With the acceleration of urbanization,the demand for water supply and drainage pipe networks has increased significantly.In the planning of urban construction,it is necessary to optimize the design of the water supply...With the acceleration of urbanization,the demand for water supply and drainage pipe networks has increased significantly.In the planning of urban construction,it is necessary to optimize the design of the water supply and drainage system pipe network to effectively save energy while providing residents with more accessible water resources.Therefore,the municipal water supply and drainage system and the water transmission methods should be designed according to the geographical conditions of the city.In this paper,we mainly analyze the design of municipal water supply and drainage systems and the selection of water transmission methods.Besides,the optimization of the water supply and drainage network zoning process and pipe network maintenance is also discussed,so as to provide a reference for municipal water supply and drainage work.展开更多
For a water supply system with long-distance diversion pipelines, in addition to the water hammer problems that occur beyond pumps, the safety of the water diversion pipeline in front of pumps also deserves attention....For a water supply system with long-distance diversion pipelines, in addition to the water hammer problems that occur beyond pumps, the safety of the water diversion pipeline in front of pumps also deserves attention. In this study, a water hammer protection scheme combined with an overflow surge tank and a regulating valve was developed. A mathematical model of the overflow surge tank was developed, and an analytical formula for the height of the overflow surge tank was derived. Furthermore, a practical water supply project was used to evaluate the feasibility of the combined protection scheme and analyze the sensitivity of valve regulation rules. The results showed that the combined protection scheme effectively reduced the height of the surge tank, lessened the difficulties related to construction, and reduced the necessary financial investment for the project. The two-stage closing rule articulated as fast first and then slow could minimize the overflow volume of the surge tank when the power failure occurred, while the two-stage opening rule articulated as slow first and then fast could be more conducive to the safety of the water supply system when the pump started up.展开更多
The potability of drinking water depends not only on the source and the treatment system, but also on the quality of the waterworks. In fact, the quality of drinking water is considerably degraded by the dilapidated s...The potability of drinking water depends not only on the source and the treatment system, but also on the quality of the waterworks. In fact, the quality of drinking water is considerably degraded by the dilapidated state and lack of maintenance of drinking water networks. In Côte d’Ivoire, the majority of drinking water networks in the various towns are ageing. In Daloa, despite the efforts made by the company in charge of water treatment and distribution to make the water drinkable, the water at consumers’ taps is often colored, has an unpleasant aftertaste and settles after collection. As a result, people are concerned about the potability of tap water, and some are turning to alternative sources of drinking water of unknown quality. In order to determine the factors responsible for the deterioration in water color and taste, as well as the sectors of the network most affected, a diagnosis of the network’s equipment was carried out. Water samples taken from the network were analyzed for color and turbidity. The diagnosis revealed that most of the equipment (suction pads, valves, drains and fire hydrants) is outdated and irregularly maintained. Analyses show that the water is more colored in cast-iron and PVC pipes than in asbestos cement pipes. Coloration values in the network range from 0 to 27 UVC for asbestos cement pipes, from 15 to 56 UCV for ductile iron pipes, and from 11 to 102 UCV for PVC pipes. On the over hand, turbidity values vary from 8.02 to 3.32 NTU for ductile cast iron pipes, 8.51 to 16.98 NTU for asbestos cement pipes and 0.9 to 6.98 NTU for PVC pipes. Old cast-iron pipes release ferric ions on contact with water, degrading their color. Old cast-iron pipes release ferric ions into the water, degrading its color. The high color values observed in the vicinity of drains are thought to be due to irregular maintenance of the network. In fact, after network maintenance, a reduction rate ranging from 2% to 73% is observed for turbidity, while for color, the rate varies from 5% to 72%. In short, the network’s obsolescence and irregular maintenance contribute significantly to the deterioration of water quality.展开更多
The extensively built long-distance water transmission pipelines have become the main water sources for urban areas. To ensure the reliability and safety of the water supply, from the viewpoint of overall management, ...The extensively built long-distance water transmission pipelines have become the main water sources for urban areas. To ensure the reliability and safety of the water supply, from the viewpoint of overall management, it would be necessary to establish a system of information management for the pipeline. The monitoring, calculating and analyzing functions of the system serve to give controlling instructions and safe operating rules to the automatic equipment and technician, making sure the resistance coefficient distribution along the pipeline is reasonable; the hydraulic state transition is smooth when operating conditions change or water supply accidents occur, avoiding the damage of water hammer. This paper covered the composition structures of the information management system of long-distance water transmission pipelines and the functions of the subsystems, and finally elaborated on the approaches and steps of building a mathematics model for the analysis of dynamic hydraulic status.展开更多
Through the transformation of hydraulic constraints into the objective functions associated with a water supply network rehabilitation problem, a non-dominated sorting Genetic Algorithm-II (NSGA-II) can be used to sol...Through the transformation of hydraulic constraints into the objective functions associated with a water supply network rehabilitation problem, a non-dominated sorting Genetic Algorithm-II (NSGA-II) can be used to solve the altered multi-objective optimization model. The introduction of NSGA-II into water supply network optimal rehabilitation problem solves the conflict between one fitness value of standard genetic algorithm (SGA) and multi-objectives of rehabilitation problem. And the uncertainties brought by using weight coefficients or punish functions in conventional methods are controlled. And also by in-troduction of artificial inducement mutation (AIM) operation, the convergence speed of population is accelerated;this operation not only improves the convergence speed, but also improves the rationality and feasibility of solutions.展开更多
The serviceability of water supply networks(WSNs)under seismic loads has significant importance for estimating the probable losses and the impact of diminished functionality on affected communities.The innovation pres...The serviceability of water supply networks(WSNs)under seismic loads has significant importance for estimating the probable losses and the impact of diminished functionality on affected communities.The innovation presented in this paper is suggesting a new strategy to evaluate the seismic serviceability of WSNs,utilizing their operational physical mechanism.On one hand,this method can obtain the seismic serviceability of each node as well as entire WSNs.On the other hand,this method can dynamically reflect the propagation of randomness from ground motions to WSNs.First,a finite element model is established to capture the seismic response of buried pipe networks,and a leakage model is suggested to obtain the leakage area of WSNs.Second,the transient flow analysis of WSNs with or without leakage is derived to obtain dynamic water flow and pressure.Third,the seismic serviceability of WSNs is analyzed based on the probability density evolution method(PDEM).Finally,the seismic serviceability of a real WSN in Mianzhu city is assessed to illustrate the method.The case study shows that randomness from the ground motions can obviously affect the leakage state and the probability density of the nodal head during earthquakes.展开更多
This study used multinomial logistic regression and Bayesian belief networks(BBN)to analyze factors influenc-ing the functionality of the community-based rural drinking water supply and sanitation program(PAMSIMAS)in ...This study used multinomial logistic regression and Bayesian belief networks(BBN)to analyze factors influenc-ing the functionality of the community-based rural drinking water supply and sanitation program(PAMSIMAS)in Indonesia.28,936 PAMSIMAS projects in 33 provinces in Indonesia were analyzed.The data indicates that 85.4%of the water supply systems were fully functioning,9.1%were partially functioning,and 5.5%were not functioning.In the regression analysis,good management is positively associated with functionality and a high investment per capita is negatively associated with the functionality.The latter suggests the need for comprehen-sive economic analysis in the feasibility study in scattered housing sites and remote-undeveloped areas.We also found that high community participation at the beginning of the project was associated with the not functioning system,while women’s participation was positively associated with the functionality.Furthermore,the household connection is more likely to be functioning than communal connection.BBN analysis shows if the beneficiaries do not pay for water,the probability of not functioning systems is 20 times higher than systems with fee collec-tion.Moreover,the combination of strong management,strong financial status,and household connection rather than communal connection increases the probability of fully functioning to 98%.Improvement of data collection is also necessary to monitor the current conditions of all PAMSIMAS systems in Indonesia.This study offers a country-level perspective for better implementation of the community-based rural water supply and sanitation program in developing countries.展开更多
Water supply network losses are an international problem especially in countries suffering from water scarcity like Jordan. Jordan is one of the poorest countries in its water resources and it is estimated to be below...Water supply network losses are an international problem especially in countries suffering from water scarcity like Jordan. Jordan is one of the poorest countries in its water resources and it is estimated to be below the water poverty line. Jordan is located in the Middle East and has a surface area of approximately 90,000 km2. Its population is around 6.3 million and it is estimated that the population will be 7.8 million in 2022. The gap between water supply and demand is widening due to development and a relatively high population growth rate. In addition, global climate change is expected to intensify the water shortage problem in Jordan. Thirteen years of complete records obtained from the Ministry of Water and Irrigation were analyzed. According to these records, water losses in Jordan reach about 50%. In view of the evaluation of the data and the case study conducted in this research, it is believed that Jordan can overcome the water shortage problem by adopting a water demand management strategy. In this context, efforts should be focused on reducing water losses. If this is achieved, it will save huge quantities of water and revenue.展开更多
An urban water supply network(WSN)is a crucial lifeline system that helps to maintain the normal functioning of modern society.However,the hydraulic analysis of a significantly damaged WSN that suffers from pipe break...An urban water supply network(WSN)is a crucial lifeline system that helps to maintain the normal functioning of modern society.However,the hydraulic analysis of a significantly damaged WSN that suffers from pipe breaks or leaks remains challenging.In this paper,a probability-based framework is proposed to assess the functionality of WSNs in the aftermath of powerful earthquakes.The serviceability of the WSN is quantified by using a comprehensive index that considers nodal water flow and nodal pressure.This index includes a coefficient that reflects the relative importance of these two parameters.The demand reduction(DR)method,which reduces the water flow of nodes while preventing the negative pressure of nodes,is proposed.The difference between the negative pressure elimination(NPE)method and the DR method is discussed by using the example of a WSN in a medium-sized city in China.The functionality values of the WSN are 0.76 and 0.99 when nodal pressure and nodal demands are used respectively as the index of system serviceability at an intensity level that would pertain to an earthquake considered to occur at a maximum level.When the intensity of ground motion is as high as 0.4 g,the DR method requires fewer samples than the NPE method to obtain accurate results.The NPE method eliminates most of the pipes,which may be unrealistic.展开更多
Decision making in drinking water supply networks is increasingly complex due to the large number of variables involved.In order to make better decisions it is necessary to use adequate and robust methodologies.This p...Decision making in drinking water supply networks is increasingly complex due to the large number of variables involved.In order to make better decisions it is necessary to use adequate and robust methodologies.This paper presents the application of the Analytic Hierarchy Process(AHP)related to the operation of the drinking water supply network of the city of Chihuahua,Mexico,where two possible alternatives are delineated with the objective to optimize the service.The application of AHP was carried out in 24 sectors that have substantial differences in their efficiency but with instrumentation and measurement in all the variables contemplated by the operating agency,with a population of 221,722 inhabitants which represent a 30%of the total population of the city,the results indicate that the best alternative is the one with less criteria to be controlled and fewer repercussions on the cost of operation and investment in the rehabilitation and replacement of the network.展开更多
This paper deals with the use of optimal control techniques in large-scale water distribution networks. According to the network characteristics and actual state of the water supply system in China, the implicit model...This paper deals with the use of optimal control techniques in large-scale water distribution networks. According to the network characteristics and actual state of the water supply system in China, the implicit model, which may be solved by utilizing the hierarchical optimization method, is established. In special, based on the analyses of the water supply system containing variable-speed pumps, a software tool has been developed successfully. The application of this model to the city of Shenyang (China) is compared to experiential strategy. The results of this study show that the developed model is a very promising optimization method to control the large-scale water supply systems.展开更多
In order to overcome the low precision and weak applicability problems of the current municipal water network state simulation model, the water network structure is studied. Since the telemetry system has been applied...In order to overcome the low precision and weak applicability problems of the current municipal water network state simulation model, the water network structure is studied. Since the telemetry system has been applied increasingly in the water network, and in order to reflect the network operational condition more accurately, a new water network macroscopic model is developed by taking the auto-control adjusting valve opening state into consideration. Then for highly correlated or collinear independent variables in the model, the partial least squares (PLS) regression method provides a model solution which can distinguish between the system information and the noisy data. Finally, a hypothetical water network is introduced for validating the model. The simulation results show that the relative error is less than 5.2%, indicating that the model is efficient and feasible, and has better generalization performance.展开更多
This study investigated a water supply recovery problem involving municipal water service piping. The problem consisted in recovering full service after network failure, in order to rapidly satisfy all urgent citywide...This study investigated a water supply recovery problem involving municipal water service piping. The problem consisted in recovering full service after network failure, in order to rapidly satisfy all urgent citywide demands. The optimal recovery solution was achieved through the application of so-called network design problems (NDPs), which are a form of combinatorial optimization problem. However, a conventional NDP is not suitable for addressing urgent situations because (1) it does not utilize the non-failure arcs in the network, and (2) it is solely concerned with stable costs such as flow costs. Therefore, to adapt the technique to such urgent situations, the conventional NDP is here modified to deal with the specified water supply problem. In addition, a numerical illustration using the Sendai water network is presented.展开更多
文摘With the acceleration of urbanization,the demand for water supply and drainage pipe networks has increased significantly.In the planning of urban construction,it is necessary to optimize the design of the water supply and drainage system pipe network to effectively save energy while providing residents with more accessible water resources.Therefore,the municipal water supply and drainage system and the water transmission methods should be designed according to the geographical conditions of the city.In this paper,we mainly analyze the design of municipal water supply and drainage systems and the selection of water transmission methods.Besides,the optimization of the water supply and drainage network zoning process and pipe network maintenance is also discussed,so as to provide a reference for municipal water supply and drainage work.
基金supported by the National Natural Science Foundation of China(Grants No.52179062 and 51879087).
文摘For a water supply system with long-distance diversion pipelines, in addition to the water hammer problems that occur beyond pumps, the safety of the water diversion pipeline in front of pumps also deserves attention. In this study, a water hammer protection scheme combined with an overflow surge tank and a regulating valve was developed. A mathematical model of the overflow surge tank was developed, and an analytical formula for the height of the overflow surge tank was derived. Furthermore, a practical water supply project was used to evaluate the feasibility of the combined protection scheme and analyze the sensitivity of valve regulation rules. The results showed that the combined protection scheme effectively reduced the height of the surge tank, lessened the difficulties related to construction, and reduced the necessary financial investment for the project. The two-stage closing rule articulated as fast first and then slow could minimize the overflow volume of the surge tank when the power failure occurred, while the two-stage opening rule articulated as slow first and then fast could be more conducive to the safety of the water supply system when the pump started up.
文摘The potability of drinking water depends not only on the source and the treatment system, but also on the quality of the waterworks. In fact, the quality of drinking water is considerably degraded by the dilapidated state and lack of maintenance of drinking water networks. In Côte d’Ivoire, the majority of drinking water networks in the various towns are ageing. In Daloa, despite the efforts made by the company in charge of water treatment and distribution to make the water drinkable, the water at consumers’ taps is often colored, has an unpleasant aftertaste and settles after collection. As a result, people are concerned about the potability of tap water, and some are turning to alternative sources of drinking water of unknown quality. In order to determine the factors responsible for the deterioration in water color and taste, as well as the sectors of the network most affected, a diagnosis of the network’s equipment was carried out. Water samples taken from the network were analyzed for color and turbidity. The diagnosis revealed that most of the equipment (suction pads, valves, drains and fire hydrants) is outdated and irregularly maintained. Analyses show that the water is more colored in cast-iron and PVC pipes than in asbestos cement pipes. Coloration values in the network range from 0 to 27 UVC for asbestos cement pipes, from 15 to 56 UCV for ductile iron pipes, and from 11 to 102 UCV for PVC pipes. On the over hand, turbidity values vary from 8.02 to 3.32 NTU for ductile cast iron pipes, 8.51 to 16.98 NTU for asbestos cement pipes and 0.9 to 6.98 NTU for PVC pipes. Old cast-iron pipes release ferric ions on contact with water, degrading their color. Old cast-iron pipes release ferric ions into the water, degrading its color. The high color values observed in the vicinity of drains are thought to be due to irregular maintenance of the network. In fact, after network maintenance, a reduction rate ranging from 2% to 73% is observed for turbidity, while for color, the rate varies from 5% to 72%. In short, the network’s obsolescence and irregular maintenance contribute significantly to the deterioration of water quality.
基金Hi-Tech Research and Development Program of China (863 Program)(2002AA601140)
文摘The extensively built long-distance water transmission pipelines have become the main water sources for urban areas. To ensure the reliability and safety of the water supply, from the viewpoint of overall management, it would be necessary to establish a system of information management for the pipeline. The monitoring, calculating and analyzing functions of the system serve to give controlling instructions and safe operating rules to the automatic equipment and technician, making sure the resistance coefficient distribution along the pipeline is reasonable; the hydraulic state transition is smooth when operating conditions change or water supply accidents occur, avoiding the damage of water hammer. This paper covered the composition structures of the information management system of long-distance water transmission pipelines and the functions of the subsystems, and finally elaborated on the approaches and steps of building a mathematics model for the analysis of dynamic hydraulic status.
基金the Natural Science Key Foundation of Heilongjiang Province of China (No. ZJG0503) China-UK Sci-ence Network from Royal Society UK
文摘Through the transformation of hydraulic constraints into the objective functions associated with a water supply network rehabilitation problem, a non-dominated sorting Genetic Algorithm-II (NSGA-II) can be used to solve the altered multi-objective optimization model. The introduction of NSGA-II into water supply network optimal rehabilitation problem solves the conflict between one fitness value of standard genetic algorithm (SGA) and multi-objectives of rehabilitation problem. And the uncertainties brought by using weight coefficients or punish functions in conventional methods are controlled. And also by in-troduction of artificial inducement mutation (AIM) operation, the convergence speed of population is accelerated;this operation not only improves the convergence speed, but also improves the rationality and feasibility of solutions.
基金National Natural Science Foundation of China under Grant No.5210082055China Postdoctoral Science Foundation under Grant No.2021M690278。
文摘The serviceability of water supply networks(WSNs)under seismic loads has significant importance for estimating the probable losses and the impact of diminished functionality on affected communities.The innovation presented in this paper is suggesting a new strategy to evaluate the seismic serviceability of WSNs,utilizing their operational physical mechanism.On one hand,this method can obtain the seismic serviceability of each node as well as entire WSNs.On the other hand,this method can dynamically reflect the propagation of randomness from ground motions to WSNs.First,a finite element model is established to capture the seismic response of buried pipe networks,and a leakage model is suggested to obtain the leakage area of WSNs.Second,the transient flow analysis of WSNs with or without leakage is derived to obtain dynamic water flow and pressure.Third,the seismic serviceability of WSNs is analyzed based on the probability density evolution method(PDEM).Finally,the seismic serviceability of a real WSN in Mianzhu city is assessed to illustrate the method.The case study shows that randomness from the ground motions can obviously affect the leakage state and the probability density of the nodal head during earthquakes.
文摘This study used multinomial logistic regression and Bayesian belief networks(BBN)to analyze factors influenc-ing the functionality of the community-based rural drinking water supply and sanitation program(PAMSIMAS)in Indonesia.28,936 PAMSIMAS projects in 33 provinces in Indonesia were analyzed.The data indicates that 85.4%of the water supply systems were fully functioning,9.1%were partially functioning,and 5.5%were not functioning.In the regression analysis,good management is positively associated with functionality and a high investment per capita is negatively associated with the functionality.The latter suggests the need for comprehen-sive economic analysis in the feasibility study in scattered housing sites and remote-undeveloped areas.We also found that high community participation at the beginning of the project was associated with the not functioning system,while women’s participation was positively associated with the functionality.Furthermore,the household connection is more likely to be functioning than communal connection.BBN analysis shows if the beneficiaries do not pay for water,the probability of not functioning systems is 20 times higher than systems with fee collec-tion.Moreover,the combination of strong management,strong financial status,and household connection rather than communal connection increases the probability of fully functioning to 98%.Improvement of data collection is also necessary to monitor the current conditions of all PAMSIMAS systems in Indonesia.This study offers a country-level perspective for better implementation of the community-based rural water supply and sanitation program in developing countries.
文摘Water supply network losses are an international problem especially in countries suffering from water scarcity like Jordan. Jordan is one of the poorest countries in its water resources and it is estimated to be below the water poverty line. Jordan is located in the Middle East and has a surface area of approximately 90,000 km2. Its population is around 6.3 million and it is estimated that the population will be 7.8 million in 2022. The gap between water supply and demand is widening due to development and a relatively high population growth rate. In addition, global climate change is expected to intensify the water shortage problem in Jordan. Thirteen years of complete records obtained from the Ministry of Water and Irrigation were analyzed. According to these records, water losses in Jordan reach about 50%. In view of the evaluation of the data and the case study conducted in this research, it is believed that Jordan can overcome the water shortage problem by adopting a water demand management strategy. In this context, efforts should be focused on reducing water losses. If this is achieved, it will save huge quantities of water and revenue.
基金the Institute of Engineering Mechanics(IEM),China Earthquake Administration(CEA)under Grant No.2019EEEVL0505the National Natural Science Foundation of China under Grant No.51908519and the Scientific Research Fund of the IEM,CEA under Grant No.2019B02。
文摘An urban water supply network(WSN)is a crucial lifeline system that helps to maintain the normal functioning of modern society.However,the hydraulic analysis of a significantly damaged WSN that suffers from pipe breaks or leaks remains challenging.In this paper,a probability-based framework is proposed to assess the functionality of WSNs in the aftermath of powerful earthquakes.The serviceability of the WSN is quantified by using a comprehensive index that considers nodal water flow and nodal pressure.This index includes a coefficient that reflects the relative importance of these two parameters.The demand reduction(DR)method,which reduces the water flow of nodes while preventing the negative pressure of nodes,is proposed.The difference between the negative pressure elimination(NPE)method and the DR method is discussed by using the example of a WSN in a medium-sized city in China.The functionality values of the WSN are 0.76 and 0.99 when nodal pressure and nodal demands are used respectively as the index of system serviceability at an intensity level that would pertain to an earthquake considered to occur at a maximum level.When the intensity of ground motion is as high as 0.4 g,the DR method requires fewer samples than the NPE method to obtain accurate results.The NPE method eliminates most of the pipes,which may be unrealistic.
基金supported by National Natural Science Foundation of China(61233004,61221003,61374109,61104091,61304078,61473184)National Basic Research Program of China(973 Program)(2013CB035500)+2 种基金the International Cooperation Program of Shanghai Science and Technology Commission(12230709600)the Higher Education Research Fund for the Doctoral Program of China(20120073130006,20110073110018)the China Postdoctoral Science Foundation(2013M540364)
文摘Decision making in drinking water supply networks is increasingly complex due to the large number of variables involved.In order to make better decisions it is necessary to use adequate and robust methodologies.This paper presents the application of the Analytic Hierarchy Process(AHP)related to the operation of the drinking water supply network of the city of Chihuahua,Mexico,where two possible alternatives are delineated with the objective to optimize the service.The application of AHP was carried out in 24 sectors that have substantial differences in their efficiency but with instrumentation and measurement in all the variables contemplated by the operating agency,with a population of 221,722 inhabitants which represent a 30%of the total population of the city,the results indicate that the best alternative is the one with less criteria to be controlled and fewer repercussions on the cost of operation and investment in the rehabilitation and replacement of the network.
基金This work has been partly funded by the National Natural Science Foundation of China(No.50078048).
文摘This paper deals with the use of optimal control techniques in large-scale water distribution networks. According to the network characteristics and actual state of the water supply system in China, the implicit model, which may be solved by utilizing the hierarchical optimization method, is established. In special, based on the analyses of the water supply system containing variable-speed pumps, a software tool has been developed successfully. The application of this model to the city of Shenyang (China) is compared to experiential strategy. The results of this study show that the developed model is a very promising optimization method to control the large-scale water supply systems.
基金Supported by Tianjin Natural Science Foundation( No. 003611611).
文摘In order to overcome the low precision and weak applicability problems of the current municipal water network state simulation model, the water network structure is studied. Since the telemetry system has been applied increasingly in the water network, and in order to reflect the network operational condition more accurately, a new water network macroscopic model is developed by taking the auto-control adjusting valve opening state into consideration. Then for highly correlated or collinear independent variables in the model, the partial least squares (PLS) regression method provides a model solution which can distinguish between the system information and the noisy data. Finally, a hypothetical water network is introduced for validating the model. The simulation results show that the relative error is less than 5.2%, indicating that the model is efficient and feasible, and has better generalization performance.
文摘This study investigated a water supply recovery problem involving municipal water service piping. The problem consisted in recovering full service after network failure, in order to rapidly satisfy all urgent citywide demands. The optimal recovery solution was achieved through the application of so-called network design problems (NDPs), which are a form of combinatorial optimization problem. However, a conventional NDP is not suitable for addressing urgent situations because (1) it does not utilize the non-failure arcs in the network, and (2) it is solely concerned with stable costs such as flow costs. Therefore, to adapt the technique to such urgent situations, the conventional NDP is here modified to deal with the specified water supply problem. In addition, a numerical illustration using the Sendai water network is presented.