Flowability of Powders in Hopper Design

The angle of friction is related to the corresponding coefficient of friction by 

It is convenient to introduce the concepts of material flow function, FF, and flow factor, ff. The material flow function, FF, relates the unconfined yield stress, To, to the corresponding major consolidating stress, cri, and is determined experimentally from the yield locus of the material, as shown in Fig. 8.9. The material flow function is presented as a plot of To versus J, as shown in Fig. 8.11. The flow factor, ff, is defined by 

Example 8.1 Three sets of yield loci under different consolidation conditions are obtained for a sample of powder of bulk density 1,500 kg/m3, as shown in Fig. E8.1. If a conical hopper is to be designed, determine the wall slope of the hopper and the opening size necessary to ensure a steady mass flow. The angle of wall friction is 15°. The design diagram for mass flow conical hoppers is given in Fig. E8.2 [BMHB, 1988]. 

Solution The kinematic angle of internal friction can be determined from the Mohr circle, which is tangential to the yield locus at the end point. This Mohr circle yields the major consolidating stress o and minor consolidating stress 73. Thus, % is found to be 30°, either from Eq. (8.27) or from a tangent of the Mohr circle which passes through the origin, as shown in Fig. E8.1. 

Therefore, to ensure mass flow of the given powder in a conical hopper, the half angle of the hopper should be no more than 35° and the circular opening should be larger than 0.21 m to prevent the formation of a stable arch that can span the opening. 

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