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Mixing 281

10.5 Turbulent Energy table. (b) Focus on the raw-water particles that will
Given=Required have varying residence times.
What is the order of magnitude of kinetic energy 10.11 Complete-Mix Reactor
dissipated by turbulence associated with jet (orthoki- Given
netic) mixing? Assume the jet discharges through a A complete-mix reactor is used for coagulation.
nozzle from a reservoir with water surface 10.0 m Required
above the centerline of the nozzle. Discuss the problem of coagulation with a
10.6 Role of G in Mixing complete-mix reactor.
Given 10.12 Imposing Similitude for Design*
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Let d(particle) 1 mm and let G 1000 s . Given
Required A Rushton impeller–basin (six blades) is to be
Estimate the ratio of particle contacts by turbulence designed based upon the characteristic P vs. R curve
and diffusion. Reference is Section 10.3.1.4 and of Figure 10.14. The detention time is u ¼ 10 s and
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Figure 10.12. Q p ¼ 0.438 m =s (10 mgd). Assume operation is in the
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10.7 Rapid-Mix Basin Design turbulent range, i.e., R 10 .
Given Required
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Rapid-mix basin in which, Q(plant-flow) ¼ 0.876 m =s Determine the basin size, the impeller diameter,
(20 mgd) divided into two treatment trains. D(impeller), rotational velocity, n, and power required
by the impeller. Reference is Section 10.3.3.4.
Required
Determine the following: *Indicates a more difficult problem.
(a) Dimensions and geometry of rapid-mix basin 10.13 Time for Five Passes through Turbulent Zone and
(b) Power of the mixing motor to be installed 0.99 Blend
(c) Size, type, and setting of impeller, and speed Given
(d) Chemicals required, sequence and rate of feed Complete-mix coagulation basin has flow Q ¼ 0.100
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(e) pH of rapid-mix basin m =s and u ¼ 10 s.
(f) Recommend rapid-mix equipment from available Required
catalogs (a) Determine the detention time, q(basin), and impeller
10.8 Flow Variability speed required so that 0.99 fraction mixing occurs such
Given=Required that 0.90 remains in the basin. (b) Suppose u ¼ 20 s.
Address the effect of flow variability on design param- Determine n(pump impeller speed) for 0.99 fraction
eters, e.g., q, t 5R =q, G, P=Q, for a ‘‘Rushton’’-type blend.
mixing system. 10.14 Power Required to Achieve Five Passes Through
10.9 Laboratory Exercise on Scale-Up Turbulent Zone
Given=Required Given
This problem is intended to provide a pseudo ‘‘hands- The problem statement is the same as in problem
on’’ laboratory experience. The scale-up will be incon- 10.13, i.e., a complete-mix Rushton-type coagulation
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clusive with conflicts seen between the various basin has flow Q ¼ 0.100 m =s and u ¼ 10 s.
approaches, e.g., geometric, detention time, G, Rey- Required
nolds, number, and power number. The exercise (a) Determine the power required for problem 10.13 (a).
should be approached looking for a ‘‘half-full’’ glass, The ‘‘solution for problem 10.13 (a) is given here for
vis-à-vis one that is ‘‘half empty.’’ reference: as seen in Table CD10.7, the time if we
10.10 Back-Mix Reactor accept the criterion that 0.90 fraction of the fluid
should be subjected to five passes through the high-
Given
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For a complete mix reactor, let Q ¼ 0.100 m =s, turbulence zone of the impeller, which will achieve
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V ¼ 5.0 m . 0.99 fraction blend (Section 10.4.1.2), then the asso-
ciated t=u ¼ 0.10, and if u ¼ 10 s, as given, then,
Required
t 5R ¼ 1 s. The task is to then calculate, n ¼ K=t(five
(a) Plot the C vs. t curve for a substance, A, fed continu- passes). Assuming we have a Rushton design, and
ously into the reactor. (b) Assume that the substance A is
that R > 1000, then from Table 10.6, the ‘‘blend
a neat alum solution. Describe what happens in the
number,’’ n t 5R ¼ 36. Thus, n (1 s)¼ 36, and
reactor with respect to the alum–particle reactions.
n ¼ 36 rps.
Hint: (a) Use the spreadsheet, Table CD10.7= (b) Determine the power required for #10.13 (b). The
CDprob10.10 (see CRC website for excel spreadsheets; ‘‘solution for problem 10.13 (b) is given for refer-
Table CD10.7 and CDprob10.10 are identical), to ence: If u ¼ 20 s, t=u ¼ 0.10, and thus,
calculate the curve, i.e., with the plot linked to the t 5R (required) ¼ 2 s. Again, from Table 10.6, the