WEBVTT
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Welcome to the second part of lecture 2 of
week 2 which is on effectiveness of screen.
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In the first part of this topic we have covered
the theory and here in this part we will demonstrate
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the computation of effectiveness of screen
through some examples.
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So here this is example 1.
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Here we will compute the effectiveness of
10 mesh screen if oversize is a desired product;
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this is the same problem for which we have
computed ya, yb and yc in part one of this
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lecture.
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So if you see this is the table where I am
having the mesh number from 4 to 65, the opening
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of screens the cumulative mass fraction for
feed overflow and underflow, till now I hope
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you can understand how these fractions of
feed overflow and underflow comes in this
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table when I am considering the effectiveness
of single screen, that is the 10 mesh screen.
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So for this particular example if oversize
is a desired product then ya, yb and yc.
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You can see either from this table or you
can refer the graph which we have discussed
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in first part of this lecture.
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So here if you see we have done the cumulative
from bottom, so if I consider oversize as
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a desired product so this particular section
over to 10 mesh screen is the region where
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we have to focus.
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So ya would
be 1-0.5 which is equal to 0.5.
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Yb = (1-0.18) = 0.82 and yc = (1-0.81) = 0.19
so in this way we can calculate ya, yb and
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yc.
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Once I am having these values of ya, yb, yc
we can put this value into this expression
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which is of effectiveness of screen and then
this particular section, the first expression
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of this is having the value 0.806984 and this
particular section is having the value 0.822857,
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multiplication of these two will give the
effectiveness of a screen that comes as 0.664
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or 66.4 % is the effectiveness of screen or
efficiency of screen which is of 10 mesh size.
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So here the same example we have completed
which we have started in the first part of
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this lecture.
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So in this slide I am considering example
2 on effectiveness of screen, in this example
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powdered coal with following screen analysis
is fed to a vibrating 48 mesh screen, the
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particle size distribution data of feed oversize
and undersize is shown in this table.
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So here if you see the table here I am having
mesh number but instead of single number here
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I have shown the value in terms of minus and
plus.
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Minus you understand I guess it is the material
which is passed through the screen and plus
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sign shows material which is retained on the
screen.
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So if you see here I am having the percentage
mass of feed, percentage of retained oversize,
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percentage of retain undersize.
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So instead of mass fraction we have shown
the value in terms of percentage.
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So here we have the screen from 32 to 100.
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And these value if I consider 1.07 it is basically
retained on 4 mesh screen, similarly 1 point
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is retained on 4 mesh screen but here the
value is shown in terms of minus and plus
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that is undersize as well as oversize, what
we have to compute over here is, effectiveness
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of screen which is of 40 mesh screen considering
oversize as a product and considering undersize
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as product.
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Further we have to compute the ratio of quantity
oversize and quantity undersize to feed.
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If I consider quantity oversize to feed it
means b/a I have to calculate when I am considering
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oversize as a desired product and quality
and quantity undersized to feed is again b/a
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when I am considering undersize as a desired
product.
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So let us start with the part a, now before
that before starting computation of part a
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here we have to convert the data into desired
format and what is desired format?
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Instead of percentage mass we have to show
the value in terms of mass fraction.
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So data should be prepared in the desired
format that is mass fraction of feed oversize
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and undersize is should be shown in this table.
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So here you see here I have written percentage
mass but it should be mass fraction.
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So it should be a not the percentage mass,
it is basically the mass fraction of feed,
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mass fraction of oversize, and mass fraction
of undersize, I apologize for this mistake.
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And here if you see the values here I have
written only one mesh number on which material
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is retained.
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So from 4 to 200 wherever material is retained
as far as feed oversize and undersize is concerned
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that values are shown in this table.
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Now let us start part 1, here I want to demonstrate
that when we do not carry out cumulative mass
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then how we can calculate the effectiveness
of a screen because in example one we have
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used the data once I am having the cumulative
values, here I am not going to make any cumulative
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mass fraction, without this I want to demonstrate
to calculate effectiveness of screen.
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And here I am considering if oversize is a
desired product.
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So if you see the 40 mesh screen for which
I have to compute the effectiveness so whatever
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section falling above to this 48 that is the
region where we have to focus as well as far
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as ya, yb and yc to be computed.
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So what is ya is the desired material in feed
so we have to consider the screen from 4 to
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48 and where the feed is retained.
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So summation of all these will speak about
the value ya which comes out as 0.8211.
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In the similar line I can calculate desired
material in products, so what is desired material
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is the oversize so obviously the column falling
between feed and undersize is the area where
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we have to focus, so summation of all these
values upto 48 will give the value yb which
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comes out as 0.973 and similarly I can calculate,
I can consider the yc while focusing on material
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retained above 248 screens and addition of
these values will give the value of yc which
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comes out as 0.3393.
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So by following this we can calculate the
ya, yb and yc once I am not having the cumulative
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mass fraction values.
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So once I am having ya, yb and yc I can put
these value in this expression and then I
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can calculate the effectiveness of screen,
this first section gives the value 0.9 and
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second section of this expression gives the
value 0.8853, multiplication of these two
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will give the effectiveness as 79.76% so this
is one part of this.
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Now I want to demonstrate the computation
of effectiveness of screen if oversize is
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a desired product considering cumulative mass.
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So here you see initially I am having the
value in this format where I have represented
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only single number and the mass retained corresponding
to these mesh is available over here, now
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how I can do the cumulative mass?
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I have two option first is to make cumulative
from top and second is to make cumulative
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from bottom.
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In this particular case I am considering cumulative
mass fraction from top.
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So here if you see this table in this table
the first value is corresponding to -3 + 4
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and the feed is having 0.0107 so that value
0.0107 is corresponding to 4 mesh screen.
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Similarly if I consider 6 mesh screen the
retain mass over here is this much, now if
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I want to make the cumulative then I have
to add, here you see in this table correspond
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to 4 I am having 0.0107, corresponding to
6 I am having value 0.0235.
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Now if I make cumulative of 6 mesh screen
it means all these two value will be added
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together because these two value would be
retained by 6 mesh screen.
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Similarly if I consider for 8 mesh screen
all these three value would be added as the
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cumulative which is retained by 8 mesh screen.
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So what is the purpose to do the cumulative
analysis that here we have to compute ya,
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yb and yc, previously also we have done the
same thing.
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But if we compute the cumulative mass fraction
then how the computation should proceed, so
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here you see if I want to make the cumulative
from top and here I am having mesh number
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of screen in terms of – and + so the cumulative
will be shown with respect to all plus number
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of screen, so if I do the cumulative analysis
I have to show the mesh number which are positive
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in this series.
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So here you see 4, 6, 8, 10 and similarly
upto 200 we can proceed so once I am reaching
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to 200 the cumulative mass comes as one which
shows that if I consider the finest opening
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screen which will retain all particles so
therefore the value comes over here is one,
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so if I do the cumulative mass from top I
have to consider the mesh number correspond
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to plus sign.
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So I hope you are getting this, now what we
have to do that correspond to 48 I have to
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calculate yA, yB and yC, here this is already
the cumulative mass so I do not have to consider
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all section above to this I can consider this
value only, so considering this I can calculate
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yA which is 0.8211.
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Now if you consider this 48 it correspond
to +48, so whatever mass is available over
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here in terms of cumulative mass is retained
on 48.
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So that would be the desired material in the
feed that is 0.8211.
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Similarly I can calculate yB 0.973 which is
desired material in product and similarly
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I can calculate desired material in reject
that is yC which comes out as 0.3393.
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Considering these three value I can calculate
the effectiveness of screen using this expression
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which comes out as 79.76%.
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Here another section I am considering the
same problem while doing the cumulative and
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considering oversize as a desired product,
but in this case I am doing the cumulative
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from bottom instead of top.
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So here you see as we have demonstrated in
the previous section.
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In this table I have shown the value which
are retained on respective screen so if I
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consider this 200 mesh it means this much
is retained on this.
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So if I consider 150 it has this much value
to be retained.
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Now if I do the cumulative from bottom then
these two would be added and the addition
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value of these two would be 0.0542.
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Now that value 0.0542 will never be in correspondence
with 150 because 150 will never retain the
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particle which are lesser than 150, so in
this case instead of using plus sign I will
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show, I will use the negative sign which shows
the material will pass through the screen.
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Therefore if I consider the cumulative analysis
from bottom.
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I can correspond this with the mesh number
where I am having the mesh number with negative
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sign.
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Therefore, if you consider this when I do
the cumulative from bottom I have to use the
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mesh number with negative sign and when I
am carrying out cumulative from top I have
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to use mesh number with positive sign.
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So here we do.
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The cumulative from bottom so obviously all
minus sign will appear in this.
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Now this we will use for the computation of
effectiveness of screen.
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Correspond to 48 these are the values of cumulative
analysis, now if you consider this 48 it comes
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as -48 it means this much material is passed
through 48 screen.
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So as far as yA is concerned I do not have
to consider with the material which is passed
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through but I have to consider the material
which is retained on 48 screen, so obviously
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yA would be 1-0.1789 which is equal to 0.8211.
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And similarly yB and yC I can consider by
considering cumulative correspond to 48 in
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oversize as well as in undersize.
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Considering all these three value in this
expression I can calculate the effectiveness
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of screen which comes out as 79.76%.
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So that is the calculation of three different
way, one is without cumulative, second is
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with cumulative when we do the cumulative
from top, and third is with cumulative when
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we do the cumulative mass from bottom.
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So this is the sieve example and here we have
to compute without cumulating and what we
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have to compute, effectiveness of screen when
undersize is a desired product, so here without
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computing the cumulative mass.
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Here you see all these three section which
are falling below 48 is the region where we
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have to focus, so what is the yA that is desired
material in feed.
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Now desired material is undersize so whatever
undersize to 48 is available below 48 mesh
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screen.
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Available in feed so that yA would be 0.1789
that is summation of these four fractions
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and similarly yB is the desired material in
product.
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In this case this is the product so summation
of these four value will give yB and similarly
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summation of these four value will give yC
which is the rejection, so here yA, yB once
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I know I can calculate the effectiveness of
screen and the first section gives the value
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0.8853 and second section 0.9, multiplication
of these two will give the value that is 79.76%.
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So here you can see that effectiveness is
79.76 only, either I consider oversize as
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a desired product or I consider undersize
as a desired product because the performance
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of equipment will not differ when I change
the desired product.
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So whatever it is either oversize or undersize
effectiveness of screen will remain same.
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Here I will show again with cumulative mass
when undersize is a desired product.
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Here you can understand I have done the cumulative
from top considering all positive mesh numbers,
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so what is the reason behind this that we
have already discussed.
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Correspond to 48 we have to compute the yA,
yB and yC so yA is the desired material in
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feed.
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So if undersize is a desired product and this
48 shows the oversize of this, so 1-0.8211
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is equal to 1 equal to 0.1789 which is the
desired material in feed.
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And similarly I can calculate yB and yC considering
oversize as well as undersize of this table.
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Here undersize is a desired product so yB
would be 1-0.3393 and similarly yC would be
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1-0.973, so once I am having yA, yB, yC I
can calculate the effectiveness using this
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expression which I can find as 79.76%.
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In continuation to this I will do the cumulative
analysis from bottom while considering all
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negative mesh number screens.
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So if undersize is a desired product correspond
to 48 mesh screen, yA would be 0.1789 and
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similarly I can calculate yB and yC, putting
these values in this expression I can calculate
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the effectiveness of mscreen.
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So in this way I can calculate the effectiveness
of screen considering oversize as well as
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undersize and in this particular problem I
have taken all possibility to make the cumulative
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mass fraction.
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Now in this slide I will consider the second
part of the problem that where I have to calculate
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the ratio of product and feed.
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If oversize is a desired product we have to
calculate B by A, so if oversize is the desired
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product these are the value of yA, yB and
yC that is nothing but the addition of this,
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I have already explained from where these
values has come.
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So considering this, this is the expression
for effectiveness of screen where we have
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to calculate B by A. And if I consider recovery
that is B/A yB and yA and here I can have
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the recovery as we have done it previously
so that recovery we have considered as 0.9,
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and considering this expression also we can
have the value of B/A which comes out as 0.7594.
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In the similar line I can calculate the ratio
of product and feed when undersize is a desired
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product and these are the fraction of undersize
where I am having values of yA, yB and yC.
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This is the expression, this is the recovery,
I am already having the value of recovery
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0.8853 you can refer the previous slides,
so considering these recovery value as well
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as this yA and yB I can calculate the ratio
B/A which comes out as 0.2397, so this is,
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it was example two.
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So here I am having third example on effectiveness
of screen which says that following is the
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particle size distribution of three cuts obtained
from a double deck vibrating screen.
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Double deck vibrating screen where I am having
two screens of 48 as well as 65 mesh.
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The mass ratio of oversize intermediate and
undersize is 3:3:4, so if you consider this
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particular table here I have shown the mesh
number of screen where I am having 48 as well
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as 65 and here the mass fraction of oversize
intermediate and undersize are shown, so what
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we have to compute over here?
22:45.740 --> 22:52.140
First of all if you see this table it has
basically three sections, oversize, intermediate,
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and undersize but it does not have any column
of feed, so first of all we have to construct
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the particle size distribution of feed to
48 and 65 mesh screen respectively.
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Secondly we have to calculate the effectiveness
of 48 and 65 mesh screen individually and
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finally we have to calculate the effectiveness
of double deck vibrating screen considering
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intermediate as a desired product.
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So before you starting the calculation the
computation for this particular example you
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should understand what is double deck screen.
23:32.950 --> 23:39.580
Double deck screen is the set of two screen
in which I am having 48 mesh screen at the
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top and below I am having 65 mesh screen and
below to 65 mesh screen I have pan and.
23:46.830 --> 23:54.300
At the top of 40 mesh screen I have the cover,
so this is a set of two screen, one pan and
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one cover.
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This particular set we put into the shaker,
screen analysis will be done and here I will
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have three different section, first is which
is retained on 48 screen which we call as
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oversize which is shown over here.
24:13.150 --> 24:19.610
Second section is which is falling over to
65 which is pass through 48 so that we have
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represented as intermediate and finally whatever
is collected in the pan which is below to.
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65 that we name as under size, so if I am
having double deck screen I will have three
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different sections, so this example is entirely
different whatever we have discussed previously.
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So here first part of this we should consider
that is particle size distribution for feed
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to 48 mesh screen how we can find that particle
size distribution on this.
24:54.260 --> 25:00.280
Here if you see the mass ratio of oversize
intermediate and under size is three, for
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example if I am having 100kg of feed in this
30kg has gone to oversize, 30kg has gone to
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intermediate, and 40kg will remain as undersize,
so when I join these three we can have the
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feed to 48 because if I am considering 48
mesh screen that is the topmost screen.
25:22.380 --> 25:30.120
In which total feed should be fed which consist
of oversize, intermediate, and undersize,
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so to compute the feed for.
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48 screen I have to consider these ratios
that is 3:3:4 and the value which is shown
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with respect to each mesh number screen.
25:44.660 --> 25:52.210
So for 40 mesh screen how we have to compute
the feed to 48 that would be nothing but simply
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the component balance that is 3 x 0.0012 which
is of oversize, 3 x 0 which is of intermediate,
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4 x 0 which is of undersize / 10, so all these
value will give the feed correspond 240 mesh
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screen to 48 screen, so here I am having the
value 0.0036.
26:19.100 --> 26:26.100
And in similar line I can calculate value
for other mesh number screens also, so in
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this way I can calculate the feed to 48.
26:29.900 --> 26:36.580
Here I have to calculate feed to 65, now if
I consider 65 it is only the single screen
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in which whatever material is available that
is distributed as oversize as well as undersize,
26:43.280 --> 26:48.340
so over size I am calling as intermediate
in this particular example and under size
26:48.340 --> 26:55.170
will remain as it is, so to compute the feed
to 65 mesh screen I will consider the ratio
26:55.170 --> 27:03.130
of intermediate to undersize and the fractions
correspond to each mesh number which are present
27:03.130 --> 27:06.680
in intermediate as well as under size columns.
27:06.680 --> 27:14.610
So if you consider the 40 mesh screen we have
feed to 65 we can compute feed to 65 as 3
27:14.610 --> 27:25.100
x 0 + 4 x 0/ 7 so 0 will appear over here,
however if I consider for 28 mesh number screens
27:25.100 --> 27:38.630
we have 3 x 0.02 and 4 x 0.0/ 7 it will give
the value 0.00857 which you can see over here,
27:38.630 --> 27:47.770
so accordingly I can calculate the PSD for
feed to 65 mesh screen for the rest of the
27:47.770 --> 27:52.230
mesh number screens, so here I am having the
complete PSD data.
27:52.230 --> 28:00.570
Complete PAD data means a feed to 48 feed
to 65 oversize, intermediate, and undersize
28:00.570 --> 28:05.620
so that we have part one of this example we
have already completed.
28:05.620 --> 28:14.140
Let us start with part two which says that
to calculate the effectiveness of 48 mesh
28:14.140 --> 28:19.830
screen here I am considering oversize as a
desired product and this is the expression
28:19.830 --> 28:25.010
which we have to consider, so if oversize
of desired product you can understand very
28:25.010 --> 28:33.590
well that above to 48 would be the region
where we have to focus, yA is the desired
28:33.590 --> 28:35.050
material in feed.
28:35.050 --> 28:45.650
So ? of all these mass fraction will give
yA ? of all these will give the value yB and
28:45.650 --> 28:53.660
? of all these will give the value yC, so
here you see feed to 65 I have consider as
28:53.660 --> 29:01.570
reject, in other word you can consider intermediate
as well as undersize as reject because in
29:01.570 --> 29:08.830
this particular case oversize to 48 is the
desired material, oversize to 48 is a desired
29:08.830 --> 29:16.060
product so considering intermediate as well
as under size in 3:4 ratio you can calculate
29:16.060 --> 29:18.700
yC which we have already shown.
29:18.700 --> 29:26.170
When we have computed the feed to 65 so therefore
this particular column we have chosen to calculate
29:26.170 --> 29:32.800
yC, once I am having yA, yB, yC we can calculate
the effectiveness of a screen which comes
29:32.800 --> 29:35.140
out as 67.
29:35.140 --> 29:36.800
8%.
29:36.800 --> 29:42.680
And similarly we have 40 mesh screen effectiveness
we have to calculate considering oversize
29:42.680 --> 29:45.030
as a desired product.
29:45.030 --> 29:51.940
Now in this case what is the difference the
expression to calculate effectiveness is different
29:51.940 --> 30:03.620
so here instead, instead of yC we have used
the ratio B over A so here yA and yB you can
30:03.620 --> 30:05.270
calculate from this table.
30:05.270 --> 30:12.510
However B/A if I consider that ratio I already
know so I can calculate B/A value which comes
30:12.510 --> 30:14.700
out as 0.3.
30:14.700 --> 30:20.980
Considering these three value effectiveness
can be calculated which comes out as 67.8%.
30:20.980 --> 30:27.560
Similarly we can calculate effectiveness of
48 mesh screen if undersize is a desired product
30:27.560 --> 30:35.410
so undersize to 48 this is the region where
we have to focus, so this is yC, this is yB,
30:35.410 --> 30:41.880
and this is yA, summation of these three will
give the value and using these value in this
30:41.880 --> 30:46.730
expression we can have the effectiveness of
screen which comes out as 67.8%.
30:46.730 --> 30:55.070
And here we have to calculate the effectiveness
of 65 mesh screen if oversize the desired
30:55.070 --> 30:57.230
product following similar method.
30:57.230 --> 31:06.880
Here this would be the product, this would
be the feed and this would be the reject.
31:06.880 --> 31:14.300
So yA, yB and yC I can calculate over here
and similarly I can calculate the effectiveness
31:14.300 --> 31:15.720
of screen.
31:15.720 --> 31:21.420
So for 65 I am getting 59.76% as.
31:21.420 --> 31:28.559
Efficiency of screen 65 mesh screen, if I
am considering undersize as a desired product
31:28.559 --> 31:36.340
so this would be the region where we have
to work in this, this is the yA section, this
31:36.340 --> 31:41.900
is yB section and this is yC section.
31:41.900 --> 31:48.220
So joining these two adding these two will
give value yA, yB, yC, using this expression
31:48.220 --> 31:56.370
I can have the effectiveness of screen which
is as 59.76%.
31:56.370 --> 32:01.330
In this case in this particular slide we are
discussing the effectiveness of double deck
32:01.330 --> 32:06.280
vibrating screen taking intermediate as desired
product.
32:06.280 --> 32:09.580
So here you see I am considering double deck
so all.
32:09.580 --> 32:15.620
We have shown in terms of all value we have
shown in terms of minus and plus.
32:15.620 --> 32:22.790
So here if I am considering double deck I
have to consider the fraction which is passing
32:22.790 --> 32:30.190
through 48 and retained on 65 that we call
intermediate as a desired product, so in this
32:30.190 --> 32:39.070
case correspond to -48 +65 this section I
have to consider as region where I have to
32:39.070 --> 32:48.120
work for yA, yB and yC, so what is yA is the
desired material in feed, so you see the value.
32:48.120 --> 32:53.530
Here I do not use the cumulative or addition,
only this particular section would be the
32:53.530 --> 32:55.880
desired material.
32:55.880 --> 33:00.180
So yA is the desired material in feed which
comes out 0.3152.
33:00.180 --> 33:01.260
yB desired material in the product
33:01.260 --> 33:04.320
So yA is the desired material in feed which
comes out 0.3152 yB desired material in the
33:04.320 --> 33:12.010
product and intermediate is the product so
point 5 to 6 and similarly yC how we can compute
33:12.010 --> 33:18.510
yC because if I am considering intermediate
as a desired product so oversize as well as
33:18.510 --> 33:23.020
undersize both would be rejected.
33:23.020 --> 33:32.420
And this its ratio is 3:1 so 3into .066 +
4 in 2.344/7.
33:32.420 --> 33:40.800
So 0.22486 is the value of yC considering
yA, yB, yC in this expression I can calculate
33:40.800 --> 33:50.740
the effectiveness of double deck screen which
is 48 as well as 65, so if you consider the
33:50.740 --> 33:56.700
double deck screen its efficiency is quite
low in comparison to individual screen or
33:56.700 --> 34:02.870
48 as well as 65 and that is quite obvious
because here I am having the hindrance at
34:02.870 --> 34:10.790
2 screens instead of single screen so if I
consider two screens the efficiency of.
34:10.790 --> 34:16.429
Both screen together would be lesser in comparison
to.
34:16.429 --> 34:23.020
Effectiveness we have computed individually
for these screens, so here in this part two
34:23.020 --> 34:30.010
of lecture two that is effectiveness of a
screen I have considered three different example
34:30.010 --> 34:35.190
to illustrate how the competition of effectiveness
of a screen will be done, now here I have
34:35.190 --> 34:38.290
the summary of the lecture two.
34:38.290 --> 34:44.990
First is effectiveness of a screen was defined
and its expression was derived based on recovery
34:44.990 --> 34:52.000
and rejection of the material, this we have
covered in part one of lecture two, second
34:52.000 --> 34:53.320
I am having effect.
34:53.320 --> 34:59.440
Of feed rate on the screen is discussed, that
also I have covered in part one of lecture
34:59.440 --> 35:00.440
two.
35:00.440 --> 35:05.820
And finally we have discussed different work
examples to illustrate the computation of
35:05.820 --> 35:11.480
effectiveness of a screen l so that is all
for this particular lecture, that is lecture
35:11.480 --> 35:12.500
two and here.
35:12.500 --> 35:17.630
The references are you can refer this, so
that is all for now, thank you.