Particle size distribution frequency histogram

Bulk particulates of various sizes can be analysed to display their particle size distribution and a frequency histogram plotted, as shown in Figure 1.8. 

Follow a procedure similar to that of Example 2.4, in order to elaborate a histogram, a frequency curve, and an undersize cumulative percentage graph, and determine the median size of the powder (note that the particle size distribution obtained will be by number, while in Example 2.4 the particle size distribution obtained was by mass). 

Solution The data on numbers of particles in each particle range given in Table El.3 can be converted to relative frequencies per unit of particle size as given in Table El. 4. The histogram for the relative frequency per unit of particle size for the data is plotted in Fig. El.2 the histogram yields a total area of bars equal to unity. Superimposed on the histogram is the density function for the normal distribution based on Eqs. (1.24) and (1.30). For this distribution, the values for do and ad are evaluated as 0.342 and 0.181, respectively. Also included in the figure is the density function for the log-normal distribution based on Eq. (1.32a). For this distribution, the values for In doi and od are evaluated as —1.209 and 0.531, respectively. 

If we plot the frequency of occurrence of a concentration versus concentration, we would expect to obtain a histogram like that sketched in Figure 26.4a. As the number of data points increases, the histogram should tend to a smooth curve such as that in Figure 26.4b. Note that very low and very high concentrations occur only rarely. We recall that aerosol size distributions exhibited a similar overall behavior there are no particles of... 

Histograms are a convenient way to represent the distribution of particles. This technique involves the discrete allocation of particles of a certain size according to frequency of occurrence. Figure 1-2 shows the histogram of a coal sample. 

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