# A Novel Procedure for Minimizing the Volume of Water Tanks in Water Supply Systems

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Background with Literature Review

## 3. Methodology and Description of the Created Application

#### 3.1. Water Tank Sizing Procedure

_{PS}, flows out of it, as represented by Q

_{WS}:

^{365}(Q

_{PS,t}− Q

_{WS,t})], 1 ≤ t ≤ 24,

_{WS}depends on the water consumption regime as influenced by the habits of end consumers, and Q

_{PS}depends on the pumping station operation regime.

_{min}(t) ≤ V (t) ≤ V

_{MAX}(t), ∀ t,

_{min}(t) is the minimum required volume of water in the tank, and V

_{MAX}(t) is the maximum allowable volume of water in the tank. It is clear that during the 24 h when the inflow Q

_{PS,t}into the water tank is constant for each hour, the water tank volume does not change, despite the outflow, i.e., water consumption Q

_{WS,t}[2].

_{i}(1) = V

_{start}, V

_{i}(t + 1) = V

_{end},

_{start}is the volume of water in the tank at the beginning of pumping, and V

_{end}is the volume of water in the tank at the end of pumping.

_{start,t}1 ≤ t ≤ 24

_{duration,t}1 ≤ t ≤ 24

_{PS,t}= f (Q

_{max,daily}, Q

_{WS,t})

_{WS,t}= f (Q

_{max,daily})

_{max,daily})

_{start,t}, and duration of the pumping, t

_{duration,t}, impact water tank volume considering maximum daily water consumption, Q

_{max,daily}. It was found that the calculation for each specific water tank volume requires the opening of a separate spreadsheet or some kind of automatic calculation to speed it up.

_{max,daily}to the water tank on the day of the maximum consumption. In relation to how many hours a day pumping is carried out (T

_{p}), the pumping capacity (flow of pumping in one hour—Q

_{i}) will vary according to Equation (9).

_{max,daily}. Due to the requirements (5)–(9), it is obvious that the classical procedure for the minimization of the water tank volume consists of the three steps:

_{start,t}and duration t

_{duration,t}of the water pumping into the tank.

#### 3.2. Software Solution for Sizing the Water Tank

^{3}] and the percentage values of consumption for each of the time intervals (hours) during the day (24 h—24 intervals—24 values), the total sum of which must be 100%.

## 4. Case Study—Results and Discussion

_{d}= 1.70), with regard to two variants of the water consumption profiles. The maximum daily water consumption was Q

_{max,daily}= 2440 m

^{3}/day. Although the presented analysis could be performed with absolutely any combination of the maximum daily consumption and the corresponding consumption patterns, for practical reasons, an example was chosen that was previously analyzed as part of already published research. The size of the settlement, as well as the specific water consumption, could therefore be chosen arbitrarily, and regardless of the choice, the functioning of the application has been unquestionably proven by multiple tests. The mentioned required water volumes and water consumption quantities for both variants are shown in Figure 4 and Figure 5 and are defined in accordance with the rules of the profession. Two different patterns of water consumption were defined with the same total maximum daily water consumption to show the influence of the water consumption regime on the required volume of water storage. The first consumption regime (Figure 4) represents the usual water consumption during the working day in settlements with three peaks of consumption: morning, noon, and evening, of which the most pronounced is the one in the middle of the day (usual lunchtime). The second consumption regime (Figure 5) shows the usual water consumption in settlements with two consumption peaks (noon and evening) characteristic of weekends in settlements of the selected size. Notwithstanding the above, the presented procedure is the same for any regime of daily water consumption, where it is only necessary to take into account that the total sum of hourly values of water consumption within one day ultimately gives the sum of Q

_{max,daily.}

_{max,daily}= 2440 m

^{3}/day for Variant I and Variant II using Equation (1) to determine their impact on the tank volume. It should be noted that the water tank volumes calculated for the Q

_{max,daily}also satisfy all requirements for the water consumption during the year, since consumption on all other days is accordingly lower.

^{3}, as shown in both Figure 6 and Figure 7, which corresponds to the maximum daily water consumption Q

_{max,daily}, while values of 394.41 m

^{3}(Figure 6) and 601.83 m

^{3}(Figure 7) correspond related to the continuous pumping throughout the day, i.e., over a duration of 24 h, with constant hourly pumping capacity Q

_{i}(Equation (9)).

^{3}was obtained for pumping starting at 6 am and lasting 16 h), or might be obtained for several different combinations of starts and durations of pumping, as in the case of Variant I (minimum water tank volume was obtained when pumping starting started at 3 am and lasted 20 h, or if pumping started at 4 am and lasted 19 or 20 h). The following will show the use of the created application and the simplified procedure for reaching the same solution. The presented results, obtained as the output of the created application, completely coincide with the results of the “manual” calculation for the considered hypothetical examples within the previously published research [2,12]. A closer look at the presented results for the analyzed examples shows the expected trend that more pronounced fluctuations in daily consumption (as in the case of Variant II compared to Variant I) resulted in a higher required minimum volume of water storage. On the other hand, the consumption regime, although it has an impact on the duration of pumping, is not expected to have a direct impact on operating costs due to different water pumping duration. This is because a longer pumping duration means less pumping capacity is needed compared to pumping with a shorter duration (or it is possible to apply frequency regulation of pumps if the same pump is selected in both cases), which will ultimately result in mostly equal total electricity consumption since in both cases the pump must deliver the same total amount of water to the tank within one day, i.e., Q

_{max,daily}. The difference in operating costs will of course be due to the period of operation of the pumps within the day if there is the usual division into cheap and expensive tariffs, as already stated by other authors [8,9,23]. There is also a possibility of using the previously mentioned alternative energy sources (for example, solar energy in the light part of the day) [3], where the upgraded application would play a role in analyzing various alternative solutions for the start and duration of water pumping. This is an additional case demonstrating the applicability of the planned upgrades of the TankOPT application in optimizing the functioning of the planned, as well as existing, water supply systems.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**Changes in water tank volume V with respect to the different hours of pumping starts and different pumping durations for Variant I.

**Figure 7.**Changes in water tank volume V with respect to the different hours of pumping starts and different pumping durations for Variant II.

**Figure 8.**Screenshot of startup and input fields of the created application with entered values for Variant I.

**Figure 9.**Screenshot of the obtained results (created MS excel file) for Variant I—multiple (3×) solutions (sheets) with minimum water tank volume.

**Figure 10.**Screenshot of the obtained results (created MS excel file) for Variant II—single solution with minimum water tank volume.

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**MDPI and ACS Style**

Nakic, D.; Djurin, B.; Hunt, J.; Dadar, S.
A Novel Procedure for Minimizing the Volume of Water Tanks in Water Supply Systems. *Water* **2022**, *14*, 1731.
https://doi.org/10.3390/w14111731

**AMA Style**

Nakic D, Djurin B, Hunt J, Dadar S.
A Novel Procedure for Minimizing the Volume of Water Tanks in Water Supply Systems. *Water*. 2022; 14(11):1731.
https://doi.org/10.3390/w14111731

**Chicago/Turabian Style**

Nakic, Domagoj, Bojan Djurin, Julian Hunt, and Sara Dadar.
2022. "A Novel Procedure for Minimizing the Volume of Water Tanks in Water Supply Systems" *Water* 14, no. 11: 1731.
https://doi.org/10.3390/w14111731