Sedimentation Methods for Determining Particle Sizes
•
Rely on Stokes’ Law
•
Sphere of diameter D falling through viscous fluid reaches a terminal
velocity, which depends on the bouyant weight of the sphere, the sphere
diameter, and the fluid viscosity (for R
e
< 1)
•
Thus, a sphere of diameter D will fall distance h in time t
D:
•
where
is the fluid viscosity,
g
s
is the unit weight (=
r
g) of the sphere
material, and
g
w
is the unit weight of water
•
This is the basis of the “pipette” method of determining the sizes of fine
soils
–
easy to explain, but requires high precision
•
Also the basis of the “hydrometer” method
–
more complex to explain, but
simpler to do
2
w
s
D
D
h
18
t
g
g
Pipette Method
•
Mix 50g of dry soil in 1 litre of
water, and put into 1 litre graduated
cylinder. Shake thoroughly so that
soil is evenly dispersed in the water
•
Any
10 ml volume of the water will
contain 0.5g of soil
•
Set on bench
–
allow to start settling
•
At pre

determined times, use pipette
to take 10 ml sample from exactly
100 mm below the surface of the
flask
•
Dry the sample, and weigh the dry
soil
•
So how can this be used to work out
particle size distribution?
1 litre flask
10 ml pipette
100 mm
t
D2
t
D1
h
Coarse spheres (D1)
Fine spheres (D2)
2
w
s
2
D
2
w
s
1
D
2
w
s
D
2
D
h
18
t
1
D
h
18
t
D
h
18
t
g
g
g
g
g
g
t
D2
t
D1
h
Coarse spheres (D1)
Fine spheres (D2)
2
w
s
2
D
2
w
s
1
D
2
w
s
D
2
D
h
18
t
1
D
h
18
t
D
h
18
t
g
g
g
g
g
g
t
D2
h
Spheres (D1 & D2)
t
D1
Before t
D1
, particles D1 are at same
concentration at height h as in
original sample
After t
D1
, but before t
D2
, particles
D1 are missing, but particles D2 are
in their original concentration
After t
D2
, none of either D1 or D2
particles present
To find percentage of particles finer
than D1, take sample just after t
D1
2
w
s
2
D
2
w
s
1
D
2
w
s
D
2
D
h
18
t
1
D
h
18
t
D
h
18
t
g
g
g
g
g
g
t
D2
h
Spheres (D1 & D2)
t
D1
Before t
D1
, particles D1 are at same
concentration at height h as in
original sample
After t
D1
, but before t
D2
, particles
D1 are missing, but particles D2 are
in their original concentration
After t
D2
, none of either D1 or D2
particles present
To find percentage of particles finer
than D1, take sample just after t
D1
2
w
s
2
D
2
w
s
1
D
2
w
s
D
2
D
h
18
t
1
D
h
18
t
D
h
18
t
g
g
g
g
g
g
Continuous distribution
•
Choosing a time for taking a sample is
like choosing a sieve size . Thus, to find
percentage finer than 20
m
m, take sample
at depth 100 mm at time 4.57 minutes.
•
Dry the sample; weigh the dry soil.
•
Weight of soil in this 10 ml sample is
same as weight of material finer than 20
mm in 10 ml of original sample.
•
Say 50 g of soil per litre
–
i.e. 0.5 g per 10
ml in original sample
•
Say 0.3 g of soil in sample taken at 4.57
minutes
•
Thus, % finer than 20
m
m is
0.3/0.5 = 60%
hours
7.62
minutes
457
longer
10
is
time
equivalent
m,
2
For
minutes
4.57
seconds
274
10
20
81
.
9
4
.
26
1
.
0
10
1
18
t
m)
(0.1
mm
100
h
(water)
kN/m
81
.
9
soils
many
for
kN/m
4
.
26
C
20
@
kPa.s
10
1
D
h
18
t
2
2
6
6
m
20
2
w
2
s
6
w
2
w
s
D
m
g
g
g
g
m
Spheres of quartz settling in water
10
20
1.13
2
3
4
5
7
1 day
10 hours
10
100
1,000
10,000
100,000
0
10
20
30
40
50
60
70
80
90
100
110
Sphere Diameter (
m)
Time to settle 100 mm (sec.) .
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Reynold's Number
Settling time
Reynolds Number
Stoke's Law only valid for Reynold's Number < 1. From below,
only valid for D < 100
m
洠楦i晬畩f楳iw慴敲a⸠
)
Pa.s
k
10
1
(
fluid
the
of
viscosity
dynamic
is
diameter
is
D
velocity
is
v
)
t/m
1
(
fluid
the
of
density
is
where
vD
R
:
)
R
(
Number
s
Reynold'
6
w
3
w
e
e
r
r
r
Equipment for Hydrometer Test
Hydrometer measures the average density of the fluid (at about the depth to the
centre of the bulb. This reduces as coarser material settles
–
hydrometer
“samples” the density at different times (like the pipette in a sense)
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