# Impact of Pressure-Driven Demand on Background Leakage Estimation in Water Supply Networks

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## Abstract

**:**

## 1. Introduction

#### Overview of Pressure-Dependent Demand Functions

## 2. Methods

#### Integrating a PDD Function and Pressure-Dependent Leakage Modeling in the WSN Hydraulic Model Formulation

## 3. Results and Analysis

#### Numerical Examples

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Continuation of the PDM with Background Leakage Model Derivation

## References

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**Figure 1.**The schematics of the case study networks used for the numerical examples: (

**a**) network 1; (

**b**) network 2.

**Figure 2.**Nodal demand vs. the leakage flow for each node for the case study network 1: (

**a**) demand-driven modeling (DDM) analysis; (

**b**) pressure-driven modeling (PDM) analysis.

**Figure 3.**The pipe discharge and the leakage flow in each pipe for the case study network 1: (

**a**) DDM analysis; (

**b**) PDM analysis.

**Figure 4.**Total network leakage flow with respect to the nodal demand and pipe discharges for the case study network 1: (

**a**) DDM analysis; (

**b**) PDM analysis.

**Figure 5.**Nodal demand vs. the leakage outflow for each node for the case study network 2: (

**a**) DDM analysis; (

**b**) PDM analysis.

**Figure 6.**The pipe discharge and the leakage flow for the case study network 2: (

**a**) DDM analysis; (

**b**) PDM analysis.

**Figure 7.**Total network leakage flow with respect to the nodal demands and pipe discharges for the case study network 2: (

**a**) DDM analysis; (

**b**) PDM analysis.

**Figure 8.**Comparison of the solution time for the case study networks: (

**a**) CPU time for the DDM case; (

**b**) CPU time for the PDM case.

Network ID | ${\mathit{n}}_{\mathit{p}}$ | ${\mathit{n}}_{\mathit{t}}$ | ${\mathit{n}}_{\mathit{j}}$ | ${\mathit{n}}_{\mathit{f}}$ | Head-Loss Model Used | ${\mathit{h}}_{\mathit{i}}^{\mathit{min}}$ (m) | ${\mathit{h}}_{\mathit{i}}^{\mathit{ser}}$ (m) | Total Required Demand (L/s) |
---|---|---|---|---|---|---|---|---|

N1 | 12 | 9 | 8 | 1 | HW | 0 | 10 | 208.1 |

N2 | 34 | 24 | 23 | 1 | HW | 10 | 30 | 282 |

N3 | 71 | 46 | 45 | 1 | HW | 5 | 20 | 88.82 |

N4 | 108 | 70 | 67 | 3 | HW | 5 | 90 | 535 |

N5 | 317 | 272 | 268 | 4 | HW | 5 | 80 | 406.94 |

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**MDPI and ACS Style**

Adedeji, K.B.; Hamam, Y.; Abu-Mahfouz, A.M.
Impact of Pressure-Driven Demand on Background Leakage Estimation in Water Supply Networks. *Water* **2019**, *11*, 1600.
https://doi.org/10.3390/w11081600

**AMA Style**

Adedeji KB, Hamam Y, Abu-Mahfouz AM.
Impact of Pressure-Driven Demand on Background Leakage Estimation in Water Supply Networks. *Water*. 2019; 11(8):1600.
https://doi.org/10.3390/w11081600

**Chicago/Turabian Style**

Adedeji, Kazeem B., Yskandar Hamam, and Adnan M. Abu-Mahfouz.
2019. "Impact of Pressure-Driven Demand on Background Leakage Estimation in Water Supply Networks" *Water* 11, no. 8: 1600.
https://doi.org/10.3390/w11081600