# Unsteady Friction Modeling Technique for Lagrangian Approaches in Transient Simulations

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Models

#### 1.2. Friction Models

## 2. Materials and Methods

#### 2.1. Mapping the Water Distribution System

#### 2.2. The Wave Characteristic Method Model

#### 2.3. Pressure Magnitude

#### 2.4. Unsteady Friction Attenuation

## 3. Results

#### 3.1. Case Study 01—Proof of Concept

#### 3.2. Sensitivity Analysis

#### 3.3. Case Study 02—Looped Water System

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The layout of the first case study describes a simple pipeline system with a junction and a valve downstream.

**Figure 3.**The transient response at node 2 with different WCM tunings, in comparison to the unsteady MOC model in red, for the first case study. The subfigures depict in black the WCM transient evolution from quasi-state friction (

**a**) to unsteady friction (

**d**), in an ascending order.

**Figure 4.**A comparison of the transient behavior at node 2 for the refined U-WCM (black) and the U-MOC (red) for the first case study—A variation. The quasi-model (Q-WCM) is illustrated in gray in the background.

**Figure 5.**A comparison of the transient behavior at node 2 for the refined U-WCM (black) and the U-MOC (red) for the first case study—B variation. The quasi-model (Q-WCM) is illustrated in gray in the background.

**Figure 6.**The layout of the second case study, depicting a looped network system with a single source and a consumer at the downstream.

**Figure 7.**Transient response at node 6 in the second case study. U-MOC, U-WCM, and WCM in red, black, and gray, respectively.

**Figure 8.**Transient response at node 2 in the second case study. U-MOC, U-WCM, and WCM in red, black, and gray, respectively.

**Figure 9.**Transient response at node 3 in the second case study. U-MOC, U-WCM, and WCM in red, black, and gray, respectively.

Link ID | Length [m] | Diameter [mm] |
---|---|---|

Pipe P1 | 610 | 900 |

Pipe P2 | 914 | 750 |

Pipe P3 | 610 | 600 |

Pipe P4 | 457 | 450 |

Pipe P5 | 549 | 450 |

Pipe P6 | 671 | 750 |

Pipe P7 | 1000 | 900 |

Pipe P8 | 457 | 600 |

Pipe P9 | 488 | 450 |

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**MDPI and ACS Style**

Zeidan, M.; Ostfeld, A.
Unsteady Friction Modeling Technique for Lagrangian Approaches in Transient Simulations. *Water* **2022**, *14*, 2437.
https://doi.org/10.3390/w14152437

**AMA Style**

Zeidan M, Ostfeld A.
Unsteady Friction Modeling Technique for Lagrangian Approaches in Transient Simulations. *Water*. 2022; 14(15):2437.
https://doi.org/10.3390/w14152437

**Chicago/Turabian Style**

Zeidan, Mohamad, and Avi Ostfeld.
2022. "Unsteady Friction Modeling Technique for Lagrangian Approaches in Transient Simulations" *Water* 14, no. 15: 2437.
https://doi.org/10.3390/w14152437