Dimensional Analysis, Dynamic Similarity, Process Functions, Empirical Equations and Experience - How Useful Are They?

By means of spatially discriminated dimensional analysis, a complete system of dimensionless groups is proposed to describe the thermodynamic performance of the kinematic Stirling engine From experimental results, homogeneous dimensionless indicated power equations are deduced, as well as equations corresponding to the maximum indicated power operating point. Spatial discrimination evidences conceptual differences between quantities, reduces the number of dimensionless parameters and improves the design method based on dynamic similarity.

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Dimensional analysis and theory of biological similarity

Physiological Reviews ◽

10.1152/physrev.1975.55.4.659 ◽

1975 ◽

Vol 55 (4) ◽

pp. 659-699 ◽

Cited By ~ 148

Author(s):

B. Gunther

Keyword(s):

Body Weight ◽

Dimensional Analysis ◽

Similarity Criterion ◽

The Body ◽

Physiological Characteristics ◽

Similarity Criteria ◽

Dimensional System ◽

Dynamic Similarity ◽

Biological Variables ◽

Biological Similarity

From this review we conclude the following: 1) The body weight of an organism is an adequate reference index for the correlation of morphological and physiological characteristics. In comparative physiology, body weight can be recommended as a unifying frame of reference, particularly if the ponderal scale includes several decades, in order to apply logarithmic scales for the variables involved. (See article). 2) The statistical analysis of the experimental data can be represented conveniently by means of the logarithmic equivalent of Huxley's allometric equation (y = a-Wb), which is the most simple and at the same time the most versatile mathematical expression for intra- or interspecies comparisons. The exponents (b) for the allometric equations can be predicted for all biological variables definable in terms of the MLT system of physics (M = mass, L = length, T = time) or of a four-dimensional system MLTt where t = temperature. 3) By means of dimensional analysis and the theory of biological similarity a range of similarity criteria can be established: a) mechanical or dynamic similarity, b) kinematic or biological similarity; and c) hydrodynamic or transport similarity. Most functions obey the so-called biological (kinematic) similarity, particularly when the concept of operational time is introduced into Lambert-Teissier's original theory. 4) A satisfactory correlation (r = 0.99) for 80 empirical allometric exponents (b) describing morphological and physiological characteristics of living beings was found. These results are discussed in relation to Rosen's optimality principles in biology. 5) Organisms should be considered as mixed regimes. This means that no single similarity criterion can predict the allometric exponent (b) of all functions that dimensionally belong to MLT or MLTt systems, despite the fact that in the great majority of cases kinematic similarity will satisfactorily predict the reduced exponent (b). Nevertheless, in some instances mechanical (dynamic) similarity must be applied, and in other circumstances hydrodynamic (transport) similarity. 6) Cellular or molecular levels are not in the domain of the present theory, since neither cell dimensions nor molecular processes (viz., blood viscosity, diffusion capacity) can be predicted by biological similarity criteria.

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Similarity and Invariance in Scaled Bilateral Telemanipulation

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2802445 ◽

1999 ◽

Vol 121 (1) ◽

pp. 79-87 ◽

Cited By ~ 8

Author(s):

Michael Goldfarb

Keyword(s):

Dimensional Analysis ◽

Physical Environment ◽

Degrees Of Freedom ◽

Sufficient Conditions ◽

Nonlinear Effects ◽

Dynamic Similarity ◽

Physical Environments ◽

Force Scaling ◽

Necessary And Sufficient ◽

Selection Of

This paper addresses the issue of dynamic similarity and intensive property invariance in scaled bilateral manipulation, and offers a design methodology based on these considerations. The methodology incorporates dimensional analysis techniques to define a set of necessary and sufficient conditions to preserve the dynamic similarity of any physical environment. These techniques are utilized to demonstrate that any combination of kinematic and force scaling in a bilateral manipulator control structure will preserve the dynamic similarity of any physical environment. Any combination of kinematic and force scaling, however, will not in general maintain intensive property invariance between the original and scaled physical environments, and thus will result in lost information. As such, the dimensional analysis methods are further utilized to form the basis of a constrained optimization problem that enables selection of a force scaling factor that minimizes the intensive distortion of the environment. The proposed formulation is applicable to any physical environment, including those that are nonlinear and contain multiple degrees of freedom. Further, the formulation does not require an exact environmental model, provided the parameters that influence the environment are known. The proposed techniques are particularly relevant to bilateral manipulation of a microscopic environment (i.e., macro-micro bilateral manipulation), since such environments are difficult to model exactly and are largely influenced by nonlinear effects.

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The Statistical Laws of Surficial Deformation of Loess Ground during Dynamic Compaction

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.250-253.1602 ◽

2011 ◽

Vol 250-253 ◽

pp. 1602-1611 ◽

Cited By ~ 1

Author(s):

Si Hai Luo ◽

Yang Wang ◽

Jian Yong Yang ◽

Tong Fa Deng

Keyword(s):

Dimensional Analysis ◽

Ground Deformation ◽

Dynamic Compaction ◽

Experimental Results ◽

Crater Depth ◽

Soil Parameters ◽

Empirical Equations ◽

Statistical Laws

Through the method of dimensional analysis, the dimension equations of loess ground deformation of dynamic compaction are established. Based on the data obtained from practices of dynamic compaction and the methods of statistics , empirical equations of both the crater depth and the average enforced settlement relating the soil parameters and construction parameters are presented. Finally, the equations are verified by several project examples, and the results show that the calculated results agree well with experimental results. These equations provide a practical way for the prediction of surficial deformation of loess ground during dynamic compaction.

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In situ investigation of the primary recrystallization of alpha titanium in HVEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100110313 ◽

1978 ◽

Vol 36 (1) ◽

pp. 634-635

Author(s):

S. Naka ◽

R. Penelle ◽

R. Valle

Keyword(s):

Dimensional Analysis ◽

Texture Evolution ◽

Cold Work ◽

Three Dimensional ◽

Primary Recrystallization ◽

Thin Foils ◽

In Situ Investigation ◽

Grain Growth Model ◽

Alpha Titanium

The in situ experimentation technique in HVEM seems to be particularly suitable to clarify the processes involved in recrystallization. The material under investigation was unidirectionally cold-rolled titanium of commercial purity. The problem was approached in two different ways. The three-dimensional analysis of textures was used to describe the texture evolution during the primary recrystallization. Observations of bulk-annealed specimens or thin foils annealed in the microscope were also made in order to provide information concerning the mechanisms involved in the formation of new grains. In contrast to the already published work on titanium, this investigation takes into consideration different values of the cold-work ratio, the temperature and the annealing time.Two different models are commonly used to explain the recrystallization textures i.e. the selective grain growth model (Beck) or the oriented nucleation model (Burgers). The three-dimensional analysis of both the rolling and recrystallization textures was performed to identify the mechanismsl involved in the recrystallization of titanium.

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