Biomass Handling - Biomass Gasification, Pyrolysis and Torrefaction - page 416

weight to surface area compared to coarser particles. So, for fine particles,
this force balance becomes an important consideration. For such particles,
the following expression is used (Carleton, 1972):

1 = 3

4V 0 sin

2 V 0 Þ

θ

15 ðρ a μ

g for d p , 500 μ m (12.1)

1 5

B

ρ p d 5 = 3

p

where

V 0 is the average solid velocity through the outlet, m/s
ρ a and ρ p are the densities of the air and solids, respectively, kg/m 3

d p is the particle size, m
μ

is the viscosity of the air, kg/m s

θ

is the semi-included angle of the hopper
g is the acceleration due to gravity, 9.81 m/s 2
B is the parameter

The mass-flow rate, m, is given in terms of the bulk solid density, ρ b , and
the outlet area, A:

m

5 ρ b AV 0

(12.2)

For coarse particles ( 500 μ m), an alternative relation is used (Johanson,

.

1965):

s

Bg

m

5 ρ b A

kg = s for d p . 500 μ m (12.3)

2 ð 1 C Þ tan θ

1

Values of the parameters A, B, and C are given as:

Parameter Conical Outlet Symmetric Slot

B Outlet diameter, D Slot width, W

/4)D 2 A ( π Width breadth

3

C 1.0 0

12.3.2.6 Design Steps
Hopper design involves determining particle properties, such as interparticle
friction, particle-to-wall friction, and particle compressibility or permeability.
With these properties known, the outlet size, hopper angle, and discharge
rate are found.
Dedicated experiments like shear tests are carried out to determine the
interparticle friction. Particle wallfrictionshouldalsobemeasuredby

purpose-designed experiments. Parameters, such as angle of repose, have
little value in hopper design, as it simply gives the heap angle when solids
are poured in.