WEBVTT
00:24.539 --> 00:30.369
Welcome to the fourth week of mechanical operations
course. And today we are starting lecture
00:30.369 --> 00:37.829
1 of fourth week and which is on particle
dynamics. This lecture 1, I will complete
00:37.829 --> 00:46.059
in two parts, in part 1, I will speak on what
is particle dynamics and what is terminal
00:46.059 --> 00:51.309
settling velocity and its derivation.
In second part we will cover the effect of
00:51.309 --> 00:57.619
wall and effect of particle shape on terminal
settling velocity and further we will discuss
00:57.619 --> 01:04.180
the hindered settling. So let us start the
part 1 of lecture 1 that is the definition
01:04.180 --> 01:11.150
of particle dynamics and further topics related
to this.
01:11.150 --> 01:18.750
Now the study of particle dynamics is utilized
in a number of mechanical operations such
01:18.750 --> 01:25.939
as classification, sedimentation, elutriation,
filtration etcetera which involve relative
01:25.939 --> 01:33.050
movement of solid particle and a fluid. So
wherever solid particle as well as fluid and
01:33.050 --> 01:42.180
their relative movement is involved that kind
of study comes under particle dynamics.
01:42.180 --> 01:48.659
So this study is required as processes for
the separation of particles of various sizes
01:48.659 --> 01:55.070
and shapes often depend on the variation in
behavior of particle when they are subjected
01:55.070 --> 02:02.880
to the action of moving fluid. So basically
in particle dynamics, in using this study
02:02.880 --> 02:11.170
we will find out the distribution or the separation
of particles of different sizes and shape,
02:11.170 --> 02:17.370
but main point is those particles should be
involved in fluids.
02:17.370 --> 02:24.590
So when a solid particle falls in a liquid,
the study of change in its velocity with time
02:24.590 --> 02:31.390
when different forces are acting on it comes
under particle dynamics. So you can understand
02:31.390 --> 02:38.830
particle means solid body and dynamics means
its movement in fluid and when we consider
02:38.830 --> 02:46.319
the movement of fluid we consider the velocity
and its changes with time. So all this study
02:46.319 --> 02:51.560
comes under particle dynamics.
When a fluid flows over the solid object the
02:51.560 --> 03:00.829
velocity of fluid varies depending on the
position. So what we can say that the velocity
03:00.829 --> 03:07.730
over the particle is not uniform, it will
depend on from what side fluid is coming and
03:07.730 --> 03:14.129
what are the different sections, different
surfaces, which are in direct contact of fluid
03:14.129 --> 03:17.890
or in not direct contact with fluid.
03:17.890 --> 03:25.659
For example, if this is the solid object we
are having and fluid is moving around this,
03:25.659 --> 03:33.199
obviously fluid cannot move through this,
fluid will move around this. So when we consider
03:33.199 --> 03:41.799
the velocity it will change at different position
of the particle. So one way of representing
03:41.799 --> 03:47.709
variation in velocity is streamlines.
I guess you already know about the streamline
03:47.709 --> 03:54.309
in fluid dynamics and that we will use to
represent the variation of velocity which
03:54.309 --> 04:01.419
follow the flow path. So constant velocity
is shown by equidistant spacing of parallel
04:01.419 --> 04:08.209
streamlines. So when streamline which are
moving parallel to each other and when the
04:08.209 --> 04:15.139
distance between these lines are constant
then we can say that velocity is constant.
04:15.139 --> 04:23.030
So the slow fluid flow is called the streamline
or laminar flow. You understand what is the
04:23.030 --> 04:31.860
streamline movement in laminar flow that they
move in a suggested pattern or in a uniform
04:31.860 --> 04:40.460
pattern. So when they move in a uniform pattern
they do not cross each other then we say that
04:40.460 --> 04:43.660
this type of movement as laminar flow.
04:43.660 --> 04:50.410
However, in fast motion fluid particles cross
and re-cross the streamline and the motion
04:50.410 --> 04:56.660
is called turbulent flow. So in laminar flow
fluid is moving in a particular streamline
04:56.660 --> 05:03.480
or fluid is moving in a streamline whereas
when we considered the turbulent flow particle
05:03.480 --> 05:12.040
will cross the streamline. So the streamline
will not be uniform anymore. So the same example
05:12.040 --> 05:17.600
we are considering here also.
Now what happens when we consider the velocity
05:17.600 --> 05:26.480
at A, B, C, D point.
So we can say that the velocity and direction
05:26.480 --> 05:33.350
of flow varies around the circumference of
the particle. So at point A as well as point
05:33.350 --> 05:40.660
D, if you see this point A as well as point
D, the fluid is almost at rest at that point.
05:40.660 --> 05:47.810
Whereas when we consider point B as well as
point C the velocity is maximum.
05:47.810 --> 05:55.270
So A and D are the point where the water remains
or fluid remains at still position, at B and
05:55.270 --> 06:03.070
C it will have the maximum velocity. So you
can understand that as the movement of or
06:03.070 --> 06:09.310
as the particle will move or the fluid is
moved over the particle it will not have uniform
06:09.310 --> 06:16.400
velocity throughout the particle surface.
So as far as dynamics of single particle is
06:16.400 --> 06:17.870
concerned.
06:17.870 --> 06:25.940
When a solid particle that is single particle
falls in a liquid its motion depends on many
06:25.940 --> 06:34.500
factors such as particle size, density, surface
characteristic, viscosity of liquid etcetera.
06:34.500 --> 06:40.920
And dynamics of a solid particle in a fluid
thus depends on many parameters and their
06:40.920 --> 06:46.880
interaction or inter-relation when we study
that is very complex.
06:46.880 --> 06:53.150
Therefore, to study the dynamics of single
particle we have taken some of the assumptions
06:53.150 --> 06:57.080
and these are.
First assumption is particle is spherical
06:57.080 --> 07:06.650
in diameter and diameter we have shown with
dP. So we are considering spherical particle.
07:06.650 --> 07:13.270
Second assumption is particle is non porous
and incompressible so particle is thus insoluble
07:13.270 --> 07:22.060
in the fluid and it will be chemically inert
with the fluid, density and viscosity of fluid
07:22.060 --> 07:23.990
is constant.
07:23.990 --> 07:29.900
The effect of surface characteristics of solid
on the dynamics of particle is negligible
07:29.900 --> 07:35.430
so here if you see this figure this figure
basically shows a smooth particle and you
07:35.430 --> 07:42.580
can understand that fluid is moving very smoothly
from the edges of this particle. On the other
07:42.580 --> 07:49.310
hand if I consider rough particle then water
which is or fluid which is moving over this
07:49.310 --> 07:57.550
it will be quite scattered or quite spreaded,
so we are considering that surface is smooth
07:57.550 --> 08:04.190
and therefore the movement of fluid through
the particle is streamlined.
08:04.190 --> 08:09.660
The particle is freely settling under gravity,
what is the meaning of this that in this case
08:09.660 --> 08:15.320
we are considering that particle is single
there is no other particle which can put hindrance
08:15.320 --> 08:22.140
in the movement of this particle, so single
particle which is moving freely under the
08:22.140 --> 08:26.410
action of gravity and final assumption we
have.
08:26.410 --> 08:32.760
The fluid forms an infinite medium, what is
the meaning of this that if we are considering
08:32.760 --> 08:39.760
a cylinder of very small diameter and when
particle is moving through this the effect
08:39.760 --> 08:46.220
of wall comes into the picture so here we
are considering that fluid is moving in infinite
08:46.220 --> 08:52.329
medium, it means cylinder diameter in which
particle is falling in a liquid is significantly
08:52.329 --> 09:01.240
large in comparison to diameter of particle,
so here significant assumptions we have taken
09:01.240 --> 09:07.060
which some of these assumption will be realized
in subsequent slides.
09:07.060 --> 09:14.329
But at this time we are considering all these
assumptions. Now as far as dynamic of particles
09:14.329 --> 09:22.620
are concerned here we are going to cover different
topics, first is terminal settling.
09:22.620 --> 09:31.470
Velocity, second effect of particle shape
and third is wall effect and apart from this
09:31.470 --> 09:40.249
we will discuss hindered settling velocity
and classification, and finally we will discuss
09:40.249 --> 09:47.959
jigging so all these six topics will come
into particle dynamics, now if we consider
09:47.959 --> 09:49.970
top three.
09:49.970 --> 09:55.230
Topics that is terminal settling velocity,
effect of particle shape and wall effect all
09:55.230 --> 10:02.610
these are corresponding to single particle
whereas next three topics are correspond to
10:02.610 --> 10:11.459
mixture of particles when we have mixture
or when we have suspension when we have slurry.
10:11.459 --> 10:19.290
So let us start the first topic of this that
is terminal settling velocity. Now to make
10:19.290 --> 10:25.540
to make you understand what is the concept
of terminal settling velocity I have taken
10:25.540 --> 10:32.970
one big container you can see.
Over here in which fluid is filled and when
10:32.970 --> 10:39.690
particle is falling in this fluid what are
the forces which are acting on the particle,
10:39.690 --> 10:45.879
the very first force is the force of gravity
which is acting downward, that we can denote
10:45.879 --> 10:54.069
as gravitational force, second is the buoyancy
force, now what is buoyancy force I guess
10:54.069 --> 11:01.230
you understand what it is as the particle
moves down it displaces a volume of liquid
11:01.230 --> 11:08.629
equal to its own volume, so when particle
is moving into the fluid it displaces the
11:08.629 --> 11:17.329
volume of its own volume towards upward and
this displaced liquid moves upward and therefore
11:17.329 --> 11:24.589
it exert an upward force on the particle and
that force we call as buoyancy force.
11:24.589 --> 11:30.190
Which is definitely equal to the weight of
displaced liquid so weight of displaced liquid
11:30.190 --> 11:37.139
means mass of displaced liquid into g, now
apart from these two another.
11:37.139 --> 11:42.830
Force which will act on the particle is frictional
resistance, it is offered by the liquid on
11:42.830 --> 11:49.959
the particle due to the relative motion between
particle and the liquid. Now here we have
11:49.959 --> 11:57.220
three different forces and net force which
is acting on the particle is the gravitational
11:57.220 --> 12:03.439
force minus buoyancy force minus frictional
force, gravitational force is acting downward,
12:03.439 --> 12:07.310
buoyancy and frictional force will act upward.
12:07.310 --> 12:13.810
And mathematically we can represent net force
acting on the particle that is ma=mg that
12:13.810 --> 12:21.929
is gravitational force minus m?p, what is
m?p is the volume of particle and when we
12:21.929 --> 12:28.730
multiply this by ?f we can get mass of the
liquid which is displaced into g so that is
12:28.730 --> 12:36.000
the weight of displaced liquid, and FD we
have used for frictional drag so FD is nothing
12:36.000 --> 12:38.160
but the kinematic force.
12:38.160 --> 12:45.059
And a is basically particle acceleration.
Now when we study this equation in detail
12:45.059 --> 12:51.790
what it shows, it shows the mechanism of a
particle movement when it is falling in a
12:51.790 --> 13:00.440
liquid, now when the particle start falling
in the liquid its velocity is very less, so
13:00.440 --> 13:08.179
when velocity is very less the frictional
drag which is putting hindrance in the movement
13:08.179 --> 13:16.129
of liquid that will also be negligible, so
when this FD is negligible at that time that
13:16.129 --> 13:22.339
magnitude of ma will increase and as m is
constant a will increase which is nothing
13:22.339 --> 13:27.319
but the particle acceleration.
So when acceleration will increase it compels
13:27.319 --> 13:33.779
the particle to move with faster velocity
so when the velocity will increase so again
13:33.779 --> 13:41.240
the drag, frictional drag which is acting
in upward direction it will increase so it
13:41.240 --> 13:48.529
will put resistance in the movement of particle.
So when FD will increase again the acceleration
13:48.529 --> 13:56.399
will keep on decreasing so at some point what
situation will occur that whatever force is
13:56.399 --> 14:02.990
acting on the particle that is mg will be
equal to the buoyancy force plus frictional
14:02.990 --> 14:10.100
drag. At that time there will not be any net
force which is acting on the particle and
14:10.100 --> 14:15.319
particle will move with 0 acceleration or
we can say it will move with the constant
14:15.319 --> 14:22.569
velocity, so that time when the velocity is
constant this we can define as terminal settling
14:22.569 --> 14:30.800
velocity of the particle. So what is the condition
that at terminal settling velocity ma would
14:30.800 --> 14:38.739
be 0 so that we will take as a base of the
derivation this was the equation which we
14:38.739 --> 14:41.910
have.
Discussed in the last slide where ma is 0
14:41.910 --> 14:51.040
because particle is reach to terminal settling
velocity, so considering this remaining expressions
14:51.040 --> 15:00.310
we can rewrite the expression in this form
mg in 21- ?f \/?p = FD. Now we have to write
15:00.310 --> 15:08.369
the expression for FD, further we have already
assumed that the particle is spherical with
15:08.369 --> 15:15.429
diameter so m can be represented in terms
of particle diameter, if you consider this
15:15.429 --> 15:26.779
the expression is ?dpq /6 x ?p x g x 1- ?F/?p
= FD so what is this ?dpq /6this is nothing
15:26.779 --> 15:35.249
but the volume of a particle into ?p so that
would be the m of mass of the particle.
15:35.249 --> 15:43.309
So this m we can represent as volume x density
so rest of the expression will remain same.
15:43.309 --> 15:51.709
Further we can consider kinematic force which
we have represented as FD so FD we can write
15:51.709 --> 16:01.959
as AK x f, now what is this AK x f A is the
projected area of particle perpendicular to
16:01.959 --> 16:09.689
the direction of motion of the particle so
A we can represent as the area of spherical
16:09.689 --> 16:17.610
particle which is ?dp2 / 4 and we can write
K which is nothing but the kinetic energy
16:17.610 --> 16:26.230
per unit volume and it is = ½ ?FV2, so that
is nothing but ½ and V2 but per unit volume
16:26.230 --> 16:29.769
is there that is why we have use the density
term.
16:29.769 --> 16:37.069
And f is nothing but a factor fD small fD,
fD is the kinematic force F we can represent
16:37.069 --> 16:47.649
as small f and subscript with fD that is the
drag force, so using the expression of A and
16:47.649 --> 16:55.339
K we can write the fD.
So considering value of AK and f where f = fD
16:55.339 --> 17:03.839
we can rewrite this equation where this expression
will remain same, however the right hand side
17:03.839 --> 17:12.890
that is A we can write as area perpendicular
to the motion into a kinetic energy per unit
17:12.890 --> 17:20.610
volume into fD, so considering all these factor
we can write the equation which we can resolve
17:20.610 --> 17:27.480
or rearrange. Now once we rearrange we can
calculate the value of fD where which comes
17:27.480 --> 17:37.020
as 4/3 ?p – ?f / ?f into gdp / Vt2 so if
you see this expression.
17:37.020 --> 17:49.020
Here we can write Vt so this Vt would Vt will
represent the velocity of particle and that
17:49.020 --> 17:56.280
comes under kinetic energy term so from here
this equation we can write fD and further.
17:56.280 --> 18:02.790
We can calculate, we can derive, we can find
the value of Vt from this expression in terms
18:02.790 --> 18:10.690
of fD so this is the expression for terminal
settling velocity. Now what happens over here
18:10.690 --> 18:18.470
that once I am having this expression it depends
on, it is directly proportional to particle
18:18.470 --> 18:25.710
size that is dp as well as particle diameter
so what is the meaning of this that velocity
18:25.710 --> 18:30.580
will increase when we are dealing with larger
particle and further velocity will increase
18:30.580 --> 18:35.360
when we consider the heavier particle which
has more density.
18:35.360 --> 18:39.840
So this is the generalized expression for
terminal settling velocity.
18:39.840 --> 18:46.710
We will further consider this equation to
derive the equation for different regions
18:46.710 --> 18:51.820
of flow.
Now to understand different regions of flow
18:51.820 --> 18:58.860
we can have the graph between Drag coefficient
vs Reynolds number this is the.
18:58.860 --> 19:06.440
Very known well known graph here we have this
fD that is Drag coefficient and here we have
19:06.440 --> 19:14.510
the Reynolds number and this is the profile
by which fD is changed, then we change the
19:14.510 --> 19:19.680
Reynolds number, so this is the well known
graph, now we will consider different regions
19:19.680 --> 19:26.230
in this graph and here we have the generalized
equation of terminal settling velocity and
19:26.230 --> 19:33.820
further we will discuss the specific equation
which can be used for particular region, so
19:33.820 --> 19:38.550
first of all we will consider.
Region1 where Reynolds number vary from 10
19:38.550 --> 19:47.770
raise to minus 4 to 0 point 1 so up to here
the region1 is available which we have shown
19:47.770 --> 19:53.800
with the red color in this graph that is region
one, and now if you consider this region 1
19:53.800 --> 20:01.990
here we have almost linear variation of fD
with respect to Reynolds number, so in this
20:01.990 --> 20:11.760
region fd can be defined as 24/Re and it is
basically laminar region where the slope between
20:11.760 --> 20:21.900
fD and Re is – 1 so all these regions are
pre defined and you can study about this in
20:21.900 --> 20:25.910
fluid dynamics in detail.
So this graph we have used between fD and
20:25.910 --> 20:35.060
Re where in region1 the slope between fD and
Re is – 1. Now once I consider the fD factor
20:35.060 --> 20:42.930
which is 24/ Re in generalized equation of
terminal settling velocity then we can rewrite
20:42.930 --> 20:53.410
the expression of Vt that is g dp2 ?p – ?F/
18 so this expression is basically used for
20:53.410 --> 21:01.170
laminar flow and we call it the Stokes’
law, so a Stokes’ law is used to calculate
21:01.170 --> 21:07.920
terminal settling velocity of particle when
it is falling in laminar zone. And now in
21:07.920 --> 21:13.950
this slide we will discuss the application
of Stokes’ law, you can understand that
21:13.950 --> 21:22.360
it, it is applied in very less velocity or
in the less Reynolds number or in laminar
21:22.360 --> 21:29.350
region. So Stokes’ law is important to understand.
The swimming of microorganisms and sperm,
21:29.350 --> 21:35.640
also the sedimentation under the force of
gravity of small particles and organisms in
21:35.640 --> 21:42.270
water, now what is the meaning of this, that
when we consider laminar flow, laminar flow
21:42.270 --> 21:48.210
can be achieved when the particle diameter
is very less. If you remember the expression
21:48.210 --> 21:56.050
of Reynolds number that is dv?/µ so in that
case if diameter of particle that is d is
21:56.050 --> 22:02.730
very small it is more likely that it will
follow, it will fall in the laminar region.
22:02.730 --> 22:10.880
So Stokes’ law basically demonstrate or
basically applicable to compute the velocity
22:10.880 --> 22:17.790
of microorganisms and sperm which are very
small as far as diameter is concerned. Another
22:17.790 --> 22:21.990
application is.
In air the same theory that is Stokes’ law
22:21.990 --> 22:29.820
can be used to explain why small water droplets
or ice crystals can remain suspended in the
22:29.820 --> 22:37.650
air as cloud until they grow to a critical
size and start falling as rain or snow. So
22:37.650 --> 22:44.140
similar use of equation can be made in the
settlement of fine particle in water and other
22:44.140 --> 22:51.740
fluid, so what is the main point of this statement
is Stokes’ law is applicable when we are
22:51.740 --> 22:58.750
considering particle size of very small diameter.
So this two application I have taken from
22:58.750 --> 23:03.540
these references.
You can go through these references for to
23:03.540 --> 23:08.111
study about this in detail.
So first region we have already covered, now
23:08.111 --> 23:16.060
we are dealing with, we are finding the second
region, second region varies from 0.1 to 500
23:16.060 --> 23:25.360
to 1000, so this is the second region where
it stops up to 500, so 500 to 1000 range we
23:25.360 --> 23:33.460
can take here we have taken as 500. Now in
this case slope of the curve varies from 0.1
23:33.460 --> 23:42.990
to 0 because at this, at the end of this region
the slope is reaching to 0 value. So the slope
23:42.990 --> 23:51.410
in this region two varies from 0, varies from
0.1 to 0. In this case drag coefficient is
23:51.410 --> 24:01.780
defined as (24/Re)+0.44.
So first expression of this fD equation is
24:01.780 --> 24:08.640
due to the Stokes’ law and other that is
0.44 which is a constant and it is due to
24:08.640 --> 24:15.030
the additional non viscous effect. So this
fD we can use to calculate the terminal settling
24:15.030 --> 24:21.300
velocity falling in this region, so there
is basically we call it a transition region
24:21.300 --> 24:30.630
because here from -1 to 0 the slope is reaching
and therefore we call it a transition region.
24:30.630 --> 24:37.600
So two regions we have already discussed,
now as far as third region is concerned this
24:37.600 --> 24:44.950
is the generalized equation which we have
discussed already. And region 3 where the
24:44.950 --> 24:52.750
Reynolds number varies from 500 to 1000 to
105, so this is the region we will call region
24:52.750 --> 25:01.180
3. In this region if you see the variation
of fD with respect to Reynolds number is almost
25:01.180 --> 25:10.440
constant. So in this case it is approaching
to turbulent flow where the velocity is so
25:10.440 --> 25:18.150
high that it will not change with the surface
significantly so that will move over the particle
25:18.150 --> 25:23.580
and it will not put significant drag or significant
resistance in the path of the flow of the
25:23.580 --> 25:27.880
particle.
So therefore in region 3 we have considered
25:27.880 --> 25:35.030
fD as constant which is equal to 0.22, you
can see the value from this graph also.
25:35.030 --> 25:43.980
Which is available over here, now once I use
the fD 0.22 in this equation what we can say
25:43.980 --> 25:53.820
that, we can have equation in this form which
is 4/3 and that is divided by 0.22 so 3.03
25:53.820 --> 25:59.220
is the factor which is coming and rest of
the parameter will remain same. So you can
25:59.220 --> 26:06.030
see this is the terminal settling velocity
equation when we are considering fD is almost
26:06.030 --> 26:11.920
constant, this is more or less a turbulent
region and this law we call as Newton’s
26:11.920 --> 26:15.270
law.
So you can understand for laminar zone we
26:15.270 --> 26:22.710
have taken, we have defined Stokes’ law,
for turbulent region we can use Newton’s
26:22.710 --> 26:30.250
law. Now beyond this further when Reynolds
number will increase that we call as developed
26:30.250 --> 26:35.550
turbulent region. So all these three region
we have already covered.
26:35.550 --> 26:42.270
Now here what we have is the same expression,
generalized expression of Vt that is terminal
26:42.270 --> 26:49.880
settling velocity as a function of fD. And
now we are considering region 4 where the
26:49.880 --> 27:00.060
Reynolds number is greater than 105. Now what
happens over here, if you consider this particular
27:00.060 --> 27:07.970
region so here in this region you see the
drag coefficient is decreased significantly
27:07.970 --> 27:14.470
and then it becomes constant. Now why it is
so, when the velocity of liquid velocity of
27:14.470 --> 27:23.640
fluid is very high what happens, when it pass
over the fluid it will basically passed with
27:23.640 --> 27:30.370
a distance from the particle surface.
It means it will not touch the particle surface
27:30.370 --> 27:35.820
it move away from the or beyond the particle
surface because particle, because velocity
27:35.820 --> 27:41.950
is significantly high, so it will for example,
when I am considering particle like this it
27:41.950 --> 27:48.180
will move like this, so it remains separated
from the particle surface. When it remains
27:48.180 --> 27:56.000
separated from the particle surface it will
not put any drag into the particle and therefore
27:56.000 --> 28:00.580
drag coefficient at that time will be significantly
decreases.
28:00.580 --> 28:09.070
So when we consider Reynolds number greater
than 2*10/5 the fd value decreases significantly
28:09.070 --> 28:18.180
and in this region fd value is found as 0.05,
that you can also read from this graph. So
28:18.180 --> 28:23.740
considering all these regions we can define
different equations for terminal settling
28:23.740 --> 28:27.600
velocity, in the same line for region 4 we
can
28:27.600 --> 28:36.060
Write the expression of terminal settling
velocity while considering fd = 0.05 and that
28:36.060 --> 28:42.600
0.05 we can put over here and for the resolve
this, so this is the final expression of terminal
28:42.600 --> 28:49.520
settling velocity when the particle is moving
in developed turbulent zone where Reynolds
28:49.520 --> 28:56.370
number is greater than 105, therefore for
different region we have defined different
28:56.370 --> 29:01.530
equations and these are the equation and all
these equation.
29:01.530 --> 29:11.260
If you see all these equations are proportional
to dp as well as ? so the equations show about
29:11.260 --> 29:17.340
for terminal settling velocity of the particle
is, and this terminal settling velocity of
29:17.340 --> 29:24.460
particle increases with the increase in particle
size as well as particle density. So when
29:24.460 --> 29:30.330
we are considering different size particles
and different density particles the heaviest
29:30.330 --> 29:38.460
and the largest particle will settle in less
time in comparison to others because that
29:38.460 --> 29:44.240
is terminal settling velocity is directly
proportional to dp as well as ?.
29:44.240 --> 29:53.690
Further if you see this table what this table
shows here this table is representing Vt and
29:53.690 --> 29:59.020
expression if you remember, this is the expression
of Stokes’ law, so here we can calculate
29:59.020 --> 30:06.521
settling velocity when the particle is falling
in laminar zone and the same equation we can
30:06.521 --> 30:13.720
use to calculate other parameters associated
in this expression, for example if I want
30:13.720 --> 30:24.720
to calculate the acceleration of gravity then
we can have g = 18 µvt by dv?p- ?m where
30:24.720 --> 30:26.450
this ?m
30:26.450 --> 30:35.190
We have taken as ?f that is density of fluid
or we also call it density of medium. Further
30:35.190 --> 30:41.780
particle diameter can be known once I know
the terminal settling velocity and here we
30:41.780 --> 30:49.520
can find the density of the medium as a function
of density of the particle, particle density
30:49.520 --> 30:55.950
also we can calculate using the Stokes’
law and viscosity of medium we can also find
30:55.950 --> 31:01.420
using the Stokes’ law. So single equation
can be used to find different parameters which
31:01.420 --> 31:11.550
are associated with this, so here you see
we have taken ?m = ?f and this is the link
31:11.550 --> 31:17.220
of where this table is taken.
So if you want to study more about this you
31:17.220 --> 31:24.600
can study here. Now in this particular part
of lecture 1 we have covered the derivation
31:24.600 --> 31:31.130
of terminal settling velocity and we also
have seen equations of terminal settling velocity
31:31.130 --> 31:37.370
when the particle is moving in different region,
so that is all for now, we will continue in
31:37.370 --> 31:39.700
next part of the same lecture, thank you.