Review of explicit approximations to the Colebrook relation for flow friction

Brkić, Dejan

doi:10.1016/j.petrol.2011.02.006

Cited by 173 publications

(171 citation statements)

References 56 publications

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“…For instance, it is observed from works of Brkić [12], Winning and Coole [6] and Fang, Xu and Zhou [13], that the most accurate approximations are those by Zigrang and Sylvester [14], Serghides [15], Romeo, Royo and Monzon [9] and Buzzelli [16]. These models, with the exception of the model by Buzzelli [16], have three logarithmic functions (either natural logarithm or logarithm to base ten).…”

Section: Accuracymentioning

confidence: 99%

“…Brkić [12], based on maximum relative error criterion, classified the existing explicit models as extremely accurate (error ≤ 0.14%), very accurate (error up to 0.5%), moderately accurate (error up to 1.5%), less accurate (error up to 5%), non advisable (error up to 25%) and extremely inaccurate (error ≥ 80%). Based on this classification, the performances of several explicit models were evaluated and their accuracies are summarized in Table 1.…”

Section: Accuracymentioning

confidence: 99%

“…The turbulent portion of the Moody chart is a graphical solution of the Colebrook equation. Hence, digitizing the Moody chart [4] may have introduced secondary errors in the overall analysis [12]. This view is supported by the error margin observed by Fang, Xu and Zhou [13].…”

Section: Accuracymentioning

confidence: 99%

“…In the bid to develop accurate explicit models, sometimes, simplicity is sacrificed for accuracy without consideration for the actual computational power of such model for massive numerical requirements [12] [18]. Generally, accuracy is obtained at the expense of additional computational complexity.…”

Section: Model Complexity and Computational Efficiencymentioning

confidence: 99%

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An Accurate and Computationally Efficient Explicit Friction Factor Model

Offor¹,

Alabi²

2016

ACES

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The implicit Colebrook equation has been the standard for estimating pipe friction factor in a fully developed turbulent regime. Several alternative explicit models to the Colebrook equation have been proposed. To date, most of the accurate explicit models have been those with three logarithmic functions, but they require more computational time than the Colebrook equation. In this study, a new explicit non-linear regression model which has only two logarithmic functions is developed. The new model, when compared with the existing extremely accurate models, gives rise to the least average and maximum relative errors of 0.0025% and 0.0664%, respectively. Moreover, it requires far less computational time than the Colebrook equation. It is therefore concluded that the new explicit model provides a good trade-off between accuracy and relative computational efficiency for pipe friction factor estimation in the fully developed turbulent flow regime.

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Section: Accuracymentioning

confidence: 99%

Section: Accuracymentioning

confidence: 99%

Section: Accuracymentioning

confidence: 99%

Section: Model Complexity and Computational Efficiencymentioning

confidence: 99%

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An Accurate and Computationally Efficient Explicit Friction Factor Model

Offor¹,

Alabi²

2016

ACES

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“…The roughness of the internal surface of pipes is an important parameter in the estimation of head loss (Bagarello et al, 1995;Brkić, 2011), especially when accuracy is a prerequisite. Bench-top roughness meters are instruments used to measure surface roughness.…”

Section: Introductionmentioning

confidence: 99%

Internal surface roughness of plastic pipes for irrigation

Rocha

Marques

Camargo

et al. 2017

Rev. bras. eng. agríc. ambient.

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A B S T R A C TAssuming that a roughness meter can be successfully employed to measure the roughness on the internal surface of irrigation pipes, this research had the purpose of defining parameters and procedures required to represent the internal surface roughness of plastic pipes used in irrigation. In 2013, the roughness parameter Ra, traditional for the representation of surface irregularities in most situations, and the parameters Rc, Rq, and Ry were estimated based on 350 samples of polyvinyl chloride (PVC) and low-density polyethylene (LDPE) pipes. Pressure losses were determined from experiments carried out in laboratory. Estimations of pressure loss varied significantly according to the roughness parameters (Ra, Rc, Rq, and Ry) and the corresponding pipe diameter. Therefore, specific values of roughness for each pipe diameter improves accuracy in pressure losses estimation. The average values of internal surface roughness were 3.334 and 8.116 µm for PVC and LDPE pipes, respectively. Rugosidade interna de tubos plásticos utilizados em irrigação R E S U M OObjetivou-se, no presente estudo, estabelecer os parâmetros de amplitude das irregularidades da superfície interna de tubos plásticos para irrigação, assim como procedimentos para sua obtenção e representação utilizando-se um rugosímetro de bancada. Durante o ano de 2013 foram avaliados 350 perfis de rugosidade de tubos de PVC e polietileno de baixa densidade (PEBDL), sendo determinados os parâmetros de rugosidade Ra, clássico para a representação das irregularidades de superfícies na maioria das situações, além dos parâmetros adicionais Rc, Rq e Ry. Determinações hidráulicas de perda de carga foram realizadas em laboratório para comparação com a perda de carga obtida pela aplicação dos parâmetros de rugosidade. Evidenciou-se diferença significativa de desempenho estatístico dos parâmetros de rugosidade (Ra, Rq, Rc e Ry) de acordo com o diâmetro do tubo e, portanto, constatou-se que a adoção de valores de rugosidade específicos para cada diâmetro contribui para a exatidão das estimativas de perda de carga. A rugosidade média para tubos de PVC e PEBDL foi 3,334 e 8,116 µm, respectivamente.

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A new six parameter model to estimate the friction factor

Díaz–Damacillo¹,

Plascencia²

2019

AIChE Journal

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Significance A new explicit formula for estimating the friction factor using six parameters is proposed. The model was set up by considering the effect of residual stresses in the flow by two distinct contributions: the first is attributed to the flow velocity (Reynolds number) and the second to the duct roughness. Compared to other models, this new equation gives the best fit with Nikuradse's results. A new model to calculate the friction is proposed. The model is based on assuming the residual stresses due to the laminar to turbulent flow transition by two distinct contributions: the first is attributed to the flow velocity (Reynolds number) and the second to the duct roughness. Compared to other models, this new equation gives the best fit with respect of Nikuradse's results. The model does not consider the effect of pipe wall on the velocity distribution. © 2019 American Institute of Chemical Engineers AIChE J, 65: 1144–1148, 2019

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Review of explicit approximations to the Colebrook relation for flow friction

Cited by 173 publications

References 56 publications

An Accurate and Computationally Efficient Explicit Friction Factor Model

An Accurate and Computationally Efficient Explicit Friction Factor Model

Internal surface roughness of plastic pipes for irrigation

A new six parameter model to estimate the friction factor

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