1. SEDIMENTATION
Aim - rapid removal of solid material by gravitational settling
Drawbacks – colloidal material is slow settling
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2. ADDITION OF CHEMICALS BEFORE SEDIMENTATION
TO AGGREGATE COLLOIDAL PARTICLES
TO PRECIPITATE DISSOLVED IMPUTITIES
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3. Water and Wastewater Treatment
Settling of discrete particles
Settling of flocculating particles
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4. Water and Wastewater Treatment
Need to consider
Dilute suspensions – potable water
Concentrated suspensions - wastewater
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5. DILUTE SUSPENSIONS
The concentration of particles is not high enough for the settling of individual particles to influence each other
The settling velocity is the same as for a single paritcle
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6. CONCENTRATED SUSPENSIONS
Interference in the flow patterns about particles
The downwards flux of particles is enough to displace significant amounts of water that moves upwards
There is a decrease in the settling velocity compared to a single particle
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7. What is the removal efficiency?
How can the amount of solids that will be removed in a settling tank be determined?
What is the removal efficiency?
What size of tank is required?
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8. Sedimentation Theory
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9. Type – 1: Discrete particle settling Type – 2: Flocculant settling
Sedimentation Theory
Particle-fluid separation processes are difficult to describe by theoretical analysis, mainly because the particles involved are not regular in shape, density, or size.
The various regimes in settling of particles are commonly referred to as:
Type – 1: Discrete particle settling
Type – 2: Flocculant settling
Type – 3: Hindered (zone) settling
Type – 4: Compression settling
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10. These particles settle at constant settling velocity.
Settling Regimes Type – I – Discrete particle settling
Type I settling (discrete of free settling) is the settling of discrete particles in low concentration, with flocculation and other interparticle effects being negligible
These particles settle at constant settling velocity.
They settle as individual particles and do not flocculate during settling
Examples: Settling of sand, grit
Applications: Presedimentation for sand removal prior to coagulation
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11. Type – II – Flocculant settling Type
Settling Regimes
Type – II – Flocculant settling Type
Type II settling is the settling of flocculent particles in a dilute suspension.
As coalescence occurs, particle masses increase and particles settle more rapidly.
Particles flocculate during sedimentation.
These types of particles occur in alum or iron coagulation
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12. Type – III – Hindered (zone) settling
Settling Regimes
Type – III – Hindered (zone) settling
Type III settling, settling in which particle concentration causes interparticle effects.
Flocculation and rate of settling is a function of particle concentration
Particles remain in a fixed position relative to each other, and all settle at a constant velocity
Mass of particles settle as a zone
Zones of different particle concentrations (different layers) may develop as a result of particles with different settling velocities
State of compression is reached at the bottom.
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13. Type – IV – Compression settling
Settling Regimes
Type – IV – Compression settling
Type IV settling, settling of particles that are of such a high concentration that the particles touch each other and settling can occur only by compression of the compacting mass.
Compression settling occurs at lower depths of the sedimentation tanks
Rate of compression is dependent on time and the force caused by the weight of solids above the compression layer.
Both discrete and flocculant particles may settle by zone or compression settling
However, flocculent particles are the most common type encountered.
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14. Settling Types
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15. Type – I – Discrete particle settling
Sedimentation Theory
Type – I – Discrete particle settling
Settling of discrete particles in low concentration, with flocculation and other interparticle effects being negligible
When particles settle discretely, the particle settling velocity can be calculated and the basins can be designed to remove a specific particle size STOKE’s LAW
Particle falling in a fluid accelerates until the frictional resistance, or drag on the particle is equal to the gravitational force of the particle Isaac NEWTON
Settling velocity remains constant Terminal velocity
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16. Type – I – Discrete particle settling
Sedimentation Theory
Type – I – Discrete particle settling
Terminal settling velocity depends on various fluid and particle properties.
To calculate the settling velocity
Particle shape is assumed to be spherical
Particles that are not spherical can be expressed in terms of a sphere of an equal volume.
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17. Acting Forces on ParticleB G F
All particles immersed in a fluid are
subject to a buoyancy force, B
A gravitational force G is always acting
on the particle due to its mass
Whenever relative motion exists between
a particle and a surrounding fluid, the
fluid will exert a drag upon the particle
creating a drag force, F
Flow direction
In a flowing viscous fluid, the drag force is made up of two components:
A pressure drag force, Fp
A shear stress drag force, Fs B
Flow direction

18. For creeping flow (flow at very low velocities, v relative to the sphere), the total drag force F on the particle with a diameter D in a fluid of viscosity  is given by Stoke’s law:
F = Fs + Fp = 2Dv + Dv = 3Dv

19. Turbulent Flows
Turbulence may arise either from an increased fluid velocity or from artificial roughening of the forward face of the immersed body (or particle)

20. Reynolds Number, Re To characterize the fluid flows on particle
Dimensionless group
Definition:
: density of the fluid
: viscosity of the fluid
v : the velocity of the fluid relative to the particle
D : the diameter of the particle
As Re increases, the pressure drag force becomes proportionately less and,
at value greater than about 20, flow separation occurs with the formation of
vortices in the wake of the sphere. So, changes of Re in the nature of the flow
would effect on the force exerted on the particle.

21. Drag Force on a Spherical Particle
The most satisfactory way of representing the relation between drag force and velocity involves the use of two dimensionless groups:
Reynolds number, Re
Drag coefficient, CD
Stokes Law
R’ is the force per unit projected area of particle in a plane perpendicular to
the direction of motion

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30. Value of CD decreases as the value of Re increases
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35. where φ is the shape factor required to correct for the lack of sphericity. For a perfectly spherical particle φ = 1.
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36. (Data ρw = 998.2 kg m-3, μ = 1.002 x10-3 Pa s).
Example: Find the settling velocity of a sphere with a diameter of 0.5 mm and a density of 2650 kg m-3 settling in water at 20 0C. At this temperature the kinematic viscosity is 1.003x10-6 m2/s
(Data ρw = kg m-3, μ = x10-3 Pa s).
Note:
μ = (kinematic viscosity * density) =1.003 x10-6 *998.8 = x10-3
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39. Vt = 0.224 m/s not similar with the calculated one using Newton
Vp = 0.109
The second iteration is to use Vp = and then calculate Re
= 0.09 m/s
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40. Vp = 0.09 m/s not similar with the calculated one using Newton
Sedimentation Tank
Vp = m/s not similar with the calculated one using Newton
Vp = 0.109
Then third iteration use 0.09 valued to estimate: CD, Re and new Vp
Stop solution is reached
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41. It is seldom possible to use the above analysis in the design of settling tanks for both water and wastewater treatment because the size of the particles must be known and the correction factor for sphericity must be determined
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42. Particles whose terminal settling velocity exceeds the liquid
Settlement in Tanks
Particles whose terminal settling velocity exceeds the liquid
up flow velocity will be retained
In an horizontal flow rectangular settling tanks, settling particles have both horizontal and rectangular parts.
L: Horizontal distance travelled
H: Depth of water
W: Width of tank
t: time of travel
Vertical distance travelled
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43. Settling Column Analysis for Type 1 Suspensions
The setting velocity of a dilute suspension can be determined indirectly from the analysis of the mass settlement rate in a settling column.
Put the suspension in a settling column, ensuring that it is well mixed so that the concentration is uniform throughout.
Allow the suspension to settle under quiescent conditions and observe the concentration of settling particles at the bottom of the settling column, as a function of time.
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48. The design of settling vessels is usually based on the results of settling column tests carried out using the material in question.
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49. Mustafa Nasser 2012 Water Surface Z0 Initial Concentration, C0
Sample Point, Concentration, C(t)
Velocity, u(t)  z0 / t
Water Surface
Initial Concentration, C0
Particle Flux = C(t)u(t)
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50. Bottom of the settling zone
Settling Column z0
Water Surface
Sampling Point
Particle with settling velocity v0 travels distance z0 in time t0
and reaches the bottom of the settling zone.
Particle with settling velocity vp travels distance zp in time t0 and does not reach the bottom of the settling zone.
Particle with settling velocity vp travels distance zp in time t0 and reaches the bottom of the settling zone.
Particle with settling velocity vp travels distance zp in time t0 and passes the bottom of the settling zone. zp
All particles dp > d0 are removed in time t0 The fraction of particles of size dp < d0 removed in time t0 is z0
Bottom of settling zone
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51. The fraction removed is also in the ratio of the settling velocities
Remembering that
The fraction removed is also in the ratio of the settling velocities
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52. x x0 All particles dp > d0 will settle in t0 (i.e. vp > v0) v0
Velocity
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53. All particles dp > d0 will settle in t0 (i.e. vp > v0)
The fraction of all particles dp > d0 is
Some particles dp < d0 will settle in t0 (i.e. vp < v0)
The fraction of particles size dp is
The fraction of all particles 0 < dp < d0 is
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54. The total fraction of particles that are removed in t0 is
Get all the information from the graph of x as a function of v
The integral is evaluated numerically
Remember x is the fraction of particles that remains in suspension
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55. The following results were obtained from a 1.8 m settling column.
Time :–
/(min)
Concentration:–
/(mg l1)
What is the theoretical removal efficiency in a settling basin with a loading rate of 24.7 m day1?
 (This is a volumetric flow of 24.7 m3 day1 per m2 of settling basin area).
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56. At time t = 0 the initial concentration C0 = 300 mg l1.
The depth of the settling zone is 1.8 m.
Calculate
e.g 189/300 = 0.63; 180/300 = 0.60
e.g. 1.8/60 = 0.03; 1.8/80 =
Time /(min) xi
vi, /(m min1)
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57. Calculate v0 for a loading rate of 25 m per day
This corresponds to a residence time of
minutes
x0 is found from the graph or by linear interpolation
So x(105) = 166/300 = 0.55
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58. x0 =0.55 x
v0 = m/min
Velocity (m per min)
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59. The mass fraction of solids that remain in suspension is x0 = 0.55
The mass fraction of solids that has settled is (1 - x0) = 0.45
The mass fraction of slow settling particles is
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60. xi vi Δxi Average vi Δxi vi
N.B. x0
xi vi Δxi Average vi Δxi vi
To four significant figures, the sum of xiv =
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61. The integral is evaluated
The total mass fraction removed, X, is
X = (1 – x0)
=(1 – 0.55) =
= 0.699
That is the solids removal is 70%. ( two sig. fig.)
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62. END
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