Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes

Winning, Herbert Keith; Coole, Tim

doi:10.1007/s10494-012-9419-7

Cited by 65 publications

(100 citation statements)

References 22 publications

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“…The same situation with this distribution of the error would occur for the explicit approximations as shown by Brkić [6,7] and Winning and Coole [33]. The relative error produced by the ANN is accumulated in the zone with small values of the relative roughness ( / ) and the high values of the Reynolds number (Re).…”

Section: Accuracy Of the Estimated Resultssupporting

confidence: 59%

“…Therefore, different strategies are used to find adequate solution for Colebrook equation: iterative solution (in the present study, it was assumed that values calculated by this method are highly accurate) [6,7], use of plenty of available explicit approximations of the Colebrook equation derived by numerous mathematical or numerical approaches [6,8,32,33], using some graphical interpretations such as the Moody diagram [4], and so forth.…”

Section: Definition Of the Problemmentioning

confidence: 99%

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Intelligent Flow Friction Estimation

Brkić¹,

Ćojbašić²

2017

Preprint

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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 ( ). 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 ( / ) were transformed to logarithmic scales. The 90,000 sets of data were fed to the ANN model involving three layers: input, hidden, and output layers with, 2, 50, and 1 neurons, respectively. This configuration was capable of predicting the values of friction factor in the Colebrook equation for any given values of the Reynolds number (Re) and the relative roughness ( / ) ranging between 5000 and 10 8 and between 10 −7 and 0.1, respectively. The proposed ANN demonstrates the relative error up to 0.07% which had the high accuracy compared with the vast majority of the precise explicit approximations of the Colebrook equation.

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Section: Accuracy Of the Estimated Resultssupporting

confidence: 59%

Section: Definition Of the Problemmentioning

confidence: 99%

Intelligent Flow Friction Estimation

Brkić¹,

Ćojbašić²

2017

Preprint

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“…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%

“…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%

“…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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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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Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes

Cited by 65 publications

References 22 publications

Intelligent Flow Friction Estimation

Intelligent Flow Friction Estimation

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

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

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Explicit Friction Factor Accuracy and Computational Efficiency for Turbulent Flow in Pipes

Cited by 65 publications

References 22 publications

Intelligent Flow Friction Estimation

Intelligent Flow Friction Estimation

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

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

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Product

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Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations