2018
DOI: 10.3390/math7010034
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Abstract: The Colebrook equation is a popular model for estimating friction loss coefficients in water and gas pipes. The model is implicit in the unknown flow friction factor, f. To date, the captured flow friction factor, f, can be extracted from the logarithmic form analytically only in the term of the Lambert W-function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert W-function also known as the Wright ω-function. The Wright ω-function is more s… Show more

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Cited by 42 publications
(103 citation statements)
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“…This is because the carefully selected Padé approximants can save computational time. For a good balance between efficiency and accuracy [9], two explicit approximations have been demonstrated based on a simplified iterative procedure with a maximal relative error of no more than 1.81% and 0.156% for the variant with one internal iterative cycle, and of no more than 0.317% and 0.0259% for two internal cycles (higher error values are for the fixed initial starting point, while lower error values are for the initial starting point given by the rational function, Equation (2), respectively). The value of the relative error, and also the tendency of its distribution, are confirmed by 2 million quasi Monte-Carlo points using the Sobol sequence for 4000 < Re < 10 8 and for 0 < ε < 0.05.…”
Section: Discussionmentioning
confidence: 99%
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“…This is because the carefully selected Padé approximants can save computational time. For a good balance between efficiency and accuracy [9], two explicit approximations have been demonstrated based on a simplified iterative procedure with a maximal relative error of no more than 1.81% and 0.156% for the variant with one internal iterative cycle, and of no more than 0.317% and 0.0259% for two internal cycles (higher error values are for the fixed initial starting point, while lower error values are for the initial starting point given by the rational function, Equation (2), respectively). The value of the relative error, and also the tendency of its distribution, are confirmed by 2 million quasi Monte-Carlo points using the Sobol sequence for 4000 < Re < 10 8 and for 0 < ε < 0.05.…”
Section: Discussionmentioning
confidence: 99%
“…The approach with Padé approximants offers an iterative procedure in which the repetition of the computationally expensive logarithmic function is avoided [24]. Using only one logarithmic function together with simple rational functions and avoiding computationally expensive functions, such as exponential functions or functions with non-integer powers, the presented method saves the processor time [7][8][9][12][13][14], which is essential for effective simulations of large pipe networks [19].…”
Section: 51mentioning
confidence: 99%
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“…From these observations, it can be stated that when used properly, W function provides a useful tool to solve Colebrook's equation analytically rather than numerically. Figure 4, shows that Brkić's solutions [18,19] are more accurate with respect to (5) than Mikata's.…”
Section: Estimation Of the Friction Factor By Solving Colebrook Equatmentioning
confidence: 93%
“…and ρ p m = (1 − H p )ρ g + H p ρ l is the mix density where p is l or s for bubble zone or slug zone, respectively. The comparative study in Brkić and Praks [26] suggests a more accurate and computationally efficient approximation than Equation (11b) for the Colebrook turbulent friction factor. However, model tuning is not the main objective for this work.…”
Section: Bubble Zonementioning
confidence: 99%