Discussion of “Gene expression programming analysis of implicit Colebrook–White equation in turbulent flow friction factor calculation” by Saeed Samadianfard [J. Pet. Sci. Eng. 92-93 (2012), 48-55]

Brkić, Dejan

doi:10.31219/osf.io/zpr2e

Cited by 6 publications

(13 citation statements)

References 9 publications

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“…Some of the existing equations of turbulent friction factor were implicit. The formula of Prandtl is based on experimental data elicited from smooth pipes resulting in an implicit equation of the friction factor for turbulent regime [4,5]: 1 ffiffiffi F p ¼ 2 log 10 Re ffiffiffi F p 2:51 ¼ 2 log 10 Re ffiffiffi F p À 0:8…”

Section: Introductionmentioning

confidence: 99%

“…In fact, this equation is a combination of the Prandtl equation for smooth pipes and the von Karman equation for rough pipes. Prandtl's and von Karman's equations are also known as Nikuradse-Prandtl-Karman (NPK) equations [4][5][6][7]. Although the Colebrook or Colebrook-White equation is considered as an acceptable standard for testing single-phase friction factor correlations in turbulent regimes, it is not easy to calculate F using this equation.…”

Section: Introductionmentioning

confidence: 99%

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Explicit Determinations of the Colebrook Equation for the Flow Friction Factor by Statistical Analysis

2015

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The implicit Colebrook equation is considered as a fundamental equation for estimating the friction factor for turbulent flows in pipes. A large number of simple and accurate explicit approximations cover just a limited area of turbulent regime inside rough or smooth pipes. Here, three explicit approximations of the friction factor were determined. The friction factor data were fitted into polynomials using the response surface design of Minitab software. To reduce the relative error of the first approximation compared with the implicit Colebrook equation, the domain was divided into two regions based on the Reynolds number (Re). To compare the accuracy and complexity of the approximations with existing relations, advanced comparison analysis based on the relative error was performed. The second set of approximations defined in two ranges of Re demonstrated high accuracy and a satisfying complexity index.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Explicit Determinations of the Colebrook Equation for the Flow Friction Factor by Statistical Analysis

2015

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“…Genetic optimization is an alternative to the traditional optimal search approaches which make difficult finding the global optimum for nonlinear and multimodal optimization problems. Thus, genetic algorithms have been successful for example in solving combinatorial problems, control applications of parameter identification and control structure design, as well as in many other areas [47][48][49][50][51][52].…”

Section: Genetic Algorithm Optimization Techniquementioning

confidence: 99%

“…in Eq. (1) instead of approximately equal sign "≈" can be treated as accurate only conditionally [48]. In this paper, iterative solution of Colebrook's equation (λ0) after enough number of iterations will be treated as accurate and will be used for comparison as standard of accuracy where accuracy of friction factor (λ) calculated using the shown approximations will be compared with it.…”

Section: Introductionmentioning

confidence: 99%

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Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

Brkić¹,

Ćojbašić²

2017

Preprint

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Today, Colebrook's equation is mostly accepted as an informal standard for modeling of turbulent flow in hydraulically smooth and rough pipes including transient zone in between. The empirical Colebrook's equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of inner pipe surface (ε/D). It is implicit in unknown friction factor (λ). Implicit Colebrook's equation cannot be rearranged to derive friction factor (λ) directly and therefore it can be solved only iteratively [λ=f(λ, R, ε/D)] or using its explicit approximations [λ≈f(R, ε/D)]. Of course, approximations carry in certain error compared with the iterative solution where the highest level of accuracy can be reached after enough number of iterations. The explicit approximations give a relatively good prediction of the friction factor (λ) and can reproduce accurately Colebrook's equation and its Moody's plot. Usually, more complex models of approximations are more accurate and vice versa. In this paper, numerical values of parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After this improvement computational burden stays unchanged while accuracy of approximations increases in some of the cases very significantly.

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Solution of the Implicit Colebrook Equation for Flow Friction Using Excel

Brkić

2017

Preprint

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Empirical Colebrook equation implicit in unknown flow friction factor (λ) is an accepted standard for calculation of hydraulic resistance in hydraulically smooth and rough pipes. The Colebrook equation gives friction factor (λ) implicitly as a function of the Reynolds number (Re) and relative roughness (ε/D) of inner pipe surface; i.e. λ 0 =f(λ 0 , Re, ε/D). The paper presents a problem that requires iterative methods for the solution. In particular, the implicit method used for calculating the friction factor λ 0 is an application of fixedpoint iterations. The type of problem discussed in this "in the classroom paper" is commonly encountered in fluid dynamics, and this paper provides readers with the tools necessary to solve similar problems. Students' task is to solve the equation using Excel where the procedure for that is explained in this "in the classroom" paper. Also, up to date numerous explicit approximations of the Colebrook equation are available where as an additional task for students can be evaluation of the error introduced by these explicit approximations λ≈f(Re, ε/D) compared with the iterative solution of implicit equation which can be treated as accurate.

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Discussion of “Gene expression programming analysis of implicit Colebrook–White equation in turbulent flow friction factor calculation” by Saeed Samadianfard [J. Pet. Sci. Eng. 92-93 (2012), 48-55]

Cited by 6 publications

References 9 publications

Explicit Determinations of the Colebrook Equation for the Flow Friction Factor by Statistical Analysis

Explicit Determinations of the Colebrook Equation for the Flow Friction Factor by Statistical Analysis

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

Solution of the Implicit Colebrook Equation for Flow Friction Using Excel

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Discussion of “Gene expression programming analysis of implicit Colebrook–White equation in turbulent flow friction factor calculation” by Saeed Samadianfard [J. Pet. Sci. Eng. 92-93 (2012), 48-55]

Cited by 6 publications

References 9 publications

Explicit Determinations of the Colebrook Equation for the Flow Friction Factor by Statistical Analysis

Explicit Determinations of the Colebrook Equation for the Flow Friction Factor by Statistical Analysis

Evolutionary Optimization of Colebrook&rsquo;s Turbulent Flow Friction Approximations

Solution of the Implicit Colebrook Equation for Flow Friction Using Excel

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Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations