484
Chapter 11
The proportionality constant depends to
a large extent on the impeller type. Another
characteristic that depends on the impeller type is the
pumping capacity, vpUmp,
which is defined
as the volume of liquid that gets expelled from the impeller per unit time (m
3
s'1). It is to be
expected that
where
ds
is the stirrer diameter. The proportionality constant is called
the flow number, N f
, and it
depends on the impeller type and on the viscosity of the medium. For a Rushton turbine and a
low-viscosity medium, it has been found that
N/=
0.72. The
circulation time, tc ,
is defined as
It is realized from Eqs. (11.2) - (11.4) that
tm
is proportional to
tc
for fully turbulent flow in a
baffled tank reactor. As a first approximation, mixing can be assumed to have occured within 4
tc.
Note 11.1: Mixing as a first-order process
If the mixing process is approximated by a first-order process, the deviation of the concentration of a tracer at
a time t,
s(t),
from its final value,
is given by
which shows that for
m =
1 -
lie
= 0.632, we have
tm
=
1/k.
Furthermore, by using Eq. (3) we can calculate
the mixing time for any value of
m
when the mixing time is known for
m:
For example, for m* = 0.99 (and m = 0.632) we get
v
pump
ccd'N
01
.
3
)
V
(11.4)
t.
v
pump
(
1
)
for which the solution is
(
2
)
-
s(t)
Rearrangement of Eq. (2) gives
m
k
ln(l - m)
(3)
(5)
- 1