Analysis of water distribution systems and head losses using the hardy-cross method

Distribution services have not been running optimally at PDAM Tirta Meulaboh, that This study aims to determine the level of pressure loss in the PDAM’s clean water pipe network. The method used in this research is a quantitative descriptive survey method supported by primary data and secondary data. Calculation of the amount of pressure loss using the hardy cross method. The results showed that the observed value of discharge with the highest water consumption was at 18:00 WIB at 0.172 m3 / person, while for the lowest use was at 14:00 WIB at 0.119 m3 / person. It can be concluded that this time is the peak time for water consumption. High-pressure water where the maximum average is 0.00000599 m, because high pressure is not adequate. The maximum loss of high pressure is found in the loop (VII) of 2.57025 m or 0.257025 atm, for the minimum pressure there is in the loop (VI) of - 0.00024 m or -0.000024 atm. It is necessary to re-evaluate the distribution network system by PDAM such as surveys to find out the causes of high water pressure losses to customers such as surveys for water leaks in distribution pipes, replacing old pipes.

ANALISIS SISTEM JARINGAN PIPA DISTRIBUSI AIR BERSIH KELURAHAN PLAJU DARAT DENGAN METODE HARDY CROSS

Jalan Talang Petai merupakan daerah atau jalan yang ada di Kelurahan Plaju Darat dengan luasan ± 115 Ha dengan jumlah penduduk ± 4528 jiwa pada tahun 2019. Daerah Jalan Talang Petai merupakan daerah/kawasan yang cukup berkembang, baik berkembang dalam pertumbuhan jumlah penduduk serta sarana dan prasarana yang terus meningkat dari tahun ke tahun, dengan demikian meningkat pula kebutuhan akan air bersih, namun dalam penyediaan air bersih yang ada sekarang masih kurang terlayani dengan baik. Untuk itu diperlukan adanya perencanaan tentang sistem jaringan distribusi air bersih, yang bertujuan mengetahui berapa besar debit air yang harus dialiri pada wilayah tersebut, sehingga kebutuhan air bersihnya terpenuhi secara merata. Dari hasil perhitungan proyeksi jumlah penduduk terlayani di daerah Jalan Talang Petai diperoleh 5.319 jiwa pada tahun 2030. Total debit kebutuhan air bersih tahun 2020 sebesar 7,7499 liter/detik dan total debit pada tahun 2030 sebesar 10,1959 liter/detik. Dengan demikian perlu dilakukan penambahan debit sebesar 2,446 liter/detik untuk mencapai kebutuhan air bersih sampai tahun 2030, serta juga dibutuhkan tekanan air pada jaringan awal pipa yang masuk ke Jalan Talang Petai agar maksimal adalah 1,1 atm sehingga tekanan air di ujung pengaliran terjauh masih diatas standar minimal Kata Kunci : Jaringan Distribusi Air, Metode Hardy Cross

Application of Third-Order Schemes to Improve the Convergence of the Hardy Cross Method in Pipe Network Analysis

In this study, twenty-two new mathematical schemes with third-order of convergence are gathered from the literature and applied to pipe network analysis. The presented methods were classified into one-step, two-step, and three-step schemes based on the number of hypothetical discharges utilized in solving pipe networks. The performances of these new methods and Hardy Cross method were compared by solving a sample pipe network considering four different scenarios (92 cases). The results show that the one-step methods improve the rate of convergence of the Hardy Cross method in 10 out of 24 cases (41%), while this improvement was found to be 39 out of 56 cases (69.64%) and 5 out of 8 cases (62.5%) for the two-step and three-step methods, respectively. This obviously indicates that the modified schemes, particularly the three-step methods, improve the performance of the original loop corrector method by taking lower number of iterations with the compensation of relatively more computational efforts.

Impacts on Head Loss in a Pumpless Solar Thermal Heater Calculated by Hardy-Cross Methodology

This project explores the impacts that temperature and various geometries have on head loss in a heat exchanger intended to be used as a component of a pumpless solar thermal heater. The heat exchanger component of the pumpless solar thermal heater is a vertical pipe configuration with one inlet pipe through which water flows downward to a well. There are a number of outlet pipes through which water flows upward from the well. The outlet pipes contain a number of conical features at some angle that act as fins to increase heat transfer. The entire heat exchanger is assumed to be submersed in a shell at constant temperature. A Python program was developed using the NTU method to calculate the temperature variation from the inlet to the outlet of the heat exchanger across a varied set of geometry parameters, including: number of outlet pipes, outlet pipe diameter, number of conical features, and angle of conical features. The impact of the temperature variation was accounted for in the head loss calculation within the Python program. For a set of head loss values, an optimized set of geometry parameters was found to maximize the outlet temperature.

An Efficient Mine Ventilation Solution Method Based on Minimum Independent Closed Loops

In this paper, according to the analysis of optimum circuits, we present an efficient ventilation network solution based on minimum independent closed loops. Our main contribution is optimizing the circuit dividing strategy to improve the iteration convergence and the efficiency of a single iteration. In contrast to a traditional circuit, a minimum closed loop may contain one or more co-tree branches but fewer high-resistance branches and fan branches. It is helpful in solving the problem of divergence or slow convergence for complex ventilation networks. Moreover, we analyze the dividing rules of closed loops and improve the dividing algorithm of minimum independent closed loops. Compared with the traditional Hardy Cross iteration method, the improved solution method has better iteration convergence and computation efficiency. The experimental results of real-world mine ventilation networks show that the improved solution method converges rapidly within a small number of iterations. We also investigate the influence of network complexity, iterative precision, and initial airflow on the iteration convergence.

The Hardy Cross method and its implementation in Spain

In May 1930, Hardy Cross (1885-1959) published an article called ‘Analysis of continuous frames by distributing fixed-end moments’ in the American Society of Civil Engineers (ASCE). This article proposed a new approach to Structural Theory, and its relevance could be compared to that of the Three Moments Theorem (also known as the Clapeyron Theorem). The Cross method, as this calculation methodology has been often called, had remarkable significance from the moment it came out until the 70s, when new calculation methods became popular. In the present article, we will be trying to evaluate its impact in locations far from its origins; in particular, how it was understood and formulated in Spain. As will be demonstrated, the importance of this method was extremely relevant for theconstruction of new buildings and the implementation of new industries, which started to appear in a decisive moment for the development of the country. Even though the Hardy Cross method was the most widely used methodology at the time, two other procedures were also available; namely, the Kani and the Takabeya methods, methods that would also appear in the technical bibliography of the time. Despite the infrequent implementation of these other methods, we have briefly referred to both of them in the present paper. This article aims to show the relevance of the Cross method as well as its early implementation in Spain, by using academic bibliography of that time.

Object-oriented integrated algorithms for efficient water pipe network by modified Hardy Cross technique

In this work, object-oriented integrated algorithms for an efficient flow analysis of the water pipe network are developed. This is achieved by treating the pipe network as a graph data structure with its nodes as the graph’s nodes and the pipes as the edges. The algorithm for cycle (real cycle or pseudo-cycle) extraction has been developed using nested breadth-first search that gives ordered cycles. Pseudo-loops are found using the shortest path algorithm between the nodes. Pipes are initialized loop by loop using conservation of mass at nodes. A modified Hardy Cross method is used in the proposed work with third-order convergence. The friction factor is updated for every change in discharges. The pressure calculation has been done by the graph traversal algorithm between the reference nodes and node where the pressure is to be calculated using the energy equation. The pressure at all intermediate nodes is obtained in the course of the traversal. Balanced discharges and nodal pressure in the pipe network are compared with the simultaneous loop flow adjustment method and EPANET software. The proposed work gives more efficient flow analysis than the traditional Newton–Raphson-based techniques for complex networks.