Simple Power Equation Research Articles

Investigation of the free overfall for discharge measurement in stone bed triangular channels

This study utilizes the freefall as a simple and useful tool for measuring end depth discharge EDD in triangular channels having stone beds. For this task, forty-five triangular channel models are constructed and examined all having 360 cm length and end drop fall of 20 cm. In these channel models, three channel side slopes z = 0.7, 1.0 and 1.3, five bed slopes St = 0.00, 0.0033, 0.005, 0.010 and 0.020 and three bed stone diameters ds = 5 mm, 10 mm and 15 mm are tested. The laboratory results demonstrated straight line relationships for the variation of end depth ye with critical depth yc and the variation of end depth with uniform normal depth yn for different values of z, St and ds tested in this study, while, the relation between ye/yc and bed slope St showed a quadratic expression. Moreover, the relationship for the dimensionless discharge with both channel bed slope St and the ratio of end water depth ye to bed stone diameter ds(ye/ds) has been presented by a simple empirical power equation with high determination coefficient which can be applied for subcritical and supercritical states of flow for the range of upstream Froude number Frn between 0.14 and 1.27.

A Field Survey of Rare Earth Element Concentrations in Process Streams Produced by Coal Preparation Plants in the Eastern USA

A field study was undertaken to experimentally measure the concentrations of rare earth elements (REEs) contained in the process streams generated by a group of 20 coal preparation plants located in the eastern USA. For each site, representative samples of clean coal product, coarse refuse, and fine refuse were collected. Each sample was then partitioned into preselected size and density classes by wet screening/sieving and float-sink testing. The resultant products were dried and subjected to laboratory analyses to determine ash contents and rare earth element concentrations including Yttrium and Scandium. A detailed analysis of the database generated by this exercise showed that coal-based products from these preparation plants contained significant quantities of rare earth elements. In particular, the coarse refuse streams currently discarded by the 20 plants examined were found to contain a sufficient tonnage of REEs to satisfy the current domestic demand for these important elements. The data also showed a strong positive correlation between ash content and REE concentration, which suggested that the primary association of REEs in eastern USA bituminous coal sources is likely within fractions containing inorganic impurities. This association was well described using a simple power equation relating ash content and REE concentration. The ratio of heavy-to-light rare earth elements was discovered to be significantly higher in organically rich fractions of clean coal, suggesting that mineral impurities intimately associated with carbonaceous matter have elevated concentrations of heavy rare earth elements. A similar trend was observed for a grouping of rare earth elements (Y, Nd, Eu, Tb, and Dy) that are likely subject to near-term supply shortages. Finally, the database showed that a linear correlation existed between La for many REEs of interest, although there were several notable exceptions for some high-value REEs (Lu, Pr, and Tb).

Estimation of stubble biomass in major field crops using residue cutting height

Crop residue is recognized as a potential feedstock for biofuels and a sustainable substitute for fossil energy sources. Expanding the acreage of biofuel crops, it is important to establish a crop residue retention regime to conserve soil fertility and prevent soil erosion. This paper presents simple linear and power equations between stubble biomass ratio (SBR, i. e. percentage of stubble biomass to whole plant biomass) and stubble height ratio (SHR, i. e. percentage of stubble height to maximum plant height) for a wide range of field crops of rice, wheat, oat, corn, sorghum, sunflower, canola, soybean and cotton, using data collected from 15 sites in production fields in 11 provinces across China from 2009 to 2012. Simple linear regressions for the crops were associated with highly significant coefficients of determination (R2) for all crops. Validation with independent datasets also showed high R2 values, indicating model goodness-of-fit. Mean relative error (MRE) and root mean square error (RMSE) values showed good fit for the two allometric relationships for each field crop studied. These results could be used to assess stubble mass for sustainable residue removal in bio-based energy systems.

Hydraulic Performance of Circular Crested Triangular Plan Form Weirs

Triangular labyrinth weirs are nonlinear weirs used to control and pass the required discharge with low afflux in case of limited width saving the upstream countryside and costly lands from submergence. In this paper, the hydraulic performance of circular crested triangular plan form weirs under free flow conditions is experimentally studied. In this regard, twenty-seven weir models have been fabricated and tested in a laboratory flume. These models had different vertex angles (\(\theta = 45^{\circ }\), \(60^{\circ }\) and \(75^{\circ }\)), different weir heights (\({P} = 15\), 20 and 25 cm) and different crest diameters (\({D} = 2.54\), 4 and 5 cm). The experimental results of all models showed that the variation of discharge coefficient (\({C}_{\mathrm{d}}\)) with relative head above crest (h/P) for the different values of \(\theta \), P and D was a simple power equation. It was observed that the values of \({C}_{\mathrm{d}}\) decreased with the increase in h/P values for all models. An empirical power equation was obtained for the estimation of \({C}_{\mathrm{d}}\) in terms of \(\theta \), h/P and h/D. The values of discharge magnification (\({Q}_{{\mathrm{TC}}}/{Q}_{{\mathrm{NS}}}\)) decreased with the increase in h/P values. Weirs of small vertex angle, low height and small crest diameter gave high values of discharge magnification (better performance). The best weir performance was found for a weir of \(\theta = 45^{\circ }\), \({P} = 15\,\hbox {cm}\) and \({D} = 2.54\,\hbox {cm}\) (\({D/P} = 0.17\)) within the limitations of this study.

Effect of Bed and Side Slopes on Flow Measurements in Trapezoidal Free Overfall Channels

The aim of the present investigation is to study the effect of both side and bed slopes on the flow over free overfalls in trapezoidal channels, three models of trapezoidal free overfall channels have been built and tested in a laboratory flume. These models had 0.1m bed width and 3.7m length with different values of side slope (m = 0.268, 0.577, and 1). Each model had four different bed slopes (S = 0, 0.0033, 0.01, and 0.02). A total of twelve series of the experiments were tested for different ranges of Froude number. Experimental results of all models showed that the variation of \({({Qm^{1.5}/\sqrt{gb^{5}}})}\) with \({({my_b /b})}\) for different values of side slope and different bed slopes is a simple power equation. It was observed that the values of \({({Qm^{1.5}/\sqrt{gb^{5}}})}\) increase with the increase in \({({my_b /b})}\) values. The correlation between \({( {my_b /b} )}\) with \({({my_c /b})}\) is found to be linear for different bed slopes. The ratio \({({y_b /y_c})}\) decreases with the increase of slope (S) with an average value of 0.729 for subcritical and supercritical flow on smooth beds of different slopes. An empirical expression is obtained for the variation of \({(Qm^{1.5}/\sqrt{gb^{5}})}\) with \({({my_b /b}),}\) and (S). The results of the present study have been compared with theoretical and experimental results obtained by other investigators showing well agreements.

Sustained release of diltiazem HCl tableted after co-spray drying and physical mixing with PVAc and PVP

In this work, aqueous diltiazem HCl and polyvinyl-pyrrolidone (PVP) solutions were mixed with Kollicoat SR 30D and spray dried to microparticles of different drug:excipient ratio and PVP content. Co-spray dried products and physical mixtures of drug, Kollidon SR and PVP were tableted. Spray drying process, co-spray dried products and compressibility/compactability of co-spray dried and physical mixtures, as well as drug release and water uptake of matrix-tablets was evaluated. Simple power equation fitted drug release and water uptake (R2 > 0.909 and 0.938, respectively) and correlations between them were examined. Co-spray dried products with PVP content lower than in physical mixtures result in slower release, while at equal PVP content (19 and 29% w/w of excipient) in similar release (f2 > 50). Increase of PVP content increases release rate and co-spray drying might be an alternative, when physical mixing is inadequate. Co-spray dried products show better compressibility/compatibility but higher stickiness to the die-wall compared to physical mixtures. SEM observations and comparison of release and swelling showed that distribution of tableted component affects only the swelling, while PVP content for both co-spray dried and physical mixes is major reason for release alterations and an aid for drug release control.

Lineal energy calibration of a spherical TEPC.

Tissue-equivalent proportional counters (TEPCs) do not always allow built-in calibration alpha-particle sources, and the lineal energy calibration of these counters must be performed with an external radiation able to penetrate the detector walls. The irradiation field can be used for calibration if a particular marker point of known lineal energy is identified in the measured spectrum. This point is often identified with the proton edge, which corresponds to the maximum energy deposited by protons in the given volume. If the proton edge cannot be identified precisely in the measured spectrum, a gamma source can be used instead, identifying the maximum lineal energy due to electrons (e-edge). The technique was already described and applied for cylindrical TEPCs, allowing a calibration with an overall uncertainty smaller than 5 % (Conte et al. Lineal energy calibration of mini tissue equivalent gas-proportional counters (TEPC). AIP Conf. Proc. 1530, 171-178 (2013)). In the present work, this study was repeated for spherical detectors. First a marker point was identified in the microdosimetric spectrum of a (137)Cs gamma source, then a precise value of lineal energy was assigned to it. Gas pressures were varied to simulate diameters from 0.5 and 3 µm at density 1 g cm(-3). A simple power equation is given for allowing calibration of TEPCs filled with C3H8-TE gas at different pressures, using an external (137)Cs gamma source.

On the opposition of dynamic recrystallization and solute dragging in steels

The influence of chemical composition on the hot deformation behavior and dynamic recrystallization was studied by conducting hot compression tests on two low alloy steels, AISI 4135 and VCN200, over a temperatures range of 1000–1150°C and at strain rates of 0.001s−1 to 1s−1. The activation energy of dynamic recrystallization in 4135 and VCN200 was determined as 374kJ/mol and 435.3kJ/mol, respectively. The different apparent activation energies (about 17%) were attributed to about 30% difference between the carbon equivalents of the steels. The results confirmed that the higher the alloying elements, the higher the peak stress and strain of DRX flow curves. The results were associated with the dragging force of solute atoms on the grain boundaries. A new formula was proposed as a chemical factor to quantify the influence of solute dragging on the dynamic recrystallization behavior. Simple power equations described how the peak stress and strain depends on the Zener–Hollomon parameter. The material constants of the developed equations were related to the proposed composition factor. Unlike to dynamic recrystallization, dynamic recovery did not delayed by solute dragging.

Self-Emulsifying Pellets: Relations Between Kinetic Parameters of Drug Release and Emulsion Reconstitution—Influence of Formulation Variables

The effects of surfactant type and content on the kinetics of emulsion reconstitution and release of drugs differing in lipophilicity from self-emulsifying microcrystalline cellulose pellets were studied. Furosemide and propranolol were the drugs, medium-chain triglyceride was the oil, and Cremophors ELP, RH40, and RH60 were the surfactants. Pellets were prepared by extrusion/spheronization with emulsions (75% water and 25%, w/w, oil/surfactant/drug). Stability of the emulsions was evaluated from changes in the back-scattered light, and re-emulsification and drug release from light transmittance and UV spectroscopy, respectively. Emulsion stability increased because of the incorporation of the drugs. Re-emulsification depended only on the surfactant content and was expressed by a simple power equation (Ra2 > 0.945, Q(2) > 0.752). Drug release was expressed by two biexponential equations (Ra2 > 0.989, Q(2) > 0.699 and Ra2 > 0.947, Q(2) > 0.693) implying initial burst and terminal slow release phase and by the linear form (Lineweaver-Burke) of Michaelis-Menten equation (Ra2 > 0.726, Q(2) > 0.397). Relationships exist between the rate constants of the equations describing emulsion reconstitution and drug release, for propranolol compositions (R(2) = 0.915), and for compositions of both drugs with less hydrophilic ELP and RH40 (R(2) = 0.511), and also, among dissolution efficiency, drug solubility in oil/surfactant, and emulsion reconstitution ability, indicating the importance of drug solubilization in oil/surfactant and re-emulsification ability on drug release.

Construction of one-way volume table for the three major useful bamboos in Japan

The one-way volume table for the three major useful bamboos in Japan, i.e., Phyllostachys pubescens Mazel ex Houz., Phyllostachys bambusoides Sieb. et Zucc. and Phyllostachys nigra var. henonis, was constructed based on a dataset of 920 felled culms collected from five different districts. Twenty-three models were fitted to the height–diameter relationship for each species, and their goodness of fit were compared. The height–diameter relationship for P. pubescens and P. nigra could be expressed by the reciprocal equation, whereas that for P. bambusoides was approximated by the simple allometric power equation. The culm height was predicted by substituting the measured diameter at breast height (dbh) into the determined height–diameter model. The apparent culm volume was then estimated from the measured dbh and the predicted culm height with the two-way volume equations derived in previous studies. For all species, there was no significant difference between the actual and estimated apparent culm volume. The one-way volume table for these bamboo species was constructed by combining the two-way volume equation and the height–diameter model, so that the apparent culm volume could be solely estimated from dbh. For the same dbh, P. bambusoides had the largest apparent culm volume compared to the other two species, whereas P. pubescens had the smallest one. The difference in the apparent culm volume was caused by the inter-specific variations in culm slenderness and/or taper. The volume table developed here will be useful in evaluating the amounts of resources of the three major useful bamboos in Japan.

Estimation Procedures for Understory Biomass and Fuel Loads in Sagerrush Steppe Invaded by Woodlands

Regression equations were developed to predict biomass for 9 shrubs, 9 grasses, and 10 forbs that generally dominate sagebrush ecosystems in central Nevada. Independent variables included percent cover, average height, and plant volume. We explored 2 ellipsoid volumes: one with maximum plant height and 2 crown diameters and another with live crown height and 2 crown diameters. Dependent variables were total, live, leaf, and dead biomass. Simple, multiple, linear, and power equations were investigated. Models were chosen based on scatter plots, residual plots, and R2 and SEE values. In general, simple power equations provided the best-fit regressions. For shrubs, the ellipsoid volume computed with maximum plant height best predicted total plant weight, and the ellipsoid volume computed with the live crown height best predicted shrub foliage weight. In addition to regression equations for biomass, ratios for division of that biomass into 1-, 10-, 100-, and 1000-hour fuels were derived for common large shrubs. Regression equations were also derived to relate litter mat sizes of major shrub species to litter weights. The equations in this paper could be used to predict biomass in other areas of the Great Basin if training data were taken to validate or adjust these models.

Prediction of salinity intrusion in Danshuei estuarine system

The main parameters that affect the flow conditions and intrusion of salt water in an estuary system are tides and the seasonal variation of water discharge. A laterally averaged two-dimensional numerical model called MIKE 11 XZ is used to simulate the hydrodynamics and salinity intrusion of Danshuei River estuarine system. This model can simulate hydrodynamics and water quality in estuaries, reservoirs and lakes. MIKE 11 XZ solves the Reynolds-averaged Navier–Stokes equations by using Abbott–Ionescu finite difference scheme in a non-dimensional vertical σ-coordinate. Vertical eddy diffusivity in the model can be determined by a constant value, a mixing length theory and a k or k−ɛ turbulence closure scheme with Richardson number correction. A series of comprehensive field data obtained from Danshuei estuarine system is used for evaluation, calibration and verification of the model. The friction coefficient was calibrated and verified using water surface elevation and velocity measurements, respectively. Then the vertical eddy diffusivity was calibrated and verified through comparison of salinity measurements in different layers of several stations. Reasonable agreement was obtained between the model results and the observed data using k−ɛ turbulence closure scheme. The model application was investigated with different discharges and the effect of discharge variation on salinity intrusion was determined. The results showed that the fresh water discharge is the main parameter that affects the salinity intrusion in this system. Finally, simple power equations are suggested to predict the salinity intrusion due to the fresh water discharge in different tributaries of the system.

Method of Estimating Fatigue-Crack Propagation Properties Based on Accumulated Damage Model

We previously developed a crack propagation model to calculate crack paths using accumulated damage in microsolder joints in semiconductor structures. We have now developed a method based on the crack propagation model, which is named accumulated damage model, to predict fatigue-crack propagation properties of solders. Generally, there is a correlation between crack propagation rates, da/dN, of solders and J-integral ranges, ΔJ. The correlation can be represented in an equation as a simple power relationship, given by da/dN=B [ΔJ] q. We derive this simple power equation from our crack propagation model and Hutchinson-Rice-Rosengren singularity theory. The equation enabled us to estimate fatigue-crack propagation properties from cyclic stress-strain curves and fatigue strength properties. We used the method to predict fatigue-crack propagation properties for center-cracked plate specimens made of Sn-40Pb and Sn-3.5Ag-1Cu. The predictions agreed well with actual fatigue-crack propagation properties determined by experiment for center-cracked plate specimens made of Sn-40Pb and Sn-3.5Ag-1Cu, indicating that our method effectively predicts solder fatigue-crack propagation properties.

<i>In Vitro</i> And <i>In Vivo</i> Evaluation Of Controlled-Release Buccoadhesive Disks Of Timolol Maleate

The aim of the present work was to develop a buccoadhesive controlled-release dosage form of timolol maleate (TM) and to evaluate the feasibility of improving the bioavailability of TM via the buccal route. Buccoadhesive disks (BDs) of TM were prepared by the direct compression method using some selective polymers like carbopol 934(CP 934) and hydroxypropyl methylcellulose (HPMC K4M) in different amounts along with other tablet excipients. The disks were evaluated for thickness uniformity, weight variation, drug content uniformity, hardness, friability and surface pH. The buccal permeability of TM was assessed in one human subject and the drug was found to permeate through the buccal mucosa. The BDs were also evaluated for swelling index and bioadhesion time using rabbit buccal tissues. The swelling index was found to increase with an increase in HPMC and CP content in the disks and none of the disks detached from the rabbit buccal tissues until completely eroded. The in vitro drug release for 12 h in pH 6.6 phosphate buffer using a USP dissolution tester revealed that the rate of drug release was increased when the polymers were incorporated in the disks at low concentrations, but was decreased when incorporated at higher concentrations. When the release data were evaluated by a simple power equation (Mt/M = ktn); it was observed that drug release from most of the formulated BDs followed non-fickian release kinetics. A selected BD formulation was evaluated in vivo in rabbits. The selected BD gave controlled blood level profile with a 50% increase in area-under-the-curve (AUC) value in comparison to oral administration of aqueous drug solution.Egyptian Journal of Biomedical Sciences Vol. 23 (1) 2007: pp. 196-217

Allometric methodology for the calculation of biokinetic parameters for marine biota

Biological half-lives of elimination ( T B1/2) and concentration factors (CF) for different radionuclides and marine organisms were analysed. Tests were carried out in order to investigate the cases in which these parameters can be described by a simple power equation as a function of the volume of the organism, to verify the hypothesis of allometric scaling. Statistically significant trends were found for the CF of plutonium and americium and the T B1/2 of technetium and radiocaesium across organisms. Some of these trends satisfy the theoretical expectation that allometric relations are a power function of the volume of the organism. For the CF, which relates to retention of a radionuclide, the mean exponent of the power function, − 0.29 ± 0.02, is close to the theoretical value of − 0.25. For the T B1/2 the mean exponent of the power function is lower at 0.16 ± 0.01. The work improves the understanding of the metabolism of radionuclides within organisms for which no direct biokinetic information exists. The allometric relationships derived can be applied to calculate a T B1/2 for caesium or technetium and a CF for plutonium and americium for any marine species. For the elements N, K, Np and Cm, the same allometric relationships as those derived for their analogues 99Tc, 137Cs, 239,240Pu and 241Am, respectively, can be applied, when no other data are available.

106 はんだの疲労き裂進展特性の推定(OS01.電子デバイス・電子材料と計算力学(2))

We previously developed a crack propagation model to calculate crack paths using accumulated damage in micro-solder joints in semiconductor structures. We have now developed a method based on this crack propagation model, which we have called an accumulated damage model, to predict fatigue-crack propagation properties of solders. Generally, there is a correlation between crack propagation rates, da/dN, of solders and J-integral ranges, ΔJ. The correlation can be represented in an equation as a simple power relationship, given by da/dN=B[ΔJ]^q. We derive this simple power equation from our crack propagation model and Hutchinson-Rice-Rosengren singularity theory. The equation enabled us to estimate fatigue-crack propagation properties from cyclic stress-strain curves and fatigue strength properties. We used the method to predict fatigue-crack propagation properties for center-cracked plate specimens made of Sn-40Pb. The predictions were consistent with actual fatigue-crack propagation properties determined by experiment for center-cracked plate specimens made of Sn-40Pb, indicating that our method can be used to effectively predict solder fatigue-crack propagation properties.

Flume or weir continuous water flow rate recorder for irrigation use

US Bureau of Reclamation projects and irrigation districts need simple, low-cost, robust devices to measure and record water use for effective water management decisions. This need has resulted in the development of a continuous flow meter and recorder (CFM). The CFM is designed to continuously measure flow rates through open channel measurement structures, such as flumes or weirs, by recording the water levels upstream. The water level measurements are then converted to flow rate using a simple weir power equation. The CFM consists of an easily programmed CPU, an LCD for displaying the flow rate and total amount of water that has passed through the measurement structure, and a water level sensor. The CFM, including a solar power supply, may be purchased for under US$1000. The majority of that cost is for the water level sensor and may be reduced depending upon the needed accuracy. Presently, some of these devices have been installed on irrigation systems in the field where they have been exposed to harsh weather conditions. Despite the harsh environments, the CFMs have been functioning as designed. This paper discusses the design, installation, and testing of the continuous flow meter. Published in © 2005 John Wiley & Sons, Ltd.

Linear Solution for Hydraulic Analysis of Tapered Microirrigation Laterals

A simplified analytical solution that takes into account the effect of the emitter discharge exponent on the hydraulic computations of tapered microirrigation laterals, is presented. The hydraulic analysis is evaluated based on the spatially variable discharge function approach. A simple power equation was used to express distribution of the variable outflow delivered from the each emitter along the lateral. An analytical solution is developed for the case of a linear relationship between the emitter discharge and pressure head, namely, the emitter discharge exponent equals to unique, y = 1.0. In this procedure, the analytical derivations can be applied for uphill, downhill, and zero slope conditions. Results are comparable to those obtained from the literature.

Microirrigation Lateral Design using Lateral Discharge Equation

A simple and accurate method is developed for designing single, paired, and tapered microirrigation laterals. The hydraulics of the lateral is evaluated using a lateral discharge equation approach. A simple power equation is used to express the relationship between the inlet flow rate and inlet pressure head of the lateral. Keeping the flow variation within the specified limit, a procedure for designing the length of the tapered section is developed. The lateral is designed using a step-by-step method. The length of the tapered section is determined by the golden section search method.

Glucose oxidase release from calcium alginate gel capsules.

Diffusion of glucose oxidase within calcium alginate gel capsules has been assayed and the experimental data fitted to a simple semi-empirical power equation, which is used to analyse the solute release from polymeric devices. It was found that an increase in the concentration of sodium alginate and calcium chloride gives rise to a reduction in the enzyme leakage. This was verified when glucose oxidase (GOD) diffusion percentages were compared in capsules with thicknesses of the same order of magnitude but obtained under different experimental conditions. So, the use of sodium alginate and calcium chloride solutions of concentrations 0.5% w/v and 2.6% w/v, respectively, lead to a diffusion percentage of 25 +/- 2. This percentage was reduced to 8 +/- 3 when sodium alginate and calcium chloride concentrations were fixed at 1% w/v and 4% w/v, respectively, even though the thicknesses of the capsules were of the same order of magnitude.