Units of measurement, dimensions, and dimensional analysis

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Dimensional Analysis ◽  
International System ◽  
Simple Procedure ◽  
Scale Up ◽  
Physical Significance ◽  
Sequential Elimination ◽  
System Of Units ◽  
Physical Quantities ◽  
Dimensional Homogeneity

In this chapter the crucial role of units and dimensions in the analysis of any problem involving physical quantities is explained. The International System of Units (SI) is introduced. The major advantage of collecting the physical quantities, which are included in either a theoretical analysis or an experiment, into non-dimensional groups is shown to be a reduction in the number of quantities which need to be considered separately. This process, known as dimensional analysis, is based upon the principle of dimensional homogeneity. Buckingham’s Π‎ theorem is introduced as a method for determining the number of non-dimensional groups (the Π‎’s) corresponding with a set of dimensional quantities and their dimensions. A systematic and simple procedure for identifying these groups is the sequential elimination of dimensions. The scale-up from a model to a geometrically similar full-size version is shown to require dynamic similarity. The definitions and names of the non-dimensional groups most frequently encountered in fluid mechanics have been introduced and their physical significance explained.

The International System of Units (SI)

1976 ◽  
Vol 46 (9) ◽  
pp. 623-628 ◽  
Author(s):  
George G. Stoner
Keyword(s):  
Physical Quantity ◽  
International System ◽  
Numerical Factor ◽  
International System Of Units ◽  
System Of Units ◽  
Physical Quantities

Le Système International d'Unités (officially designated SI in all languages) provides a logical, interconnected framework for measurements in commerce, industry, and science, including the textile and allied fields. SI is based on only nine elemental units. Seventeen important derived units have special names. Any number of derived units is possible to meet particular needs. SI has only one unit for each type of physical quantity. Prefixes cover a range of 1036 to form multiples and submultiples. SI has explicitly distinct units for mass (the kilogram) and force (the newton). Numerous older units of pressure, energy, and power are superseded by the pascal, the joule, and the watt, respectively. Each equation defining a derived unit contains only the number 1 as the numerical factor. SI has salient advantages because it is a system of units coherent with respect to the system of physical quantities and the equations relating them.

Quantity Dimension Indexing for Design Knowledge Management

2007 ◽  
Author(s):  
Tamotsu Murakami ◽  
Yasushi Suehisa
Keyword(s):  
Knowledge Management ◽  
Dimensional Space ◽  
International System ◽  
Design Knowledge ◽  
Design Problems ◽  
Future Design ◽  
Similarity Estimation ◽  
System Of Units ◽  
Physical Phenomena ◽  
Physical Quantities

Although many knowledge management techniques based on text expression have been developed, they are not necessarily sufficient for managing engineering design knowledge. In this paper, we propose quantity dimension indexing of design knowledge as a fundamental method for design knowledge management. Physical quantities describing physical phenomena can be represented as vectors in a seven-dimensional space where the orthogonal axes are the seven base units of the SI (The International System of Units). Because of the generality, objectivity and universality of the SI, this space covers all physical quantities that appear in the past, present and future design knowledge and design problems, and the same quantities are represented as the same vectors regardless of the differences in people, products, domains, organizations, nations and languages. We assume that the similarities of physical phenomena lead to similarities in the dimensions of quantities describing the phenomena, and propose to use this seven-dimensional vector for estimating the similarity of design knowledge from the viewpoint of physical phenomena. Based on this basic idea, we mathematically define similarity between two quantities using quantity dimensions. We prepared design knowledge examples and retrieval keys and conducted design knowledge retrieval and design knowledge similarity estimation by quantity dimension indexing and confirmed that we obtained adequate results without using a concept dictionary or thesaurus elaborated in advance, which are indispensable in the text approach.

scholarly journals The role of the international prototype of the kilogram after redefinition of the International System of Units

2011 ◽  
Vol 369 (1953) ◽  
pp. 3975-3992 ◽  
Author(s):  
R. S. Davis
Keyword(s):  
International System ◽  
Physical Constant ◽  
Reference Standards ◽  
First Century ◽  
Planck Constant ◽  
Practical Matter ◽  
International System Of Units ◽  
System Of Units ◽  
Great Progress

Since 1889, the international prototype of the kilogram has served to define the unit of mass in what is now known as the International System of Units (SI). This definition, which continues to serve mass metrology well, is an anachronism for twenty-first century physics. Indeed, the kilogram will no doubt be redefined in terms of a physical constant, such as the Planck constant. As a practical matter, linking the quantum world to the macroscopic world of mass metrology has, and remains, challenging although great progress has been made. The international prototype or, more likely, a modern ensemble of reference standards, may yet have a role to play for some time after redefinition, as described in this paper.

Bye-Bye, IPK!

2019 ◽  
Vol 41 (2) ◽  
pp. 53-54
Author(s):  
Daniel Rabinovich
Keyword(s):  
Electric Current ◽  
International System ◽  
Golf Ball ◽  
Weights And Measures ◽  
Units Of Measurement ◽  
International System Of Units ◽  
System Of Units ◽  
Utmost Care ◽  
Physical Quantities

Abstract The International Prototype Kilogram, after 130 years of dutiful service, is finally retiring. The IPK, a golf ball-sized cylinder made of a special platinum-iridium alloy (90:10), was introduced in 1889 at the first General Conference on Weights and Measures (CGPM) near Paris to define the unit of mass using an artifact fabricated with the utmost care and precision available at the time. New units were subsequently adopted for other physical quantities such as electric current (the ampere) and temperature (the kelvin), and the increasing need for a more cohesive set of units of measurement led to the implementation of the International System of Units (SI) in 1960.

scholarly journals Time scales in the context of general relativity

2011 ◽  
Vol 369 (1953) ◽  
pp. 4131-4142 ◽  
Author(s):  
Bernard Guinot
Keyword(s):  
Relativistic Effect ◽  
International System ◽  
Centre Of Mass ◽  
Frequency Standards ◽  
The Earth ◽  
International Astronomical ◽  
System Of Units ◽  
Definition Of ◽  
Atomic Time

Towards 1967, the accuracy of caesium frequency standards reached such a level that the relativistic effect could not be ignored anymore. Corrections began to be applied for the gravitational frequency shift and for distant time comparisons. However, these corrections were not applied to an explicit theoretical framework. Only in 1991 did the International Astronomical Union provide metrics (then improved in 2000) for a definition of space–time coordinates in reference systems centred at the barycentre of the Solar System and at the centre of mass of the Earth. In these systems, the temporal coordinates (coordinate times) can be realized on the basis of one of them, the International Atomic Time (TAI), which is itself a realized time scale. The definition and the role of TAI in this context will be recalled. There remain controversies regarding the name to be given to the unit of coordinate times and to other quantities appearing in the theory. However, the idea that astrometry and celestial mechanics should adopt the usual metrological rules is progressing, together with the use of the International System of Units, among astronomers.

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