Page 883 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

838 Appendix F: Alum Data and Conversions

which if satisfied, 90% of the contents of the reactor Example F.6 Size an Alum Dissolution Reactor
remains to be circulated by the impeller. Now if we
let u ¼ 90 s, then, Given
Data from F.5
t T =90 s 0:2, Q(alum feed) ¼ 200 mL=s
t T 18 s C(alum feed) ¼ 100 g Al 2 (SO 4 ) 3 14H 2 O=L solution
Required
2. Apply criterion for 10 circulation passes (McCabe a. V(dissolution reactor)
et al., 1993), b. Mixer speed and power

nt T ¼ 78 Solution
a. Calculate reactor volume, i.e.,
n 18 s ¼ 78
n ¼ 4:3 rev=s V
Q
u ¼
(for 10 passes through the impeller). V
90 s ¼
Discussion ð 0:200 L=sÞ
The mixing speed, n ¼ 4.3 rev=s may be low and there will V ¼ 18:0L
be no harm if n is much higher, say n ¼ 10 rev=s. If we let
n ¼ 10 rev=s, then t T ¼ 7.8 s, a considerable reduction. Dimensions
This means that t T =u ¼ 7.8 s=90 s ¼ 0.086. This can be
interpreted in two ways: (1) about 95% of the contents of Dimensions for a cube are D ¼ H ¼ 0.26 m
the reactor will have the 10 passes through the impeller in And,
only 7.8 s, or (2) in 16 s, the number of passes for 90% of D(impeller) ¼ 0.333 D ¼ 0.086 m
the contents through the impeller 20. This hedges the bet
considerably more with respect to the fraction of alum b. Mixer power
dissolved. On the other hand, the detention time can be The reactor=impeller should be a ‘‘back-mix’’ type,
reduced considerably if we increase n further, let n ¼ 20 i.e., with the impeller at the bottom causing a pump-
rev=s, for example. ing effect to recirculate the flow. A ‘‘standard’’
design as described by McCabe et al. (1993) pro-
vides a known dimensionless power number, i.e.,
F.3.4 SIZING THE REACTOR AND MIXER P ¼ 6.0
By definition, the power number, P,is
The volume of the reactor may be calculated as
P
P ¼ 3 5
V(reactor) rn D
(F:3)
Q(alum feed) And the power number for a ‘‘standard’’ mixer is
u ¼
P ¼ 6.0, to give
The mixing power may be determined by the power number
relation, P
6:0 ¼ 3
998 kg 5 rev 5
(0:0865 m)
P m 3 s
(F:4)
rn D
P ¼ 3 5
P ¼ 3.5 W
in which Discussion
P is the power number (dimensionless) . This is too small, so let n ¼ 10 rps, giving P ¼ 28 W
P is the power applied to the impeller (Watts) (0.0013 hp)
3
r is the density of solution (kg=m ) . Try, n ¼ 20 rps, giving P ¼ 224 W (0.30 hp)
3
3
n is the rotational velocity of impeller (rev=s) . Check P=V ¼ 224 W=0.018 m ¼ 12.4 kW=m ,
3
D is the diameter of impeller (m) which is P=V 0.8–2.0 kW=m (for intense
mixing)
3
. As a check, if we use P=V ¼ 2.0 kW=m , then
As a check, the criterion, P=V may be used, i.e., for ‘‘intense’’ 3 3
mixing (McCabe et al., 1993), P=0.018 m ¼ 2.0 kW=m , then P ¼ 0.036 kW ¼
36 W (0.05 hp). Thus, if n ¼ 10 rps, the mixing
would be ‘‘intense,’’ which requires only 36 W.
P 3 The second estimate, P ¼ 28 W looks reasonable,
0:8 2:0 kW=m 4 10 hp=1000 galð Þ (F:5)
V but to hedge our bets, let P ¼ 36 W (or the next
larger mixer available in a catalog). Actually, to
Example F.6 illustrates the application. select an even larger size such as 224 W would