# At-Site Assessment of a Regional Design Criterium for Water-Demand Peak Factor Evaluation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Case Study

## 3. Hourly Peaks Frequency Analysis

_{max}(h) is the daily maximum of the hourly flow rate and Q

_{m}is the average daily flow (reported in Table 1).

## 4. Instantaneous Peaks Frequency Analysis

_{max}(i) is the instantaneous peak flow and Q

_{m}is the average daily flow (reported in Table 1). Considering for each of the towns investigated the observed two years of peak factor data, good performances are obtained by fitting the Gumbel probability distribution (see Figure 4) with parameters obtained through the method of moments. The sample mean (μ) and standard deviation (σ) are reported in Table 2.

## 5. Regional Distribution of the Instantaneous Peak Factor

_{i}) for residential water use, using a probabilistic approach based on the Poisson Rectangular Pulse (PRP) representation, leading to an extreme value distribution of the Gumbel type. Under this hypothesis the water consumption is characterized by a rectangular water pulse of random duration, with mean equal to τ, mean intensity equal to α and mean arrival rate of water pulses at a single home equal to λ; so ρ = λ × τ is daily average utilization factor for a single-family home.

_{F}is the pth percentile (frequency factor) of Gumbel distribution given by Chow et al. [25] and ρ is the daily average utilization factor for a single-family home θ

_{q}is the coefficient of variation of PRP indoor water demand pulse, ψ* is the dimensionless peak hourly demand factor. It is worth noting that, due to the structure of such equation, the instantaneous peak demand factor, Cp

_{i}, tends to ψ*, the dimensionless hourly peak factor, for increasing N. In other terms the instantaneous peak factor converges to the hourly peak coefficient for growing population.

_{q}equal to 0.55 as in Zhang et al. [22], a regional behavior (using data extracted from 150 towns in Puglia) of the instantaneous peak flow factor was found by Balacco et al. [15].

## 6. Fitting the Probability Distribution of the Peak Factor to the Observed Local Values

_{i}), for a town with N number of homes; considering that such expression can be easily turned into town population (P) if an average number of inhabitants for home is known.

_{i}distribution and the mean and standard deviation of the population of the peak factors:

_{q}and ψ* as a function of the sample mean, and standard deviation of instantaneous peak factors reported in Table 2 by means of Equations (6) and (7). The resulting values of θ

_{q}and ψ* are reported in Table 3.

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Typical daily patterns in hourly water demand [23].

**Figure 2.**Typical daily patterns in hourly water demand for the seven days of the week [23].

**Figure 5.**Comparison between Cp

_{i}sample values (grey rhombs), regional curve (in green) and 99.9th percentile peak factors (red triangles) obtained from the at-site Gumbel distributions.

Town | Inhabitants | Q_{m} (m^{3}/s) | 2015–2016 | |
---|---|---|---|---|

μ | σ | |||

Palagiano | 16,067 | 30.54 | 1.50 | 0.11 |

Palagianello | 7857 | 14.14 | 1.58 | 0.15 |

Roccaforzata | 1827 | 6.81 | 1.32 | 0.14 |

Town | Inhabitants | 2015–2016 | |
---|---|---|---|

μ | σ | ||

Palagiano | 16,067 | 1.56 | 0.11 |

Palagianello | 7857 | 1.74 | 0.15 |

Roccaforzata | 1827 | 1.54 | 0.24 |

**Table 3.**Parameters of the Cp

_{i}distribution according to the data series recorded at Roccaforzata, Palagianello and Palagiano.

Town | Inhabitants | N | θ_{q} | ψ* |
---|---|---|---|---|

Palagiano | 16,067 | 6180 | 1.10 | 1.56 |

Palagianello | 7857 | 3022 | 0.94 | 1.74 |

Roccaforzata | 1827 | 703 | 0.43 | 1.54 |

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**MDPI and ACS Style**

Balacco, G.; Gioia, A.; Iacobellis, V.; Piccinni, A.F.
At-Site Assessment of a Regional Design Criterium for Water-Demand Peak Factor Evaluation. *Water* **2019**, *11*, 24.
https://doi.org/10.3390/w11010024

**AMA Style**

Balacco G, Gioia A, Iacobellis V, Piccinni AF.
At-Site Assessment of a Regional Design Criterium for Water-Demand Peak Factor Evaluation. *Water*. 2019; 11(1):24.
https://doi.org/10.3390/w11010024

**Chicago/Turabian Style**

Balacco, Gabriella, Andrea Gioia, Vito Iacobellis, and Alberto Ferruccio Piccinni.
2019. "At-Site Assessment of a Regional Design Criterium for Water-Demand Peak Factor Evaluation" *Water* 11, no. 1: 24.
https://doi.org/10.3390/w11010024