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Flocculation 323

11.12 Characteristics of Full-Scale Paddle Wheel by same as Basin #1, except that there are only two blades
Mathematical Model per arm. Radial distances to the center of each blade
Given are: r 1 ¼ 241 mm, r 2 ¼ 368 mm.
A flocculation basin is to be designed for Q ¼ 0.263 Required
3
m =s (6.0 mgd) at T ¼ 208C. Determine the power versus rpm curve and the G
versus rpm curve using a spreadsheet and show the
Required
results on an associated plot.
(a) Calculate the power, P, required by the paddle
1
wheel using Table 11.6 such that G ¼ 60 s .
(b) Generate plots as in Figure 11.15a through d. ACKNOWLEDGMENTS
Reference Kevin Heffernan, PE, principal project manger, CH2M HILL,
Table 11.6, i.e., file ‘‘11.6FlocBDes.082105.xls,’’ is INC., Denver office, provided the three-dimensional animated
copied and renamed, as file ‘‘TableCDprob11.12= drawing files, seen as Figures CD11.17a and b. The anima-
11.6FlocBDes.082105.xls.’’ tions were included by permission from both the City of Fort
11.13 Algorithm for End-Around Flocculation Basin Collins and CH2M HILL, INC. Heffernan was design
Given manager and resident engineer during the construction of the
3
Assume flow, Q ¼ 1.0 m =s. new flocculation basins and building, i.e., as illustrated in
Required Figure CD11.17, during the period 1998–2000.
Set up a spreadsheet algorithm to design an end-around Kevin Gertig, water resources and treatment operations
flocculator basin. Use headings to identify variables manager, City of Fort Collins, was superintendent of the
with rows for the assumed numerical values with cal- Fort Collins Water Treatment Facility during the aforemen-
culated values across. Show a design sketch, i.e., both tioned flocculation capacity expansion. As with other projects,
plan and profile as well as the design spreadsheet. Gertig was intimately involved with the flocculation system
11.14 Plot of Power and G versus rpm for Paddle-Wheel expansion and passed-on his knowledge freely as related to its
Flocculator design, construction, and operation, which helped in formu-
lating this chapter.
Given
Data of Table CD11.7 give measurements for the pilot
scale flocculation basin of Figure 11.14. For this prob- APPENDIX 11.A: DERIVATION OF CAMP
lem, consider the third basin, Basin #3, which is the AND STEIN G FOR THREE-DIMENSIONAL CUBE

TABLE 11.A.1
Development of Camp and Stein G for Three-Dimensional Infinitesimal Cube
Term One Dimension Three Dimensions a

dv qu qv qu qw qv qw
Velocity gradient
dn qy þ qx þ qz þ qx þ qz þ qy

dv qu qv qu qw qv qw
Total shear t ¼ m t ¼ m þ þ þ þ þ
dn qy qx qz qx qz qy
" #
2 2 2
dv dv dv dv qu qv qu qw qv qw
Work of shear=unit time ¼ m t ¼ m
t

dn dn dn dn qy þ qx þ qz þ qx þ qz þ qy
" #
2 2 2 2
P dv qu qv qu qw qv qw
Work of shear=unit time ¼ m F ¼ m
V dn qy þ qx þ qz þ qx þ qz þ qy
" # 1=2
2 2 2
dv qu qv qu qw qv qw
G defined G G þ þ þ þ þ
dn qy qx qz qx qz qy
1=2 1=2
dv P F
G in practical terms
G
dn ¼ mV G ¼ m
Source: Abstracted from Camp, T.R. and Stein, P.C., J. Boston Soc. Civil Eng., October, 1943.
a
In addition to G, another defined term introduced by Camp and Stein (1943) was
P
(11:A:1)
V
F
3
where F is the work of shear per unit volume per unit time (N m=m =s).
The term has not been adopted in this work in order to minimize the use of defined terms; it is given here for reference.