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

Pimenta, Bruna Dalcin; Robaina, Adroaldo Dias; Mezzomo, Wellington; Kirchner, Jardel Henrique; Ben, Luis Humberto Bahú

doi:10.1590/1807-1929/agriambi.v22n5p301-307

Cited by 38 publications

(52 citation statements)

References 30 publications

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“…The majority of the models proposed are explicit, i.e., they allow to estimate values for the friction factor directly as a function of both, the Reynolds number and the relative roughness of the pipe conducting the flow. Some good reviews on this particular subject matter are also available in the literature …”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

A new six parameter model to estimate the friction factor

Díaz–Damacillo¹,

Plascencia²

2019

AIChE Journal

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“…Tabela 1. Critério para interpretação do Índice de Concordância, do Coeficiente de Correlação e do Índice de Desempenho e suas respectivas classificações Pimenta et al (2018)…”

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Desempenho Do Medidor Ultrassônico De Vazão Em Diferentes Tubos De Policloreto De Vinila

Pimenta

Robaina

Peiter

et al. 2018

R_I

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DESEMPENHO DO MEDIDOR ULTRASSÔNICO DE VAZÃO EM DIFERENTES TUBOS DE POLICLORETO DE VINILA BRUNA DALCIN PIMENTA1; ADROALDO DIAS ROBAINA1; MARCIA XAVIER PEITER1; JARDEL HENRIQUE KIRCHNER1; WELLINGTON MEZZOMO1 E ROGÉRIO RICALDE TORRES2 1Departamento de Engenharia Rural, Pós-Graduação em Engenharia Agrícola, Universidade Federal de Santa Maria, Av. Roraima, nº 1000, Bairro Camobi, 97105-900, Santa Maria, RS, Brasil. E-mail: brunadpimenta@gmail.com; diasrobaina@gmail.com; mpeiter@gmail.com; jardelkirchner@hotmail.com; wmezzomo@hotmail.com.2Departamento de Ensino, Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul, Rua João Viterbo de Oliveira, nº 3061, Zona Rural, 95200-000, Vacaria, RS, Brasil. E-mail: rogerio.torres@vacaria.ifrs.edu.br. 1 RESUMO Os projetos relacionados à utilização ou manejo da água tem como ponto de partida a medida da vazão através de medidores específicos para sua mensuração. Um exemplo disso são os medidores de vazão ultrassônicos, os quais utilizam o método ultrassom e suas principais características são alta precisão e mobilidade, sendo de fácil utilização no meio urbano, industrial e rural. Este trabalho teve como propósito avaliar o desempenho de um medidor ultrassônico de vazão comparado com o método padrão hidrômetro, em diferentes tubos de PVC. O experimento foi realizado em um sistema de bombeamento de água em circuito fechado, no Laboratório de Hidráulica Agrícola da Universidade Federal de Santa Maria, RS. Foram utilizados tubos de PVC de distintas cores e utilizações, todos com 50 mm de diâmetro nominal e diferentes espessuras da parede. Foi atribuído o Índice de Desempenho e seu enquadramento em classes de desempenho, a fim de comparar os valores de vazão obtidos pelos dois métodos (ultrassônico e hidrômetro). Para os tubos de PVC branco e marrom, a classe de desempenho foi classificada como “Excelente”, enquanto que para o tubo de PVC azul foi “Bom”. Palavras chave: condutos forçados, hidrometria, método ultrassom. PIMENTA, B. D.; ROBAINA, A. D.; PEITER, M. X.; KIRCHNER, J. H.; MEZZOMO, W.; TORRES, R. R.PERFORMANCE OF ULTRASONIC FLOW METER IN DIFFERENT VINYL POLYCHLORIDE PIPES 2 ABSTRACT The projects related to the use or management of water have as starting point the measurement of flow through meters specific for their measurement. An example of this is the ultrasonic flowmeters, which use the ultrasound method and having as main characteristics high precision and mobility, being easy to use in urban, industrial and rural environments. The purpose of this work was to evaluate the performance of an ultrasonic flow meter compared to the standard hydrometer method in different PVC pipes. The experiment was carried out in a closed water pumping system at the Agricultural Hydraulics Laboratory of the Federal University of Santa Maria, RS. PVC tubes of different colors and uses were used, all with a nominal diameter of 50 mm and different wall thicknesses. The Performance Index and performance classes were assigned to compare the flow values obtained by the two methods (ultrasonic and hydrometer). For the white and brown PVC tubes, the performance class was rated "Excellent", while for the blue PVC pipe it was "Good". Keywords: penstocks, hydrometric, ultrasound method.

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“…Unfortunately, in our case using the input parameters in their raw form the accuracy was not at a high level without acceleration, so having previous experience with the same problem where we used Artificial Neural Network [15,16] to simulate results, we normalized parameters a=log10(Re), b=-log10(ε/D), in order to avoid discrepancy in the scale which are in raw form 1000<Re<10 8 and ε/D<<1 and after normalization 3.5<a<8 and 1.3<b<6.5 (Eureqa, software used a as genetic programming tool also suggested to us a data normalization process) [34][35][36]. The normalization gives relatively good results, and genetic programming tool generated more accurate results without knowing that the logarithmic form of the Colebrook equation was originally used but only knowing the predicted input and output datasets; Figure 3: Using our previous experience [15] with the training of the Artificial Neural Network where very good results were achieved through the normalization of parameters; a=log10(Re), b=-log10(ε/D), the genetic programming tool generated a dozen equations with different levels of accuracy and complexity, but fortunately none of them contain logarithms or non-integer power terms.…”

Section: Normalized Input Parametersmentioning

confidence: 99%

“…The main idea is to use already computed parameter b=-log10(ε/D) and to use Padé polynomial in from ln(1-θ), where θ is given by Eq. (8). In Eq.…”

Section: Possible Simplificationsmentioning

confidence: 99%

Symbolic Regression-Based Genetic Approximations of the Colebrook Equation for Flow Friction

Praks

Brkić

2018

Water

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Widely used in hydraulics, the Colebrook equation for flow friction relates implicitly to the input parameters; the Reynolds number, Re and the relative roughness of inner pipe surface, ε/D with the output unknown parameter; the flow friction factor, λ; λ=f(λ, Re, ε/D). In this paper, a few explicit approximations to the Colebrook equation; λ≈f(Re, ε/D), are generated using the ability of artificial intelligence to make inner patterns to connect input and output parameters in explicit way not knowing their nature or the physical law that connects them, but only knowing raw numbers, {Re, ε/D}→{λ}. The fact that the used genetic programming tool does not know the structure of the Colebrook equation which is based on computationally expensive logarithmic law, is used to obtain better structure of the approximations which is less demanding for calculation but also enough accurate. All generated approximations are with low computational cost because they contain a limited number of logarithmic forms used although for normalization of input parameters or for acceleration, but they are also sufficiently accurate. The relative error regarding the friction factor λ, in best case is up to 0.13% with only two logarithmic forms used. As the second logarithm can be accurately approximated by the Padé approximation, practically the same error is obtained also using only one logarithm.

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

Cited by 38 publications

References 30 publications

A new six parameter model to estimate the friction factor

A new six parameter model to estimate the friction factor

Desempenho Do Medidor Ultrassônico De Vazão Em Diferentes Tubos De Policloreto De Vinila

Symbolic Regression-Based Genetic Approximations of the Colebrook Equation for Flow Friction

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