1
Exercise 1:
The particle size distribution of a particulate material should be determined by analysing a test
sieving. The masses being on the single sieves (see picture) were determined by balancing [in
g]. The initial weight was 190 g.
sieve mesh [mm]
2.5
mass fraction [g]
1.33
1.0
15.34
0.63
13.44
0.4
36.56
0.25
40.34
0.1
64.02
0.063
10.79
0.04
5.31
2.27
1. Calculate the cumulative particle size distribution Q3(d) and the particle size frequency
distribution q3(d),
2. Show Q3(d) and q3(d) in a normal diagram, q3(d) in a log - normal diagram,
3. Determine the median particle size d50 from the graphical picture of Q3(d) and the modal
particle size dh from the graphical picture of q3(d),
4. Calculate mean particle size dm,3,
5. Show Q3(d) in a logarithmical probability diagram and in a RRSB - diagram,
6. Calculate the specific surface area, related to mass, As,m and the Sauter - diameter dST,
7. Calculate the cumulative particle size distribution Q0(d) and the particle size frequency
distribution q0(d), related to quantity number, show Q0(d) and q0(d) in a normal diagram
and in a logarithmical probability diagram.
© Dr. Werner Hintz
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Exercise sheet :
particle size
mass
mass fraction cumulative interval
fraction
fraction
width
frequency
mean
distribution
interval
diameter
i
di-1 - di
[mm]
1
2
3
4
5
6
7
8
9
Σ
© Dr. Werner Hintz
mi
[g]
μ3,i
[%]
Q3,i
[%]
Δ di
[mm]
q3,i
[% mm-1]
dm,i
[mm]
d m,i ⋅ μ3,i
μ3,i
100
d m,i ⋅ 100
[mm]
[mm-1]
1 μ3 , i
⋅
d m3 ,i 100
[mm-3]
n
∑d
i =1
μ 3, i
3
m ,i
Q0(d)
q0(d)
[-]
[mm-1]
⋅100
[mm-3]