Computer-based analysis of explicit approximations to the implicit Colebrook–White equation in turbulent flow friction factor calculation

Yıldırım, Gürol

doi:10.1016/j.advengsoft.2009.04.004

Cited by 68 publications

(34 citation statements)

References 24 publications

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“…Yıldırım [14] conducted comprehensive analysis of existing correlations for single-phase friction but he used Techdig 2.0 software to read date from the Moody diagram which caused remarkable reading error. One must be always aware that the Moody diagram [3] was constructed using Colebrook's equation [2] and not opposite.…”

Section: Explicit Approximations Of Colebrook's Equationmentioning

confidence: 99%

“…One must be always aware that the Moody diagram [3] was constructed using Colebrook's equation [2] and not opposite. After all, main conclusion of all papers [10][11][12][13][14][15][16] is that the relative error, δ, is non-uniformly distributed over the domain of the Reynolds number (R) and the relative roughness (ε/D).…”

Section: Explicit Approximations Of Colebrook's Equationmentioning

confidence: 99%

“…Accuracy of existing approximations of Colebrook's equation was thoroughly checked by many researchers [10][11][12][13][14][15][16]. Yıldırım [14] conducted comprehensive analysis of existing correlations for single-phase friction but he used Techdig 2.0 software to read date from the Moody diagram which caused remarkable reading error.…”

Section: Explicit Approximations Of Colebrook's Equationmentioning

confidence: 99%

“…The Colebrook equation (1) relates hydraulic flow friction (λ) through Reynolds number (R) and relative roughness (ε/D) of inner pipe surface but in implicit way; λ=f(λ, R, ε/D) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. On the other hand, to express flow friction (λ) in implicit way a number of approximations can be used .…”

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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Section: Explicit Approximations Of Colebrook's Equationmentioning

confidence: 99%

Section: Explicit Approximations Of Colebrook's Equationmentioning

confidence: 99%

Section: Explicit Approximations Of Colebrook's Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

Brkić¹,

Ćojbašić²

2017

Preprint

View full text Add to dashboard Cite

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“…The Colebrook Equation (1) relates hydraulic flow friction (λ) through the Reynolds number (R) and the relative roughness (ε/D) of the inner pipe surface, but in an implicit way; λ = f(λ, R, ε/D) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. On the other hand, to express flow friction (λ) in an explicit way, a number of approximations can be used; λ ≈ f(R, ε/D) .…”

Section: Introductionmentioning

confidence: 99%

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

Brkić¹,

Ćojbašić²

2017

Preprint

View full text Add to dashboard Cite

This paper presents evolutionary optimization of explicit approximations of the empirical Colebrook's equation that is used for the calculation of the turbulent friction factor (λ), i.e., for the calculation of turbulent hydraulic resistance in hydraulically smooth and rough pipes including the transient zone between them. The empirical Colebrook's equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of the inner pipe surface (ε/D). It is implicit in the unknown friction factor (λ). The implicit Colebrook's equation cannot be rearranged to derive the 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)], which introduce certain error compared with the iterative solution. The optimization of explicit approximations of Colebrook's equation is performed with the aim to improve their accuracy, and the proposed optimization strategy is demonstrated on a large number of explicit approximations published up to date where numerical values of the parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After that improvement, the computational burden stays unchanged while the accuracy of approximations increases in some of the cases very significantly.

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