Semi-theoretical Equations Research Articles

Psychrometric charts for hydrocarbon vapours in nitrogen

Psychrometric charts for six different systems involving condensing hydrocarbon vapour in nitrogen are presented. The hydrocarbons considered are benzene, toluene, acetone, n-pentane, n-hexane and cyclohexane. The charts are based upon semi-theoretical equations and make use of published physical property data and correlations. The behaviour of the vapour phase is characterised by the Virial Equation of State truncated at the third term. The solubility of nitrogen in the liquid hydrocarbons is also considered. The charts are constructed with the dry bulb temperature and absolute humidity scales as the orthogonal axes. Curves of constant adiabatic saturation temperature, constant relative humidity, constant gas specific volume and constant enthalpy deviation are plotted on the charts.

Multisite analyses of spectral-biophysical data for wheat

Reflectance factors and biophysical plant measurements for wheat ( Triticum aestivum L.) experiments conducted at Lubbock, Texas, Manhattan, Kansas, Phoenix, Arizona, Sidney, Montana, and Weslaco, Texas were fit by various equation forms for six currently used vegetation indices (VI): n-space greenness (GVI), perpendicular (PVI), NIR/RED ratio (RVI), soil adjusted (SAV12), normalized difference (NDVI), and transformed soil adjusted (TSAVI). The objective was to produce relations from the data pooled across all locations that could be recommended for general use for wheat. Data were analyzed by premaximum leaf area (pre- L max), post-maximum leaf area (post- L max), and whole season portions of the growing seasons, Leaf area index ( L) was best estimated from RVI and TSAVI by linear equations, from NDVI and TSAVI by exponential equations, and from the orthogonal indices GVI and PVI equally well by power and quadratic equation forms. These equation forms gave coefficients of determination ( R 2) that ranged from 0.72 to 0.86, and root mean square errors (RMSE) in estimating L that ranged from 0.63 to 0.90 across locations and measurements that differed in soils, sun angles, cultivars, agronomic treatments, and radiometers. The single best equation form for estimating L from VI across all VI was the power form. The orthogonal indices GVI and PVI were more responsive to canopy architecture than the ratio vegetation indices, and GVI ranked as the best single index. Equations for estimating fractional absorbed photosynthetically active radiation (FPAR) from VI given herein agree well with empirical and semitheoretical equations and their coefficients found in the literature. Our results demonstrate the robustness of vegetation indices across experiment variables and measurement conditions, and provide general functional relations that should be useful for wheat.

DRAG FORCES ON NONSPHERICAL AEROSOL PARTICLES

This report is a review of current knowledge, based on the modified Stokes drag, of drag forces on nonspherical aerosol particles. The Knudsen numbers (Kn) for the aerosol studies are between 0 and 150, ranging from the continuum regime (Kn = 0) to the transition regime (0 20). The drag force on an aerosol particle can be expressed in terms of Stokes drag, dynamic shape factor, slip correction factor and non-Stokesian factor. The dynamic shape factor accounts for shape effects, the slip correction factor for the slip condition of gas-particle interaction, and the non-Stokesian effect for increased drag at a Reynolds number greater than 0.05. The dynamic shape factors of many shapes were measured in a sedimentation tank, using macroscopic objects, and also in aerosol systems. Theoretical and semi-theoretical equations have been developed for spheroids, cylinders, aggregates and rectangular prisms. The Knudsen-Weber equation with the adjustment for sphere diameter c...

A p‐V‐T Surface for Trifluoromethane

AbstractThe density of trifluoromethane has been measured from 126 to 332 K and up to 1000 bar. The results have been correlated in terms of the Strobridge equation of state, and compared with results from the literature. The ability of other semitheoretical equations of state to fit the data has been tested, as well as a variational theory. The spinodal curve has been estimated from the expansivity data.

Viscosity and densities of binary mixtures of acetonitrile with substituted anilines. Part 4

Viscosity and density data are presented for five binary liquid mixtures of acetonitrile with aniline and substituted anilines at five different temperatures. The experimental data are fitted to semitheoretical equations proposed by McAllister and Heric. Excess viscosity, excess volume and the excess Gibbs energy of activation of flow have been calculated from the experimental data. Various thermodynamic parameters of activation of flow are calculated from the dependence of viscosity on temperature. The deviations from ideality of thermodynamic and transport functions are explained on the basis of molecular interactions between the components of the mixture.

Semi-Empirical Equations for Three Components of Resultant Cutting Force

For the determination of adequate cutting conditions and the selection and design of both cutting tool and machine tool, not only the cutting force but also the feed force and thrust force must be known quantitatively. This paper presents the semi-empirical semi-theoretical equations for the three cdmponents of resultant cutting force. These equationa are dorived from theoretical equations by simplifying them using the empirical relations which exist in practical range of cutting conditions. Eaoh component is indicated as the function of depth of cut, feed, cutting speed, rake angle and opproach angle. For the work material, these equations include the specific forcesata standard set of cutting conditions, the coefficiantsof cutting speed and undeformed chip thickness, and the coefficientsof rake angle. These material constants are obtained from a series of cutting tests on each work material and approach angle.

Process analysis and optimal design of a fermentation process based upon elemental balance equations: Generalized semitheoretical equations for estimating rates of oxygen demand and heat evolution

AbstractBased upon elemental balance equations, generalized semitheoretical equations are developed for estimating the rates of oxygen demand and heat evolution of a fermentation process. The results estimated by these equations are in good agreement with data obtained from yeast–hydrocarbon and yeast–carbohydrate fermentation processes for citric acid production. Furthermore, a direct relationship between rates of oxygen demand and heat evolution is derived with a correlation constant of 0.18 kcal/mM O2.The relationship has been verified by data of citric acid fermentation processes and also confirmed by published data. These derived equations would be useful for process design and optimization.

製銅に関する物理化学的研究（第5報）熔銅と硫化水素，水素混合瓦斯との平衡に関する統計熱力学的解析

Assuming that the liquid state of copper is quasicrystalline and the gas atoms dissolved are situated interstitially in the vacant positions of the lattice, the theoretical formulae on the equilibrium between H2S-H2 gas mixture and sulphur in molten copper has been derived by the statistical thermodynamical method. Next, for comparing with the experimental data obtained by the author, the values of some unknown constants ΨS, \varphiSS, θS in theoretical formulae, which correspond to the interaction energy between S-Cu and S-S pairs and the vibrational characteristic temperature of sulphur atom in molten copper have been determined numerically. So, when these values are substituted into the theoretical formulae, the following semi-theoretical equations can be obtained:(This article is not displayable. Please see full text pdf.) \ oindentin which, x and y are the atomic concentration of sulphur and hydrogen in molten copper respectively.

Frictional Phenomena. VIII

GEL formation in colloidal systems causes the viscosity of such systems to vary with the stress: these are called non-Newtonian liquids. Because the physical cause of such behavior is related to the gel structure, the phenomenon is called structural viscosity. Three particular features are observed with such systems: a non-linearity of the rate of shear vs. stress relation in the case of stationary flow; a finite relaxation process for suddenly applied stresses or deformations; and a frequency dependent dynamic viscosity in the case of alternating processes. The chief experimental facts in these three fields are presented, together with certain semitheoretical equations best suited to describe the experiments.