No abstract is provided for this article.
A mathematical model for the assessment of the pressure head maxima that air pockets within a pipeline can originate on start-up is presented. This model is based on a general model addressing the filling of a pipeline with several air pockets published by the authors. Here the simulation of the operation of a discharge valve in order to control the peak pressure following the pump start-up is included. Also, in order to correctly model reverse flow through the pump use is made of the dimensionless Suter curves. Water movement is modelled through rigid column theory and air - water straight cross section moving interfaces are considered. Because of the huge pressure values that the very rapid compression of the air can cause, and in order to avoid pipe breaks, practical engineers must lend great attention to this problem.
This work aims to study in detail the methods of experimental characterization of air valves. In the first part, different experimental techniques are compared to the measurements made in the Air Valves Test Bench built by Bermad CS at its factory in Evron (Israel). The second part deals with the study of a collection of commercial air valves from different manufacturers. Finally, the Wylie and Streeter discharge coefficient Cd for air valve characterization [1] has been obtained. The results have been also compared with a simplified proposed model representation of the air valve.
No abstract is provided for this article.
Las conducciones con perfil irregular presentan una serie de particularidades que no pueden ser ignoradas, como puede ser la posible cavitación en los puntos altos. Para evitar el colapso de la conducción se recurre a la instalación de ventosas, las cuales permiten la entrada de aire cuando la presión en el interior de la tubería es inferior a la atmosférica. Pero el aire introducido en la conducción debe ser expulsado cuando se vuelva a producir el llenado de la tubería, y ello debe hacerse de forma adecuada para evitar sobrepresiones indeseables. La presencia de ventosas no siempre ofrece la fiabilidad necesaria y puede llevar a situaciones más adversas de las que se pretendían evitar. Incluso sin ventosas, el aire puede entrar en la conducción a través de las juntas, válvulas, etc., durante las interrupciones temporales del suministro, situación muy común en sistemas de riego pero que debería evitarse en abastecimientos urbanos. El aire atrapado entre dos columnas de agua en una conducción a presión, con o sin ventosas, puede provocar importantes sobrepresiones cuando se proceda al arranque de la instalación. En el presente artículo se pretende estudiar y modelizar el problema del llenado de tuberías con aire atrapado para predecir el transitorio que se producirá y tratar de evaluar los peligrosos picos de presión que pueden generarse. No se contempla la presencia de ventosas por cuanto supone considerar las peores condiciones y, en consecuencia, la situación más desfavorable. Se utiliza el modelo rígido para analizar el comportamiento de n bolsas de aire atrapado en tuberías de perfil irregular y se aplica a un caso concreto, del cual se extraen interesantes conclusiones.
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.
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.
For the design of stormwater pumping stations, there is often uncertainty regarding the selection of an appropriate rainfall event to determine the required pumping capacity and temporary storage volume for managing extreme events of a given magnitude. To account for the risk of system failure, the return period is considered, as recommended based on the size of the catchment’s drainage area or other considerations, depending on the local regulations of a country. This study focused on analysing the direct runoff volume from the catchment, the storage volume required for the operation of the pumping system, and the order of magnitude of the design flow rate. The results indicate that a rainfall event with a duration of at least twice the time of concentration should be used. The design flow rate should range between 50% and 70% of the peak discharge, and designing for flow rates near the peak is not advisable, as it can lead to intermittent pump operation and result in an oversized installed capacity. The methodology developed in this research was applied to the Coastal Protection Project located in the city of Cartagena, Colombia, which includes a 2045.6-m-long box culvert with a cross-sectional area of 2 × 2 m, and three pumping stations, each equipped with three pumps rated at 0.75 m3/s, for a total installed capacity of 6.75 m3/s.
