Grain size distribution in a granular medium

More sophisticated apparatuses, which cormt particles according to their size, have been developed using electrical or optical techniques. Their use is more closely related to laboratories than to everyday engineering studies. 

Figtrre 13.3 illustrates the principle of a pycnometer, which is a sirrtple device allowing measuremerrt of the derrsity of a solid or the average derrsity of a granular mediurtt, based on four weighing operations. The pycnometer is a container, of which the errrpty rrtass is first measured (operation 1), as well as the rrtass of the 

Different definitions of concentration can be used to characterize the quantity of particles within a fluid. These different definitions are all related to the porosity s, defined as the ratio of the fluid volume to the total volume. They include  

Both the porosity and the volume concentration are dimensionless quantities. The mass concentration and wet density have the dimension kg-m. Another frequently used unit is g L (the change of unit between kg-m and g L does not bring in a multiplicative constant). The M and V indices are generally omitted from the notations of the various concentrations, but the units are self-explanatory enough for guidance. In practice, the mass concentration is most cotranonly used and denoted by C. 

Even when dispersed at a low concentration, particles are very nnmerous and close to one another. Consider a set of particles dispersed in a homogeneous suspension in a given volume. For spherical particles of density p and diameter D with a mass concentration C, let us calculate the number N of particles per unit volume, the porosity e, the wet density of the equivalent fluid ph, and the average distance f between the centers of two particles closest together. The following mathematical relations are established  

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