Aim:
1. To measure the angle of repose of
a particular type of sand.
2. To identify the factors that may
affect the angle of repose of sand.
3. To observe and investigate the
effect of glidant on angle of repose of sand.
Introduction:
When granular material is poured
onto a flat surface, it mounds up into a pile in the general shape of a
cone. Particles bounce, roll, or slide down the side of the pile until they
come to a stop. The angle that the side of the pile makes with the horizontal
plane is called the angle of repose. Each granular material has its own
characteristic angle of repose. The size of this angle depends on the size and
the shape of the grains, among other things. When a mixture of two granular
materials with different angles of repose is poured, sometimes the result is
spontaneous stratification or segregation. With stratification, alternating
layers of the two materials form parallel to the sloping side of the pile. With
segregation, larger grains end up at the bottom of the slope while smaller
grains remain near the top of the slope.
When instances of spontaneous
stratification and segregation occur, take extra time to observe the behavior
of the poured mixture closely and discuss the observations.
Apparatus and materials:
100 g of 355, 500, 850 micron
sand and mixed sand of various sizes
Glidant (Mg stearate)
Electronic balance
Weighing boat
Funnel+base
Ruler
Procedure:
1.
100g
of 355 micron (mm) sand was weighed.
2.
The
sand was then poured into a funnel attached to its base.
3.
The
funnel was pulled off of its base slowly and the sand was let to flow and form
a pile of cone shape.
4.
The
height of the pile was measured from the peak to the base surface while the
diameter of the pile was measured by measuring the diameter of the base using a
ruler and recorded.
5. The angle of repose of sand was
calculated using formula tan-1 x height/width, where width= 1/2 diameter.
6.
Procedures
1 until 5 were repeated using 355 micron sand of similar weight with the addition
of glidant.
7.
Procedures
1 until 6 were repeated using 500, 850 micron sand and mixed sand of various
sizes.
Results and calculations:
Diameter of pile: 4.8 cm
Therefore, the width of the pile is: 4.8 cm/2= 2.4 cm
Formula: tan-1 height/width
Magnesium stearate:
0.5 % w/w
Size of sand particles (mm)
|
Height, (cm)
|
Angle of repose, θ (°)
|
||
Without glidant
|
With glidant
|
Without glidant
|
With glidant
|
|
355
|
2.0
|
2.1
|
39.81
|
41.19
|
500
|
2.1
|
2.2
|
41.19
|
42.51
|
850
|
2.2
|
2.1
|
42.51
|
41.19
|
Various sizes
|
2.3
|
2.4
|
43.78
|
45.00
|
Magnesium stearate:
1% w/w
Size of sand particles (mm)
|
Height, (cm)
|
Angle of repose, θ (°)
|
||
Without glidant
|
With glidant
|
Without glidant
|
With glidant
|
|
355
|
1.4
|
1.7
|
30.26
|
35.31
|
500
|
1.3
|
1.7
|
28.44
|
35.31
|
850
|
1.3
|
1.2
|
28.44
|
26.57
|
Various sizes
|
1.5
|
1.8
|
32.01
|
36.87
|
Magnesium stearate: 2%
w/w
Size of sand particles (mm)
|
Height, (cm)
|
Angle of repose, θ (°)
|
||
Without glidant
|
With glidant
|
Without glidant
|
With glidant
|
|
355
|
1.7
|
2.0
|
35.31
|
39.81
|
500
|
2.0
|
2.2
|
39.81
|
42.51
|
850
|
1.8
|
1.9
|
36.87
|
38.37
|
Various sizes
|
2.2
|
2.6
|
42.51
|
47.29
|
Magnesium stearate: 3%
w/w
Size of sand particles (mm)
|
Height, (cm)
|
Angle of repose, θ (°)
|
||
Without glidant
|
With glidant
|
Without glidant
|
With glidant
|
|
355
|
2.0
|
2.5
|
39.81
|
46.17
|
500
|
2.1
|
2.5
|
41.19
|
46.17
|
850
|
1.7
|
2.0
|
35.31
|
39.81
|
Various sizes
|
2.4
|
2.9
|
45.00
|
50.39
|
Question:
1.
What is the angle of repose for each of the
materials?
Size of sand particles (mm)
|
Angle of repose, θ (°)
|
|
Without glidant
|
With glidant (1%)
|
|
355
|
30.26
|
35.31
|
500
|
28.44
|
35.31
|
850
|
28.44
|
26.57
|
Various sizes
|
32.01
|
36.87
|
2.
What are the factors that influence the angle of
repose of the materials?
(i)
The individual material will affect the angle of
repose, a reflection of the different coefficients of friction between
different substances.
(ii)
Size of particles: While other factors being equal;
fine grained material will form a shallower pile, with a smaller angle of
repose than coarser grains.
(iii)
Shape of particles: Material with particles of
rough, blocky shapes might create a steeper pile with a larger angle of repose
than material with smoother particles because rough, blocky particles do not
move down the slope as readily as smoother particles.
(iv)
Water content: Moist sand has a much higher
angle of repose than dry sand. If a small amount of water is able to bridge the
gaps between particles, electrostatic attraction of the water to mineral
surfaces will increase soil
strength.
(v)
The method by which the angle of repose is
measured can also affect the measurement.
3. What are the other methods that can be used to
asses the angle ofrepose of the materials?
Tilting box method
This method is appropriate for
fine-grained, non-cohesive materials, with individual particle size less than
10 mm.
Fixed funnel method
The material is poured through a
funnel to form a cone. The tip of the funnel should be held close to the
growing cone and slowly raised as the pile grows, to minimize the impact of
falling particles.
Revolving cylinder method
The material is placed within a
cylinder with at least one transparent face. The cylinder is rotated at a fixed
speed and the observer watches the material moving within the rotating
cylinder.
Shipboard test method
The quantity of the material to be
tested is poured very carefully out of a flask onto a sheet of rough textured
paper, in such a way that a symmetrical cone is formed.
Conclusion:
The angle of repose of 355mm, 500mm,
850mm and various sizes of sand are 30.26°, 28.44°, 28.44°, and 32.01° without
glidant, 35.31°, 35.31°, 26.57°, and 36.87° with glidant respectively. From the
result obtained, glidant does affect the angle of repose of the sand. The angle
of repose of sand with glidant is higher than that of sand with glidant. The
main factors that affect the angle of repose of sand are cohesion of particles,
size of particles, moisture, and ways of measuring angle of repose.
References:
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