Page 308 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Mixing 263

where
n(impeller) is the rotational velocity of impeller (rev=s)
t 5R time for five circulations through impeller (s)
¼ 5 u(impeller)
K(0.99 blend) is the mixing constant for 0.99 fraction
blend valid for turbulent zone (dimensionless)

The ‘‘blend number,’’ i.e., ‘‘n(impeller) t 5R ,’’ is designated
here as K(0.99 blend) and is constant in the turbulent range, i.e.,
high R. The blend numbers for four systems are given in Table
10.6 and illustrate range in values, e.g., 36 K(0.99 blend,
turbines) 60; and 120 K(0.99 blend, propellers) 550. The
utility of the blend number is that from it the rotational velocity
of the impeller, n(impeller), may be estimated.
To illustrate how the blend number may be used,
assume the system is a turbine in a baffled tank, in which
K(0.99 blend) as in Table 10.6, and assume that u(raw
water) ¼ 10 s.
First, from Equation 10.35,
n(impeller) t 5R ¼ K(0:99 blend)

and since we let

t 5R ¼ 5 u(impeller) ¼ u(raw water),
(a)
then,

n(impeller) u(raw water) ¼ K(0:99 blend)

Next, substitute numerical values, i.e., u(raw water) ¼ 10 s,
and from Table 10.6, for a turbine in a baffled, tank, K(0.99
blend) ¼ 36, to give

n(impeller) (10s) ¼ 36

Thus, n(impeller) ¼ 3.6 rev=s.

(b)
TABLE 10.6
FIGURE 10.17 Two kinds of impeller mixer systems. (Courtesy of
City of Fort Collins Utilities, Fort Collins, CO, 2010). (a) Back-mix Values of ‘‘Blend Number,’’ K(0.99 Blend)
reactor. (b) In-line mixer. Impeller Type Conditions D=T b H=T b R c K(0.99 Blend)
Propeller 1=6 1.0 20,000 550
where Propeller 1=3 1.0 20,000 120
3
Q(neat alum) is the flow of neat alum into reactor (m =s) Turbine a 1=3 1.0 4,000 60
C(neat alum) is the concentration of neat alum solution as Turbine Baffled 1=3 1.0 2,000 36
3
provided by manufacturer (647 kg neat alum=m neat
alum solution) Source: Adapted from McCabe, W.L. et al., Unit Operations of Chemical
Engineering, 5th edn., McGraw-Hill, New York, p. 259, 1993.
a A turbine is a radial-flow impeller.
10.4.1.2.1 Blend Number
b D, diameter of impeller; T, diameter of tank; H, depth of water; R,
The product ‘‘n(impeller) t 5R ’’ is a constant for a given sys-
Reynolds number.
tem (McCabe et al., 1993, p. 258), i.e., c Threshold value of Reynolds number at which K(0.99 blend) becomes
constant.
n(impeller) t 5R ¼ K(0:99 blend) (10:35)