Relationship between Hazen-William coefficient and Colebrook-White friction factor : Application in water network analysis (original) (raw)
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Mathematical Problems in Engineering, 2022
In this work, we applied the modified Chun-Hui He’s algorithm to evaluate for estimation of flow friction factor f for value of friction factor by using Colebrook–White relation. The speedy, precise, and consistent evaluation of flow friction factor f are essential for evaluation of pressure dips and streams in complex network prototypes at distinct values of diameters of pipes. Friction factor estimated outcomes are applied in everyday engineering routine. Numerous computational systems tested for distinguishing of water pipe networks resolution, such as Hardy Cross method (HCM), Newton method (NM), and modified Newton method (MNM), are presented. As a novelty, a modified Newton method tabulated data, graphical results, and comparisons that are presented with different numerical schemes.
Iranian Journal of Science and Technology, Transactions of Civil Engineering, 2020
Although many explicit correlations have already been presented as alternatives to implicit Colebrook-White (C-W) formula, performances of C-W-based relations in pipe network analysis have not been investigated. In this study, 56 explicit relations available in the literature were implemented in the analysis of four water distribution networks while the benchmark solution is computed considering the implicit C-W formula. In the numerical experiment, these pipe networks were solved using three different h-based methods including h-based Newton-Raphson method, finite element method, and the gradient algorithm. In each scenario, one of these explicit relations was considered in the process of analyzing water networks. According to the obtained results, 15 explicit relations face the convergence problems which were identified as unreliable equations. Moreover, 15 explicit equations, which were successfully performed in analyzing all sample networks with the closest results to that of the benchmark solution, were introduced as the most accurate ones. Moreover, as many scenarios outperform those of the outdated explicit equation used for the same purpose in professional hydraulic solvers such as EPANET and WaterGEMS, it was recommended they be replaced with one of the explicit equations with higher accuracy. Finally, the achieved results demonstrate that the equation selected for computing Darcy-Weisbach friction factor has an inevitable impact not only on the accuracy but also on the convergence of pipe network analysis.
COMPUTATION OF FRICTION FACTOR AND ITS EFFECT ON DESIGN OF WATER PIPE LINE
IRJET, 2022
The title of our Major Project is 'calculation of friction factor in different and its effect on design of water Pipe line '. Form friction factor we can calculate friction loss and friction loss is the energy loss of fluid inflow in Pipe. When a fluid flows through a pipe it came across lot of resistance like be bends, turns, change in pitch, roughness, friction and other factors like diameter, velocity, viscosity and density of fluid causes fluid inflow to decelerate down which affect in loss of energy or simply further energy is needed for the fluid inflow. This loss of energy is known as energy loss. The significance of friction factor in pipe design is that we can be suitable to find out the pressure loss in the pipe by knowing the values of friction factor. Consequently, One can calculate the pumping power needed or demanded to carry the fluid in the pipe and thereby we can elect the pump of needed power and capacity. In this Project, by using various empirical equations, friction factor for various pipe diameter, different pipe material and by considering smooth and rough pipe is determined. The result obtained by empirical equations is validated by actual performing the test and for friction factor in the laboratory. By using various friction factor the most economic diameter is obtained. It is recommended that Darcy-Wiesbach equation is more reliable and gives the optimum diameter of the pipe network.
Urban Water Journal, 2008
An approximation of the friction factor of the Colebrook-White equation is proposed, which is expressed as a power-law function of the pipe diameter and the energy gradient and is combined with the Darcy-Weisbach equation, thus yielding an overall powerlaw equation for turbulent pressurized pipe flow. This is a generalized Manning equation, whose exponents are not unique but depend on the pipe roughness. The parameters of this equation are determined by minimizing the approximation error and are given either in tabulated form or as mathematical expressions of roughness. The maximum approximation errors are much smaller than other errors resulting from uncertainty and misspecification of design and simulation quantities and also much smaller than the errors in the original Manning and the Hazen-Willians equations. Both these can be obtained as special cases of the proposed generalized equation by setting the exponent parameters constant. However, for large roughness the original Manning equation improves in performance and becomes practically equivalent with the proposed generalized equation. Thus its use, particularly when the networks operate with free surface flow is absolutely justified. In pressurized conditions the proposed generalized Manning equation can be a valid alternative to the combination of the Colebrook-White and Darcy-Weisbach equations, having the advantage of simplicity and speed of calculation both in manual and computer mode.
International Journal of Water, 2019
Scope of the Journal IJW is a fully refereed journal providing a high profile international outlet for analyses and discussions of all aspects of water, environment and society. IJW highlights the importance and multidisciplinarity of water in our vital ecosystems. It promotes contributions in the areas of integration, synthesis and assessment in scientific research, engineering solutions and technological innovations in support of adaptation planning and management to maximize the resultant economic and social welfare, paving the way towards sustainable development. Contents IJW publishes original and review papers, technical reports, case studies, conference reports, management reports, book reviews, and notes, commentaries, opinions, and news. Contribution may be by submission or invitation, and suggestions for special issues and publications are welcome. Subject coverage: • Water and life, water in the economy, water/food security • Marine/freshwater ecosystems, aquatic/coastal biodiversity • Consumptive/non-consumptive uses of water, recycling/reuse, tourism • Cultural perceptions and health hazards of water pollution • Political economy of water, water geopolitics, symbolic dimensions • Technical/ecological economics analyses of water use, pollution, treatment • Comparative legal aspects of water resource management • Agricultural and marine pollution, water degradation, water basin analyses • Protection/rehabilitation of ground/surface water, sustainable development • Climate change, hydrology, hydrosystems engineering, desertification • Public sector strategies for pollution management • High latitude and altitude hydrology, precipitation • New technologies in water monitoring/assessment; adaptation planning, remote sensing of water cycle • Innovation in education/professional development; interdisciplinary research,
A novel method for the inclusion of pipe roughness in the Hazen-Williams equation
FME Transaction
Accurate estimation of friction losses in pipes is an important engineering task. Due to their simplicity, empirical equations are often used for determining pressure drops in pipes. One of the most widely used empirical equations for calculation of pressure drops in straight pipes is Hazen-Williams equation. In this paper, the authors have established a simple method of the inclusion of pipe roughness in Hazen-Williams equation by comparison with a widely accepted Darcy-Weisbach method coupled with Colebrook friction factor formula for developed turbulent flow.
Numerical modeling of Darcy-Weisbach friction factor and branching pipes problem
Advances in Engineering Software, 2004
First, a numerical algorithm for the friction factor in the Darcy-Weisbach pipe friction head loss formula is developed by an effective linear iteration scheme of the Colebrook-White equation, which precisely determines, with a small load of computations, the friction factor within the ranges of: 0!relative roughness!0.1 and 2!10 3 !Reynolds number!10 9. The developed subroutine can be adapted to any pipe friction loss parts of any pipe network problems. Next, the branching pipes problem is formulated as a system of non-linear equations, and an efficient, practical, and always convergent numerical algortihm for its solution is developed, in which the Darcy-Weisbach equation is used for the friction losses, the friction factor being computed by the above-mentioned algorithm. The model can handle many reservoirs which are interconnected by pipes branching from a common junction in just a couple of seconds of execution time.
The regularities of resistance and flow in pipes and wide channels
MATEC Web of Conferences, 2018
The data of hydraulic characteristics of flow are required to be more accurate to increase reliability and accident-free work of water conducting systems and hydraulic structures. One of the problems in hydraulic calculations is the determination of friction loss that is associated with the distribution of velocities over the cross section of the flow. The article presents a comparative analysis of the regularities of velocity distribution based on the logarithmic velocity profile and hydraulic resistance in pipes and open channels. It is revealed that the Karman parameter is associated with the second turbulence constant and depend on the hydraulic resistance coefficient. The research showed that the behavior of the second turbulence constant in the velocity profile is determined mainly by the Karman parameter. The attached illustrations picture the dependence of logarithmic velocity profile parameters based on different values of the hydraulic resistance coefficient. The results of the calculations were compared to the experimental-based Nikuradze formulas for smooth and rough pipes.
Explicit pipe friction factor equations: evaluation, classification, and proposal
Revista Facultad de Ingeniería Universidad de Antioquia
The Colebrook equation has been used to estimate the friction factor (f) in turbulent fluids. In this regard, many equations have been proposed to eliminate the iterative process of the Colebrook equation. The goal of this article was to perform an evaluation, classification, and proposal of the friction factor for better development of hydraulic projects. In this study, Gene Expression Programming (GEP), Newton-Raphson, and Python algorithms were applied. The accuracy and model selection were performed with the Maximum Relative Error (∆f/f), Percentage Standard Deviation (PSD), Model Selection Criterion (MSC), and Akaike Information Criterion (AIC). Of the 30 equations evaluated, the Vatankhah equation was the most accurate and simplest to obtain the friction factor with a classification of very high, reaching a value of ∆f/f<0.5% and 1.5
Improved method of determining friction factor in pipes
International Journal of Numerical Methods for Heat & Fluid Flow, 2015
Purpose– The purpose of this paper is to present an improved computational method for determining the friction factor for turbulent flow in pipes.Design/methodology/approach– Given that the absolute pipe roughness is generally constant in most systems, and that there are few changes to the pipe diameter, the proposed method uses a simplified equation for systems with a specific relative pipe roughness. The accuracy of the estimation of the friction factor using the proposed method is compared to the values obtained using the implicit Colebrook-White equation while the computational efficiency is determined by comparing the time taken to perform 300 million calculations.Findings– The proposed method offers a significant improvement in computational efficiency for its accuracy and is compared 28 of the explicit equations currently in use.Practical implications– This method enables a simplified equation to offer a significant improvement in computational efficiency for its accuracy and...