Analytical Modelling of Water Pipeline Start-Up Processes
[EN] The start-up process of water-distribution networks has been extensively investigated in recent years, particularly regarding the pressure surges that may occur during such transient events. In this context, researchers have concentrated on exploring physical formulations capable of describing...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/229582 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/229582 |
| Access Level: | acceso abierto |
| Palabra clave: | Pipeline filling Entrapped air Analytical solution Transient flow |
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Analytical Modelling of Water Pipeline Start-Up ProcessesPatiño-Vanegas, AlbertoPayares Guevara, Carlos R.Pereira-Batista, EnriqueCoronado-Hernández, Oscar E.Fuertes-Miquel, Vicente S.|||0000-0003-3524-2555Pipeline fillingEntrapped airAnalytical solutionTransient flow[EN] The start-up process of water-distribution networks has been extensively investigated in recent years, particularly regarding the pressure surges that may occur during such transient events. In this context, researchers have concentrated on exploring physical formulations capable of describing the behaviour of the two interacting phases-water and air-typically resolved through numerical approaches. This paper presents an analytical solution to the nonlinear mathematical model governing the start-up of water pipelines containing a trapped air pocket. The model adopts the rigid water column approximation for the liquid phase and a polytropic gas law to account for the compressibility of the air. The resulting system can be formulated as a second-order nonlinear differential equation. The analytical approach consists of transforming the governing equation into a first-order linear ordinary differential equation, in which the square of the water front velocity is expressed as a function of the water column length. This transformation yields a closed-form solution expressed as a special integral series. The required integrals are evaluated using binomial expansions and incomplete gamma functions, enabling the derivation of a general solution valid within alternating intervals of monotonic motion. A practical application involving an 800 m pipeline is presented. Furthermore, the proposed solution is validated against experimental measurements, demonstrating the accuracy and effectiveness of the analytical approach in capturing the system's transient behaviour.MDPI AGDepartamento de Ingeniería Hidráulica y Medio AmbienteEscuela Técnica Superior de Ingeniería IndustrialRepositorio Institucional de la Universitat Politècnica de València Riunet20252025-09-12journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/229582reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2295822026-06-13T07:49:27Z |
| dc.title.none.fl_str_mv |
Analytical Modelling of Water Pipeline Start-Up Processes |
| title |
Analytical Modelling of Water Pipeline Start-Up Processes |
| spellingShingle |
Analytical Modelling of Water Pipeline Start-Up Processes Patiño-Vanegas, Alberto Pipeline filling Entrapped air Analytical solution Transient flow |
| title_short |
Analytical Modelling of Water Pipeline Start-Up Processes |
| title_full |
Analytical Modelling of Water Pipeline Start-Up Processes |
| title_fullStr |
Analytical Modelling of Water Pipeline Start-Up Processes |
| title_full_unstemmed |
Analytical Modelling of Water Pipeline Start-Up Processes |
| title_sort |
Analytical Modelling of Water Pipeline Start-Up Processes |
| dc.creator.none.fl_str_mv |
Patiño-Vanegas, Alberto Payares Guevara, Carlos R. Pereira-Batista, Enrique Coronado-Hernández, Oscar E. Fuertes-Miquel, Vicente S.|||0000-0003-3524-2555 |
| author |
Patiño-Vanegas, Alberto |
| author_facet |
Patiño-Vanegas, Alberto Payares Guevara, Carlos R. Pereira-Batista, Enrique Coronado-Hernández, Oscar E. Fuertes-Miquel, Vicente S.|||0000-0003-3524-2555 |
| author_role |
author |
| author2 |
Payares Guevara, Carlos R. Pereira-Batista, Enrique Coronado-Hernández, Oscar E. Fuertes-Miquel, Vicente S.|||0000-0003-3524-2555 |
| author2_role |
author author author author |
| dc.contributor.none.fl_str_mv |
Departamento de Ingeniería Hidráulica y Medio Ambiente Escuela Técnica Superior de Ingeniería Industrial Repositorio Institucional de la Universitat Politècnica de València Riunet |
| dc.subject.none.fl_str_mv |
Pipeline filling Entrapped air Analytical solution Transient flow |
| topic |
Pipeline filling Entrapped air Analytical solution Transient flow |
| description |
[EN] The start-up process of water-distribution networks has been extensively investigated in recent years, particularly regarding the pressure surges that may occur during such transient events. In this context, researchers have concentrated on exploring physical formulations capable of describing the behaviour of the two interacting phases-water and air-typically resolved through numerical approaches. This paper presents an analytical solution to the nonlinear mathematical model governing the start-up of water pipelines containing a trapped air pocket. The model adopts the rigid water column approximation for the liquid phase and a polytropic gas law to account for the compressibility of the air. The resulting system can be formulated as a second-order nonlinear differential equation. The analytical approach consists of transforming the governing equation into a first-order linear ordinary differential equation, in which the square of the water front velocity is expressed as a function of the water column length. This transformation yields a closed-form solution expressed as a special integral series. The required integrals are evaluated using binomial expansions and incomplete gamma functions, enabling the derivation of a general solution valid within alternating intervals of monotonic motion. A practical application involving an 800 m pipeline is presented. Furthermore, the proposed solution is validated against experimental measurements, demonstrating the accuracy and effectiveness of the analytical approach in capturing the system's transient behaviour. |
| publishDate |
2025 |
| dc.date.none.fl_str_mv |
2025 2025-09-12 |
| dc.type.none.fl_str_mv |
journal article http://purl.org/coar/resource_type/c_6501 VoR http://purl.org/coar/version/c_970fb48d4fbd8a85 |
| dc.type.openaire.fl_str_mv |
info:eu-repo/semantics/article |
| format |
article |
| dc.identifier.none.fl_str_mv |
https://riunet.upv.es/handle/10251/229582 |
| url |
https://riunet.upv.es/handle/10251/229582 |
| dc.language.none.fl_str_mv |
Inglés eng |
| language_invalid_str_mv |
Inglés |
| language |
eng |
| dc.rights.none.fl_str_mv |
open access http://purl.org/coar/access_right/c_abf2 Reconocimiento (by) http://creativecommons.org/licenses/by/4.0/ |
| dc.rights.openaire.fl_str_mv |
info:eu-repo/semantics/openAccess |
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open access http://purl.org/coar/access_right/c_abf2 Reconocimiento (by) http://creativecommons.org/licenses/by/4.0/ |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.publisher.none.fl_str_mv |
MDPI AG |
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MDPI AG |
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reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname:Universitat Politècnica de València (UPV) |
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Universitat Politècnica de València (UPV) |
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RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
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RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
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1869419631333081088 |
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15.811543 |