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

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Sedimentation

Sedimentation

Sedimentation

Click HERE for animations about 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

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