White Formula Research Articles

Determination of the coefficient of friction in the penstock of a hydro-electric dam: Application of two approaches

ABSTRACT Several formulae of the coefficient of friction have emerged after that of Nikuradse such as the Colebrook–White formula adopted for the calculation of the coefficient of friction in penstocks. However, this requires enormous computing resources because it suffers from an implicit nature. Other authors have proposed explicit formulae for this in order to reduce calculation times and make applications easy. Among these authors, the most used are the formulae of Swamee–Jain and Haaland. In this work, we set out to study the evolution of friction on the top, bottom and side walls of a penstock using these two formulas. The objective is to find which one best characterizes the friction and gives results close to the implicit Colebrook–White formula. To carry out this work, the study was made by a numerical approach in FLUENT. It appears that the Swamee–Jain correlation gives values closer to that of Colebrook–White along the walls. On the side walls, Haaland's formula better describes the constancy of friction with a much larger range of values than Swamee–Jain. On the upper and lower walls, the friction has a linear character.

A new approach for explicit approximation of the Colebrook–White formula for pipe flows

ABSTRACT A novel approach is presented for explicit assessment of the friction factor of the Darcy–Weisbach formula for a pipe turbulent flow, a topic being especially useful in practical applications requiring a large number of pipes has to be calculated a great many times in a short time. In such applications, in fact, an explicit formula shortening computation time, with respect to a trial-and-error solution of the Colebrook–White formula, is very advisable. To this aim, in the paper analytical simplicity is pursued besides accuracy, the latter being kept high enough for practical purposes. Unlike previous studies, the ratio between the actual friction factor and that relating to a fully turbulent flow is analysed as a function of the relative roughness and the relative Reynolds number (i.e., the ratio between the actual Reynolds number and the Reynolds number separating the transition regime from the fully turbulent regime). By processing a dataset obtained by systematically solving the C-W formula over suited ranges of the Reynolds number and the relative roughness, two expressions are obtained: a simpler first-step accuracy expression giving generally acceptable accuracy for most engineering practical purposes; and a second-step accuracy expression allowing adequately high accuracy for all situations.

A Comparative Analysis of Sediment Concentration Using Artificial Intelligence and Empirical Equations

Morphological changes in canals are greatly influenced by sediment load dynamics, whose estimation is a challenging task because of the non-linear behavior of the sediment concentration variables. This study aims to compare different techniques including Artificial Intelligence Models (AIM) and empirical equations for estimating sediment load in Upper Chenab Canal based on 10 years of sediment data from 2012 to 2022. The methodology involves utilization of a newly developed empirical equation, the Ackers and White formula and AIM including 20 neural networks with 10 training functions for both Double and Triple Layers, two Artificial Neuro-Fuzzy Inference System (ANFIS), Particle Swarm Optimization, and Ensemble Learning Random Forest models. Sensitivity analysis of sediment concentration variables has also been performed using various scenarios of input combinations in AIM. A state-of-the-art optimization technique has been used to identify the parameters of the empirical equation, and its performance is tested against AIM and the Ackers and White equation. To compare the performance of various models, four types of errors—correlation coefficient (R), T-Test, Analysis of Variance (ANOVA), and Taylor’s Diagram—have been used. The results of the study show successful application of Artificial Intelligence (AI) and empirical equations to capture the non-linear behavior of sediment concentration variables and indicate that, among all models, the ANFIS outperformed in simulating the total sediment load with a high R-value of 0.958. The performance of various models in simulating sediment concentration was assessed, with notable accuracy achieved by models AIM11 and AIM21. Moreover, the newly developed equation performed better (R = 0.92) compared to the Ackers and White formula (R = 0.88). In conclusion, the study provides valuable insights into sediment concentration dynamics in canals, highlighting the effectiveness of AI models and optimization techniques. It is suggested to incorporate other AI techniques and use multiple canals data in modeling for the future.

Whiteness Perception under LED Source with High Content of UV Radiation

Whiteness is an attribute of color perception with high brightness and low colorfulness. In this study, the correlation between instrumental measurement and visual assessment of whiteness of 40 optically brightened white samples was investigated under a LED light source of correlated color temperature (CCT) 5000K combined with Wood's UV-A lamp. Due to over exposure of UV radiation, tested samples were outside of CIE limit. In those cases, standard CIE whiteness formula show significant shift in whiteness interval scale. A high correlation was identified between visual assessment and modified Vik-Viková whiteness formula. The investigations have also shown that the existing CIBA plastic whiteness scale needs to be expanded.

Whiteness evaluation: A review and new proposals

AbstractThis publication carries out an in‐depth study of whiteness, various numerical evaluation methods that have been developed over the past 75 years, and review their application and deficiencies in the context of a new proposed Commission Internationale de l'Eclairage (CIE) whiteness formula. The publication first introduces the basic principle of whiteness evaluation from the work of Judd and Selling around 1950, then that of Ganz in the 1970s and finally that of the CIE from 1969 to 1986. The defects of the Judd and Selling formulas became apparent with the use of fluorescent whitening agents. The CIE linear formula cannot predict an optimum for the optical whitening process. Hyperbolic formulas published are much too complicated and are unable to predict correctly the best conditions for that optical whitening. We present a new formula derived from that of the CIE, much simpler than the hyperbolic formulas, and able to predict an optimal shade in the optical whitening process. The formula takes into account the limitations of the white domain; when the blue saturation becomes too great, or when a tint deviation toward green or toward red is too noticeable. The formula gives results identical to those of the CIE formula when the materials are far from commercial whiteness limits. In addition, the formula can be very easily adapted to the CIELAB system and so, gives promising results.

Formulas Estimating Glomerular Filtration Rate in the Evaluation of Living Kidney Donor Candidates: Comparison of Different Formulas With Scintigraphy-Measured Glomerular Filtration Rate

IntroductionEstimation of kidney function is crucial in the evaluation of living kidney donor candidates. Despite the multitude of glomerular filtration rate (GFR) formulas, no equation is universal, and none were validated in the population of kidney donors. Novel biomarkers, including beta trace protein (BTP) and cystatin C, are studied to help estimate GFR and improve the safe qualification of living kidney donors. AimThis study compares the accuracy of different formulas that estimate GFR with reference scintigraphy-measured GFR in the population of living kidney donor candidates. Material and MethodsThis study enrolled 30 healthy living kidney donor candidates. GFR was measured using the following 11 different formulas. For reference, GFR was assessed using 99m-Technetium-diethylenetriaminepentaacetic acid. ResultsThe accuracy of estimation was generally low in all formulas. The strongest correlation between measured GFR (mGFR) and estimated GFR (eGFR) was achieved by the Nankivell formula (R = 0.47, P = .009); however, in the group of patients with a body mass index of >25 kg/m2, only the equations based on BTP had a statistically significant correlation with mGFR: White (R = 0.59; P = .016) and Poge (R = 0.53; P = .035). Bland-Altman plots revealed wide limits of agreement between eGFRs and mGFR in all groups of patients. ConclusionIn living kidney donor candidates, GFR estimation formulas should be chosen individually. White formula, which is based on BTP, may be a promising tool in estimating GFR in overweight potential living kidney donor candidates. More than 1 formula and personalized choice of GFR estimation method regarding the given patient should be performed in qualification of kidney donors.

Alternate formula for calculating the Darcy Coefficient in turbulent flow in pipes

The purpose of this research was to determine an alternative formula for calculating the Darcy coefficient in turbulent flow in pipes. The proposed alternate formula is an explicit formula that should be used to replace the Colebrook-White formula for calculating the Darcy coefficient in turbulent flow in pipes since it has higher precision than the explicit formulas that are currently in use. In this investigation, the alternate formula was compared with two explicit formulas commonly used in pipe design, the Swamee-Jain and Pavlov formulas. To determining which formula is better, all of them were compared with the Colebrook-White formula. For this, the average percentage and maximum percentage errors of the Darcy coefficient values calculated with each of the explicit formulas were determined, with the values obtained with the Colebrook - White formula. It was determined that the maximum errors in the calculation of the Darcy coefficient concerning the Colebrook-White formula were: 3,104% for the Swamee-Jain formula, 7,973% for the Pavlov formula and 2,740% for the alternate formula.

Discussion of “Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function” by Dejan Brkić and Pavel Praks, Mathematics 2019, 7, 34; doi:10.3390/math7010034

Estimating the Darcy–Weisbach friction factor is crucial to various engineering applications. Although the literature has accepted the Colebrook–White formula as a standard approach for this prediction, its implicit structure brings about an active field of research seeking for alternatives more suitable in practice. This study mainly attempts to increase the precision of two explicit equations proposed by Brkić and Praks. The results obviously demonstrate that the modified relations outperformed the original ones from nine out of 10 accuracy evaluation criteria. Finally, one of the improved equations estimates closer friction factors to those obtained by the Colebrook–White formula among 18 one-step explicit equations available in the literature based on three of the considered criteria.

Comparison of Explicit Relations for Calculating Colebrook Friction Factor in Pipe Network Analysis Using h-based Methods

Although many explicit correlations have already been presented as alternatives to implicit Colebrook–White (C–W) formula, performances of C–W-based relations in pipe network analysis have not been investigated. In this study, 56 explicit relations available in the literature were implemented in the analysis of four water distribution networks while the benchmark solution is computed considering the implicit C–W formula. In the numerical experiment, these pipe networks were solved using three different h-based methods including h-based Newton–Raphson method, finite element method, and the gradient algorithm. In each scenario, one of these explicit relations was considered in the process of analyzing water networks. According to the obtained results, 15 explicit relations face the convergence problems which were identified as unreliable equations. Moreover, 15 explicit equations, which were successfully performed in analyzing all sample networks with the closest results to that of the benchmark solution, were introduced as the most accurate ones. Moreover, as many scenarios outperform those of the outdated explicit equation used for the same purpose in professional hydraulic solvers such as EPANET and WaterGEMS, it was recommended they be replaced with one of the explicit equations with higher accuracy. Finally, the achieved results demonstrate that the equation selected for computing Darcy–Weisbach friction factor has an inevitable impact not only on the accuracy but also on the convergence of pipe network analysis.

Опыт применения препарата «Селенопиран» для оптимизации показателей воспроизводства молочных коров

As a result of research and production experience in the economy of the Nizhny Novgorod region, the effect of three-time administration of the drug «Selenopiran» at a dose of 300 mg during the dry season on the ease of calving, milk productivity and reproductive functions of cows was studied. For this purpose, two groups of cows (n=10) were selected: an experimental group and a control group. Starting from the confirmation of 6-month pregnancy, 25% oil solution of the drug «Selenopiran» at a dose of 30 ml was administered three times at intervals of 5–6 days to animals of the experimental group. 14 days after last injection from experimental and control animals were taken blood samples for haematological study determined the red blood indices: the number of red blood cells and hemoglobin, white blood: white blood cell count and leukocyte formula, and lysozime and bactericidal activity of blood serum. Further, the animals were monitored both during calving and postpartum period, and during subsequent artificial insemination and lactation, the duration of independent and manual separation of the afterbirth, the frequency of occurrence, form, duration of the course and outcome of specific diseases of the postpartum period (endometritis and early mastitis) were recorded. Fruitful insemination was determined based on the results of rectal studies. Based on these observations, the main indicators of herd reproduction were calculated, i.e. the insemination index (the number of inseminations per 36 fruitful), the duration of the period and the interbody period. As a result, the service period in the experimental group decreased by 113,7% relative to the control animals (178,2 days versus 2,3), the insemination index also improved in the experimental group – 3,8, against 1,6 in the control group. The average daily milk yield in the experimental group is 2,9 kg higher, and the live weight of calves at birth is XNUMX kg. A comparative analysis of hematological parameters of experimental and control cows obtained a higher level of markers of nonspecific immunity in the experimental group. Consequently, along with relatively rapid recovery of reproductive organs and shortening of the service period, the cows of the experimental group also had higher indicators of non-specific resistance compared to the cows of the control group.

New Metrics for Evaluating Whiteness of Fluorescent Samples

A magnitude estimation experiment was carried out to scale the extent of whiteness from a set of near white textile samples including fluorescent white agent. Each was assessed under 4 different CCTs, each having a high and a low level of UV energy. The results were used to test various existing whiteness formulae. Finally, by fitting to the present data, two new metrics were developed. One is based on CIECAM02, and the other is based on the present CIE whiteness formula by transforming the data to D65 chromaticity from the other white sources via CAT02 chromatic adaption transform with a proper incomplete adaptation factor (D). It was also tested using an independent set of data. Both formulae gave accurate prediction to the data. The former metric is proposed because it is based on a colour appearance model.

Evaluation of white sweet potato tube-feeding formula in elderly diabetic patients: a randomized controlled trial

BackgroundElderly people with type 2 diabetes mellitus (T2DM) have an increased risk of diabetes-related microvascular and macrovascular complications, thus diabetic patients with a functioning gastrointestinal tract but without sufficient oral intake require enteral nutrition (EN) formulas to control blood glucose. White sweet potato (WSP) was a kind of sweet potato could provide a healthy carbohydrate source to EN formula. The aim of this study was to examine at risk of malnutrition T2DM patients whether a WSP-EN would attenuate glucose response and elevate nutritional index compared to a standard polymeric formulas.MethodsIn this randomized, parallel, placebo-controlled, pilot clinical trial to investigate the effects of EN with WSP on aged residents with T2DM in long-term care institutions. In total, 54 eligible participants were randomly assigned to either the non-WSP-EN or WSP-EN group. For 60 days, the WSP-EN group received a WSP formula through nasogastric tube via a stoma with a large-bore syringe. The participants received EN of standard polymeric formulas without WSP in the non-WSP-EN group.ResultsThe body weight, body mass index, Mini Nutritional Assessment score, and Geriatric Nutritional Risk Index were significantly higher in the WSP-EN group (p < 0.05). Moreover, the WSP-EN intervention reduced glycated hemoglobin levels (6.73% ± 1.47% vs. 6.40% ± 1.16%), but increased transferrin (223.06 ± 38.85 vs. 245.85 ± 46.08 mg/dL), high-density lipoprotein cholesterol (42.13 ± 10.56 vs. 44.25 ± 8.43 mg/dL), and vitamin A (2.45 ± 0.77 vs 2.74 ± 0.93 μM) levels (p < 0.05). In addition, there was no important side effects including gastrointestinal intolerance with prescribed doses in our WSP-EN treated patients when compared with control ones.ConclusionsThe results suggest WSP incorporated into enteral formulas can improve nutrition status and glycemic control in elderly diabetic patients.Trial registrationNCT02711839, registered 27 May 2015.

Performance Comparison of Various Whiteness Formulas Based on Visual Evaluation Experiments

Performance Comparison of Various Whiteness Formulas Based on Visual Evaluation Experiments

SMALL-TIME ASYMPTOTICS IN GEOMETRIC ASIAN OPTIONS FOR A STOCHASTIC VOLATILITY JUMP-DIFFUSION MODEL

The aim of this paper is to study the small time to maturity of the behavior of the geometric Asian option price and implied volatility under a general stochastic volatility model with Lévy process. The volatility process does not need to be a diffusion or a Markov process, but the future average volatility in the model is a nonadapted process. An anticipating Itô formula for Lévy process and the decomposition of the price (Hull–White formula) are obtained using the Malliavin calculus techniques. The decomposition formula is applied to find the small-time limit of the geometric Asian option price and the implied volatility for the model in at-the-money and out-of-the-money cases.

Development of a whiteness formula for surface colors under an arbitrary light source.

The whiteness specification is critically important in surface color industry, especially when fluorescent whitening agents (FWAs) are added to objects. The CIE whiteness formula, the most widely used whiteness formula, only characterizes the whiteness under CIE standard D65, which ignores the change of whiteness under different light sources due to the spectral content of the light sources. Though the adoption of a Chromatic Adaptation Transform (CAT02) in the CIE whiteness formula was found effective in recent studies, it failed to allow a comparison across different correlated color temperatures (CCTs). In this study, a haploscopic viewing condition was employed, with a D65 simulator in the left booth, for evaluating the whiteness of eight samples under different light sources in the right booth. The whiteness of the four samples under the D65 simulator was employed as a whiteness scale to aid the evaluation. Based on the experiment results, the characterization of whiteness for a surface under an arbitrary light source is proposed to use the CIE whiteness formula with the sample chromaticities being transformed using CAT02 and an adjusted degree of chromatic adaptation factor D.

Judgment of White Appearance for Surface Colors under Individual and Simultaneous Observations

ABSTRACT The weakness of the CIE whiteness formula, the most widely used formula to characterize the whiteness of surface colors, has been well documented. It cannot characterize the whiteness under the illuminants other than CIE standard D65 and has a small whiteness boundary. A psychophysical experiment was carried out to investigate the whiteness boundary toward the blue-tint direction under 3000 and 6500 K illuminants with high violet radiations to excite the fluorescent whitening agents (FWAs) and to cover a wide range of whiteness appearance. Sixty samples (that is, 30 paper and 30 fabric samples) were individually and simultaneously evaluated for whether the samples appeared white or not by the same group of human observers. The judgments made by the observers were significantly different between the two evaluations. When the samples were simultaneously evaluated, the samples needed to have higher whiteness values to be judged as white and there were large interobserver variations, which was speculated to be due to the variation in chromatic adaptation among the observers. Such a variation was likely caused by the wide range of whiteness appearance included in this experiment and each observer was adapted to the color of the whitest sample selected by him or her during the simultaneous evaluations.

Mathematical modeling for prediction of complicated acute appendicitis in children

Endogenous intoxication, which accompanies the complicated course of acute appendicitis in children, is one of the serious conditions, which are the main cause of complications in the postoperative period. Diverse clinical observations done by clinicians suggest that despite the use of modern technologies in operating equipment, anesthetic support, the number of complications in the postoperative period has no tendency to decrease, and the main cause of lethal outcomes with appendicular peritonitis is lightning development of severe degree of endotoxicosis, which develops as a result of resorbing toxic substances formed of many components, including pathogenic microflora and destruction metabolism.&#x0D; Purpose. Creation of a mathematical model for prediction of complicated acute appendicitis in children using the functions of regression analysis of EXCEL spreadsheet by approximating experimental data.&#x0D; Materials and methods. In the work, there is information about 59 patients with acute appendicitis treated at the clinic of pediatric surgery at the National Pirogov Memorial Medical University. The data on patients were divided into two groups: patients with not complicated course of pathology – 24 patients, and patients with complicated course of acute appendicitis – 35 children. The control group served the data of 37 healthy children. In each of the three groups, the following parameters were studied: gender, age, bed day, duration of the disease, presence of symptoms of peritoneal irritation, the nature of exudate in the abdominal cavity, the number of red blood cells, hemoglobin, leukocytosis, quantitative characteristics of white blood formula, ESR, cellogenic endogenous intoxication: leukocyte index of intoxication and hematological index of intoxication. All the data were determined directly at the time of hospitalization of a patient to the hospital.&#x0D; Results. Discussion. Based on multiple correlation x = f (x1 , x2 ) a two-factor mathematical model of probability of the complicated course of acute appendicitis in children was created. According to the obtained results of the study of the system of three equations with three unknowns, it was established that if the indicator of the form of the disease is y = 2.67 and above, when, in numerical terms, the result falls into the zone of complicated flow of acute appendicitis and completely coincides with data analysis of the three groups of patients.&#x0D; Conclusions. The components that determine the uncomplicated course of acute appendicitis in children, according to the developed two-factor model, include LII and GPI, which exceed the values intoxication of certain intervals studied at the time of hospitalization. The analyzed indices were determined by the degree of severity of the pathological process, duration of disease, virulence of microflora and age of patients against the background of the formed endogenous intoxication syndrome.

Perfil hematológico del guajolote criollo de traspatio en la región de Tecamachalco, Puebla.

Los guajolotes criollos en el medio rural han tenido un papel de suma importancia ya que han aportado a la población humana proteínas de alta calidad biológica (carne y huevo) por lo general en condiciones adversas. La presente investigación tiene como objetivo describir el perfil hematológico del guajolote criollo de traspatio de la región de Tecamachalco, Puebla. Se seleccionaron y adquirieron 23 guajolotes criollos (GC), que se mantuvieron en confinamiento durante un mes alimentándose con maíz molido y alfalfa, similar al lugar de origen. Para el estudio hematológico se tomó una muestra de dos ml de sangre del ala. Se colocó en un tubo vial con anticoagulante EDTA rotulándose para su identificación. Se realizaron las siguientes determinaciones: Hematocrito (método del Micro hematocrito con tubos capilares, centrifugados a 12.000 r.p.m. durante 5 minutos), Hemoglobina (método de Drabkin), Glóbulos blancos (Neubauer) y Formula leucocitaria (recuento diferencial en frotis según Giemsa). Los resultados obtenidos fueron los siguientes: para hematocrito, proteínas plasmáticas, leucocitos totales, linfocitos, heterófilos, eosinòfilos, basófilos y monocitos, 49.39%, 5.56 g/dl, 22.55x 103/ul, 50.48%,35.35%, 11.57%, 1.65% y 5.87%, respectivamente. Los valores de referencia son: 49.39%, 5.56g/dl, 20 x 103/ul, 50%, 43%, 19%, 3% y 9%, por lo que se considera mínima la diferencia entre lo obtenido y los rangos referenciales. Esta información hematológica de los GCM en las condiciones descritas es la base para futuras investigaciones sobre esta especie animal, en particular para los estudios de resistencia a enfermedades y otros factores ambientales.

Chromaticity and characterization of whiteness for surface colors

Whiteness is an important colorimetric characteristic for surface colors. The CIE whiteness formula, the most widely used formula, only characterizes the whiteness of a surface color under CIE standard D65 and requires a sample to be within a small chromaticity region. In this study, 20 observers evaluated the whiteness appearance of 88 samples under four light settings at different CCT levels (i.e., 3000, 4000, 5000, and 6500 K). The 88 samples were carefully selected and the spectral power distributions of the light settings were carefully designed using a spectrally tunable LED device, so that the chromaticities of the samples under each light settings uniformly covered a wide range along the yellow/blue direction in a color space, which had never been realized before. The results, together with the two recent studies, allowed the derivation of ellipsoids for classifying the whiteness appearance for surface colors. For the samples within the derived ellipsoids, though the Uchida whiteness formula with CAT02 (WUchida,CAT02) had a higher correlation to the perceived whiteness than the CIE whiteness formula with CAT02 (WCIE,CAT02), samples that were perceived as white and had a high chroma with a hue angle of blue due to the high violet/ultraviolet radiation in the illumination may had a negative WUchida,CAT02 value. A comprehensive whiteness formula that can accurately characterize the whiteness appearance for surface colors under an arbitrary light source by considering different conditions is still necessary and the work is undergoing.

Evaluation of whiteness formulas for FWA and non-FWA whites.

Whiteness is an important colorimetric characteristic for surface colors. Currently, the CIE whiteness formula is widely used to characterize the whiteness of a surface in industry, whose limitations have been well documented. In this study, the whiteness appearance of 55 textile samples [43 non-fluorescent whitening agents (FWAs) and 12 FWA samples] were evaluated under six lighting conditions, comprising three levels of correlated color temperature (CCT) (i.e., 3000, 4000, and 6500 K) and two levels of UV radiation (i.e., zero and high), by 12 observers with normal color vision. The results indicated that the CIE whiteness formula with the CAT02 chromatic adaptation transform and the optimized CIE whiteness formula had the best performance in predicting the whiteness of surface colors, regardless of whether FWAs are contained, among the six formulas.