where g
u
G and p
u
G are the gas and particle velocity vectors respectively. For
small volume (
1
C ) and weight (
1
C
V ) concentrations the density
fluctuations are:
'
'
C
U VU ,
(6.32)
where
/
p
g
g
V
U U U
.
(6.33)
For water drops in the air
/
/
a
a
a
V
U U U U U
|
.
The equation for the turbulent energy balance of the admixture is as
follows:
' ' /
' '
0
u w du dz
w g
U
U
H
(6.34)
where is the dissipation of the turbulent kinetic energy. With (6.32), this
equation can be presented in the form:
' ' /
' '
0
u w du dz
C w g
U
V U
U H
(6.35)
The physical meaning of this equation is that the energy of turbulence from
the mean shear flow is then spent partially for suspension and partially for
dissipation. Introducing the nondimensional parameter,
' ' /
' ' /
a
t
gC w
K
u w du dz
U U
(6.36)
presented in the following form:
' '
/
1
0
t
u w du dz
K
H
(6.37)
The solution of the problem appears to depend on a nondimensional
parameter already familiar to us (see Section 6.2.2)
/
t
a
w
u
Z
N ,
(6.38)
Chapter 6: HIGH WIND SPEED REGIME
431
which is known as the Kolmogorov number, equation (6.35) can then be