Derivation of the differential continuity equation in an introductory engineering fluid mechanics course

The differential continuity equation is elegantly derived in advanced fluid mechanics textbooks using the divergence theorem of Gauss, where the surface integral of the mass flux flowing out of a finite control volume is replaced by the volume integral of the divergence of the mass flux within the control volume. To avoid the need for introducing the Gauss divergence theorem in an introductory fluid mechanics course, introductory textbooks in fluid mechanics have opted to use a more simple approach, which depends on the consideration of an infinitesimal control volume and the use of Taylor series expansion. This approach, however, involves a first order truncation of the Taylor series expansion and the use of approximate equality signs which may imply to undergraduate students that the derived continuity equation is an approximate equation. The present study proposes an alternative derivation of the differential continuity equation using a finite control volume and is based on the simple concept of the antiderivative function and the fundamental theorem of calculus. The proposed derivation eliminates the need to formally introduce the Gauss divergence theorem in an introductory engineering fluid mechanics course while avoiding the use of truncated Taylor series expansion and approximate equality signs, hence providing a more simple and sound understanding of the derivation of the differential continuity equation to undergraduate engineering students.

Equality

Equality has long been a source of political and philosophical controversy. A central question about equality is how one might link empirical or moral claims about the extent to which persons are equal to judgements about the moral acceptability or unacceptability of social inequalities, and in particular how far considerations of equality license social action to bring about greater social equality. A traditional liberal argument holds that approximate equality of human strength makes it prudent for humans to place themselves under a common political authority, thus producing a justification for equality before the law. But any generalization of this argument ignores the cases where strength is unequal and the resulting balance of power unjust. Equality of worth is a principle recognized in many philosophical traditions, but its broad acceptance leaves open many problems of interpretation. In particular, it is not clear how far the principle calls for greater equality of social conditions. Persons may derive a sense of worth from enjoying the fruits of their labour, and this will legitimately block some redistribution; certain inequalities may work to everyone’s advantage; and the impartial concern of the equality principle may be at odds with the sense of ourselves as persons with specific attachments. In this context, some have wanted to soften the interpretation of equality to mean equality of opportunity or merely that inequalities should not be cumulative, although how far these moves are justified is a matter for dispute. By contrast, challenges to the equality principle from considerations of incentives, desert or difference can more easily be met.

Evaluation of recent combined global geopotential models in Brazil

The aim of this paper is to present a quantitative analysis of the adequacy of the main currently existing combined Global Geopotential Models (GGMs) for modeling normal-geoid heights throughout Brazil. As major advances have been reached since mid-2016 in the combined GGMs elaboration and development, the main objective of this analysis is to verify if, in fact, the most recent models present superior or equivalent performance to the most performant previous models. The analysis was based on comparisons between normal-geoid height values obtained fromGNSS/leveling solutions and values calculated from GGMs XGM2016, GOCO05C, EIGEN-6C4 and EGM2008, according to different geopotential functionals - geoid height and height anomaly - and in different degrees of development, always through the relative method. This procedure was applied to 997 stations which carry information of both ellipsoidal and normal-orthometric heights, located all over Brazil. As a main result, it was observed the superior performance of the recent combined GGMs, GOCO05C and XGM2016, when compared to the older models, EIGEN-6C4 and EGM2008, when all of them are developed up to degree 720, the maximum degree of the recent models; and a approximate equality of results when all of the models are used in their individual maximum degrees.

Testing for Approximate Measurement Invariance of Human Values in the European Social Survey

Measurement invariance is a necessary precondition for meaningful cross-country comparisons, and three levels have been differentiated: configural, metric, and scalar. Unfortunately, establishing the most stringent form, that is, scalar measurement invariance, across groups is difficult. Recently, Muthén and Asparouhov proposed testing for approximate rather than exact measurement invariance, as this may be sufficient for meaningful comparisons. Following their strategy, the results of cross-country approximate measurement invariance tests of the 21-item Portrait Value Questionnaire (PVQ-21) scale to measure values in the European Social Survey are presented ( N = 274,447 respondents from 15 countries participating in all six rounds). Applying the new approximate method for the test of measurement invariance allows both using more moderate constraints of approximate equality of parameters across groups and exploring the extent of noninvariance. Approximate measurement invariance was established in almost all rounds for two higher-order values: openness to change and self-enhancement. In the case of the two other higher-order values, self-transcendence and conservation, approximate measurement invariance was established across a subset of countries.

Lossless Join Decomposition for Extended Possibility-Based Fuzzy Relational Databases

Functional dependency is the basis of database normalization. Various types of fuzzy functional dependencies have been proposed for fuzzy relational database and applied to the process of database normalization. However, the problem of achieving lossless join decomposition occurs when employing the fuzzy functional dependencies to database normalization in an extended possibility-based fuzzy data models. To resolve the problem, this study defined fuzzy functional dependency based on a notion of approximate equality for extended possibility-based fuzzy relational databases. Examples show that the notion is more applicable than other similarity concept to the research related to the extended possibility-based data model. We provide a decomposition method of using the proposed fuzzy functional dependency for database normalization and prove the lossless join property of the decomposition method.

Temporal and Spatial Aspects of Velocity Variance in the Urban Surface Roughness Layer

Data from six urban areas in a nationwide network of sites within the surface roughness layer are examined. It is found that the average velocity variances in time, derived by averaging the conventional variances from a network of n stations, are nearly equal to the velocity variances in space, derived as the variances among the n average velocities. This similarity is modified during sunlit hours, when convection appears to elevate the former. The data show little dependence of the ratio of these two variances on wind speed. It is concluded that the average state of the surface roughness layer in urban and suburban areas like those considered here tends toward an approximate equality of these two measures of variance, much as has been observed elsewhere for the case of forests.

Optical Path Analysis of the Optical Fiber Bundle Hydrogen Sensor

The present work investigates reflectivity and optimal reflective distance of optical fiber hydrogen sensor in over 0～4000um range. The approximate equality of reflective distance in two optical paths increases signal to noise ratio for optical hydrogen sensor, the fabrication of optical path could eliminate the internal noise and external interferences, and provides higher stability for hydrogen sensor. Through a series of simulation experiments it was found that different reflective distances determine the sensitivity and amplitude response of hydrogen sensor. When the reflective distance was about 1mm in optical path, the sensitivity of optical hydrogen sensor could reach the peak value.

Use of theoretical efficiencies of protein and fat synthesis to calculate energy requirements for growth in pigs

From the observation that fasting heat production includes the cost of body protein resynthesis and the evidence that protein resynthesis is included in the regression estimate of protein retention efficiency it is conjectured that the estimate of maintenance from fasting heat production must be conceptually equal to the regression intercept estimate of maintenance plus the cost of body protein resynthesis. Experimental evidence for comparable situations shows an approximate observational equality in agreement with the conjectured conceptual equality. This approximate equality implies that the theoretical (stiochiometric) efficiency of protein synthesis should be used in conjunction with the estimate of maintenance from fasting heat production for the prediction of growth energy requirements. The approximate maintenance equalities suggest furthermore approximate equality of theoretical fat synthesis efficiency and regression fat retention efficiency. This conjecture is also supported by experimental evidence. Some practical nutrition and pig breeding implications of the foregoing conclusions are indicated.