System for controlled distribution of non-demand-covering water availability: concept, design and modelling

This paper presents a novel water supply system to distribute limited water resources with varying quantity. The system enables a controlled and planned and, thus, fair distribution of the water availability independently from the consumption patterns. The system input is transported by gravitation through a branched pipe system to decentralised storage tanks. Each storage tank is allocated to a supply unit which comprises several consumers and, possibly, distribution structures connecting the consumers and the tank. At every junction the water is divided by a distribution tank with several chambers which are separated by weir over ﬂ ows. Water which is not consumed is redistributed in the system automatically. The concept, the components, planning criteria and system design as well as the system modelling are described within the paper. The application of the solution in a supply area located in northern Vietnam is shortly outlined.


INTRODUCTION
of the supply infrastructure is constantly deteriorating and water losses are gradually increasing. The fed-in water quality cannot be maintained, the water has to be boiled and additional drinking water has to be purchased. Finally, con- This article presents a technical solution with the primary purpose of distributing limited and fluctuating water availability in a planned and controlled manner within a supply area. In this way, a fair distribution of non-demand covering water quantities can be realized (e.g., a distribution proportional to the population). The requirements to the solution are low-maintenance components and low efforts for operation and control. The central element of the solution is a so-called distribution tank, which consists of several chambers. The water flowing into a chamber of the distribution tank is divided into further chambers via weir overflows with variable widths, to which lower-lying distribution tanks are connected via pipes. Thus, the system input flows by means of gravity through a branched pipe network, in which a distribution tank is arranged at each junction, to the consumers' storage tanks at the ends of the network branches. If the available water at a storage tank is not totally withdrawn, a float valve closes the storage tank and thus the system branch. The water flows through the next higher distribution tank into the parallel branch.
If in this branch is no consumption either, the water flows through the next higher distribution tank into the parallel branch again. Regardless of the inflow, the fed in water can be divided in a predetermined ratio by adjusting the weir widths. If the demand exceeds the availability or if the availability is (temporarily) zero, the system or individual branches can run empty.
The basic principle of dividing water by weir overflows is well known. For example, in the first century BC the Roman engineer Vitruvius described a solution for dividing the water flowing into a city with several basins that are connected by pipes (Perrault ; Callebat ). Similar systems for dividing water were actually implemented in the Roman Empire, e.g. in Pompeii, in Thuburbo Minus in today's Tunisia and in Nemausus, today's Nîmes in France (de Montauzan ; Stübinger ; Kretschmer ; Ohlig ). The approach also was used later on, e.g. in the medieval city of Heidelberg in Germany (Walter ).
In nowadays drinking water or raw water supply, the principle is not known to being applied anymore. Applications This paper focuses on the explanation of the concept and the components of the solution as well as the system design and modelling. The implementation of the system in a supply area in northern Vietnam is briefly described.

CONCEPT AND COMPONENTS
The task of a distribution tank (DT) is to divide and forward water within the distribution system. A DT consists of a prechamber (PC) and several sub-chambers (SCs). Inflowing water first reaches the PC and is then divided into the SCs. Via pipes connected to the SC the resulting partial flows are forwarded to the next lower-lying DT or storage tanks (STs) of the consumers.
The division of the water is archived by weir overflows, which are arranged between the PC and the SCs. The weir overflows must allow an adjustment of the weir widths.
The ratio of the weir widths to each other defines which proportion of the inflow reaches the respective SC. The adjustment of the weir widths should be flexible so that the division can be adjusted during operation in order to consider long-term or short-term changes in water demand.
With exception of the highest-lying, central DT, which is located at the beginning of a distribution system, all DTs and all STs are equipped with float valves. Float valves allow the inflow to be throttled during demand-covering operation. If there is no demand, the flow is interrupted. Excess water is backed up and redistributed throughout the system via the higher-lying DT. Hence there exist three possible operating scenarios for a DT. consumers connected to each SC in order to achieve a fair distribution. In scenario 1 there is no coverage of the water demand. The water flows from the SC directly to the consumers and the division is based on the set weir widths.
During a non-demand-covering operation, the inflow is distributed in a controlled manner. In scenario 2, the water demand is partially covered. Since the inflow in SC 2 exceeds the demand, water is backed up and SC 2 fills up to the water level of the PC. The excess water is now redistributed proportionally to the remaining SCs according to the weir widths.
With an excess amount of 20% from SC 2, 14% flows into SC 1 and 6% into SC 3. During a partially-demand-covering operation, excess water is also proportionally divided and redistributed in the system. In scenario 3, the demand is fully met. The outflow from the SC is in line with demand.
The excess water backs up in all SCs and impounds the weir overflows, which lose their function. The flow into the DT is now throttled by the float valve. During a demand-covering operation, the DT behaves like a filled flow tank.
The system concept is based on a decentralised water storage near the consumers and a branched feeder system with DTs. The system input takes place at the highestlying, central DT. Here the water is divided for the first time and forwarded to lower-lying DTs and STs. Further system inputs into lower-lying DTs from additional resources are possible as well. Each system branch ends in the ST of a so-called supply unit (SU), which comprises several consumers. Between the ST and the consumers of a SU different distribution structures can be implemented. A typical example of this would be a village with a shared village tank. The decentralised water storage creates a hydraulic separation that only allows the consumers to withdraw the water allocated to their SU.
The system concept is shown schematically in Figure 2.
The notation of the SUs and the system elements results from their position in the distribution system and from the associated supply path. The division within the DT is determined as percentages p n . Each percentage refers to the weir overflow of a SC, whereby all percentages are considered relative to each other within a DT. Thus, the absolute share of a SU is the product of all relative percentages within the supply path.

DESIGN Pipe system
Since the distribution system is supposed to allow a demandcovering operation when there is sufficient water available, Due to the atmospheric pressure inside the DTs and STs these components must therefore be arranged along a system branch at successively decreasing elevations.
Since the feeder pipes always connect two components, the flow rate in a connecting pipe section depends on the elevation difference of the components, the length of the pipe section, the pipe diameter and the continuous and local energy losses. The locations of the DTs therefore have a direct influence on the system layout. Depending on the design flow rate and pipe lengths, it is important to choose elevations that allow the smallest possible pipe diameters in the overall system to attain an economic system dimensioning.
Depending on the water availability and demand situation, an emptying, filling or partial filling of the pipe system must be taken into account. However, a non-permanently filled pipe system has negative impacts on water quality and system operation. Particles can be intruded into empty pipe sections through leaks, or air pockets can arise during the filling process and cause a flow reduction.
The elevation profile of the pipe routing has a significant influence on the characteristics of these negative effects.
Typical pipe routings are shown in Figure 3. In routings with a continuously decreasing elevation profile or with a pronounced low point, an even emptying and filling results. Hence, the negative effects are reduced to the part of the pipe with varying water level. If a certain altitude is to be    The weirs are implemented as pressure sustaining valves with pressure settings zero and elevations equal to the geodetic elevations of the weirs h geo,weir . As soon as the water level of the PC reaches the elevation of the weir the pressure sustaining valve opens and a discharge into the SC occurs.
When the SC water level reaches the water level of the PC the hydraulic grade line is horizontal and, thus, the discharge zero. In case the demand is fully met (demandcovering operation) the respective SC is filled and the discharge equals the demand. The excess water leads to a rising water level in the PC and, thus, to an increase of the discharges into the other SCs of the DT.
The water division is realised by local minor losses assigned to the inlet pipes of the SCs (L4 and L8 in Figure 4).
By defining a short pipe length of, e.g., 0.1 m, and a small roughness of, e.g., 0.1 mm the continuous friction losses are negligible. At the input side of the inlet pipes of the SCs the pressure head H is the same as it equals the geodetic elevation of the PC water level. Hence, the energy losses and, thus, the discharges into the SCs solely result from the minor losses h minor ¼ ζ · v²/(2 g) with the loss coefficient ζ, the velocity v and the gravitational acceleration constant g. Thus, the division of the tank input can be defined by the loss coefficients ζ n of the pipes. The following proportionality law can be formulated for calculating the loss coefficients ζ n in dependence of the tank input percentages p n in % of each pipe: The discharges in the outlet pipes of the SCs are controlled by pressure sustaining valves with pressure settings zero and elevations equal to the geodetic elevation h geo,outlet .
In case of no coverage of the demand (non-demand covering operation) the inflow equals the outflow.
It has to be considered that pipes are assumed to be always totally filled and under pressure for the interpretation of the simulation results. The filling and emptying processes of the pipe system cannot be simulated using pipe network modelling tools. This leads to a time shift regarding the tank filling in the simulation results compared to the reality. However, there is no falsification of the simulation results of the water division, distribution and redistribution.

A minimal example system comprising a DT and two
STs is shown in Figure 5. The simulated water levels are shown in Figure 6. In the example the system input is

CONCLUSION
The technical solution presented in this paper allows for a controlled and planned distribution of a limited and fluctuating water availability within a supply area, in which the distribution cannot be influenced by consumption patterns.
In this way, the fair distribution of a non-demand covering water supply can be realised in water-scarce areas.
The principle of the approach is the transmission of the water storage towards the consumers and the division of the system input within a branched distribution system by socalled distribution tanks. Due to the decentralised water storage, the influence of consumer behaviour on the system hydraulics is limited to the system parts after storage. In contrast to a conventional centralized water distribution, the consumer behaviour cannot influence the division of the water availability. A distribution tank is arranged at each junction of the branched pipe network to divide the flow.
Each distribution tank consists of a pre-chamber and several sub-chambers. Sub-chambers are connected to the prechamber by weir overflows with variable weir widths. The inflow into the pre-chamber is divided proportionally to the weir widths into the sub-chambers and thus into the system branches. If the demand is covered in a system branch, the flow is backed up and redistributed within the rest of the system. If the demand exceeds the allocated portion of the available water, the system branch runs empty.
The water division by weir overflows is simple and transparent. If a system is set, no personnel are required for the standard operation and control. The proportional water distribution to the supply units is regulated automatically. The maintenance effort is low due to components of limited complexity, simple constructions and simple fittings (float valves, shut-off valves).
A crucial prerequisite limiting the application of the solution are sufficient elevation differences within the supply area, which enable gravitational water transport and pipe routing in accordance with the design criteria. The water resources do not necessarily have to be higher than all consumers. In order to use spatially distributed water resources, additional system inputs can also be connected at lowerlying distribution tanks.
Since the system design includes the temporary emptying of the system, a deterioration of the water quality must be accepted. However, the deterioration is probably smaller than in a 'classic' intermittent system because negative pressures are not occurring and, thus, the potential for the intrusion of contaminants is decreased. This deterioration is also deliberately tolerated, in favour of the plannable and controllable water distribution, the robust and lowmaintenance system structure and the self-acting operation aspects that are crucial for the sustainable implementation of the solution in lower-developed regions. It is also possible to complement the distribution system with semi-central or decentralised solutions for water treatment.
With the theoretical planning and a first implementation in the supply area Dong Van, it has been shown that the outlined solution can achieve a planned and fair distribution of a limited and fluctuating water availability with low maintenance and operating efforts. The modelling could possibly be improved by applying storm water models to consider time depended filling and emptying of the pipe system or combined methods to model the total system.