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AS 4932.
ISO 9276-2:2001
AS 4932.2
Representation of results of particle size analysis Part 2: Calculation of average particle sizes/diameters and moments from particle size distributions
This Australian Standard was prepared by Committee CH-032, Particle Size Analysis. It was approved on behalf of the Council of Standards Australia on 30 April 2002 and published on 20 June 2002.
The following are represented on Committee CH-032: Australian Concrete Association CSIRO Land and Water
Queensland University of Technology Royal Australian Chemical Institute Science Industry Australia Inc University of South Australia The University of Sydney
Standards are living documents which reflect progress in science, technology and systems. To maintain their currency, all Standards are periodically reviewed, and new editions are published. Between editions, amendments may be issued. Standards may also be withdrawn. It is important that readers assure themselves they are using a current Standard, which should include any amendments which may have been published since the Standard was purchased. Detailed information about Standards can be found by visiting the Standards Australia web site at www.standards.com.au and looking up the relevant Standard in the on-line catalogue. Alternatively, the printed Catalogue provides information current at 1 January each year, and the monthly magazine, The Australian Standard, has a full listing of revisions and amendments published each month. We also welcome suggestions for improvement in our Standards, and especially encourage readers to notify us immediately of any apparent inaccuracies or ambiguities. Contact us via email at mail@standards.com.au, or write to the Chief Executive, Standards Australia International Ltd, GPO Box 5420, Sydney, NSW 2001.
This Standard was issued in draft form for comment as DR 01326.
AS 4932.22002
First published as AS 4932.22002.
ISBN 0 7337 4520 2
This Standard was prepared by the Standards Australia Committee CH-032, Particle Size Analysis. This Standard is identical with and has been reproduced from ISO 9276-2:2001, Representation of results of particle size analysis, Part 2: Calculation of average particle sizes/diameters and moments from particle size distributions. The objective of this Standard is to provide the relevant equations for the calculation of average particle sizes or average particle diameters from a given particle size distribution. It is assumed that the size distribution is available as a histogram. The same mathematical treatment can, however, also be applied, if the size distribution is represented by an analytical function. It is furthermore assumed in this Standard that the size of a particle is described by the diameter of a sphere. Depending on the problem, size may also represent an equivalent diameter of a particle of any other shape.
This Standard is part of a series comprising: AS 4932 4932.1 4932.2 4932.4 Representation of results of particle size analysis Part 1: Graphical representation Part 2: Calculation of average particle sizes/diameters and moments from particle size distributions Part 4: Characterization of a classification process
As this Standard is reproduced from an International Standard, the following applies: (a) (b) (c) (d) (e) Its number appears on the cover and title page while the International Standard number appears only on the cover. In the source text, this part of ISO 9276 should read this Australian Standard. A full point substitutes for a comma when referring to a decimal marker. Substitute mL for ml wherever it appears. ISO 565:1999, listed as a normative reference in Clause 2, has not been adopted as an Australian Standard.
References to International Standards should be replaced by references to equivalent Australian Standards as follows: Reference International Standard ISO 9276 Representation of results of particle size analysis 9276-1 Part 1: Graphical representation Australian Standard AS 4932 Representation of results of particle size analysis 4932.1 Part 1: Graphical representation
Introduction ...............................................................................................................................................................iv 1 2 3 4 5
Scope ..............................................................................................................................................................1 Normative references ....................................................................................................................................1 Symbols and abbreviated terms ..................................................................................................................1 Basic definition of a moment........................................................................................................................3 Average particle diameters...........................................................................................................................4 Arithmetic average particle diameters ........................................................................................................4 Weighted average particle diameters ..........................................................................................................5 The calculation of Mk,r and average particle diameters from a number or a volume density distribution, q0(x) or q3(x) ...............................................................................................................................5 Calculation of Mk,r from a number or a volume density distribution, q0(x) or q3(x), given as a histogram........................................................................................................................................................6 Calculation of volume specific surface area...............................................................................................7 The variance of a particle size distribution.................................................................................................7
Annex A (informative) Calculation of different average particle diameters from the histogram of a given volume density distribution, numerical example.............................................................................9 Annex B (informative) Further average particle diameters ...................................................................................11 Bibliography ..............................................................................................................................................................12
In particle size analysis, particulate matter is often characterized based on representative samples of the population with the final aim of linking the size information with some other important physical property such as strength, flowability, solubility, etc. In general, a correlation between the physical property and the size of the particles, the so-called property function, can be obtained if an average particle size has been derived or calculated from the measured distribution of sizes. A unique definition of the average size, x k,r , is given in this part of ISO 9276, using the so-called moments, Mk,r, of a size distribution. Apart from average sizes, moments are also used in the calculation of volume related surface area, the spread and other statistical measures of a particle size distribution.
The object of this part of ISO 9276 is to provide the relevant equations for the calculation of average particle sizes or average particle diameters and moments from a given particle size distribution. It is assumed that the size distribution is available as a histogram. It is nevertheless also possible to apply the same mathematical treatment if the particle size distribution is represented by an analytical function. It is furthermore assumed in this part of ISO 9276 that the particle size x of a particle of any other shape may also be represented by the diameter of an equivalent sphere, e.g. a sphere having the same volume as the particle concerned.
The following normative documents contain provisions which, through reference in this text, constitute provisions of this part of ISO 9276. For dated references, subsequent amendments to, or revisions of, any of these publications do not apply. However, parties to agreements based on this part of ISO 9276 are encouraged to investigate the possibility of applying the most recent editions of the normative documents indicated below. For undated references, the latest edition of the normative document referred to applies. Members of ISO and IEC maintain registers of currently valid International Standards. ISO 565:1990, Test sieves Metal wire cloth, perforated metal plate and electroformed sheet Nominal sizes of openings. ISO 9276-1, Representation of results of particle size analysis Part 1: Graphical representation.
For the purposes of this part of ISO 9276, the following symbols and abbreviated terms apply. i k n r number of the size class with upper particle size, xi power of x total number of size classes type of quantity of a distribution (general description) r=0 r=1
type of quantity, number type of quantity, length
AS 4932.2-2002, Representation of results of particle size analysis Calculation of average particle sizes/diameters and moments from particle size distributions
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