scholarly journals COMPARAÇÃO DE MÉTODOS DE ESTIMATIVA DE ETO E ANÁLISE DE SENSIBILIDADE PARA DIFERENTES CLIMAS BRASILEIROS

Irriga ◽  
2019 ◽  
Vol 24 (3) ◽  
pp. 538-551
Author(s):  
João Guilherme Araújo Lima ◽  
Paula Carneiro Viana ◽  
José Espínola Sobrinho ◽  
João Paulo Chaves Couto

COMPARAÇÃO DE MÉTODOS DE ESTIMATIVA DE ETO E ANÁLISE DE SENSIBILIDADE PARA DIFERENTES CLIMAS BRASILEIROS     JOÃO GUILHERME ARAÚJO LIMA1; PAULA CARNEIRO VIANA1; JOSÉ ESPÍNOLA SOBRINHO2 E JOÃO PAULO CHAVES COUTO3   1Departamento de Engenharia Civil, UNINASSAU, BR 104, KM 68, N° 1215, Agamenon Magalhães, 55000-000, Caruaru, Pernambuco, Brasil. [email protected]; [email protected]; 2Departamento de Ciências Ambientais e Tecnológicas, UFERSA, Rua Francisco Mota, N° 572, Presidente Costa e Silva, 59625-900 Mossoró, Rio Grande do Norte, Brasil. [email protected]; 3Programa de Pós-Graduação em Engenharia Agrícola, Núcleo de Engenharia de Água e Solo, UFRB, Rua Rui Barbosa, N° 710, Centro, 44380-000, Cruz das Almas, Bahia, Brasil. E-mail: [email protected].     1 RESUMO    A estimativa da evapotranspiração de referência (ETo) tem grande importância para a agricultura e manejo da irrigação. O método Penman-Monteith é considerado padrão para estimativa da ETo. No entanto, por ser completo, o método padrão apresenta como desvantagem a necessidade de uma gama de variáveis meteorológicas. O objetivo dessa pesquisa foi, em escala diária, avaliar o desempenho dos métodos de Hargreaves-Samani, Makkink, Priestley-Taylor, Turc, Radiação FAO-24 e Blaney-Criddle, para as condições climáticas das seis regiões do Brasil. A verificação do desempenho desses modelos foi por meio da comparação ao método de Penman-Monteith. Para avaliar o desempenho dos métodos foi utilizada a raiz quadrada do quadrado médio do erro (RQME), erro absoluto médio (EAM), erro de estimativa (PE) e coeficiente de determinação (R2). Entre os métodos estudados, o de Turc foi o que apresentou melhores resultados para todos os climas do Brasil, exceto para o clima Tropical litorâneo. O método de Makkink foi o que apresentou melhor resultado para o clima Tropical litorâneo. A análise de sensibilidade revelou que a temperatura do ar e a radiação global são as variáveis mais importantes para o método do método Penman-Monteith, exceto para o município BL, em que a variável umidade relativa do ar foi a mais importante.   Palavras-Chave: irrigação, consumo de água, evapotranspiração.     LIMA, J. G. A.; VIANA, P. C.; SOBRINHO, J. E.; COUTO, J. P. C. COMPARISON OF ETO ESTIMATION METHODS AND SENSITIVITY ANALYSIS FOR DIFFERENT BRAZILIAN CLIMATES     2 ABSTRACT   Estimation of reference evapotranspiration (ETo) is of great importance for agriculture and irrigation management. The Penman-Monteith method is considered standard for estimating ETo. However, because it is complete, the standard method presents as a disadvantage the need for a range of meteorological variables. The objective of this research was to evaluate the performance of Hargreaves-Samani, Makkink, Priestley-Taylor, Turc, FAO-24 and Blaney-Criddle methods for the climatic conditions of the six Brazilian regions. The verification of the performance of these models was made by comparison to the Penman-Monteith method. To evaluate the performance of the methods, the square root of mean-square error (MSE), mean absolute error (MAE), error of estimate (EE) and coefficient of determination (R2) were used. Among the methods studied, that of Turc was the one that presented the best results for all the climates of Brazil, except for the tropical coastal climate. The Makkink method was the one that presented the best result for the coastal tropical climate. Sensitivity analysis revealed that air temperature and global radiation are the most important variables for the Penman-Monteith method, except for BL municipality, where the variable relative humidity was the most important.   Keywords: irrigation, water consumption, evapotranspiration.

Irriga ◽  
2017 ◽  
Vol 22 (4) ◽  
pp. 701-714
Author(s):  
Andre Dalla Bernardina Garcia ◽  
José Carlos Mendonça ◽  
Claudio De Almeida Martins

MÉTODOS DE ESTIMATIVA DA EVAPOTRANSPIRAÇÃO DE REFERÊNCIA (ET0) NO MUNICÍPIO DE SANTA TERESA, ES  ANDRE DALLA BERNARDINA GARCIA1; JOSÉ CARLOS MENDONÇA2 E CLAUDIO MARTINS DE ALMEIDA3 1Instituto Federal do Espírito Santo, Rodovia ES 080, Km 93, São João de Petrópolis, CEP 29660-000, Santa Teresa, ES, Fone:(27)3259-7878, E-mail:[email protected]ório de Engenharia Agrícola/UENF, Av. Alberto Lamego, 2000,P1,sl 209, Horto, Campos dos Goytacazes, RJ, Fone (22) 2739-7308, E-mail: [email protected]ório de Engenharia Agrícola/UENF, Av. Alberto Lamego, 2000,P1,sl 209, Horto, Campos dos Goytacazes, RJ, Fone (22) 2739-7308, E-mail: [email protected]                                                                   1 RESUMO                                                                            Devido aos constantes debates ocorridos sobre a racionalização dos recursos hídricos, a busca de maneiras e boas práticas de utilização da água têm sido cada vez mais difundidas, principalmente na agricultura. Dentre os meios de preservar os recursos hídricos está o manejo de irrigação, por isso é muito importante realizar a estimativa da evapotranspiração de referência (ET0). Neste contexto, o presente trabalho foi desenvolvido para o município de Santa Teresa, localizado na meso região Central Espírito-Santense com o objetivo de avaliar e comparar diferentes métodos de estimativa da ET0 com o método de Penman-Monteith FAO56, considerado como padrão de calibração, na ausência de dados lisimétricos. Os métodos utilizados foram os de Hargreaves-Samani, Radiação Solar, Makkink, Jesen-Haise, Linacre e Penman Simplificado. O coeficiente de determinação (R2), índice de concordância de Willmott (D), o erro médio absoluto (MAE), o erro máximo (EMAX), a eficiência do método (EF) e o índice de desempenho (c) foram utilizados para avaliar os indicadores observados. Dentre os métodos avaliados, os que apresentaram melhores resultados foram os de Makkink e Penman Simplificado (R2 = 0,96 e 0,96; D= 0,99 e 0,97; MAE = 0,23 e 0,44; EMAX = 1,36 e 1,07; EF = 0,95 e 0,87 e c = 0,97 e 0,95) respectivamente, seguidos do método de Hargreaves-Samani (R2 = 0,86; D= 0,91; MAE = 0,60; EMAX = 2,16; EF = 0,69 e c = 0,85). Os resultados obtidos com os métodos de Linacre, Radiação Solar e Jensen-Haise foram inferiores e sendo a sua utilização não recomendada para a região de Santa Teresa, ES. Palavras-chave: Agrometeorologia, demanda hídrica, irrigação, Penman-Monteith  GARCIA, A. D. B.; MENDONÇA, J. C.; MARTINS, C. A.METHODS FOR ESTIMATING REFERENCE EVAPOTRANSPIRATION (ET0) FOR THE CITY OF SANTA TERESA, ES  2 ABSTRACT Due to constant discussion about rationalization of water resources, the search for ways and good practices in water use have been increasingly widespread, especially in agriculture. Among the means of preserving water resources is irrigation management, so it is very important to estimate the reference evapotranspiration (ET0). In this context, the present work was developed for the municipality of Santa Teresa, located in Central Espírito-Santo mesoregion with the objective of evaluating and comparing different ET0 estimation methods with Penman-Monteith FAO56 method considered as calibration standard, in the absence of lysimetric data. The methods used were those of Hargreaves-Samani, Solar Radiation, Makkink, Jesen-Haise, Linacre and Penman Simplified. The coefficient of determination (R2), Willmott concordance index (D), mean absolute error (MAE), maximum error (EMAX), method efficiency (EF) and performance index (c) were used for assessing the observed indicators. Among the evaluated methods, the ones with the best results were Makkink and Penman Simplified (R² = 0.96 and 0.96 D = 0.99 and 0.97, MAE = 0.23 and 0.44, EMAX = 1.36 and 1.07, EF = .95 and 0.87 and c = 0.97 and 0.95) respectively, followed by Hargreaves-Samani methods (R² = 0.86, D = 0.91, MAE = 0.60, EMAX = 2.16, EF = 0.69 and c = 0.85). The results obtained with the methods of Linacre, Solar Radiation and Jensen-Haise were lower and their use is not recommended for the region of Santa Teresa, ES. Keywords:  Agrometeorology, hydric demand, irrigation, Penman-Montheith 


Irriga ◽  
2022 ◽  
Vol 1 (4) ◽  
pp. 714-721
Author(s):  
Lucas da Costa Santos ◽  
Lucas Santos do Patrocínio Figueiró ◽  
Alex Xavier Ribeiro Andrade ◽  
Antônio Costa Ferreira Neto ◽  
Caroline Salezzi Bonfá

ESTUDO COMPARATIVO ENTRE METODOLOGIAS DE ESTIMATIVA DA EVAPOTRANSPIRAÇÃO DE REFERÊNCIA PARA LOCALIDADES DO NORTE DE MINAS GERAIS     LUCAS DA COSTA SANTOS1; LUCAS SANTOS DO PATROCÍNIO FIGUEIRÓ1; ALEX XAVIER RIBEIRO DE ANDRADE1; ANTÔNIO COSTA FERREIRA NETO1 E CAROLINE SALEZZI BONFÁ1   1 Departamento de Agronomia, Universidade Federal dos Vales do Jequitinhonha e Mucuri – UFVJM, Campus JK, Rodovia MGT 367-KM 583, nº 5000, Alto da Jacuba. CEP: 39.100-000, Diamantina, Minas Gerais, Brasil. E-mail: [email protected];[email protected];[email protected]; [email protected]; [email protected].     1 RESUMO   A determinação da evapotranspiração é imprescindível para a prática racional da irrigação, o que tem conduzido à formulação de diversas equações para estimativa desta importante variável meteorológica. Nesse sentido, faz-se necessário estudos comparativos com estas equações de modo a avaliar, localmente, sua aplicabilidade. Em linha com o exposto, objetivou-se comparar, para as condições climáticas de Salinas e Januária (ambos situados no Norte de Minas Gerais, Brasil), métodos empíricos de estimativa da evapotranspiração com o método padrão de Penman-Monteith (FAO56). Para tanto, utilizou-se dados meteorológicos de cinco anos (2016 a 2020) obtidos do Instituto Nacional de Meteorologia (INMET). Para a análise comparativa foram utilizados os seguintes indicadores estatísticos: coeficientes de determinação (R²) e correlação (r), erro absoluto médio (EAM), raiz do erro quadrado médio (REQM), índice de concordância (d) e índice de desempenho (c). Os resultados obtidos demonstram que, para as duas localidades avaliadas, o método de Blaney-Criddle apresenta o melhor desempenho para a estimativa da evapotranspiração, por outro lado, as equações de Hargreaves-Samani e Priestley-Taylor exibiram performance insatisfatória.   Palavras-chave: métodos empíricos, demanda hídrica de cultivos, manejo da irrigação.     SANTOS, L. C.; FIGUEIRÓ, L. S. P.; ANDRADE, A. X. R.; FERREIRA NETO, A. C.; BONFÁ, C. B. COMPARATIVE STUDY BETWEEN REFERENCE EVAPOTRANSPIRATION ESTIMATION METHODOLOGIES FOR NORTHERN MINAS GERAIS LOCATIONS     2 ABSTRACT   The determination of evapotranspiration is essential for the rational practice of irrigation, which has led to the formulation of several equations to estimate this important meteorological variable. In line with the above objective was to compare, for the climatic conditions of Salinas and Januária (both located in the North of Minas Gerais, Brazil), empirical methods for estimating evapotranspiration with the standard method of Penman-Monteith (FAO56). For this purpose, meteorological data for five years (2016 to 2020) obtained from the National Institute of Meteorology (INMET) were used. For the comparative analysis, the following statistical indicators were used: coefficients of determination (R²) and correlation (r), mean absolute error (EAM), root mean square error (REQM), agreement index (d) and performance index (c). The results obtained demonstrate that, for the two locations evaluated, the Blaney-Criddle method presents the best performance for estimating evapotranspiration, on the other hand, the Hargreaves-Samani and Priestley-Taylor equations showed unsatisfactory performance.   Keywords: crop water demand, empirical methods, irrigation management.


2021 ◽  
Author(s):  
Hangsik Shin

BACKGROUND Arterial stiffness due to vascular aging is a major indicator for evaluating cardiovascular risk. OBJECTIVE In this study, we propose a method of estimating age by applying machine learning to photoplethysmogram for non-invasive vascular age assessment. METHODS The machine learning-based age estimation model that consists of three convolutional layers and two-layer fully connected layers, was developed using segmented photoplethysmogram by pulse from a total of 752 adults aged 19–87 years. The performance of the developed model was quantitatively evaluated using mean absolute error, root-mean-squared-error, Pearson’s correlation coefficient, coefficient of determination. The Grad-Cam was used to explain the contribution of photoplethysmogram waveform characteristic in vascular age estimation. RESULTS Mean absolute error of 8.03, root mean squared error of 9.96, 0.62 of correlation coefficient, and 0.38 of coefficient of determination were shown through 10-fold cross validation. Grad-Cam, used to determine the weight that the input signal contributes to the result, confirmed that the contribution to the age estimation of the photoplethysmogram segment was high around the systolic peak. CONCLUSIONS The machine learning-based vascular aging analysis method using the PPG waveform showed comparable or superior performance compared to previous studies without complex feature detection in evaluating vascular aging. CLINICALTRIAL 2015-0104


2020 ◽  
Vol 35 (6) ◽  
pp. 628-640 ◽  
Author(s):  
Julia E. Stone ◽  
Elise M. McGlashan ◽  
Nina Quin ◽  
Kayan Skinner ◽  
Jessica J. Stephenson ◽  
...  

There is large interindividual variability in circadian timing, which is underestimated by mathematical models of the circadian clock. Interindividual differences in timing have traditionally been modeled by changing the intrinsic circadian period, but recent findings reveal an additional potential source of variability: large interindividual differences in light sensitivity. Using an established model of the human circadian clock with real-world light recordings, we investigated whether changes in light sensitivity parameters or intrinsic circadian period could capture variability in circadian timing between and within individuals. Healthy participants ( n = 12, aged 18-26 years) underwent continuous light monitoring for 3 weeks (Actiwatch Spectrum). Salivary dim-light melatonin onset (DLMO) was measured each week. Using the recorded light patterns, a sensitivity analysis for predicted DLMO times was performed, varying 3 model parameters within physiological ranges: (1) a parameter determining the steepness of the dose-response curve to light ( p), (2) a parameter determining the shape of the phase-response curve to light ( K), and (3) the intrinsic circadian period ( tau). These parameters were then fitted to obtain optimal predictions of the three DLMO times for each individual. The sensitivity analysis showed that the range of variation in the average predicted DLMO times across participants was 0.65 h for p, 4.28 h for K, and 3.26 h for tau. The default model predicted the DLMO times with a mean absolute error of 1.02 h, whereas fitting all 3 parameters reduced the mean absolute error to 0.28 h. Fitting the parameters independently, we found mean absolute errors of 0.83 h for p, 0.53 h for K, and 0.42 h for tau. Fitting p and K together reduced the mean absolute error to 0.44 h. Light sensitivity parameters captured similar variability in phase compared with intrinsic circadian period, indicating they are viable targets for individualizing circadian phase predictions. Future prospective work is needed that uses measures of light sensitivity to validate this approach.


SLEEP ◽  
2020 ◽  
Vol 43 (Supplement_1) ◽  
pp. A166-A166
Author(s):  
J E Stone ◽  
E M McGlashan ◽  
S W Cain ◽  
A J Phillips

Abstract Introduction Existing models of the human circadian clock accurately predict phase at group-level but not at individual-level. Interindividual variability in light sensitivity is not currently accounted for in these models and may be a practical approach to improving individual-level predictions. Using the gold-standard predictive model, we (i) identified whether varying light sensitivity parameters produces meaningful changes in predicted phase in field conditions; and (ii) tested whether optimizing parameters can significantly improve accuracy of circadian phase prediction. Methods Healthy participants (n=12, 7 women, aged 18-26) underwent continuous light and activity monitoring for 3 weeks (Actiwatch Spectrum). Salivary dim light melatonin onset (DLMO) was measured each week. A model of the human circadian clock and its response to light was used to predict the three weekly DLMO times using the individual’s light data. A sensitivity analysis was performed varying three model parameters within physiological ranges: (i) amplitude of the light response [p]; (ii) advance vs. delay bias of the light response [K]; and (iii) intrinsic circadian period [tau]. These parameters were then fitted using least squares estimation to obtain optimal predictions of DLMO for each individual. Accuracy was compared between optimized parameters and default parameters. Results The default model predicted DLMO with mean absolute error of 1.02h. Sensitivity analysis showed the average range of variation in predicted DLMOs across participants was 0.65h for p, 4.28h for K and 3.26h for tau. Fitting parameters independently, we found mean absolute error of 0.85h for p, 0.71h for K and 0.75h for tau. Fitting p and K together reduced mean absolute error to 0.57h. Conclusion Light sensitivity parameters capture similar or greater variability in phase as intrinsic circadian period, indicating they are a viable option for individualising circadian phase predictions. Future prospective work is needed using measures of light sensitivity to validate this approach. Support N/A


2010 ◽  
Vol 47 (12) ◽  
pp. 1382-1400 ◽  
Author(s):  
Kheng-Boon Chin ◽  
Eng-Choon Leong ◽  
Harianto Rahardjo

This paper proposes a simplified method to estimate the soil-water characteristic curve (SWCC) for both coarse- and fine-grained soils using one-point SWCC measurement and basic index properties. Parameters of the Fredlund and Xing SWCC equation were correlated with the basic properties of 60 soils: 30 soils each of coarse- and fine-grained types. Sensitivity analysis revealed that the location of the one-point measurement at matric suctions of 10 and 500 kPa gave the most reliable SWCC using the proposed method for coarse- and fine-grained soils, respectively. The validity of the proposed method was evaluated using a total of 62 soils collated from published literature with 31 soils each of the coarse- and fine-grained types. The proposed method gives a good estimation of the SWCC and uses fewer parameters when compared with existing one-point SWCC estimation methods.


Author(s):  
Drissa Boro ◽  
Ky Thierry ◽  
Florent P. Kieno ◽  
Joseph Bathiebo

In order to estimate the power output of a wind turbine, optimise its sizing and forecast the economic rate of return and risks of a wind energy project, wind speed distribution modelling is crucial. For which, Weibull distribution is considered as one of the most acceptable model. However, this distribution does not fit certain wind speed regimes. The objective of this study is to model the frequency distribution of the three-hourly wind speed at ten sites of Burkina Faso. In this context, we compared the accuracy of five distributions (Weibull, Hybrid Weibull, Rayleigh, Gamma and inverse Gaussian) which gave satisfactory results in this field. The maximum likelihood method was used to fit the distributions to the measured data. According to the statistical analysis tools (the coefficient of determination and the root mean square error), it was found that the Weibull distribution is most suited to the Bobo, Dédougou, Ouaga and Ouahigouya sites. On the other hand, for the sites of Bogandé, Fada and Po, the hybrid Weibull distribution is the most suitable one. As to the inverse Gaussian distribution, it is the most suitable for the Boromo, Dori and Gaoua sites. In addition, the analysis focused on comparing the mean absolute error of the annual wind power density estimation using the distributions examined. The Hybrid Weibull distribution was found to have a minimal mean absolute error for most study sites.


Author(s):  
A. U. Noman ◽  
S. Majumder ◽  
M. F. Imam ◽  
M. J. Hossain ◽  
F. Elahi ◽  
...  

Export plays an important role in promoting economic growth and development. The study is conducted to make an efficient forecasting of tea export from Bangladesh for mitigating the risk of export in the world market. Forecasting has been done by fitting Box-Jenkins type autoregressive integrated moving average (ARIMA) model. The best ARIMA model is selected by comparing the criteria- coefficient of determination (R2), root mean square error (RMSE), mean absolute percentage error (MAPE), mean absolute error (MAE) and Bayesian information criteria (BIC). Among the Box-Jenkins ARIMA type models for tea export the ARIMA (1,1,3) model is the most appropriate one for forecasting and the forecast values in thousand kilogram for the year 2017-18, 2018-19, 2019-20, 2020-21 and 2021-22, are 1096.48, 812.83, 1122.02, 776.25 and 794.33 with upper limit 1819.70, 1348.96, 1862.09, 1288.25, 1318.26 and lower limit 660.69, 489.78, 676.08, 467.74, 478.63, respectively. So, the result of this model may be helpful for the policymaker to make an export development plan for the country.


Irriga ◽  
2019 ◽  
Vol 1 (1) ◽  
pp. 94-100
Author(s):  
EUGENIO PACELI MIRANDA ◽  
TATIANA BELO DE SOUSA CUSTODIO ◽  
FRANCISCO UCHOA de LIMA ◽  
TAIANE ALMEIDA Pereira ◽  
ANDRE LUIZ RIBEIRO BICUDO

AJUSTE DA EQUAÇÃO DE HAZEN-WILLIANS PARA DETERMINAÇÃO DA PERDA DE CARGA CONTÍNUA EM TUBULAÇÕES DE PVC     EUGENIO PACELI MIRANDA1; TATIANA BELO DE SOUSA CUSTODIO2; FRANCISCO UCHOA DE LIMA3; TAIANE ALMENDA PEREIRA4 E ANDRE LUIZ RIBEIRO BICUDO5   1Professor, Doutor IFCE, Campus Iguatu/CE, Rua Plácido Almino Uchoa, 60, Iguatu/Ceará. CEP: 63.500-000, Brasil, email:[email protected]; 2 Tecnólogo em Irrigação e Drenagem, IFCE, Campus Iguatu, Rodovia Iguatu-Várzea Alegre km 05, CEP: 63.500-000, Brasil, email: [email protected]; 3Graduando em Tecnologia em Irrigação e Drenagem, IFCE, Campus Iguatu, Rodovia Iguatu-Várzea Alegre km 05, CEP: 63.500-000, Brasil, e-mail: [email protected]; 4Graduandos em Tecnologia em Irrigação e Drenagem, IFCE, Campus Iguatu, Rodovia Iguatu-Várzea Alegre km 05, CEP: 63.500-000, Brasil, e-mail: [email protected]; 5 Prof. do Colégio Técnico Industrial "Prof. Isaac Portal Roldan", Unesp, Campus Bauru. Av. Eng. Luis Edmundo Carrijo Coube, 14-01, CEP: 17.033-360, Brasil, e-mail: [email protected]     1 RESUMO   A perda de carga é um parâmetro fundamental para o dimensionamento das tubulações, estando diretamente relacionada ao custo dessas tubulações, a seleção do sistema de bombeamento e o custo com o consumo de energia elétrica. Nesse estudo ajustou-se a equação de Hazen-Willians e comparou com a equação de Darcy-Weisbach. O desempenho da equação ajustada foi determinada pelo índice de concordância (c), Erro Padrão Estatístico (EPE) e o Erro Absoluto Médio (EAM). Os resultados mostram que todos os índices usados para verificar o desempenho da equação de Hazen-Willians ajustada melhoraram. A maior diferença entre os valores da perda de carga contínua entre o método de Darcy-Weisbach e a equação de Hazen-Willians ajustada ficou em torno de 0,08%, valor que pode ser considerado extremamente baixo.   Palavras-chave: Perda de carga, Darcy- Weisbach, diâmetro.     MIRANDA, E. P; CUSTODIO, T. B. S; LIMA, F. U; PEREIRA, T. A.; BICUDO, A. L. R. ADJUSTMENT OF THE HAZEN-WILLIANS EQUATION FOR DETERMINATION OF CONTINUOUS PRESSURE DROP IN PVC PIPE     2 ABSTRACT   The head loss is a fundamental parameter for the dimensioning of the pipes, being directly related to the cost of these pipes, the selection of the pumping system and the energy cost of electricity. That study fitted the Hazen-Williams equation and compared it with the Darcy-Weisbach equation. The performance of the adjusted equation was determined by the concordance index (c), Statistical Standard Error (EPE) and Mean Absolute Error (EAM). The results show that all gridded indices to verify the performance of the adjusted Hazen-Willians equation have improved. The largest difference between the values of continuous load loss between the Darcy-Weisbach method and the adjusted Hazen-Williams equation was about 0.08%, which can be considered extremely low   Keywords: Head loss, Darcy-Weisbach, diameter.


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