Biomass Handling - Biomass Gasification, Pyrolysis and Torrefaction - page 417

The stress distribution on the silo wall is important, especially for a tall
unit. Figure 12.7 compares the wall pressure in a biomass-filled silo with
that of a liquid-filled silo. As we can see, the wall pressure in a solid-filled
silo does not vary linearly with height, but it does in a liquid-filled silo. In
the former case, the pressure increases with depth, reaching an asymptotic
value that depends on the diameter of the hopper rather than on the height.
Because there is no further increase in wall stress with height, large silos are
made smaller in diameter but taller.
To find the stress in the barrel, or the vertical wall section, of a hopper,
we consider the equilibrium of forces on a differential element, dh,ina
straight-sided silo ( Figure 12.8 ):

Vertical force due to pressure acting from above: P v A
Weight of material in element:

ρ Ag dh

Vertical force due to pressure acting from below: (P v 1 dP v )A

Solid friction on the wall acting upward: τπ D dh

The force balance on the elemental solid cross section gives
ð P v 1 dP v Þ A

1 τπ

D dh P v A

1 ρ

Ag dh (12.4)

5

The wall friction is equal to the particle wall friction coefficient, k f ,

times the normal pressure on wall, P w :
τ 5 k f P w (12.5)

Janssen (1895) assumed the lateral pressure to be proportional to the ver-
tical pressure, as shown in the following equation:

P w 5 KP v (12.6)

Pressure

Hydraulic pressure

Depth

Change in pressure
due to change in
cross section

Pressure of solid

FIGURE 12.7 Wall pressure distribution in a hopper filled with solids. The pressure profile
changes in the inclined section.