1

© Dr. Werner Hintz

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

1.0

0.63

0.4

0.25

0.1

0.063

0.04

mass fraction [g]

1.33

15.34

13.44

36.56

40.34

64.02

10.79

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.

2

© Dr. Werner Hintz

Exercise sheet :

particle size

fraction

mass mass fraction cumulative

fraction

interval

width

frequency

distribution

mean

interval

diameter

i

di-1 - di mi μ3,i Q3,i Δ di q3,i dm,i dm i i, ,⋅ μ3

100μ3

100,

,

i

m id ⋅

11003

3

dm i

i

,

,⋅μ

∑= ⋅

μn

1i3

i,m

i,3

100d

Q0(d) q0(d)

[mm] [g] [%] [%] [mm] [% mm-1] [mm] [mm] [mm-1] [mm-3] [mm-3] [-] [mm-1]

1

2

3

4

5

6

7

8

9

Σ