An Improved Empirical Equation for Uniaxial Soil Compression for a Wide Range of Applied Stresses

2001 ◽  
Vol 65 (3) ◽  
pp. 678-684 ◽  
Author(s):  
D.D. Fritton
Keyword(s):  
Empirical Equation ◽  
Wide Range ◽  
Soil Compression ◽  
Applied Stresses

scholarly journals The viscosity of dilute solutions of strong electrolytes

1931 ◽  
Vol 134 (824) ◽  
pp. 413-427 ◽  
Keyword(s):  
Empirical Equation ◽  
Relative Viscosity ◽  
Theoretical Treatment ◽  
High Dilution ◽  
Equivalent Concentration ◽  
Pure Solvent ◽  
Wide Range ◽  
Strong Electrolytes ◽  
Negative Viscosity ◽  
Stiffening Effect

Until very recently, no empirical equation had been found to represent satisfactorily the variation with concentration of the relative viscosity of electrolytes, nor had any adequate theoretical treatment of the problem been put forward. In 1929, however, Jones and Dole showed that the fluidity (or reciprocal of the relative viscosity) of a salt solution could be represented over a fairly wide range of concentration by an equation of the form ϕ = 1 + A√ c +B c , where ϕ is the fluidity, c the equivalent concentration, and A and B are empirical constants. The value of B is negative in the case of salts which increase the viscosity of water, and positive in cases of so-called “negative viscosity,” where the viscosity of the solution is less than that of the pure solvent. Jones and Dole argued further that the stiffening effect of the interionic forces would tend to make the constant A, which determines the viscosity at high dilution, always negative. A little later, Falkenhagen and Dole treated the problem theoretically from the standpoint of the ion-atmosphere theory of Debye and Huckel. They confirmed the suggestion that at high dilution the electrolyte must always increase the viscosity of the solvent, and showed that the relative viscosity of an electrolyte solution at high dilution must be represented by an equation of the form η μ / η 0 = 1 + K √ μ , where η μ is the viscosity of the solution, η 0 is the viscosity of the solvent, μ is the equivalent concentration, K is a constant.

Moisture Quenching of Solid-Matrix Phosphorescence on Hydrophilic and Partially Hydrophobic Filter Papers

2002 ◽  
Vol 56 (10) ◽  
pp. 1368-1375 ◽  
Author(s):  
Amanda H. Ackerman ◽  
Robert J. Hurtubise
Keyword(s):  
Exponential Function ◽  
Filter Paper ◽  
Empirical Equation ◽  
Solid Matrix ◽  
Intensity Data ◽  
Moisture Adsorption ◽  
Wide Range ◽  
Simple Exponential Function ◽  
Filter Papers ◽  
Adsorbed Moisture

A detailed investigation was undertaken to determine the important parameters that were responsible for the solid-matrix phosphorescence (SMP) moisture quenching of phosphors adsorbed in Whatman No. 1 (hydrophilic) and Whatman 1PS (partially hydrophobic) papers. The three phosphors used were phenanthrene, perdeuterated phenanthrene, and benzo[ e]pyrene. Both SMP lifetime and SMP intensity data were obtained over a wide range of adsorbed moisture. In addition, moisture isotherms were obtained for the No. 1 and 1PS papers. The SMP lifetimes of phenanthrene and benzo[ e]pyrene were independent of the amount of adsorbed moisture on both the No. 1 and 1PS papers. However, the SMP lifetimes of perdeuterated phenanthrene on No. 1 and 1PS papers were dependent on the extent of the adsorbed moisture. The changes in the SMP intensities as a function of adsorbed moisture for phenanthrene, benzo[ e]pyrene, and perdeuterated phenanthrene on No. 1 paper could be modeled by a simple exponential function with phenanthrene and benzo[ e]pyrene giving better correlations compared to perdeuterated phenanthrene. The change in the modulus of filter paper samples with moisture adsorption was a major factor in causing the SMP intensity to decrease. The decrease in the SMP intensities with moisture adsorption for the three phosphors adsorbed on 1PS paper did not correlate with the simple Stern–Volmer model and several other quenching models discussed in the literature. Thus, these data were fit to a relatively simple empirical equation. The results showed that the SMP quenching phenomena for the three phosphors on No. 1 paper and on 1PS paper were considerably different.

Variably Reinforced Circular Holes in Stressed Plates

1958 ◽  
Vol 9 (3) ◽  
pp. 213-231 ◽  
Author(s):  
Raymond Hicks
Keyword(s):  
Infinite Plate ◽  
Shear Stresses ◽  
List Type ◽  
Principal Stresses ◽  
Cross Sectional ◽  
Uniform Shear ◽  
Uniform Tension ◽  
Wide Range ◽  
Circular Holes ◽  
Applied Stresses

SummaryExpressions are obtained for the radial, tangential, and shear stresses in an infinite plate containing a variably reinforced circular hole. The variation in the cross-sectional area of the reinforcement is chosen so that the maximum tensile resistance of the reinforcement occurs at points around the hole where the stresses in the plate tend to be high. It is shown that when the reinforcement has a given weight, the effect of varying its cross section is to reduce the stress concentration in the plate.The following particular applied stress systems are considered:— (i)Uniform tension or compression in one direction.(ii)Uniform shear.(iii)Unequal principal stresses.For the particular cases of uniform end loading and unequal applied stresses in the ratio 2:1, data have been obtained which enable the designer to determine the stress distribution in plates with reinforcements having a reasonably wide range of practical dimensions.

scholarly journals Refractometric study on binary, ternary, and quaternary solutions made by water, methanol, ethanol, glycerol, D-glucose monohydrate (DGMH), sucrose, and sodium chloride at T = 293.15 K and atmospheric pressure

2019 ◽  
Vol 62 (4) ◽  
Author(s):  
Fardad Koohyar ◽  
Javad Nasiri ◽  
Farhoush Kiani
Keyword(s):  
Refractive Index ◽  
Sodium Chloride ◽  
Atmospheric Pressure ◽  
Empirical Equation ◽  
Refractive Indices ◽  
Glycerol Water ◽  
Binary Solutions ◽  
Wide Range ◽  
Water Glycerol ◽  
Semi Empirical

The glycerol, D-glucose monohydrate (DGMH), sucrose, and sodium chloride are used in food industries and the measurement of properties for these components and their aqueous solutions can be important. In this research work, the refractive indices for binary solutions of (methanol + glycerol), (ethanol + glycerol), ternary solutions of (water + glycerol + DGMH), (water + glycerol + sucrose), (water + sucrose + DGMH), (water + sucrose + ethanol), (water + ethanol + DGMH), (water + NaCl + DGMH), (water + methanol + NaCl), (water + ethanol + NaCl), (water + NaCl + glycerol), (water + sucrose + NaCl), and quaternary solutions of (water + ethanol + sucrose + DGMH), (water + ethanol + sucrose + glycerol), (water + NaCl + sucrose + glycerol) were measured in wide range of mole fractions at T = 293.15 K and atmospheric pressure. For binary solutions of this study, the changes of refractive index on mixing, ∆nD, were calculated in each mole fraction at T = 293.15 K. Also, the refractive index of binary solutions was fitted by a semi-empirical equation. The constant of this equation, Kr, was represented by Koohyar et al. in 2011. This constant can be used to investigate power of interactions between solute and solvent molecules. For ternary and quaternary solutions of this study, a semi-empirical equation was used to determine refractive indices at given temperature. The comparison between calculated and experimental refractive indices shows that there is a good agreement between them especially in lower molal concentrations.    

Development of an Empirical Equation To Predict Hydraulic-Fracture Closure Pressure From the Instantaneous Shut-In Pressure Using Subsurface Solids-Injection Data

SPE Journal ◽  
2018 ◽  
Vol 24 (01) ◽  
pp. 290-301 ◽  
Author(s):  
S. M. Kholy ◽  
I. M. Mohamed ◽  
M.. Loloi ◽  
O.. Abou-Sayed ◽  
A.. Abou-Sayed
Keyword(s):  
Empirical Equation ◽  
Single Point ◽  
Rock Properties ◽  
Hydraulic Fractures ◽  
Pressure Data ◽  
Tight Sandstone ◽  
Wide Range ◽  
Fracture Closure ◽  
Tight Formations ◽  
Injection Formation

Summary During hydraulic-fracturing operations, conventional pressure-falloff analyses (G-function, square root of time, and other diagnostic plots) are the main methods for estimating fracture-closure pressure. However, there are situations when it is not practical to determine the fracture-closure pressure using these analyses. These conditions occur when closure time is long, such as in mini-fracture tests in very tight formations, or in slurry-waste-injection applications where the injected waste forms impermeable filter cake on the fracture faces that delays fracture closure because of slower liquid leakoff into the formation. In these situations, applying the conventional analyses could require several days of well shut-in to collect enough pressure-falloff data during which the fracture closure can be detected. The objective of the present study is to attempt to correlate the fracture-closure pressure to the early-time falloff data using the field-measured instantaneous shut-in pressure (ISIP) and the petrophysical/mechanical properties of the injection formation. A study of the injection-pressure history of many injection wells with multiple hydraulic fractures in a variety of rock lithologies shows a relationship between the fracture-closure pressure and the ISIP. An empirical equation is proposed in this study to calculate the fracture-closure pressure as a function of the ISIP and the injection-formation rock properties. Such rock properties include formation permeability, formation porosity, initial pore pressure, overburden stress, formation Poisson's ratio, and Young's modulus. The empirical equation was developed using data obtained from geomechanical models and the core analysis of a wide range of injection horizons with different lithology types of sandstone, carbonate, and tight sandstone. The empirical equation was validated using different case studies by comparing the measured fracture-closure-pressure values with those predicted by using the developed empirical equation. In all cases, the new method predicted the fracture-closure pressure with a relative error of less than 6%. The new empirical equation predicts the fracture-closure pressure using a single point of falloff-pressure data, the ISIP, without the need to conduct a conventional fracture-closure analysis. This allows the operator to avoid having to collect pressure data between shut-in and the time when the actual fracture closure occurs, which can take several days in highly damaged and/or very tight formations. Moreover, in operations with multiple-batch injection events into the same interval/perforations, as is often the case in cuttings/slurry-injection operations, the trends in closure-pressure evolution can be tracked even if the fracture is never allowed to close.

A New Empirical Equation for the Specific Thermal Capacity of Aqueous LiCl Solutions in a Wide Range of Conditions

2019 ◽  
Vol 40 (11) ◽  
Author(s):  
Yijian He ◽  
Chao Cao ◽  
Jiachen Xu ◽  
Yue Sun ◽  
Zepeng Chen ◽  
...  
Keyword(s):  
Empirical Equation ◽  
Thermal Capacity ◽  
Wide Range

Ultrasonic Measurement of Residual Stresses in Welded Specimens and Structures

2013 ◽  
Author(s):  
Yuri Kudryavtsev
Keyword(s):  
Large Scale ◽  
Ultrasonic Method ◽  
Ultrasonic Measurement ◽  
Measurement Unit ◽  
Surface Layers ◽  
Stress Relieving ◽  
Wide Range ◽  
Destructive Measurement ◽  
Non Destructive ◽  
Applied Stresses

The application of an ultrasonic non-destructive method for residual stress (RS) measurements has shown that, in many cases, this technique is very efficient and allows measuring the RS both in laboratory conditions and in real structures in field for a wide range of materials. Using this technique, one can measure the RS at the same points many times, studying for instance, the changes of RS under the action of service loading or effectiveness of stress-relieving techniques. An ultrasonic computerized complex (UCC) for non-destructive measurement of residual and applied stresses was developed recently. The complex includes a measurement unit with transducers, basic supporting software, an advanced database and an Expert System, housed in a laptop, for analysis of the influence of RS on the fatigue life of welded elements. In general, the ultrasonic method allows one to measure the RS in both cases: averaged through thickness or in surface layers. The present version of UCC allows measuring the averaged through thickness biaxial RS in plates 2–150 mm thick. The results of ultrasonic RS measurement in large scale welded specimens and structures are also discussed in this paper.

Cumulative degradation methodology to predict reliability of electronic systems

Circuit World ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
George Thiel ◽  
Flavio Griggio ◽  
Sanjay Tiku
Keyword(s):  
Empirical Equation ◽  
Mechanical Load ◽  
Consistency Condition ◽  
Consumer Electronics ◽  
Electronic Systems ◽  
Physics Of Failure ◽  
Content Type ◽  
Performance Metric ◽  
Wide Range ◽  
Speed Up

Purpose The purpose of this paper is to describe a novel methodology for predicting reliability for consumer electronics or any other hardware systems that experience a complex lifecycle environmental profile. Design/methodology/approach This Physics-of-Failure–based three-step methodology can be used to predict the degradation rate of a population using a Monte Carlo approach. The three steps include: using an empirical equation describing the degradation of a performance metric, a degradation consistency condition and a technique to account for cumulative degradation across multiple life-cycle stress conditions (e.g. temperature, voltage, mechanical load, etc.). Findings Two case studies are provided to illustrate the methodology including one related to repeated touch-load induced artifacts for displays. Originality/value This novel methodology can be applied to a wide range of applications from mechanical systems to electrical circuits. The results can be fed into the several stages of engineering validation to speed up product qualification.

Pressions de vapeur des mélanges eau – nitrate d'éthylammonium à 298,15 K. Propriétés thermodynamiques des milieux eau – sel fondu

1985 ◽  
Vol 63 (12) ◽  
pp. 3587-3592 ◽  
Author(s):  
M. Biquard ◽  
P. Letellier ◽  
M. Fromon
Keyword(s):  
Activity Coefficient ◽  
Empirical Equation ◽  
Pure Water ◽  
Partial Molar Volumes ◽  
Pressure Measurements ◽  
Text Interpretation ◽  
Wide Range ◽  
Ethylammonium Nitrate ◽  
Vapor Pressure Measurements ◽  
Fused Salt

The activity and activity coefficient of water in water and ethylammonium nitrate (EAN) mixtures were determined by vapor pressure measurements between pure water and pure fused salt at 298.15 K. For a wide range of mole fractions of salt, (0.3 < X ≤ 1) the behaviour of water can be described very accurately by a "one parameter" empirical equation which involves activity coefficient, γE, mole fraction of EAN, and limiting Gibbs energy of the dilution of water in pure fused salt, [Formula: see text]:[Formula: see text]Interpretation of experimental results was also attempted by use of the B.E.T. equation. It appears that the energy, ΔEd = E − EL, in those solutions is very low. Partial molar volumes of water and salt are also discussed in relation to empirical and B.E.T. equations. It can be shown that the two equations lead to similar results.

Semi-Empirical Approach for Fission Fragment Energy Degradation in any Elementary Medium

1971 ◽  
Vol 49 (23) ◽  
pp. 3036-3040 ◽  
Author(s):  
M. Hakim ◽  
N. H. Shafrir
Keyword(s):  
Experimental Data ◽  
Energy Loss ◽  
Physical State ◽  
Empirical Equation ◽  
Electronic Energy ◽  
Fission Fragments ◽  
Fitting Procedure ◽  
Wide Range ◽  
Energy Degradation ◽  
Semi Empirical

A semi-empirical equation for the electronic energy loss of fission fragments has been derived by fitting the theoretical approach of Bohr, specifically developed for heavy stopping materials, to experimental data in gases and solids in a wide range of atomic numbers. The fitting procedure was performed by choosing a different expression for the number of electrons of the medium taking part in the stopping process, which includes empirical parameters obtained by fitting to experiment.The equation enables the energy loss of fission fragments in substances of any Z2, regardless of their physical state, to be predicted to a good degree of accuracy down to energies of approximately 20 MeV.

Sign in / Sign up

Export Citation Format

Share Document