An Accurate and Computationally Efficient Explicit Friction Factor Model

Offor, Uchechukwu Herbert; Alabi, Sunday Boladale

doi:10.4236/aces.2016.63024

Cited by 35 publications

(51 citation statements)

References 22 publications

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“…Brkić (2011a), Winning & Coole (2013) and Offor & Alabi (2016) analyzing explicit equations of the f, found that the RE values of Rao & Kumar's (2007) equation were the highest in relation to all the explicit equations analyzed in their research, being consistent with what was obtained in this study.…”

Section: Methodssupporting

confidence: 86%

“…Models 2,3,5,9,14,23,27,29,28, and 20 presented an MRE above 1.00%, with the last two standing out owing to value of 2.375% for an Ɛ/D of 10 -6 and an Re of 4 × 10³. For Offor & Alabi (2016), the minimum value of RE was 0.005% for an Ɛ/D of 5 × 10 -6 and an Re of 10 8 , and the maximum RE value was 2.128% for an Ɛ/D of 5 × 10 -6 and an Re of 4 × 10³.…”

Section: Resultsmentioning

confidence: 94%

“…1. The equations of Chen (1979), Shacham (1980), Sonnad & Goudar (2006), Buzzelli (2008), Vantankhah & Kouchakzadeh (2008), Fang et al (2011), and Offor & Alabi (2016 showed higher performance indexes and precision when compared to the Colebrook-White approximation.…”

Section: Discussionmentioning

confidence: 96%

“…2. The equation of Offor & Alabi (2016), in relation to the explicit models analyzed, stood out from the others, presenting the highest performance index and precision, apart from covering the widest range of Reynolds number applicability and showing the highest relative roughness, and, therefore, can be used as an alternative to the implicit Colebrook-White equation.…”

Section: Discussionmentioning

confidence: 99%

See 3 more Smart Citations

Performance of explicit approximations of the coefficient of head loss for pressurized conduits

Pimenta

Robaina

Mezzomo

et al. 2018

Rev. bras. eng. agríc. ambient.

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A B S T R A C TOne 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 approximations of the f for pressurized conduits in comparison to the Colebrook-White formulation, determining the most precise ones so that they can be used as an alternative solution that is valid for the turbulent flow regime. Twenty nine explicit equations found in the literature were analysed, determining the f through the Reynolds number in the range of 4 × 10 3 ≤ Re ≤ 10 8 and a relative roughness (Ɛ/D) of 10 -6 ≤ Ɛ/D ≤ 5 × 10 -2 , and obtaining 160 points for each equation. The performance index and relative error of the formulations were analyzed in relation to the Colebrook-White equation. Considering the equations analyzed, we found seven that presented excellent performance and high precision, highlighting the formulation of Offor & Alabi, which can be used as an alternative to the Colebrook-White standard equation.Desempenho de aproximações explícitas do coeficiente de perda de carga para condutos pressurizados R E S U M O Um dos parâmetros envolvido no dimensionamento de sistemas hidráulicos pressurizados é a perda de carga das tubulações. Essa verificação pode ser realizada através da formulação de Darcy-Weisbach, que considera um coeficiente de perda de carga (f) que pode ser mensurado pela equação implícita de Colebrook-White. No entanto, para essa determinação é necessário utilizar métodos numéricos ou o diagrama de Moody. Devido a isso, numerosas aproximações explícitas são propostas para superar essa limitação. Nesse sentido, o objetivo desse trabalho é analisar as aproximações explícitas do f para condutos pressurizados em comparação a formulação de Colebrook-White, determinando as mais precisas para que possam ser uma solução alternativa, válidas para o regime de fluxo turbulento. Foram analisadas 29 equações explícitas encontradas na literatura, determinando o f através do número de Reynolds (Re) na faixa de 4 × 10 3 ≤ Re ≤ 10 8 e rugosidade relativa (Ɛ/D) de 10 -6 ≤ Ɛ/D ≤ 5 × 10 -2 , obtendo 160 pontos para cada equação. O índice de desempenho e o erro relativo das formulações foram analisados em relação a equação de Colebrook-White. Considerando as equações analisadas, sete apresentaram excelente desempenho e alta precisão, destacando a formulação de Offor & Alabi, a qual pode ser utilizada como alternativa à equação padrão de Colebrook-White.

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Section: Methodssupporting

confidence: 86%

Section: Resultsmentioning

confidence: 94%

Section: Discussionmentioning

confidence: 96%

Section: Discussionmentioning

confidence: 99%

See 2 more Smart Citations

Performance of explicit approximations of the coefficient of head loss for pressurized conduits

Pimenta

Robaina

Mezzomo

et al. 2018

Rev. bras. eng. agríc. ambient.

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show abstract

“…Any effort to present a simple full-range solution for the friction factor would be of practical importance. Offor & Alabi (2016) suggested a new equation for the friction factor that focuses on precision and computational efficiency. Vatankhah (2018) proposed analytical solutions for the Colebrook equation with a minimal number of natural logarithms and noninteger powers (lower computational cost).…”

Section: Introductionmentioning

confidence: 99%

The Performance of Explicit Formulas for Determining the Darcy-Weisbach Friction Factor

et al. 2020

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The Darcy-Weisbach equation is the most recommended equation for determining the pressure loss in pressurized pipes because of its wide applicability. However, one of the largest obstacles to implementing this equation is the friction factor (f) calculation. This factor can be precisely determined using the Colebrook equation, which is implicit. Thus, the objective of this study was to compare six explicit equations for calculating the Darcy-Weisbach friction factor with the implicit Colebrook equation based on the relative error. Based on the results, the equations of Vatankhah and Offor & Alabi were the most highly recommended. These six explicit formulas showed a mean relative error of less than ± 1% compared to the Colebrook equation, except for the Swamee and Jain equation, for which the laminar regime generated a mean relative error of 1.83%.

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Modelling the Darcy–Weisbach friction factor and the energy gradient of the lateral line*

Jardim

Silva

et al. 2021

Irrigation and Drainage

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The objective was to adjust explicit mathematical models to determine the friction factor ( f ). Besides, an adaptation of the Blasius model is presented and an application of the Darcy-Weisbach equation to estimate the energy loss along the lateral line for four types of microsprinklers. f was determined by the model of Offor and Alabi and the model of Blasius for velocities between 0.5 to 3.0 m s À1 and internal pipe diameters of 0.0130, 0.0161, 0.0206, 0.0270, 0.0288, and 0.0368 m. The friction factor determined by Offor and Alabi was associated with the pipe diameters utilizing regression, and based on that an adaptation to the Blasius model was proposed. From the results of f, the energy and flow gradient along the lateral line for four NaanDanJain microsprinklers was simulated. The models of Offor and Alabi, Blasius, and Adapted Blasius showed excellent precision in determining f. The results of unit head loss, determined by the three mathematical models, showed dispersion close to zero among the pairs, showing a high correlation between the models (R 2 = 0.99).The Blasius equation is the most suitable to be inserted into the Darcy-Weisbach model to determine the maximum length of the lateral line.

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An Accurate and Computationally Efficient Explicit Friction Factor Model

Cited by 35 publications

References 22 publications

Performance of explicit approximations of the coefficient of head loss for pressurized conduits

Performance of explicit approximations of the coefficient of head loss for pressurized conduits

The Performance of Explicit Formulas for Determining the Darcy-Weisbach Friction Factor

Modelling the Darcy–Weisbach friction factor and the energy gradient of the lateral line*

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