Efficient Use Of Water
By: Felipe I. Arreguin Cortés / Mexican Institute of Water Technology, CNA
Spanish version: Uso eficiente del agua
This article describes the techniques for efficient water usage in home, industrial, municipal, agricultural and basin level areas. Their advantages and disadvantages are discussed as well as its potential savings and some related examples are provided. It concludes that although there are techniques and more efficient equipment, actions taken are usually isolated, and in case they come to integrate into programs, this happens only at the level of the areas already mentioned. The final recommendation is that programs should support efficient water use at the basin, with a perfect definition of the participation of all water users.
70% of our planet is covered by water, but 98% is salt and current technology to treat and use it for human consumption or irrigation is still restricted due to their high costs. Furthermore, most of the 2% of freshwater is located in the polar caps or aquifers, so only the 0.014% in the lakes and rivers of the earth’s surface is available.
The spatial distribution of water is unequal, and is even more if he is related to the population, for example, annual water availability per capita in thousands of cubic meters, is 109 for Canada, 15 for the Soviet Union 10 for the United States, 4 for Mexico and 0.16 for Saudi Arabia and Jordan.
It is estimated that 3,400 million people have an endowment of only 50 liters per day, and the United Nations reports that 40,000 children die every day in the world, many of them victims of diarrheal diseases and other side effects to the lack of water. The current epidemic of cholera is an example of this. In the past decade there was a decrease of 7% of the irrigated area in the world; grain reserves in 1987 were 101 days and in 1989 had decreased to 54. Sandra Postel (1989), reports that 61 million hectares under irrigation in the world have salinity problems. Mexico is no exception to this, their problems are similar in most cases.
To this situation should be added another problem: pollution. Most rivers, lakes and seas are in a degree of deterioration such that urgent steps are necessary to protect them. Attention to these problems in an integrated manner requires a combination of decisions of political, economic, social and technical order.
By integral way the attention of the problems with specific responsibility among all countries is understood. Inside them is recommended to attend, at least at the basin level, taking into account their interactions with others, resource transfers, common activity in most countries.
One of the components to address the problems cited are saving programs, conservation or efficient water use. The three types of programs have conceptual differences. In Mexico it has been chosen for the latter in its widest sense, ie, optimizing the use of water and related infrastructure, with the active participation of users and a high sense of social equity.
This article presents the main techniques of efficient water use in the home, industrial, municipal, agricultural and basin areas. The examples and quotations to works carried out in Mexico, are restricted in almost all cases to those made by the Mexican Institute of Water Technology (MIWT), because in this review facts are included by other institutions. Such is the case of the Federal District Department (FDD), an institution that has worked for many years in the efficient use of water in urban areas.
The concern for better water use is not new, in fact, many of the irrigation techniques, such as land leveling or a reduction of evaporation with stubble beds , are as old as the building in England’s first low-consumption toilet beyond by 1890, by Thomas Crapper (Corpening, 1990). Some of these actions were isolated as the case of risk or were designed to reduce the problem of pollution by sewage, which was the objective of low consumption toilet.
However, as the water was scarce, they began to combine the actions to become real programs. These are stated as such in the early 70s in urban areas, where severe droughts struck the southwestern of the United States. Of course, initially were emerging programs, but due to their efficiency and water shortage have become in programs of medium and long term (Gordon, 1990;.. Van Dyke et al, 1990) _ Mexico, the DDF implemented its program efficient water usage in 1984 (FDD, 1990).
Efficient use not only is beneficial to system which uses it, but it also means improvements for users. For example, saving the liquid in residential areas means less exploitation of rivers and aquifers, improved water quality, a reduced need for new constructions (and lower tax burdens) ; in addition, by reducing consumptionthere is less waste water, less need for drainage, the treatment is easier and less risk of pollution of the receiving bodies.
Traditionally, the demands of the population, procedures for the management of credit, machinery and commercialized equipment and even the study plans of universities are focused on building more deeds to solve problems of supply, irrigation, hydropower generation or even recreation, forgetting perhaps options more simple, and permanent such improving efficiency in water use. This is the time, now that is even more evident the shortage of this element and its increasing pollution, to implement actions of intense promotion, dissemination, research and general support to efficient use. The other options, such as construction of new deeds, have their own inertia and will defend themselves and sometimes even we will have to fight them.
At this level, water use can be classified into internal and external. In those homes that have gardens can reach the use of 50% of water in each type of use.
In a house can be used up to 35% of domestic consumption in the toilets; 30% in the showers, 20% in washing machines, between 3 and 10% in water taps and lavatories and 5% in dishwasher.
- Low consumption toilets. The traditional use from 16-20 liters per flush, which means a consumption of 80-100 liters per day per capita; low consumption operates with 6 liters per flush and consumption can be reduced to 30 liters per capita per day. The MIWT has tried a lot of toilets from different countries and have been found to have a variable operation, depending on the brand and the measured batch (García and Cortés, 1989-1990).
Search for saving water in these devices has come to the use of pressurized tanks, which works by connecting the feed line into the tank that is hermetically sealed (Stevens Institute of Technology, 1991), whereby the pressure load within the same can be equal to the difference in level of the free surface of water in the water tank and the toilet tank; or to the pressure of the supply network, which improves efficiency and reduces the amount toilet water at levels below of the 6 liters per flush. Other types of toilets which go to the extreme of not using water as the biological and incinerators (García and Cortés, dic. 1989), which degrade the stool placed, in lower deposits , until it becomes compost (see illustration 1).
Efforts have been made to improve the efficiency of traditional toilets, reducing the capacity of the tank by placing containers, partitions, water-filled bags or plastic dams (García and Cortés, July, 1990), however in most cases this reduces the drag capacity of the cup. One option that seems feasible to save water in these toilets is the prolongation of the discharge siphon, reducing water consumption, according mediciones made by the MIWT (García and Cortés, Tues, 1991).
- Showers. As already noted, is the second water device with the highest demand within a residencial house; hence on the FD has ruled that the discharge in these devices should not exceed 10 liters / min. This can be achieved through new designs of sprinklers or using flow restrictors. Illustration 2 shows the behavior of a traditional shower, a low-consumption and a conventional with integrated reduction gear (García and Cortés, Tues, 1989).
- Taps and dishwashers. Reducing the flow of these devices is achieved by means of aerators, which includes air and disperse the stream, increasing the coverage area and, therefore, the washing efficiency. An aerator can reduce the flow up to 6%.
Another option that has been explored and provides excellent results, is the placement of valves or sensors that makes water to flow out only when you place your hands under them. In a recent study done at the MIWT was found that a Lavatory Faucet with sensor had discharges of 1.5 liters / min with a pressure of 0.2 kg / cm2; and 5.9 liters / s with a pressure of 2.5 kg / cm2 (García and Cortés, May, 1989).
- Washers. These savings are achieved by placing adequate loads of clothing , using the necessary water levels for proper operation or with washers that use less water. There are basically two types of washing machines, front loading and tub, the first may even use half the water, 50% of hot water and detergent 33% demanded by the second. Building efficient washers has achieved savings up to 24% of water consumption compared to the traditional ones.
Another factor that must be considered when evaluating washing is energy consumption. García and Cortés (May, 1990) presented the results of the evaluation of some front-loading washers.
- Dishwashers. Consumption from this machine can vary between 49 and 95 liters per day, however, efficient models have been built using between 36 and 45 liters in the same period. A recommendation to improve the efficiency of these washers is loading up its design capacity.
- Intradomiciliary leak detection. In the houses a lot of water is lost due to leakage of pipes and hydraulic and sanitary fittings.
One of the furniture that presents more leaks is the toilet, primarily in fittings of the tanks. One way to detect such leakage is the use of dyes that allow precisely locate where water is leaking; once detected it, we recommend making the necessary repairs. However, the real solution is manufacturing of reliable hardware that do not cause failures; in this sense pressurized tanks which do not employ this fittings, rocker toilets or replacing fittings by siphons are options that are in development.
Often in the taps of toilet, sink and showers, also leak. The wear of the packing or leaks from the top nut, could be easily repaired. This promotes a significant water saving.
Home exterior uses
- Watering gardens. Adequate gardens irrigation practices are the best technique to save water. The most appropriate time to water is between 4 and 8 am, because during that time the network pressure is higher, the dispersion caused by the wind is low and evaporation losses are desapreciables. However, this schedule may be uncomfortable and is recommended as an option watering from 8-12 night, or early morning hours.
The amount of water applied varies with the weather. It is recommended that the depth wetted during the irrigation period should be 15 cm. In areas with steep slopes should not be applied a greater amount of water than the amount that can be absorbed by the soil.
One way to reduce soil evaporation is to cover it with ground leaf or plastic along the surface. It is equally important to eliminate weeds that compete with plants for water, nutrients and sunlight; Arreguin and Buenfil (1990) makes a number of recommendations for saving water in these cases.
- Plants native to the region. The plant that more efficiently consume water in a region are the natives. The combination of these with rocks and gravel can give an attractive appearance and consume very little water. A recent trend is the use of xerophytes (chaste, nopales, etc.). as ornamental plants; the promotion of use of these, must done taking into consideration the possible impact on the ecosystem that could cause its massive transplantation (Cuthbert, 1989, Nero and Sorensen, 1990; Jacoby, 1990).
- Car wash. One of the biggest way of waste water is washing cars through the hose; It is recommended to do with a bucket and a dishcloth and support the development of public services that reuse water (Arreguin and Buenfil, 1990).
- Pools. Almost never have to change the water for more green or turbid than can be, you can always qualify with portable equipment and appropriate chemicals. The factors causing waste in the pools are filtration and evaporation. To reduce losses from these causes is recommended to check the state of the walls and the bottom of pools and the use of covers to avoid evaporation (Arreguin and Buenfil, 1990).
- Pressure reduction. Most of the devices discussed above, whether external or internal, increase their discharge in direct relation to the pressure. In those places where it is high, we recommend using pressure-reducing valves due to with this it is possible to achieve reductions in water consumption up to 10%. Table 1 shows some techniques for efficient use and examples
Industries can also make a better use of water: machinery, processes and ancillary services require large amounts of this resource that can be reduced with efficient techniques (Brown and Caldwell, 1990; Campos et al., 1990). The quality of water required varies by type of industry (eg, oil mining require less quality than pharmaceuticals) and their use in the process, so in the same industrial plant may be required different water quality in several processes.
Industrial uses of water can be divided into three groups: heat transfer, power generation and application to processes.
- Heat transfer. It is used in heating or cooling processes. For the first, usually steam generation boilers by using the combustion of coal, oil, gas or waste products are used.
For cooling, water circulation is used, by means of cooling towers or ponds.
- Power generation. Most of the energy generated in many countries comes from power plants using steam generators adapted to move turbines. Vapor recovery capacitors are used, making to establish replacement volumes at 1% of total water supplied to the plant (American Society for Testing and Materials, 1982).
- Application to processes. There are many processes in which water is needed, one of which is the transport of materials, case in which pipes or channels are used. The industries of pulp and paper, food canneries, coal and sugar mills are the most likely to use this method.
Techniques and efficient use of water
|Reduction of consumption||
|Leak detection and repair||
|Decomposition and multilevel optimization||
The main actions of efficient use in the industrial level are recirculation, reuse and reduction in consumption; in all three cases two basic activities are necessary: measuring and monitoring water quality.
Measurement is the fundamental action of any efficiency program in the industrial sector, in determining consumption in hours, days, months, season and means, as concerned; in the processes, equipment, accessories, irrigation areas, bathrooms, etc., is used to program how to better use water and to motivate workers to participate in the saving of the liquid.
As noted above, not all industrial processes and the annexed areas, require the same water quality, and to establish actions for recirculation, reuse or reduction, it is essential to know the water quality in every part of the industrial process.
- Recirculation. This action consists of use water in the process where initially used. In general, the first time the water has been used, it changes its physical and chemical characteristics and, therefore, may require some treatment. It is then necessary to know water quality demanded by the process in question, the level of quality degradation therein and, therefore, the type of treatment required (see Illustration 3).
One of industrial applications where recirculation is employed is cooling of heat generating equipment, such as pumps or gas condensing systems, such as cooling or condensing steam. In these cases, for recirculating water cooling towers are used, thereby reducing the amount of heat through evaporation of some of the water. Recirculation also used in the washing process aimed at removing residues or contaminants of products or manufacturing equipment; in this case it is necessary to establish the appropriate treatment system for removal.
In the transport processes of materials, for example mineral or food, water can be recirculated, even without treatment. Currently, in the manufacture of paper, the recycling of water and fibers is a common activity.
- Reuse. In this situation, the effluent from a process (with or without treatment) is used in another that requires a different water quality (see figure 4). You need to determine water quality required for each process, identify which effluent could be used and, when it corresponds, define which would be the minimum treatment required and the mechanisms for transporting the liquid. Waste water from the washing process can be reused in other process requiring a lower quality, as in cooling the material transport or air purification.
In a study by the MIWT in a sugar mill (Romero González, 1990), it was found that the water could be reused for washing floors, cooling systems, sanitary services and agricultural irrigation (28% of total demand ), by:
– The effluent treatment of systems for vacuum generation and distiller process;
– Upflow anaerobic reactors, of primary and secondary sedimentation and biodiscs;
– Treatment of effluents of sanitary and other processes through
oxidation ponds and
– the cooling of the effluents from the vapor condensation process.
The same institute found in a factory of dyed wool thread and manufactures cashmeres, you could reuse up to 50% of water demanded by industry (García, 1991).
- Reduced consumption. Another option is to reduce consumption. For this is possible to optimize processes, improve operation or modifying equipment and attitude of water users. Herein is necessary to calculate the amount of fluid required for a given process compared with actual consumption and evaluate options to reduce their consumption.
In industries there are ancillary areas (gardens or sanitary services) in which they can achieve significant reductions in consumption, for example, planting native plants of the geographical area where the industry is located, using efficient irrigation equipment, night irrigation, etc. As regards to sanitary services, both eliminating leaks as the use of flow restrictors in toilets and low consumption showers contribute to reduce industrial water consumption.
In the process of transporting materials can also use this technique, for example, by intermittent discharges, which guarantee the same transport capacity than continuous.
In the program of efficient water use in any industry involving all staff is important (Brown Caldwell, 1990).
The main problems of supply to the urban centers are the depletion of local sources, pollution thereof, the high cost of capture and conveyance of water and the conflicts generated by the interests of different users about the sources. Paradoxically, in this difficult situation, in cities large percentages of leaks occur, water-wasteful technologies are used, the resource is not reused, the billing and collection systems are deficient, fees for service often do not cover the costs of providing and there is little citizen awareness.
In a city, on average is consumed 71% of total production of water in houses, 12% in industry, 15% in trade and 2% in the services sector. The techniques for efficient use in cities can be classified into five groups: communication and education, leak detection and repair, metering, rate systems and regulations.
Communication and education
For any program for water efficiency to be successful, must have citizen participation, and it is therefore essential to establish communication actions and education. Other activities of these programs, as mentioned above, will be easier to make if one includes the population (Grisham Flemming, 1989).
The means to inform users of the objectives, goals and results of the program are varied, ranging from advertisements in receipts, advertising in print, radio and television advertisements on public roads transport system and the distribution of saving devices. It is estimated that these programs can produce savings of between 4 and 5% of the total water production (Grisham Flemming, 1989).
In relation to formal education, it is necessary to strengthen the programs of primary and secondary education, in basic aspects as the hydrologic cycle, where it comes from, how much and where the water used in cities goes but especially through actions that a child or young person can carry out immediately as the proper use of water in gardens, toilets, showers and lavatories.
Leak detection and repair
The losses in the drinking water and sewage are due to evaporation and filtration from storage vessels and regulation, to leakages in networks and household connections; to imprecision of metering or the lack of it and consequently, poor estimation, the illegal connections and unaccounted water used in municipal services such as landscape irrigation or buttresses to control fires.
Leaking networks can be seen and unseen the first emerge from the ground or pavement, the second are not detected at first glance, since water can go to the drainage system or the aquifer. Factors that influence the network losses are age and pipe material, the acting loads (traffic, earthquakes, etc.), quality and water pressure, soil type, compliance with building regulations and maintaining (Hammer, 1987). Leaks can be located in the network or in the household tap.
In a recent study done by MIWT, it was found that in the city of Guaymas, Son., 30% of total water supplied to the city is lost, and of this total, 89% occur in the home outlets the remaining 11% in the network (Ochoa et al., 1990).
There are a number of techniques and equipment for leaks (Echavez, 1991, AWWA, 1986; AWWA, 1987; Camacho et al., 1990). As for those used to locate leaks in the network can be identified as tracers, water audits and districts of Pitometry. The latter was used in the study mentioned above with good results (see Figure 5.) The location not visible in the household tap leakage is performed by measuring pressures therein; a pressure drop index in adjacent shots is a leak. In the study of Guaymas it was found that two factors have a decisive influence on leakage is the quality of the material and the lack of follow installation standards (see Figures 6 and 7).
The first step in any program and efficient use of water is the metering, since it allows to induce the reduction of consumption and make more fair the collection. This can be expensive from initial installation to maintenance, so you should plan carefully the administration of metering.
It is recommended to annually inspect all meters with more than two inches in diameter and conduct random sampling in smaller diameter. In this regard, already exist programs to determine the appropriate maintenance period to these devices (Planells et al., 1987). Age, water quality and improper installation are some of the factors that influence an incorrect functioning. In an analysis of a sample of 350 meters in Guaymas, Son, it was found that 43% worked in the lower range, 55.8% were within the normal and 1.2% at the top also found that 23.4% measured in excess, 71.4% worked under and only 5.2% had a good measurement (Ochoa et al., 1990).
|Section||gauging jacks||Crack||Perf.||Cut or break||Loose thread|
The rates are a key element in the programs of efficient use of water. According Grisham and Flemming (1989), rates can help save water if the following conditions are observed in its structure: reflect the actual cost, be related to consumption, differential increases large enough in order to lead to save water and fee changes are accompanied by communication and education programs.
In Mexico, water is charged with a metered or non-metered service to domestic, commercial and industrial customers. The collection of the second is done in several ways: one-fee, fixed fee for different sectors of the population, domestic outlet diameter, commerce size, the type of industry or by simple estimation, among others. The tariff structure in cities where water is metered, is based on four parameters: number, limits, price and minimum quotas of blocks considered in the rate. In the last two years there have been very important works for rates organization throughout Mexico.
In general, the regulations for water use more efficient are restrictive in nature and are effective in saving the liquid; may be of medium or long term or applicable only during times of scarcity; these last usually require very strict surveillance and, therefore, it is recommended that apply only if it is really necessary.
In Mexico there is The Regulation of Water and Sewer Service for the Federal District (Official Gazette, 1990), which in its second title, third chapter deals with the responsible, rational and efficient use of water. Some key points made in the relevant articles refer to that users should keep in good conditions their interiors hydraulic installations, in order to avoid waste; toilets have a maximum discharge of six liters in each service, the sprinklers an expenditure of 10 liters/ min and urinals four liters per flush.
It is mentioned as well; the obligation to participate in the program for toilet replacement. Also notes that pools of any size, should have filtration equipment, water purification and recycling; and the use of hose for washing motor vehicles and public roads, among others is prohibited.
In some states of the Mexican Republic also exists regulations regarding the efficient use of water, and today is promoted to be established throughout the country.
Grisham and Flemming (1989) have combined the techniques for efficient use of water in the municipal level, pointing out the advantages and disadvantages as well as the percentage reduction in consumption in the US (see Table 2). To have a global conception of efficient techniques recommended, see Table 1.
- Techniques for efficient use of water in the municipal average (according to Grisham and Flemming)
Agriculture is the main consumer of water system in most countries. In it for irrigation large volumes both in small and large systems are used; however, usually use efficiencies are very low and can be improved with control systems, transmission, distribution and application of irrigation to suitable crops (Carvajal and Davidof, 1990; Phene, 1990; Kromm and White, 1990).
There are many techniques for efficient irrigation. Kromm and White (1990) have classified into three groups: field methods oriented toward retention and distribution of water; management strategies, aimed at programming the efficient use and modifications or adaptation of new irrigation systems.
They excel subsoiling compact soils, construction of dams in furrows, leveling soil and reducing evaporation with stubble bed.
Include monitoring of soil humidity, precipitation water measurement and consumed, and irrigation scheduling according to the humidity needs.
Modifications and adoption of new systems
Highlights include the replacement of sprinklers with underground piping, installing recovery systems for water queues, drip irrigation and intermittent.
39 saving methods for water irrigation are presented in Table 3 used in the High Plains of USA, reported by Kromm and White (1990).
As in the previous cases, there are several factors that influence the selection of any of the above techniques, among which may be mentioned the geographical location of the agricultural area, the amount of water available and the knowledge of farmers. In this sense the training programs to producers become important and mechanisms to put at your disposal information about techniques for efficient use.
- Techniques for efficient use of water in the municipal medium (according to Grisham and Flemming)
In the MIWT has been evaluated, among others, two options for intermittent irrigation: a valve and a fluidic device, developed at the same institute (Martínez and Barrios, 1990). The latter, called diabeto (fro greek diabetes, which means siphon), has no moving parts, requires no additional power, or pressurized systems. Consists of a deposit and one or more siphons (see Illustration 8). Its operation is as follows: at first begins to fill the tank without any discharge, this will happen only when the siphon is primed; then the spending output will be greater than the input, lowering the level until the siphon is unprimed to start a new phase of filling. Thus, the two phases of intermittent irrigation, “application” and “suspension of irrigation” are defined. It is recommended see table 1, where water saving techniques are summarized.
The watershed is the natural unit for planning efficient water use and assess their performance, because in there cities, industries, irrigation districts hydroelectric plants and fish farms are located. It is at this level that most clearly reflect the needs and benefits, because although some actions represents small individual savings of water to any of these users, may represent much to others reduce significant risks of pollution or over exploitation of resources.
Efficient use at this level is very complex due to the multiplicity of objectives and the large number of possible solutions. This has forced to creating a series of logical procedures that allow to rationally eliminate a large number of options to solve a problem until reduced to a few, or perhaps tp one in very particular cases.
To optimize water exploitation must not lose sight of the overall context of the planning process of water resources (see Illustration 9). In this process, the starting point are the values and social goals (national), from which can be derived the objectives of the use of water that will be limited by restrictions, resources, environment and existing technology. The next step is to quantify objectives and constraints, ie make them measurable, with maximum numerical accuracy. Then you must develop a model to evaluate alternatives, to finally establish the consequences, direct and indirect that the adoption of the solution may cause.
It is not always possible to set quantitative targets (at least in its totality), as on an objective there are a series of factors that are not measurable, meaning that, are not quantifiable. However, authors like Ralph L. Keeney, Erick F. Wood and others have developed methods that attempt to consider subjective aspects such as social, recreation, the political, and so on.
An objective function is any statement by which can be determined consequences or the system product for an operation policy, given the initial values of the state variables and parameters of the hydraulic system.
The restrictions are defined as the set of functions quantitatively expressing the limitations acting on the hydraulic system.
When you have to do quantitative objectives and restrictions, you can proceed to develop the mathematical model. This is a set of equations (algebraic, differential, etc.), which represents a real system. This system of equations establishes relationships between system components and of the environment and its restrictions.
Thus, to analyze a physical system a mathematical model is developed to represent it, and its results are applied to that system. Efforts should be made that for the entries represent the mathematical model as closely as possible to the inputs to the physical system, and the degree of coincidence of the outputs of the model and the real system will indicate the goodness of the designed model.
According to the nature of the objective function and restrictions can be made linear or nonlinear, deterministic or probabilistic, static or dynamic models. Once the mathematical model of a system is done it is usual to look for the optimal solution, which is the set of values of variables that maximizes (or minimizes) the objective function subject to the restrictions, which physically corresponds to project dataset and / or operating policies which make a more efficient use of resources.
An optimization technique is that which allows to obtain the best solution from a set of feasible solutions, from an objective function subject to restrictions. There are many optimization techniques such as linear programming, in which the objective function can be expressed as a linear algebraic function and the restrictions can be linear equations or inequations, in this case there are graphical, analytical and numerical solutions. One problem that is solved with this technique is the transport, which is to take water from m origins to n destinations.
The nonlinear programming problems are those in which the restrictions, the objective function or both are nonlinear. The main difficulty in solving these problems is that unlike linear programming, where was enough to get a basic solution in one of the vertices of the feasible region to review other solutions and reach the optimum, in the case of nonlinear programming rarely optimal solution is located in a vertex. This implies that often can be reached an approximate optimal solution because obtaining the optimal in many cases may involve an infinite number of calculations.
When the restrictions are nonlinear functions and the objective function is linear, two cases may arise: the feasible region is convex or not convex. The first one is easier to solve, once identified a possible optimal solution you can proceed to check with other values the function to maximize (or minimize); in the second, this is more difficult because you can present local maximum or minimum in the entire region.
When the objective function is nonlinear, the problem is difficult because the distinction between local and absolute values is complicated. Dynamic programming can be defined as a mathematical technique for solving a series of decisions in sequence. This sequencial solution implies that the problem is decomposed into a series of stages, where in each one is necessary to take a small number of decisions, or preferably only one. The dynamic programming allows you to solve linear or nonlinear problems and is based on Bellman optimity principle: “A series of optimal decisions (optimal policies) have the property that whatever the initial state and initial decision, the remaining decisions must be optimal with respect to the state resulting from the first decision”.
From this principle may be obtained the recursive equation of dynamic programming.
One type of dynamic programming, is one that includes trajectories. Within these models of trajectories are found the networks.
A network is a model that relates an origin to a destination as well as with intermediate points called network nodes. Trajectories that unite are called arches, and generally, the problem is reduced to optimize the transport of a product through the network.
A real problem of hydraulic exploitation usually has several goals, a large number of variables and complexity functions (for example, nonlinearity). To solve this, a number of simplifications can be done as despise variables, functions linearization, etc., but all these actions, while it simplify the problem, lead the mathematical model farther of a true or at least similar representation of the phenomenon studied.
Recently established theoretical bases which allow to decompose a complex problem in a number of subproblems that can be optimized independently, even with different techniques and objectives defined for each subsystem. Once optimized this, you can do the same with the system in general. This technique is called hierarchies and multilevel of approach.
Decomposition of the system into subsystems is known as the first level, and the step of optimizing the whole system is called the second level of the problem; to reach this is necessary to have interrelationship between subsystems, which is achieved by including new variables called pseudovariables. Some advantages of decomposition and the establishment of levels are:
- Conceptual simplification of complex system.
- Dimensionality reduction.
- Simpler Programming procedures and computation.
- Models of systems more realistic.
- Interaction between subsystems.
- Applicability to static and dynamic models.
- Utilization of different optimization techniques in solving subsystems.
- Use of existing models.
The applications of this technique to the problems of hydraulic uses are many, for example when planning horizons in short, medium and long term, with defined objectives on each of them, or in the case of large basins that can be divided into sub-basins and to associate optimization problems to each one or when there are hydraulic systems in different political areas, or in cases where there are different uses in the hydraulic exploitation.
The general problem can be stated like this, given an R region:
u = system input vector
m = vector of decision variables
α = model parameter vector
The R region can be decomposed into i subregions, then for the Ri subregion, the problem can be stated as follows:
σ = coordination vector, pseudovariable
zz = subvectors of u, m y α
Xi= is a vector of inputs to the subregion
Ri of others subregions
The latter implies that the subregions have a relationship of input-output to subsystems also:
yj = output vector of the subregion j
cij = parameter matrix
Thus the whole problem is:
In many cases the efficient use of water is not an option, it’s the only one.
There are techniques and equipment to allow better use of water and infrastructure, and yet are not applied.
The user participation in the programs of efficient use of water is low, there is no awareness of the real problem that involves the lack of water and the potential that exists in them to use it better.
The actions of efficient use are grouped in programs by area, ie there are efficiency programs for industries, municipalities, or basins, but there is no the adequate relationship between them to truly optimize the use of the resource.
It is necessary to support the programs of efficient water use in the basin level with a perfect definition of the participation of all users in their respective field. Only in this way can be oriented all the subprogrammes of efficient use in the same direction.
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American Water Works Association. Water Audit and Leak Detection Guidebook, Department of Water Resources Office of Water Conservation, EUA, agosto de 1986.
American Water Works Association. Leaks in Water Distribution Systems, AWWA, EUA, 1987.
Arreguín, C. F y Buenfil R. M. 68 Recomendaciones para ahorrar agua en domicilios, riego a industrias, Instituto Mexicano de Tecnología del Agua, Cuernavaca, Morelos, México, octubre de 1990.
Baklund, V y Land Ross A. E. On Farm Management, Proceedings of the Conserv 90, agosto 12-16, Phoenix, Arizona, EUA, 1990.
Brown and Caldwell Consultants. Case Studies of Industrial Water Conservation in the San José Area, City of San Jose, Brown and Caldwell Consultants and Department of Water Resources, EUA, febrero de 1990.
Camacho, C. A., Enríquez Z. S. y Maldonado S.J. recomendaciones para equipos detectores, Instituto Mexicano de Tecnología del Agua, Cuernavaca, Mor, México, diciembre de 1990.
Campos, M., Maddaus W. y Manzione M. California Industries Discover that Water Conservation Pays, Proccedings of the Conserv 90, agosto 12-16, Phoenix, Arizona, EUA, 1990.
Carvajal, A. y Davidoff B. California Agriculture Irrigation Efficiency and Distribution Uniformity, Proceedings of the Conserv 90, agosto 12-16, Phoenix, Arizona, EUA, 1990.
Corpening, W. L. Why Toilets – A History of the Consumption toilet and its Introduction into the U. S. Market, Proceedings of the Conserv 90, agosto, 12-16, Phoenix, Arizona, EUA, 1990.
Cuthbert, R. W.`Effectiveness of Conservation – Oriented Water Rates in Tucson’, Journal of the American Water Works Association, EUA, marzo de 1989.
Departamento del Distrito Federal. “Programa de Uso Eficiente del Aguá”, Memoria, D. F., agosto de 1990.
Diario Oficial de la Federación. Reglamento del Servicio de Agua y Drenaje para el Distrito Federal, México, enero de 1990.
Echávez, A. G. Fugas en redes de agua potable, División de Estudios de Posgrado, Facultad de Ingeniería, UNAM, México, mayo de 1991.
García, B. A. y Cortés M. P Evaluación del funcionamiento hidráulico de regaderas marca Nova de fabricación extranjera. Instituto Mexicano de Tecnología del Agua, Cuernavaca, Morelos, México, marzo de 1989.
García, B. A. y Cortés M. P Evaluación del funcionamiento hidráulico de una lláve para lavabo automática marca Watermatic. Instituto Mexicano de Tecnología del Agua, Cuernavaca, Morelos, México, mayo de 1989.
García, B. A. y Cortés M. P Evaluación del funcionamiento hidráulico de excusados de bajo consumo de fabricación extranjera. Instituto Mexicano de Tecnología del Agua, Cuernavaca, Morelos, México, mayo de 1989.
García, B. A. y Cortés M. P Evaluación del funcionamiento hidráulico de excusados Lamosa Sahara de fabricación nacional, Instituto Mexicano de Tecnología del Agua, Cuernavaca, Morelos, México, julio de 1989.
García, B. A. y Cortés M. P, Informe final del Proyecto UE-9003. Instituto Mexicano de Tecnología del Agua, Cuernavaca, Morelos, México, diciembre de 1989.
García, B. A. y Cortés M. P Evaluación del funcionamiento hidráulico de tres excusados Saver 1.6 Gpf. de fabricación chilena. Instituto Mexicano de Tecnología del Agua, Cuernavaca, Morelos, México, enero de 1990.
García, B. A. y Cortés M. P Evaluación del funcionamiento de dos lavadoras de ropa. Instituto Mexicano de Tecnología del Agua, Cuernavaca, Morelos, México, mayo de 1990.
García, B. A. y Cortés M. P Evaluación del funcionamiento de retenedores para excusados de alto consumo de fabricación nacional. Instituto Mexicano de Tecnología del Agua, Cuernavaca, Morelos, México, julio de 1990.
García, B. A. y Cortés M. P Evaluación del funcionamiento hidráulico del supersifón marca Supersifón en excusados de alto consumo de fabricación nacional. Instituto Mexicano de Tecnología del Agua, Cuernavaca, Morelos, México, marzo de 1991.
García, O. J. Aprovechamiento de las aguas residuales en la Empresa Rivetex, Instituto Mexicano de Tecnología del Agua, Cuernavaca, Morelos, México, junio de 1991.
Gordon, L. D. Water Conservation for Oahu, Proceedings of the Conserv 90, agosto, 12-16, Phoenix, Arizona, EUA, 1990.
Grisham, A. y Flemming W. “Long Term Options for Municipal Water Conservation”, Journal of the American Water Works Association, EUA, marzo de 1989.
Hammer, M. Análisis de fugas de agua, Kontakt Und Stuadium Band 229, Expert Velag, 7031 Ehningen, 1987.
Jacoby, B. Xeriscape Ordinances for New Development, Proceedings of the Conserv 90, agosto 12-16, Phoenix, Arizona, EUA, 1990.
Kromm, D. E. y White S. E. Conservation Water in the High Plains, Kansas State University, EUA, 1990.
Martínez, A. P y Barrios D. J. N. “Validación en laboratorio y en campo de un dispositivo fluídico para riego intermitente”, 11o. Congreso Nacional de Hidráulica, Zacatecas, Zac, Tomo III, 443 pp., México, 1990
Nero, W. y Sorensen L. Residential Xeriscape: A Working Demostration, Proceedings of the Conserv 90, agosto, 12-16, Phoenix, Arizona, EUA, 1990.
Ochoa, L., Camacho C. A., Enríquez Z. S. y Maldonado S. J. Resumen del Informe final del Proyecto Detección y Control de Fugas a Impacto de Micromedición en Guaymas, Son, Instituto Mexicano de Tecnología del Agua, Cuernavaca, Mor., México, diciembre de 1990.
Phene, C. J. Drip Irrigation Saves Water, Proceedings of the Conserv 90, agosto 12-16, Phoenix, Arizona, EUA, 1990.
Planells, V F., González A. A., López V V., Sanz T F. y García-Serra G. J. Diagnóstico de la gestión óptima de contadores en un sistema de distribución de agua, Tecnología del Agua, España, 1987.
Postel, Sandra. Water for Agriculture: Facing the Limits, Worldwatch, Paper 93, diciembre de 1989.
Romero, G. A. y González M. J. Estudio para la reutilización de las aguas residuales en la industria azucarera, Instituto Mexicano de Tecnología del Agua, Cuernavaca, Mor., México, diciembre de 1990.
Stevens Institute of Technology. Study of Reduce Water Closet Volume, Research Report 91-01, ASPE Research Foundation, Hoboken, Nueva Jersey, 1991.
Van Dyke, P y Pettit P. Pennsylvania Comprehensive Drinking Water Facilities Plan: Innovative Policy For Over. 2400 Community Water Systems, Proceedings of the Conserv 90, agosto, 12-16, Phoenix, Arizona, EUA, 1990.