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# Simplified Mathematical Model for Computing Draining Operations in Pipelines of Undulating Profiles with Vacuum Air Valves

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Departamento de Ingeniería Hidráulica y Medio Ambiente, Universitat Politècnica de València, 46022 Valencia, Spain
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Faculty of Engineering, Universidad Andres Bello, Santiago de Chile 7500971, Chile
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Producom, Universidad de la Costa, Barranquilla 080002, Colombia
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Author to whom correspondence should be addressed.
Water 2020, 12(9), 2544; https://doi.org/10.3390/w12092544
Received: 21 August 2020 / Revised: 4 September 2020 / Accepted: 6 September 2020 / Published: 11 September 2020
The draining operation involves the presence of entrapped air pockets, which are expanded during the phenomenon occurrence generating drops of sub-atmospheric pressure pulses. Vacuum air valves should inject enough air to prevent sub-atmospheric pressure conditions. Recently, this phenomenon has been studied by the authors with an inertial model, obtaining a complex formulation based on a system composed by algebraic-differential equations. This research simplifies this complex formulation by neglecting the inertial term, thus the Bernoulli’s equation can be used. Results show how the inertial model and the simplified mathematical model provide similar results of the evolution of main hydraulic and thermodynamic variables. The simplified mathematical model is also verified using experimental tests of air pocket pressure, water velocity, and position of the water column. View Full-Text
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MDPI and ACS Style

Coronado-Hernández, Ó.E.; Fuertes-Miquel, V.S.; Quiñones-Bolaños, E.E.; Gatica, G.; Coronado-Hernández, J.R. Simplified Mathematical Model for Computing Draining Operations in Pipelines of Undulating Profiles with Vacuum Air Valves. Water 2020, 12, 2544. https://doi.org/10.3390/w12092544

AMA Style

Coronado-Hernández ÓE, Fuertes-Miquel VS, Quiñones-Bolaños EE, Gatica G, Coronado-Hernández JR. Simplified Mathematical Model for Computing Draining Operations in Pipelines of Undulating Profiles with Vacuum Air Valves. Water. 2020; 12(9):2544. https://doi.org/10.3390/w12092544

Chicago/Turabian Style

Coronado-Hernández, Óscar E., Vicente S. Fuertes-Miquel, Edgar E. Quiñones-Bolaños, Gustavo Gatica, and Jairo R. Coronado-Hernández 2020. "Simplified Mathematical Model for Computing Draining Operations in Pipelines of Undulating Profiles with Vacuum Air Valves" Water 12, no. 9: 2544. https://doi.org/10.3390/w12092544

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