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UST CHEMICAL ENGINEERING DEPARTMENT
1
CHE 2117
LECTURE 2
SCREENING
Engr. Divine Angela G. Sumalinog, Ph.D.
Engr. Aldrin Lorrenz A. Chan, M.Sc.
Course Instructors
Lecture Objectives
At the end of this lecture, the student should be able to
 Familiarize the different screening equipment, mesh materials
and standard sieve scales used in screening operation;
 Understand the mechanisms and types of screening operation;
 Construct and convert various types of particle size distribution
data; and
 Perform material balance to determine screen effectiveness in a
standard screening operation and in a rotary trommel screen.
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screening
Screening
 Screening is a method of
separating particles according
to size alone.
 Separation of mixture of
particles of various sizes into
two or more fractions by a
screening surface.
 Applications: mining and mineral
processing, agriculture,
pharmaceutical, food, plastics, and
recycling
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screening equipment
Screening equipment
 Grizzly Screen
 Shaking Screen
 Vibrating Screen
 Oscillating Screen
 Rotary Screen
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screening surface
Screening surface
 Interwoven wire mesh (carbon
or stainless steel, phosphor
bronze)
 Cloth (silk, plastic, nylon,
fiberglass)
 Perforated plates
 Bars
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standard sieve scales
Standard sieve scales
 US Tyler (Mesh 4-325)
 US ASTM (Mesh 4-325)
 British Standard Sieve
(BSS) (Mesh 5-300)
 Institute of Mining and
Metallurgy (IMMS) (Mesh
5-200)
 French standard sieves
(FSS) (Mesh 17-38)
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standard sieve scales
Tyler
Standard
Sieve Series
Source: McCabe, 7th ed.
(Appendix 5)
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screening operation
Screening schematic
Feed
• Mixture of differentlysized particles
• Larger than screen opening
• Retained on the screen
Oversize (Tails)
Undersize (Fines)
Screen
• Smaller than screen opening
• Passes through the screen
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screening operation
Types of Screening Operation
 Unsized function
 A single screen can make a single separation into two fractions, i.e.,
undersize and oversize.
 Sized function
 When a solid mixture is divided into many fractions by passing
through a series of screens.
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screening operation
Mesh
1”
 The holes on the screen
 Mesh number
 Defined as the number of holes
per linear inch
 The higher the mesh number,
the smaller is the screen
opening
1”
Mesh 4
1”
Mesh 200
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1”
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screening operation
Mesh
 Screen aperture
 Clear opening in the screen surface
 Maximum clear space between the edges of
the screen opening. It is usually given in
inches or millimeter
1 𝑖𝑛.
𝐴𝑝𝑒𝑟𝑡𝑢𝑟𝑒 =
− 𝐷𝑤𝑖𝑟𝑒
𝑀𝑒𝑠ℎ 𝑁𝑜.
 A Mesh 3 screen has 3 openings per inch
and the aperture is 1/3” minus the diameter
of the wire.
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standard sieve scales
Tyler
Standard
Sieve Series
Source: McCabe
(Appendix 5)
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screening operation
Indicating Particle Size
 Unsized Function
 Oversize 4 Mesh, +4, +4.76 mm
 Undersize 4 Mesh, -4, -4.76 mm
 Sized Function
 Through 4 on 6
 -4+6
 4/6
 -4.76 mm + 3.36 mm
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particle size distribution
Particle Size Distribution
 Differential Screen Analysis (DSA)
 Data consist of Mesh No. (n) vs Weight fraction or % retained on the
screen (ΔΦn)
 Cumulative Screen Analysis - larger than Dp (CSA larger)
 Data consist of n vs Cumulative fraction larger than n (Φn)
 Cumulative Screen Analysis - smaller than Dp (CSA smaller)
 Data consist of n vs Cumulative fraction smaller than n (1-Φn)
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particle size distribution
Particle Size Distribution
Feed
50 kg
DSA
5 kg
Mesh 6
n
ΔΦn
6
0.10
20 kg
Mesh 8
8
0.40
10
0.24
14
0.12
20
0.08
pan
0.06
Total
1.00
12 kg
Mesh 10
6 kg
Mesh 14
4 kg
Mesh 20
3 kg
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particle size distribution
Particle Size Distribution
Feed
50 kg
DSA
CSA larger
5 kg
Mesh 6
n
ΔΦn
Φn
6
0.10
0.10
20 kg
Mesh 8
8
0.40
0.50
10
0.24
0.74
14
0.12
0.86
20
0.08
0.94
pan
0.06
1.00
Total
1.00
12 kg
Mesh 10
6 kg
Mesh 14
4 kg
Mesh 20
3 kg
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particle size distribution
Particle Size Distribution
Feed
50 kg
DSA
CSA larger
CSA smaller
5 kg
Mesh 6
n
ΔΦn
Φn
1-Φn
6
0.10
0.10
0.90
20 kg
Mesh 8
8
0.40
0.50
0.50
10
0.24
0.74
0.26
14
0.12
0.86
0.14
20
0.08
0.94
0.06
pan
0.06
1.00
0
Total
1.00
12 kg
Mesh 10
6 kg
Mesh 14
4 kg
Mesh 20
3 kg
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particle size distribution
Particle Size Distribution
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DSA
CSA
larger
CSA
smaller
DSA
19
screening material balance
Material Balance
Feed
D, xD
F, xF
xF, xD and xB be the mass fraction
of the oversized material in the
3 streams.
Overflow
Underflow
Screen
Let F, D and B be the mass flow
rates of the Feed, Overflow and
Underflow, respectively; and
B, xB
1-xF, 1-xD and 1-xB are the mass
fractions of the undersized
material in the 3 streams.
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screening material balance
Material Balance
 Overall Material Balance
𝑭=𝑫+𝑩
Feed
D, xD
F, xF
Overflow
 Oversize Material Balance
𝑭𝒙𝑭 = 𝑫𝒙𝑫 + 𝑩𝒙𝑩
Underflow
 Overflow to Feed Ratio
𝑫 𝒙𝑭 − 𝒙𝑩
=
𝑭 𝒙𝑫 − 𝒙𝑩
Screen
B, xB
 Underflow to Feed Ratio
𝑩 𝒙𝑫 − 𝒙𝑭
=
𝑭 𝒙𝑫 − 𝒙𝑩
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screen effectiveness
Screen Effectiveness (E)
 A measure of success of the completeness of the separation.
 Irregularly sized materials could cause blind screens which
lowers the screen effectiveness.
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screen effectiveness
Low screen effectiveness
Actual screens do not give perfect separations.
 Closest separations are obtained with spherical particles on
standard testing screens.
 Needle-like or fibrous or where the particle tend to aggregate
into clusters that act as large particles.
 Long, thin particles may strike the screen surface endwise and
pass through easily.
 Other particles of the same size and shape may strike the screen
sideways and be retained.
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screen effectiveness
Screen Effectiveness (E)
 EA = recovery of oversized material
𝑫𝒙𝑫
𝒙𝑭 − 𝒙𝑩 𝒙𝑫
𝑬𝑨 =
=
𝑭𝒙𝑭
𝒙𝑫 − 𝒙𝑩 𝒙𝑭
 EB = recovery of undersized material
𝑩(𝟏 − 𝒙𝑩 ) (𝒙𝑫 − 𝒙𝑭 )(𝟏 − 𝒙𝑩 )
𝑬𝑩 =
=
𝑭(𝟏 − 𝒙𝑭 ) (𝒙𝑫 − 𝒙𝑩 )(𝟏 − 𝒙𝑭 )
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Feed
D, xD
F, xF
Overflow
Underflow
Screen
B, xB
24
screen effectiveness
Screen Effectiveness (E)
 E = screen effectiveness
𝑫𝒙𝑫 𝑩(𝟏 − 𝒙𝑩 )
𝑬 = 𝑬𝑨 𝑬𝑩 =
×
𝑭𝒙𝑭 𝑭(𝟏 − 𝒙𝑭 )
Feed
D, xD
Overflow
𝒙𝑭 − 𝒙𝑩 𝒙𝑫 (𝒙𝑫 − 𝒙𝑭 )(𝟏 − 𝒙𝑩 )
𝑬=
×
𝒙𝑫 − 𝒙𝑩 𝒙𝑭 (𝒙𝑫 − 𝒙𝑩 )(𝟏 − 𝒙𝑭 )
Underflow
Unsized Function
𝑫𝒆𝒔𝒊𝒓𝒆𝒅
𝑼𝒏𝒅𝒆𝒔𝒊𝒓𝒆𝒅
𝑬=
×
𝑭𝒆𝒆𝒅𝒅𝒆𝒔𝒊𝒓𝒆𝒅 𝑭𝒆𝒆𝒅𝒖𝒏𝒅𝒆𝒔𝒊𝒓𝒆𝒅
F, xF
Screen
B, xB
Sized Function
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unsized function
Example 1
It is desired to remove small particles from a crushed stone
mixture by screening through a 10-mesh screen. The screen
analysis of feed, overflow and underflow are given in the table.
a) Calculate the mass ratios of the overflow and underflow to
feed.
b) Plot Dp vs Screen analysis for the feed, overflow and
underflow
c) Find the effectiveness of the screen
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unsized function
Example 1
Mesh
4
6
8
10
14
20
28
35
65
Pan
Dp (mm)
4.699
3.327
2.362
1.651
1.168
0.833
0.589
0.417
0.208
Feed
0
0.025
0.125
0.32
0.26
0.155
0.055
0.02
0.02
0.02
Overflow
0
0.071
0.43
0.85
0.97
0.99
1.0
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Underflow
xF = 0.47
xD = 0.85
xB = 0.195
1
0.805
0.42
0.17
0.09
0.06
0.025
0
27
unsized function
Example 1
a) Overflow/Underflow to Feed ratio
Overflow to Feed ratio:
𝑫 𝒙𝑭 − 𝒙𝑩
=
= 𝟎. 𝟒𝟐
𝑭 𝒙𝑫 − 𝒙𝑩
Underflow to Feed ratio:
𝑩 𝒙𝑫 − 𝒙𝑭
=
= 𝟎. 𝟓𝟖
𝑭 𝒙𝑫 − 𝒙𝑩
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unsized function
Example 1
b) Dp vs Feed/Overflow/Underflow
1
Mass fraction
0.8
Feed
0.6
Overflow
Underflow
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Dp (mm)
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unsized function
Example 1
c) Screen Effectiveness
𝑫𝒙𝑫 𝑩(𝟏 − 𝒙𝑩 )
𝑬 = 𝑬𝑨 𝑬𝑩 =
×
𝑭𝒙𝑭 𝑭(𝟏 − 𝒙𝑭 )
𝒙𝑭 − 𝒙𝑩 𝒙𝑫 (𝒙𝑫 − 𝒙𝑭 )(𝟏 − 𝒙𝑩 )
𝑬=
×
= 𝟎. 𝟔𝟔𝟗
𝒙𝑫 − 𝒙𝑩 𝒙𝑭 (𝒙𝑫 − 𝒙𝑩 )(𝟏 − 𝒙𝑭 )
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unsized function
Practice Problem
Using the same data in
Example 1, consider the
20-Mesh screen.
a) Calculate the overflow
and underflow to feed
ratios.
b) What is the
effectiveness of the 20mesh screen?
c) Why is the 20-mesh
screen an
effective/ineffective
screen?
Mesh
Dp (mm)
Feed
Overflow
4
4.699
0
0
6
3.327
0.025
0.071
8
2.362
0.125
0.43
1
10
1.651
0.32
0.85
0.805
14
1.168
0.26
0.97
0.42
20
0.833
0.155
0.99
0.17
28
0.589
0.055
1.0
0.09
35
0.417
0.02
0.06
65
0.208
0.02
0.025
0.02
0
Pan
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Underflow
31
sized function
Example 2
It is desired to separate 1000 kg of a mixture of crushed solids into three
fractions, a coarse fraction retained on a 20-mesh screen; a middle
fraction passing through a 20-mesh screen and retained on a 65-mesh
screen; and a fine fraction passing through a 65-mesh screen. Two Tyler
Standard Screens are used to remove particles 20/65. Screen analysis of
the feed, coarse, medium and fine fractions are given. What are the
effectiveness of the 20 and 65 screens, given the following screen
analysis?
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sized function
Example 2
It is desired to separate 1000 kg of a mixture of crushed solids into three
fractions, a coarse fraction retained on a 20-mesh screen; a middle
fraction passing through a 20-mesh screen and retained on a 65mesh screen; and a fine fraction passing through a 65-mesh screen.
Two Tyler Standard Screens are used to remove particles 20/65. Screen
analysis of the feed, coarse, medium and fine fractions are given. What
are the effectiveness of the 20 and 65 screens, given the following screen
analysis?
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Example 2
F
1000 kg
P
20
65
R
Q
Streams:
Mesh
-4+6
-6+8
-8+10
-10+14
-14+20
-20+28
-28+35
-35+48
-48+65
-65+100
-100+150
-150+200
pan
F
Feed
2.51
12.5
32.07
25.7
15.9
5.38
2.1
1.02
0.77
0.58
0.41
0.31
0.75
100
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P
Coarse
3.27
13.59
38.04
27.17
16.3
1.36
0.27
0
0
0
0
0
0
100
Q
sized function
Medium
0.5
11.26
18.03
22.53
13.52
18.03
8.11
4.51
3.42
0.09
0
0
0
100
R
Fines
0
0
1.65
16.63
21.38
9.03
2.38
0.48
0.24
13.3
9.74
7.36
17.81
100
35
Example 2
Streams:
Fraction 1
+20
F
1000 kg
P
20
65
R
Q
Fraction 2
-20+65
(undesired)
Fraction 3
-65
Mesh
-4+6
-6+8
-8+10
-10+14
-14+20
-20+28
-28+35
-35+48
-48+65
-65+100
-100+150
-150+200
pan
F
Feed
2.51
12.5
32.07
25.7
15.9
5.38
2.1
1.02
0.77
0.58
0.41
0.31
0.75
100
UST CHEMICAL ENGINEERING DEPARTMENT
P
Coarse
3.27
13.59
38.04
27.17
16.3
1.36
0.27
0
0
0
0
0
0
100
Q
sized function
Medium
0.5
11.26
18.03
22.53
13.52
18.03
8.11
4.51
3.42
0.09
0
0
0
100
R
Fines
0
0
1.65
16.63
21.38
9.03
2.38
0.48
0.24
13.3
9.74
7.36
17.81
100
36
Example 2
Streams:
1
F
1000 kg
F1, F2, F3
P
P1, P2, P3
2
Q
Q1, Q2, Q3
R
R 1, R 2, R 3
3
Mesh
-4+6
-6+8
-8+10
-10+14
-14+20
-20+28
-28+35
-35+48
-48+65
-65+100
-100+150
-150+200
pan
F
Feed
2.51
12.5
32.07
25.7
15.9
5.38
2.1
1.02
0.77
0.58
0.41
0.31
0.75
100
UST CHEMICAL ENGINEERING DEPARTMENT
P
Coarse
3.27
13.59
38.04
27.17
16.3
1.36
0.27
0
0
0
0
0
0
100
Q
sized function
Medium
0.5
11.26
18.03
22.53
13.52
18.03
8.11
4.51
3.42
0.09
0
0
0
100
R
Fines
0
0
1.65
16.63
21.38
9.03
2.38
0.48
0.24
13.3
9.74
7.36
17.81
100
37
sized function
Example 2
Solving for F1, F2 and F3:
F1 = (sum of mass fractions of all fraction 1 particles in F stream)*(Feed rate)
F2 = (sum of mass fractions of all fraction 2 particles in F stream)*(Feed rate)
F3 = (sum of mass fractions of all fraction 3 particles in F stream)*(Feed rate)
F1 = (1000 kg)*(0.8868) = 886.8 kg
F2 = (1000 kg)*(.0927) = 92.7 kg
F3 = (1000 kg)*(0.0205) = 20.5 kg
*Do the same for other streams
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sized function
Example 2
F
Material Balance Equations
Overall:
1000 = P + Q + R
Fraction 1: 886.8 = 0.9837P + 0.6584Q + 0.3966R
Fraction 2: 92.7 = 0.0163P + 0.3407Q + 0.1213R
Fraction 3: 20.5 = 0.0009Q + 0.4821R
Solving simultaneously (3 unknowns, 3 equations):
P = 736.010 kg
Q = 221.882 kg
R = 42.108 kg
UST CHEMICAL ENGINEERING DEPARTMENT
1000 kg
F1 = 886.8
F2 = 92.7
F3 = 20.5
P
P1 = 0.9837P
P2 = 0.0163P
P3 = 0
Q
R
Q1 = 0.6584Q
Q2 = 0.3407Q
Q3 = 0.0009Q
R1 = 0.3966R
R2 = 0.1213R
R3 = 0.4821R
39
sized function
Example 2
F
1000 kg
F1 = 886.8
F2 = 92.7
F3 = 20.5
Screen Effectiveness
𝐷𝑒𝑠𝑖𝑟𝑒𝑑
𝑈𝑛𝑑𝑒𝑠𝑖𝑟𝑒𝑑
𝐸=
∗
𝐹𝑒𝑒𝑑𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝐹𝑒𝑒𝑑𝑢𝑛𝑑𝑒𝑠𝑖𝑟𝑒𝑑
P
S
S 1, S 2, S 3
P1 = 724.01
P2 = 12.00
P3 = 0
Q
𝑂𝑣𝑒𝑟𝑠𝑖𝑧𝑒𝑑
𝑈𝑛𝑑𝑒𝑟𝑠𝑖𝑧𝑒𝑑
𝐸=
∗
𝐹𝑒𝑒𝑑𝑜𝑣𝑒𝑟𝑠𝑖𝑧𝑒𝑑 𝐹𝑒𝑒𝑑𝑢𝑛𝑑𝑒𝑟𝑠𝑖𝑧𝑒𝑑
Solving for Stream S:
OMB for Mesh 20: F = P + S → S = F – P
Fraction 1: 𝑺𝟏 = 𝑭𝟏 − 𝑷𝟏 = 𝟏𝟔𝟐. 𝟕𝟗 𝒌𝒈
Fraction 2: 𝑺𝟐 = 𝑭𝟐 − 𝑷𝟐 = 𝟖𝟎. 𝟕𝟎 𝒌𝒈
Fraction 3: 𝑺𝟑 = 𝑭𝟑 − 𝑷𝟑 = 𝟐𝟎. 𝟓𝟎 𝒌𝒈
UST CHEMICAL ENGINEERING DEPARTMENT
R
Q1 = 146.09
Q2 = 75.60
Q3 = 0.20
R1 = 16.70
R2 = 5.11
R3 = 20.30
40
sized function
Example 2
Screen Effectiveness
𝑂𝑣𝑒𝑟𝑠𝑖𝑧𝑒𝑑
𝑈𝑛𝑑𝑒𝑟𝑠𝑖𝑧𝑒𝑑
𝐸=
∗
𝐹𝑒𝑒𝑑𝑜𝑣𝑒𝑟𝑠𝑖𝑧𝑒𝑑 𝐹𝑒𝑒𝑑𝑢𝑛𝑑𝑒𝑟𝑠𝑖𝑧𝑒𝑑
𝐸20
𝑃1 𝑆2 + 𝑆3
= ∗
= 𝟎. 𝟕𝟑𝟎
𝐹1 𝐹2 + 𝐹3
𝐸65
𝑄1 + 𝑄2 𝑅3
=
∗
= 𝟎. 𝟗𝟎𝟐
𝑆1 + 𝑆2 𝑆3
F
1000 kg
F1 = 886.8
F2 = 92.7
F3 = 20.5
P
S1 = 162.79
S2 = 80.70
S3 = 20.50
P1 = 724.01
P2 = 12.00
P3 = 0
S
Q
R
Q1 = 146.09
Q2 = 75.60
Q3 = 0.20
R1 = 16.70
R2 = 5.11
R3 = 20.30
UST CHEMICAL ENGINEERING DEPARTMENT
41
rotar y trommel screen
Rotary Trommel Screen
 A mechanical screening machine consisting
of a perforated cylindrical drum that is
normally elevated at an angle at the feed
end.
 Physical size separation is achieved as the
feed material spirals down the rotating drum,
where the undersized material smaller than
the screen apertures passes through the
screen, while the oversized material exits at
the other end of the drum.
UST CHEMICAL ENGINEERING DEPARTMENT
42
rotar y trommel screen
Rotary Trommel Screen
UST CHEMICAL ENGINEERING DEPARTMENT
43
rotar y trommel
Example 3
It is desired to separate a 1000-kg mixture of crushed stone clinker in a
rotary trommel to obtain three products, namely stream D, C and B
passing through 150, 35 and 10 mesh screens, respectively. Find the
effectiveness of each screen using the given screen analysis.
UST CHEMICAL ENGINEERING DEPARTMENT
44
SCREEN MESH FEED COARSE MIDDLE
-3+4
-4+6
-6+8
-8+10
-10+14
-14+20
-20+28
-28+35
-35+48
-48+65
-65+100
-100+150
-150+170
-170+200
-200+270
2.5
7.5
12.4
7.4
21.3
8.2
7.5
3.8
8.1
11.6
5.3
1.4
2.1
0.7
0.2
UST CHEMICAL ENGINEERING DEPARTMENT
0.087
0.208
0.417
0.243
0.045
0.039
0.01
0.01
0.521
0.156
0.182
0.053
0.029
FINE VERY FINE
0.075
0.017
C
0.061
0.238
0.395
0.17
0.041
0.003
EXAMPLE 3
DATA
0.088
0.059
0.588
0.206
0.059
45
CHE 2117
LECTURE 2
SCREENING
EN D O F LECTURE