Liquid temperature effect on the hydraulic shock wave velocity in polyethylene pipes

Introduction. Providing people with high quality drinking water has always come first. However, its transportation through pipeline systems was often associated with some problems, such as the temperature of the water and the environment, as well as the possibility of water hammer on certain pipe sections. This was especially true for systems that use polyethylene pipes. Temperature is a key factor affecting the flexibility properties of polyethylene pipes, and it affects not only the design, but also the investment in the development of water supply networks. The purpose of these studies was to study the effect of water and ambient temperature on the density, properties of the pipe material and the speed of propagation of a hydraulic shock wave in polyethylene pipes.Materials and Methods. In the experiments performed, the method of field research was used, when tests are carried out on specialized equipment on samples specially made for the pursued purposes. Here, samples of high-density polyethylene pipes were used, which were subjected to tensile tests on a tensile testing machine, and each experiment was carried out three times.In the course of the experiments, the samples were exposed to certain temperature regimes (both external and internal), while the influence of the hydrodynamic pressure of the liquid in the pipe was also investigated, as a result of the change in time of the liquid velocity in its sections. To do this, the samples were supplied with liquid under a certain pressure in order to find out the influence on the pipes of an effect known as water hammer.Results. In the course of the research, it was found that the value of the elastic modulus of high-density polyethylene PE100 decreases with increasing water temperature, and the decrease at a temperature of 60° C reaches 60.21% compared to its value at a water temperature of +4° C. Based on the results of experiments to determine the effect of the elastic modulus of polyethylene with increasing temperature, an exponential equation was derived to calculate the value of the polyethylene coefficient as a function of time E = 1.312e-0,01t with the correlation coefficient R2 = 0.988 ; and based on the results of the studies carried out to calculate the value of the propagation velocity of a hydraulic shock wave, an exponential equation was derived as a function of time C = 275.9e-0,01t with the coefficient correlation R2 = 0.987 .Discussion and Conclusions. In the course of the research, it was found that such a phenomenon as water hammer has a harmful effect on the pipe walls, which, if possible, should be avoided even at the design stage of the water supply network. During the experiments, it was found that with an increase in temperature, the values of the elastic modulus of polyethylene decreased with a simultaneous decrease in the values of the propagation velocity of the hydraulic shock wave.

Modeling Optimal Cadence as a Function of Time during Maximal Sprint Exercises Can Improve Performance by Elite Track Cyclists

In track cycling sprint events, optimal cadence PRopt is a dynamic aspect of fatigue. It is currently unclear what cadence is optimal for an athlete’s performance in sprint races and how it can be calculated. We examined fatigue-induced changes in optimal cadence during a maximal sprint using a mathematical approach. Nine elite track cyclists completed a 6-s high-frequency pedaling test and a 60-s isokinetic all-out sprint on a bicycle ergometer with continuous monitoring of crank force and cadence. Fatigue-free force-velocity (F/v) and power-velocity (P/v) profiles were derived from both tests. The development of fatigue during the 60-s sprint was assessed by fixing the slope of the fatigue-free F/v profile. Fatigue-induced alterations in PRopt were determined by non-linear regression analysis using a mono-exponential equation at constant slope. The study revealed that PRopt at any instant during a 60-s maximal sprint can be estimated accurately using a mono-exponential equation. In an isokinetic mode, a mean PRopt can be identified that enables the athlete to generate the highest mean power output over the course of the effort. Adding the time domain to the fatigue-free F/v and P/v profiles allows time-dependent cycling power to be modelled independent of cadence.

Gaussian exponential regression method for modeling open circuit voltage of lithium-ion battery as a function of state of charge

Purpose The purpose of the article is to develop an equation to accurately represent OCV as a function of SoC with reduced computational burden. Dependency of open circuit voltage (OCV) on state of charge (SoC) is often represented by either a look-up table or an equation developed by regression analysis. The accuracy is increased by either a larger data set for the look-up table or using a higher order equation for the regression analysis. Both of them increase the memory requirement in the controller. In this paper, Gaussian exponential regression methodology is proposed to represent OCV and SoC relationships accurately, with reduced memory requirement. Design/methodology/approach Incremental OCV test under constant temperature provides a data set of OCV and SoC. This data set is subjected to polynomial, Gaussian and the proposed Gaussian exponential equations. The unknown coefficients of these equations are obtained by least residual algorithm and differential evolution–based fitting algorithms for charging, discharging and average OCV. Findings Root mean square error (RMSE) of the proposed equation for differential evolution–based fitting technique is 35% less than second-order Gaussian and 74% less than a fifth-order polynomial equation for average OCV with a 16.66% reduction in number of coefficients, thereby reducing memory requirement. Originality/value The knee structure in the OCV and SoC relationship is accurately represented by Gaussian first-order equation, and the exponential equation can accurately describe the linear relation. Therefore, this paper proposes a Gaussian exponential equation that accurately represents the OCV as a function of SoC. The results obtained from the proposed regression methodology are compared with the polynomial and Gaussian regression in terms of RMSE, mean average, variance and number of coefficients.

Development of Kinetic Models For Biogas Production From Tofu Liquid Waste

Biogas promises bioenergy to be developed as a renewable fuel to reduce the fossil energy crisis. Biogas raw material can be derived from tofu liquid waste. Biogas is processed by anaerobic digestion. This study aimed to develop a simulation of the kinetic model variations of biogas production from tofu liquid waste. The results showed that the ascending limb of the exponential equation had a greater coefficient (R2 = 1) than the ascending limb of the linear equation (R2 = 0.9574). The descending limb of the linear equation had a better coefficient (R2 = 0.9574) than the descending limb of the exponential equation (R2 = 0.95). The Gaussian model had the greatest R2 of 0.9937. Logistic growth had the greatest coefficient (R2 = 0.9951) compared to modified Gompertz (R2 = 0.9817) and exponential rise to maximum (R2 = 0.9852) in the simulation of cumulative biogas production. The fit model for kinetic biogas production from tofu liquid waste is Gaussian Model.Abstrak: Biogas merupakan salah satu bioenergi yang menjanjikan untuk dikembangkan dalam mengurangi krisis energi fosil. Bahan baku biogas dapat berasal dari limbah cair tahu yang diolah secara anaerobic digestion. Penelitian ini bertujuan untuk mengembangkan variasi model simulasi kinetika produksi biogas dari limbah cair tahu. Hasil penelitian menunjukkan bahwa persamaan eksponensial untuk grafik kenaikan memilki koefisien yang lebih besar (R2 = 1) dibandingkan grafik kenaikan dengan persamaan linier (R2 = 0,9574). Grafik penurunan pada persamaan linier memiliki nilai koefisien lebih besar (R2 = 0,9574) dibandingkan grafik penurunan pada persamaan eksponensial (R2 = 0,95). Model Gaussian menghasilkan nilai koefisien tertinggi R2 = 0,9937. Logistic growth menghasilkan nilai R2 terbesar (0,9951) dibandingkan modified Gompertz (R2 = 0,9817) dan exponential rise to maximum (R2 = 0,9852) pada simulasi produksi biogas kumulatif. Model yang paling cocok untuk kinetika produksi biogas dari limbah cair adalah model Gaussian.

Spatial and Temporal Variation Characteristics of Snowfall in the Haihe River Basin from 1960 to 2016

The spatio-temporal variation of precipitation under global warming had been a research hotspot. Snowfall is an important part of precipitation, and its variabilities and trends in different regions have received great attention. In this paper, the Haihe River Basin is used as a case, and we employ the K-means clustering method to divide the basin into four sub-regions. The double temperature threshold method in the form of the exponential equation is used in this study to identify precipitation phase states, based on daily temperature, snowfall, and precipitation data from 43 meteorological stations in and around the Haihe River Basin from 1960 to 1979. Then, daily snowfall data from 1960 to 2016 are established, and the spatial and temporal variation of snowfall in the Haihe River Basin are analyzed according to the snowfall levels as determined by the national meteorological department. The results evalueted in four different zones show that (1) the snowfall at each meteorological station can be effectively estimated at an annual scale through the exponential equation, for which the correlation coefficient of each division is above 0.95, and the relative error is within 5%. (2) Except for the average snowfall and light snowfall, the snowfall and snowfall days of moderate snow, heavy snow, and snowstorm in each division are in the order of Zones III > IV > I > II. (3) The snowfall and the number of snowfall days at different levels both show a decreasing trend, except for the increasing trend of snowfall in Zone I. (4) The interannual variation trend in the snowfall at the different levels are not obvious, except for Zone III, which shows a significant decreasing trend.

Explosion and high-temperature plasma-as a consequence of the exponential equation of motion of gas molecules

In this paper, an exponential equation of motion for gas molecules is derived for the first time. The paper shows that the Kadic-Edelen forces, written in 1983 by analogy with electrodynamics, are forces that act on the momentum of particles as on a charge. The paper considers the application of the centrally symmetric force of the tensor compensating field in gas in the active state. It is shown that the intensity tensor in the gas is diagonal, so it leads to an increase in the momentum of the gas molecules exponentially in the direction of their movement. Thus, there is an exponential change in the kinetic energy of the gas molecules in the volume where the centrally symmetric intensity tensor acts. The action of a large positive intensity tensor in the gas leads to an explosion and high-temperature plasma.

How Do Statistical Parameters of Induced Seismicity Correlate with Fluid Injection? Case of Oklahoma

The seismicity evolution in Oklahoma between 2010 and 2018 is analyzed systematically using an epidemic-type aftershock sequence model. To retrieve the nonstationary seismicity component, we systematically use a moving window of 200 events, each within a radius of 20 km at grid points spaced every 0.2°. Fifty-three areas in total are selected for our analysis. The evolution of the background seismicity rate μ is successfully retrieved toward its peak at the end of 2014 and during 2015, whereas the triggering parameter K is stable, slightly decreasing when the seismicity is activated. Consequently, the ratio of μ to the observed seismicity rate is not stationary. The acceleration of μ can be fit with an exponential equation relating μ to the normalized injected volume. After the peak, the attenuation phase can be fit with an exponential equation with time since peak as the independent variable. As a result, the evolution of induced seismicity can be followed statistically after it begins. The turning points, such as activation of the seismicity and timing of the peak, are difficult to identify solely from this statistical analysis and require a subsequent mechanical interpretation.

Novel Approach of Existence of Solutions to the Exponential Equation (3m2 + 3) x + (7m2 +1) y = z2

In this manuscript the exponential equation (3m2 + 3) x + (7m2 +1) y = z2 where m Î Z in three variables for the occurrence of solutions belonging to the set of all integers or the concerned equation has no solution for various alternatives of m is investigated.

Derivation of pesticide aged sorption parameters from laboratory incubation data

The results of the incubation laboratory experiment showed that the decomposition of cyantraniliprole is bi-phasic and the rapid decomposition in the period after the application of the pesticide is accompanied by a subsequent slowdown of this process. The use of the biexponential equation increased the accuracy of the description of the dynamics of decomposition of cyantraniliprole, as evidenced by the static indices. The bi-exponential equation coefficients were used to calculate the parameters of non-equilibrium sorption. The obtained parameters served as input data for the PEARL model. Modelling the migration of cyantraniliprole with considering aged sorption, showed a significant decrease in the predicted concentrations of the pesticide in percolate.

Nonlinear Prediction Models for Estimation of Pre-weaning Body Weight of Pigs using Morphometric Traits

Background: In the present study, a set of non-linear prediction equation was developed using records of body measurement traits, namely heart girth, punch girth, height at shoulder, height at back, height at fore leg, height at back leg and body length of pigs. Repeated measurement of traits at birth, 15 d, 30 d and weaning (42 d) of 394 piglets were used. Methods: The regression of body weight on body measurement traits showed non-linear relationship based on equation, Y = aXb. Correlation of heart girth with body weight (r2 = 0.968 for male and 0.969 for females; P less than 0.01) was highest among the traits studied. Result: Heart girth was found to be most suited among the traits to predict body weight in an exponential equation, Y = 0.00058 H2.49 and Y = 0.00061 H2.47 for male and females, respectively, explaining 96 percent of variation.