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The Dependence of Water Consumption on the Pressure Conditions and Sensitivity Analysis of the Input Parameters^{ †}

^{*}

^{†}

## Abstract

**:**

_{3}coefficient. Parameters for sensitivity analysis are number of workers in the building, pulse value from water meter and length of time step for expressing unevenness of water consumption during the day.

## 1. Introduction

_{3}set coefficients within the meaning of [13] based on real studies. Value of this coefficient explains degree of dependency of water consumption on pressure. However, for example the value of the “inside the house” consumption coefficient was set at 0.2 for the Johannesburg students ‘campus in [15]. According to [16], the dependence of consumption on pressure for pressure flushers in Great Britain was also demonstrated and the value of the coefficient was set at 0.07 and 0.025. The course of water consumption over time under various pressure conditions was given attention in the study [17], where the dependence of the water consumption during the day on the pressure conditions was determined.

## 2. Methodology

_{3}coefficient and the demand coefficients.

_{3}coefficient, first it was necessary to take into account that working hours are not the same every working day. This means that the consumption per working day was related to the selected time unit, in this case it was 1 h. In [8] the influence of the number of workers in the building during working hours was also included. For further comparison, the format was considered litre-1.person-1.hour-1. According to the relation:

_{i}is the standard water consumption for the ith day (for working hours of the day), V

_{i}is the volume of water consumed during the ith working day, p

_{i}is the number of people on the shift of the ith day, and h

_{i}is the number of working hours on the ith day. For the purposes of performing the sensitivity analysis in this article, the value of the N

_{3}coefficient was calculated without including the number of shift workers, with the relationship (1) being then adjusted as follows:

_{3}coefficient, the individual working days are classified into pressure categories according to the average daily pressure (during the working hours of the given day). The categorization has been done with respect to the balance of the number of values in each class, but also with respect to the size of the intervals of the individual categories. The criterion was also the absolute number of values in each category. The category division is shown in Figure 1. The value of the N

_{3}coefficient was determined in the meaning of [13]. This coefficient was set on the basis of the average values of water consumption and pressure for each category according to the following relations:

_{1k}is the actual water consumption for the kth category, C

_{1k}is the calculated water consumption for the kth category, w

_{k}is the weight of the kth category determined by [8] and m is the number of pressure categories. It follows from this equation that the weighted square deviation of the calculated water consumption values from the actual measured water consumption for the given pressure category has been minimized. The consumption was calculated according to the following formula with accordance to [13]:

_{0}is the water consumption for the highest pressure category, P

_{1k}is the mean pressure in the kth pressure category, P

_{0}is the mean pressure in the highest pressure category, and N

_{3}is the coefficient expressing the effect of the change in pressure conditions on the water consumption.

_{ij}represents flow, Q

_{MEANi}is mean flow, c

_{ij}is coefficient of water demand variation.

_{MEANik}is mean coefficient, k is pressure category, m

_{k}is the total number of days in category k.

_{MAXk}[-] is the maximal coefficient in k category.

_{k}[-] represents square deviation of coefficients from optimal value in each time step (as optimal value is considered 1. It corresponds to constant consumption during day).

## 3. Case Study

_{3}coefficient. The simulation of the pulse size was performed in the way that at each time the water meter was recorded, this state was rounded to the nearest lower multiple of the selected pulse size.

^{−1}. The pulse value was chosen as a percentage of this value, but also respected the technical practice and commonly used pulse values. The relative pulse value considering AHC was chosen as 2.5, 5, 10, 20, 50 and 100%, which in absolute values corresponded to the pulse size of 2, 5, 10, 20, 50 and 100 L.

## 4. Results

_{3}coefficient for changing input parameters was determined on the basis of Equations (1)–(4). Achieved results of the sensitivity analysis of N

_{3}value are well evident from Table 2 and Figure 2.

_{3}coefficient values. Inaccuracies when determining the value of the N

_{3}coefficient without monitoring the number of people in the building and with the monitoring amount at 53%, even when considering the smallest pulse of 1 L (real measurement). In case the number of workers was observed, it was found out that up to 10% of AHC the high accuracy of the N

_{3}value is achieved.

## 5. Discussion

## 6. Conclusions

_{3}coefficient for an office building, the most important input parameter was the number of workers in the building during individual working days. The most accurately determined value was 0.150 (with a pulse value of 1 L and with monitoring the number of workers), while retaining a pulse value of 1 L and not including the number of workers, the value of the N

_{3}coefficient was only 0.071, that makes the inaccuracy of 53%. This high inaccuracy in determining the N

_{3}coefficient was not found out even in the case of a pulse size of 100 L (approximately 110% of the average hourly consumption) when the inaccuracy of the N

_{3}value was 27%. The inaccuracy of the N

_{3}determination increased with the increasing pulse value, but the N

_{3}set values up to 10% of the AHC and 10 L, respectively, were considered to be accurate enough, with the inaccuracy of <2% in both cases.

_{3}coefficient, for example, for an office building, it is absolutely essential to monitor the number of shift workers, which guarantees that even if the pulse value is badly selected, the result will not be burdened with such a large error. However, for the determination of the N

_{3}value, the pulse value should not exceed 10% of the AHC. It is very unsuitable to use pulse values of >20% of AHC. To monitor the water consumption process over time and determine the maximum coefficients in the selected time steps, it is advisable that the pulse size does not exceed the 5% pulse value of the AHC.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Water Consumption in Working Hours | Minimal Consumption | Mean Consumption | Maximal Consumption |
---|---|---|---|

Day (Working Hours) | (Liters) | (Liters) | (Liters) |

Monday + Wednesday (7–17) | 608 | 892 | 1307 |

Tuesday + Thursday (7–15) | 481 | 710 | 1252 |

Friday (7–13) | 307 | 623 | 927 |

All days (7–13) | 307 | 545 | 982 |

N_{3} Coefficient Value | Pulse Value (Liter) | ||||||
---|---|---|---|---|---|---|---|

1 | 2 | 5 | 10 | 20 | 50 | 100 | |

number of workers not included | 0.071 | 0.072 | 0.072 | 0.071 | 0.059 | 0.076 | 0.026 |

number of workers included | 0.150 | 0.151 | 0.151 | 0.150 | 0.137 | 0.157 | 0.109 |

ε_{k} (-) | Pulse Value (Liter) | ||||||
---|---|---|---|---|---|---|---|

Pressure Category | 1 | 2 | 5 | 10 | 20 | 50 | 100 |

A | 0.475 | 0.486 | 0.484 | 0.466 | 0.436 | 0.677 | 2.363 |

B | 0.325 | 0.333 | 0.342 | 0.508 | 0.376 | 0.455 | 0.799 |

C | 0.394 | 0.387 | 0.385 | 0.417 | 0.469 | 0.394 | 0.809 |

D | 0.496 | 0.466 | 0.500 | 0.521 | 0.461 | 0.517 | 0.957 |

E | 0.431 | 0.434 | 0.442 | 0.410 | 0.418 | 0.435 | 0.580 |

Inaccuracy (%) | Pulse Value (Liter) | ||||||
---|---|---|---|---|---|---|---|

Pressure Category | 1 | 2 | 5 | 10 | 20 | 50 | 100 |

A | - | 2 | 1 | 4 | 6 | 55 | 249 |

B | - | 2 | 3 | 49 | 26 | 21 | 76 |

C | - | 2 | 0 | 8 | 13 | 16 | 105 |

D | - | 6 | 7 | 4 | 11 | 12 | 85 |

E | - | 1 | 2 | 7 | 2 | 4 | 33 |

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**MDPI and ACS Style**

Tuhovcak, L.; Suchacek, T.; Rucka, J. The Dependence of Water Consumption on the Pressure Conditions and Sensitivity Analysis of the Input Parameters. *Proceedings* **2018**, *2*, 592.
https://doi.org/10.3390/proceedings2110592

**AMA Style**

Tuhovcak L, Suchacek T, Rucka J. The Dependence of Water Consumption on the Pressure Conditions and Sensitivity Analysis of the Input Parameters. *Proceedings*. 2018; 2(11):592.
https://doi.org/10.3390/proceedings2110592

**Chicago/Turabian Style**

Tuhovcak, Ladislav, Tomas Suchacek, and Jan Rucka. 2018. "The Dependence of Water Consumption on the Pressure Conditions and Sensitivity Analysis of the Input Parameters" *Proceedings* 2, no. 11: 592.
https://doi.org/10.3390/proceedings2110592