# Impact of Self-Cleansing Criteria Choice on the Optimal Design of Sewer Networks in South America

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Optimal Sewer Network Design

#### 2.1.1. Design Cost

^{3}), as defined in Equation (2).

#### 2.1.2. Design Constraints

- Minimum pipe diameter required for the cleaning and maintenance of the network;
- Maximum filling ratio that must be enabled to allow adequate aeration in the system;
- Minimum velocity and shear stress inside the pipes necessary to prevent particle sedimentation;
- Maximum velocity required to prevent problems such as cavitation and pipe wall erosion;
- Minimum and maximum depth below ground level necessary to protect the pipe structure from overloading and axial stresses, respectively.

#### 2.2. Self-Cleansing Limits

^{−1/3}s for all the conduits of the sewer network, $y$ is the water depth, $D$ is the pipe diameter, $\tau $ is the minimum shear stress value constraint, and $\gamma $ is the specific weight of water.

## 3. Case Studies

#### 3.1. Description

#### 3.2. Design Constraints

#### Self-Cleansing Limits

- Select a minimum velocity or minimum shear stress from Table 1;
- Select a pipe diameter;
- Define the filling ratio $\frac{y}{D}$;
- Solve Equation (3), for the minimum velocity, or Equation (4), for shear stress, to estimate the minimum self-cleansing slope;
- Move to the next pipe diameter and repeat step 4;
- Move to the next self-cleansing criterion in Table 1 and start the entire procedure over again.

#### 3.3. Design Procedure

- Create a .txt file that includes the manholes of the main path of the network. Each manhole must include ground elevation and inflow information;
- Define design constraints and list of available commercial diameters;
- Create a graph with all the possible arcs (pipes). Each arc has an associated pipe diameter as well as upstream and downstream elevation to calculate the slope;
- Calculate the cost of each pipe using Equation (1);
- Calculate the hydraulic of each arc, i.e., determine flow, hydraulic radius, wetted area, and top width, amongst other hydraulic parameters, using the Manning equation using Equation (3). If the arc does not fulfill all the design constraints it will not be created;
- Use the Bellman–Ford algorithm to estimate the combination of arcs that minimize network cost;
- Report the results of the slope and diameter of each pipe in the network.

## 4. Results and Discussion

## 5. Sensitivity Analysis

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Sewer networks used for the analyses: (

**A**) Mini-Chicó network; (

**B**) Mays and Wenzel [13] network and (

**C**) Kerman city network.

**Figure 2.**Design results and total costs for the three networks: (

**A**) Mini-Chicó, (

**B**) Mays and Wenzel [13], (

**C**) Kerman city Design I, and (

**D**) Kerman city Design II.

**Figure 3.**Network costs for the five wastewater proposed simulations: (

**A**) Simulation 1 (Inflow per node 1 L/s), (

**B**) Simulation 2 (Inflow per node 2 L/s), (

**C**) Simulation 3 (Inflow per node 3 L/s), (

**D**) Simulation 4 (Inflow per node 5 L/s), and (

**E**) Simulation 5 (Inflow per node 10 L/s). Cost in (USD).

Criterion No. | Source | Country | Sewer Type | ${\mathit{v}}_{\mathit{m}\mathit{i}\mathit{n}}$ [m/s] | ${\mathit{\tau}}_{\mathit{m}\mathit{i}\mathit{n}}$ [Pa] |
---|---|---|---|---|---|

(1) | Lysne [18] | USA | All | - | 2.0–4.0 |

(2) | ASCE [19] | USA | WW | 0.6 | - |

SW | 0.9 | - | |||

(3) | Yao [20] | USA | SW | - | 3.0–4.0 |

WW | - | 1.0–2.0 | |||

(4) | Minister of Interior [21] | France | WW | 0.3 | - |

C | 0.6 | - | |||

(5) | British Standard BS 8001 [22] | UK | SW | 0.75 | - |

C | 1 | - | |||

(6) | Ecuadorian Normalization Institute (Instituto Ecuatoriano de Normalización) [23] | Ecuador | WW | 0.45 | - |

SW | 0.9 | - | |||

(7) | European Standard EN 752-4 [24] | Europe | All | 0.7 | - |

(8) | ATV-DVWK-Regelwerk [15] | Germany | All | Depends on pipe diameter | - |

(9) | Great Lakes [25] | USA | WW | 0.6 | - |

(10) | National Water Commission (Comisión Nacional del Agua) [26] | Mexico | SW | 0.6 | - |

WW | 0.3 | - | |||

(11) | Bolivian Institute for Standarization and Quality (Instituto Boliviano de Normalización y Calidad) [27] | Bolivia | WW | - | 1 |

SW and C | - | 1.5 | |||

(12) | Medellin Public Enterprises (Empresas Públicas de Medellín) [28] | Colombia | WW | 0.45 | 1.5 |

SW and C | 0.75 | 3 | |||

(13) | Colombia. Ministry of Housing, City and Territory (Colombia. Ministerio de Vivienda, Ciudad y Territorio) [29] | Colombia | WW | 0.45 | 1.5 |

SW and C | 0.75 | 3 |

**Table 2.**Hydraulic design constraints modified from Duque et al. [12].

Design Constraint | Threshold Value |
---|---|

Minimum diameter | 200 mm |

Maximum filling ratio | 0.85 |

Minimum self-cleansing velocity | 0.6–0.9 m/s |

Minimum shear stress | 2.0–4.0 Pa |

Maximum velocity | 5.0 m/s |

Minimum depth below ground level | 1.2 m |

Maximum depth below ground level | 5.0 m |

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**MDPI and ACS Style**

Montes, C.; Kapelan, Z.; Saldarriaga, J. Impact of Self-Cleansing Criteria Choice on the Optimal Design of Sewer Networks in South America. *Water* **2019**, *11*, 1148.
https://doi.org/10.3390/w11061148

**AMA Style**

Montes C, Kapelan Z, Saldarriaga J. Impact of Self-Cleansing Criteria Choice on the Optimal Design of Sewer Networks in South America. *Water*. 2019; 11(6):1148.
https://doi.org/10.3390/w11061148

**Chicago/Turabian Style**

Montes, Carlos, Zoran Kapelan, and Juan Saldarriaga. 2019. "Impact of Self-Cleansing Criteria Choice on the Optimal Design of Sewer Networks in South America" *Water* 11, no. 6: 1148.
https://doi.org/10.3390/w11061148