Thursday, 19 December 2013

PRACTICAL 4: ANGLE OF REPOSE


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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