Empirical Equation for Determination of Alternate Bar Height

2019 ◽  
Vol 145 (11) ◽  
pp. 04019037
Author(s):  
Yunshuo Cheng ◽  
Ana Maria Ferreira da Silva
Keyword(s):  
Empirical Equation

A Reconsideration of the Geometry Factor for the Standard and Profile Shifted Teeth

1989 ◽  
Vol 111 (3) ◽  
pp. 402-413 ◽  
Author(s):  
J. H. Kuang ◽  
Y. T. Yang
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Stress Concentration Factor ◽  
Empirical Equation ◽  
Design Parameters ◽  
Spur Gears ◽  
Geometry Factor ◽  
Gear Teeth ◽  
Semi Empirical

A semi-empirical equation for the determination of the stress concentration factor for spur gears is introduced. The effects of some design parameters such as fillet radii of rack cutters, teeth number, and profile shifting factor, on the stress distribution at the fillets of gear teeth are investigated. Values of the modified geometry factors for the standard and profile shifted teeth are also derived. It is hoped that the present investigation may yield a more accurate prediction of the localized stresses at tooth fillets than the results thus far available.

Heat Transfer From a Flat Surface to an Oblique Impinging Jet

1988 ◽  
Vol 110 (1) ◽  
pp. 84-90 ◽  
Author(s):  
R. J. Goldstein ◽  
M. E. Franchett
Keyword(s):  
Heat Transfer ◽  
Empirical Equation ◽  
Plane Surface ◽  
Temperature Sensitive ◽  
Composite Sheet ◽  
Test Plate ◽  
Nusselt Numbers ◽  
Main Portion ◽  
Areas Of Interest

Experiments are conducted to determine the heat transfer to a jet impinging at different oblique angles to a plane surface. The main portion of the test plate contains a composite sheet of temperature-sensitive liquid crystal, which is sandwiched between a thin metallic-foil heater and a specially designed liquid bath. The results indicate a displacement of the peak heat transfer from the geometric center of the jet origin, the displacement being a function primarily of impingement angle. Contours of constant heat transfer coefficient are obtained and correlated with an empirical equation that permits determination of average Nusselt numbers over areas of interest.

scholarly journals Mechanical dispersion of clay from soil into water: readily-dispersed and spontaneously-dispersed clay

2015 ◽  
Vol 29 (1) ◽  
pp. 31-37 ◽  
Author(s):  
Ewa A. Czyż ◽  
Anthony R. Dexter
Keyword(s):  
Qualitative Method ◽  
Empirical Equation ◽  
Soil Samples ◽  
Exchangeable Cations ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Mechanical Dispersion ◽  
Energy Inputs ◽  
Water Contents

Abstract A method for the experimental determination of the amount of clay dispersed from soil into water is described. The method was evaluated using soil samples from agricultural fields in 18 locations in Poland. Soil particle size distributions, contents of organic matter and exchangeable cations were measured by standard methods. Sub-samples were placed in distilled water and were subjected to four different energy inputs obtained by different numbers of inversions (end-over-end movements). The amounts of clay that dispersed into suspension were measured by light scattering (turbidimetry). An empirical equation was developed that provided an approximate fit to the experimental data for turbidity as a function of number of inversions. It is suggested that extrapolation of the fitted equation to zero inversions enables the amount of spontaneously-dispersed clay to be estimated. This method introduces the possibility of replacing the existing subjective, qualitative method of determining spontaneously-dispersed clay with a quantitative, objective method. Even though the dispersed clay is measured under saturated conditions, soil samples retain a ‘memory’ of the water contents at which they have been stored.

Computerized Computation of Emission Spectrometric Data of Trace Elements in Biological Fluids

1968 ◽  
Vol 22 (5) ◽  
pp. 552-557 ◽  
Author(s):  
Richard S. Johnson ◽  
William Niedermeier ◽  
James H. Griggs ◽  
Janice F. Lewis
Keyword(s):  
Trace Elements ◽  
Experimental Error ◽  
Functional Relationship ◽  
Empirical Equation ◽  
Biological Fluids ◽  
Transcendental Equation ◽  
Direct Reading ◽  
Spectrometric Data ◽  
Entire Procedure

It has been found that a four-constant generalized transcendental equation can be used to relate emission spectroscopy data to concentration of trace elements in biological fluids. For each element the constants in the- empirical equation are evaluated by a three-step successive approximation, based on the data from standards. The functional relationship, which gives values well within the range of experimental error, is then used in the quantitative determination of the concentration of each of 17 trace elements in unknown samples. In these studies a Jarrell—Ash direct reading spectrometer was used. The entire procedure of data reduction and concentration printout was done on a digital computer.

XVIII.—On a Continued Investigation of the Application of the Law of Torsional Oscillation to Various Metals and Alloys

1914 ◽  
Vol 33 ◽  
pp. 183-193
Author(s):  
James B. Ritchie
Keyword(s):  
Empirical Equation ◽  
Large Range ◽  
Initial Conditions ◽  
Torsional Oscillation ◽  
Subsequent Treatment ◽  
Metals And Alloys ◽  
Torsional Oscillations ◽  
The Subject ◽  
The Law

This paper is a continuation of one already submitted to the Society, and published in their Proceedings.It showed that an equation of the form yn(x + a) = b could be applied to give close representation of results in the determination of the law of decrease of torsional oscillations of wires of different materials. This empirical equation, in which y represented the range of oscillation, x the number of oscillations since the commencement of observations, and n, a, and b constants for any one experiment, their numerical values depending upon the initial conditions of the wire and its subsequent treatment, was found to hold over a large range of oscillation for wires of many metals, and the present paper gives an account of further work on the subject.

Analyses and Determination of Current Density and Energy Density in Electric Melting Glass Furnace

2011 ◽  
Vol 287-290 ◽  
pp. 2945-2951
Author(s):  
Wei Ning ◽  
Li Da Luo ◽  
Xing Yang Xu ◽  
Qing Wei Wang ◽  
Jian Chen
Keyword(s):  
Energy Density ◽  
Glass Furnace ◽  
Current Density ◽  
Empirical Equation ◽  
Melting Rate ◽  
Optimum Operating ◽  
Electric Melting ◽  
Optimum Operating Condition ◽  
Melting Glass

Current density and energy density is one of the most important parameters for designing the electric melting glass furnace. This paper analyzed the relation between current density and energy density based upon the generated representation, mathematical simulation and empirical equation, defined the bearing scope of current density for several kinds of electrodes, discussed the tendency of the change of current density and volume melting rate on different kinds of glasses, provided the theoretical basis to design electric melting glass furnace and established proper thermotechnical regime, so as to ensure the optimum operating condition in electric melting glass furnace.

scholarly journals Flood hazard in Slovenia and assessment of extreme design floods

2020 ◽  
pp. 43-59
Author(s):  
Matjaž Mikoš
Keyword(s):  
Empirical Equation ◽  
Flood Hazard ◽  
Monitoring Network ◽  
Empirical Equations ◽  
Hydraulic Modelling ◽  
Extreme Flows ◽  
Catchment Areas ◽  
High Dams ◽  
Hydrological Monitoring

Due to the lack of hydrological measurements in the torrential areas and smaller catchment areas of Slovenian rivers, in accordance with the European Floods Directive, we used an empirical equation to estimate the magnitude of a 500-year flood (Q500). In this paper, we critically evaluate the proposed empirical equations for estimating the Q500 discharge, as defined in the Slovenian Rules on the methodology for determining areas at risk of floods and related erosion of inland waters and the sea, and on the method of classifying land into risk classes. In this assessment, we use publicly available measured data from Slovenia’s hydrological monitoring network and data on extreme flows for selected Slovenian high dams, and thus compare the database with empirical equations for determining extreme flows in Europe and elsewhere in the world that are used for planning high dams. Although the reach of the Q500 flood line determines the area of residual flood danger, it makes sense to abandon the determination of extreme flows in Slovenia using empirical equations and move to a hydrological-hydraulic modelling system using modern software tools.

Determination of Natural Loss of Gasoline and Diesel Fuel during the Tank Storage

2021 ◽  
Vol 627 (5) ◽  
pp. 28-31
Author(s):  
D .S. Kopitsyn ◽  
◽  
P. A. Gushchin ◽  
A. A. Panchenko ◽  
F. V. Timofeev ◽  
...  
Keyword(s):  
Experimental Data ◽  
Temperature Dependence ◽  
Gas Phase ◽  
Diesel Fuel ◽  
Empirical Equation ◽  
Petroleum Products ◽  
Antoine Equation ◽  
Tank Storage

In this work, we studied the processes of evaporation of gasoline and diesel fuel during their storage. We assessed of the temperature dependence of the content of hydrocarbon vapors in the gas phase over petroleum products. It was found that the experimental data are best described by the empirical equation based on the Antoine equation. An algorithm is proposed for calculating the natural loss of gasoline and diesel fuel, as well as approaches to its reduction.

scholarly journals Research on the initial abstraction – storage ratio and its effect on hydrograph simulation at a watershed in Greece

2007 ◽  
Vol 4 (4) ◽  
pp. 2169-2204 ◽  
Author(s):  
E. A. Baltas ◽  
N. A. Dervos ◽  
M. A. Mimikou
Keyword(s):  
Empirical Equation ◽  
Storm Events ◽  
Rainfall Runoff ◽  
Unit Hydrograph ◽  
Time To Peak ◽  
Initial Abstraction ◽  
Time Period ◽  
The Difference ◽  
Runoff Events

Abstract. The present research was conducted at an experimental watershed in the prefecture of Attica, Greece, using the selected observed rainfall-runoff events from a four-year time period. The objectives of this study were two: The first was the determination of the initial abstraction Ia – watershed storage S ratio. The average ratio (Ia/S) was equal to 0.014. The corresponding ratio at a subwatershed was 0.037. The difference was attributed to the different spatial distribution of landuses at the extent of the watershed. The second objective of the study was to examine the effect of the SCS empirical equation on hydrograph simulation. This was investigated through the comparison between the observed and two different simulated hydrographs at each one out of eighteen selected storm events. The simulated hydrographs were calculated by applying on the watershed's unit hydrograph two time distributions of excess rainfall that derived from the SCS method using two different approaches. In the first approach, the initial abstraction was determined from the observed rainfall-runoff data, while in the second, it was calculated using the SCS empirical equation. It was found that the SCS empirical equation estimates greater amount of initial abstraction and leads to the delayed start of the excess rainfall and the simulated runoff. This resulted in the overestimation of the peak flow rate and the time to peak at the majority of the storm events.

Combined empirical–analytical method for determining contact radius and indenter displacement during Hertzian indentation on coating/substrate systems

2004 ◽  
Vol 19 (9) ◽  
pp. 2774-2781 ◽  
Author(s):  
Chun-Hway Hsueh ◽  
Pedro Miranda
Keyword(s):  
Finite Element ◽  
Analytical Method ◽  
Empirical Equation ◽  
Contact Radius ◽  
Finite Element Analyses ◽  
Modulus Ratio ◽  
Properties Of Coatings ◽  
Hertzian Indentation ◽  
Potential Applications

An analytical model was developed in a previous work to relate the normalized indenter displacement to both the coating-to-substrate Young's modulus ratio and the coating-thickness-to-contact-radius ratio for Hertzian indentation on coating/substrate systems. However, application of this model is contingent upon the determination of the contact radius during indentation. Using the data from finite element analyses, an empirical equation is proposed in this paper to determine the normalized contact radius. Combining this empirical equation with the previous analytical equation, both the contact radius and the indenter displacement for Hertzian indentation on coating/substrate systems are predicted. The predictions obtained by this combined empirical–analytical method are shown to agree with the finite element results in general although the indenter displacement is over-estimated when the coating is stiffer than the substrate. Finally, the potential applications of this method to determine the elastic properties of coatings from the indentation data are envisaged.

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