this does not mean that the network should initially be able to serve house connections. This can be shown as follows. The investment stream for the service levels discussed in paragraphs 66 and 69 is: * Cost Present Value US$ --- US$* Year 0 5080 m network D = 47 mm 32,500 32,500 30 standpipes 15,000 15,000 Year 5 19,720 m extension D = 47 mm 126,200 78,400 Year 8 ** 3,000 house connections 300,000 140,000 473,700 265,900 *at 10% discount rate. **installed between Years 6 and 10. If the full network is installed immediately, but house connections are delayed until needed, the corresponding investment stream is Cost Present Value US$ --- US$*---- Year 0 24,800 m D = 47 mm 158,700 158,700 30 standpipes 15,000 15,000 Year 8 3,000 house connections 300,000 140,000 473,700 313,700 *at 10% discount rate. -19- Laying the whole network initially therefore increases the present worth of the investments by nearly 2Q. percent ($313,700 compared to $265,900), without pro- ducing any corresponding henefits to the undertaking Cin the form of increased revenues) or to the consumer (in the form of better service). On the' few occasions where it may be essential to lay the whole network initially, this analysis suggests that the undertaking should endeavour to install house con- .nections'as soon as possible so as to obtain 'full benefits from the investment. 1/ Budget Constraints 71. In designing systems for sqiatter neighborhoods the designer often has to keep within a predetermined per capita cost, which is all that is affordable by the consumers. For example, assume that for health or other reasons it is decided that a flow of 25 lcd must provided with a peaking factor of 3, and yet the per capita cost must not exceed $2.50 (i.e., a total expenditure of $75,000). The problem is then to determine the appropriate aumber of standpipes, N. The length of the network from paragraph 55 is 0.5 0.490.55 L = 82 N0'55 1000.49 7833N5 The average pipe size from paragraph 46 is 29 (30,00)0.21 0x 25)039 -0.21 -0,21 29 300) (3 2) N_ 138N The unit cost of pipe is then 0.2 (138 N 0.21)09 = 16.8 N-0.19 Putting pipework plus standpipe costs equal to total maxinum permitted cost, we obtain: 0.55 -019 0.36 (783 N ) (16.8 N ) + 500 N = 75,000, or 13,154 0' + 500 N = 75,000 whence (by trial and error) N = 45. There will therefore be 670 persons/stand- pipe, and each standpipe will have a mean service radius of 84 m (from paragraph 30). The-average pipe diamecer (from paragraph 46) will be 62 = (note that since there are so few standpipes the pipe diameter is comparati-vely largse; it therefore presents no problems of compatibility when funds are available to install a more extensive network). Intermittent Supply 72. In many cities in the developing world, water supply is intermittent; consumers receive service for as little as 2 hours each day, often at low pres- sures. This situation has come about by acc-ident rather than idesign - the systems have not been expanded as necessary or have not been maintained satis- factorily - but the argument is sometimes put forward that this technique is 1/ Throughout this discussion, the costs- of wastes disposal associated with increased water usage - which could be substantially higher than those of water supply - have been omitted, but they must of course be taken into account in making staging decisions. -20-, an effective way of allocating a limited supply and should be incorporated into new system designs. This paper is not an appropriate forum to discuss the issue, which has important public health and operational implications in addition to its impact on system costs. However, the effects on secondary distribution of adopting intermittent supply can be forecast from the results obtained in this research.. 73. The "basic needs" network (paragraph 66) can distribute a peak flow equivalent to 30 lcd. If a "basic needs" network designed for 24-hour supply is placed on intermittent sunply for, say, 4 hours/day, then the quantity of water that can be distributed is only 30 x 4/24 = 5 lcd. This is about the basic minimum to sustain life in many climates; it is certainly unsatisfactory for maintenance of personal hygiene and basic sanitation. 74. It might be thought that the situation could be improved by accepting a lower pressure at the distribution device. Since the peak flow and the number of persons/device remain constant, this implies modifying the delivery system: house connections serving upper floors may have to be converted to ground floor or courtyard connections, and multiple outlets have to be fitted to standpipes to maintain the same flow even at the lower pressure. Both those changes cost money. However, the benefits are slight. From the equations in paragraph 45 it can be seen that, with. all other variables constant, flow is proportional to H0 6. Most of the work herein assumed a head drop of 15 m across the network, (from an initial 25 m to 10 m at the distribution device). Increasing this by 33 percent, from 15 m to 20 m, would only increase Q by 19 percent, from 5 lcd to 6 lcd. 75. If at the time of initial construction it were anticipated that the system mighc eventually have to operate under intermittent supply conditions (for example, because financial constraints seemed likely to prevent needed source development), then appropriate provisions could be made in the original network. For example, to supply a "basic need" of 15 lcd during 4 hours implies a flow equivalent to 90 lcd. With such a short supply, there would probably be no peak and the network would operate continuously at full capacity. D therefore would have to increase (paragraph 46), to 72 mm. Average pipe cost would increase from $6.4 to $9.4 per m (about 45%) resulting in C = $47,750. The additional expenditure on providing for eventual intermitten'tpsupply would therefore be about $0.50 per capita. Whether this is justifiable is a matter of judgment in the circumstances of each individual case. However, three ob- servations may be made: The network cost for this contingency could instead be used to give a far better continuous supply. The 72 mm D pipe size may be larger than is necessary for later conversion to house connections (paragraph 69-70), and so may be uneconomical. Tha primary distribution network associated with intermittent supply will also be more expensive both to build (because of valves and mains needed to serve discrete zones) and to cperate (because of the large number of valve operations each day). -21- Pub.lic vs. Private Storage 0 76. Designing for a peak factor of 3, +as has been done in the analyses above, imples that the storage tank provided to compensate for the difference between treatment. plant output and peak demand is a public tank upstream of the networks under consideration; the networks therefore have to carry the peak flows. The storage to be provided in public tanks would depend bn the variation of demand throughout the day; normally it would be equivalent to 6 to 8 hours average supply (for balancing purposes only, exclusive of allowances for breakdown, firefighting, etc.). 77. Alternatively, the storage could be provided. by individuals in their own homes. If properly designed throttling devices are installed. in the inlets of private storage tanks, the ,peak flows trar.mitted to the network could be substantially reduced, perhaps to 1.5 time' the average flow. This enables average. network pipe sizes to be reduced, and the potential. economies can be calculated using the equations presented earlier. 78. Consider the same area described in paragraph 64, with house connections supplying an average 100 lcd. The corresponding consumption is 3000 m3/d. Ser- vice reservoir storage of 1000 m3 would provide the equivalent of rather over 8 hours' supply, sufficierLt to balance out daily fluctuations in demand. Storage costs vary widely with ssite conditions; for a ground level tank of this size, assume a cost of $75,000. The associated network will include 24,800 m of D = 44 mm (paragraph 69); using the cost function in paragraph. g4,' its cost would be estimated at $149,500. House connections (3000 at $100 each) will add a further $300,000.1/If private storage tanks were provided, the public balancing storage could be omitted. With 10 persons/connection the avrerage daily flow per connection is 100 1; a 350-1 tank in each house would provide over, 8 hours' storage and would minimize transmission of peak loads to the network. If each tank (including inlet control devices) costs $125 installed (this aggain will vary widely depending orn house arrangement and materials), the total cost is $375,000. If these tanikS permit a reduction in design peak factor from 3 to 1.5, D will be correspcaidingly reduced to 34 =, and network costs will fall *to $118,5,00 . Summarizing -these -calculations: Public Storage Private S'torage Storage. $ 75,000 375.,000 Network 149,500 118,500 House Connections 300,:00 . 300,000 Total $524,500 $793,500 79. This analysis shows a substantial margin in favor of public storage. Clearly there may be exceptional circumstances TAhere private storage would be competitive with storage provided by the water undertaking, and this. is an alternative which designers should bear in mind... Eaowever, there are several factor-s which tend to make private storage less attractive than the figures above might indicate: - Lhere are substantial economies of scale in the costs of service reservoirs. Since these reservoirs are necessary 1/ No reduction has, been llowed for the- smaller diameter (say 6 =) house - connections wnicn may te used wnere in-house storage is provided. -22- in any case to provide reserve capacity in case of supply system failure Cignored in the example above), the incre- mental cost of providing balancing storage is relatively low. In addition, since service reservoirs are normally designed to serve a number of supply zones, thoy are sub- stantially larger than the calculated example; and this again reduces the unit cost of the balancing storage. With intermittent supply, storage requirements rise rapidly (e.g. 6-hour supply needs storage equivalent to at least 75 percent of daily usage). This favors public storage. with its economy of scale and potential for lessening the effects of the peaks due to intermittent supply by serving supply zones in rotation. 3 The weight Qf private storage tanks (1 m of water weighs 1 totne) may be more than could be supported by the houses in which the poor live. - Pr-,Vate storage is more likely to become contaminated and to provide suitable breeding habitat'for mosquitoes. 80. Most commonly, private storage is installed because the public system has proved inadequate and can only provide an intermittent supply. Under these circumstances the network is subjected to peak demands almost all the time it is under pressure: consumers leave taps wide op.-.a or remove them entire,ly, and some may even connect pumps directly to the mains. In theory, advratage could be taken of these individual facilities to economize on public storage requirements when designing the works necessary to put the system back onto 24-hour supply. However, in practice the amount of modification require, to individual systems, and the need for public education to establish new water usage habits and restore confidence in the public system would probably make it more efficient to provide the full amount of balancing storage in a public tank. // TABLE 1 ALTERNATMvE DESIGNS R Nominal Q N a L C Service Avg. No . of Head Pipe Avg . Pipe Radius Flow Stand- Loss Length Diam. Cost (M) (lcd) pi-es (m) (m) (mm) ($1000) - STUDY ZONE lE1- 100 20 9 10 1,450 59.0 26'. 7 100 50 9 10 1,450 88.0 37.4 100 100 9 10 1,450 110.5 46.4 100 50 9 5 1,450 95.6 40.4 50. 20 33 10 3,007 42.6 44.4 50 50 33 10 3,007 61.2 58.1 50 100 33 10 3,007 79.8 72.9 50. 50 33 5 3,007 67.7 63.1 8 50 1475 10 10,788 35.6 '142.1. 8 100 1475 10 10,788 43.0 160.6 STUDY ZONE IME2 100 20 11 10 2,080 45.8 31.9 100 50 11 10 2,080 66.8 42o2 100 100 11 10 2,080 85.8 52.8 100 50 11 5 2,080 76.3 47.7 50 20 43 10 3,780 35.4 49.8 50 50 43 10 3,780 50.8 63.0 50 100 43 10 3,780 65.2 76.8 50 50 43 5 3,780 56.4 68.9 13 50 785 10 .12,580 34.4 159.5 13 100 785 1.0 12,580 42.7 184.9 STUDY ZONE WA 240 10 10 15 -4,040 55.3 44.6 240 20 10 7.5 4,040 87.1 70.4 240 20 10 10 4,040' 80.1 64.8 240 20 10 15 4,040 711 57.9 240 20 10 20 4,040 67.2 5404 240 30 10 15 4,040 84.4 68.3 240 40 10 15 4 ,040 93.6 75.6 240 50 10 15 4,040 102.0 82.4 240 100 10 15 4,040 132.2 106.9 TABLE 1 (cont.) 185 10 17 15 5,690 51.2 58.3 185 20 17 10 5,690 75.7 86.3 185 20 17 15 5,690 65.9 75.0 185 20 17 20 5,690 61.0 69.5 185 50 17 15 5,690 93.6 106.5 185 100 17 15 5,690 123.1 140.1 135 10 31 15 8,670 46.6 80.9 135 20 31 7.5 8,670 73.6 127.6 135 20 31 10 -8,670 69.8 121.1 135 20 31 15 8,670 60.4 104.6 135 20 31 20 8,670 55.8 96.8 135 30 31 15 8,670 70.2 121.6 1-35 40 31 15 8,-670 78.8 1'36.6 135 50 31 15 8,670 85.6 148.5 135 100 31 15 8,670 111.0 192.5 STUDY ZONE LA 50 50 15 30 1,604 40.2 5.1 50 100 15 30 1,604 53.5 7.1 STUDY ZONE WP1 35 25 10 10 715 40 2.5 35 50 10 10 715 52 3.5 35 100 .10 10 715 70 5.3 5 100 540 10 1,905 35 7.6 STUDY ZONE WP2 30 25 48 10 3,082 62 18.5 3Q 50 48 10 3,082 83 27.5 30 100 48 10 3,082 109 39.9 60 12.5 13 10 1,880 49 8.0 60 25 13 10 1,880 68 11.8 60 50 13 10 1,880 85 17.2 60 100 13 10 1,880 111 24.1 6 100 2640 10 8,839 52 43.8 TABLE 1. (cout.) STUDY ZONE SP1 100 25 9 10: 1,790 70.7 7'. 9 100 50 9. 10 1,790 91-.8 10.3 100 . 100. 9 ICY- 1,790 118.3 13.5 .50 25. 30 10 2,974 . 53.2 9.7 50 50 30 10 2,974 69 .O 13.2 .50 100" 30 - 10 . 2,974 90.0 17.4. 10 100 1646 10 9,868 STUDY ZONE SP2 45 2; 10- 1,382 65.3 5.6 45 50 16 10 1,382 85.5 7.4 -4.5 100 .6 1-0 1,38 10 .2 9 .7 25 25. 38 10 1,952 49 .6 5.8 25 50 38 10 1,95Z 64..7 7.7 25 100 38 10 1.,9:52. 83.6 ..0.I. 5 100 1470 1Q 5583 .-, , @ jj ; O. 01 O...: I X lo 1._ O I STANDPOSTS PER HIECTARtE (N/A) AVERAGE PElt CAPITA FLOW (Q) led Eno -S -' Ho ' - 0. 0 0 '-4