This part of ISO 9276 provides relevant equations and coherent nomenclatures for the calculation of moments, mean particle sizes and standard deviations from a given particle size distribution. Two notation systems in common use are described. One is the method of moments while the second describes the moment-ratio method. The size distribution may be available as a histogram or as an analytical function.<\/p>\n
The equivalent diameter of a particle of any shape is taken as the size of that particle. Particle shape factors are not taken into account. It is essential that the measurement technique is stated in the report in view of the dependency of sizing results of measurement principle. Samples of particles measured are intended to be representative of the population of particles.<\/p>\n
For both notation systems, numerical examples of the calculation of mean particle sizes and standard deviation from histogram data are presented in an annex.<\/p>\n
The accuracy of the mean particle size may be reduced if an incomplete distribution is evaluated. The accuracy may also be reduced when very limited numbers of size classes are employed.<\/p>\n
| PDF Pages<\/th>\n | PDF Title<\/th>\n<\/tr>\n | ||||||
|---|---|---|---|---|---|---|---|
| 6<\/td>\n | Foreword <\/td>\n<\/tr>\n | ||||||
| 7<\/td>\n | Introduction <\/td>\n<\/tr>\n | ||||||
| 9<\/td>\n | Section sec_1 Section sec_2 Section sec_3 1\tScope 2\tNormative references 3\tDefinitions, symbols and abbreviated terms <\/td>\n<\/tr>\n | ||||||
| 11<\/td>\n | Section sec_4 Section sec_4.1 4\tThe moment-notation 4.1\tDefinition of moments according to the moment-notation <\/td>\n<\/tr>\n | ||||||
| 12<\/td>\n | Section sec_4.2 Section sec_4.2.1 4.2\tDefinition of mean particle sizes according to the moment-notation <\/td>\n<\/tr>\n | ||||||
| 13<\/td>\n | Table tab_1 Section sec_4.2.2 Section sec_4.2.3 <\/td>\n<\/tr>\n | ||||||
| 14<\/td>\n | Section sec_4.2.4 <\/td>\n<\/tr>\n | ||||||
| 15<\/td>\n | Section sec_4.2.5 Section sec_4.3 Section sec_4.3.1 4.3\tCalculation of moments and mean particle sizes from a given size distribution <\/td>\n<\/tr>\n | ||||||
| 16<\/td>\n | Section sec_4.3.2 <\/td>\n<\/tr>\n | ||||||
| 17<\/td>\n | Section sec_4.4 Section sec_4.5 4.4\tVariance and standard deviation of a particle size distribution 4.5\tCalculation of moments and mean particle sizes from a lognormal distribution <\/td>\n<\/tr>\n | ||||||
| 18<\/td>\n | Section sec_4.6 Section sec_5 Section sec_5.1 4.6\tCalculation of volume specific surface area and the Sauter mean diameter 5\tThe moment-ratio-notation 5.1\tDefinition of moments according to the moment-ratio-notation <\/td>\n<\/tr>\n | ||||||
| 19<\/td>\n | Section sec_5.2 Section sec_5.2.1 Table tab_2 5.2\tDefinition of mean particle sizes according to the moment-ratio-notation <\/td>\n<\/tr>\n | ||||||
| 20<\/td>\n | Section sec_5.2.2 Section sec_5.2.3 <\/td>\n<\/tr>\n | ||||||
| 21<\/td>\n | Section sec_5.3 5.3\tCalculation of mean particle sizes from a given size distribution <\/td>\n<\/tr>\n | ||||||
| 22<\/td>\n | Section sec_5.4 5.4\tVariance and standard deviation of a particle size distribution <\/td>\n<\/tr>\n | ||||||
| 23<\/td>\n | Section sec_5.5 5.5\tRelationships between mean particle sizes <\/td>\n<\/tr>\n | ||||||
| 24<\/td>\n | Section sec_5.6 Section sec_6 5.6\tCalculation of volume specific surface area and the Sauter mean diameter 6\tRelationship between moment-notation and moment-ratio-notation <\/td>\n<\/tr>\n | ||||||
| 25<\/td>\n | Table tab_3 <\/td>\n<\/tr>\n | ||||||
| 26<\/td>\n | Section sec_7 7\tAccuracy of calculated particle size distribution parameters <\/td>\n<\/tr>\n | ||||||
| 27<\/td>\n | Annex sec_A Annex\u00a0A \n(informative)<\/p>\n Numerical example for calculation of mean particle sizes and standard deviation from a histogram of a volume based size distribution <\/td>\n<\/tr>\n | ||||||
| 28<\/td>\n | Table tab_A.1 Table tab_A.2 <\/td>\n<\/tr>\n | ||||||
| 29<\/td>\n | Table tab_A.3 <\/td>\n<\/tr>\n | ||||||
| 30<\/td>\n | Annex sec_B Annex\u00a0B \n(informative)<\/p>\n Numerical example for calculation of mean particle sizes and standard deviation from a histogram of a volume based size distribution <\/td>\n<\/tr>\n | ||||||
| 31<\/td>\n | Table tab_B.1 Table tab_B.2 <\/td>\n<\/tr>\n | ||||||
| 32<\/td>\n | Table tab_B.3 <\/td>\n<\/tr>\n | ||||||
| 33<\/td>\n | Annex sec_C Annex\u00a0C \n(informative)<\/p>\n Accuracy of calculated particle size distribution parameters <\/td>\n<\/tr>\n | ||||||
| 34<\/td>\n | Table tab_e Figure fig_C.1 <\/td>\n<\/tr>\n | ||||||
| 35<\/td>\n | Reference ref_1 Reference ref_2 Reference ref_3 Reference ref_4 Reference ref_5 Reference ref_6 Reference ref_7 Reference ref_8 Reference ref_9 Reference ref_10 Reference ref_11 Reference ref_12 Reference ref_13 Reference ref_14 Reference ref_15 Bibliography <\/td>\n<\/tr>\n<\/table>\n","protected":false},"excerpt":{"rendered":" Representation of results of particle size analysis – Calculation of average particle sizes\/diameters and moments from particle size distributions<\/b><\/p>\n |