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Journal articles on the topic 'Colebrook-White'

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Published: 4 June 2021

Last updated: 4 February 2022

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1

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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2

Keady, Grant. "Colebrook-White Formula for Pipe Flows." Journal of Hydraulic Engineering 124, no. 1 (1998): 96–97. http://dx.doi.org/10.1061/(asce)0733-9429(1998)124:1(96).

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3

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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4

Robaina, Adroaldo Dias. "ANÁLISE DE EQUAÇÕES EXPLICITAS PARA O CÁLCULO DO COEFICIENTE "f" DA FÓRMULA UNIVERSAL DE PERDA DE CARGA." Ciência Rural 22, no. 2 (1992): 157–59. http://dx.doi.org/10.1590/s0103-84781992000200006.

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Neste estudo foram comparadas três equações explícitas para o cálculo do coeficiente "f da fórmula universal de perda de carga com a equação de Cole-brook-White. A equação obtida pela substituição do segundo termo (<img border=0 width=26 height=21 src="../../../../../../img/revistas/cr/v22n2/a06img01.gif">) do argumento do logaritmo da equação de Colebrook-White, pela aproximação de Konakov (NEKRASOV, 1968), foi a que apresentou o melhor ajuste (r² = 0.9996), quando se correlacionou os resultados obtidos pelas três equações explícitas aos valores fornecidos pela fórmula de Colebrook-Whit

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5

Hafsi, Zahreddine. "Accurate explicit analytical solution for Colebrook-White equation." Mechanics Research Communications 111 (January 2021): 103646. http://dx.doi.org/10.1016/j.mechrescom.2020.103646.

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6

Mikata, Yozo, and Walter S. Walczak. "Exact Analytical Solutions of the Colebrook-White Equation." Journal of Hydraulic Engineering 142, no. 2 (2016): 04015050. http://dx.doi.org/10.1061/(asce)hy.1943-7900.0001074.

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7

Rollmann, P., and K. Spindler. "Explicit representation of the implicit Colebrook–White equation." Case Studies in Thermal Engineering 5 (March 2015): 41–47. http://dx.doi.org/10.1016/j.csite.2014.12.001.

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8

Olivares Gallardo, Alan Paulo, Rodrigo Alejandro Guerra Rojas, and Marco Antonio Alfaro Guerra. "Evaluación experimental de la solución analítica exacta de la ecuación de Colebrook-White." Ingeniería Investigación y Tecnología 20, no. 2 (2019): 1–11. http://dx.doi.org/10.22201/fi.25940732e.2019.20n2.021.

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En el presente trabajo se diseñó y construyó un sistema hidráulico para la determinación experimental delfactor de fricción en una tubería de PVC bajo flujo turbulento. Este sistema permite conducir el agua por una tubería donde se midieron el caudal y la diferencia de presión para calcular la pérdida de carga entre dos puntos de control, considerando las propiedades asociadas a la tubería como es la rugosidad relativa, su diámetro y longitud. Utilizando la ecuación de Darcy-Weisbach se determinó el factor de fricción experimental. El objetivo del presente trabajo fue evaluar en forma experime

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9

NIKITIN, Maxim Nikolaevich, Tatyana Sergeevna SOLOVYOVA, and Olga Vladimirovna SHLYAHTINA. "SOLUTIONS IN EXPLICIT FORM FOR DETERMINING THE HYDRAULIC RESISTANCE COEFFICIENT FOR TURBULENT FLOW." Urban construction and architecture 9, no. 4 (2019): 39–46. http://dx.doi.org/10.17673/vestnik.2019.04.7.

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A comparative analysis of explicit solutions of the Colebrook-White equation is carried out. The median values of relative deviations, coefficients of determination and computational complexities for each approximation were obtained. The results of the iterative solution of the Colebrook-White equation by successive substitution method were used as the intrinsic solution. Approximations by B. Eck and A.R. Vatankhah were identified as the most effective in terms of computational complexity. It was shown that widely used approximations by P.R.H. Blasius, A.D. Altshul and J. Nikuradze although si

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10

Niazkar, Majid. "Discussion of “Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function” by Dejan Brkić and Pavel Praks, Mathematics 2019, 7, 34; doi:10.3390/math7010034". Mathematics 8, № 5 (2020): 793. http://dx.doi.org/10.3390/math8050793.

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Estimating the Darcy–Weisbach friction factor is crucial to various engineering applications. Although the literature has accepted the Colebrook–White formula as a standard approach for this prediction, its implicit structure brings about an active field of research seeking for alternatives more suitable in practice. This study mainly attempts to increase the precision of two explicit equations proposed by Brkić and Praks. The results obviously demonstrate that the modified relations outperformed the original ones from nine out of 10 accuracy evaluation criteria. Finally, one of the improved e

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11

Travis, Quentin B., and Larry W. Mays. "Relationship between Hazen–William and Colebrook–White Roughness Values." Journal of Hydraulic Engineering 133, no. 11 (2007): 1270–73. http://dx.doi.org/10.1061/(asce)0733-9429(2007)133:11(1270).

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12

Giustolisi, O., L. Berardi, and T. M. Walski. "Some explicit formulations of Colebrook–White friction factor considering accuracy vs. computational speed." Journal of Hydroinformatics 13, no. 3 (2010): 401–18. http://dx.doi.org/10.2166/hydro.2010.098.

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The Colebrook–White formulation of the friction factor is implicit and requires some iterations to be solved given a correct initial search value and a target accuracy. Some new explicit formulations to efficiently calculate the Colebrook–White friction factor are presented herein. The aim of this investigation is twofold: (i) to preserve the accuracy of estimates while (ii) reducing the computational burden (i.e. speed). On the one hand, the computational effectiveness is important when the intensive calculation of the friction factor (e.g. large-size water distribution networks (WDN) in opti

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13

Qiu, Mengning, and Avi Ostfeld. "A Head Formulation for the Steady-State Analysis of Water Distribution Systems Using an Explicit and Exact Expression of the Colebrook–White Equation." Water 13, no. 9 (2021): 1163. http://dx.doi.org/10.3390/w13091163.

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Steady-state demand-driven water distribution system (WDS) solution is the bedrock for much research conducted in the field related to WDSs. WDSs are modeled using the Darcy–Weisbach equation with the Swamee–Jain equation. However, the Swamee–Jain equation approximates the Colebrook–White equation, errors of which are within 1% for ϵ/D∈[10−6,10−2] and Re∈[5000,108]. A formulation is presented for the solution of WDSs using the Colebrook–White equation. The correctness and efficacy of the head formulation have been demonstrated by applying it to six WDSs with the number of pipes ranges from 454

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14

Olivares Gallardo, Alan Paulo, Rodrigo Alejandro Guerra Rojas, and Marco Antonio Alfaro Guerra. "Evaluación de la profundidad de recursión de la solución analítica de la ecuación de Colebrook-White en la exactitud de la predicción del factor de fricción." Ingeniería Investigación y Tecnología 21, no. 4 (2020): 1–15. http://dx.doi.org/10.22201/fi.25940732e.2020.21.4.036.

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La ecuación de Colebrook, más conocida como ecuación de Colebrook-White, es valorada por su exactitud en la predicción del factor de fricción en tuberías cilíndricas en zona de flujo turbulento y por ello, es ampliamente utilizada en el cálculo de pérdidas de carga. Esta ecuación es implícita y debe ser resuelta utilizando métodos numéricos o mediante aproximaciones como la función W de Lambert. En 2015, Mikata y Walczak, propusieron una solución analítica exacta de la ecuación del factor de fricción que presenta una estructura recursiva, por lo que la búsqueda de la solución exacta de la ecua

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15

Lira, Ignacio. "On the Uncertainties Stemming from Use of the Colebrook-White Equation." Industrial & Engineering Chemistry Research 52, no. 22 (2013): 7550–55. http://dx.doi.org/10.1021/ie4001053.

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16

Sonnad, Jagadeesh R., and Chetan T. Goudar. "Constraints for Using Lambert W Function-Based Explicit Colebrook–White Equation." Journal of Hydraulic Engineering 130, no. 9 (2004): 929–31. http://dx.doi.org/10.1061/(asce)0733-9429(2004)130:9(929).

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17

MATTHEW, G. D. "THE COLEBROOK-WHITE EQUATION - AN OFT CITED RESULT BUT NEGLECTED DERIVATION ?" Proceedings of the Institution of Civil Engineers 89, no. 1 (1990): 39–45. http://dx.doi.org/10.1680/iicep.1990.5250.

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18

Augusto, Gerardo L., Alvin B. Culaba, and Renan Ma T. Tanhueco. "Pipe Sizing of District Cooling Distribution Network Using Implicit Colebrook-White Equation." Journal of Advanced Computational Intelligence and Intelligent Informatics 20, no. 1 (2016): 76–83. http://dx.doi.org/10.20965/jaciii.2016.p0076.

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An implicit solution of Colebrook-White equation was used in calculating the friction factor for commercial steel pipes using Newton-Raphson method with Reynolds number ranging from 4.0 × 103to 1.3 × 107. Initial value for iterative friction factor estimation was based on expanded form of Colebrook-White equation for larger values of Reynolds number with tolerance value of 1.0 × 10-8. Numerical results were compared with known explicit solutions and iterative procedure proposed by Lester in which, their mean difference, root-mean square deviation, mean relative error and correlation coefficien

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19

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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20

BARR, DIH. "CHANNEL TRANSFORM APPROACH FOR EXPLICIT COLEBROOK-WHITE SOLUTIONS FOR PARTIALLY FULL PIPES." Proceedings of the Institution of Civil Engineers 81, no. 1 (1986): 81–94. http://dx.doi.org/10.1680/iicep.1986.705.

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21

Aji, Anas Satria, and Rudi Siswanto. "RE-DESIGN SISTEM DISTRIBUSI AIR BERSIH DAN FIRE HYDRANT DI GEDUNG PLN UP3B KALSELTENG." JTAM ROTARY 3, no. 1 (2021): 29. http://dx.doi.org/10.20527/jtam_rotary.v3i1.3464.

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Sistem penyediaan dan distribusi air bersih di gedung-gedung bertingkat sering mengalami kendala. Tidak terkecuali PT. PLN (Persero) Gedung UP3B Kalselteng yang tidak luput dari permasalahan tersebut. Untuk itu perlu dilakukan perancangan ulang sistem distribusi dan penyediaan air bersih serta hidran kebakaran pada gedung. Tujuan dari penelitian ini antara lain menganalisis kebutuhan dan distribusi air bersih dan hidran kebakaran di dalam gedung. Kebutuhan air bersih dihitung berdasarkan jumlah penduduk yang mengkonsumsi air bersih, jenis dan jumlah unit beban alat perpipaan. Perhitungan head

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22

Lamri, Ahmed Amine. "Design of the Pressurized Tepula Channel." Applied Mechanics and Materials 797 (November 2015): 219–24. http://dx.doi.org/10.4028/www.scientific.net/amm.797.219.

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In order to calculate the linear dimension of a Tepula channel which is frequently used as water supply lines, irrigation, sanitary sewers we adopt a referential model arbitrarily chosen that gives value to the friction coefficient of 1/16. We base on the fundamental formulas of uniform turbulent flow Darcy-Weisbach, Colebrook-white. We find explicit and direct formulas for the calculation of linear dimensions of the channel.

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23

Sonnad, Jagadeesh R., and Chetan T. Goudar. "Explicit Reformulation of the Colebrook−White Equation for Turbulent Flow Friction Factor Calculation." Industrial & Engineering Chemistry Research 46, no. 8 (2007): 2593–600. http://dx.doi.org/10.1021/ie0340241.

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24

Achour, Bachir, and Sabah Sehtal. "The Rough Model Method (RMM) Application to The Computation of Normal Depth in Circular Conduit." Open Civil Engineering Journal 8, no. 1 (2014): 57–63. http://dx.doi.org/10.2174/1874149501408010057.

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A new method is presented to compute the normal depth in circular conduit. This is the rough model method (RMM). It states that the linear dimension of a conduit or channel is equal to the linear dimension of a referential rough model corrected by the effect of a non-dimensional correction factor. The method is based on the Colebrook-White and Darcy-Weisbach relationships, applicable to the entire domain of turbulent flow. From the relationship governing the flow in the rough model, the normal depth in a circular conduit is explicitly deduced.

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25

Samadianfard, Saeed. "Gene expression programming analysis of implicit Colebrook–White equation in turbulent flow friction factor calculation." Journal of Petroleum Science and Engineering 92-93 (August 2012): 48–55. http://dx.doi.org/10.1016/j.petrol.2012.06.005.

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26

Sonnad, Jagadeesh R., and Chetan T. Goudar. "Turbulent Flow Friction Factor Calculation Using a Mathematically Exact Alternative to the Colebrook–White Equation." Journal of Hydraulic Engineering 132, no. 8 (2006): 863–67. http://dx.doi.org/10.1061/(asce)0733-9429(2006)132:8(863).

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27

Eser, Dursun, and Yılmaz Dereli. "Comparisons of rotordynamic coefficients in stepped labyrinth seals by using Colebrook-White friction factor model." Meccanica 42, no. 2 (2007): 177–86. http://dx.doi.org/10.1007/s11012-006-9036-4.

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28

Santos-Ruiz, Ildeberto, Francisco-Ronay López-Estrada, Vicenç Puig, and Guillermo Valencia-Palomo. "Simultaneous Optimal Estimation of Roughness and Minor Loss Coefficients in a Pipeline." Mathematical and Computational Applications 25, no. 3 (2020): 56. http://dx.doi.org/10.3390/mca25030056.

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This paper presents a proposal to estimate simultaneously, through nonlinear optimization, the roughness and head loss coefficients in a non-straight pipeline. With the proposed technique, the calculation of friction is optimized by minimizing the fitting error in the Colebrook–White equation for an operating interval of the pipeline from the flow and pressure measurements at the pipe ends. The proposed method has been implemented in MATLAB and validated in a serpentine-shaped experimental pipeline by contrasting the theoretical friction for the estimated coefficients obtained from the Darcy–W

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29

CHEN, JJJ. "TECHNICAL NOTE. SYSTEMATIC EXPLICIT SOLUTIONS OF THE PRANDTL AND COLEBROOK-WHITE EQUAT IONS FOR PIPE FLOW." Proceedings of the Institution of Civil Engineers 79, no. 2 (1985): 383–89. http://dx.doi.org/10.1680/iicep.1985.997.

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30

Vatankhah, Ali R. "Comment on “Gene expression programming analysis of implicit Colebrook–White equation in turbulent flow friction factor calculation”." Journal of Petroleum Science and Engineering 124 (December 2014): 402–5. http://dx.doi.org/10.1016/j.petrol.2013.12.001.

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31

Mikata, Yozo, and Walter S. Walczak. "Closure to “Exact Analytical Solutions of the Colebrook-White Equation” by Yozo Mikata and Walter S. Walczak." Journal of Hydraulic Engineering 143, no. 9 (2017): 07017008. http://dx.doi.org/10.1061/(asce)hy.1943-7900.0001340.

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32

Brkić, Dejan. "Discussion of “Exact Analytical Solutions of the Colebrook-White Equation” by Yozo Mikata and Walter S. Walczak." Journal of Hydraulic Engineering 143, no. 9 (2017): 07017007. http://dx.doi.org/10.1061/(asce)hy.1943-7900.0001341.

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33

Ciprian, Bacoţiu. "The Quest for the Ideal Darcy-Weisbach Friction Factor Equation from the Perspective of a Building Services Engineer." Ovidius University Annals of Constanta - Series Civil Engineering 21, no. 1 (2019): 65–73. http://dx.doi.org/10.2478/ouacsce-2019-0008.

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Abstract The calculation of the friction factor involved in the Darcy-Weisbach equation has a key role in the accurate assessment of distributed head losses. For the turbulent flow regime, this friction factor was mathematically expressed in the form of the Colebrook-White (C-W) equation, widely accepted by engineers and scientists. Nevertheless, the C-W equation is an implicit one and must be solved using numerical methods. This is a major disadvantage for the average engineer, who always prefers an explicit equation which could be easily integrated into his familiar spreadsheet environment.

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34

Davidson, J. W., D. Savic, and G. A. Walters. "Method for the identification of explicit polynomial formulae for the friction in turbulent pipe flow." Journal of Hydroinformatics 1, no. 2 (1999): 115–26. http://dx.doi.org/10.2166/hydro.1999.0010.

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The paper describes a new regression method for creating polynomial models. The method combines numerical and symbolic regression. Genetic programming finds the form of polynomial expressions, and least squares optimization finds the values for the constants in the expressions. The incorporation of least squares optimization within symbolic regression is made possible by a rule-based component that algebraically transforms expressions to equivalent forms that are suitable for least squares optimization. The paper describes new operators of crossover and mutation that improve performance, and a

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35

CHEN, JJJ, DIH BARR, JS MONTES, and EJ SARGINSON. "DISCUSSION OF TECHNICAL NOTE. SYSTEMATIC EXPLICIT SOLUTIONS OF THE PRANDTL AND COLEBROOK-WHITE EQUAT IONS FOR PIPE FLOW." Proceedings of the Institution of Civil Engineers 81, no. 1 (1986): 159–65. http://dx.doi.org/10.1680/iicep.1986.713.

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36

More, Ajinkya A. "Analytical solutions for the Colebrook and White equation and for pressure drop in ideal gas flow in pipes." Chemical Engineering Science 61, no. 16 (2006): 5515–19. http://dx.doi.org/10.1016/j.ces.2006.04.003.

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37

Yıldırım, Gürol. "Computer-based analysis of explicit approximations to the implicit Colebrook–White equation in turbulent flow friction factor calculation." Advances in Engineering Software 40, no. 11 (2009): 1183–90. http://dx.doi.org/10.1016/j.advengsoft.2009.04.004.

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38

Chau, K. W., and S. L. Ng. "A ROBUST INTEGRATED COMPUTER-AIDED DESIGN PACKAGE FOR URBAN DRAINAGE NETWORKS." Water Science and Technology 30, no. 1 (1994): 117–20. http://dx.doi.org/10.2166/wst.1994.0012.

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This paper presents the development and verification of a computer aided design and drafting package for medium sized municipal storm water drainage systems (DRAINAGE). The numerical model, which is designed for use on microcomputers, is written in PASCAL Language and is compiled by PC software TURBO PASCAL version 6.0. The computer package for flow prediction and drainage design applies the Colebrook White Equation and the Rational Method to route pipe flows through tree-type drainage networks, automatically adjusting drainage pipe diameters to fulfil flow requirements and backwater effects.

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39

Brkić, Dejan, and Pavel Praks. "Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow." Applied Sciences 8, no. 11 (2018): 2036. http://dx.doi.org/10.3390/app8112036.

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This paper provides a new unified formula for Newtonian fluids valid for all pipe flow regimes from laminar to fully rough turbulent flow. This includes laminar flow; the unstable sharp jump from laminar to turbulent flow; and all types of turbulent regimes, including the smooth turbulent regime, the partial non-fully developed turbulent regime, and the fully developed rough turbulent regime. The new unified formula follows the inflectional form of curves suggested in Nikuradse’s experiment rather than the monotonic shape proposed by Colebrook and White. The composition of the proposed unified

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40

Beluco, Alexandre, and Edith Beatriz Camano Schettini. "An Improved Expression for a Classical Type of Explicit Approximation of the Colebrook White Equation with Only One Internal Iteration." International Journal of Hydraulic Engineering 5, no. 1 (2016): 19–23. http://dx.doi.org/10.5923/j.ijhe.20160501.03.

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Giustolisi, Orazio, and Dragan A. Savic. "A symbolic data-driven technique based on evolutionary polynomial regression." Journal of Hydroinformatics 8, no. 3 (2006): 207–22. http://dx.doi.org/10.2166/hydro.2006.020b.

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This paper describes a new hybrid regression method that combines the best features of conventional numerical regression techniques with the genetic programming symbolic regression technique. The key idea is to employ an evolutionary computing methodology to search for a model of the system/process being modelled and to employ parameter estimation to obtain constants using least squares. The new technique, termed Evolutionary Polynomial Regression (EPR) overcomes shortcomings in the GP process, such as computational performance; number of evolutionary parameters to tune and complexity of the s

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42

Ladino Moreno, Edgar Orlando, César Augusto García Ubaque, and María Camila García Vaca. "Darcy-Weisbach resistance coefficient determination using Newton-Raphson approach for android 4.0." Tecnura 23, no. 60 (2019): 52–58. http://dx.doi.org/10.14483/22487638.14929.

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Context: The article presents the friction coefficient calculation for pressure pipes, from Newton-Raphson numerical method, under JavaScript source code for Android 4.0 or higher. Methodology: The code development is based on Colebrook-White model for turbulent flows. The app also establishes the friction coefficient for laminar flows from the Poiseuille equation and determines the range for the enter flow in a transition zone (unstable flow). An algorithm of successive approximations was implemented for non-linear equation solution based on the relative roughness and Reynolds number.&#

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43

MANKOFF, KENNETH D., JASON D. GULLEY, SLAWEK M. TULACZYK, et al. "Roughness of a subglacial conduit under Hansbreen, Svalbard." Journal of Glaciology 63, no. 239 (2017): 423–35. http://dx.doi.org/10.1017/jog.2016.134.

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ABSTRACTHydraulic roughness exerts an important but poorly understood control on water pressure in subglacial conduits. Where relative roughness values are <5%, hydraulic roughness can be related to relative roughness using empirically-derived equations such as the Colebrook–White equation. General relationships between hydraulic roughness and relative roughness do not exist for relative roughness >5%. Here we report the first quantitative assessment of roughness heights and hydraulic diameters in a subglacial conduit. We measured roughness heights in a 125 m long section of a subglacial

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44

Yıldırım, Gürol. "Discussion of “Turbulent Flow Friction Factor Calculation Using a Mathematically Exact Alternative to the Colebrook–White Equation” by Jagadeesh R. Sonnad and Chetan T. Goudar." Journal of Hydraulic Engineering 134, no. 8 (2008): 1185–86. http://dx.doi.org/10.1061/(asce)0733-9429(2008)134:8(1185).

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45

Vatankhah, Ali R., and Salah Kouchakzadeh. "Discussion of “Turbulent Flow Friction Factor Calculation Using a Mathematically Exact Alternative to the Colebrook–White Equation” by Jagadeesh R. Sonnad and Chetan T. Goudar." Journal of Hydraulic Engineering 134, no. 8 (2008): 1187. http://dx.doi.org/10.1061/(asce)0733-9429(2008)134:8(1187).

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Sonnad, Jagadeesh R., and Chetan T. Goudar. "Closure to “Turbulent Flow Friction Factor Calculation Using a Mathematically Exact Alternative to the Colebrook–White Equation” by Jagadeesh R. Sonnad and Chetan T. Goudar." Journal of Hydraulic Engineering 134, no. 8 (2008): 1188. http://dx.doi.org/10.1061/(asce)0733-9429(2008)134:8(1188).

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Winning, Herbert Keith, and Tim Coole. "Improved method of determining friction factor in pipes." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 4 (2015): 941–49. http://dx.doi.org/10.1108/hff-06-2014-0173.

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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 efficien

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Rodríguez Molina, Yeraldo Andrés, and Henry Eduardo Loaísiga. "Comparación método Hardy Cross y Sofware Epanet en diseño de redes de agua potable." Revista Ciencia y Tecnología El Higo 7, no. 1 (2017): 2–10. http://dx.doi.org/10.5377/elhigo.v7i1.8615.

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Los problemas de hidráulica de tuberías (por ejemplo, proyectos de sistemas de abastecimiento de agua potable) históricamente se han venido resolviendo por medio del método “empírico” de Hazen Williams debido a su naturaleza explícita. Sin embargo, dicho método tiene restricciones para su aplicabilidad, las que muchas veces no se tienen en cuenta en el proceso de diseño. Razón por la cual es importante retomar la metodología con fundamento en la física clásica como es el caso del método de Darcy – Weisbach que no posee limitación alguna. Con ayuda de las computadoras este método deja de ser ta

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Yıldırım, Gürol. "Closure to the Discussion of “Computer-based analysis of explicit approximations to the implicit Colebrook–White equation in turbulent flow friction factor calculation” by Dejan Brkić." Advances in Engineering Software 42, no. 3 (2011): 114–15. http://dx.doi.org/10.1016/j.advengsoft.2010.10.015.

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Averkeev, I. "Об особенностях определения коэффициента эквивалентной шероховатости полимерных труб(в порядке обсуждения)". Vodosnabzhenie i sanitarnaia tehnika, № 12 (13 грудня 2019): 32–34. http://dx.doi.org/10.35776/mnp.2019.12.05.

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Рассмотрены и оценены применяемые при гидравлическом расчете критерии оценки качества внутренней поверхности трубопроводов систем водоснабжения и канализации. В частности, обосновывается целесообразность использования в качестве такого критерия коэффициента эквивалентной шероховатости Кэ. Представлены и описаны два основных способа определения параметра Кэ: с помощью гидравлических экспериментов с последующей обработкой результатов по зависимостям Прандтля и Колбрука Уайта прямым измерением профилометром среднеарифметического отклонения профиля внутренней поверхности трубы от средней линии Ra

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