A Hardy Cross Approach for Hydraulic Modelling of Water Pipe Networks (original) (raw)
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Our paper presents a model of the water-pipe network for the Kawie Góry supply zone. The zone under analysis is part of the network operated by the PWiK (Water-Pipe and Sewage Company) in Czestochowa. The model was made in the Epanet program using numerical and operational data. The water-pipe network under examination supplies water to a family housing estate and is fed from a field water-supply reservoir. The total population of the area is approx. 1,500 people, the length of the waterpipe network is 11,704 running meters, and the pipe diameter range is 100-150 mm. The pipes are made of grey cast-iron, PE, and PVC. Based on the selected measurement points, calibration of the model was performed. Within the validation of the model, sensitivity analysis was made. Then, a series of simulations were performed to illustrate the network operation for variable water supply and demand conditions. Multi-period analysis was employed for modeling. The developed model made it possible to determine the magnitude of pressure in the network points, and flows in particular sections for operational parameters under consideration. The prepared model can also provide a base for alternative network management variants, for example in the case of failure or increased water demand and enable the forecasting of possible water shortage locations. In the event of the development of the network, in turn, it will enable the optimal design of new lines.
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The analysis of water piping system have been presented by several authors in the past and in recent years proposing several solution algorithms. Among the notable methods are the Hardy cross method, linear approximation method, Newton Raphson method and the hybrid method to mention but a few, to solve a system of partly linear, and partly nonlinear hydraulic equations. In this paper, the authors demonstrate the use of Excel solver to verify the Hardy Cross method for the analysis of flow in water piping networks. A single-loop water network derived from real situation was used as numerical example and case study. Detailed numerical data are presented to explain the results of the studied network.
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This paper presents an analysis of the operation of the water supply system. The analysed network provides water to six small towns. The water supply network covers rural areas of approximately 50 square kilometres with a total of 6130 inhabitants (2020). The area is characterised by relatively large differences in elevation. The water-pipe network supplies water mostly to family housing, public utility buildings, recreational buildings, service and craft entities, religious buildings, and commercial facilities and farms, including breeding farms. The network is supplied from one deep water well and a centrally located water supply tank. A hydraulic model was used for the analysis. The model was developed using the Epanet program, based on numerical and operational data. After validation, selected measurement points were used to calibrate the model. Furthermore, a series of simulations were performed to illustrate the network operation for variable water supply and demand conditions...
Applicability of Using the Multiple Lateral Demands for Designing Water Networks
2005
Many mathematical algorithms have been evolved for solving and analyzing the water distribution system such as Hardy-Cross and linear theory methods. In these traditional design methods, demands (consumption flow) are allocated to the two end nodes of the system pipes. Grouping water usage at the end nodes instead of at the actual locations where water is withdrawn from the system, produces differences between computer-predicted and actual field performance. In real-world water supply pipelines, the demands are withdrawn at different distances not at the ends of the pipeline. A numerical analysis of flow through the main pipes of water networks utilizing a hypothetical assumption of equate distribution of multiple lateral withdrawal lines (demands) along the pipe length has been presented. With the modified approach, head loss calculations in water pipes should be modified in the situations with a limited number of intermediate pipes withdrawing water from the pipe. Equations for friction head loss could be reduced by a coefficient equals to 0.5 for intermediate water laterals less than two points. This coefficient is applied in case of inflow rate which is less than two times the withdrawal rate (Q<2Q c ). The uniform withdraw method could be used in situations when the number of lateral withdrawals more than 10 points. Using this introduced approach (multiple and equate uniform lateral withdrawals) does not need the process of demand allocation used in the traditional methods for design of water pipes. Thus, the actual demand is allocated to the pipe itself instead of its nodes. Therefore, the developed approach is expected to improve the design and simulation processes of water distribution systems to match its reality.
Modelling of Hardy Cross Method for Pipe Networks
SSRG-International Journal of Mechanical Engineering, 2023
The transport of fluids through pipes is very common in core engineering practice. The main issue that came up when the pipe flow networks were its analysis part. The Hardy Cross approach is very accurate and reliable for solving these issues, but because it is iterative, the likelihood of errors increases as the number of circuit loops grows. Therefore, in this research, a piece of effort has been made to automate the Hardy Cross technique using Python programming (as it is userfriendly and has a large library backup) to remove the errors that come with using hand calculations. The built program has been applied to four different pipe flow network problems, and the outcomes are the same as those presented in the literature.
Hydraulic Analysis of Water Supply Networks Using a Modified Hardy Cross Method
International Journal of Engineering, 2014
There are different methods for the hydraulic analysis of water supply networks. In the solution process of most of these methods, a large system of linear equationsis solved in each iteration. This usually requires a high computational effort. Hardy Cross method is one of the approaches that do not need such aprocess and may converge to the solution through scalar divisions. However,this method has two short comings: first, initial discharges should satisfy continuity equation at each node; second a large number of iterations are required to converge to solution. In this article an algorithm is suggested for the selection of initial discharges that are close to the final results while the continuity equations are automatically established. This algorithm may be directly implemented in the Hardy Cross method. To reduce the number of iterations the Hardy Cross method is combined with third-order and sixteenthorder methods. The results of some numerical examples demonstrate that the use of the combined approach with the suggested initial guess reduces the number of iterations and hydraulic analysis time and the solutions converge with a high accuracy.
Developed hydraulic simulation model for water pipeline networks
Alexandria Engineering Journal, 2013
A numerical method that uses linear graph theory is presented for both steady state, and extended period simulation in a pipe network including its hydraulic components (pumps, valves, junctions, etc.). The developed model is based on the Extended Linear Graph Theory (ELGT) technique. This technique is modified to include new network components such as flow control valves and tanks. The technique also expanded for extended period simulation (EPS). A newly modified method for the calculation of updated flows improving the convergence rate is being introduced. Both benchmarks, ad Actual networks are analyzed to check the reliability of the proposed method. The results reveal the finer performance of the proposed method.
The History of Water Distribution Network Analysis: The Computer Age
Many methods have been used in the past to compute flows in networks of pipes. Such methods range from graphical methods to the use of physical analogies and finally to the use of mathematical models. This paper will attempt to catalog and review those methods that have been developed and applied since the dawn of the "computer age" in 1957 when the original Hardy Cross method was first adapted for solution using a computer in analyzing the water distribution system of the city of Palo Alto, California. Subsequent methods have included the "simultaneous node: method, the "simultaneous loop" method, the "simultaneous pipe" method, and the "simultaneous network" method. A brief review of the theoretical framework of each method will be presented along with a critique of the relative advantages and/or limitations of each method.
Applied Sciences
Hardy Cross originally proposed a method for analysis of flow in networks of conduits or conductors in 1936. His method was the first really useful engineering method in the field of pipe network calculation. Only electrical analogs of hydraulic networks were used before the Hardy Cross method. A problem with flow resistance versus electrical resistance makes these electrical analog methods obsolete. The method by Hardy Cross is taught extensively at faculties, and it remains an important tool for the analysis of looped pipe systems. Engineers today mostly use a modified Hardy Cross method that considers the whole looped network of pipes simultaneously (use of these methods without computers is practically impossible). A method from a Russian practice published during the 1930s, which is similar to the Hardy Cross method, is described, too. Some notes from the work of Hardy Cross are also presented. Finally, an improved version of the Hardy Cross method, which significantly reduces ...