# Introduction to Sedimentation

Mechanics

Feb 21, 2014 (4 years and 2 months ago)

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Treatment Processes
Screening
Aeration
Prechlorination
CoagulationFlocculation
Sedimentation
Sedimentation
Sedimentation is the downwards movement of an object
relative to its surrounding medium, due to the force of gravity.
Sedimentation
Dissolved-air flotation (DAF) is a method whereby bubbles are
produced by the reduction of pressure in a water stream
saturated with air.
Sedimentation
The purpose of sedimentation is to remove preexisting solids,
as well as the precipitates formed in coagulation and
flocculation.
Sedimentation
The purpose of sedimentation is to remove preexisting solids,
as well as the precipitates formed in coagulation and
flocculation.
Sedimentation
Model of a circular settlement tank with sludge scrapers was
used to estimate the distribution of particulate concentration
over time
CIVL 1112
Water Treatment - Sedimentation
1/7
Sedimentation
Sedimentation
Sedimentation
http://techalive.mtu.edu/meec/module03/WastewaterandWildlife.htm
Sedimentation
 Sedimentation is the accumulation through gravity of
particulate matter at the bottom of a fluid.
 This natural process is frequently used to separate
contaminants from air, water, and wastewater.
 There are four types of settling:
 discrete
 flocculant
 hindered
 compression
Sedimentation
 Discrete - Individual particles settle independently, neither
agglomerating nor interfering with the settling of the other
particles present. This occurs in water with a low
concentration of particles.
 Flocculant - Particle concentrations are high enough that
agglomeration occurs. This reduces the number of
particles and increases average particle mass. The
heavier particles sink faster.
Sedimentation
 Hindered - Particle concentration is sufficient that
particles interfere with the settling of other particles.
 Compression - In the lower reaches of clarifiers where
particle concentrations are highest, particles can settle
only by compressing the mass of particles below.
CIVL 1112
Water Treatment - Sedimentation
2/7
Q
sludge layer
V
h
V
p
w
Q
Path of smallest
consistently settled
particle
Sedimentation
z
L
Q
sludge layer
Q
Sedimentation
L
V
h
V
p
If the V
p
> V
h
then settling can occur
Q
sludge layer
Q
Sedimentation
L
V
h
V
p
If the V
p
< V
h
then “short-circuiting can occur
Sedimentation
The horizontal velocity,
V
h
, of a particle can be approximated
by considering the flowrate,
Q
, and the cross-sectional flow
area of the tank.
h
Q V A

h
Q
V
A

h
Q
V
wz

Sedimentation
The residence time of water in the sedimentation tank can be
approximated as:
h
Q
V
wz

h
L
V
t

Lwz
t
Q

Sedimentation
Estimate of the residence time of water in a small
sedimentation tank where Q = 1 liter/min, L = 6 in.,
w = 6 in., and z = 10 in. (dimensions of a tank in the lab).
Lwz
t
Q

6in.(6in.)10in.
ml
1,000
min

3
360in.min
1000ml
t 
5.9 min
3
16.39ml
in.

CIVL 1112
Water Treatment - Sedimentation
3/7
Sedimentation
 The forces acting on a particle are:
 gravity in the downward direction,
 drag acting in the upward direction as the particle settles
 upward buoyancy due the water displaces by the particle
 Discrete settling, can be analyzed by calculating the settling
velocity of the individual particles contained within the water.
Sedimentation
The forces acting on a settling particle are:
F
b
F
g
F
d
F
g
= F
d
+ F
b
F
g
is the force due to gravity
F
d
is the drag force
F
b
is the buoyant force
Sedimentation
The gravitational force can be expressed as:
g p
F m g
Using the density and volume of the particle yields:
where: 
p
is the density of the particle, lb-mass/ft.
3
,
V
p
is the volume of the particle, ft.
3
, and
g is the gravitational constant, ft./s
2
g p p
F V g

Sedimentation
The drag on the particle can be calculated by the drag
equation from fluid mechanics
2
1
2
d d w
F C A v
where C
d
is the drag coefficient, dimensionless,
A is the particle cross-sectional area, ft.
2
,

w
is the density of water, lb-mass/ft.
3
,
v is the velocity, ft./sec.
Sedimentation
The buoyant force acting on the particle is:
b w
F m g
Substituting the particle volume and density of water, yields:
b w p
F V g

where: 
w
is the density of water,
lb-mass/ft
3
,
Sedimentation
By balancing the forces acting on a settling particle and using
the relationships for
F
g
the force due to gravity,
F
d
the drag
force, and
F
b
the buoyant force, the following relationship
can be developed:
2
1
2
p
p d w w p
V g C A v V g   
CIVL 1112
Water Treatment - Sedimentation
4/7
Sedimentation
Solving for the settling velocity, v, results in:
If the particle is assumed to round and the formulas for area
and volume of a sphere are used:
2( )
p w p
d w
V g
v
C A
 

4( )
3
p w p
d w
d g
v
C
 

where d
p
is the
diameter of the
particle
Sedimentation
At low Reynolds numbers (for
N
Re
, < 1) C
d
, can be
approximated by:
For Reynolds Numbers is transition flow, 1 <
N
Re
< 10,000,
the drag coefficient for spheres is:
For turbulent flow,
N
Re
> 10,000, the relationship for the drag
coefficient for spheres is:
Re
24
d
C
N

Re Re
24 3
0.34
d
C
N
N
  
0.4
d
C 
Sedimentation
The Reynolds Number is:
2
( )
18
p w
p
d g
v
 

For N
Re
, < 1 the particle settling velocity can be estimated as
a function of the properties of the particle and water, and the
particle diameter, or
Re
vd
N

where
u
is the absolute viscosity of the water, lb-force-
sec./ft.
2
(at 50
0
F,
μ
= 2.73(10
-5
) lb.-sec./ft.
2
).
Sedimentation
2
( )
18
p w
p
d g
v
 

The vertical velocity of water in a settling basin is often
described as the
overflow rate (OFR)
.
It is usually expressed as gal./ft.
2
-day (m
3
/m
2
-day).
This relationship is known as Stokes' law, and the velocity is
known as the Stokes velocity.
Sedimentation
The overflow rate is calculated in the following way:
Q
OFR
A

where:
OFR
is the overflow rate, gal./ft.
2
-day,
Q
is the flowrate, gal./day, and
A
is the clarifier area, ft.
2
.
Sedimentation Example 1

Estimate the settling velocity of sand (

p
= 2,650
kg/m
3
) with a mean particle diameter of 0.21 mm.

Assume the sand is approximately spherical.

Using a safety factor of 1.4 to account for inlet and
outlet losses, estimate the area required for a chamber
to remove the sand if the flowrate is 0.10 m
3
/sec
(1,000 liters = 1 m
3
).
CIVL 1112
Water Treatment - Sedimentation
5/7
Sedimentation Example 1
The density of water at 20
0
C is 998 kg/m
3
and the viscosity of
water at 20
0
C is 1.01(10
-3
) N-s/m
2
(Newton = kg-m/s
2
). The
Stokes settling velocity is:
2
( )
18
p w
p s
d g
v v OFR
 

  
 
2
4
3 3 2
3
2650 998 2.1 10 9.81
18 1.01 10
kg kg m
m
m m s
kg
ms

   
 
   
   

 

 
 
=
0.039 m/s = 3.9 cm/s
Sedimentation Example 1
Knowing the overflow rate, the area required is:
( )
Q
A
SF
OFR

where
SF
is the safety factor, 1.4
3
2
0.10
(1.4) 3.6
0.039
m
s
m
m
s
 
Sedimentation Example 2

Estimate the settling velocity of the floc particles we have
seen in lab - especially the jar test results.

Use Stokes' law to estimate the settling velocity.

What are “good” estimates of the particle density and
diameter?

How does your estimate compare to what you have seen in
the lab?
Group Problem
Sedimentation Example 2

What are “good” estimates of the particle density and
diameter?

Let’s assume the following values:
 Particle density = 1,100 kg/m
3
 Particle diameter = 10
-4
m
Group Problem
Sedimentation Example 2
Group Problem
2
( )
18
p w
p s
d g
v v OFR
 

  
 
2
4
3 3 2
3
1,100 998 1 10 9.81
18 1.01 10
kg kg m
m
m m s
kg
ms

   
 
   
   

 

 
 
= 5.5 x 10
-4
m/s = 0.055 cm/s
Sedimentation Example 2
Group Problem
2
2
2 3
0.055 86,400 1 gal 30.48
13785.41
cm cm s cm
OFR
s day ftcm cm
      

 
    
      
 
OFR =
5.5 x 10
-4
m/s = 0.055 cm/s
2
1,166.3
gpd
OFR
ft

For ferric chloride typical OFRs are in the 700 - 1,000 gpd/ft.
2
CIVL 1112
Water Treatment - Sedimentation
6/7
Sedimentation Example 3

If the settling velocity of the floc particles is 0.055 cm/s,
determine the area of the sedimentation tank.

Assume a factor of safety of 1.3

Assume the system flowrate can varying from 750 ml/min
to 1,250 ml/min

How does your estimate compare to what you have seen in
the lab?
Group Problem
Sedimentation Example 3
Knowing the overflow rate and the minimumflowrate,
the area required is:
( )
Q
A
SF
OFR

750
min
(1.3)
0.055
ml
cm
s

3
1
m
60
min
cm
l
s
2
295.5 cm
2
2
1in.
295.5
2.54
A cm
cm
 

 
 
2
45.8 in.
In lab, each tank is 6 in. by 6 in. or 36 in.
2
.
Therefore, for this estimate of particle velocity we need 1.27 tanks
or 2 sedimentation tanks
Sedimentation Example 3
Knowing the overflow rate and the minimumflowrate,
the area required is:
( )
Q
A
SF
OFR

1,250
min
(1.3)
0.055
ml
cm
s

3
1
m
60
min
cm
l
s
2
492.4 cm
2
2
1in.
492.4
2.54
A cm
cm
 

 
 
2
76.3 in.
In lab, each tank is 6 in. by 6 in. or 36 in.
2
.
Therefore, for this estimate of particle velocity we need 2.1 tanks
or 3 sedimentation tanks
Sedimentation Example 3

What if the settling velocity of the floc particles is greater
than the computed 0.055 cm/s?

What if the settling velocity of the floc particles is less than
the computed 0.055 cm/s?

How do these estimates compare to what you have seen in
the lab?
Group Questions
Any Questions?
Treatment Processes
CIVL 1112
Water Treatment - Sedimentation
7/7