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BhuviPandey
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Mar 05, 2025
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About This Presentation
ss,s,s
Slide Content
Material Processing Industries
Receives diverse raw materials from primary industry and transformed them either
finished products or raw material for other industry
Chemical Industries
Pharmaceutical Industries Metallurgy IndustriesTextile industries
Basic Chemical Industries (acid, alkali, glass, Oil…other chemicals)
Soap industry (detergent)
Cement industries
Petrochemical industries
Food industries
Fertilizer industries
Pulp and Paper Industries
Pigment industries
Cosmetic industries
Fuel industries
Receives diverse raw materials from primary industry and transformed them either
finished products or raw material for other industry
Chemical Industries
Pharmaceutical Industries Metallurgy IndustriesTextile industries
Basic Chemical Industries (acid, alkali, glass, Oil…other chemicals)
Soap industry (detergent)
Cement industries
Petrochemical industries
Food industries
Fertilizer industries
Pulp and Paper Industries
Pigment industries
Cosmetic industries
Fuel industries
Mechanical Operations
Series of Physical operations that
participate mainly in storage and
distribution of materials through a
process line
Understanding behavior
of particulate materials
and industrial powders
Powder Technology
Operations mainly for
granular solids and
fluid
Series of Physical operations that
participate mainly in storage and
distribution of materials through a
process line
Understanding behavior
of particulate materials
and industrial powders
Powder Technology
Operations mainly for
granular solids and
fluid
S. No. Contents Contact
Hours
1 Particle Size Analysis: Sieve analysis, size distribution, size averaging and equivalence, size
estimation in sub-sieve range, calculation of average size of particles in mixture by screen analysis,
Size Reduction: Theory of crushing and grinding, crushing and grinding equipment and their
selection.
Screening: Capacity and Effectiveness of a screen, types of screens.
12
2 Agitation and Mixing: Agitation of low viscosity particle suspensions: axial flow impellers, radial
flow impellers, close-clearance stirrer, unbaffled tanks, baffled tanks, basic idea for designing
agitators. power consumption in agitation.
Mixing of Solids: Types of mixers, power requirements, mixing index. Mixers for free flowing solids
10
3 Filtration: Flow through filter cake and medium, washing and drying of cake, filter aids, selection of
filtration equipment, constant rate and constant pressure filtration, micro filtration
7
4 Settling: Motion of particles through fluids, Terminal velocity, hindered settling, Stoke’s law, gravity
settling processes: Classifiers, clarifiers, thickeners, flocculation, rate of sedimentation. Centrifugal
Settling processes: Cyclones, hydro clones, decanters, principles of centrifugal, sedimentation
7
5 Fluid-Solid Conveying :Pneumatic and hydraulic transport of solids, general characteristics and flow
relations.
6
Mechanical Operations
Hours
1 Particle Size Analysis: Sieve analysis, size distribution, size averaging and equivalence, size
estimation in sub-sieve range, calculation of average size of particles in mixture by screen analysis,
Size Reduction: Theory of crushing and grinding, crushing and grinding equipment and their
selection.
Screening: Capacity and Effectiveness of a screen, types of screens.
12
2 Agitation and Mixing: Agitation of low viscosity particle suspensions: axial flow impellers, radial
flow impellers, close-clearance stirrer, unbaffled tanks, baffled tanks, basic idea for designing
agitators. power consumption in agitation.
Mixing of Solids: Types of mixers, power requirements, mixing index. Mixers for free flowing solids
10
3 Filtration: Flow through filter cake and medium, washing and drying of cake, filter aids, selection of
filtration equipment, constant rate and constant pressure filtration, micro filtration
7
4 Settling: Motion of particles through fluids, Terminal velocity, hindered settling, Stoke’s law, gravity
settling processes: Classifiers, clarifiers, thickeners, flocculation, rate of sedimentation. Centrifugal
Settling processes: Cyclones, hydro clones, decanters, principles of centrifugal, sedimentation
7
5 Fluid-Solid Conveying :Pneumatic and hydraulic transport of solids, general characteristics and flow
relations.
6
Mechanical Operations
Course Outcomes
CO-1: Apply concept of particle size and shape, size reduction, separation, filtration,
agitation, mixing , storage for mechanical unit operations.
CO-2: Operate size analysis instrument, size reduction equipment, separators, filtration,
agitators, mixer and conveyors.
CO-3 Calculate properties of solid particles, power consumption and crushing law
constants, screen efficiency and material balance
CO-4 Analyze the cake filtration process and calculate the filtration resistance, time and
flow.
CO-5 Apply the principles of gravity and centrifugal to separate the solid and liquids
Mechanical Operations (CH206)
CO-1: Apply concept of particle size and shape, size reduction, separation, filtration,
agitation, mixing , storage for mechanical unit operations.
CO-2: Operate size analysis instrument, size reduction equipment, separators, filtration,
agitators, mixer and conveyors.
CO-3 Calculate properties of solid particles, power consumption and crushing law
constants, screen efficiency and material balance
CO-4 Analyze the cake filtration process and calculate the filtration resistance, time and
flow.
CO-5 Apply the principles of gravity and centrifugal to separate the solid and liquids
Mechanical Operations (CH206)
Mechanical Operations
Mechanical Principle Based Fluid Mechanics Based
➢Screening
➢Solid handing & Conveying
➢Size reduction
➢Magnetic separation
➢Electrostatic operation
➢Material transportation
➢Mixing/Agitation
➢Solid solid mixing
➢Filtration
➢Sedimentation
➢Centrifugation
Mechanical Principle Based Fluid Mechanics Based
➢Screening
➢Solid handing & Conveying
➢Size reduction
➢Magnetic separation
➢Electrostatic operation
➢Material transportation
➢Mixing/Agitation
➢Solid solid mixing
➢Filtration
➢Sedimentation
➢Centrifugation
Academic Evaluation Plan for the Course
Practical Exam (10)
After 10
th
Experiment
Class
Assignments/
Class tests (5)
CWS (15) PRS (25)
MTE (20) ETE (40)
Class
Attendance (5)
Practical performance &
Practical File continuous
evaluation : (15)
Unit-1
Unit-2
Unit-3
Unit-4
Unit-5
Create own experiment/
Market survey (5)
Class experiments based on
each unit of syllabus
Unit-1
Unit-2
(30)
(10)
Industry Survey
of Chemical
processing
industry and
uses of
mechanical
operations
machines (5)
Unit-3
Practical Exam (10)
After 10
th
Experiment
Class
Assignments/
Class tests (5)
CWS (15) PRS (25)
MTE (20) ETE (40)
Class
Attendance (5)
Practical performance &
Practical File continuous
evaluation : (15)
Unit-1
Unit-2
Unit-3
Unit-4
Unit-5
Create own experiment/
Market survey (5)
Class experiments based on
each unit of syllabus
Unit-1
Unit-2
(30)
(10)
Industry Survey
of Chemical
processing
industry and
uses of
mechanical
operations
machines (5)
Unit-3
CH-206: Mechanical Operations
Books
Books
CH-206: Mechanical Operations
Unit-1,
Particle Size Analysis: Sieve analysis, size distribution, size averaging and
equivalence, size estimation in sub-sieve range
Size Reduction: Theory of crushing and grinding, crushing and grinding equipment
and their selection.
Screening: Capacity and Effectiveness of a screen, calculation of average size of
particles in mixture by screen analysis, types of screens.
Unit-1,
Particle Size Analysis: Sieve analysis, size distribution, size averaging and
equivalence, size estimation in sub-sieve range
Size Reduction: Theory of crushing and grinding, crushing and grinding equipment
and their selection.
Screening: Capacity and Effectiveness of a screen, calculation of average size of
particles in mixture by screen analysis, types of screens.
Solids/Granule/Powder in Chemical Industries
Cement Industry
Soap industry
Detergent powder
Fertilizer
Powder
Pigments
Petrochemical
Polymer GranulesPowder
Cement Industry
Soap industry
Detergent powder
Fertilizer
Powder
Pigments
Petrochemical
Polymer GranulesPowder
Properties of Solids ( Mineral sources)
Limestone
Properties of solids changes with
its Particle Size and Shape
✓Density
✓Hardness
✓Fragility
✓Tenacity
✓Surface area
✓Friction
✓Adsorption
✓Melting Point
✓Optical properties
✓Electrical Properties
✓Magnetic Properties
Limestone
Properties of solids changes with
its Particle Size and Shape
✓Density
✓Hardness
✓Fragility
✓Tenacity
✓Surface area
✓Friction
✓Adsorption
✓Melting Point
✓Optical properties
✓Electrical Properties
✓Magnetic Properties
Powder: Any relatively small division of matter, ranging from a few angstroms to few
millimeter
Properties of Solids ( Mineral sources)
Size
Particle size Units
Coarse
Inches or miliimeters
Fine Screen size
Very Fine
Micrometer
Ultrafine
Surface area per unit
mass or Nanometer
millimeter
Properties of Solids ( Mineral sources)
Size
Particle size Units
Coarse
Inches or miliimeters
Fine Screen size
Very Fine
Micrometer
Ultrafine
Surface area per unit
mass or Nanometer
Molecular structure determines the shape of the particles
Piece of solids fracture following exfoliation planes determine by its molecular structure
Properties of Bulk Solids ( Mineral sources)
Shape
Mica Limestone Clay Wollastonite Galena
WollastoniteClayLimestoneMica
Galena
Piece of solids fracture following exfoliation planes determine by its molecular structure
Properties of Bulk Solids ( Mineral sources)
Shape
Mica Limestone Clay Wollastonite Galena
WollastoniteClayLimestoneMica
Galena
Density: Mass per unit Volume
Properties of Bulk Solids ( Mineral sources)
Ore of Wollastonite
Rock of Iron oxide
Homogeneous Compound
Heterogenous compound
Properties of Bulk Solids ( Mineral sources)
Ore of Wollastonite
Rock of Iron oxide
Homogeneous Compound
Heterogenous compound
Hardness
Properties of Bulk Solids ( Mineral sources)
: Measures the resistance of the solids to be scratched
Properties of Bulk Solids ( Mineral sources)
: Measures the resistance of the solids to be scratched
Properties of Bulk Solids ( Mineral sources)
Fragility
Tenacity: Resistance to cutting, breaking, bending or deformation or character of
cohesion
: property representing how easy a substance may be crumbled or broken by
impact.
Point to remember: It does not have direct
relation with hardness: Gypsum is soft but
not Fragile
Sectile Malleable Brittle
Cut by
knife
Talc,
Graphite
Flatten into seat
by hammering
Silver
gold
Crumble
into grains
or
particles
Quartz,
Calcite
Flexible Elastic
Easily
bend
Bend and
regain its
shape
Chlorites Muscovite
Fragility
Tenacity: Resistance to cutting, breaking, bending or deformation or character of
cohesion
: property representing how easy a substance may be crumbled or broken by
impact.
Point to remember: It does not have direct
relation with hardness: Gypsum is soft but
not Fragile
Sectile Malleable Brittle
Cut by
knife
Talc,
Graphite
Flatten into seat
by hammering
Silver
gold
Crumble
into grains
or
particles
Quartz,
Calcite
Flexible Elastic
Easily
bend
Bend and
regain its
shape
Chlorites Muscovite
Size Equivalence
Selection of a relevant characteristic particle size for analysis or measurement: Major
Problem
As particles get smaller, and by the influence of attrition due to handling ,their edges
may become smoother and thus they can consider to be spherical
The term” Diameter” is used to refer to the characteristics linear dimension.
Selection of a relevant characteristic particle size for analysis or measurement: Major
Problem
As particles get smaller, and by the influence of attrition due to handling ,their edges
may become smoother and thus they can consider to be spherical
The term” Diameter” is used to refer to the characteristics linear dimension.
Size Equivalence
Irregular Particles can be described by a number of sizes
Equivalent Sphere Diameters
Statical diameters
Equivalent Circle Diameter
Sieve Diameter
Irregular Particles can be described by a number of sizes
Equivalent Sphere Diameters
Statical diameters
Equivalent Circle Diameter
Sieve Diameter
Statical diameters
Size is obtained when a linear dimension is measured (by
Microscope) parallel to a fixed direction.
Defined on the basis of projected image of a single particle
Martin’s
diameter
Defined as the average cord length of a particle
which equally divides the projected area
Size is obtained when a linear dimension is measured (by
Microscope) parallel to a fixed direction.
Defined on the basis of projected image of a single particle
Martin’s
diameter
Defined as the average cord length of a particle
which equally divides the projected area
Feret’s diameterIt is average distance between pairs of
parallel tangents to the projected outline
of the particle.
Statical diameters
Equivalent Circle Diameters
The diameter of a circle which would have the same property of the projected outline
of the particle are considered
Symbol Name Equivalent property of a circle
Xa Projected area
diameter
Projected area if the particle is resting
in a stable position
Xc
Perimeter
diameter
Perimeter of the outline
parallel tangents to the projected outline
of the particle.
Statical diameters
Equivalent Circle Diameters
The diameter of a circle which would have the same property of the projected outline
of the particle are considered
Symbol Name Equivalent property of a circle
Xa Projected area
diameter
Projected area if the particle is resting
in a stable position
Xc
Perimeter
diameter
Perimeter of the outline
Projected Area
diameter
The diameter of the circle having same
projected area as the particle
A= Projected area of irregular particle
Ac=Area of Circle=
�
�
�
d= (4A/)
Equivalent Circle Diameters
Perimeter Diameter
The diameter of the circle having same
perimeter as the particle
P= Perimeter of irregular particle
Pc= Perimeter of circle= ��
�=
�
??????
A=Ac
P=Pc
diameter
The diameter of the circle having same
projected area as the particle
A= Projected area of irregular particle
Ac=Area of Circle=
�
�
�
d= (4A/)
Equivalent Circle Diameters
Perimeter Diameter
The diameter of the circle having same
perimeter as the particle
P= Perimeter of irregular particle
Pc= Perimeter of circle= ��
�=
�
??????
A=Ac
P=Pc
Equivalent Sphere Diameter
The diameter of a sphere which have the same property of the particle itself are found.
The diameter of a sphere which have the same property of the particle itself are found.
Equivalence Sphere diameter
??????
�=
4
3
??????�
3
??????
�=
4
3
?????? (????????????/2)3
d
v
V V
s
V=V
s??????
�=??????
??????
??????
3
6
??????
??????=
6??????
??????
1
/
3 The volume diameter of particle useful in applications
where equivalent volume is primary interest
Example
Estimation of solids holdup in a fluidized bed
The calculation of Buoyancy forces of the particles
Volume of Sphere
??????
�=
4
3
??????�
3
??????
�=
4
3
?????? (????????????/2)3
d
v
V V
s
V=V
s??????
�=??????
??????
??????
3
6
??????
??????=
6??????
??????
1
/
3 The volume diameter of particle useful in applications
where equivalent volume is primary interest
Example
Estimation of solids holdup in a fluidized bed
The calculation of Buoyancy forces of the particles
Volume of Sphere
Equivalence Sphere diameter
S S
S
d
s
S= S
s
Surface area of sphere having d
s diameter
S=��
�
�
�
�
�
=��/�
S= S
s
�
�
�
=�/�
�
�=
�
�
�
/
�
The concept of surface diameter mostly used in the
field of adsorption and reaction engineering where
equivalent surface area is important.
S S
S
d
s
S= S
s
Surface area of sphere having d
s diameter
S=��
�
�
�
�
�
=��/�
S= S
s
�
�
�
=�/�
�
�=
�
�
�
/
�
The concept of surface diameter mostly used in the
field of adsorption and reaction engineering where
equivalent surface area is important.
Volume to Surface Area Equivalence Sphere diameter
V
S
d
v
d
s
d
vs=
�
�
�
�
d
vs= (6V/S) = d
v
3
/ d
s
2
Sauter’s Diameter
Used in the field of reacting gas-solid flows such as in studies of pulverized
coal combustion
Flow through packed or fluidized beds
�=��=�
�
�
�
�
S=��=��
�
�
V
S
d
v
d
s
d
vs=
�
�
�
�
d
vs= (6V/S) = d
v
3
/ d
s
2
Sauter’s Diameter
Used in the field of reacting gas-solid flows such as in studies of pulverized
coal combustion
Flow through packed or fluidized beds
�=��=�
�
�
�
�
S=��=��
�
�
Storke’s Equivalence Diameter (dynamic diameter)
The dynamic response of a particle in Fluid-solid flow may be characterized by the
settling or terminal velocity at which the drag force balances the gravitational force.
The dynamic diameter is defined as the diameter
of a sphere having the same density and the
same terminal velocity as the particle in a fluid
of the same density and velocity
The dynamic response of a particle in Fluid-solid flow may be characterized by the
settling or terminal velocity at which the drag force balances the gravitational force.
The dynamic diameter is defined as the diameter
of a sphere having the same density and the
same terminal velocity as the particle in a fluid
of the same density and velocity
Storke’s Equivalence Diameter (dynamic diameter)
Valid only when Re <2
Where, V
t= terminal velocity
f = mass density of fluid
p= Mass density of sphere or particle
d
p= stoke equivalent diameter of particle
= Viscosity of Fluid
g= acceleration of gravity
s =
p
Valid only when Re <2
Where, V
t= terminal velocity
f = mass density of fluid
p= Mass density of sphere or particle
d
p= stoke equivalent diameter of particle
= Viscosity of Fluid
g= acceleration of gravity
s =
p
Size Equivalence
Shape name Particle shape description
Acicular Needle shape
Angular/irregularRoughly polyhedral
geometry
Porous
Having pore
Dentritic
Branched Crystalline
shape
Shapes of Particles
Acicular Needle shape
Angular/irregularRoughly polyhedral
geometry
Porous
Having pore
Dentritic
Branched Crystalline
shape
Shapes of Particles
Shapes of Particles
Shape name Particle shape description
Fibrous Regular or irregular
thread like
Flaky Plate like
Modular Rounded irregular shape
Spherical Global shape
Shape name Particle shape description
Fibrous Regular or irregular
thread like
Flaky Plate like
Modular Rounded irregular shape
Spherical Global shape
The shape of particle can be describe using length (L), Breath (B) and thickness (T)
Shapes of Particles
Elongation ratio = L/B
Flakiness ratio = B/T
Aspect ratio= ratio of highest dimension/lowest dimension
Shapes of Particles
Elongation ratio = L/B
Flakiness ratio = B/T
Aspect ratio= ratio of highest dimension/lowest dimension
Sphericity
The simplest three-dimensional shape is sphere
The dimensionless term sphericity is in common use to compare particles of irregular
shapes with that of spherical one
Hakon wadell (1935)
Defined sphericity as the surface area of a sphere of the same volume
as the particle divided by the actual surface area of the particle
= Surface to volume ratio of sphere of diameter D
p/ surface to volume ratio of
particle whose nominal size is D
p
The simplest three-dimensional shape is sphere
The dimensionless term sphericity is in common use to compare particles of irregular
shapes with that of spherical one
Hakon wadell (1935)
Defined sphericity as the surface area of a sphere of the same volume
as the particle divided by the actual surface area of the particle
= Surface to volume ratio of sphere of diameter D
p/ surface to volume ratio of
particle whose nominal size is D
p
Sphericity
=
??????
??????
??????
??????
��ℎ��� �� �??????��????????????�� ??????�����
??????
??????
??????
??????
�??????��????????????��
D
p
S
p V
p
=
6
??????
�
(V
p/S
p)
particle
For a spherical particle
of diameter Dp the
sphericity =1
Sphericity defined as how close the irregular particle is to a spherical particle
Surface area of sphere S
p = D
p
2
Volume of sphere Vp = D
p
3
/6
�
�
�
�
������ �� �������� ������= 6/D
p
=
??????
??????
??????
??????
��ℎ��� �� �??????��????????????�� ??????�����
??????
??????
??????
??????
�??????��????????????��
D
p
S
p V
p
=
6
??????
�
(V
p/S
p)
particle
For a spherical particle
of diameter Dp the
sphericity =1
Sphericity defined as how close the irregular particle is to a spherical particle
Surface area of sphere S
p = D
p
2
Volume of sphere Vp = D
p
3
/6
�
�
�
�
������ �� �������� ������= 6/D
p
Sphericity
s
Question 1 : Find the Sphericity of a cube of dimension “a”
=
6
??????
�
(V
p/S
p)
particle =
6
??????
�
(V
p/S
p)
Cube
V
p = Volume of Cube = a
3
S
p = Surface area of Cube = 6a
2
To find Dp, equivalent sphere volume with cube volume
/6 D
p
3
=a
3
Dp = [6/]
1/3
a
Cube = 0.81
??????
����=
�
[6/]
1/3
a
[
�
�
��
�]
a
??????
����=
�
�
�
[
�
�
��
�]
s
Question 1 : Find the Sphericity of a cube of dimension “a”
=
6
??????
�
(V
p/S
p)
particle =
6
??????
�
(V
p/S
p)
Cube
V
p = Volume of Cube = a
3
S
p = Surface area of Cube = 6a
2
To find Dp, equivalent sphere volume with cube volume
/6 D
p
3
=a
3
Dp = [6/]
1/3
a
Cube = 0.81
??????
����=
�
[6/]
1/3
a
[
�
�
��
�]
a
??????
����=
�
�
�
[
�
�
��
�]
Question 2: What is the sphericity of a cylinder particle whole length is equal to its
diameter?
Answer:0.873
d=a mm
l=a mm
=
6
??????
�
(V
p/S
p)
particle
V
p= Volume of cylinder= �
�
�
�
�=
�
�
�
�
S
p= Surface area of Cylinder= � � �+
�
�
�
�
= ��
�
+
�
�
�
�
Volume of Sphere= Volume of Cylinder
�
�
D
p
3
=
�
�
�
�
D
p =[
�
�
]
�
/
�
a
cylinder=
6
??????
�
(V
p/S
p)
cylinder
diameter?
Answer:0.873
d=a mm
l=a mm
=
6
??????
�
(V
p/S
p)
particle
V
p= Volume of cylinder= �
�
�
�
�=
�
�
�
�
S
p= Surface area of Cylinder= � � �+
�
�
�
�
= ��
�
+
�
�
�
�
Volume of Sphere= Volume of Cylinder
�
�
D
p
3
=
�
�
�
�
D
p =[
�
�
]
�
/
�
a
cylinder=
6
??????
�
(V
p/S
p)
cylinder
Sphericity
Sphericity defined as how close the irregular particle is to a spherical particle
Sphericity defined as how close the irregular particle is to a spherical particle
Sphericity
s
s
Sphericity
Sphericity is independent of particle size. It is only defining particle shape
For fine granular particles , it is very difficult to determine the exact volume and
surface area of a particle.
For these materials D
p is usually taken to be the nominal size based on the
screen analysis or microscopic examination
The surface area can be found from adsorption experiment or from pressure
drop in a bed of particles
The reciprocal of sphericity is known as the surface shape factor “
s”
Sphericity is independent of particle size. It is only defining particle shape
For fine granular particles , it is very difficult to determine the exact volume and
surface area of a particle.
For these materials D
p is usually taken to be the nominal size based on the
screen analysis or microscopic examination
The surface area can be found from adsorption experiment or from pressure
drop in a bed of particles
The reciprocal of sphericity is known as the surface shape factor “
s”
Sphericity
Mixed Particle Sizes
A sample of solid particles contains a wide range of particles sizes and densities
for which their analysis becomes extremely difficult.
For this reason, the whole sample is separated into a number of fractions, each of
constant density and nearly constant size by some mechanical means and then each
fraction is analyzed
A sample of solid particles contains a wide range of particles sizes and densities
for which their analysis becomes extremely difficult.
For this reason, the whole sample is separated into a number of fractions, each of
constant density and nearly constant size by some mechanical means and then each
fraction is analyzed
Sieve (Screen) Analysis
Sieving is the simplest and most widely used technique for powder classification and
analysis.
Made of wire mesh cloth, the wire diameter
and interspacing between wire carefully
standardize.
The openings are square
Screen: an open container (cylindrical) with
uniformly spaced opening at the base
Designated by their mesh number
Sieving is the simplest and most widely used technique for powder classification and
analysis.
Made of wire mesh cloth, the wire diameter
and interspacing between wire carefully
standardize.
The openings are square
Screen: an open container (cylindrical) with
uniformly spaced opening at the base
Designated by their mesh number
Sieve (Screen) Analysis
The minimum clear space between the edges of the opening in a screening surface is
called aperture, w.
Aperture is expressed in inches, cm or mm
The aperture of woven wire screens is expressed
as “mesh”: the number of apertures per linear
inch
The minimum clear space between the edges of the opening in a screening surface is
called aperture, w.
Aperture is expressed in inches, cm or mm
The aperture of woven wire screens is expressed
as “mesh”: the number of apertures per linear
inch
Sieve (Screen) Analysis
For example
This kind of designation is valid only when the wire size is defined
w=
�
�
- d
Where, m = mesh
Aperture of Screen
Higher the number smaller will be the screen aperture
For example
This kind of designation is valid only when the wire size is defined
w=
�
�
- d
Where, m = mesh
Aperture of Screen
Higher the number smaller will be the screen aperture
Sieve (Screen) Analysis
Standard screens: American standard:Tyler, ASTM
: British standard (BS)
: German standard (DIN)
: Indian standard (IS)
: International Standard Organization (ISO)
w=
�
�
- dWhere, m =
meshISO, BS, DIN standards are based on the aperture
ASTM &Tyler standards are based on the mesh count, using number of wires per
linear inch
Standard screens: American standard:Tyler, ASTM
: British standard (BS)
: German standard (DIN)
: Indian standard (IS)
: International Standard Organization (ISO)
w=
�
�
- dWhere, m =
meshISO, BS, DIN standards are based on the aperture
ASTM &Tyler standards are based on the mesh count, using number of wires per
linear inch
Sieve (Screen) Analysis
Example : Tyler Series
This set of screens is based on the
opening of the 200 mesh screen which
is established at 0.074 mm with wire
diameter 0.0021 inch
The area of the openings in any one
screen in the series is twice that of the
opening in the next smaller screen
Example:
Area of opening of mesh size 3
= 6.680 x 6.680 44.6224
Area of opening of mesh size 4
= 4.699 x 4.699 22.0806
Example : Tyler Series
This set of screens is based on the
opening of the 200 mesh screen which
is established at 0.074 mm with wire
diameter 0.0021 inch
The area of the openings in any one
screen in the series is twice that of the
opening in the next smaller screen
Example:
Area of opening of mesh size 3
= 6.680 x 6.680 44.6224
Area of opening of mesh size 4
= 4.699 x 4.699 22.0806
The ratio of the actual mesh
dimension of any screen to that of
the next smaller screen is 1.41 .
For closer sizing, intermediate screen,
which has mesh dimension 1.18 times
that of next smaller standard screen
Sieve (Screen) Analysis
�
�
+�
�
=�.��
�
�
�
+�
�
= 1.18
dimension of any screen to that of
the next smaller screen is 1.41 .
For closer sizing, intermediate screen,
which has mesh dimension 1.18 times
that of next smaller standard screen
Sieve (Screen) Analysis
�
�
+�
�
=�.��
�
�
�
+�
�
= 1.18
Sieve (Screen) Analysis
Screen
designati
on
number
(IS)
Width of
aperture
(mm)
Wire
diameter
(mm)
Equivalent Mesh number of
other standard screen
ASTM BSS Tyler
60 0.592 0.417 30 25 28
50 0.500 0.345 35 30 32
40 0.420 0.284 40 36 35
35 0.351 0.224 45 44 42
30 0.296 0.193 50 52 48
20 0.211 0.142 70 72 65
15 0.151 0.102 100 100 100
10 0.104 0.066 140 150 150
9 0.089 0.061 170 170 170
8 0.075 0.051 200 200 200
Indian Standard: the mesh is
equal to its aperture size
expressed to the nearest
deca-micron (0.01mm)
An IS screen of 100 mesh
will have an aperture of
approximately 1.00 mm
IS screen series, higher the
mesh number higher is the
screen aperture
Screen
designati
on
number
(IS)
Width of
aperture
(mm)
Wire
diameter
(mm)
Equivalent Mesh number of
other standard screen
ASTM BSS Tyler
60 0.592 0.417 30 25 28
50 0.500 0.345 35 30 32
40 0.420 0.284 40 36 35
35 0.351 0.224 45 44 42
30 0.296 0.193 50 52 48
20 0.211 0.142 70 72 65
15 0.151 0.102 100 100 100
10 0.104 0.066 140 150 150
9 0.089 0.061 170 170 170
8 0.075 0.051 200 200 200
Indian Standard: the mesh is
equal to its aperture size
expressed to the nearest
deca-micron (0.01mm)
An IS screen of 100 mesh
will have an aperture of
approximately 1.00 mm
IS screen series, higher the
mesh number higher is the
screen aperture
Sieve (Screen) Analysis
Procedure for Analysis
The individual test sieves of one specified sieve scale series are staked one above
the other in the ascending order of their openings.
A pan at the bottom and cover at the top
are put to make a complete set
A weighed amount of material is fed to the
topmost sieve.
The whole assembly can be shaken continuously
either manually or by machines
Then the material retained on each sieve
including the pan are weighed
Procedure for Analysis
The individual test sieves of one specified sieve scale series are staked one above
the other in the ascending order of their openings.
A pan at the bottom and cover at the top
are put to make a complete set
A weighed amount of material is fed to the
topmost sieve.
The whole assembly can be shaken continuously
either manually or by machines
Then the material retained on each sieve
including the pan are weighed
Sieve (Screen) Analysis
Commercial sieves and sieves shakers
Commercial sieves and sieves shakers
Sieve (Screen) Analysis
Material
Retained on
Weight (gm)
ISS no. 600.0
50 M1
40 M2
35 M3
30 M4
20 M5
Pan M6
400
340
320
280
240
M1
M2
M3
M4
M5
The material that pass through the screen :
minus material or undersize
The material that is retained on the screen :
Plus material or oversize
50
40
35
30
20
M
M6
Material
Retained on
Weight (gm)
ISS no. 600.0
50 M1
40 M2
35 M3
30 M4
20 M5
Pan M6
400
340
320
280
240
M1
M2
M3
M4
M5
The material that pass through the screen :
minus material or undersize
The material that is retained on the screen :
Plus material or oversize
50
40
35
30
20
M
M6
M1
M2
M3
M4
M5
50
40
35
30
20
Material
Retained on
Weight (gm)
ISS no. 60 0.0
50 M1
40 M2
35 M3
30 M4
20 M5
Pan M6
Sieve (Screen) Analysis
The material which has passes the 60 mesh sieve but
retained on the 50 mesh sieve: designated as (60/50)
or (-60 +50) fraction
The average size of the particle in this fraction
= arithmetic average of the aperture sizes of
these two screens
Average size of fraction M1=
(0.592+0.500)/2= 0.546 mm
M
M2
M3
M4
M5
50
40
35
30
20
Material
Retained on
Weight (gm)
ISS no. 60 0.0
50 M1
40 M2
35 M3
30 M4
20 M5
Pan M6
Sieve (Screen) Analysis
The material which has passes the 60 mesh sieve but
retained on the 50 mesh sieve: designated as (60/50)
or (-60 +50) fraction
The average size of the particle in this fraction
= arithmetic average of the aperture sizes of
these two screens
Average size of fraction M1=
(0.592+0.500)/2= 0.546 mm
M
Sieve (Screen) Analysis
Results obtained from sieve analysis can be
complied in three different ways
➢By calculating the mean size of fraction
➢By calculating the cumulative mass/weight
fractions retained on each sieve
➢By calculating the cumulative mass/weight
fractions passing through each sieve.
M1
M2
M3
M4
M5
50
40
35
30
20
Material
Retained on
Weight (gm)
ISS no. 60 0.0
50 M1
40 M2
35 M3
30 M4
20 M5
Pan M6
M
Results obtained from sieve analysis can be
complied in three different ways
➢By calculating the mean size of fraction
➢By calculating the cumulative mass/weight
fractions retained on each sieve
➢By calculating the cumulative mass/weight
fractions passing through each sieve.
M1
M2
M3
M4
M5
50
40
35
30
20
Material
Retained on
Weight (gm)
ISS no. 60 0.0
50 M1
40 M2
35 M3
30 M4
20 M5
Pan M6
M
Sieve (Screen) Analysis
IS meshAverage
size (mm)
(D
iavg)
Weight
fraction
(X
i)
+60 >0.592 0.0
-60+500.546 M1/M
-50+400.460 M2/M
-40+350.385 M3/M
-35+300.324 M4/M
-30+200.254 M5/M
Pan 0.105
(<0.211)
M6/M
Screen
designation
number (IS)
Width of
aperture (mm)
60 0.592
50 0.500
40 0.420
35 0.351
30 0.296
20 0.211
Pan 0
the cumulative mass
fractions retained
the cumulative mass
fractions pass
0 1
M1/M (M2+M3+M4+M5+M6)/M
(M1+M2)/M (M3+M4+M5+M6)/M
(M1+M2+M3)/M (M4+M5+M6)/M
(M1+M2+M3+M4)/M (M5+M6)/M
(M1+M2+M3+M4+M5)/M M6/M
1 0
IS meshAverage
size (mm)
(D
iavg)
Weight
fraction
(X
i)
+60 >0.592 0.0
-60+500.546 M1/M
-50+400.460 M2/M
-40+350.385 M3/M
-35+300.324 M4/M
-30+200.254 M5/M
Pan 0.105
(<0.211)
M6/M
Screen
designation
number (IS)
Width of
aperture (mm)
60 0.592
50 0.500
40 0.420
35 0.351
30 0.296
20 0.211
Pan 0
the cumulative mass
fractions retained
the cumulative mass
fractions pass
0 1
M1/M (M2+M3+M4+M5+M6)/M
(M1+M2)/M (M3+M4+M5+M6)/M
(M1+M2+M3)/M (M4+M5+M6)/M
(M1+M2+M3+M4)/M (M5+M6)/M
(M1+M2+M3+M4+M5)/M M6/M
1 0
Mixed Particles: Average Particle Size
Mean Based on Volume and surface (Sauter mean diameter)
The volume surface mean diameter D
vs =
�
σ
�=�
�=�
(�
�/�
�� ���)
This is the diameter of the average volume of the particles found in the mixture and is
found by dividing the total volume of the sample by the number of particles in the mixture.
Mean based on volume
The volume surface mean diameter is related to specific surface area of the particles
D
v = [
�
σ
�=�
�=�
(
�
�
�
��
���
�
)
]
�
/
�
Useful in the study
of mass transfer,
catalytic reaction
Useful in the study
of Spray drying
Mean Based on Volume and surface (Sauter mean diameter)
The volume surface mean diameter D
vs =
�
σ
�=�
�=�
(�
�/�
�� ���)
This is the diameter of the average volume of the particles found in the mixture and is
found by dividing the total volume of the sample by the number of particles in the mixture.
Mean based on volume
The volume surface mean diameter is related to specific surface area of the particles
D
v = [
�
σ
�=�
�=�
(
�
�
�
��
���
�
)
]
�
/
�
Useful in the study
of mass transfer,
catalytic reaction
Useful in the study
of Spray drying
Mixed particles: Average Particle Size
Mean based on Mass
D
m = σ
�=�
�=�
�
� �
�� ���
Gravitation free
settling velocity of
particles in liquid
Mean based on Mass
D
m = σ
�=�
�=�
�
� �
�� ���
Gravitation free
settling velocity of
particles in liquid
Example
Calculate the surface volume mean diameter for the for the following particulate
sample analyzed using sieve analysis.
Sieve size range
(µm)
Mass of the
Particle (gm)
-704+352 25
-352+176 37.5
-176+88 62.5
-88+44 75
Pan 50
The volume surface mean diameter D
vs =
�
σ
�=�
�=�
(�
�/�
�� ���)
Solution
Total Mass = 25+37.5+62.5+75+50 = 250 gm
Calculate the surface volume mean diameter for the for the following particulate
sample analyzed using sieve analysis.
Sieve size range
(µm)
Mass of the
Particle (gm)
-704+352 25
-352+176 37.5
-176+88 62.5
-88+44 75
Pan 50
The volume surface mean diameter D
vs =
�
σ
�=�
�=�
(�
�/�
�� ���)
Solution
Total Mass = 25+37.5+62.5+75+50 = 250 gm
Solution
The volume surface mean diameter D
vs =
�
σ
�=�
�=�
(�
�/�
�� ���)
= 1/ 0.016285= 61.40µm
The volume surface mean diameter D
vs =
�
σ
�=�
�=�
(�
�/�
�� ���)
= 1/ 0.016285= 61.40µm
Mixed Particles: Surface area of the particles
For a sample of uniform particles having average diameter as D
p, total mass as m
and density of each particle as
p
Total volume of the particles V
s =
�
p
If Volume of one particle is v
p then the number of particles in the sample are
N
s =
�
�
�
�
=
�
p
�
�
If the surface area of the each particle is S
p then the total surface area of particles is
A
s = N
s S
P =
� ��
p
�
A
For a sample of uniform particles having average diameter as D
p, total mass as m
and density of each particle as
p
Total volume of the particles V
s =
�
p
If Volume of one particle is v
p then the number of particles in the sample are
N
s =
�
�
�
�
=
�
p
�
�
If the surface area of the each particle is S
p then the total surface area of particles is
A
s = N
s S
P =
� ��
p
�
A
We know, �
�
�
�
=
�
∅ �
�
A
s = N
s S
P =
� ��
p
�
�
=
� �
∅
p
�
�
A
s =
� �
∅
p
�
�
For a mixture of particles, the analysis is done for each fraction of constant density
and constant size
B
Equation A and B are applied to each fraction to
estimate the number of particles and total surface
area and the results are added
Mixed Particle: Surface area of the particles
total surface area of particles
�
�
�
=
�
∅ �
�
A
s = N
s S
P =
� ��
p
�
�
=
� �
∅
p
�
�
A
s =
� �
∅
p
�
�
For a mixture of particles, the analysis is done for each fraction of constant density
and constant size
B
Equation A and B are applied to each fraction to
estimate the number of particles and total surface
area and the results are added
Mixed Particle: Surface area of the particles
total surface area of particles
Example
What is the total number of particles and total surface area of uniform particulate
sample consisting of spherical particles of size 2mm and density 2650 Kg/ m
3
if the
sample mass is 20Kg.
Mass of sample, m = 20 kgDensity of particle
p= 2650 kg/m
3
Volume of particulate sample V
s = m/
p
= 20/2650= 7.54 x10
-3
m
3
Volume of single particle V
p=
� �
�
�
=
� (����
−
�
)
�
�
= 4.18 x 10
-9
m
3
Total number of Particles N = V
s/V
p = 1.80 x 10
6
Surface area of particle S
p = � �
�
= 1.256 x 10
-5
m
2
Surface area of the sample = N S
p= 22.5 m
2
A
s =
� �
∅
p
�
�
Alternate
=
� � ��
� x 2650 � ����
−�
= 22.6 m
2
What is the total number of particles and total surface area of uniform particulate
sample consisting of spherical particles of size 2mm and density 2650 Kg/ m
3
if the
sample mass is 20Kg.
Mass of sample, m = 20 kgDensity of particle
p= 2650 kg/m
3
Volume of particulate sample V
s = m/
p
= 20/2650= 7.54 x10
-3
m
3
Volume of single particle V
p=
� �
�
�
=
� (����
−
�
)
�
�
= 4.18 x 10
-9
m
3
Total number of Particles N = V
s/V
p = 1.80 x 10
6
Surface area of particle S
p = � �
�
= 1.256 x 10
-5
m
2
Surface area of the sample = N S
p= 22.5 m
2
A
s =
� �
∅
p
�
�
Alternate
=
� � ��
� x 2650 � ����
−�
= 22.6 m
2
Using equation B, we can calculate the surface area of the particles in each fraction
provided the particle density and sphericity are known.
The results for all the fractions are added to give Specific Surface of the mixture, A
ss
or total surface area of a unit mass of particles
For particles having constant density and Sphericity , the specific surface of the
sample is
A
ss =
� �
�
∅ �
�
��
�
+
� �
�
∅ �
�
��
�
+
� �
�
∅ �
�
��
�
………………………..+
� ��
∅ �
�
���
A
ss =
�
∅ �
�
σ
�=�
�=�
(
�
�
�
��
)
Where, X
i= Mass Fraction in given increment
D
pi = average particle diameter
n =Number of increments
Mixed Particle: Surface area of the particles
provided the particle density and sphericity are known.
The results for all the fractions are added to give Specific Surface of the mixture, A
ss
or total surface area of a unit mass of particles
For particles having constant density and Sphericity , the specific surface of the
sample is
A
ss =
� �
�
∅ �
�
��
�
+
� �
�
∅ �
�
��
�
+
� �
�
∅ �
�
��
�
………………………..+
� ��
∅ �
�
���
A
ss =
�
∅ �
�
σ
�=�
�=�
(
�
�
�
��
)
Where, X
i= Mass Fraction in given increment
D
pi = average particle diameter
n =Number of increments
Mixed Particle: Surface area of the particles
Mixed Particle Sizes: Specific Surface Ratio
For irregular particle it is very difficult to estimate the specific surface
Specific Surface ratio (N
SSR): defined as the ratio of the specific surface of the
particle to the specific surface of a spheric particle of the same diameter.
The specific surface ratio is a function of average particle diameter
If D
p avg is the average size of the particle then
N
SSR =
�
���
[
�
�
�
�
����
]
For irregular particle it is very difficult to estimate the specific surface
Specific Surface ratio (N
SSR): defined as the ratio of the specific surface of the
particle to the specific surface of a spheric particle of the same diameter.
The specific surface ratio is a function of average particle diameter
If D
p avg is the average size of the particle then
N
SSR =
�
���
[
�
�
�
�
����
]
Finely divided clay is used as a catalyst in the petroleum industry. It has density of 1.2 g/cc and sphericity
of 0.5. The size analysis is as follows
Example
Average
diameter Di avg
(cm)
0.0252 0.0178 0.0126 0.0089 0.0038
Mass fraction x
i
(gm)
0.088 0.178 0.293 0.194 0.247
Find the specific surface area and Sauter mean diameter of the clay materials
Solution
The specific surface area and Sauter mean diameters
A
ss =
�
∅ �
�
σ
�=�
�=�
(
�
�
�
��
)
Where, X
i= Mass Fraction in given increment
D
pi = average particle diameter
n =Number of increments
D
vs =
�
σ
�=�
�=�
(�
�/�
�� ���)
of 0.5. The size analysis is as follows
Example
Average
diameter Di avg
(cm)
0.0252 0.0178 0.0126 0.0089 0.0038
Mass fraction x
i
(gm)
0.088 0.178 0.293 0.194 0.247
Find the specific surface area and Sauter mean diameter of the clay materials
Solution
The specific surface area and Sauter mean diameters
A
ss =
�
∅ �
�
σ
�=�
�=�
(
�
�
�
��
)
Where, X
i= Mass Fraction in given increment
D
pi = average particle diameter
n =Number of increments
D
vs =
�
σ
�=�
�=�
(�
�/�
�� ���)
Average diameter D
piavg (cm)Mass fraction x
i (g/g) x
i/D
piavg
0.0252 0.088 3.492
0.0178 0.178 10.000
0.0126 0.293 23.254
0.0089 0.194 21.797
0.0038 0.247 65.000
�
�=�.��
�
�
�
�����
=���.���
The specific surface area
A
ss =
�
∅ �
�
σ
�=�
�=�
�
�
�
��
=
� � ���.���
�.� � �.�
=����.�� ��
�
/�
Sauter mean diameter
D
vs =
�
σ
�=�
�=�
(�
�/�
�� ���)
=
�
���.���
= 0.008094 = 8.094 x10
-3
cm
piavg (cm)Mass fraction x
i (g/g) x
i/D
piavg
0.0252 0.088 3.492
0.0178 0.178 10.000
0.0126 0.293 23.254
0.0089 0.194 21.797
0.0038 0.247 65.000
�
�=�.��
�
�
�
�����
=���.���
The specific surface area
A
ss =
�
∅ �
�
σ
�=�
�=�
�
�
�
��
=
� � ���.���
�.� � �.�
=����.�� ��
�
/�
Sauter mean diameter
D
vs =
�
σ
�=�
�=�
(�
�/�
�� ���)
=
�
���.���
= 0.008094 = 8.094 x10
-3
cm
Density of Particle
Defined as total mass particle divided by its total volume
Depending on how the total volume is measured, different definitions of particle
density can be given
True particle density
➢Represents the mass of the particle divided by its volume
excluding open and closed pores
➢The density of the solid material of which the particle is made
➢For pure chemical substances, organic or inorganic, this is the
density quoted in reference books of physical/chemical data.
�
�
=�
cracks, flaws, hollows,
and closed pores
Defined as total mass particle divided by its total volume
Depending on how the total volume is measured, different definitions of particle
density can be given
True particle density
➢Represents the mass of the particle divided by its volume
excluding open and closed pores
➢The density of the solid material of which the particle is made
➢For pure chemical substances, organic or inorganic, this is the
density quoted in reference books of physical/chemical data.
�
�
=�
cracks, flaws, hollows,
and closed pores
Density of Particle
Apparent particle density
Defined as the mass of a particle divided by its volume excluding only the
open pores
Measured by gas or liquid displacement methods such as liquid or air pycnometry
�
�=
�
�−�
��
�
�−�
�−(�
��−�
�)
Apparent Particle Density
m
s=
weight of the bottle filled with the powder
m
o =
weight of the empty bottle
is the density of the liquid
m
l
= weight of the bottle filled with the liquid
m
sl
= weight of the bottle filled with both the solid and the liquid
m
o
m
s m
l
m
sl
Apparent particle density
Defined as the mass of a particle divided by its volume excluding only the
open pores
Measured by gas or liquid displacement methods such as liquid or air pycnometry
�
�=
�
�−�
��
�
�−�
�−(�
��−�
�)
Apparent Particle Density
m
s=
weight of the bottle filled with the powder
m
o =
weight of the empty bottle
is the density of the liquid
m
l
= weight of the bottle filled with the liquid
m
sl
= weight of the bottle filled with both the solid and the liquid
m
o
m
s m
l
m
sl
Size Reduction (comminution)
Operation carried out for reducing the size of bigger particles into smaller one of
desired size and shape with the help of external forces
COMMINUTION is another term used for size reduction
Refers to the process of converting the object from one physical dimension of
higher order to another dimension of smaller order.
Operation carried out for reducing the size of bigger particles into smaller one of
desired size and shape with the help of external forces
COMMINUTION is another term used for size reduction
Refers to the process of converting the object from one physical dimension of
higher order to another dimension of smaller order.
Objectives of Size reductions
✓Toincreasethesurfacearea, because in most chemicals reactions and some unit
operations (drying, adsorption, leaching etc) involving solid particles, the
reaction/ transfer rate is directly proportional to the area of contact between the
solid and the second phase
✓To produce solid particles of desired shape, size ranges and specific surface
✓To separate unwanted particles effectively
✓Toincreasethesurfacearea, because in most chemicals reactions and some unit
operations (drying, adsorption, leaching etc) involving solid particles, the
reaction/ transfer rate is directly proportional to the area of contact between the
solid and the second phase
✓To produce solid particles of desired shape, size ranges and specific surface
✓To separate unwanted particles effectively
Objectives of Size reductions
✓To mix solid particles more intimately
✓To improve handling (storage and transportation) characteristics
✓To dispose the solid waste easily
✓To mix solid particles more intimately
✓To improve handling (storage and transportation) characteristics
✓To dispose the solid waste easily
Mechanism/patterns of size reduction
Various size reduction equipment employ different actions to solid particles for size
reduction
Various size reduction equipment employ different actions to solid particles for size
reduction
There are five basic ways to reduce the size of material
Mechanism/patterns of size reduction
Impact
The particle is subjected to a single violent force and in crushing terminology, it
refers to the sharp, instantaneous collision of one moving object against another
Mechanism/patterns of size reduction
Impact
The particle is subjected to a single violent force and in crushing terminology, it
refers to the sharp, instantaneous collision of one moving object against another
Mechanism/patterns of size reduction
Impact
There are two varieties of impact : Gravity impact and dynamic impact
In gravity impact the free falling material is momentarily stopped by the stationary object
Example: Coal dropped onto a hard steel surface
Used when it is necessary to separate two materials which have relatively different
friability.
The more friable material is broken first, while the less friable material remains unbroken
Material Dropping in front of a moving hammer is an example of dynamic impact
When crushed by dynamic impact, the material is unsupported and the force of impact
accelerate movement of the reduced particles towards the breaker plate/hammer
Impact
There are two varieties of impact : Gravity impact and dynamic impact
In gravity impact the free falling material is momentarily stopped by the stationary object
Example: Coal dropped onto a hard steel surface
Used when it is necessary to separate two materials which have relatively different
friability.
The more friable material is broken first, while the less friable material remains unbroken
Material Dropping in front of a moving hammer is an example of dynamic impact
When crushed by dynamic impact, the material is unsupported and the force of impact
accelerate movement of the reduced particles towards the breaker plate/hammer
Mechanism/patterns of size reduction
Impact
dynamic impact is specially need when
✓ Cubical particle is needed
✓Finished product must be graded and must meet
intermediate sizing specification, as well as top and
bottom specifications
✓Ores must be broken along natural cleavage lines in
order to free and separate undesirable particles
Example: Mica in Feldspars
✓Materials are too hard and abrasive
Impact
dynamic impact is specially need when
✓ Cubical particle is needed
✓Finished product must be graded and must meet
intermediate sizing specification, as well as top and
bottom specifications
✓Ores must be broken along natural cleavage lines in
order to free and separate undesirable particles
Example: Mica in Feldspars
✓Materials are too hard and abrasive
Mechanism/patterns of size reduction
Cleavage: the tendency of a material to break along smooth planes parallel to zones of
weak bonding
Cleavage: the tendency of a material to break along smooth planes parallel to zones of
weak bonding
Mechanism/patterns of size reduction
The particle is broken by two forces and the size reduction is done between two
surfaces, with the work being done by one or both surfaces.
As a mechanical reduction method compression is chosen
✓for hard, tough, abrasive and non sticky material
✓Where finished product is relatedly coarser in size
✓When the material will break cubically
Compression
The particle is broken by two forces and the size reduction is done between two
surfaces, with the work being done by one or both surfaces.
As a mechanical reduction method compression is chosen
✓for hard, tough, abrasive and non sticky material
✓Where finished product is relatedly coarser in size
✓When the material will break cubically
Compression
Mechanism/patterns of size reduction
Attrition or rubbing
Method of size reduction by rubbing or scrubbing the
materials between two hard surfaces
Useful when the material is friable or not too abrasive
Shear
Consist of a trimming or cleaving action
The particles are compressed between the edges of two hard
surfaces moving tangentially
Used for friable material
Production of relatively coarse particles
Attrition or rubbing
Method of size reduction by rubbing or scrubbing the
materials between two hard surfaces
Useful when the material is friable or not too abrasive
Shear
Consist of a trimming or cleaving action
The particles are compressed between the edges of two hard
surfaces moving tangentially
Used for friable material
Production of relatively coarse particles
Mechanism/patterns of size reduction
Cutting or tearing
Fibrous material like wood and asbestos
Specified sizes are cut by knives or cutters
Commercial operations
Size reduction process : conduct in three different stages
Coarse size reductionIntermediate size reductionFine size reduction
Feed
rock
250 mm to 50 mm 75 mm to 25 mm 15 mm to 5 mm
Compression shear and impact Impact and attrition
Chopped vegetablePolymer Chips
Cutting or tearing
Fibrous material like wood and asbestos
Specified sizes are cut by knives or cutters
Commercial operations
Size reduction process : conduct in three different stages
Coarse size reductionIntermediate size reductionFine size reduction
Feed
rock
250 mm to 50 mm 75 mm to 25 mm 15 mm to 5 mm
Compression shear and impact Impact and attrition
Chopped vegetablePolymer Chips
Factors affecting the size reduction: material properties
For a particular size reduction , the choice of the machine to be used mainly depends on
✓The size and the quantity of material to be handled
✓The nature of the product
➢Hardness
➢Structure
➢Friability
➢Moisture content
➢Explosive nature
➢Soapiness
➢Temperature sensitivity
Affect the power consumption and wear of machine
Materials do not flow well if the moisture content is higher(3-4%). They tend to
clog the machine which reduces the crushing effectiveness.
Too dry : excessive dust
Must be grounded under wet condition or in presence of inert environment
Soapiness is the measure of Coefficient of friction , . If is less the crushing is
more difficult
Tendency to fracture during normal handling
For a particular size reduction , the choice of the machine to be used mainly depends on
✓The size and the quantity of material to be handled
✓The nature of the product
➢Hardness
➢Structure
➢Friability
➢Moisture content
➢Explosive nature
➢Soapiness
➢Temperature sensitivity
Affect the power consumption and wear of machine
Materials do not flow well if the moisture content is higher(3-4%). They tend to
clog the machine which reduces the crushing effectiveness.
Too dry : excessive dust
Must be grounded under wet condition or in presence of inert environment
Soapiness is the measure of Coefficient of friction , . If is less the crushing is
more difficult
Tendency to fracture during normal handling
Energy and power consumption in size reduction
Energy and power consumption in size reduction
The unit area of solid has a definite amount of surface energy and when its size is
reduced, the surface area per unit mass “specific surface” increases.
The unit area of solid has a definite amount of surface energy and when its size is
reduced, the surface area per unit mass “specific surface” increases.
Energy and power consumption in size reduction
The energy efficiency is less and when most of the energy is lost , the cost of power
becomes major constraint.
The energy efficiency is less and when most of the energy is lost , the cost of power
becomes major constraint.
Crushing Efficiency
In size reduction/ comminution process , energy in one form is converted into another
form.
Kinetic energy = Surface energy (potential energy) + Sound + Heat
Crushing Efficiency can be defined as the ratio of the surface energy created to the
energy absorbed (kinetic energy) by the solid.
It may also be defined as the ratio of the energy absorbed by the solid to form heat and
the energy input to the machine.
The crushing or grinding efficiency: 10
-3
to 1%
In size reduction/ comminution process , energy in one form is converted into another
form.
Kinetic energy = Surface energy (potential energy) + Sound + Heat
Crushing Efficiency can be defined as the ratio of the surface energy created to the
energy absorbed (kinetic energy) by the solid.
It may also be defined as the ratio of the energy absorbed by the solid to form heat and
the energy input to the machine.
The crushing or grinding efficiency: 10
-3
to 1%
Power Consumption
Cost of power is a major expense in any size reduction operation, and it determined
using crushing efficiency
Crushing efficiency
c =
������� ������ ������� �� ��������
����� ������ �������� �� ��� �����
If, W
a = total energy absorbed by a unit mass of solid, J/Kg
E
s= Surface energy per unit area, J/m
2
A
ssf, A
ssp = Area per unit mass of feed and product (specific surfaces)
respectively, m
2
/kg
Then, the surface energy created by crushing will be
E
S (A
ssp - A
ssf )
Crushing efficiency
c =
E
S
�
���−�
���
W
a
Cost of power is a major expense in any size reduction operation, and it determined
using crushing efficiency
Crushing efficiency
c =
������� ������ ������� �� ��������
����� ������ �������� �� ��� �����
If, W
a = total energy absorbed by a unit mass of solid, J/Kg
E
s= Surface energy per unit area, J/m
2
A
ssf, A
ssp = Area per unit mass of feed and product (specific surfaces)
respectively, m
2
/kg
Then, the surface energy created by crushing will be
E
S (A
ssp - A
ssf )
Crushing efficiency
c =
E
S
�
���−�
���
W
a
Power Consumption
The energy absorbed by unit mass of the solid (W
a) is less than the energy fed (W) for
the purpose to the machine
A portion of the total energy input is used to overcome friction in the bearings and
other moving parts and the rest is available tor size reduction, which lead to
mechanical efficiency
Mechanical efficiency,
m , is defined as the ratio of energy absorbed and the
energy fed to the machine
m =
�
�
�
Total energy input
� =
�
�
m
W=
E
S
���� −����
m
�
The energy absorbed by unit mass of the solid (W
a) is less than the energy fed (W) for
the purpose to the machine
A portion of the total energy input is used to overcome friction in the bearings and
other moving parts and the rest is available tor size reduction, which lead to
mechanical efficiency
Mechanical efficiency,
m , is defined as the ratio of energy absorbed and the
energy fed to the machine
m =
�
�
�
Total energy input
� =
�
�
m
W=
E
S
���� −����
m
�
Power Consumption
If ሶ� is the flow rate of solids to the machine, then the power required P by the
machine is the product of the total energy input and the flow rate
P = W x ሶ�
P=
E
S
����−����ሶ�
m
�
The expression for the specific surfaces of the feed and product materials are
A
ssf =
�
�
�
���
��
A
ssp =
�
�
�
���
��
Where,
�,
� = Sphericity of the feed and the product materials
�
���, �
��� = Sauter mean diameter for the feed and the product
��,
�� = density of the feed and the product materials
For a homogeneous material
��
=
�� =
�
A
If ሶ� is the flow rate of solids to the machine, then the power required P by the
machine is the product of the total energy input and the flow rate
P = W x ሶ�
P=
E
S
����−����ሶ�
m
�
The expression for the specific surfaces of the feed and product materials are
A
ssf =
�
�
�
���
��
A
ssp =
�
�
�
���
��
Where,
�,
� = Sphericity of the feed and the product materials
�
���, �
��� = Sauter mean diameter for the feed and the product
��,
�� = density of the feed and the product materials
For a homogeneous material
��
=
�� =
�
A
Power Consumption
P=
6 E
S
ሶ�
�
m
�
[
�
∅
�
�
���
−
�
∅
�
�
���
]
The power requirement for crushing will be more for higher flow rate
The power requirement becomes more and more for reducing fine particles to still finer
ones than for breaking down large pieces of rock.
It is almost impossible to find out the accurate amount of energy requirement in
order to effective size reduction of a given material , Because
(i) There is a wide variation in the size and shape of particles both in the feed and product
(ii) Some energy is wasted as heat and sound, which can not determine exactly
P=
6 E
S
ሶ�
�
m
�
[
�
∅
�
�
���
−
�
∅
�
�
���
]
The power requirement for crushing will be more for higher flow rate
The power requirement becomes more and more for reducing fine particles to still finer
ones than for breaking down large pieces of rock.
It is almost impossible to find out the accurate amount of energy requirement in
order to effective size reduction of a given material , Because
(i) There is a wide variation in the size and shape of particles both in the feed and product
(ii) Some energy is wasted as heat and sound, which can not determine exactly
Laws of Comminution
Number of empirical laws have been proposed to relate the size reduction with the
energy input to the machine.
Rittinger’s Law (1867), Kick’s Law (1885), Bond’s Law (1952)
Rittinger’s Law
“ The work required for size reduction is proportional to the new surface created”
W
R=
??????
ሶ�
= (�
��� − A
ssf )
Where, K= constant = 1/
c
Using equation, A
W
R=
??????
ሶ� ሶ
=� ??????E
S[
�
∅
�
��
�
���
−
�
∅
�
��
�
���
]
For particle of constant sphericity and density
Number of empirical laws have been proposed to relate the size reduction with the
energy input to the machine.
Rittinger’s Law (1867), Kick’s Law (1885), Bond’s Law (1952)
Rittinger’s Law
“ The work required for size reduction is proportional to the new surface created”
W
R=
??????
ሶ�
= (�
��� − A
ssf )
Where, K= constant = 1/
c
Using equation, A
W
R=
??????
ሶ� ሶ
=� ??????E
S[
�
∅
�
��
�
���
−
�
∅
�
��
�
���
]
For particle of constant sphericity and density
W
R=
??????
ሶ�
=
�??????��
∅ �
�
�
�
���
−
�
�
���
=??????
�
�
�
���
−
�
�
���
Laws of ComminutionRittinger’s Law
Where K
R=
�??????��
∅ �
�
is known as Rittinger’s constant
The inverse of Rittinger’s constant is known as Rittinger’s number
✓Applicable where new surface being created
✓Holds more accurately for fine grinding where the increase in surface per unit mass
of material is predominant
✓Law is applied in cases where the energy input per unit mass of material is not
too high
✓Applicable for feed size of less than 0.05 mm
R=
??????
ሶ�
=
�??????��
∅ �
�
�
�
���
−
�
�
���
=??????
�
�
�
���
−
�
�
���
Laws of ComminutionRittinger’s Law
Where K
R=
�??????��
∅ �
�
is known as Rittinger’s constant
The inverse of Rittinger’s constant is known as Rittinger’s number
✓Applicable where new surface being created
✓Holds more accurately for fine grinding where the increase in surface per unit mass
of material is predominant
✓Law is applied in cases where the energy input per unit mass of material is not
too high
✓Applicable for feed size of less than 0.05 mm
Example-1
Particles of the average feed size of 50 x 10
-4
m are crushed to an average product size of 10
x 10
-4
m at the rate of 20 tonnes per hour. At this rate, the crusher consumes 40 kW of
power of which 5 kW are required for running the mill empty. Calculate the power
consumption if 12 tonnes/h of this product is further crushed to 5 x10
-4
m size in the same
mill? Assume that Rittinger’s law is applicable.
??????
ሶ�
=??????
�
�
�
���
−
�
�
���
Solution
Rittenger’s Law is
Given: D
vsp = 10 x 10
-4
m
D
vsf= 50 x 10
-4
m, ሶ�= 20 tonnes/h, Power required to
crush the particle P= 40-5 = 35 kW
K
R= 2.1875 x 10
-3
kW.m/tonne This value of K
R is constant for the machine
��
ሶ��
=??????
�
�
�����
−
�
−
�
��� ��
−
�
Particles of the average feed size of 50 x 10
-4
m are crushed to an average product size of 10
x 10
-4
m at the rate of 20 tonnes per hour. At this rate, the crusher consumes 40 kW of
power of which 5 kW are required for running the mill empty. Calculate the power
consumption if 12 tonnes/h of this product is further crushed to 5 x10
-4
m size in the same
mill? Assume that Rittinger’s law is applicable.
??????
ሶ�
=??????
�
�
�
���
−
�
�
���
Solution
Rittenger’s Law is
Given: D
vsp = 10 x 10
-4
m
D
vsf= 50 x 10
-4
m, ሶ�= 20 tonnes/h, Power required to
crush the particle P= 40-5 = 35 kW
K
R= 2.1875 x 10
-3
kW.m/tonne This value of K
R is constant for the machine
��
ሶ��
=??????
�
�
�����
−
�
−
�
��� ��
−
�
Now for
D
vsp = 5 x 10
-4
m
D
vsf= 10 x 10
-4
m, ሶ�= 12 tonnes/h,
??????
ሶ�
=??????
�
�
�
���
−
�
�
���
P= 26.25 kW
K
R= 2.1875 x 10
-3
kW.m/tonne
??????
ሶ��
=�.����� ��
−
�
�
�� ��
−
�
−
�
��� ��
−
�
D
vsp = 5 x 10
-4
m
D
vsf= 10 x 10
-4
m, ሶ�= 12 tonnes/h,
??????
ሶ�
=??????
�
�
�
���
−
�
�
���
P= 26.25 kW
K
R= 2.1875 x 10
-3
kW.m/tonne
??????
ሶ��
=�.����� ��
−
�
�
�� ��
−
�
−
�
��� ��
−
�
Example -2
Find the power required for crushing 5 tonne/h of limestone (Rittinger’s number =
0.0765 m
2
/J) if the specific surface area of the feed and the product are 100 and 200
m
2
/kg respectively. If the machine consumes a power of 4 hp, calculate its efficiency.
Solution
??????
ሶ�
=??????
R (A
ssp − A
ssf )=
(A
ssp − A
ssf )
���������
′
� ������
P = 1816.99 J/s or W
P = 1816.99/ 745.7 = 2.43 hp
Efficiency of Machine
�.��
�
X 100= 60.75%
??????
�.��
=
(200 − 100 )
�.����
Given: ሶ�=5 tonne/hr= 1.39kg/s, A
ssf= 100 m
2
/kg, A
ssp= 200 m
2
/kg
Find the power required for crushing 5 tonne/h of limestone (Rittinger’s number =
0.0765 m
2
/J) if the specific surface area of the feed and the product are 100 and 200
m
2
/kg respectively. If the machine consumes a power of 4 hp, calculate its efficiency.
Solution
??????
ሶ�
=??????
R (A
ssp − A
ssf )=
(A
ssp − A
ssf )
���������
′
� ������
P = 1816.99 J/s or W
P = 1816.99/ 745.7 = 2.43 hp
Efficiency of Machine
�.��
�
X 100= 60.75%
??????
�.��
=
(200 − 100 )
�.����
Given: ሶ�=5 tonne/hr= 1.39kg/s, A
ssf= 100 m
2
/kg, A
ssp= 200 m
2
/kg
Laws of Comminution
Kick’s Law
The work required for crushing a given mass of material is constant for a given reduction
ratio irrespective of the initial size
Reduction ratio is the ratio of initial particle size to final particle size.
Kick’s law is based on stress analysis of plastic deformation within the elastic limit.
This law is more accurate than Rittinger’s law for coarse crushing where the surface
area produced per unit mass is considerably less.
This law is applicable for feed size of greater than 50 mm
W
k=
??????
ሶ�
= K
k ln[
�
���
�
���
]
Where, K
k = kick’s constant
Kick’s Law
The work required for crushing a given mass of material is constant for a given reduction
ratio irrespective of the initial size
Reduction ratio is the ratio of initial particle size to final particle size.
Kick’s law is based on stress analysis of plastic deformation within the elastic limit.
This law is more accurate than Rittinger’s law for coarse crushing where the surface
area produced per unit mass is considerably less.
This law is applicable for feed size of greater than 50 mm
W
k=
??????
ሶ�
= K
k ln[
�
���
�
���
]
Where, K
k = kick’s constant
Example-1
A sample of materials is crushed in a Jaw crusher such that the average size of the
particles is reduced from 50 mm to 10 mm with the energy consumption of 3.61
kWh/tonne. Determine the consumption of energy to crush the same material of 75
mm average size to an average size of 25 mm using Kick’s Law.
Energy consumption = ??????/??????̇ = 3.61 kWh/ tonne
Solution
??????
ሶ�
= K
k ln[
�
���
�
���
]
K
k = 2.24 kWh/ tonne
Energy consumption for crushing the same material from 75 mm to 25 mm size
??????
ሶ�
= 2.24 ln[
��
��
]
= 2.46 kWh/tonne
�.��= K
k ln[
��
��
]
A sample of materials is crushed in a Jaw crusher such that the average size of the
particles is reduced from 50 mm to 10 mm with the energy consumption of 3.61
kWh/tonne. Determine the consumption of energy to crush the same material of 75
mm average size to an average size of 25 mm using Kick’s Law.
Energy consumption = ??????/??????̇ = 3.61 kWh/ tonne
Solution
??????
ሶ�
= K
k ln[
�
���
�
���
]
K
k = 2.24 kWh/ tonne
Energy consumption for crushing the same material from 75 mm to 25 mm size
??????
ሶ�
= 2.24 ln[
��
��
]
= 2.46 kWh/tonne
�.��= K
k ln[
��
��
]
Laws of Comminution
Bond’s Law
The work required to form particles of D
pp from a very large particle size is proportional
to the square root of the surface to volume ratio (S
p/V
p) of the product.
This law is applicable for feed size between 0.05 and 50 mm
�
�
�
�
=
�
∅ ��
�
�=
??????
ሶ�
=??????
�
�
�
�
� = �
�
∅ ���
= �
�
∅
x
�
�
��
= ??????
�
�
�
��
K
b= �
�
∅
= Bond’s constant
Bond’s Law
The work required to form particles of D
pp from a very large particle size is proportional
to the square root of the surface to volume ratio (S
p/V
p) of the product.
This law is applicable for feed size between 0.05 and 50 mm
�
�
�
�
=
�
∅ ��
�
�=
??????
ሶ�
=??????
�
�
�
�
� = �
�
∅ ���
= �
�
∅
x
�
�
��
= ??????
�
�
�
��
K
b= �
�
∅
= Bond’s constant
�
�=
??????
ሶ�
= ??????
�
�
�
��
−
�
�
��
Laws of Comminution
Bond’s Law
When feed size is very large, the term
�
�
��
becomes negligible and expression of Bond
law remain as
�
�=
??????
ሶ�
= ??????
�
�
�
��
The bond constant is dependent on the type of machine used and, on the material, to be
crushed
Work index W
i, defined as the gross energy requirement in kilowatt hours per short ton of
feed to reduce a very large particle to such a size that 80% of the product will pass through
a 100 m or 0.1 mm screen.
�=
??????
ሶ�
= ??????
�
�
�
��
−
�
�
��
Laws of Comminution
Bond’s Law
When feed size is very large, the term
�
�
��
becomes negligible and expression of Bond
law remain as
�
�=
??????
ሶ�
= ??????
�
�
�
��
The bond constant is dependent on the type of machine used and, on the material, to be
crushed
Work index W
i, defined as the gross energy requirement in kilowatt hours per short ton of
feed to reduce a very large particle to such a size that 80% of the product will pass through
a 100 m or 0.1 mm screen.
Laws of Comminution
Bond’s Law
�
�= ??????
�
�
�
��
If P is in kW, ሶ � is in tons per hours
(i)D
pp is in m then K
b= 10 W
i
(ii)D
pp is in mm then K
b = �.� W
i = 0.3162 W
i
Thus ,If 80% of feed particles pass through a D
pf mm screen and 80% of product
particles pass through a D
pp mm Screen then
�
�=
??????
ሶ�
= �.���� ��
�
�
��
−
�
�
��
The Bond work index provides a measure of how much energy is required to
grind a sample of materials
Bond’s Law
�
�= ??????
�
�
�
��
If P is in kW, ሶ � is in tons per hours
(i)D
pp is in m then K
b= 10 W
i
(ii)D
pp is in mm then K
b = �.� W
i = 0.3162 W
i
Thus ,If 80% of feed particles pass through a D
pf mm screen and 80% of product
particles pass through a D
pp mm Screen then
�
�=
??????
ሶ�
= �.���� ��
�
�
��
−
�
�
��
The Bond work index provides a measure of how much energy is required to
grind a sample of materials
Laws of Comminution
Bond’s Law
Values of work index for different types of materials for wet grinding
PropertySoft Medium Hard Very Hard
Bond Wi
(kWh/ton)
7-9 9-14 14-20 >20
For dry grinding the materials, these values are multiplied by 4/3
Bond’s Law
Values of work index for different types of materials for wet grinding
PropertySoft Medium Hard Very Hard
Bond Wi
(kWh/ton)
7-9 9-14 14-20 >20
For dry grinding the materials, these values are multiplied by 4/3
Example:1
270 kW of power is required to crush 150 tonnne/h of a material. If 80% of the feed
passes through a 50 mm screen and 80% of the product passes through a 3 mm
screen, calculate the work index of the material. And what will be the power
required for the same feed at 150 tonnes/h to be crushed to a product such that 80%
is to pass through a 1.5mm screen
??????
ሶ�
= �.���� ��
�
�
��
−
�
�
��
Bond’s Law
Solution
P= 270 kW
m= 150 tonnes/h
D
pp= 3 mm
D
pf = 50 mm
���
���
= �.���� ��
�
�
−
�
��
Wi= 13.06 kWh/tonne
270 kW of power is required to crush 150 tonnne/h of a material. If 80% of the feed
passes through a 50 mm screen and 80% of the product passes through a 3 mm
screen, calculate the work index of the material. And what will be the power
required for the same feed at 150 tonnes/h to be crushed to a product such that 80%
is to pass through a 1.5mm screen
??????
ሶ�
= �.���� ��
�
�
��
−
�
�
��
Bond’s Law
Solution
P= 270 kW
m= 150 tonnes/h
D
pp= 3 mm
D
pf = 50 mm
���
���
= �.���� ��
�
�
−
�
��
Wi= 13.06 kWh/tonne
the power required for the same feed at 150 tonnes/h to be crushed to a product such that 80% is to
pass through a 1.5mm screen
m= 150 tonnes/h
D
pp= 1.5 mm
D
pf = 50 mm
Wi= 13.06 kWh/tonne
??????
ሶ�
= �.���� ��
�
�
��
−
�
�
��
??????
���
= �.���� � ��.��
�
�.�
−
�
��
P= 418.16 kW
pass through a 1.5mm screen
m= 150 tonnes/h
D
pp= 1.5 mm
D
pf = 50 mm
Wi= 13.06 kWh/tonne
??????
ሶ�
= �.���� ��
�
�
��
−
�
�
��
??????
���
= �.���� � ��.��
�
�.�
−
�
��
P= 418.16 kW
Example:2
Feed sample Milled sample
Sieve size
(mm)
Mass fraction
retain
Sieve size
(mm)
Mass fraction
retain
6730 0.00 605 0.00
4760 0.05 425 0.08
3360 0.15 300 0.12
2380 0.70 212 0.65
1680 0.10 150 0.11
100 0.04
Grain is milled at a rate of 10 tonnes/h and the power required for this operation is
67.5 kW. The details of size analysis before and after the milling is given in the
table. Assuming that Bond’s law best describes the relationship between energy
required and change in particle size, determine the work index for the grain and
thus find the total power requirement to mill down to a distribution where 80%
passes 100 mm.
Feed sample Milled sample
Sieve size
(mm)
Mass fraction
retain
Sieve size
(mm)
Mass fraction
retain
6730 0.00 605 0.00
4760 0.05 425 0.08
3360 0.15 300 0.12
2380 0.70 212 0.65
1680 0.10 150 0.11
100 0.04
Grain is milled at a rate of 10 tonnes/h and the power required for this operation is
67.5 kW. The details of size analysis before and after the milling is given in the
table. Assuming that Bond’s law best describes the relationship between energy
required and change in particle size, determine the work index for the grain and
thus find the total power requirement to mill down to a distribution where 80%
passes 100 mm.
Feed sample Milled sample
Sieve size (mm)Mass fraction
retain
%
cumulative
mass
fraction pass
Sieve size
(mm)
Mass fraction
retain
% cumulative
mass fraction
pass
6730 0.00 100 605 0.00 100
4760 0.05 95 425 0.08 92
3360 0.15 80 300 0.12 80
2380 0.70 10 212 0.65 15
1680 0.10 00 150 0.11 4
100 0.04 0
Solution
??????
ሶ�
= �.���� ��
�
�
��
−
�
�
��
P= 67.5 kW
m= 10 tons/h
D
pp= 300 mm
D
pf = 3360 mm
��.�
��
= �.���� ��
�
���
−
�
����
W
i= 527.34 kWh/ton
Sieve size (mm)Mass fraction
retain
%
cumulative
mass
fraction pass
Sieve size
(mm)
Mass fraction
retain
% cumulative
mass fraction
pass
6730 0.00 100 605 0.00 100
4760 0.05 95 425 0.08 92
3360 0.15 80 300 0.12 80
2380 0.70 10 212 0.65 15
1680 0.10 00 150 0.11 4
100 0.04 0
Solution
??????
ሶ�
= �.���� ��
�
�
��
−
�
�
��
P= 67.5 kW
m= 10 tons/h
D
pp= 300 mm
D
pf = 3360 mm
��.�
��
= �.���� ��
�
���
−
�
����
W
i= 527.34 kWh/ton
power requirement to mill down to a distribution where 80% passes 100 mm.
??????
ሶ�
= �.���� ��
�
�
��
−
�
�
��
m= 10 tons/h
D
pp= 100 mm
D
pf = 300 mm
Wi= 527.34 kWh/ton??????
��
= �.���� � ���.��
�
���
−
�
���
P= 70.533 kW
??????
ሶ�
= �.���� ��
�
�
��
−
�
�
��
m= 10 tons/h
D
pp= 100 mm
D
pf = 300 mm
Wi= 527.34 kWh/ton??????
��
= �.���� � ���.��
�
���
−
�
���
P= 70.533 kW
Example-3
A grinder is to be used (which is 8% efficient ) to handle 10 tonnes per hour of a
siliceous ore (specific gravity = 2.65) The feed and product analysis are given below:
Screen size (mm)Feed Mass
Fraction retain
Product Mass
Fraction reatin
-3.327+2.362 0.143 0.0
-2.362+1.651 0.211 0.0
-1.1651+1.168 0.230 0.0
-1.168+0.833 0.186 0.098
-0.833+0.589 0.120 0.234
-0.589+0.471 0.076 0.277
-0.417+0.295 0.03 0.149
-0.295+0.208 0.0 0.101
-0.208+0.147 0.0 0.068
-0.147+0.104 0.0 0.044
-0.104 0.0 0.029
The Grinder costs Rs. 25,00,000/-. It
operates on a 24 hours basis for 300
days per year and the maintenance ,
overhead and replacement cost amount
to 50% of the power cost. Electricity cost
Rs. 4 per unit (1 unit=1kWh). If the
machine depreciates on a straight line
basis for 10 years, estimate the annual
processing cost of the ore if the work
index of the ore is 13.57 kWh/tonne
�
�=
??????
ሶ�
= �.���� ��
�
�
��
−
�
�
��
A grinder is to be used (which is 8% efficient ) to handle 10 tonnes per hour of a
siliceous ore (specific gravity = 2.65) The feed and product analysis are given below:
Screen size (mm)Feed Mass
Fraction retain
Product Mass
Fraction reatin
-3.327+2.362 0.143 0.0
-2.362+1.651 0.211 0.0
-1.1651+1.168 0.230 0.0
-1.168+0.833 0.186 0.098
-0.833+0.589 0.120 0.234
-0.589+0.471 0.076 0.277
-0.417+0.295 0.03 0.149
-0.295+0.208 0.0 0.101
-0.208+0.147 0.0 0.068
-0.147+0.104 0.0 0.044
-0.104 0.0 0.029
The Grinder costs Rs. 25,00,000/-. It
operates on a 24 hours basis for 300
days per year and the maintenance ,
overhead and replacement cost amount
to 50% of the power cost. Electricity cost
Rs. 4 per unit (1 unit=1kWh). If the
machine depreciates on a straight line
basis for 10 years, estimate the annual
processing cost of the ore if the work
index of the ore is 13.57 kWh/tonne
�
�=
??????
ሶ�
= �.���� ��
�
�
��
−
�
�
��
Screen size (mm)Screen size (mm)Feed Mass
Fraction
retain
Cumulative feed
mass fraction pass
Product Mass
Fraction
Cumulative
product mass
fraction pass
-3.327+2.362 2.8445 0.143 0.857 0.0 1.0
-2.362+1.651 2.0065 0.211 0.646 0.0 1.0
-1.1651+1.0681.1165 0.230 0.416 0.0 1.0
-1.068+0.833 0.9505 0.186 0.230 0.098 0.902
-0.833+0.589 0.711 0.120 0.110 0.234 0.668
-0.589+0.471 0.53 0.076 0.034 0.277 0.391
-0.417+0.295 0.356 0.03 0.004 0.149 0.242
-0.295+0.208 0.2515 0.0 0.0 0.101 0.141
-0.208+0.147 0.1775 0.0 0.0 0.068 0.073
-0.147+0.104 0.1255 0.0 0.0 0.044 0.029
-0.104 0.104 0.0 0.0 0.029 0.0
Solution
Fraction
retain
Cumulative feed
mass fraction pass
Product Mass
Fraction
Cumulative
product mass
fraction pass
-3.327+2.362 2.8445 0.143 0.857 0.0 1.0
-2.362+1.651 2.0065 0.211 0.646 0.0 1.0
-1.1651+1.0681.1165 0.230 0.416 0.0 1.0
-1.068+0.833 0.9505 0.186 0.230 0.098 0.902
-0.833+0.589 0.711 0.120 0.110 0.234 0.668
-0.589+0.471 0.53 0.076 0.034 0.277 0.391
-0.417+0.295 0.356 0.03 0.004 0.149 0.242
-0.295+0.208 0.2515 0.0 0.0 0.101 0.141
-0.208+0.147 0.1775 0.0 0.0 0.068 0.073
-0.147+0.104 0.1255 0.0 0.0 0.044 0.029
-0.104 0.104 0.0 0.0 0.029 0.0
Solution
Size mm
Cumulative mass fraction pass %
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.5 1 1.5 2 2.5 3
Feed sample
2.6 mm
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2 2.5 3
Product sample
0.8 mm
Cumulative mass fraction pass %
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.5 1 1.5 2 2.5 3
Feed sample
2.6 mm
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2 2.5 3
Product sample
0.8 mm
Solution
Bond’s law for estimating the power consumption
�
�=
??????
ሶ�
= �.���� ��
�
�
��
−
�
�
��
W
i= 13.57 kWh/tonneGiven: �=10 tonnes/hr
D
pp and D
pf are the aperture size (in mm) of screen through which 80% of the
material (product and feed) passes through.
P= 0.3162x 13.57 x 10
�
�.�
−
�
�.�
P= 21.36kW
Since the efficiency of the grinder is 8%
Total power consumption= 21.36/0.08 = 267 kW
Annual power consumption=267 x 24 x 300 = 1922400 kW.
Annual Power Cost= 1922400 x 4 = Rs. 76,89,600/-
� =
�
�
m
Bond’s law for estimating the power consumption
�
�=
??????
ሶ�
= �.���� ��
�
�
��
−
�
�
��
W
i= 13.57 kWh/tonneGiven: �=10 tonnes/hr
D
pp and D
pf are the aperture size (in mm) of screen through which 80% of the
material (product and feed) passes through.
P= 0.3162x 13.57 x 10
�
�.�
−
�
�.�
P= 21.36kW
Since the efficiency of the grinder is 8%
Total power consumption= 21.36/0.08 = 267 kW
Annual power consumption=267 x 24 x 300 = 1922400 kW.
Annual Power Cost= 1922400 x 4 = Rs. 76,89,600/-
� =
�
�
m
Maintenance , overhead and replacement cost= Rs. 76,89,600x 0.5 = Rs. 38,44,800/-
Annual depreciation cost = Rs 25,00,000/10 = Rs. 2,50,000/-
Annual processing cost of the ore = Rs. 76,89,600 + Rs. 38,44,800 + Rs. 2,50,000/-
Annual processing cost of the ore = Rs. 1,17,84,480/-
Annual depreciation cost = Rs 25,00,000/10 = Rs. 2,50,000/-
Annual processing cost of the ore = Rs. 76,89,600 + Rs. 38,44,800 + Rs. 2,50,000/-
Annual processing cost of the ore = Rs. 1,17,84,480/-
Size Reduction Machines
Classification of size reduction machines : Based on Size of Feed and Product
Coarse Crushers
(larger feed
(1500mm)to (50-5)
mm product size
Intermediate
Crushers (50-5
mm to (5 - 0.1)
mm product size
Fine Crusher/
Grinder
(5-2 mm to 200
mesh)
Ultrafine
Grinder
(6 mm to 1
micron)
✓Jaw Crusher
✓Gyratory Crusher
✓Cone Crusher
✓Crushing Roll
(Smooth and
toothed)
✓Bradford breaker
✓Roller Mill
✓Cage Mill
✓Granulator
✓Hammer Mill
✓Impactor
✓Ball Mill
✓Pebble Mill
✓Rod Mill
✓Tube Mill
✓Attrition Mill
✓Jet Mill
✓Colloidal Mill
✓Classifying
Hammer Mill
✓Fine Impact
mill
Classification of size reduction machines : Based on Size of Feed and Product
Coarse Crushers
(larger feed
(1500mm)to (50-5)
mm product size
Intermediate
Crushers (50-5
mm to (5 - 0.1)
mm product size
Fine Crusher/
Grinder
(5-2 mm to 200
mesh)
Ultrafine
Grinder
(6 mm to 1
micron)
✓Jaw Crusher
✓Gyratory Crusher
✓Cone Crusher
✓Crushing Roll
(Smooth and
toothed)
✓Bradford breaker
✓Roller Mill
✓Cage Mill
✓Granulator
✓Hammer Mill
✓Impactor
✓Ball Mill
✓Pebble Mill
✓Rod Mill
✓Tube Mill
✓Attrition Mill
✓Jet Mill
✓Colloidal Mill
✓Classifying
Hammer Mill
✓Fine Impact
mill
Selection Criteria of Size Reduction Machines
✓Produce the materials of desired shape and size or size distribution
✓Accept the maximum input size expected
✓Should not choke or plug
✓Power input per unit weight of product should be small
✓Resist abrasive wear
✓Prolonged service life
✓Replacement part should be readily available at cheaper price
✓Initial fix cost and operating cost should be minimum
✓Easy and safe to operate
✓Easy access to internal parts for maintenance
✓Produce the materials of desired shape and size or size distribution
✓Accept the maximum input size expected
✓Should not choke or plug
✓Power input per unit weight of product should be small
✓Resist abrasive wear
✓Prolonged service life
✓Replacement part should be readily available at cheaper price
✓Initial fix cost and operating cost should be minimum
✓Easy and safe to operate
✓Easy access to internal parts for maintenance
Coarse Crushers
➢Employed mainly the compressive action to large lumps of solid materials
➢Slow speed machine
➢The size reduction results from stresses that are applied to the solid particles to be
crushed by some moving part in the machine and against a stationary part or
against some other moving part
(larger feed to (50-5) mm product size)
➢Compression action build up strain within the particles to be broken which results
in fracturing whenever they exceed the elastic limit of the materials
➢NOTE: Bradford Breaker crushes the particle by gravity Impact
➢Employed mainly the compressive action to large lumps of solid materials
➢Slow speed machine
➢The size reduction results from stresses that are applied to the solid particles to be
crushed by some moving part in the machine and against a stationary part or
against some other moving part
(larger feed to (50-5) mm product size)
➢Compression action build up strain within the particles to be broken which results
in fracturing whenever they exceed the elastic limit of the materials
➢NOTE: Bradford Breaker crushes the particle by gravity Impact
Jaw Crusher
Blake: the movable Jaw is hinged at the top so that greatest movement at the bottom
is given to the smaller Lumps
Dodge: the movable jaw is pivoted at the bottom giving minimum movement of the
jaw at the bottom by which more uniform products are obtained
Blake: the movable Jaw is hinged at the top so that greatest movement at the bottom
is given to the smaller Lumps
Dodge: the movable jaw is pivoted at the bottom giving minimum movement of the
jaw at the bottom by which more uniform products are obtained
Jaw Crusher
Works on the principle of compression and Produces cubical products with minimum
fines
Causes the pitman to
oscillate vertically
Vertical motion of pitman is
transmitted to the movable
jaw to have back and forth
motion horizontally by the
toggles
The movable Jaws moves
in a horizontal plane
making 20-30° with the
fixed jaw
Cast steel lined supported
frames for fixed jaw and
movable jaw
Pivoted at top to form V
opening at the top
Works on the principle of compression and Produces cubical products with minimum
fines
Causes the pitman to
oscillate vertically
Vertical motion of pitman is
transmitted to the movable
jaw to have back and forth
motion horizontally by the
toggles
The movable Jaws moves
in a horizontal plane
making 20-30° with the
fixed jaw
Cast steel lined supported
frames for fixed jaw and
movable jaw
Pivoted at top to form V
opening at the top
Jaw Crusher
Jaw CrusherJaw Plate Profiles
Manganese Steel: Abrasion resistance
Several patterns for gripping the material and for concentrating the pressure on smaller
areas
Recommended for
extremely hard materials
Rock and gravel
Manganese Steel: Abrasion resistance
Several patterns for gripping the material and for concentrating the pressure on smaller
areas
Recommended for
extremely hard materials
Rock and gravel
Technical Specifications of Jaw Crusher
Hammer Mills
Hammer Mills
Hammer Mills
Hammer mill crushed the materials in two stages
1. The size reduction occurs by dynamic reduction
2. Sizing occurs in the second zone where small clearance exist between hammers
and screen base by attrition and shear.
Advantage
Ability to produce the specified top size without the need for a closed- circuits
crushing system and to produce cubical product.
Large particle can not scape the screen bars until sized, resulting in great product
uniformity with a minimum of oversize
Hammer mills have high reduction ratio
Due to excessive wear, these are not recommended for the fine grinding of very hard
and abrasive material
Hammer mill crushed the materials in two stages
1. The size reduction occurs by dynamic reduction
2. Sizing occurs in the second zone where small clearance exist between hammers
and screen base by attrition and shear.
Advantage
Ability to produce the specified top size without the need for a closed- circuits
crushing system and to produce cubical product.
Large particle can not scape the screen bars until sized, resulting in great product
uniformity with a minimum of oversize
Hammer mills have high reduction ratio
Due to excessive wear, these are not recommended for the fine grinding of very hard
and abrasive material
Hammer Blade Types
Hammer Blade Types
Hammer Screens
Technical specification of Hammer Mill
Fine Crushers (Grinders)
Grinders are a variety of size reduction machines employed for fine grinding which
reduces the intermediate product to a finer size.
These mills are different in their ration of diameter to length of the cylinder and the type
of grinding media.
For example, Ball mill, rod mill, pebble mill.
Grinders are a variety of size reduction machines employed for fine grinding which
reduces the intermediate product to a finer size.
These mills are different in their ration of diameter to length of the cylinder and the type
of grinding media.
For example, Ball mill, rod mill, pebble mill.
Ball Mills
The principle of size reduction in ball mills is impact of balls which fall from the top of the
shell on to the feed particles near the bottom of the shell.
Popular due to their low operating cost and maintenance cost
Suitable for materials of all degrees of hardness
Can be operated batchwise or continuously and wet or dry
Grinding takes place inside the mill where an inert environment can be easily
maintained and therefore, it can be used for explosive materials
Grinding can be carried out under wet or dry conditions
The principle of size reduction in ball mills is impact of balls which fall from the top of the
shell on to the feed particles near the bottom of the shell.
Popular due to their low operating cost and maintenance cost
Suitable for materials of all degrees of hardness
Can be operated batchwise or continuously and wet or dry
Grinding takes place inside the mill where an inert environment can be easily
maintained and therefore, it can be used for explosive materials
Grinding can be carried out under wet or dry conditions
Ball Mills
Hollow cylindrical or conical shells
Made of steel or rubber lined steel
Half full of steel balls
Rotating horizontal or at a small angle to horizontal
Grinding media is the steel balls
Inner surface made of manganese steel:
abrasion resistance or rubber lining
Hollow cylindrical or conical shells
Made of steel or rubber lined steel
Half full of steel balls
Rotating horizontal or at a small angle to horizontal
Grinding media is the steel balls
Inner surface made of manganese steel:
abrasion resistance or rubber lining
Ball Mills
Advantage of rubber lined mills is that due to higher coefficient of friction between the
balls and the cylinder, the balls are carried to a greater height in contact with the cylinder
and thus drop on to the feed particles from a greater height causing size reduction to be
more effective.
The length of ball mill is nearly equal to its diameter (L/D ratio varies from 1 to 1.5:1)
The balls occupy about 30 to 50% of the volume
of the mill
The diameter of the balls varies from 12 to
125 mm.
The optimum ball diameter is nearly
proportional to the square root of the size of
the feed.
The mill rotated at speed between 60-100 rpm
Advantage of rubber lined mills is that due to higher coefficient of friction between the
balls and the cylinder, the balls are carried to a greater height in contact with the cylinder
and thus drop on to the feed particles from a greater height causing size reduction to be
more effective.
The length of ball mill is nearly equal to its diameter (L/D ratio varies from 1 to 1.5:1)
The balls occupy about 30 to 50% of the volume
of the mill
The diameter of the balls varies from 12 to
125 mm.
The optimum ball diameter is nearly
proportional to the square root of the size of
the feed.
The mill rotated at speed between 60-100 rpm
Ball Mills
cascading
cataracting
cascading
cataracting
Ball Mills
During grinding, the balls themselves wear and are constantly replaced by new ones.
So, at any point of time, balls of different sizes are found inside the mill.
The speed of rotation is a crucial factor for ball mills.
At low speeds of rotation, the balls are lifted and
simply roll back over feed materials.
Size reduction is caused by attrition and little crushing
action takes place.
Under this condition, the mill is said to be cascading
This is advantageous because the larger ball crushes the coarse and the smaller ball
grind the material to a finer product.
During grinding, the balls themselves wear and are constantly replaced by new ones.
So, at any point of time, balls of different sizes are found inside the mill.
The speed of rotation is a crucial factor for ball mills.
At low speeds of rotation, the balls are lifted and
simply roll back over feed materials.
Size reduction is caused by attrition and little crushing
action takes place.
Under this condition, the mill is said to be cascading
This is advantageous because the larger ball crushes the coarse and the smaller ball
grind the material to a finer product.
Ball Mills
At slightly higher speeds, the balls are carried up further
inside the mill and fall back due to gravity on the feed
particles at the bottom.
Grinding takes place by impact and the mill is said to be
cataracting.
If the speed of rotation is increased further, a stage is
reached when the balls are carried along with the inside
wall of the mill due to high centrifugal force and do not fall
at all. The mill is said to be centrifuging.
The minimum speed at which centrifuging occurs is call the
critical speed of the mill.
The operating speed of the ball milling is 50-75% of the
critical speed
At slightly higher speeds, the balls are carried up further
inside the mill and fall back due to gravity on the feed
particles at the bottom.
Grinding takes place by impact and the mill is said to be
cataracting.
If the speed of rotation is increased further, a stage is
reached when the balls are carried along with the inside
wall of the mill due to high centrifugal force and do not fall
at all. The mill is said to be centrifuging.
The minimum speed at which centrifuging occurs is call the
critical speed of the mill.
The operating speed of the ball milling is 50-75% of the
critical speed
Factors affecting the size of the product
With high feed rates, less size reduction is achieved as the material remains inside the
mill.
Feed rate
The properties of Feed materials
For hard material, less size reduction is achieved under a given operating conditions
The weight of balls
Heavy weight ball produce a fine
product
Increased by increasing the number of balls
By using material of high densities
Diameter of balls
Small size balls the production of fine size materials is more, and they are not effective
for larger feed particles.
For a given size of balls, the limiting size reduction achieved is known as the free grinding
limit.
With high feed rates, less size reduction is achieved as the material remains inside the
mill.
Feed rate
The properties of Feed materials
For hard material, less size reduction is achieved under a given operating conditions
The weight of balls
Heavy weight ball produce a fine
product
Increased by increasing the number of balls
By using material of high densities
Diameter of balls
Small size balls the production of fine size materials is more, and they are not effective
for larger feed particles.
For a given size of balls, the limiting size reduction achieved is known as the free grinding
limit.
Factors affecting the size of the product
Speed of rotation of Mill
For effective grinding, the ball mills are operated between 50-75% of the critical speed,
i.e, in the fringe area between cascading and free fall. This is referred to as the angle of
break
Level of Material in the Mill
With increasing in the level of material inside the mill, cushioning action increases causing
wastage of power, which produces excessive quantity of undersize materials
Slope of the Mill
With the increase in the slope of the mill, the capacity increases, at the same time a
coarser product is obtained.
Speed of rotation of Mill
For effective grinding, the ball mills are operated between 50-75% of the critical speed,
i.e, in the fringe area between cascading and free fall. This is referred to as the angle of
break
Level of Material in the Mill
With increasing in the level of material inside the mill, cushioning action increases causing
wastage of power, which produces excessive quantity of undersize materials
Slope of the Mill
With the increase in the slope of the mill, the capacity increases, at the same time a
coarser product is obtained.
Industrial/ Mechanical Screening operations
Process of separating of particles of different sizes into two or more number of
fractions, each of which is more uniform in particle size than the original mixture.
In screening practice, a mixture of particles is taken and separated into multiple
grades on the basis of particle size.
Purpose of Screening
To remove the coarse particles for further size
reduction
To remove the fine particles from crusher feeds to
save power by preventing over grinding
To grade the crushed products into commercial size
To perform a step in a concentration process
Process of separating of particles of different sizes into two or more number of
fractions, each of which is more uniform in particle size than the original mixture.
In screening practice, a mixture of particles is taken and separated into multiple
grades on the basis of particle size.
Purpose of Screening
To remove the coarse particles for further size
reduction
To remove the fine particles from crusher feeds to
save power by preventing over grinding
To grade the crushed products into commercial size
To perform a step in a concentration process
Accomplished by passing the material in an open cylindrical container with uniformly
spaced openings of the desired size at the base called Screen
The screen through which the particles have passes is called limiting screen and which
has retained them is called retaining screen
Industrial/ Mechanical Screening operations
Dry screening operations
Refers to the treatment of material containing
a natural amount of moisture or a material that
has been dried before screening
Products: cement, talcum powder, aluminum power
Wet screening operations
Refer to operation in which water is added to the material on the screen to remove
undesirable materials, mostly clay or extremely fine particles.
spaced openings of the desired size at the base called Screen
The screen through which the particles have passes is called limiting screen and which
has retained them is called retaining screen
Industrial/ Mechanical Screening operations
Dry screening operations
Refers to the treatment of material containing
a natural amount of moisture or a material that
has been dried before screening
Products: cement, talcum powder, aluminum power
Wet screening operations
Refer to operation in which water is added to the material on the screen to remove
undesirable materials, mostly clay or extremely fine particles.
Screening Mechanism
Fundamental function: to pass the undersize particles through the apertures
: to reject the oversize particles for some meaningful purpose
For screening surface having least thickness, if every individual particles are
brought to the opening at zero velocity in a direction perpendicular to the plane
of the screen opening then all the particles pass through it readily.
But due to tonnage requirement, we use thicker
screening surfaces and give some kind of motion
to the screen.
Fundamental function: to pass the undersize particles through the apertures
: to reject the oversize particles for some meaningful purpose
For screening surface having least thickness, if every individual particles are
brought to the opening at zero velocity in a direction perpendicular to the plane
of the screen opening then all the particles pass through it readily.
But due to tonnage requirement, we use thicker
screening surfaces and give some kind of motion
to the screen.
Screening Mechanism
Practically, Particles are crowded, they rebound and continuously interfere at the
openings.
Many undersize particles stay
away from the access of screen
openings
Particles are brought to the screen opening at such a velocity and in such direction
that the passage of under size particles is not affected by the edges or walls of the
openings
Screening Phenomenon can be divided into two
process: (a) Stratification (b) separation probability
Practically, Particles are crowded, they rebound and continuously interfere at the
openings.
Many undersize particles stay
away from the access of screen
openings
Particles are brought to the screen opening at such a velocity and in such direction
that the passage of under size particles is not affected by the edges or walls of the
openings
Screening Phenomenon can be divided into two
process: (a) Stratification (b) separation probability
Screening Mechanism
Materials to be screened is delivered to the screen surface at a continuous rate.
Dropped on to the screen surface
It loses its vertical component of velocity and undergoes a change in direction of travel
By vibration, the bed of material tend to develop a fluid state
Due to this, the large particles rise to the top of the material bed while the smaller
particles sift through the voids and find a way to the bottom of the bed to reach the
screen opening.
This characteristics of particle orientation is called stratification.
Stratification is essential for transport of oversize particles and for preventing of
blinding of screen openings
Materials to be screened is delivered to the screen surface at a continuous rate.
Dropped on to the screen surface
It loses its vertical component of velocity and undergoes a change in direction of travel
By vibration, the bed of material tend to develop a fluid state
Due to this, the large particles rise to the top of the material bed while the smaller
particles sift through the voids and find a way to the bottom of the bed to reach the
screen opening.
This characteristics of particle orientation is called stratification.
Stratification is essential for transport of oversize particles and for preventing of
blinding of screen openings
Screening Mechanism
Screening Mechanism
Factors affecting stratification
Material travel flow: function of material stratification, bed thickness, and screen slope
Stroke characteristics: amplitude, direction, rotation, type of motion and frequency
Surface particle moisture: high moisture content makes stratification difficult.
Separation probability
It is the process by which particles reach the opening and are rejected, if they are larger
than the openings or pass through them if they are smaller than the openings
Separation probability of a particle is a function of the particle size and the screen opening
Larger the difference between two: better screening
Factors affecting stratification
Material travel flow: function of material stratification, bed thickness, and screen slope
Stroke characteristics: amplitude, direction, rotation, type of motion and frequency
Surface particle moisture: high moisture content makes stratification difficult.
Separation probability
It is the process by which particles reach the opening and are rejected, if they are larger
than the openings or pass through them if they are smaller than the openings
Separation probability of a particle is a function of the particle size and the screen opening
Larger the difference between two: better screening
Screening Mechanism
Particles having dimension greater than 1.5 times the screen opening (dp > 1.5w) :
will not at all pass-through screen opening
Particles having dimension less than half the size of screen opening (dp< 0.5w) :
will pass through easily
0.5w <dp < 1.5w: Critical class: which determine both efficiency and capacity of screen
0.5w <dp < 1.5w, require several attempts before passing through
Particles of
w< dp <1.5 w, clog many openings before leaving the screen as they
are oversized material
Particles having dimension greater than 1.5 times the screen opening (dp > 1.5w) :
will not at all pass-through screen opening
Particles having dimension less than half the size of screen opening (dp< 0.5w) :
will pass through easily
0.5w <dp < 1.5w: Critical class: which determine both efficiency and capacity of screen
0.5w <dp < 1.5w, require several attempts before passing through
Particles of
w< dp <1.5 w, clog many openings before leaving the screen as they
are oversized material
Screening Mechanism
A-B: stratification starts
B: maximum stratification
B-C: maximum particle removal:
high percentage of fines and having
high separation probability
C-D: larger percentage of
particles in the critical class
and the probability of the
particles passing through
the screen is less
100% screen efficiency : not practical possible
A-B: stratification starts
B: maximum stratification
B-C: maximum particle removal:
high percentage of fines and having
high separation probability
C-D: larger percentage of
particles in the critical class
and the probability of the
particles passing through
the screen is less
100% screen efficiency : not practical possible
Trommel Screens
Effect of feed rate on effectiveness
The effectiveness is markedly decreased by high feed rates
At low feed rates, upto point “a”, the
efficiency/effectiveness increases with feed rate.
Because: at low feed rates, the percentage of screen
openings with respect to the total screening surface
is more which increases the number of attempts for
undersize materials to pass through the screen.
With increasing feed rate: the undersize particles
stay away from the access of screen opening for a
considerable time, causing rapid decrease in
effectiveness/efficiency
With the increase in screen length, the effectiveness increases.
The effectiveness is markedly decreased by high feed rates
At low feed rates, upto point “a”, the
efficiency/effectiveness increases with feed rate.
Because: at low feed rates, the percentage of screen
openings with respect to the total screening surface
is more which increases the number of attempts for
undersize materials to pass through the screen.
With increasing feed rate: the undersize particles
stay away from the access of screen opening for a
considerable time, causing rapid decrease in
effectiveness/efficiency
With the increase in screen length, the effectiveness increases.
Capacity of screening operations
Mass of material that can be treated pe unit time to a unit area of the screen to
satisfactorily perform the desired size separation.
Ideal Screening Process
The ideal screen process is the one which separates the feed mixture in such a way
that all the oversize particles in feed go to over flow and all the undersize particles go
to the underflow streams
This process makes the separation between oversize and undersize particles around a
cut diameter, DC, which is nearly equal to the size of the screen opening.
Mass of material that can be treated pe unit time to a unit area of the screen to
satisfactorily perform the desired size separation.
Ideal Screening Process
The ideal screen process is the one which separates the feed mixture in such a way
that all the oversize particles in feed go to over flow and all the undersize particles go
to the underflow streams
This process makes the separation between oversize and undersize particles around a
cut diameter, DC, which is nearly equal to the size of the screen opening.
Ideal Screening Process
There will be sharp separation of over flow and
under flow at Dc
Under
Flow
Over flow
Actual Screening Process
Over Flow
Under
flow
The overflow is found to contain some particles
smaller than the cut diameter and underflow is found
to contain some particles larger than the cut diameter.
There will be sharp separation of over flow and
under flow at Dc
Under
Flow
Over flow
Actual Screening Process
Over Flow
Under
flow
The overflow is found to contain some particles
smaller than the cut diameter and underflow is found
to contain some particles larger than the cut diameter.
Actual Screening Process
The separation quality of an actual screening process can be judged from the overlap
zone, D between the passing and the retained materials curves.
An increased D indicates the existence of more contaminates in both the fractions
which is undesirable.
This happens in case of
➢Cohesive, fibrous and needle like particles
The separation quality of an actual screening process can be judged from the overlap
zone, D between the passing and the retained materials curves.
An increased D indicates the existence of more contaminates in both the fractions
which is undesirable.
This happens in case of
➢Cohesive, fibrous and needle like particles
Effectiveness of Screen
Screening efficiency: difficult to quantify
Effectiveness:Separation quality of a screening operation
It is a measure of the success of a screen in separating undersize
and oversize materials from a mixed feed.
The effectiveness largely depends on the product (oversize or undersize) taken
into consideration.
Effectiveness is based upon both the recovery in the product of the desired material
in the feed and the rejection from the product of the undesired material in the feed.
Effectiveness of Screen (E)= Recovery x Rejection
Screening efficiency: difficult to quantify
Effectiveness:Separation quality of a screening operation
It is a measure of the success of a screen in separating undersize
and oversize materials from a mixed feed.
The effectiveness largely depends on the product (oversize or undersize) taken
into consideration.
Effectiveness is based upon both the recovery in the product of the desired material
in the feed and the rejection from the product of the undesired material in the feed.
Effectiveness of Screen (E)= Recovery x Rejection
v
v
F (mass or mass flow rate)
D
B
X
F (Blue) Mass fraction of desired material
X
D Blue
X
B Blue
Desired material: Blue particles (Product)
Undesirable material: Red particles
Screen Effectiveness (Efficiency) and Capacity
1-X
F (red) Mass fraction of undesired material
1-X
D (Red)
1-X
B (Red)
v
F (mass or mass flow rate)
D
B
X
F (Blue) Mass fraction of desired material
X
D Blue
X
B Blue
Desired material: Blue particles (Product)
Undesirable material: Red particles
Screen Effectiveness (Efficiency) and Capacity
1-X
F (red) Mass fraction of undesired material
1-X
D (Red)
1-X
B (Red)
Screening Efficiency and Capacity
Let F, D and B be the mass (Kg) or Mass flow rate of feed, product and rejected streams
respectively
If X
F, X
D and X
B are the mass fractions of the desired material in the feed, product and
reject streams
(1-X
F), (1-X
D) and (1-X
B) will be the mass fractions of the undesired material in their
respective streams
Recovery: defined as the ratio of amount of desired material in the product to the
amount of desired materials in the feed
Rejection: defined as the amount of undesired material in the reject to the amount of
undesired material in the feed.
Recovery=
�
�
�
�
�
�
Rejection =
(�−�
�)�
(�−��)�
Let F, D and B be the mass (Kg) or Mass flow rate of feed, product and rejected streams
respectively
If X
F, X
D and X
B are the mass fractions of the desired material in the feed, product and
reject streams
(1-X
F), (1-X
D) and (1-X
B) will be the mass fractions of the undesired material in their
respective streams
Recovery: defined as the ratio of amount of desired material in the product to the
amount of desired materials in the feed
Rejection: defined as the amount of undesired material in the reject to the amount of
undesired material in the feed.
Recovery=
�
�
�
�
�
�
Rejection =
(�−�
�)�
(�−��)�
Screening Efficiency and Capacity
Effectiveness E=recovery x rejection=
(�−��)�
(�−�
�)�
x
�
�
�
�
�
�
Effectiveness E=
(�−��)
(�−�
�)
x
�
�
�
�
x (
�
�
) � (
�
�
)
The ratio D/F and B/F can be expressed in terms of mass fractions by making a material
balance around the screen
Material balance F= D+B
Material balance for desired material givesX
F F = X
D D+ X
B B
X
F F = X
D D + X
B (F-D)
(X
F- X
B) F = (X
D-X
B) D
�
�
=
�
�
−��
�
�
−��
Similarly,
�
�
=
�
�−�
�
�
�−�
�
Effectiveness E=
�−��
�−�
�
x
�
�
�
�
x
�
�
−��
�
�
−�
�
x
�
�
−��
�
�
−�
�
Mass ratio of desired to feed =
Mass ratio of undesired to feed
Effectiveness E=recovery x rejection=
(�−��)�
(�−�
�)�
x
�
�
�
�
�
�
Effectiveness E=
(�−��)
(�−�
�)
x
�
�
�
�
x (
�
�
) � (
�
�
)
The ratio D/F and B/F can be expressed in terms of mass fractions by making a material
balance around the screen
Material balance F= D+B
Material balance for desired material givesX
F F = X
D D+ X
B B
X
F F = X
D D + X
B (F-D)
(X
F- X
B) F = (X
D-X
B) D
�
�
=
�
�
−��
�
�
−��
Similarly,
�
�
=
�
�−�
�
�
�−�
�
Effectiveness E=
�−��
�−�
�
x
�
�
�
�
x
�
�
−��
�
�
−�
�
x
�
�
−��
�
�
−�
�
Mass ratio of desired to feed =
Mass ratio of undesired to feed
Example 1: A sand mixture was screened through a standard 12 mesh screen. The
mass fraction of the oversize material in feed, overflow and underflow were found to
be 0.4, 0.8 and 0.2 respectively. Calculate the screen effectiveness based on the
oversize materials
X
F = 0.4, X
D= 0.8 and X
B= 0.2
E = 0.59
Solution
Effectiveness E=
�−��
�−�
�
x
�
�
�
�
x
�
�
−��
�
�
−�
�
x
�
�
−��
�
�
−�
�
mass fraction of the oversize material in feed, overflow and underflow were found to
be 0.4, 0.8 and 0.2 respectively. Calculate the screen effectiveness based on the
oversize materials
X
F = 0.4, X
D= 0.8 and X
B= 0.2
E = 0.59
Solution
Effectiveness E=
�−��
�−�
�
x
�
�
�
�
x
�
�
−��
�
�
−�
�
x
�
�
−��
�
�
−�
�
A quartz mixture is screened through a 10 mesh screen. The cumulative screen
analysis of the feed, overflow and underflow are given in the following table.
Mesh Dp (mm) Cumulative mass fraction greater than Dp
Feed Overflow Underflow
4 4.6999 O O O
8 2.362 0.15 0.43 0
10 1.651 0.47 0.85 0.195
28 0.589 0.94 1.00 0.91
65 0.208 0.98 - 0.975
Pan - 1 - 1.00
Calculate the mass ratios of overflow to feed and underflow to feed. Also calculate
the overall effectiveness of screen
Example-2
analysis of the feed, overflow and underflow are given in the following table.
Mesh Dp (mm) Cumulative mass fraction greater than Dp
Feed Overflow Underflow
4 4.6999 O O O
8 2.362 0.15 0.43 0
10 1.651 0.47 0.85 0.195
28 0.589 0.94 1.00 0.91
65 0.208 0.98 - 0.975
Pan - 1 - 1.00
Calculate the mass ratios of overflow to feed and underflow to feed. Also calculate
the overall effectiveness of screen
Example-2
Solution
Given: X
F= 0.47, X
D= 0.85, X
B= 0.195
Mass ratio of overflow to feed =
�
�
=
�
�
−��
�
�
−��
�
�
=�.��
The mass ratio of underflow to feed =
�
�
=
�
�−�
�
�
�−�
�
�
�
= 0.58
E= 0.6692
Effectiveness E=
�−�
�
�−�
�
x
�
�
�
�
x
�
�
−�
�
�
�
−�
�
x
�
�
−�
�
�
�
−�
�
Given: X
F= 0.47, X
D= 0.85, X
B= 0.195
Mass ratio of overflow to feed =
�
�
=
�
�
−��
�
�
−��
�
�
=�.��
The mass ratio of underflow to feed =
�
�
=
�
�−�
�
�
�−�
�
�
�
= 0.58
E= 0.6692
Effectiveness E=
�−�
�
�−�
�
x
�
�
�
�
x
�
�
−�
�
�
�
−�
�
x
�
�
−�
�
�
�
−�
�
Screening Equipments
Classify: Based on size of material: Coarse: Intermediate: fine
: based on method: Stationary: Moving
Grizzly
Trommels
Vibrating
Gyratory
Banana
Classify: Based on size of material: Coarse: Intermediate: fine
: based on method: Stationary: Moving
Grizzly
Trommels
Vibrating
Gyratory
Banana
Grizzly Screens
Used for material containing large percentage of coarse particles (major application with
primary crushers)
Recommended for separating particles from 20 to 300 mm
Characterized by very high capacity up to 10
6
kg/h and low efficiency
Used for material containing large percentage of coarse particles (major application with
primary crushers)
Recommended for separating particles from 20 to 300 mm
Characterized by very high capacity up to 10
6
kg/h and low efficiency
Grizzly Screens
The slope and path of materials flow are
parallel to the length of the bars
The cross section of the bar is trapezoidal
with the wider cross section placed upwards
to prevent clogging of materials between the
bars.
The bars are set with a slope of 20 to 50 degree with horizontal, depending upon the
natural of the materials to be treated.
Consist of set of parallel bars, evenly spaced at some predetermined opening by using
spacers
The slope and path of materials flow are
parallel to the length of the bars
The cross section of the bar is trapezoidal
with the wider cross section placed upwards
to prevent clogging of materials between the
bars.
The bars are set with a slope of 20 to 50 degree with horizontal, depending upon the
natural of the materials to be treated.
Consist of set of parallel bars, evenly spaced at some predetermined opening by using
spacers
Trommel Screens
Recommended for separating particles from 6 mm to 55 mm
Applications for sizing gravels and crushed stones
Consist of rotating cylindrical frames surrounded by wire cloth screens.
The operating speed of the trommel 15 to
20 rpm or 30 to 40 % of critical speed.
Recommended for separating particles from 6 mm to 55 mm
Applications for sizing gravels and crushed stones
Consist of rotating cylindrical frames surrounded by wire cloth screens.
The operating speed of the trommel 15 to
20 rpm or 30 to 40 % of critical speed.
Trommel Screens
Vibrating Screens
Most widely used due its high capacity and efficiency
Consist of plane screening surface which is made to vibrate rapidly by some mechanism
The screening surfaces are set in a multi deck fashion either horizontally or inclined
with coarsest screen at the top
Most widely used due its high capacity and efficiency
Consist of plane screening surface which is made to vibrate rapidly by some mechanism
The screening surfaces are set in a multi deck fashion either horizontally or inclined
with coarsest screen at the top
Vibrating Screens
Vibrating Screens
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