An Analytical Model for the Prediction of Emptying Processes in Single Water Pipelines
Air pockets in water distribution networks can cause various operational issues, as their expansion during drainage operations leads to sub-atmospheric conditions that may result in pipeline collapse depending on soil conditions and pipe stiffness. This study presents an analytical solution for calc...
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MDPI AG
2025-05-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/15/11/6000 |
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| author | Carlos R. Payares Guevara Alberto Patiño-Vanegas Enrique Pereira-Batista Oscar E. Coronado-Hernández Vicente S. Fuertes-Miquel |
| author_facet | Carlos R. Payares Guevara Alberto Patiño-Vanegas Enrique Pereira-Batista Oscar E. Coronado-Hernández Vicente S. Fuertes-Miquel |
| author_sort | Carlos R. Payares Guevara |
| collection | DOAJ |
| description | Air pockets in water distribution networks can cause various operational issues, as their expansion during drainage operations leads to sub-atmospheric conditions that may result in pipeline collapse depending on soil conditions and pipe stiffness. This study presents an analytical solution for calculating air pocket pressure, water column length, and water velocity during drainage operations in a pipeline with an entrapped air pocket and a closed upstream end. The existing system of three differential equations is reduced to two first-order nonlinear differential equations, enabling a rigorous analysis of the existence and uniqueness of solutions. The system is then further reduced to a single secondorder nonlinear ordinary differential equation (ODE), providing an intuitive framework for examining the physical behaviour of the hydraulic and thermodynamic variables. Furthermore, through a change of variables, the second-order ODE is transformed into a first-order linear ODE, facilitating the derivation of an analytical solution. The analytical solution is validated by comparing it with a numerical solution. Additionally, a practical application demonstrates the effectiveness of the developed tool in predicting the extreme pressure values in the air pocket during the water drainage process in a pipe, within a controlled environment. |
| format | Article |
| id | doaj-art-7c4c57c55e194bc8a3cf67b96715e08e |
| institution | OA Journals |
| issn | 2076-3417 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj-art-7c4c57c55e194bc8a3cf67b96715e08e2025-08-20T02:23:44ZengMDPI AGApplied Sciences2076-34172025-05-011511600010.3390/app15116000An Analytical Model for the Prediction of Emptying Processes in Single Water PipelinesCarlos R. Payares Guevara0Alberto Patiño-Vanegas1Enrique Pereira-Batista2Oscar E. Coronado-Hernández3Vicente S. Fuertes-Miquel4Dirección de Ciencias Básicas, Universidad Tecnológica de Bolívar, Cartagena de Indias 131001, ColombiaDirección de Ciencias Básicas, Universidad Tecnológica de Bolívar, Cartagena de Indias 131001, ColombiaDirección de Ciencias Básicas, Universidad Tecnológica de Bolívar, Cartagena de Indias 131001, ColombiaInstituto de Hidráulica y Saneamiento Ambiental, Universidad de Cartagena, Cartagena de Indias 130001, ColombiaDepartamento de Ingeniería Hidráulica y Medio Ambiente, Universitat Politècnica de València, 46022 Valencia, SpainAir pockets in water distribution networks can cause various operational issues, as their expansion during drainage operations leads to sub-atmospheric conditions that may result in pipeline collapse depending on soil conditions and pipe stiffness. This study presents an analytical solution for calculating air pocket pressure, water column length, and water velocity during drainage operations in a pipeline with an entrapped air pocket and a closed upstream end. The existing system of three differential equations is reduced to two first-order nonlinear differential equations, enabling a rigorous analysis of the existence and uniqueness of solutions. The system is then further reduced to a single secondorder nonlinear ordinary differential equation (ODE), providing an intuitive framework for examining the physical behaviour of the hydraulic and thermodynamic variables. Furthermore, through a change of variables, the second-order ODE is transformed into a first-order linear ODE, facilitating the derivation of an analytical solution. The analytical solution is validated by comparing it with a numerical solution. Additionally, a practical application demonstrates the effectiveness of the developed tool in predicting the extreme pressure values in the air pocket during the water drainage process in a pipe, within a controlled environment.https://www.mdpi.com/2076-3417/15/11/6000nonlinear differential equationspipeline drainagepressure oscillations |
| spellingShingle | Carlos R. Payares Guevara Alberto Patiño-Vanegas Enrique Pereira-Batista Oscar E. Coronado-Hernández Vicente S. Fuertes-Miquel An Analytical Model for the Prediction of Emptying Processes in Single Water Pipelines Applied Sciences nonlinear differential equations pipeline drainage pressure oscillations |
| title | An Analytical Model for the Prediction of Emptying Processes in Single Water Pipelines |
| title_full | An Analytical Model for the Prediction of Emptying Processes in Single Water Pipelines |
| title_fullStr | An Analytical Model for the Prediction of Emptying Processes in Single Water Pipelines |
| title_full_unstemmed | An Analytical Model for the Prediction of Emptying Processes in Single Water Pipelines |
| title_short | An Analytical Model for the Prediction of Emptying Processes in Single Water Pipelines |
| title_sort | analytical model for the prediction of emptying processes in single water pipelines |
| topic | nonlinear differential equations pipeline drainage pressure oscillations |
| url | https://www.mdpi.com/2076-3417/15/11/6000 |
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