Unit-2.pdfnssnsnsnsnssnsnsnsnsnsnsnsnsnsns
BhuviPandey
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Mar 05, 2025
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About This Presentation
xxxxxxx
Slide Content
Mixing of Solids: Types of mixers, mixing index. Mixers for free flowing solids
Mixing of paste: Dispersive mixing and distributive mixing
Agitation of low viscosity particle suspensions: axial flow impellers, radial flow
impellers, unbaffled tanks, baffled tanks, basic idea for designing agitators.
power consumption in agitation.
CH-206: Mechanical Operations
Unit-2
Mixing of paste: Dispersive mixing and distributive mixing
Agitation of low viscosity particle suspensions: axial flow impellers, radial flow
impellers, unbaffled tanks, baffled tanks, basic idea for designing agitators.
power consumption in agitation.
CH-206: Mechanical Operations
Unit-2
Mixing
Defined as a process that tends to result in a randomization of dissimilar particles
within a system
Random distribution of two initially separated phase
Defined as a process that tends to result in a randomization of dissimilar particles
within a system
Random distribution of two initially separated phase
Mixing is concerned with all combination of phases such as
Gas with gas
Gas with liquids: dispersion
Liquid into gases: spraying
Liquids with liquids: dissolution, emulsification, dispersion
Liquid with granular solids: suspension
Paste with each other and with solids
Solids with solids: mixing of powders
Mixing
Blending: combination
of things in a unified
manner
Gas with gas
Gas with liquids: dispersion
Liquid into gases: spraying
Liquids with liquids: dissolution, emulsification, dispersion
Liquid with granular solids: suspension
Paste with each other and with solids
Solids with solids: mixing of powders
Mixing
Blending: combination
of things in a unified
manner
Solid-Solid Mixing
Mixing of product for homogenization of
quality or reduction of variance
Coating of Cohesive components onto a carrier particle
Nature of application and process requirement will dictate the selection and specification
of mixing equipment
Mixing of product for homogenization of
quality or reduction of variance
Coating of Cohesive components onto a carrier particle
Nature of application and process requirement will dictate the selection and specification
of mixing equipment
Type of Mixtures
Perfect Mixture /Ideal mixture
Random Mixture
When two non interacting components with similar
properties (size, shape, elasticity) are mixed in a mixer,
reach in a state in which there is a
✓probability of finding the particles of a given
components the same at all points in the mixture
✓the same ratio of component in the entire mixture.
Alternate arrangement of blue and red particles will create ideal mixture
Perfect Mixture /Ideal mixture
Random Mixture
When two non interacting components with similar
properties (size, shape, elasticity) are mixed in a mixer,
reach in a state in which there is a
✓probability of finding the particles of a given
components the same at all points in the mixture
✓the same ratio of component in the entire mixture.
Alternate arrangement of blue and red particles will create ideal mixture
Type of Mixtures
Random Mixture
Statical process: each particle (blue or red) has 50:50
to arrange themselves alternative
✓For particles with different physical properties
✓In the presence of significant interparticle forces (Vander wall, electrostatic, Cohesive)
Random mix can not achieved
Random Mixture
Statical process: each particle (blue or red) has 50:50
to arrange themselves alternative
✓For particles with different physical properties
✓In the presence of significant interparticle forces (Vander wall, electrostatic, Cohesive)
Random mix can not achieved
Type of Mixtures
Ordered Mixture
When two interacting components are mixed together, a structure or order can build
up into the mixture.
The units ordered could be a result of agglomeration or cohesion of one component
to the other.
Apply sufficient energy to break any agglomerate of cohesive fraction and distributing it
on available site on the carrier particles
The available sites should be sufficient to hold the cohesive fraction, otherwise, the
cohesive particles can re-agglomerate.
Ensuring randomization of carrier particles
Ordered Mixture
When two interacting components are mixed together, a structure or order can build
up into the mixture.
The units ordered could be a result of agglomeration or cohesion of one component
to the other.
Apply sufficient energy to break any agglomerate of cohesive fraction and distributing it
on available site on the carrier particles
The available sites should be sufficient to hold the cohesive fraction, otherwise, the
cohesive particles can re-agglomerate.
Ensuring randomization of carrier particles
Type of Mixtures
Ordered Mixture
Ordered Mixture
Objectives of Mixing
Attainment of complete and mutual distribution of the constituent materials
Increase the contact surface thus promoting chemical and physical reactions
Attainment of complete and mutual distribution of the constituent materials
Increase the contact surface thus promoting chemical and physical reactions
Mechanisms of mixing
For mixing of powders
Application of shear force for change the position
of particles and give efficient overall movement
of particles
Change the interfacial surface area between the phases
Local shear forces are applied, this causes overall movement of powder giving efficient
mixing
However, may cause some sort of size
reduction which would be undesirable
For mixing of powders
Application of shear force for change the position
of particles and give efficient overall movement
of particles
Change the interfacial surface area between the phases
Local shear forces are applied, this causes overall movement of powder giving efficient
mixing
However, may cause some sort of size
reduction which would be undesirable
Mechanisms of mixing
Solid mixing is achieved by a combination of one or more of the following mechanisms
Convective mixing
Transfer of groups of particles takes place from one location to another by means of blades
or paddles in the mixture
Shear mixing
Slip planes are set up within the mass
Diffusive mixing
Mixing occurs by diffusion process by random movement of particles within a powder
bed and cause them to change their relative position.
Solid mixing is achieved by a combination of one or more of the following mechanisms
Convective mixing
Transfer of groups of particles takes place from one location to another by means of blades
or paddles in the mixture
Shear mixing
Slip planes are set up within the mass
Diffusive mixing
Mixing occurs by diffusion process by random movement of particles within a powder
bed and cause them to change their relative position.
Factors Affecting Mixing of Solids
Particle size
Density
The particle sizes must be nearly similar
Increasing the difference in particle size will lead to segregation, since small
particles can fall through the voids between the larger particles
Constant movement of the mixer may lead to suspension of fine particles in air
The difference in densities among mixed particles will lead to segregation.
The heavy particles settle down while light ones will rise up
This is aggravated if the heavy particles are coarse and the light particles are
fine
Particle size
Density
The particle sizes must be nearly similar
Increasing the difference in particle size will lead to segregation, since small
particles can fall through the voids between the larger particles
Constant movement of the mixer may lead to suspension of fine particles in air
The difference in densities among mixed particles will lead to segregation.
The heavy particles settle down while light ones will rise up
This is aggravated if the heavy particles are coarse and the light particles are
fine
Factors Affecting Mixing of Solids
Electrostatic Charges
Charges are formed due to constant friction among the mixed particles
Similar charges repel particles from each other leading to segregation
This can be overcome by
Stopping the mixing equipment
Adding wetting agent or surface active agent which neutralize similar developed
charges on the particles
Add small quality of water and evaporate it after mixing operation completed
(if water do not affect stability of components)
Electrostatic Charges
Charges are formed due to constant friction among the mixed particles
Similar charges repel particles from each other leading to segregation
This can be overcome by
Stopping the mixing equipment
Adding wetting agent or surface active agent which neutralize similar developed
charges on the particles
Add small quality of water and evaporate it after mixing operation completed
(if water do not affect stability of components)
Factors Affecting Mixing of Solids
Capacity of mixer or volume of mixer
The mixer must allow sufficient space for dilation of bed
Overfilling reduces the efficiency and may prevent mixing entirely
Mixing Time
Optimum time of Mixing
Increasing the time of mixing will cause segregation while decreasing
the time of mixing will not complete mixing
Handling of mixer product
Mix powder should be handled in such a way that segregation is minimized
Capacity of mixer or volume of mixer
The mixer must allow sufficient space for dilation of bed
Overfilling reduces the efficiency and may prevent mixing entirely
Mixing Time
Optimum time of Mixing
Increasing the time of mixing will cause segregation while decreasing
the time of mixing will not complete mixing
Handling of mixer product
Mix powder should be handled in such a way that segregation is minimized
Types of Mixers: Non cohesive solids/free flowing solids
Ribbon Blender/ Agitator Mixer
Ribbon Blender/ Agitator Mixer
Ribbon Blender/ Agitator Mixer
Ribbon Blender/ Agitator Mixer
Tumbler Mixer
Tumbler Mixer
Measurement of Extent of Mixing
Degree of Mixing : Mixing Index
Degree of Mixing : Mixing Index
Degree of Mixing: Mixing Index
Mixing Process begins with the components put together in some container with a
suitable mixing device
With progress of mixing, if samples are taken at different time intervals and
analysed
The proportions of the components need to be approximately equal to the overall
proportion of the components in the container
Complete mixing can be achieved when all
samples tested are found to contain the
components in the same proportion as in the
entire mixture
Mixing Process begins with the components put together in some container with a
suitable mixing device
With progress of mixing, if samples are taken at different time intervals and
analysed
The proportions of the components need to be approximately equal to the overall
proportion of the components in the container
Complete mixing can be achieved when all
samples tested are found to contain the
components in the same proportion as in the
entire mixture
Degree of Mixing: Mixing Index
The statistical variation in composition among samples withdrawn at any time from a
mix is used as a measure of the degree of mixing
The standard deviation or the variance
2
Particulate material cannot attain the perfect mixing, and the best that can be obtained
is a degree of randomness in which two similar particles may well be side by side
Uniform mosaic Overall but not point uniform in Mix
The statistical variation in composition among samples withdrawn at any time from a
mix is used as a measure of the degree of mixing
The standard deviation or the variance
2
Particulate material cannot attain the perfect mixing, and the best that can be obtained
is a degree of randomness in which two similar particles may well be side by side
Uniform mosaic Overall but not point uniform in Mix
Degree of Mixing: Mixing Index
A mixture in which one component is randomly distributed through another is said
to be completely mixed.
Consider a mixture of component A and B from which N spot samples, each
containing n particles are taken and analyzed
1 2 3 4 5
A mixture in which one component is randomly distributed through another is said
to be completely mixed.
Consider a mixture of component A and B from which N spot samples, each
containing n particles are taken and analyzed
1 2 3 4 5
In the mixture, the value of x
i in the various spot samples will not be the same.
There is always some chance that a sample drawn from a random mixture will contain a
larger(or small) proportion of one kind of particles than the population from which it was
taken.
=
σ
�=�
�
�
�−�
�
�−�
Where x
i= number fraction of A in each fraction
x= average value of measured number fraction
Degree of Mixing: Mixing Index
The extent of mixing at a particular instant can be expressed in terms of the deviation
of the sample composition from the mean composition of the overall mixture
Mathematically expressed,
i in the various spot samples will not be the same.
There is always some chance that a sample drawn from a random mixture will contain a
larger(or small) proportion of one kind of particles than the population from which it was
taken.
=
σ
�=�
�
�
�−�
�
�−�
Where x
i= number fraction of A in each fraction
x= average value of measured number fraction
Degree of Mixing: Mixing Index
The extent of mixing at a particular instant can be expressed in terms of the deviation
of the sample composition from the mean composition of the overall mixture
Mathematically expressed,
Degree of Mixing: Mixing Index
The theoretical standard deviation
r for completely random mixture is given by
??????
�=
?????? (�−??????)
�
Where = overall mass fraction of type A particles
n = number of particles in each sample
The standard deviation for the mixture
o,
??????
�=?????? (�−??????) Where, = overall mass fraction of component A in the mix
At initial stage of Mixing
For very small sized particles, the value of n is very large n=
The theoretical standard deviation
r for completely random mixture is given by
??????
�=
?????? (�−??????)
�
Where = overall mass fraction of type A particles
n = number of particles in each sample
The standard deviation for the mixture
o,
??????
�=?????? (�−??????) Where, = overall mass fraction of component A in the mix
At initial stage of Mixing
For very small sized particles, the value of n is very large n=
M = 0 for an unmixed material and 1 for a completely randomized material
KRAMERS
Mixing Index (M)=
??????
�
�
−??????
�
??????
�
�
−??????
�
�
Degree of Mixing: Mixing Index
2
= Variance
KRAMERS
Mixing Index (M)=
??????
�
�
−??????
�
??????
�
�
−??????
�
�
Degree of Mixing: Mixing Index
2
= Variance
Example-1
Fine Particles of sodium bisulphite (NaHSO
3) at a rate of 5 weight % is to be mixed to sodium sulphite
(Na
2SO
3) to make a 100 Kg batch for a particular process. With the sample of NaHSO
3 compositions
express as percentage of NaHSO
3 in 100 gm samples taken after 5 and 10 minutes given below, Find the
value of the mixing Index.
After 5
min, %
NaHSO
3
0 16.5 3.2 2.2 12.6 9.6 0.2 4.6 0.5 8.5
After 10
Min, %
NaHSO
3
3.4 8.3 7.2 6.0 4.3 5.2 6.7 2.6 4.3 2.0
Solution
After 5 min, the composition of NaHSO
3 in the sample can be expressed in mass
fraction
Xi = 0, 0.165, 0.032, 0.022, 0.126, 0.096, 0.002, 0.046, 0. 005, 0.085
N= 10, X( mean)= 0.0579
2
(5 Min)= 0.003297 =
σ
�=�
�
�
�−�
�
�−�
Fine Particles of sodium bisulphite (NaHSO
3) at a rate of 5 weight % is to be mixed to sodium sulphite
(Na
2SO
3) to make a 100 Kg batch for a particular process. With the sample of NaHSO
3 compositions
express as percentage of NaHSO
3 in 100 gm samples taken after 5 and 10 minutes given below, Find the
value of the mixing Index.
After 5
min, %
NaHSO
3
0 16.5 3.2 2.2 12.6 9.6 0.2 4.6 0.5 8.5
After 10
Min, %
NaHSO
3
3.4 8.3 7.2 6.0 4.3 5.2 6.7 2.6 4.3 2.0
Solution
After 5 min, the composition of NaHSO
3 in the sample can be expressed in mass
fraction
Xi = 0, 0.165, 0.032, 0.022, 0.126, 0.096, 0.002, 0.046, 0. 005, 0.085
N= 10, X( mean)= 0.0579
2
(5 Min)= 0.003297 =
σ
�=�
�
�
�−�
�
�−�
Example-1
0
2
= (0.05) (1-0.05)= 0.0475
r
2
= (0.05) (1-0.05)/ N= 0.0475/ N Since number of particles are large, N=
r
2
= 0
Mixing Index after 5 Min=
??????
�
�
−??????
�
??????
�
�
−??????
�
�
= 0.9305
=
�.����−�.������
�.����
After 10 min, the composition of NaHSO
3 in the sample can be expressed in mass
fraction
Xi = 0.034, 0.083, 0.072, 0.06, 0.043, 0.052, 0.067, 0.026, 0.043, 0.02
N= 10, X( mean)= 0.05
2
(10 Min)= 0.00042
Mixing Index after 10 Min=
�.����−�.�����
�.����
= 0.991
0
2
= (0.05) (1-0.05)= 0.0475
r
2
= (0.05) (1-0.05)/ N= 0.0475/ N Since number of particles are large, N=
r
2
= 0
Mixing Index after 5 Min=
??????
�
�
−??????
�
??????
�
�
−??????
�
�
= 0.9305
=
�.����−�.������
�.����
After 10 min, the composition of NaHSO
3 in the sample can be expressed in mass
fraction
Xi = 0.034, 0.083, 0.072, 0.06, 0.043, 0.052, 0.067, 0.026, 0.043, 0.02
N= 10, X( mean)= 0.05
2
(10 Min)= 0.00042
Mixing Index after 10 Min=
�.����−�.�����
�.����
= 0.991
The performance of a solids mixer was assessed by calculating the variance occurring
in the mass fraction of a component amongst a selection of samples withdrawn from
the mixture. The quality was tested at intervals of 30 s and the data obtained are:
Example-2
sample
variance
0.025 0.006 0.015 0.018 0.019
mixing
time (s)
30 60 90 120 150
If the component analysed represents 20 per cent of the mixture by mass and each of
the samples removed contains approximately 100 particles, comment on the quality of
the mixture produced and present the data in graphical form showing the variation of
the mixing index with time.
in the mass fraction of a component amongst a selection of samples withdrawn from
the mixture. The quality was tested at intervals of 30 s and the data obtained are:
Example-2
sample
variance
0.025 0.006 0.015 0.018 0.019
mixing
time (s)
30 60 90 120 150
If the component analysed represents 20 per cent of the mixture by mass and each of
the samples removed contains approximately 100 particles, comment on the quality of
the mixture produced and present the data in graphical form showing the variation of
the mixing index with time.
Solution
For a completely unmixed system:
??????
�
�=??????�−??????Where, = overall mass fraction of component A in the mix
Here, = 20% = 0.20
??????
�
�=??????�−??????= 0.20 (1-0.20)= 0.16
For a completely random mixture
??????
�
�=
?????? (�−??????)
�
={0.20 (1-0.20)}/100 =0.0016
The degree of mixing M
�=
??????
�
�
−??????
�
??????
�
�
−??????
�
�
�=
�.��−??????
�
�.��−�.����
For a completely unmixed system:
??????
�
�=??????�−??????Where, = overall mass fraction of component A in the mix
Here, = 20% = 0.20
??????
�
�=??????�−??????= 0.20 (1-0.20)= 0.16
For a completely random mixture
??????
�
�=
?????? (�−??????)
�
={0.20 (1-0.20)}/100 =0.0016
The degree of mixing M
�=
??????
�
�
−??????
�
??????
�
�
−??????
�
�
�=
�.��−??????
�
�.��−�.����
sample variance (
2
)0.0250.0060.015 0.018 0.019
mixing time (s) 30 60 90 120 150
Degree of mixing (b)0.8520.9720.915 0.896 0.890
Solution
the degree of mixing is a
maximum at t = 60s.
2
)0.0250.0060.015 0.018 0.019
mixing time (s) 30 60 90 120 150
Degree of mixing (b)0.8520.9720.915 0.896 0.890
Solution
the degree of mixing is a
maximum at t = 60s.
Rate of Mixing
The rate of mixing
��
��
=� (�−�)
Where, M = mixing index and K constant
K depends on the type of mixing
equipment and operating conditions
න
�
�
��
(�−�)
=�න
�
�
��
�=�−�
−��
The rate of mixing
��
��
=� (�−�)
Where, M = mixing index and K constant
K depends on the type of mixing
equipment and operating conditions
න
�
�
��
(�−�)
=�න
�
�
��
�=�−�
−��
Example-3
For the preparation of soup powder, a mixture of dry vegetables and starch in the initial
proportion of 35:65 is put to a batch mixer for blending. After 4 minutes, the variance of
the sample compositions measures in terms of fractional composition was 0.07. How
long should the mixing continue so as to reach the specified maximum sample
composition variance for a 25 particle sample 0.02?. Assume the size of starch and
dried vegetable particles to be almost equal.
Solution Fraction content of dried vegetable µ= 0.35
1-µ = 0.65
2
0= µ (1-µ) = 0.2275
2
r=
?????? (�−??????)
�
= 0.0091=
�.����
��
Mixing index
after 4 minute
Mixing Index (M)=
??????
�
�
−??????
�
??????
�
�
−??????
�
�
=
�.����−�.��
�.����−�.����
=0.721
For the preparation of soup powder, a mixture of dry vegetables and starch in the initial
proportion of 35:65 is put to a batch mixer for blending. After 4 minutes, the variance of
the sample compositions measures in terms of fractional composition was 0.07. How
long should the mixing continue so as to reach the specified maximum sample
composition variance for a 25 particle sample 0.02?. Assume the size of starch and
dried vegetable particles to be almost equal.
Solution Fraction content of dried vegetable µ= 0.35
1-µ = 0.65
2
0= µ (1-µ) = 0.2275
2
r=
?????? (�−??????)
�
= 0.0091=
�.����
��
Mixing index
after 4 minute
Mixing Index (M)=
??????
�
�
−??????
�
??????
�
�
−??????
�
�
=
�.����−�.��
�.����−�.����
=0.721
�=�−�
−��
t= 4 min= 240 s
M= 0.721
K = 0.005317
target variance = 0.02
Mixing index (M’)=
??????
�
�
−??????
�
??????
�
�
−??????
�
�
=
�.����−�.��
�.�����−�.����
= 0.95
0.95=�−�
−�.������ �
t = 563 s
Additional time of mixing = 563-240= 323s
−��
t= 4 min= 240 s
M= 0.721
K = 0.005317
target variance = 0.02
Mixing index (M’)=
??????
�
�
−??????
�
??????
�
�
−??????
�
�
=
�.����−�.��
�.�����−�.����
= 0.95
0.95=�−�
−�.������ �
t = 563 s
Additional time of mixing = 563-240= 323s
Cohesive Solids: Mechanism of mixing
Paste, plastic materials, rubber/elastomersVery high viscosity liquids
Case-1: mixing of two highly viscous liquids
stretching
Folding
Cutting &
stacking
or
Mixing of paste :by exchange of layer
:Enhancement of interfacial surface area
Paste, plastic materials, rubber/elastomersVery high viscosity liquids
Case-1: mixing of two highly viscous liquids
stretching
Folding
Cutting &
stacking
or
Mixing of paste :by exchange of layer
:Enhancement of interfacial surface area
Cohesive Solids: Mechanism of mixing
Case -2Mixing of paste with solid filler
Case -2Mixing of paste with solid filler
Cohesive Solids: Machines
Two Roll Mill
Two Roll Mill
Two Roll Mill
Two Roll Mill
Internal batch Mixer
Internal batch Mixer
Tangential Intermeshing
Tangential Intermeshing
Double Arm Kneaders/ Blade mixers
Double Arm Kneaders/ Blade mixers
https://www.youtube.com/watch?v=1fWI1MIu80k
https://www.youtube.com/watch?v=1fWI1MIu80k
Double Arm Kneaders/ Blade mixers
Double Arm Kneaders/ Blade mixers
Double Arm Kneaders/ Blade mixers
Double Arm Kneaders/ Blade mixers
Double Arm Kneaders/ Blade mixers
Liquid Liquid Mixing
Agitated Vessels
Agitation of Liquids
Agitation
Refers to induced motion of a material in a specified way {circulatory pattern} inside a
container or tank
Purposes of agitation
✓To suspend solid particles
✓To Blend miscible liquids
✓To disperse a gas through liquid in the form of small bubbles
✓To disperse a second liquid, immiscible with the first , to form an emulsion or
suspension of fine drops
✓To promote heat transfer between the liquid and a coil or jacket
Agitation
Refers to induced motion of a material in a specified way {circulatory pattern} inside a
container or tank
Purposes of agitation
✓To suspend solid particles
✓To Blend miscible liquids
✓To disperse a gas through liquid in the form of small bubbles
✓To disperse a second liquid, immiscible with the first , to form an emulsion or
suspension of fine drops
✓To promote heat transfer between the liquid and a coil or jacket
Impellers
Impeller causes the liquid to circulate through the vessel and in the end return to the
impeller
Generate currents parallel with the
axis of impeller shaft
Radial flow impellers
Generate currents in radial direction
Axial flow impellers
The blades make an
angle equal to or
less than 90° to the
driving shaft
Blades are
parallel to the
axis of the
driving shaft
Impeller causes the liquid to circulate through the vessel and in the end return to the
impeller
Generate currents parallel with the
axis of impeller shaft
Radial flow impellers
Generate currents in radial direction
Axial flow impellers
The blades make an
angle equal to or
less than 90° to the
driving shaft
Blades are
parallel to the
axis of the
driving shaft
Types of Impellers
Low to moderate viscosity Liquids (<10
4
cP) High viscosity liquids
✓Propellers
✓Turbines
✓High efficiency impellers
✓Helical impellers
✓Anchor agitators
Propellers
A propeller is axial flow, high speed impeller for liquids of
low viscosity.
Speed varies : Small size propeller : 1000 rpm to 1800 rpm
: Large size propeller: 400 to 800 rpm
Low to moderate viscosity Liquids (<10
4
cP) High viscosity liquids
✓Propellers
✓Turbines
✓High efficiency impellers
✓Helical impellers
✓Anchor agitators
Propellers
A propeller is axial flow, high speed impeller for liquids of
low viscosity.
Speed varies : Small size propeller : 1000 rpm to 1800 rpm
: Large size propeller: 400 to 800 rpm
Propellers
Propellers
Diameter is the distance across the circle made by the blade tips
as the propeller rotates
A revolving propeller traces out a helix in the fluid
Pitch is the distance that a propeller would move liquid in
one revolution
One full revolution would move the liquid longitudinally a
fixed distance depending on the angle of inclination of the
propeller blade
The ratio of longitudinally fix distance (Pitch) to the
propeller diameter is known as pitch ratio of propeller
Diameter is the distance across the circle made by the blade tips
as the propeller rotates
A revolving propeller traces out a helix in the fluid
Pitch is the distance that a propeller would move liquid in
one revolution
One full revolution would move the liquid longitudinally a
fixed distance depending on the angle of inclination of the
propeller blade
The ratio of longitudinally fix distance (Pitch) to the
propeller diameter is known as pitch ratio of propeller
Propellers
A propeller with a pitch ratio of 1 is called as square pitch
Maximum diameter: 18 inch
A propeller with a pitch ratio of 1 is called as square pitch
Maximum diameter: 18 inch
Propellers
The direction of rotation:
✓chosen to force the liquid downwards
✓the flow currents leaving the impeller continue until
deflected by the floor of the vessel.
propeller blades vigorously cut or shear the liquid
In deep tank two or more propellers may be mounted on
the same shaft, usually directing the liquid in the same
direction
The direction of rotation:
✓chosen to force the liquid downwards
✓the flow currents leaving the impeller continue until
deflected by the floor of the vessel.
propeller blades vigorously cut or shear the liquid
In deep tank two or more propellers may be mounted on
the same shaft, usually directing the liquid in the same
direction
Turbines
A turbine consists of a circular disc or central hub to
which a number of short blades are attached.
The blades may be straight or curved
The diameter of the turbine ranges from 30-50%
of the diameter of the vessel
Turbines rotates at a lower speed than the
propellers (50-200 rpm)
Flat blade turbines produced radial and
tangential flow but as the speed increases
radial flow dominates
Radial flow pattern
A turbine consists of a circular disc or central hub to
which a number of short blades are attached.
The blades may be straight or curved
The diameter of the turbine ranges from 30-50%
of the diameter of the vessel
Turbines rotates at a lower speed than the
propellers (50-200 rpm)
Flat blade turbines produced radial and
tangential flow but as the speed increases
radial flow dominates
Radial flow pattern
Turbines
The simple straight blade turbine pushes the liquid radially
and tangentially with almost no vertical motion at the
impeller.
The current it generates travel outwards to the vessel
wall and then flow either upwards or downward.
It is also known as Paddles
Speed: 20 to 150 rpm
The simple straight blade turbine pushes the liquid radially
and tangentially with almost no vertical motion at the
impeller.
The current it generates travel outwards to the vessel
wall and then flow either upwards or downward.
It is also known as Paddles
Speed: 20 to 150 rpm
High Efficiency Impellers
Variation in pitched blade turbine have been developed to provide more uniform
axial flow and better mixing as well as to reduce the power required for a given
flow rate
High efficiency impellers has three blades that are crimped to decrease the blade
angle near the tip.
High Efficiency impellersPitched Blade turbine
Used to mix low or moderate viscosity liquids
Variation in pitched blade turbine have been developed to provide more uniform
axial flow and better mixing as well as to reduce the power required for a given
flow rate
High efficiency impellers has three blades that are crimped to decrease the blade
angle near the tip.
High Efficiency impellersPitched Blade turbine
Used to mix low or moderate viscosity liquids
Impellers for Highly Viscous Liquids
For viscosities above 20 Pa. s
Helical Ribbon Impeller
The diameter of the helix is very
close to the inside diameter of
tank
Provide liquid motion all the way
to the tank wall
Used upto viscosities : 25000 Pa.s
Double flight helical
ribbon impeller
Single flight helical
ribbon Impeller
For viscosities above 20 Pa. s
Helical Ribbon Impeller
The diameter of the helix is very
close to the inside diameter of
tank
Provide liquid motion all the way
to the tank wall
Used upto viscosities : 25000 Pa.s
Double flight helical
ribbon impeller
Single flight helical
ribbon Impeller
Impellers for Highly Viscous Liquids
Anchor Impeller
Provide good agitation near the
floor of the tank
It is not creating vertical motion, less effective mixer than helical ribbon
Promote good heat transfer to
or from the vessel wall
Anchor Impeller
Provide good agitation near the
floor of the tank
It is not creating vertical motion, less effective mixer than helical ribbon
Promote good heat transfer to
or from the vessel wall
Flow Pattern in Agitation Vessel
The Flow Pattern in agitated vessels depends on the following factors;
✓Type of Impeller
✓Characteristics of the fluid (Viscosity)
✓ Size and Proportions of the tank
✓ Baffles
The velocity of the fluid at any point in the tank has three components and overall flow
pattern in the tank depends on the variations in these three components
✓Radial Component (It acts in a direction perpendicular to the
shaft of the impeller)
✓Axial or Longitudinal Component (It acts in a direction
parallel with the shaft)
✓Tangential / Rotational Component (It acts in a direction
tangent to a circular path around the shaft)
The Flow Pattern in agitated vessels depends on the following factors;
✓Type of Impeller
✓Characteristics of the fluid (Viscosity)
✓ Size and Proportions of the tank
✓ Baffles
The velocity of the fluid at any point in the tank has three components and overall flow
pattern in the tank depends on the variations in these three components
✓Radial Component (It acts in a direction perpendicular to the
shaft of the impeller)
✓Axial or Longitudinal Component (It acts in a direction
parallel with the shaft)
✓Tangential / Rotational Component (It acts in a direction
tangent to a circular path around the shaft)
Axial Radial Tangential
Flow Pattern in Agitation Vessel
Flow Pattern in Agitation Vessel
Flow Pattern in Agitation Vessel
Vertically Mounted Shaft
Radial and Tangential components are in horizontal plane
Longitudinal component is in vertical plane
Radial and longitudinal are useful for mixing action
Tangential component is generally disadvantageous
Tangential component follows a circular path around
the shaft and creates a vortex in the liquid.
In an un baffled vessel circulatory flow is induced by
all types of impellers i.e. axial or radial
Vertically Mounted Shaft
Radial and Tangential components are in horizontal plane
Longitudinal component is in vertical plane
Radial and longitudinal are useful for mixing action
Tangential component is generally disadvantageous
Tangential component follows a circular path around
the shaft and creates a vortex in the liquid.
In an un baffled vessel circulatory flow is induced by
all types of impellers i.e. axial or radial
Flow Pattern in Agitation Vessel
For strong swirling, flow pattern is same regardless of
design of Impeller and at high speed the vortex may be
so deep to reach at the impeller surface.
If the solid particles are present in the liquid, circulatory
currents tends to throw the particles to the outside by
centrifugal force and they move downward and to the
Centre of the tank at the bottom.
For strong swirling, flow pattern is same regardless of
design of Impeller and at high speed the vortex may be
so deep to reach at the impeller surface.
If the solid particles are present in the liquid, circulatory
currents tends to throw the particles to the outside by
centrifugal force and they move downward and to the
Centre of the tank at the bottom.
Prevention of swirling
Swirling or circulatory flow can be prevented by any of three ways
In small tanks the impeller can be mounted off
center (shaft is moved away from center then tilted
in a plane perpendicular to the direction of move)
In Large tanks, the agitator may be mounted in the
side of the tank with shaft in horizontal plane but
at an angle with radius.
In large tanks with vertical agitators, swirling can
be prevented by installing baffles.
Swirling or circulatory flow can be prevented by any of three ways
In small tanks the impeller can be mounted off
center (shaft is moved away from center then tilted
in a plane perpendicular to the direction of move)
In Large tanks, the agitator may be mounted in the
side of the tank with shaft in horizontal plane but
at an angle with radius.
In large tanks with vertical agitators, swirling can
be prevented by installing baffles.
Prevention of swirling
Effect on Mixing: off center impeller and Baffled
Four baffles are sufficient to prevent swirling and vortex formation (Even two
have a strong effect on swirling effect).
For turbines, width of baffle need to be no more than one-tweflth of vessel
diameter and for propellers no more than one eighteenth of tank diameter.
No baffles are required for side entering, inclined or off center propellers
Prevention of swirling
Once the swirling is stopped, the specific flow pattern in the vessel depends on
the type of impeller
have a strong effect on swirling effect).
For turbines, width of baffle need to be no more than one-tweflth of vessel
diameter and for propellers no more than one eighteenth of tank diameter.
No baffles are required for side entering, inclined or off center propellers
Prevention of swirling
Once the swirling is stopped, the specific flow pattern in the vessel depends on
the type of impeller
Draft tubes
Draft tube is a cylindrical duct slightly larger than the impeller diameter and is positioned
around the impeller
Used with axial impellers to direct the suction and discharge flows.
They are particularly useful for tall
vessels having large ratio of height to
diameter.
Draft tube is a cylindrical duct slightly larger than the impeller diameter and is positioned
around the impeller
Used with axial impellers to direct the suction and discharge flows.
They are particularly useful for tall
vessels having large ratio of height to
diameter.
Static mixers can also be used to mix gas streams, disperse gas into liquid or blend
immiscible liquids.
Static mixers are used in continuous processes where they homogenize fluids with
no moving parts.
Static Mixer
Pumps or blowers are used to deliver the components to be mixed at the desired
volumetric flow rates and to also supply the pressure energy required for mixing.
immiscible liquids.
Static mixers are used in continuous processes where they homogenize fluids with
no moving parts.
Static Mixer
Pumps or blowers are used to deliver the components to be mixed at the desired
volumetric flow rates and to also supply the pressure energy required for mixing.
Static Mixer
Static Mixer
Design of Agitated Vessel
Standard agitated vessel Design
�
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=
�
�
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=
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=�
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=
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=
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=
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�
Number of baffles :4
Number of impeller blade: 3-16
Standard agitated vessel Design
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=
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=
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=�
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=
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=
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=
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Number of baffles :4
Number of impeller blade: 3-16
Shape factors
Various linear measurements can all be converted to dimensionless ratios ,called “shape
factors”, by dividing each of them by one of their number which is arbitrarily chosen as a
basis..
Let the shape factors, so defined, be denoted by S
1, S
2 ,S
3 ,……………S
n. (the diameter of the
impeller ,D
I ,is taken as base measurement.
Two mixers of the same geometrical proportions throughout but of different sizes will
have identical shape factors but will differ in magnitude of D
I. Devices meeting these
requirements are called geometrically similar.
Diameter of tank, D
t, or the diameter of impeller, D
I, are the suitable choices for the base
measurement
Design of Agitated Vessel
Various linear measurements can all be converted to dimensionless ratios ,called “shape
factors”, by dividing each of them by one of their number which is arbitrarily chosen as a
basis..
Let the shape factors, so defined, be denoted by S
1, S
2 ,S
3 ,……………S
n. (the diameter of the
impeller ,D
I ,is taken as base measurement.
Two mixers of the same geometrical proportions throughout but of different sizes will
have identical shape factors but will differ in magnitude of D
I. Devices meeting these
requirements are called geometrically similar.
Diameter of tank, D
t, or the diameter of impeller, D
I, are the suitable choices for the base
measurement
Design of Agitated Vessel
Design of Agitated Vessel
Power consumption in agitation of Impeller: Important Aspect
Power required to rotate a given impeller,
✓empirical correlations of power with variables of the system
✓represented in dimensionless form.
Power consumption in agitation of Impeller: Important Aspect
Power required to rotate a given impeller,
✓empirical correlations of power with variables of the system
✓represented in dimensionless form.
✓Measurements of tank and impeller
✓The distance of the impeller from the tank floor
✓The liquid depth
✓Dimension of baffles
✓Number of baffles and the number of blades in the
impeller
✓Viscosity of liquid
✓Density of liquid
✓Speed n
Process
Variables
✓Acceleration of due to gravity “g”
✓Absence / presence of swirling
Power Consumption in Agitation
Factors which can affect the Power consumption
Vessel
design
✓The distance of the impeller from the tank floor
✓The liquid depth
✓Dimension of baffles
✓Number of baffles and the number of blades in the
impeller
✓Viscosity of liquid
✓Density of liquid
✓Speed n
Process
Variables
✓Acceleration of due to gravity “g”
✓Absence / presence of swirling
Power Consumption in Agitation
Factors which can affect the Power consumption
Vessel
design
Power Consumption in Agitation
Power consumption: Low viscosity Newtonian fluids
For Baffled tank
= viscosity of the liquid, N.s/m
2
= density of the liquid, Kg/m
3
D
I = diameter of impeller, m
N= rotational speed of the impeller, rps
D
t= diameter of tank/vessel, m
P= power input to impeller or power consumption by impeller, N.m/s
Power consumption in terms of dimensionless groups
??????
� �
�
�
�
�
=�
��
�
�
�
??????
,
�
�
�
�
�
,
�
�
�
�
,
�
�
�
…….
A
Where,
??????
� �
�
�
�
� = Power Number, P
o
���
�
�
??????
= Reynolds number, Re
�
�
�
�
�
= Froude number, Fr
Power consumption: Low viscosity Newtonian fluids
For Baffled tank
= viscosity of the liquid, N.s/m
2
= density of the liquid, Kg/m
3
D
I = diameter of impeller, m
N= rotational speed of the impeller, rps
D
t= diameter of tank/vessel, m
P= power input to impeller or power consumption by impeller, N.m/s
Power consumption in terms of dimensionless groups
??????
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=�
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,
�
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,
�
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,
�
�
�
…….
A
Where,
??????
� �
�
�
�
� = Power Number, P
o
���
�
�
??????
= Reynolds number, Re
�
�
�
�
�
= Froude number, Fr
Power Consumption in Agitation
??????
� �
�
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�
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=�
���
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,
�
�
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�
,
�
�
�
�
,
�
�
�
,……….
�
�
�
�
,
�
�
�
are shape factors or dimensionless length ratios, relate to
specific impeller vessel arrangement
For Specific vessel-impeller combination
??????
� �
�
�
�
�
=�
���
�
�
??????
,
�
�
�
�
�
P
o = f(Re, Fr)
As power law function, the equation is
P
o= K Re
m
Fr
n B
Value of K, m and r : Obtained from
experimental measurements which depends on
impeller- vessel configuration and the nature of
flow (laminar/turbulent/transition) prevailing
in the mixer.
??????
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�
�
�
�
=�
���
�
�
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,
�
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,
�
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�
�
,
�
�
�
,……….
�
�
�
�
,
�
�
�
are shape factors or dimensionless length ratios, relate to
specific impeller vessel arrangement
For Specific vessel-impeller combination
??????
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=�
���
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,
�
�
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�
�
P
o = f(Re, Fr)
As power law function, the equation is
P
o= K Re
m
Fr
n B
Value of K, m and r : Obtained from
experimental measurements which depends on
impeller- vessel configuration and the nature of
flow (laminar/turbulent/transition) prevailing
in the mixer.
Power Consumption in Agitation
It is the ratio of inertial forces to viscous forces within a fluid which is subjected to
relative internal movement due to different fluid velocities.
Reynolds's number
Re =
���
�
�
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=
��
�
�
�
�
??????
??????
�
�
�
��
??????
Where u
2= Impeller tip speed = nπD
I
Reynolds's number calculated from the diameter and peripheral speed of impeller
✓It’s the ratio of drag force acting on a unit area of impeller and the inertial stresses.
✓It is analogous to a friction factor or a drag coefficient
Power number or Newton number
??????
� �
�
�
�
�
=??????
�=��
It is the ratio of inertial forces to viscous forces within a fluid which is subjected to
relative internal movement due to different fluid velocities.
Reynolds's number
Re =
���
�
�
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=
��
�
�
�
�
??????
??????
�
�
�
��
??????
Where u
2= Impeller tip speed = nπD
I
Reynolds's number calculated from the diameter and peripheral speed of impeller
✓It’s the ratio of drag force acting on a unit area of impeller and the inertial stresses.
✓It is analogous to a friction factor or a drag coefficient
Power number or Newton number
??????
� �
�
�
�
�
=??????
�=��
Froude Number
✓Ratio of the inertial stress to the gravitational force per unit area acting on the fluid.
✓Appears in the fluid dynamic situations where there is significant wave motion on a
liquid surface.
✓Used to study the vortex motion during scale up of mixer
Power Consumption in Agitation
P
o= K Re
m
Below Reynolds number of 300, Froude number has no effect.
Froude number affects power consumption only if vortex is present
If baffles present in the tank, the Froude number is not used in the
calculations
✓Ratio of the inertial stress to the gravitational force per unit area acting on the fluid.
✓Appears in the fluid dynamic situations where there is significant wave motion on a
liquid surface.
✓Used to study the vortex motion during scale up of mixer
Power Consumption in Agitation
P
o= K Re
m
Below Reynolds number of 300, Froude number has no effect.
Froude number affects power consumption only if vortex is present
If baffles present in the tank, the Froude number is not used in the
calculations
Experimental Correlation between Power number and Reynolds number
Power Correlations For Specific Impellers
Curve A: Vertical
blades with S
4= 0.2
Curve B: similar impeller
with narrower blades
(S
4=0.125)
Curve C: For pitched
blades turbine
Curve A: Vertical
blades with S
4= 0.2
Curve B: similar impeller
with narrower blades
(S
4=0.125)
Curve C: For pitched
blades turbine
Power Correlations For Specific Impellers
Curve A: Three blade
propeller centrally
mounted in a baffle
tank.
Propellers and pitched
blade turbines draw
considerably less power
than a turbine with
vertical blades
Curve A: Three blade
propeller centrally
mounted in a baffle
tank.
Propellers and pitched
blade turbines draw
considerably less power
than a turbine with
vertical blades
At low Reylond number (less than 10), the lines of Po vs Re for both baffled and
unbaffled tank coincide and the slope of the line on logarithmic coordinates is -1
Therefore,
Po = K
L/Re
??????
�
�
�
�
�
�
= K
L / (
��
�
�
�
)
P = K
L n
2
D
I
3
The flow is laminar in this range and density is no longer a factor
Power Consumption in Agitation
P
o= K Re
m
Log Po = m Log Re + Log K
P
o= K Re
-1
K= K
L=Constant under
laminar condition
unbaffled tank coincide and the slope of the line on logarithmic coordinates is -1
Therefore,
Po = K
L/Re
??????
�
�
�
�
�
�
= K
L / (
��
�
�
�
)
P = K
L n
2
D
I
3
The flow is laminar in this range and density is no longer a factor
Power Consumption in Agitation
P
o= K Re
m
Log Po = m Log Re + Log K
P
o= K Re
-1
K= K
L=Constant under
laminar condition
In baffled Tanks at Reynolds number larger than about 10,000 the power
number is independent of the Reynolds number and viscosity is not a factor
Power number Po = Constant
Po= K
??????
�
�
�
�
�
�
= K
T
P = K
T n
3
D
I
5
K= K
T= Constant under turbulent condition
For Flow condition with Reynolds number between 10 to 10000, the values of power
number can be obtained from the Figure 9.12 and 9.13
Power Consumption in Agitation
number is independent of the Reynolds number and viscosity is not a factor
Power number Po = Constant
Po= K
??????
�
�
�
�
�
�
= K
T
P = K
T n
3
D
I
5
K= K
T= Constant under turbulent condition
For Flow condition with Reynolds number between 10 to 10000, the values of power
number can be obtained from the Figure 9.12 and 9.13
Power Consumption in Agitation
Magnitude of Constant K
T and K
L for various types of impellers and tanks
Calculation of Power Consumption
T and K
L for various types of impellers and tanks
Calculation of Power Consumption
Example-1
A disk turbine with six blades is installed centrally in a vertical baffled tank 2 m in
diameter. The turbine is 0.67 m in diameter and positioned 0.67 m above the bottom
of the tank. The turbine blades are 134 mm wide. The tank is filled to a depth 2m with
an aqueous solution of 50 % NaOH at 65° C, which has a viscosity of 12 cP and a
density of 1500 Kg/m
3
. The turbine impeller turns at 90 rpm. What power will be
required?
SolutionReynolds number
Re=
��
�
�
�
n= 90/60= 1.5 rps
D
I= 0.67 m
=12 cP= 0.012 Pa.s
= 1500 Kg/m
3
Re= 84169
Re>10
4
N
p= K
TSix flat blade turbine K
T= 5.75=5.8
P = K
T n
3
D
I
5
P= 3964.30 watt or 5.31 hp
A disk turbine with six blades is installed centrally in a vertical baffled tank 2 m in
diameter. The turbine is 0.67 m in diameter and positioned 0.67 m above the bottom
of the tank. The turbine blades are 134 mm wide. The tank is filled to a depth 2m with
an aqueous solution of 50 % NaOH at 65° C, which has a viscosity of 12 cP and a
density of 1500 Kg/m
3
. The turbine impeller turns at 90 rpm. What power will be
required?
SolutionReynolds number
Re=
��
�
�
�
n= 90/60= 1.5 rps
D
I= 0.67 m
=12 cP= 0.012 Pa.s
= 1500 Kg/m
3
Re= 84169
Re>10
4
N
p= K
TSix flat blade turbine K
T= 5.75=5.8
P = K
T n
3
D
I
5
P= 3964.30 watt or 5.31 hp
Example-2
A disk turbine with six blades is installed centrally in a vertical baffled tank 2 m in
diameter. The turbine is 0.67 m in diameter and positioned 0.67 m above the bottom
of the tank. The turbine blades are 134 mm wide. The tank is filled to a depth 2m with
rubber latex having viscosity of 120 Pa.s and a density of 1120 Kg/m
3
. The turbine
impeller turns at 90 rpm. What power will be required?
SolutionReynolds number
Re=
��
�
�
�
n= 90/60= 1.5 rps
D
I= 0.67 m
= 120 Pa.s
= 1120 Kg/m
3
Re= 6.3
Re< 10, laminar regime
P = K
L n
2
D
I
3
K
L= 65
P=5278.39 watt= 7.07 hp
A disk turbine with six blades is installed centrally in a vertical baffled tank 2 m in
diameter. The turbine is 0.67 m in diameter and positioned 0.67 m above the bottom
of the tank. The turbine blades are 134 mm wide. The tank is filled to a depth 2m with
rubber latex having viscosity of 120 Pa.s and a density of 1120 Kg/m
3
. The turbine
impeller turns at 90 rpm. What power will be required?
SolutionReynolds number
Re=
��
�
�
�
n= 90/60= 1.5 rps
D
I= 0.67 m
= 120 Pa.s
= 1120 Kg/m
3
Re= 6.3
Re< 10, laminar regime
P = K
L n
2
D
I
3
K
L= 65
P=5278.39 watt= 7.07 hp
Power Consumption in Agitation
For unbaffled Vessel
At low values of the Reynolds number below about 300, the power number Vs
Reynolds number curve for both the baffled and the unbaffled tank are identical.
At higher Reynolds number, Vortex formation being prevalent
Power consumption is influenced by the Froude number also
P
o= K Re
m
Fr
n
n=
�−���
��
??????�
�
Where a and b are the constants, and their values depends on the type of the impeller
The value of the power number obtained from Po Vs Re plot for the unbaffled tank is
multiplied with Fr
n
to get the correct value of Po, from which power consumption can
be calculated
For unbaffled Vessel
At low values of the Reynolds number below about 300, the power number Vs
Reynolds number curve for both the baffled and the unbaffled tank are identical.
At higher Reynolds number, Vortex formation being prevalent
Power consumption is influenced by the Froude number also
P
o= K Re
m
Fr
n
n=
�−���
��
??????�
�
Where a and b are the constants, and their values depends on the type of the impeller
The value of the power number obtained from Po Vs Re plot for the unbaffled tank is
multiplied with Fr
n
to get the correct value of Po, from which power consumption can
be calculated
Example-3
A flat blade turbine type impeller is installed in a vertical 1.8 m diameter tank which is
filled with 48% sodium hydroxide solution to a depth of 1.8 m. The turbine is 60 cm in
diameter and is positioned 60 cm from the bottom of tank. The turbine is operated at 90
rpm. The tank is fitted with four baffles, each having a width of 18 cm. Calculate the
power consumption for the baffled mixer.
Data : density of 48% sodium hydroxide= 1450 kg/m
3
, viscosity of solution is 10cP.
The value of power number may be approximated from the following table for Po Vs Re
Re Po
30,000 5.5
50,000 5.8
70,000 5.9
80,000 6.0
A flat blade turbine type impeller is installed in a vertical 1.8 m diameter tank which is
filled with 48% sodium hydroxide solution to a depth of 1.8 m. The turbine is 60 cm in
diameter and is positioned 60 cm from the bottom of tank. The turbine is operated at 90
rpm. The tank is fitted with four baffles, each having a width of 18 cm. Calculate the
power consumption for the baffled mixer.
Data : density of 48% sodium hydroxide= 1450 kg/m
3
, viscosity of solution is 10cP.
The value of power number may be approximated from the following table for Po Vs Re
Re Po
30,000 5.5
50,000 5.8
70,000 5.9
80,000 6.0
SolutionD
I= 0.6 m
N=90 rpm= 90/60= 1.5 rps
= 10 cP= 0.1 gm/cm.s = 0.1 x 10
-1
Kg/m.s
= 1450 Kg/m
3
Re=
����
�
??????
=
�.�
�
� �.� � ����
�.� � ��
−−
�=�����
From table, the value of Po may be taken as 6
Thus ,
??????�=
??????
� �
�
�
�
�
= 6
P= ����.��� ���� ��
�
�
=�.�� ��
746 watt= 1hp
I= 0.6 m
N=90 rpm= 90/60= 1.5 rps
= 10 cP= 0.1 gm/cm.s = 0.1 x 10
-1
Kg/m.s
= 1450 Kg/m
3
Re=
����
�
??????
=
�.�
�
� �.� � ����
�.� � ��
−−
�=�����
From table, the value of Po may be taken as 6
Thus ,
??????�=
??????
� �
�
�
�
�
= 6
P= ����.��� ���� ��
�
�
=�.�� ��
746 watt= 1hp
Example-4
The tank mentioned in example -1 is unbaffled. If all the operating conditions and tank
dimensions remain same, what will be the power consumption? Values of constant
a=1.0, b=40. Comment on your result
Solution
Re= 78300 Po= 6
The value of n
n=
�−���
��
??????�
�
=
�.�−���
��
�����
��
= -0.097
Since Re> 300, the Froude number will affect the power consumption
Fr =
�
�
�
�
�
=
�.�
�
�.�
�.��
=�.���
(Fr)
n
= (0.138)
-0.097
= 1.212
The corrected power number= power number for baffled tank x (Fr)
n
= 6 x 1.212 = 7.272
The tank mentioned in example -1 is unbaffled. If all the operating conditions and tank
dimensions remain same, what will be the power consumption? Values of constant
a=1.0, b=40. Comment on your result
Solution
Re= 78300 Po= 6
The value of n
n=
�−���
��
??????�
�
=
�.�−���
��
�����
��
= -0.097
Since Re> 300, the Froude number will affect the power consumption
Fr =
�
�
�
�
�
=
�.�
�
�.�
�.��
=�.���
(Fr)
n
= (0.138)
-0.097
= 1.212
The corrected power number= power number for baffled tank x (Fr)
n
= 6 x 1.212 = 7.272
P = 2767.27 watt or j/s = 3.7 hp
??????�=
?????? �
� �
�
�
�
�
= 7.272
The power required for the same service is more in case of an unbaffled tank a
compared to the baffled tank
??????�=
?????? �
� �
�
�
�
�
= 7.272
The power required for the same service is more in case of an unbaffled tank a
compared to the baffled tank
Scale Up of Agitation Vessel
Need for Scale Up
Experimental data: laboratory or
piolet scale
Industry scale set up
Scale up Calculations
Scale up process can be approached with diverse requirements
Geometric similarity: important and simple to achieve
Kinematic similarity: ratio of velocities or times
Dynamic similarities: fixed ratios of inertial or gravitational forces
Even if geometric similarity is achieved, dynamic and kinematic similarity cannot be
obtained at the same time
Need for Scale Up
Experimental data: laboratory or
piolet scale
Industry scale set up
Scale up Calculations
Scale up process can be approached with diverse requirements
Geometric similarity: important and simple to achieve
Kinematic similarity: ratio of velocities or times
Dynamic similarities: fixed ratios of inertial or gravitational forces
Even if geometric similarity is achieved, dynamic and kinematic similarity cannot be
obtained at the same time
Scale Up of Agitation Vessel
Objectives of scaleup operations can be different
Equal liquid motion
Equal suspension of solid
Equal power per unit volume
Scale up Procedure
Step-1
Calculate the scale up ratio R
R is defined as the cube root the volume ration for the final and initial conditions
??????=
�
�
�
�
��
v
1
V
2
Objectives of scaleup operations can be different
Equal liquid motion
Equal suspension of solid
Equal power per unit volume
Scale up Procedure
Step-1
Calculate the scale up ratio R
R is defined as the cube root the volume ration for the final and initial conditions
??????=
�
�
�
�
��
v
1
V
2
Scale Up of Agitation Vessel
V
1, D
a1, D
t1, H
1 V
2, D
a2, D
t2, H
2
�
�=
��
�
��
�
�
�
�
�=
��
�
�
��
�
�
Dt= H
�
�=
���
�
�
�
�
�=
��
��
�
�
�
�
�
�
=
�
��
�
�
��
�
=
�
��
�
�
��
�
??????=
�
�
�
�
��
R=
�
��
�
��
Step-2: using R, apply it to all the dimensions to calculate the new values
D
t2=RD
t1 H
2= RH
1 J
2= RJ
1
V
1, D
a1, D
t1, H
1 V
2, D
a2, D
t2, H
2
�
�=
��
�
��
�
�
�
�
�=
��
�
�
��
�
�
Dt= H
�
�=
���
�
�
�
�
�=
��
��
�
�
�
�
�
�
=
�
��
�
�
��
�
=
�
��
�
�
��
�
??????=
�
�
�
�
��
R=
�
��
�
��
Step-2: using R, apply it to all the dimensions to calculate the new values
D
t2=RD
t1 H
2= RH
1 J
2= RJ
1
Scale Up of Agitation Vessel
V
1, D
a1, D
t1, H
1, n
1, t
1
V
2, D
a2, D
t2, H
2, n
2, t
2
Step-3: the scale up rule is then applied to determine
the agitator speed
�
�
�
�
=
�
??????
??????
Where, =1/3 for equal liquid motion
= ¾ for equal suspension solid
= 2/3 for equal power per unit Volume
Step-4 Knowing n
2, the required power can be calculated
n
1t
1= n
2 t
2
Relationship between the speed and time of mixing
V
1, D
a1, D
t1, H
1, n
1, t
1
V
2, D
a2, D
t2, H
2, n
2, t
2
Step-3: the scale up rule is then applied to determine
the agitator speed
�
�
�
�
=
�
??????
??????
Where, =1/3 for equal liquid motion
= ¾ for equal suspension solid
= 2/3 for equal power per unit Volume
Step-4 Knowing n
2, the required power can be calculated
n
1t
1= n
2 t
2
Relationship between the speed and time of mixing
Example-5
A pilot plant vessel 0.3 m in diameter is agitated by a six blade turbine impeller 0.1 m
diameter. At Reynolds number is 10
4
, the blending time of two miscible liquids is found
to be 15 sec. The power required is 0.4 kW/m3 of liquid. What power input will be
required to give the same blending time in a vessel of 1.8 m in diameter.
Solution
The blending time remains the same i.e. blending speed is same
n
1t
1= n
2 t
2
t
1=t
2
n
1= n
2
V ��
�
Reynolds number= 10
4
, turbulent conditionP= K
T�
�
�
�
�
�
??????
�
=� �
�
�
�
�
�
A pilot plant vessel 0.3 m in diameter is agitated by a six blade turbine impeller 0.1 m
diameter. At Reynolds number is 10
4
, the blending time of two miscible liquids is found
to be 15 sec. The power required is 0.4 kW/m3 of liquid. What power input will be
required to give the same blending time in a vessel of 1.8 m in diameter.
Solution
The blending time remains the same i.e. blending speed is same
n
1t
1= n
2 t
2
t
1=t
2
n
1= n
2
V ��
�
Reynolds number= 10
4
, turbulent conditionP= K
T�
�
�
�
�
�
??????
�
=� �
�
�
�
�
�
V
1, D
a1, D
t1, H
1, n
1, t
1
V
2, D
a2, D
t2, H
2, n
2, t
2
P
1
P
2
??????
�
=� �
�
�
�
�
�
Power per unit volume for pilot scale
??????
�
�
�
=� �
�
�
�
��
�
�
??????
�
�
�
=� �
�
�
�
��
�
�
Power per unit volume for large scale vessel
൙
൘
(??????
�
�
�
)
൘
(??????
�
�
�
)
=
�
�
�
�
�
�
��
�
��
� �
��
�
��
=
�
��
�
��
=
�.�
�.�
=�
n
2=n
1
൙
൘
(??????
�
�
�
)
൘
(??????
�
�
�
)
=�
�
�
�
=���
�
�
�
=�� � �.�= ��.� ��/�
�
1, D
a1, D
t1, H
1, n
1, t
1
V
2, D
a2, D
t2, H
2, n
2, t
2
P
1
P
2
??????
�
=� �
�
�
�
�
�
Power per unit volume for pilot scale
??????
�
�
�
=� �
�
�
�
��
�
�
??????
�
�
�
=� �
�
�
�
��
�
�
Power per unit volume for large scale vessel
൙
൘
(??????
�
�
�
)
൘
(??????
�
�
�
)
=
�
�
�
�
�
�
��
�
��
� �
��
�
��
=
�
��
�
��
=
�.�
�.�
=�
n
2=n
1
൙
൘
(??????
�
�
�
)
൘
(??????
�
�
�
)
=�
�
�
�
=���
�
�
�
=�� � �.�= ��.� ��/�
�
Example-6
In order to blend vitamin concentration to molasses, a small tank of 0.6 m diameter,
0.7 m height with a propeller of 0.3 m diameter rotating at 450 rpm is used and the
mixing has been found to be satisfactory. If a large-scale plant is to be designed which
will require a tank of 1.8 m diameter, what will be the suitable values to choose for
tank depth, propeller diameter and rotational speed, if it is desired to preserve the
same mixing conditions as in the smaller unit? What would be the power requirement
for the motor driving the propeller? The viscosity of the molasses may be taken as 6.5
Ns/m
2
and its density as 1500 kg/m
3
. use K=41 and m= -1 in equation Po= K Re
m
to get
power in J/s
In order to blend vitamin concentration to molasses, a small tank of 0.6 m diameter,
0.7 m height with a propeller of 0.3 m diameter rotating at 450 rpm is used and the
mixing has been found to be satisfactory. If a large-scale plant is to be designed which
will require a tank of 1.8 m diameter, what will be the suitable values to choose for
tank depth, propeller diameter and rotational speed, if it is desired to preserve the
same mixing conditions as in the smaller unit? What would be the power requirement
for the motor driving the propeller? The viscosity of the molasses may be taken as 6.5
Ns/m
2
and its density as 1500 kg/m
3
. use K=41 and m= -1 in equation Po= K Re
m
to get
power in J/s
Solution
To preserve geometrical similarity, the dimensional ratios should
be the same in the large tank as in the small.
Given that the full-scale tank is three times the model one
Thus,
(D
T)
L = 3(D
T)s = 1.8 m (3x 0.6)
Depth of large tank H
L= 3 H
s= 3x 0.7 = 2.1 m
Propeller diameter in large tank (D
I)
L= 3 ( D
I)
s = 3 x 0.3 = 0.9 m
For dynamic similarity
(Re)
L = (Re)
s
(
����
�
??????
)
�=(
����
�
??????
)
�
(ND
I
2
)
L = (N D
I
2
)
s
N
L=
�
�
�
�
��
�
�
�
�
=�� ���Speed of impeller in large tank
To preserve geometrical similarity, the dimensional ratios should
be the same in the large tank as in the small.
Given that the full-scale tank is three times the model one
Thus,
(D
T)
L = 3(D
T)s = 1.8 m (3x 0.6)
Depth of large tank H
L= 3 H
s= 3x 0.7 = 2.1 m
Propeller diameter in large tank (D
I)
L= 3 ( D
I)
s = 3 x 0.3 = 0.9 m
For dynamic similarity
(Re)
L = (Re)
s
(
����
�
??????
)
�=(
����
�
??????
)
�
(ND
I
2
)
L = (N D
I
2
)
s
N
L=
�
�
�
�
��
�
�
�
�
=�� ���Speed of impeller in large tank
For the large tank
Re= (
����
�
??????
)
� = 155.8
Since Re< 300, the Froude number has no effect
Power number Po= K Re
m
Po= 41 (155.8)
-1
=
??????
�
�
�
�
�
�
P= 134.8 J/s
Re= (
����
�
??????
)
� = 155.8
Since Re< 300, the Froude number has no effect
Power number Po= K Re
m
Po= 41 (155.8)
-1
=
??????
�
�
�
�
�
�
P= 134.8 J/s
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