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Thematische Bibliographien / Colebrook equation

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Auswahl der wissenschaftlichen Literatur zum Thema „Colebrook equation“

Autor: Grafiati

Veröffentlicht am 5. Juni 2025

Zuletzt aktualisiert am 2. August 2025

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Zeitschriftenartikel zum Thema "Colebrook equation"

1

Zigrang, D. J., and N. D. Sylvester. "A Review of Explicit Friction Factor Equations." Journal of Energy Resources Technology 107, no. 2 (1985): 280–83. http://dx.doi.org/10.1115/1.3231190.

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A review of the explicit friction factor equations developed to replace the Colebrook equation is presented. Explicit friction factor equations are developed which yield a very high degree of precision compared to the Colebrook equation. A new explicit equation, which offers a reasonable compromise between complexity and accuracy, is presented and recommended for the calculation of all turbulent pipe flow friction factors for all roughness ratios and Reynold’s numbers.

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2

Praks, Pavel, and Dejan Brkić. "Advanced Iterative Procedures for Solving the Implicit Colebrook Equation for Fluid Flow Friction." Advances in Civil Engineering 2018 (December 10, 2018): 1–18. http://dx.doi.org/10.1155/2018/5451034.

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The empirical Colebrook equation from 1939 is still accepted as an informal standard way to calculate the friction factor of turbulent flows (4000 < Re < 108) through pipes with roughness between negligible relative roughness (ε/D ⟶ 0) to very rough (up to ε/D = 0.05). The Colebrook equation includes the flow friction factor λ in an implicit logarithmic form, λ being a function of the Reynolds number Re and the relative roughness of inner pipe surface ε/D: λ = f(λ, Re, ε/D). To evaluate the error introduced by the many available explicit approximations to the Colebrook equation, λ ≈ f(Re

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3

Zeghadnia, Lotfi, Bachir Achour та Jean Robert. "Discussion of “Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function” by DejanBrkić; and Pavel Praks, Mathematics 2019, 7, 34; doi:10.3390/math7010034". Mathematics 7, № 3 (2019): 253. http://dx.doi.org/10.3390/math7030253.

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The Colebrook-White equation is often used for calculation of the friction factor in turbulent regimes; it has succeeded in attracting a great deal of attention from researchers. The Colebrook–White equation is a complex equation where the computation of the friction factor is not direct, and there is a need for trial-error methods or graphical solutions; on the other hand, several researchers have attempted to alter the Colebrook-White equation by explicit formulas with the hope of achieving zero-percent (0%) maximum deviation, among them Dejan Brkić and Pavel Praks. The goal of this paper is

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Praks, Pavel, та Dejan Brkić. "Suitability for coding of the Colebrook’s flow friction relation expressed by symbolic regression approximations of the Wright-ω function". Reports in Mechanical Engineering 1, № 1 (2020): 174–79. http://dx.doi.org/10.31181/rme200101174p.

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This article analyses a form of the empirical Colebrook’s pipe flow friction equation given originally by the Lambert W-function and recently also by the Wright ω-function. These special functions are used to explicitly express the unknown flow friction factor of the Colebrook equation, which is in its classical formulation given implicitly. Explicit approximations of the Colebrook equation based on approximations of the Wright ω-function given by an asymptotic expansion and symbolic regression were analyzed in respect of speed and accuracy. Numerical experiments on 8 million Sobol’s quasi-Mon

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5

Pimenta, Bruna D., Adroaldo D. Robaina, Marcia X. Peiter, Wellington Mezzomo, Jardel H. Kirchner, and Luis H. B. Ben. "Performance of explicit approximations of the coefficient of head loss for pressurized conduits." Revista Brasileira de Engenharia Agrícola e Ambiental 22, no. 5 (2018): 301–7. http://dx.doi.org/10.1590/1807-1929/agriambi.v22n5p301-307.

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ABSTRACT One of the parameters involved in the design of pressurized hydraulic systems is the pressure drop in the pipes. The verification of the pressure drop can be performed through the Darcy-Weisbach formulation, which considers a coefficient of head loss (f) that can be estimated by the implicit Colebrook-White equation. However, for this determination, it is necessary to use numerical methods or the Moody diagram. Because of this, numerous explicit approaches have been proposed to overcome such limitation. In this sense, the objective of this study was to analyze the explicit approximati

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6

Cahyono, Muhammad. "Hybrid Models for Solving the Colebrook–White Equation Using Artificial Neural Networks." Fluids 7, no. 7 (2022): 211. http://dx.doi.org/10.3390/fluids7070211.

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This study proposes hybrid models to solve the Colebrook–White equation by combining explicit equations available in the literature to solve the Colebrook–White equation with an error function. The hybrid model is in the form of fH=fo−eA. fH is the friction factor value f predicted by the hybrid model, fo is the value of f calculated using several explicit formulas for the Colebrook–White equation, and eA is the error function determined using the neural network procedures. The hybrid equation consists of a series of hyperbolic tangent functions whose number corresponds to the number of neuron

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Brkić, Dejan, and Žarko Ćojbašić. "Intelligent Flow Friction Estimation." Computational Intelligence and Neuroscience 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/5242596.

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Nowadays, the Colebrook equation is used as a mostly accepted relation for the calculation of fluid flow friction factor. However, the Colebrook equation is implicit with respect to the friction factor (λ). In the present study, a noniterative approach using Artificial Neural Network (ANN) was developed to calculate the friction factor. To configure the ANN model, the input parameters of the Reynolds Number (Re) and the relative roughness of pipe (ε/D) were transformed to logarithmic scales. The 90,000 sets of data were fed to the ANN model involving three layers: input, hidden, and output lay

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Falade, A., A. Olaberinjo, M. Oyewola, F. Babalola, and S. Adaramola. "KPIM of Gas Transportation: Robust Modification of Gas Pipeline Equations." Latvian Journal of Physics and Technical Sciences 45, no. 5 (2008): 39–47. http://dx.doi.org/10.2478/v10047-008-0024-4.

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KPIM of Gas Transportation: Robust Modification of Gas Pipeline Equations Studies of the flow conditions of natural gases in pipelines have led to the development of complex equations for relating the volume transmitted through a gas pipeline to the various factors involved, thus deciding the optimum pressures and pipeline dimensions to be used. From equations of this type, various combinations of pipe diameter and wall thickness for a desired rate of gas throughput can be calculated. This research work presents modified forms of the basic gas flow equation for horizontal flow developed by Wey

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Clamond, Didier. "Efficient Resolution of the Colebrook Equation." Industrial & Engineering Chemistry Research 48, no. 7 (2009): 3665–71. http://dx.doi.org/10.1021/ie801626g.

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10

López-Silva, Maiquel, Hernández Dayma Sadami Carmenates, Nancy Delgado-Hernández, and Bereche Nataly Noelia Chunga. "Explicit pipe friction factor equations: evaluation, classification, and proposal." Revista Facultad de Ingeniería, Universidad de Antioquia, no. 111 (October 9, 2023): 38–47. https://doi.org/10.17533/udea.redin.20230928.

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The Colebrook equation has been used to estimate the friction factor (<em>f</em>) 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 (∆<em>f/f</em>), Percentage Standard Deviation (PS

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Bücher zum Thema "Colebrook equation"

1

Kumar, M. A. Solve Implicit Equations Inside Your Excel Worksheet: Solve Colebrook and Other Implicit Equations in Seconds! CreateSpace Independent Publishing Platform, 2010.

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Buchteile zum Thema "Colebrook equation"

1

Kumbhakar, Manotosh, and Vijay P. Singh. "Numerical Solutions for the Colebrook Equation." In Homotopy-Based Methods in Water Engineering. CRC Press, 2023. http://dx.doi.org/10.1201/9781003368984-5.

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2

Rapp, Christoph. "Steady pipe flow." In Hydraulics in Civil Engineering. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-54860-4_11.

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AbstractChapter 11 is dedicated to steady pipe flow; however, the derivation of the Prandtl-Colebrook equations has been shifted to the Appendix. Hydraulic losses are considered for both, laminar and turbulent flow and the friction coefficient introduced into the energy equation, which is consequently depicted through energy diagrams. Minor losses, pumps and turbines are considered as local impacts and pipe junctions round up this important topic that is also accompanied by codes, experiments, and examples.

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Ayed, Lazhar, Oussama Choura, Zahreddine Hafsi, and Sami Elaoud. "A Haaland Based Explicit Solution for Colebrook-White Equation." In Lecture Notes in Mechanical Engineering. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-14615-2_70.

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Mileikovskyi, Viktor, and Tetiana Tkachenko. "Precise Explicit Approximations of the Colebrook-White Equation for Engineering Systems." In Lecture Notes in Civil Engineering. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-57340-9_37.

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Konferenzberichte zum Thema "Colebrook equation"

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Assunção, Germano Scarabeli Custódio, Dykenlove Marcelin, João Carlos Von Hohendorff Filho, Denis José Schiozer, and Marcelo Souza De Castro. "Friction Factor Equations Accuracy for Single and Two-Phase Flows." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18682.

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Abstract Estimate pressure drop throughout petroleum production and transport system has an important role to properly sizing the various parameters involved in those complex facilities. One of the most challenging variables used to calculate the pressure drop is the friction factor, also known as Darcy–Weisbach’s friction factor. In this context, Colebrook’ s equation is recognized by many engineers and scientists as the most accurate equation to estimate it. However, due to its computational cost, since it is an implicit equation, several explicit equations have been developed over the decad

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2

Yen, Tey Wah, Tan Lit Ken, and Ang Chun Kit. "A Highly Computationally Efficient Explicit-Iterative Hybrid Algorithm for Colebrook-White Equation." In ICSCA 2018: 2018 7th International Conference on Software and Computer Applications. ACM, 2018. http://dx.doi.org/10.1145/3185089.3185091.

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3

Yetiskin, Begum, and Sibel Arslan. "Approximation of the Colebrook Equation for Flow Friction with Immune Plasma Programming." In 2022 30th Signal Processing and Communications Applications Conference (SIU). IEEE, 2022. http://dx.doi.org/10.1109/siu55565.2022.9864682.

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4

Long, Li, Ze Wang, Xuelin Yang, and Dan Li. "Transferring Methods of Efficiency for Hydraulic Machines Using Model Based on Smooth-Pipes Flow." In ASME 2008 Fluids Engineering Division Summer Meeting collocated with the Heat Transfer, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/fedsm2008-55139.

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The scope of Reynolds number in the model experiment and the serviceability on Blasius friction factor equation were analyzed. The exponent of prototype–model scale and the proper distribution of the friction and vortex head loss in Moody’s formula were studied. It was consider that the friction head loss could not be reduced with the accession of vortex head loss. New conversion method of hydraulic efficiency for prototype pump performance using model based on Prandtl-Colebrook formula with a wide Reynolds number range and Nikuradse’s experiments to be consistent with was proposed The convers

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5

Zang, Jinguang, Xiao Yan, Shanfang Huang, Zejun Xiao, and Yanping Huang. "Analytical Prediction of Turbulent Friction Factor in Circular Pipe Under Supercritical Conditions." In 2012 20th International Conference on Nuclear Engineering and the ASME 2012 Power Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/icone20-power2012-55159.

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An analytical method was proposed for the prediction of the turbulent friction factor in a circular pipe under supercritical conditions. The friction factor equation was based on the new wall function by Van Direst transformation which is widely used in compressed flow. The law of the wall of two layers was used and integrated over the entire flow area to obtain the algebraic form of the turbulent friction factor. The new turbulent friction formula was first adjusted to Colebrook equation in isothermal flow at supercritical pressures. And then it was validated in heated supercritical flow by s

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6

Rajvanshi, Saurabh, Rajiv Nischal, Bulusu V. R. V. Prasad, et al. "A Mathematical Modelling of the Plunger Lift Considering Effects of Fluid Friction and Plunger Travel Velocity." In Gas & Oil Technology Showcase and Conference. SPE, 2023. http://dx.doi.org/10.2118/214043-ms.

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Abstract Plunger lift technique is a well-known, widely accepted and economical artificial lift alternative, especially in deliquification of gas wells and to increase the efficiency of intermittently flowing oil wells. This study includes impact of fluid friction losses and variable plunger travel velocity in mathematical modelling of plunger lift design. The design of plunger lift system, in most models, is simulated by a fix value of fluid friction losses based on plunger velocity, which does not consider the variable effects of the friction factor calculation based on Colebrook equation or

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Brackbill, Timothy P., and Satish G. Kandlikar. "Effects of Roughness on Turbulent Flow in Microchannels and Minichannels." In ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2008. http://dx.doi.org/10.1115/icnmm2008-62224.

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The effect of roughness ranging from smooth to 24% relative roughness on laminar flow has been examined in previous works by the authors. It was shown that using a constricted parameter, εFP, the laminar results were predicted well in the roughened channels ([1],[2],[3]). For the turbulent regime, Kandlikar et al. [1] proposed a modified Moody diagram by using the same set of constricted parameters, and using the modification of the Colebrook equation. A new roughness parameter εFP was shown to accurately portray the roughness effects encountered in laminar flow. In addition, a thorough look a

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Ghazi, Nima, and Julia M. Race. "Techno-Economic Modelling and Analysis of CO2 Pipelines." In 2012 9th International Pipeline Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/ipc2012-90455.

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The main focus of this paper is on techno-economic modeling and analysis of CO2 pipelines, as it strives to develop a thorough understanding of the essential fluid-mechanics variables involved in modeling and analysis of such pipelines. The authors investigate and analyze the reasons behind the variations in the techno-economic results generated from seven different techno-economic models which are commonly used for construction and operation of CO2 pipelines. Such variations often translate into tens or, at times, hundreds of millions of dollars in terms of initial financial estimates at the

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Zhang, Yifan, Zeyu Yan, Pradeepkumar Ashok, Dongmei Chen, and Eric van Oort. "Drilling Hard Abrasive Rock Formations with Differential Hydraulic Hammers: Dynamic Modeling of Drillstring Vibrations for ROP Optimization." In IADC/SPE International Drilling Conference and Exhibition. SPE, 2022. http://dx.doi.org/10.2118/208670-ms.

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Abstract In deep oil, gas, and geothermal well construction, percussion drilling is sometimes used to improve rate of penetration (ROP) and promote drilling efficiency when breaking hard abrasive rocks (with a uniaxial compressive strength (UCS) &gt; 25 kpsi). Down-the-hole (DTH) differential pressure hydraulic hammers can be used to convert the hydraulic energy of the drilling mud into the percussion energy necessary for rock destruction. The appeal of using DTH hammers for deep hard rock drilling is that this is a highly mature, low-cost, and proven technology. Lacking, however, is a goo

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Pease, Leonard F., Judith Ann Bamberger, and Michael J. Minette. "Jet Erosion of Particle Beds: Projecting Critical Suspension Velocities From Effective Clearing / Cleaning Radii." In ASME 2022 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/fedsm2022-85965.

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Abstract Here we explore the relationship between effective cleaning/clearing radii, ECR, and critical suspension velocities, Ucs. Although one set of physics controls both the radial extent of erosion (i.e., the ECR) and the velocity needed to erode from the center of jet impingement to any given location (i.e., Ucs, typically defined from nozzle center to the vessel center), the relationship between these two remains unexplored quantitatively for nominally non-cohesive solids. Here we advance the model of Kuhn, et al., (PNNL-22816, 2013) as described by Pease, et al. (FEDSM2017-69444, 2017)

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