# Evaluation of Peak Water Demand Factors in Puglia (Southern Italy)

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## Abstract

**:**

## 1. Introduction

_{p}, evaluated as the ratio, over a defined time period, between the maximum value and the average value of water consumption measured in several nodes of the AQP supply system.

## 2. Fluctuations in Demand: Literature Review

_{p}reported in Table 3.

## 3. Field Campaign

#### 3.1. Dataset Analysed

#### 3.2. Flow Data Definition

#### 3.3. Effect of the Sampling Time Interval on the Peak Factor

_{p}values have been estimated and results are shown in Figure 2 where, considering a 1-h time interval, instead of the smaller (3, 5, or 10 min), leads to an underestimation ranging from about 5% to 11%, smaller than those observed by de Marinis et al. [26] and Tricarico et al. [25].

## 4. Analysis of Water Demand Variability

_{p}for towns with less than 20,000 inhabitants: it is possible to observe the absence of a marked seasonal trend. Peak factors show a maximum value in correspondence of May, but also a strong random variability. The overall observation suggests that drinking water demand in Puglia is unaffected by climate and temperature demonstrating, following Cole et al. [31] that indoor consumption mainly affects the nature of water use in this region.

_{p}, computed as the maximum of the values for the different days of measurement, can be considered not affected by weekly and/or monthly variation.

_{p}is shown in Figure 6, where a general decreasing trend can be observed. On the other hand, numerical values are significantly lower than those proposed by most of the empirical relationships just mentioned in Section 2. Observed values, except for two towns, Alezio and Sannicola, do not exceed 2.50. A comparison among measured data and the empirical formulas of Harmon [13], Babbitt [14], Metcalf and Eddy [16], Johnson [17], Gifft [18] and De Marinis et al. [22] is illustrated in Figure 6. It can be observed that all the used literature formulas, except De Marinis et al. [22], tend to overestimate the value of the peak coefficient C

_{p}. This is quite evident, in particular, for towns of less than 10,000 inhabitants where the overestimation reaches 150%. A different result is obtained, instead, using Equation (3) proposed by de Marinis et al. [22] that seems to represent well the average value of the measured data. On the other hand, this last formula is not sufficiently precautionary suggesting peak factors lower than the higher observed values.

_{p}can be represented as a function of the number of users, like most of the relationships provided by the technical literature and in particular the Harmon formula.

## 5. Theoretical Distribution of Peak Coefficient

_{p}is the pth percentile (frequency factor) of Gumbel distribution given by Chow et al. [33]:

_{q}are the daily average utilization factor for a single family home and a coefficient of variation of PRP indoor water demand pulse, respectively assumed equal to 0.045 and 0.55, as reported in Zhang et al. [21]. Using the above described parameters and considering the 99.9th percentile, and Equation (7) becomes:

_{e}is the exponential distribution frequency factor and α is the scale parameter of the exponential distribution. Following the approach proposed by the Zhang et al. [21] the frequency factor of the Gumbel distribution, ξ

_{p}, may be calculated using the Equation (7) as follows:

_{p}can be written also ξ

_{p}= α × (PF − μ) with α and μ parameters of the Gumbel distribution. On the other hand, the Gumbel distribution is the extreme value distribution of the annual maxima of a Poissonian number of independent and identically exponentially distributed random variables, with the scale (α) parameter of Gumbel distribution equal to the scale parameter of the exponential distribution [36]. Consequently, Equation (11) allows the evaluation of the α scale parameter of the exponential distribution hereafter reported:

_{e}is equal to:

^{2}= 0.97. Thus, demonstrating that by filtering the effect of population of different towns, the randomly sampled peak factors can be ascribed to a unique regional exponential distribution.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 6.**Comparison of experimental data and literature formulas for the corresponding population using a logarithmic scale.

**Figure 8.**Theoretical relationship curve and measured data of others Italian studies using the logarithmic scale of population.

**Figure 9.**The exponential probability plot of the Peak Factor distribution (diamonds points) and the linear regression (black line).

**Table 1.**Peak flow factors computed at different time scales [9].

Peak Flow Factor | Climate | |||
---|---|---|---|---|

Temperate | Warm, Dry | |||

Range | Typical | Range | Typical | |

Max hourly/average day * | 2.0–4.0 | 2.5 | 3.0–6.0 | 3.5 |

Max daily/average day * | 1.3–2.0 | 1.5 | 2.0–4.0 | 2.5 |

Max weekly/average day * | 1.1–1.3 | 1.2 | 1.7–2.3 | 2.0 |

**Table 2.**Ratio of peak hourly flow to annual average flow [10].

Population | C_{p} |
---|---|

<500 | 2.9 |

500–5000 | 2.9–2.5 |

5000–50,000 | 2.5–2.1 |

50,000–500,000 | 2.1–1.9 |

**Table 3.**Peak flow factor [19].

Population | C_{p} |
---|---|

<10,000 | 5–3 |

10,000–50,000 | 3–2.5 |

50,000–100,000 | 2.5–2 |

100,000–200,000 | 2–1.5 |

**Table 4.**Peak flow factor [20].

Population | C_{p} |
---|---|

50,000–200,000 | 2.50 |

200,000–500,000 | 2.00 |

>1,000,000 | 1.70 |

Babbitt | Gifft | Harmon | Zhang | |
---|---|---|---|---|

Overestimated data | 99.22% | 100.00% | 99.22% | 100.00% |

Average overestimation | 1.98 | 2.13 | 1.84 | 2.07 |

Maximum overestimation | 3.76 | 3.83 | 3.09 | 3.48 |

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**MDPI and ACS Style**

Balacco, G.; Carbonara, A.; Gioia, A.; Iacobellis, V.; Piccinni, A.F.
Evaluation of Peak Water Demand Factors in Puglia (Southern Italy). *Water* **2017**, *9*, 96.
https://doi.org/10.3390/w9020096

**AMA Style**

Balacco G, Carbonara A, Gioia A, Iacobellis V, Piccinni AF.
Evaluation of Peak Water Demand Factors in Puglia (Southern Italy). *Water*. 2017; 9(2):96.
https://doi.org/10.3390/w9020096

**Chicago/Turabian Style**

Balacco, Gabriella, Antonio Carbonara, Andrea Gioia, Vito Iacobellis, and Alberto Ferruccio Piccinni.
2017. "Evaluation of Peak Water Demand Factors in Puglia (Southern Italy)" *Water* 9, no. 2: 96.
https://doi.org/10.3390/w9020096