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

[EN] 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-di erential 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.Coronado-Hernández, ÓE.; Fuertes-Miquel, VS.; Quiñones-Bolaños, EE.; Gatica, G.; Coronado-Hernández, JR. (2020). Simplified Mathematical Model for Computing Draining Operations in Pipelines of Undulating Profiles with Vacuum Air Valves. Water. 12(9):1-12. https://doi.org/10.3390/w12092544S112129Fuertes-Miquel, V. S., Coronado-Hernández, O. E., Mora-Meliá, D., & Iglesias-Rey, P. L. (2019). Hydraulic modeling during filling and emptying processes in pressurized pipelines: a literature review. Urban Water Journal, 16(4), 299-311. doi:10.1080/1573062x.2019.1669188Fuertes-Miquel, V. S., Coronado-Hernández, O. E., Iglesias-Rey, P. L., & Mora-Meliá, D. (2018). Transient phenomena during the emptying process of a single pipe with water–air interaction. Journal of Hydraulic Research, 57(3), 318-326. doi:10.1080/00221686.2018.1492465Tijsseling, A. S., Hou, Q., Bozkuş, Z., & Laanearu, J. (2015). Improved One-Dimensional Models for Rapid Emptying and Filling of Pipelines. Journal of Pressure Vessel Technology, 138(3). doi:10.1115/1.4031508Coronado-Hernández, O. E., Fuertes-Miquel, V. S., Besharat, M., & Ramos, H. M. (2018). Subatmospheric pressure in a water draining pipeline with an air pocket. Urban Water Journal, 15(4), 346-352. doi:10.1080/1573062x.2018.1475578Ramezani, L., Karney, B., & Malekpour, A. (2016). Encouraging Effective Air Management in Water Pipelines: A Critical Review. Journal of Water Resources Planning and Management, 142(12), 04016055. doi:10.1061/(asce)wr.1943-5452.0000695Zhou, L., & Liu, D. (2013). Experimental investigation of entrapped air pocket in a partially full water pipe. Journal of Hydraulic Research, 51(4), 469-474. doi:10.1080/00221686.2013.785985Carlos, M., Arregui, F. J., Cabrera, E., & Palau, C. V. (2011). Understanding Air Release through Air Valves. Journal of Hydraulic Engineering, 137(4), 461-469. doi:10.1061/(asce)hy.1943-7900.0000324Bianchi, A., Mambretti, S., & Pianta, P. (2007). Practical Formulas for the Dimensioning of Air Valves. Journal of Hydraulic Engineering, 133(10), 1177-1180. doi:10.1061/(asce)0733-9429(2007)133:10(1177)Ramezani, L., Karney, B., & Malekpour, A. (2015). The Challenge of Air Valves: A Selective Critical Literature Review. Journal of Water Resources Planning and Management, 141(10), 04015017. doi:10.1061/(asce)wr.1943-5452.0000530Coronado-Hernández, O., Fuertes-Miquel, V., Besharat, M., & Ramos, H. (2017). Experimental and Numerical Analysis of a Water Emptying Pipeline Using Different Air Valves. Water, 9(2), 98. doi:10.3390/w9020098Laanearu, J., Annus, I., Koppel, T., Bergant, A., Vučković, S., Hou, Q., … van’t Westende, J. M. C. (2012). Emptying of Large-Scale Pipeline by Pressurized Air. Journal of Hydraulic Engineering, 138(12), 1090-1100. doi:10.1061/(asce)hy.1943-7900.0000631Coronado-Hernández, O. E., Fuertes-Miquel, V. S., Iglesias-Rey, P. L., & Martínez-Solano, F. J. (2018). Rigid Water Column Model for Simulating the Emptying Process in a Pipeline Using Pressurized Air. Journal of Hydraulic Engineering, 144(4), 06018004. doi:10.1061/(asce)hy.1943-7900.0001446Coronado-Hernández, O. E., Fuertes-Miquel, V. S., Iglesias-Rey, P. L., & Martínez-Solano, F. J. (2020). Closure to «Rigid Water Column Model for Simulating the Emptying Process in a Pipeline Using Pressurized Air» by Oscar E. Coronado-Hernández, Vicente S. Fuertes-Miquel, Pedro L. Iglesias-Rey, and Francisco J. Martínez-Solano. Journal of Hydraulic Engineering, 146(3), 07020002. doi:10.1061/(asce)hy.1943-7900.0001681Vasconcelos, J. G., & Wright, S. J. (2008). Rapid Flow Startup in Filled Horizontal Pipelines. Journal of Hydraulic Engineering, 134(7), 984-992. doi:10.1061/(asce)0733-9429(2008)134:7(984)Vasconcelos, J. G., Klaver, P. R., & Lautenbach, D. J. (2014). Flow regime transition simulation incorporating entrapped air pocket effects. Urban Water Journal, 12(6), 488-501. doi:10.1080/1573062x.2014.881892Wang, L., Wang, F., & Lei, X. (2018). Investigation on friction models for simulation of pipeline filling transients. Journal of Hydraulic Research, 56(6), 888-895. doi:10.1080/00221686.2018.1434693Malekpour, A., Karney, B. W., & Nault, J. (2016). Physical Understanding of Sudden Pressurization of Pipe Systems with Entrapped Air: Energy Auditing Approach. Journal of Hydraulic Engineering, 142(2), 04015044. doi:10.1061/(asce)hy.1943-7900.0001067Coronado-Hernández, Ó. E., Fuertes-Miquel, V. S., Mora-Meliá, D., & Salgueiro, Y. (2020). Quasi-static Flow Model for Predicting the Extreme Values of Air Pocket Pressure in Draining and Filling Operations in Single Water Installations. Water, 12(3), 664. doi:10.3390/w12030664Leon, A. S., Ghidaoui, M. S., Schmidt, A. R., & Garcia, M. H. (2010). A robust two-equation model for transient-mixed flows. Journal of Hydraulic Research, 48(1), 44-56. doi:10.1080/0022168090356591

Sensitivity of Empirical Equation Parameters for the Calculation of Time of Concentration in Urbanized Watersheds

settingsOrder Article Reprints Open AccessArticle Sensitivity of Empirical Equation Parameters for the Calculation of Time of Concentration in Urbanized Watersheds by Jamilton Echeverri-Díaz 1,Óscar E. Coronado-Hernández 2,*ORCID,Gustavo Gatica 3ORCID,Rodrigo Linfati 4ORCID,Rafael D. Méndez-Anillo 2 andJairo R. Coronado-Hernández 5ORCID 1 Departamento de Recursos Hídricos, Sertet SAS, Montería 230002, Colombia 2 Facultad de Ingeniería, Universidad Tecnológica de Bolívar, Cartagena 131001, Colombia 3 Faculty of Engineering—CIS, Universidad Andres Bello, Santiago de Chile 7500971, Chile 4 Department of Industrial Engineering, Universidad del Bío-Bío, Concepción 4030000, Chile 5 Departamento de Productividad e Innovación, Universidad de la Costa, Barranquilla 080001, Colombia * Author to whom correspondence should be addressed. Water 2022, 14(18), 2847; https://doi.org/10.3390/w14182847 Received: 17 August 2022 / Revised: 5 September 2022 / Accepted: 9 September 2022 / Published: 13 September 2022 (This article belongs to the Section Urban Water Management) Download Browse Figures Review Reports Versions Notes Abstract The time of concentration is the time it takes a drop of water in a basin to travel from the most distant point to the outlet, and is one of the most important parameters, along with the morphometric characteristics, for determining the design flow rate in rainfall-runoff models. This study aims to determine the sensitivity of the parameters included in different equations for the calculation of the time of concentration. A case study was conducted on small, urbanized watersheds in the city of Montería, Colombia. The study uses information obtained through field work using GPS equipment and electronic total station, supplemented by geographic information contained in the city drawings of the local sewage company, which includes data on elevations above sea level with sub-metric precision. The time of concentration determined by the 12 empirical equations was compared to the results obtained from the equation proposed by the Natural Resources Conservation Service (NRCS), which was considered as a baseline formulation for the intricacy of calculation. Based on this comparison, it was found that the Carter equation is the one that best fits the results obtained from the NRCS equation because it displayed highly significant goodness of fit values. Even though the equations by Kirpich, Ventura, California Culvert Practice, Simas-Hawkins and TxDOT provide a relatively good fit compared to other empirical equations, they tend to over-estimate time of concentration values, which could lead to the under-estimation of the design flow rates. For this reason, sensitivity analysis of the parameters of these equations represents an alternative for improving the calculation of the time of concentration. The current research analyses deepen the influence of some parameters in the estimation of time of concentration. The research can also be used by designers and engineers in the city of Montería, Colombia, as an important reference to compute time of concentrations in urbanized watersheds

Assessment of steady and unsteady friction models in the draining processes of hydraulic installations

The study of draining processes without admitting air has been conducted using only steady friction formulations in the implementation of governing equations. However, this hydraulic event involves transitions from laminar to turbulent flow, and vice versa, because of the changes in water velocity. In this sense, this research improves the current mathematical model considering unsteady friction models. An experimental facility composed by a 4.36 m long methacrylate pipe was configured, and measurements of air pocket pressure oscillations were recorded. The mathematical model was performed using steady and unsteady friction models. Comparisons between measured and computed air pocket pressure patterns indicated that unsteady friction models slightly improve the results compared to steady friction models

An implicit formulation for calculating final conditions in drainage maneuvers in pressurized water installations

[EN] Emptying processes are typical maneuvers that should be performed by water distribution companies for operation purposes. These processes involve a complex numerical analysis, since a set of algebraic and ordinary differential equations needs to be solved for the intricacy of hydraulic and thermodynamic formulations for two analyzed phases (liquid and gas). This research provides an implicit equation to compute exactly the final conditions in water emptying operations in single pipelines without an air valve (or admitted air). The implicit expression was developed by considering that for all final conditions, the water velocity is null, and thus, the water column length and air pocket pressure can be computed. The friction factor, internal pipe diameter, and opening maneuvers of drain valves do not disturb the final conditions in draining processes. The developed implicit formulation was validated using experimental measurements in a pipeline with a total length of 4.36 m. The equation is of utmost importance, since it can be utilized for engineers to easily plan for future conditions in water distribution networks.This research was funded by the Escuela Naval de Cadetes "Almirante Padilla"-Armada de Colombia with the financial support of the ARC-Minciencias for the project entitled "Console Prototype of engineering in virtual reality and simulation in the training of crew members in emergency procedures" with grant number 75926.Coronado-Hernández, OE.; Bonilla-Correa, DM.; Lovo, A.; Fuertes-Miquel, VS.; Gatica, G.; Linfati, R.; Coronado-Hernández, JR. (2022). An implicit formulation for calculating final conditions in drainage maneuvers in pressurized water installations. Water. 14(21):1-13. https://doi.org/10.3390/w14213364113142

Modelo fuzzy de programación lineal entera-mixta para el cálculo de stocks objetivos

[ESP] Este trabajo presenta un modelo matemático de programación entera fuzzy para el cálculo de stock objetivos con el fin de dar visión de largo plazo a modelos de planificación en el corto plazo. La aplicación de este modelo se enmarca en sistemas con múltiples productos con demanda estacional e incierta, múltiples periodos de tiempo, capacidad limitada en el sistema de producción y almacenes. La problemática es extraída de una empresa objeto de estudio, especializada en fabricar marcas de distribución y co-packing. En ese sentido los stocks objetivos se determinan a través de un modelo de planificación fuzzy, bajo el supuesto fundamental que existe incertidumbre en los parámetros de demanda y de la función de costes. Este modelo hace el papel de un modelo de planificación agregada de la producción los cuales son los más apropiados para problemas con estacionalidad (Buxey, 2003). Con el modelo que se propone, se realiza una planificación semestral desde una perspectiva tradicional de la planificación agregada de la producción (aunque no se agregan los productos, sino los periodos) con el propósito de calcular los stocks objetivos semanales que serán entradas a modelos de planificación en el corto plazo. Una de las ventajas principales de este modelo es que no se requiere una estimación precisa de la demanda del mercado

Models Markovian to CSP Plans for acceptance sampling

En este trabajo se presentan modelos para crear planes CSP de muestreo por aceptación a través de modelos matemáticos estadísticos apoyado de las teorías de markov, cadenas de estados de markov y los diferentes planes de muestreo. De esta manera, se diseña un modelo matemático-estadístico bajo los lineamientos de las teorías bayesiana y markoviana de estados probabilísticos aplicados a los planes CSP de muestreo por aceptación en producción continua. Este modelo funciona como medio de control para la reducción de productos no conformes en la entrega a clientes con el propósito de mejorar la productividad y competitividad de la empresa.In this work presents models of statistical sampling plans for acceptance CSP supported Marcov theories, states of Markov chains and different sampling plans in this way to design a mathematical-statistical model under the guidance of the Bayesian theory and applied probabilistic Markov state CSP plans for acceptance sampling in continuous production function as control means for reducing non-conforming products delivery to customers by the company with production lines of this type, capable of improving competitiveness in international organizations and national and international markets, supported both in the technology resulting in reduced costs and increased productivity

Modelo estocástico para planificar cadenas de suministro con productos de ciclos de vida cortos

En este trabajo se presenta un modelo de optimización estocástica para la planificación de cadenas de suministros para productos con ciclo de vida corto, a través de la decisión de reservar la capacidad a contratar en los recursos de los proveedores antes de tener certeza del comportamiento de la demanda. Se consideran recursos alternativos, múltiples productos con lista de materiales complejas, demanda distribuida a lo largo de periodos consecutivos, ciclos de vida cortos, lead time largos y altos niveles de incertidumbre representados en forma de escenarios

Selección de distribuciones de probabilidad hidrológica para eventos de lluvia extrema en las regiones de Colombia

Frequency analysis of extreme events is used to estimate the maximum rainfall associated with different return periods and is used in planning hydraulic structures. When carrying out this type of analysis in engineering projects, the hydrological distributions that best fit the trend of maximum 24 h rainfall data are unknown. This study collected maximum 24 h rainfall records from 362 stations distributed throughout Colombia, with the goal of guiding hydraulic planners by suggesting the probability distributions they should use before beginning their analysis. The generalized extreme value (GEV) probability distribution, using the weighted moments method, presented the best fits of frequency analysis of maximum daily precipitation for various return periods for selected rainfall stations in Colombia.El análisis de frecuencia de eventos extremos se utiliza para estimar la precipitación máxima asociada con diferentes períodos de retorno y se utiliza en la planificación de estructuras hidráulicas. Al realizar este tipo de análisis en proyectos de ingeniería, las distribuciones hidrológicas que mejor se ajustan a la tendencia de máxima Se desconocen los datos de precipitación de 24 h. Este estudio recopiló registros de precipitación máxima de 24 h de 362 estaciones distribuidos por toda Colombia, con el objetivo de orientar a los planificadores hidráulicos sugiriendo distribuciones de probabilidad que deben usar antes de comenzar su análisis. El extremo generalizado La distribución de probabilidad del valor (GEV), utilizando el método de momentos ponderados, presentó los mejores ajustes de análisis de frecuencia de la precipitación máxima diaria para varios períodos de retorno para lluvias seleccionadas estaciones en Colombia

Waste reduction in Rectangular Figure Cutting using a Genetic Algorithm

This paper introduces a genetic algorithm (GA) to minimize the waste produced during the cutting process of rectangular figures on a sheet. The chromosomes for solution codification use an object-based representation. It has the following operator: Partially Mapped Crossover (PMX), mutation based in double interchange (2-opt), and the elitism strategy for the selection process. The proposed algorithm was applied in a real case situation problem, where the numbers of items were 55 pieces. The result of this implementation was a reduction of the waste as a result of the decrease in the number of sheets used in the cutting process and at the same time an effective employment of the used area. Este artículo presenta un algoritmo genético para minimizar el desperdicio producido durante el proceso de corte de figuras rectangulares en una lámina. Los cromosomas para la codificación de la solución usan una representación basada en objetivos. Este tiene el siguiente operador: Mapa de cruce por emparejamiento parcial (PMX), mutación basada en el doble intercambio (2-opc) y la estrategia de elitismo para el proceso de selección. El algoritmo propuesto fue aplicado en una situación problema de un caso real, donde el número de ítems eran 55 piezas. El resultado de esta implementación fue la reducción de desperdicio como resultado de la disminución del número de láminas usadas en los proceso de corte y al mismo tiempo el empleo efectivo del área usada.

Hydrological considerations for sizing of a barge discharge pipeline runway

A key element for water supply systems is the design of the water intake components. Mobile floating platforms (barges) are helpful when the hydraulic system displays substantial variations in water levels. This study presents the hydrological considerations that should be considered for the design of the barge’s pipeline runway. The analysis takes into consideration the maximum and minimum water levels measured at the location. The study was carried out at the Magdalena River -Plato (Colombia) station, finding variations in water levels of between 12.3 m and 16.1 m for return periods of 25 and 100 years, respectively. This information is helpful for designers and consultants in order to design an appropriate barge pipeline runway