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Mixing 267

10.4.2.2.2 Radial Flow Example 10.7 Pumping Capacity from Q
The motion induced by a radial-flow impeller, Figure 10.20b,
Given
is characterized by ‘‘high shear’’ and ‘‘low flow’’ and has three
A six-blade radial-flow impeller is installed in a Rushton-
main components: 3
type basin. Q(raw water) ¼ 1.0 m =s.
Required
1. A radial flow of high velocity, which creates a high-
Determine the pumping capacity of a suitable impeller,
shear zone just at the tip of the impeller
i.e., Q(impeller) and its rotational speed, n.
2. The flat blade of the impeller causes a separation
effect, i.e., wake turbulence’’ on the trailing side Solution
3. The radial-flow jet sets up advection currents that 1. Let q(raw water) ¼ 1.0 s
3
move up and down the walls of a tank, recirculating 2. V(basin) ¼ Q(raw water) q(raw water) ¼ (1.0 m =s)
3
to the center. These currents also experience shear (1.0 s) ¼ 1.0 m
3. For a Rushton system: T ¼ diameter of tank (m);
and thus eddies peel off. Eventually, all of the energy
H(water) ¼ depth of water in tank (m);
is dissipated as turbulence.
T ¼ H(water) and D(impeller)=T ¼ 0:33:
10.4.2.3 Impeller Pumping
In general, the purpose of mixing is to disperse chemicals so 4. Basin dimensions: [pT =4] H(water) ¼ 1.0 m 3
2
that the intended reactions such as coagulation, disinfection,
oxidation, etc., can occur through increasing the probability T ¼ H(water) ¼ 1:08 m
of contacts. The objectives are (1) to create turbulence, i.e., D(impeller)=T ¼ 0:33
a shear zone; and (2) to provide advection through the
D(impeller) ¼ 0:33 1:08 m ¼ 0:36 m
shear zone.
5. Flow number, Q,
10.4.2.3.1 Flow Patterns From Table 10.8, let Q ¼ 0.70
6. Impeller pumping, Q(impeller)
Flow patterns are determined by the configuration of the
impeller and the confining boundary. For a ‘‘back-mix’’ Let Q(impeller)=Q(raw water) 5
reactor, the primary flow pattern is circulation. For a ‘‘flow- 3
through’’ reactor, the flow pattern must be designed for a Q(impeller) ¼ 5 1:0m =s
3
single pass through the turbulence zone. ¼ 5m =s
7. Impeller rotational speed, n,
10.4.2.3.2 Pumping Rate
The pumping rate for a radial-flow impeller is proportional 3
to its tip speed, i.e., nD(impeller), and the area swept, i.e., Q(impeller) ¼ QnD(impeller) (10:37)
2
3
D(impeller) , to give 5 (1:0m =s) ¼ 0:70 n (0:36) 3
n ¼ 153 rev=s
3
Q(impeller) ¼ QnD(impeller) (10:37)
Discussion
With q(raw water) ¼ 1.0 s, the impeller pumping rate
where was selected as five times the raw-water flow, which
3
Q(impeller) is the flow of water pumped by impeller (m =s) was a ‘‘guess’’ on the high side that should give high
n is the rotational velocity of impeller (rev=s) probability, i.e., 0.99 fraction, that almost all raw-water
D(impeller) is the diameter of impeller (m) particles will have contact with coagulant as they pass
through the reactor. The other selections are also arbitrary,
Q is the empirical constant, i.e., the ‘‘flow number’’
(dimensionless)
TABLE 10.8
10.4.2.3.3 Flow Number Flow Numbers for Representative Impellers
The constant, Q, in Equation 10.37 is called the ‘‘flow num- Impeller Type Q Reference
ber,’’ a dimensionless number, that characterizes the pumping Rushton—four blades 0.70 Oldshue (1983, p. 169)
capacity of an impeller (McCabe et al., 1993, p. 244). Rushton—six blades 0.54 Q 0.88 Oldshue (1983, p. 169)
Table 10.8 provides flow numbers for several impeller types Marine-square pitch 0.5 McCabe et al. (1993, p. 244)
for R 1000; the basin proportions are assumed the same as Turbine—four blades, 458 0.87 McCabe et al. (1993, p. 244)
given for a ‘‘Rushton basin’’ (see glossary).