Friction in Flow through Beds of Solids

Values of the sphericity for several materials are given in Table 28.1. For granular solids, ranges from 0.6 to 0.95. 

The volume fraction particles in the bed is 1 — , where e is the porosity or void fraction. If the particles are porous, the pores are generally too small to permit any significant flow through them, so e is taken to be the external void fraction of the bed and not the total porosity. 

To determine the equivalent channel diameter the surface area for n parallel channels of length L is set equal to the surface-volume ratio times the particle volume, S L (1 — e), where is the cross-sectional area of the bed  

The void volume in the bed is the same as the total volume of the n channels  

The pressure drop depends on the average velocity in the channels V, which is proportional to the superficial or empty-tower velocity Fq and inversely 

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