Water and Wastewater Engineering
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6-46 WATER AND WASTEWATER ENGINEERING
Solution:
a . To provide redundancy, the flow will be divided into two flocculation basins. The flow
in each is
Q
each
m /d
m /d
5010
2
25 10
33
33
b. Using Equation 6-13, calculate the volume of a flocculator basin as
()
()
25 10
1 440
22 381 94
33
m /d
min/d
min o
,
.rr m382
3
V
c. With three compartments, each compartment volume is
382
3
127 33
3
3
m
m.
V
d. Assuming a trial water depth of 4.0 m, the surface area of a compartment is
A
surface
m
m
m
127 33
40
3183
3
2
.
.
.
e. With a basin depth of 4.0 m and the design criterion of a basin depth 1 m greater than the
diameter of the paddle wheel, the paddle wheel diameter is
40 1 3 0..mm m
f. The minimum length of a stage (compartment) is the diameter of the paddle wheel plus
the design criterion of 1 m minimum between stages.
Minimum length mm m3 0140..
g. The nominal width of a compartment is the surface area divided by the minimum length
of a stage
W
3183
40
796
2
.
.
.
m
m
m
h. The required clearance is twice the minimum clearance from the walls plus 1 m between
paddle wheels on a shaft.
Required c learance mm m203 1160()..
i. The total length of the two paddle wheels is then
796 160 636.. .mm m
COAGULATION AND FLOCCULATION 6-47
j. Each paddle wheel is then
6 36
2
3 18
.
.
m
m long
k. Place three paddle boards on each of four paddle arms with leading edge at 1/3 points, that is,
1 5
3
0 5
.
.
m
m
The dimensions of each paddle board will be 15 cm 3.18 m. A sketch of the layout of
the paddle flocculator is shown below.
Paddle
Shaf
t
w
L
Plan
r
3
r
2
r
1
Profile
Baffle Wall
F
lo
cc
ulator
l. Solve Equation 6-12 for P to determine the water power required to ac hieve a G 40
s
1
for the first chamber (compartment). Using Appendix A and a water temperature of
15 C find
113910
40 1 13910
3
22
..
.
Pa s
sG
()(
33
127 33 23204 23 0Pa sm or W
)( )
..
V
1
P
6-48 WATER AND WASTEWATER ENGINEERING
m. Determine the rotational speed required by the paddles using Equation 6-19 . Note that
the area of each paddle blade is the same, so the equation may be written
P
CA
vvv
Dp
rr r
2
1
3
2
3
3
3
[( )( )( )]
at at at
and substituting Equation 6-20 for the velocity term
P
CA
nr r r
Dp
2
2075
3
1
3
2
3
3
3
[( )][()()()].
The area of a paddle blade is
A
p
015318 0 477
2
.. .mm m
From the length to width ratio select the appropriate value for C
D
.
L
W
3 18
015
21 2
.
.
.
m
m
Select C
D
of 1.5
Using P 232.04 W, solve the rearranged equation for n with the radii for the paddle
blades computed to the center of each blade.
r
r
1
2
0 5
015
2
0425
10
015
.
.
.
.
.
m
m
m
m
⎛
⎝
⎜
⎞
⎠
⎟
m
m
m
m
2
0925
1 5
015
2
1
3
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
.
.
.
.r 4425
2
2075
1 3
3
1
3
2
3
m
/
n
P
CA r r
Dp
[ ( )] [( ) ( ) (.
rr
3
3
1 3
3
223204
1 000
)]
()
()(
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
/
W
kg/m
.
,11 5 0 477 104 65 0425 0925
2 33
.. . . .)( )( )[( ) ( ) (m 11425
464 08
78 877 07 3 762
3
1 3
.
.
,. .
)]
()()
⎛
⎝
⎜
⎞
⎠
⎟
/
⎛⎛
⎝
⎜
⎞
⎠
⎟
()165 10 0 116
3 1 3
..
/
rpsor 6.96 rpmmor rpm7
n. Assuming an efficiency of 0.65, the motor power required is
Motor power or W
23204
065
35698 357
.
.
.
COAGULATION AND FLOCCULATION 6-49
Comments:
1 . Because G i s tapered, n must be calculated for each of the following chambers as well as
the first chamber.
2. A motor power of (1.5)(357 W) 535.5 or 540 W or larger is recommended.
3. Add 0.60 m to depth of tank for freeboard.
6-8 OPERATION AND MAINTENANCE
The most important operation and maintenance (O&M) task in coagulation is the selection of
the appropriate chemicals and the adjustment of the dose to ever-changing raw water quality and
plant flow. Frequent jar testing is the standard technique for adjusting the chemical dose. Because
of the time delay in
conducting the test, other techniques such as zeta potential measurements and
the use of a streaming current detector (SCD) have been used to augment the jar test. None of
these relieve the operator of the necessity of a significant amount of attention.
Monitoring of the chemical feed system to detect clogging of the lines and maintenance of
the mixers
ranks second in the need for close O&M oversight. Appropriate mixing energy is an
important part of optimization of the chemical dose. Excess dosing with coagulant to compensate
for inefficient mixing not only is u neconomical in terms of chemical usage, it is expensive in
terms of slud
ge production.
Hints from the Field. Suggestions from operators include the following:
• All of the design calculations in this chapter were based on the design flow, that is, the maxi-
mum daily flow rate at the end of the design life. Because the minimum flow rate at start-up
will probably be considerably less than the design flow, operational problems ma
y be severe.
It is highly recommended that the design be evaluated at minimum flow conditions.
• M o st d rive failures are caused when the unit is started at the top rotational speed. O&M
manuals should note that mixers shou ld be started at low speed to avoid very
high torque
force and a high power requirement.
Visit the text website at www.mhprofessional.com/wwe for supplementary materials
and a gallery of additional photos.
6-9 CHAPTER REVIEW
When you have completed studying this chapter, you should be able to do the following without
the aid of your textbooks or notes:
1 . Explain what NOM is and why it may be one of the goals of coagulation/flocculation to
remove it from drinking water.
2. Differentiate between the terms coagulation and flocculation.
3. Explain how colloidal particles become negatively charged.
6-50 WATER AND WASTEWATER ENGINEERING
4. Sketch a particle showing the charge of the Helmholtz layer and the diffuse layer.
5. Sketch the family of zeta potential curves under the influence of increasing ionic
strength.
6. Sketch the family of zeta potential curves under the influence of increasing cationic
charge of a coagulant.
7. Explain the Schulze-Hardy rule an
d why it is seldom achieved in natural waters.
8. Explain the physics of coagulation using the four mechanisms of coagulation.
9. Explain why the jar test is conducted in two steps.
10. Explain the purpose of enhanced coagulation and select appropriate coagulant(s) from
a li
st.
11. Given a set of chemicals chosen for coagulation, select the order of addition.
12. In terms of the physics of coagulation, explain the difference between adsorption/
destabilization and sweep coagulation.
13. From a list of mixing devices select appropriate mixers for either adsorption/
des
tabilization or sweep coagulation.
W ith the use of this text, you should be able to do the following:
14. Estimate the alkalinity consumed by the addition of alum or ferric chloride to water
with varying amounts of alkalinity including no alkalinity.
15. Estimate the pH from the addition of coagulant given the alkalinity.
16. Given the alkalinity, estimate the amount of base to neutralize an excess of c
oagulant
over the available alkalinity.
17. Determine the optimum dose of coagulant from jar test data.
18. Select the appropriate coagulant and mixer system from jar test data.
19. Design an in-line blender, a static mixer, and a mechanical mixer in a stirred tank.
20. Design a baffle wall for a flocculation tank.
21. Design a vertical t
urbine mixer for flocculation or a paddle flocculator.
6-10 PROBLEMS
6-1. What is the “exact” alkalinity of a water that contains 0.6580 mg/L of bicarbonate, as
the ion, at a pH of 5.66? No carbonate is present.
6-2. Calculate the “approximate” alkalinity (in mg/L as CaCO
3
) of a water containing 120
mg/L of bicarbonate ion and 15 mg/L of carbonate ion.
6-3. Calculate the “exact” alkalinity of the water in Problem 6-2 if the pH is 9.43.
COAGULATION AND FLOCCULATION 6-51
6-4. Calculate the “approximate” alkalinity (in mg/L as CaCO
3
) of a water containing
15 mg/L of bicarbonate ion and 120 mg/L of carbonate ion.
6-5. A jar test has shown that the optimum dose of ferric chloride consumes all of the
alkalinity. If the amount of ferric chloride that is in excess is 10 mg/L, how much
lime (Ca(OH)
2
), in mg/L must be added to neutralize the acid formed?
6-6. Shown below are the results of water quality analyses of the Thames River in London.
If the water is treated with 60 mg/L of alum to remove turbidity, how much alkalinity
will remain? Ignore side reactions with phosphorus and assume all the alkalinity is
HCO
3
.
Thames River, London
Constituent Expressed as Milligrams per liter
Total hardness CaCO3 260.0
Calcium hardness CaCO3 235.0
Magnesium hardness CaCO3 25.0
Total iron Fe 1.8
Copper Cu 0.05
Chromium Cr 0.01
Total alkalinity CaCO3 130.0
ChlorideCl 52.0
Phosphate (total) PO4 1.0
Silica SiO2 14.0
Suspended solids 43.0
Total solid
s 495.0
pH
a
7.4
a
Not in mg/L.
6-7. Shown below are the results of water quality analyses of the Mississippi River at Baton
Rouge, Louisiana. If the water is treated with 30 mg/L of ferric chloride for turbidity
coagulation, how much alkalinity will remain? Ignore the side reactions with phos-
phorus and assume all the alkalinity is
HCO
3
.
Mississippi River, Baton Rouge, Louisiana
(continued)
Constituent Expressed as Milligrams per liter
Total hardness CaCO3 164.0
Calcium hardness CaCO3 108.0
Magnesium hardness CaCO356.0
Total iron Fe 0.9
Copper Cu 0.01
Chromium Cr 0.03
Total alkalinity CaCO3 136.0
6-52 WATER AND WASTEWATER ENGINEERING
6-8. Determine the size (liters/hour) of a proportioning pump to feed ferric chloride for
a 0.438 m
3
/ s water treatment plant. The optimum dose selected is 50 mg/L. Ferric
chloride may be obtained in a liquid form that is 42% pure. The density of this solu-
tion is 1.797 kg/L.
6-9. Using Table 6-4 , select an in-line blender to mix alum with a design flow rate of
485 m
3
/h. The design water temperature is 10 C. Verify that the detention time
and velocity gradient meet the design criteria for adsorption/destabilization. As-
sume that the water power is 80% of the motor power, that the mixing time must
be between 0.3 and 0.8 s, and that there will be a stand-by mixer for redundancy.
Because this problem will require
some iteration, a spreadsheet solution is highly
recommended.
6-10. U sing Table 6-4 , select a combination of in-line blenders to mix ferric chloride with
a design flow rate that varies from a minimum of 8,200 m
3
/ d in winter to a maximum
of 49,200 m
3
/ d in summer. The design water temperatures are 4 C in the winter and
15 C in the summer. The plant will operate 8 hours per day for seven days per week
in the winter and 24 hours per day for seven days per week in the summer. Assume
that the water power is 80% of the motor power and that the mixing time must be
between 0.3 and 0.8 s. Because this proble
m will require some iteration, a spread-
sheet solution is highly recommended.
6-11. Rework Example 6-6 to find an appropriate static mixer from those shown in Figure 6-16
that conforms to the design criteria. Because this problem will require some iteration,
a spreadsheet solution is highly recomm
ended. The variables that may be adjusted
include the number of mixing elements and the mixer diameter.
6-12. Design a static mixer for the following conditions:
D e sign flow rate 350 m
3
/h
Minimum water temperature 12 C
M i xer aspect ratio 1.0
To complete this des ign, specify the following: number of static mix ers, number of
mixing elements, and mixer diameter.
6 -13. As a junior field engineer, y ou have been asked to assist the contractor on yo
ur
job in resolving the following problem. A 4.9 kW motor and gear drive rated
Constituent Expressed as Milligrams per liter
ChlorideCl 32.0
Phosphate (total) PO4 3.0
Silica SiO2 10.0
Suspended solids 29.9
Turbidity
a
NTU 12.0
pH
a
7.6
a
Not in mg/L.
Mississippi River, Baton Rouge, Louisiana (continued)
COAGULATION AND FLOCCULATION 6-53
at 175 rpm has been shipped with the four impellers described below. The
baffled rapid mix tank into whic h it is to be installed is 3.0 m
3
in volume (1.56 m
diameter by 1.56 m deep). Which impeller should be used? Assume a water tem-
perature of 10 C, a G 1,000 s
1
, a water density of 1,000 kg/m
3
, and that the
motor power to water power efficiency is 80%. Show the calculations to justify
your decision.
Impellers
A. Propeller, pitch of 2, 3 blades, diameter 0.48 m, N
p
1.0
B. Propeller, pitch of 2, 3 blades, diameter 0.61 m, N
p
1.0
C. Turbine, 6 flat blades, vaned disc, diameter 0.48 m, N
p
6.3
D. Turbine, 6 flat blades, vaned disc, diameter 0.61 m, N
p
6.3
6-14. The town of Eau Gaullie has requested proposals for a new coagulation water treat-
ment plant. The design flow for the plant is 0.1065 m
3
/ s. The average annual water
temperature is 19 C. The following design assumptions for a rapid-mix tank have
been made:
1. Number of tanks 1 (with 1 backup spare)
2. Tank configuration: circular with liquid depth 2 diameter
3. Detention time 10 s
4. Velocity gradient 800 s
1
5. Impeller type: turbine, 6 flat blades, N
p
5.7
6. Available impeller diameters: 0.45, 0.60, and 1.2 m
7. Assume B (1/3) H
Design the rapid-mix system by providing the following:
1. Water power input in kW
2. Tank dimensions in m
3. Diameter of the impeller in m
4. Rotational speed of impeller in rpm
6-15. Yo
ur boss has assigned you the job of designing a rapid-mix tank for the new water
treatment plant for the town of Waffle. The design flow rate is 0.050 m
3
/ s. The aver-
age water temperature is 8 C. The following design assumptions for a rapid-mix tank
have been made:
1. Number of tanks 1 (with 1 backup)
2. Tank configuration: circular with liquid depth 1.0 m
3. Detention time 5 s
6-54 WATER AND WASTEWATER ENGINEERING
4. Velocity gradient 750 s
1
5. Impeller type: turbine, 6 flat blades, N
p
3.6
6. Available impeller diameters: 0.25, 0.50, and 1.0 m
7. Assume B (1/3) H
Design the rapid-mix system by providing the following:
1. Water power input in kW
2. Tank dimensions in m
3. Diameter of the impeller in m
4. Rotational speed of impeller in rpm
6-16. Rework Example 6-8 to find the orifice diameter using a headloss if one of the floc-
culation basins is out of service when the design flow rate occurs.
6-17. Determine the number of orifices for a baffle wall with the following design parameters:
D e sign flow rate 0.11 m
3
/ s
Orifice coefficient 0.75
Orifice diameter 150 mm
6-18. Using a spreadsheet program you have written, rework Example 6-8 for the follow-
ing cases:
a . Given velocities of 0.55, 0.45, and 0.35 m/s, find the corresponding diameters in cm
and headlosses for 60 orifices
.
b . Given headlosses of 3, 6 and 9 mm, find the corresponding diameters and veloci-
ties for 60 orifices.
6-19. Continuing the preparation of the proposal for the Eau Gaullie treatment plant
( Problem 6-14 ), design the flocculation tank by providing the following for the first
two compartments only:
1. Water power input in kW
2. Tank dimensions in m
3. Diameter of the impeller in m
4. Rotational speed of impeller in rpm
Use the following assumptions:
1. Number of tanks 2
2. Tapered G in three compartments: 90, 60, and 30 s
1
3. Gt 120,000
COAGULATION AND FLOCCULATION 6-55
4. Compartment length width depth
5. Impeller type: axial-flow impeller, three blades, N
p
0.31
6. Available impeller diameters: 1.0, 1.5, and 2.0 m
7. Assume B (1/3) H
6-20. Continuing the preparation of the proposal for the Waffle treatment plant ( Problem 6-15 ),
design the flocculation tank by providing the following for the first two compart-
ments only:
1. Water power input in kW
2. Tank dimensions in m
3. Diameter of the impeller in m
4. Rotational speed of impeller in rpm
Use the following assumptions:
1. Number of tanks 1 (with 1 backup)
2. Tapered G in three compartments: 60, 50, and 20 s
1
3. Detention time 30 min
4. Depth 3.5 m
5. Impeller type: axial-flow impeller, three blades, N
p
0.43
6. Available impeller diameters: 1.0, 1.5, and 2.0 m
7. Assume B (1/3) H
6-21. Determine the required width of the paddle blade and recommend a motor power (in
watts) and rotational speed (in rpm) for the horizontal shaft a cross-flow paddle floc-
culator for the first compartment of a three compartment flocc
ulation basin shown in
Figure P-6-23. ( Note: there are three paddle wheels on one shaft.) Figure P-6-23 and
the following assumptions are to be used in the design:
L i q uid volume 257.2 m
3
Velocity gradient 40 s
1
Motor efficiency 80%
P a ddle velocity 0.5 m/s
Water temperature 15 C
Drag coefficient 1.8
No stators are present *
* A stator is a vertical baffle.