Static Stress Distributions in Standpipes and Hoppers

So far, we understand that the flowability of powders depends on their failure stresses from the Mohr-Coulomb failure criterion. Therefore, analyses of powder flows 

A simple model for the estimation of stress distribution in cohesionless bulk solids stored in a tall cylindrical bin was presented by Janssen in 1895. The system of consideration is shown in Fig. 8.6(a). In Janssen s model, it is assumed that 

From Assumption (4), the wall shear stress, z , can be related to the horizontal stress, rr, by 

Equations (8.15) and (8.16) show that, as z increases, az and ar approach the maximum values of 

Moreover, the horizontal wall pressure, xr, may be estimated from Eq. (8.16). The results are illustrated in Fig. 8.6(b). 

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