Water and Wastewater Engineering
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6-36 WATER AND WASTEWATER ENGINEERING
d. The required input water power can be calculated by using Equation 6-12. Using Table
A-1 in Appendix A and the temperature of the water, find 1.519 10
3
Pa · s.
P
()( )( )600 1 519 10 0 6653
12 33
s Pa sm..663 6 3 60.or W
Because the efficiency of transfer of motor power to water power is about 80%, the
motor power should be
Motor power
W
W
360
08
450
.
e. Using Table 6-5 , evaluate the different size radial impellers using the geometric ratios.
Below is a comparison of the ratios for the available sizes of radial impellers and the
rapid mix basin dimensions.
Radial impeller diameter
Geometric ratio Allowable range 0.3 m 0.4 m 0.5 m
D/T
0.14 – 0.5 0.4 0.53 0.67
H/D
2 – 4 5.0 3.8 3.0
H/T
0.28–2 2 2 2
B/D
0.7–1.6 1.7 1.3 1.0
Although the 0.4 m diameter impeller has a D / T slightly larger than the allowable range,
it is satisfactory in all the other aspects and, therefore, is selected.
f. The rotational speed is calculated by solving Equation 6-17 for n:
n
P
N D
p i
13
5
13
450
57 04
/
/
W
m
()
()( )
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
..
553
1 000
1 976 118 5
(),
..
kg/m
rps or
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
rrpm or 120 rpm
Comments:
1 . To meet redundancy requirements, two rapid mix basins with this design are provided.
2. Because the average day and minimum flow rates will be less, the detention time at these
flows will be longer than 5 s.
3. To account for variations in water height and wave action, as well as adding a factor of
safety in the d
esign volume, the tank is made deeper than the design water depth. This
additional depth is called freeboard. The freeboard may vary from 0.45 to 0.60 m.
COAGULATION AND FLOCCULATION 6-37
Flocculation Mixing Design Criteria
While rapid mix is the most important physical factor affecting coagulant efficiency, flocculation is
the most important factor affecting particle-removal efficiency. The objective of flocculation is to
bring the particles into contact so that they will collide, stick together, and grow to a size that will
readily settle or filter out. Enough
mixing must be provided to bring the floc into contact and to keep
the floc from settling in the flocculation basin. Too much mixing will shear the floc particles so that
the floc is small and finely dispersed. Therefore, the velocity gradient must be controlled within a
relatively narrow range. Flexibility should also be bu
ilt into the flocculator so that the plant operator
can vary the G value by a factor of two to three. Heavier floc and higher suspended solids concen-
trations require more mixing to keep the floc in suspension. For example, softening floc is heavier
than coagulation floc and, therefore, requires a higher G value to flocculate. This is reflected in the
reco
mmended G values shown in Table 6-6 . An increase in the floc concentration (as measured
by the suspended solids concentration) also increases the required G. Although GLUMRB (2003)
specifies a minimum detention time of 30 minutes for flocculation, cu
rrent practice is to use shorter
times that are adjusted by temperature. With water temperatures of approximately 20 C, modern
plants provide about 20 minutes of flocculation time at plant capacity. With lower temperatures,
the detention time is increased. At 15 C the detention time is in
creased by 7 percent, at 10 C it is
increased 15 percent, and at 5 C it is increased 25 percent.
Flocculation Basin. The flocculation basin should be divided into at least three compartments.
The velocity gradient is tapered so that the G values decrease from the first c
ompartment to the last
and that the average of the compartments is the design value selected from Table 6-6 . GLUMRB
(2003) recommends flow through velocities be not less than 0.15 m/s nor greater than 0.45 m/s.
Water depths in the basin range from 3 to 5 m (Kawamura, 2000). The velocity of flow from the
flocculation basin to the settling basin s
hould be low enough to prevent shear and breakup of the
floc but high enough to keep the floc in suspension.
Baffle Wall. A baffle wall is used to separate the flocculation basin compartments ( Figure 6-19 ).
The top of the baffle is slightly submerged (1 to 2 cm), and the bottom should have a space of 2
to 3 cm above the floor to allow for drainage and sludge re
moval (Kawamura, 2000). Each baffle
should have orifices that are uniformly distributed over the vertical surface. The size should be
selected with the objective of providing a velocity gradient that does not exceed the gradient in
the compartment immediately upstream.
TABLE 6-6
Gt values for flocculation
Type
G, s
1
Gt (unitless)
Low-turbidity, color
removal coagulation
20–70 60,000 to 200,000
High-turbidity, solids
removal coagulation
30–80 36,000 to 96,000
Softening, 10% solids 130–200 200,000 to 250,000
Softening, 39% solids 150–300 390,000 to 400,000
6-38 WATER AND WASTEWATER ENGINEERING
The headloss through the orifice may be determined from the orifice (Reynolds and
Richards , 1996):
QCAgh
d
()2
12/
(6-18)
where Q flow rate through orifice, m
3
/ s
C
d
coefficient of discharge
A area of orifice, m
2
g gravity acceleration 9.81 m/s
2
h headloss through the orifice, m
The coefficient of discharge varies from 0.60 to 0.80. Various authors have suggested that the
orifices be 10 to 15 cm in diameter, the velocities be between 0.25 to 0.55 m/s, and the headloss
range from 3 to 9 mm through each baffle orifice hole at the maximum flow rate. The higher velocity
i
s found at the first baffle and the lower velocity at the last baffle (Kawamura, 2000; MWH, 2005).
Example 6-8. Design a baffle wall for one of a pair of flocculation basins using the following
design parameters:
Q 10,000 m
3
/ d
Diameter of orifices 100 mm
Orifice coefficient of discharge 0.60
Paddle flocculator
Baffle wall
Baffle walls
FIGURE 6-19
Baffle wall arrangement for three compartment flocculator. Note that there are two parallel
treatment trains and that each baffle wall will have a different orifice arrangement.
COAGULATION AND FLOCCULATION 6-39
Solution:
a . A Solver* program in a spreadsheet was used to perform the iterations for the solution of
this problem. The spreadsheet cells are shown in Figure 6-20 . The cell locations used in
the figure are identified by brackets [ ] in the discussion below.
b. Begin with the average design flow for one basin by setting the fixed parameters as follow
s:
[ B 3] Q 10, 000 m
3
/ d
[B4] Write an equation to convert to m
3
/ s for use in the orifice equation
[]B
s/d
m /d
s/d
3
86 400
10 000
86 400
0 116
3
,
,
,
. m /s
3
[ B 5] C
d
0.60
[B6] Diameter of orifice 100 mm
*Solver is a “tool” in Excel®. Other spreadsheets may have a different name for this program.
A B C
Solver Parameters
Set target cell: $B$12
Equal to: Max. Min. Value of: 0
By changing cells:
Subject to the constraints:
Guess
Close
Solve
Options
Reset all
Help
Add
Change
Delete
$B$12 < = 0.55
$B$12 > = 0.25
$B$15 < = 9
$B$15 > = 3
$B$9
3 Q 10000 m
3
/d
4 0.116 m
3
/s
5 C
d
0.6
6 Diameter of each orifice 100 mm
7 0.1 m
8 Area of each orifice 0.00785 m
2
9 No. of orifices 58.44863
10 Q/orifice 0.00198 m
3
/s
11
12 Check orifice velocity 0.25 m/s
13
14 Headloss 0.0090 m
15 9.0 mm
FIGURE 6-20
Example 6-8 spreadsheet with solver dialog box. The values in the spreadsheet
are the final values not the starting values.
6-40 WATER AND WASTEWATER ENGINEERING
c. In cell [B7] write an equation to convert to m for use in the orifice equation
[]B
mm/m
mm
mm/m
m
6
1 000
100
1 000
01
,,
.
d. In cell [B8] calculate the area of an individual orifice
[] ()B
m
7
4
01
4
0 00785
22
2
.
.
e. In cell [B9] place a trial guess at the number of orifices
f. In cell [B10] calculate the flow for an individual orifice
[]
[]
B
B
4
9
g. In cell [B12] check the velocity
[]
[]
B
B
10
8
h. In cell [B14] check the headloss by solving Equation 6-18 for h
∗
⎛
⎝
⎜
⎞
⎠
⎟
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
⎡
⎣
⎢
⎤
∗
2
10
5 8
1
19 62
[]
([ ] [ ])
.
B
BB
⎦⎦
⎥
i. In cell [B15] convert the result from [B14] to mm
[]B14 100
0
∗
j. Activate the dialog box for Solver and designate the target cell [B12], that is, the one for
the velocity.
k. Set Equal to to “Max.”
l. Set By changing to the cell containing the number of orifices, that is, [B9].
m. Add the following four constraints in the dialog box:
(1) Velocity
[B12] 0.55
[B12] 0.25
(2) Headloss
[ B 1 5] 9
[B15] 3
COAGULATION AND FLOCCULATION 6-41
n. Execute solve to find the number of cells is 58.44863. Because this is not an integer, it is
NOT the final answer. Acceptable answers are 59 or 60 orifices. The velocity and headloss
may be checked by typing the integer in cell [B9].
Comments:
1 . This design calculation lends itself to a spread
sheet because the design is iterative in
selecting the appropriate number of orifices.
2. A scale drawing of the orifices on the cross section of the baffle will provide a visual
check on the reasonableness of the design.
Mixer Alternatives. Flocculation is normally accomplished with one of the following
systems: vertical turbine mixing similar to that u
sed in flash mixing, a paddle flocculator
( Figure 6-21 ), or a baffled chamber ( Figure 6-22 ). Vertical turbine mixing with an axial-flow
impeller ( Figure 6-18 ) in a mixing basin is recommended over the other types of flocculators
because they impart a nearly constant G throughout the tank (Hudson, 1981). However,
the paddle flocc
ulator has been the d esign choice for numerous plants. They are especially
chosen for conventional treatment when a high degree of solids removal by sedimentation is
desired. In addition, they are the unit of c hoice when very large volum es of water are to be
treated and the number of vertical shaft units becomes ex
cessive, that is 5 0 (Kawamura,
2000; MWH, 2005).
Vertical Turbine Mixing. Design recommendations include: using a nearly cubical shape for
each compartment with the impeller located at a depth equal to two-thirds of the water d epth
(MWH, 2005), placing the shaft bearings above the water surface and providing a 1.2 m walkway
space around the mi
xer for control panels, power connections, and space for maintenance work
(Kawamura, 2000).
The design of the mechanical mixing system follows that used in flash mixing with appropri-
ate substitution of constants for the axial flow impeller N
p
and tank/impeller ratios from Table 6-5 .
The design process is illustrated in the following example.
Paddles
Baffles Setting
tank
Flash mixer
Raw water
FIGURE 6-21
Paddle flocculator with paddle wheels arranged parallel to the flow.
6-42 WATER AND WASTEWATER ENGINEERING
Example 6-9. Des ign a floccu lation bas in by determining the basin volume, tank dimensions,
required input power, impeller diameter, and its rotational speed using the following parameters
and the manufacturer’s data:
D e sign flow rate 11.5 10
3
m
3
/ d
Flocculation t 30 min
Three flocculator compartments with G 70, 50, 30 s
1
Water temperature 5 C
Place impeller at one-third the water depth
From manufacturer’s data the following impellers are available:
Impeller type
Impeller diameters (m) Power number (N
p
)
Radial 0.3 0.4 0.6 5.7
Axial 0.8 1.4 2.0 0.31
Solution. Two flocculation basins are provided for redundancy at the design flow rate. The
maximum day flow rate is assumed to be twice the average day flow rate.
a . Convert 11.5 10
3
m
3
/ d to m
3
/ min.
11 5 10
1 440
7 986 8 0
33
3
.
,
..
m /d
min/d
or m /
()
mmin
b. With two flocculation basins, the maximum day flow through each will be
Q
80
2
40
3
3
.
.
m /min
m /min
c. Using Equation 6-13, determine the volume of the flocculation basin.
Qt ()()40 30 120
33
. m /min min m
V
Over-and-under baffled channel type (section)Around-the-end baffled channel type (plan)
FIGURE 6-22
Baffled channel flocculation system.
COAGULATION AND FLOCCULATION 6-43
d. Each basin is divided into three equal volume compartments or tanks
compartment
m
m
120
3
40
3
3
V
e. With the recommended water depth range of 3 to 4.5 m, assume water depth of 4.0 m.
The surface area is then
A
surface
m
m
m
40
40
10 0
3
2
.
.
f. With a rectangular plan, the length equals the width and
LW ()10 0 3 16
212
..mm
/
g. The equivalent diameter exist
T
12
2
4100
357
/
m
m
()( ).
.
⎧
⎨
⎩
⎪
⎫
⎬
⎪
⎭
h. The required input water power for each c ompartment can be calculated by using
Equation 6-12 . Using Table A-1 in Appendix A and the temperature of the water, find
1.519 10
3
Pa · s.
P
()( )( )70 1 519 10 40 0 297
12 33
s Pa sm....
.
7 300
501519 10
12 3
or W
s Pa sP
()( )(440 0 1519 150
301519 1
3
12
..
.
m or W
s
)
()(
P 00400547 55
33
Pa sm or W)( )..
Because the efficiency of transfer of motor power to water power is about 80%, the mo-
tor power for each compartment should be
Motor power
W
W
Motor power
W
300
08
375
150
.
008
187 5 190
55
08
68 7
.
.
.
.
or W
Motor power
W
55 70or W
i. The impeller is located at B (0.333)(4.0 m) 1.587 or 1.6 m above the bottom of the
tank.
j. Using Table 6-5 , evaluate the different size radial impellers using the geometric ratios.
Below is a comparison of the ratios for the available sizes of radial impellers and the
rapid mix basin dimensions.
6-44 WATER AND WASTEWATER ENGINEERING
Axial impeller diameter
Geometric ratio Allowable range 0.8 m 1.4 m 2.0 m
D/T
0.17 – 0.4 0.22 0.390.56
H/D
2– 4 5.0 2.9 2.0
H/T
0.34 –1.6 1.12 1.12 1.12
B/D
0.7–1.6 1.7 0.95 0.67
The 1.4 m diameter impeller is satisfactory in all aspects.
k. The tip speed is checked by first computing the rotational speed at G 70 s
1
.
n
P
ND
pi
13
5
13
300
031 14
/
/
W
m
()
()(
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
..
))( )
53
1 000
056 3387
,
..
kg/m
rps or
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
rrpm or 34 rpm
The tip speed is then
Tip speed rpsm ( )()( ) ( )()( )D
i
0 5614 24...6625or m/s.
This is less than the design criterion of a maximum tip speed of 2.7 m/s.
Comments:
1 . The provision of two flocculation basins meets redundancy requirements.
2. An additional 0.60 m is added to the water depth as freeboard so the tank depth is 4.6 m.
Paddle Flocculator. The power input to the water by horizontal paddles may be esti
mated as
P
CA v
Dp p
3
2
(6-19)
where P power imparted, W
C
D
coefficient of drag of paddle
A
p
cross-sectional area, m
2
v
p
relative velocity of paddles with respect to fluid, m/s
The velocity of the paddles may be estimated as
vkrn
p
2
(6-20)
where k constant 0.75
r radius to centerline of paddle, m
n rotational speed, rps
COAGULATION AND FLOCCULATION 6-45
Design recommendations for a paddle wheel flocculator are given in Table 6-7 .
The maximum G for paddle flocculators is limited to about 60 s
1
with a recommended
maximum value of 5 0 s
1
to avoid severe wear of the shaft bearings in a very short time. Each
arm should have a minimum of three paddles so that the dead space near the shaft will be mini-
mized (Kawamura, 2000).
Example 6-10. Design a paddle floccu lator by determining the basin dimens ions, the paddle
configuration, the power requirement, and rotational speeds for the following para
meters:
D e sign flow rate 50 10
3
m
3
/ d
t 22 min
Three flocculator compartments with G 40, 30, 20 s
1
Water temperature 15 C
Parameter Recommendation
G 50 s
1
Basin
Depth 1 m wheel diameter
Clearance between wheel and walls 0.3–0.7 m
Wheel
Diameter 3–4 m
Spacing between wheels on same shaft 1 m
Spacing between wheel
“rims” on adjacent shafts 1 m
Paddle board
Width 10–15 cm
Length 2–3.5 m
Area of paddles/tank cross section 0.10–0.25
Number per arm3
Spacing at 1/3 points on arm
Tip speed 0.15–1
m/s
C
D
L/W 5
1.20
L/W 20
1.50
L/W 20
1.90
Motor
Power 1.5–2 water power
Turn down ratio 1:4
Sources: Kawamura, 2000; MWH, 2005; Peavy et al., 1985
TABLE 6-7
Design recommendations for a paddle wheel flocculator