Unformatted text preview: 0.063 0.0
8.8
21.3
138.2
211.6
161.7
81.6
44.1
28.7
13.2
9.6
8.8
7.4 0.00
1.20
2.90
18.80
28.79
22.00
11.10
6.00
3.90
1.80
1.31
1.20
1.01 2.855
2.030
1.440
1.015
0.725
0.513
0.363
0.256
0.181
0.128
0.098
0.077 0.0120
0.0290
0.1880
0.2879
0.2200
0.1110
0.0600
0.0390
0.0180
0.0131
0.0120
0.0101 3.350
2.360
1.700
1.180
0.850
0.600
0.425
0.300
0.212
0.150
0.106
0.090
0.063 100.00
98.80
95.90
77.10
48.31
26.31
15.21
9.21
5.31
3.51
2.20
1.01
0.00 735.0 100.00 Total 1.0000 Exercise 17.3 (continued)
0.35
0.30 Differential Plot 0.25
0.20
Mass Fraction
0.15
0.10
0.05
0.00
0.0 0.5 1.0 1.5 2.0 2.5 3.0 Average Particle Size, mm 100
90
80
70
60
Cumulative Mass, % Cumulative Undersize Plot 50
40
30
20
10
0
0.0 0.5 1.0 1.5 2.0
Aperture Size, mm 2.5 3.0 3.5 4.0 Exercise 17.4
Subject: Mean particle diameter from a particlesize analysis
Given: Particlesize analysis in terms of the number of particles in each size fraction
Assumptions: All particles have the same shape
Find: Expressions for the surfacemean and massmean diameters based on numbers of
particles, Ni, rather than mass fractions, xi, for each size range.
Analysis: It is important to note that regardless of whether the expression is in terms of mass
fractions or numbers of particles, the numerical result for the mean diameter is the same.
Surfacemean diameter:
From (177), the surfacemean diameter in terms of mass fractions is:
1
DS = n
xi
i =1 D pi (1) From (1710), mass fraction is related to number of particles by, xi = ( )ρ N i f v D pi p (2) Mt Substituting (2) into (1) gives, DS = 3 1 fvρ p n Mt i =1 Ni D 2
pi Summing (2) over all mass fractions gives,
fvρ p
1
=n
3
Mt
N i D pi
i =1 Substituting (4) into (3) gives the desired expression for surfacemean diameter:
n DS = i =1
n
i =1 3 N i D pi
2 N i D pi (3) (4) Exercise 17.4 (continued)
Massmean diameter:
From (178), the massmean diameter in terms of mass fractions is:
n DW = i =1 Substitution of (2) into (5) gives, DW = (5) xi D pi fvρ p n Mt i =1 () N i D pi 4 Substitution of (4) into (6) gives the desired expression for massmean diameter:
n DW = i =1
n
i =1 4 N i D pi
3 N i D pi It may be noted that expressions for the other two mean diameters in terms of numbers of
particles are given as (179) for arithmetic mean and as (1714) for the volume mean. (6) Exercise 17.5
Subject: Calculation of mean particle diameters from a screen analysis.
Given: Screen analysis of sodium thiosulfate crystals from Exercise 17.3.
Assumptions: All particles have the same sphericity and volume shape factor.
Find: Surfacemean, massmean, arithmeticmean, and volumemean diameters
Analysis: The following equations apply for n screen fractions, i:
Surfacemean diameter, (177): DS = 1
n
i =1 Massmean diameter, (178): DW = n
i =1 where D pi is average aperture xi
D pi xi D pi n Volumemean diameter, (1715): i =1 D pi n xi i =1 Arithmeticmean diameter, (1712): D N = xi D pi 2 3 1 DV =
n xi i =1 1/ 3 D pi 3 The calculations are made with a spreadsheet on the following page where mesh
apertures...
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 Spring '11
 Levicky
 The Land

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