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

Heydari, Asghar; Narimani, Elhameh; Pakniya, Fatemeh

doi:10.1002/ceat.201400590

Cited by 8 publications

(7 citation statements)

References 48 publications

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“…Time ratio the correlation by Heidary et al [22] (Eqs. (34) and (35)), which is the point in the top of Fig.…”

Section: Equation(s)mentioning

confidence: 98%

“…(27)) and by Sonnad and Goudar [15] (Eqs. (22) and 23) have maximum relative errors between 0.30384% and 0.99267%. The correlations by Heydari et al [22] (Eqs.…”

Section: Equation(s)mentioning

confidence: 99%

“…(22) and 23) have maximum relative errors between 0.30384% and 0.99267%. The correlations by Heydari et al [22] (Eqs. (34) and (35)), by Gregory and McEnery [32] (Eqs.…”

Section: Equation(s)mentioning

confidence: 99%

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Accuracy/Speed Analysis of Pipe Friction Factor Correlations

et al. 2019

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“…Time ratio the correlation by Heidary et al [22] (Eqs. (34) and (35)), which is the point in the top of Fig.…”

Section: Equation(s)mentioning

confidence: 98%

“…(27)) and by Sonnad and Goudar [15] (Eqs. (22) and 23) have maximum relative errors between 0.30384% and 0.99267%. The correlations by Heydari et al [22] (Eqs.…”

Section: Equation(s)mentioning

confidence: 99%

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Accuracy/Speed Analysis of Pipe Friction Factor Correlations

et al. 2019

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“…All the instrumentation, viz., temperature sensors, flow meters, and pressure sensors are connected to the datalogger The experimental setup is initially validated by comparing the experimental heat transfer coefficient and friction factor of water with that of Dittus Boelter [3,13] and Gnielinski [3] correlations for heat transfer coefficient and Colebrook correlation [14] for friction factor. After, the validation, the experiments are repeated with 20:80 EG-Water, Fe 3 O 4 /20:80 EG-Water and Hybrid nanofluids.…”

Section: Fig 5b Schematic Diagram Of the Experimental Setupmentioning

confidence: 99%

Heat Transfer Performance of EG-Water Based Fe3O4 and its Hybrid Nanofluids in a Double Pipe Heat Exchanger

Kanthimathi*,

Bhramara,

Shaik

2019

IJRTE

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Nanofluids have good potential in enhancing the heat transfer performance of conventional fluids. In the present paper, the heat transfer performance of Fe3O4 and its Hybrid mixture with Fe3O4 and SiC nanoparticles in the volume ratio of 50:50 in 20:80 Ethylene Glycol (EG) –Water as base fluid are determined experimentally and the results are compared with that of the base fluid. The volume concentration range of nanoparticles considered in the analysis is 0.01% to 0.08%. The experiment is carried under turbulent flow conditions with Reynolds number ranging from 5000 to 20000 in a Double Pipe Heat Exchanger (DPHE) with U-bend. Results indicate that the thermal conductivity of hybrid nanofluid is higher by 16.19% and its viscosity is lower by 11.6% compared to Fe3O4 /20:80 EG-Water nanofluid at an operating temperature of 45°C. The heat transfer coefficient and overall performance of hybrid nanofluid are better than Fe3O4 /20:80 EG-Water nanofluid. The overall performance of Hybrid nanofluid is 27.75% better than that of Fe3O4 /20:80 EG-Water nanofluid.

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“…The Colebrook-White (1937) (CW) equation has been considered as the most accurate approximation for the determination of the head loss coefficient (f) and has been used as a reference standard; it uses the Reynolds number (Re) and the relative roughness of the pipe (Ɛ/D) (Heydari et al, 2015;Brkić & Ćojbašić, 2016) and is valid for a wide range of applicability: 2 × 10³ < Re < 10 8 and 0 ≤ Ɛ/D ≥ 0.05. However, it is implicit in relation to f and requires an iterative process for the solution (Brkić, 2016;Brkić & Ćojbašić, 2017).…”

Section: Introductionmentioning

confidence: 99%

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

Cited by 8 publications

References 48 publications

Accuracy/Speed Analysis of Pipe Friction Factor Correlations

Accuracy/Speed Analysis of Pipe Friction Factor Correlations

Heat Transfer Performance of EG-Water Based Fe3O4 and its Hybrid Nanofluids in a Double Pipe Heat Exchanger

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

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