TITLE: Experiment 4 (Angle of Repose)
OBJECTIVES:
1) To calculate the angle of repose for each type of sand with different particle size
2) To measure the change of angle of repose after addition of magnesium stearate
INTRODUCTION:
The angle of repose is one of the most important macroscopic parameters in characterising the behaviour of granular materials. It has been found that the angle of repose strongly depends on material properties such as sliding and rolling frictions and density of particles and particle characteristics such as size. It is generally reported that the angle of repose increases with increasing sliding and rolling friction coefficients and deviation from spheres, and decreases with increasing particle size and container thickness. Angle of repose is the maximum angle to the horizontal at which rocks and soil will remain without sliding and the slope of a powder cone is formed by pouring a powder from a specific height. In general, the flowability of a powder is judged to be good when the angle of repose is less than 30 degrees and to be poor when the angle is larger than 40 degrees. The downhill movement of soil and loose unconsolidated sediments is due to the force of gravity and is resisted by friction. At angles steeper than the angle of repose friction is not sufficient to counter gravity and mass wasting occurs. At angles less than the angle of repose gravity cannot overcome friction and sediments may accumulate to form steeper slopes. Magnesium stearate was used in this experiment as glidants in which it will promote the flow of granulations or powder materials by reducing the friction between the particles.
METHODS:
APPARATUS
Plastic cylinder, stopper, 15% magnesium Stearate, 150 mm, 500 mm, 850 mm, 355 mm, various sand, funnel, newspaper, weighing boat, spatula, weighing balance
PROCEDURE
1) 100g of each type of sand (150 mm, 355 mm, 500 mm, 850 mm, and various sizes) was measured using weighing balance
2) For each type of sand, it was poured into plastic cylinder with the stopper at the bottom of it.
3) Plastic cylinder was pulled upwards and the substances was flowed to form a peak/heap.
4) The height of peak/heap was measured also the width of the stopper. This is to measure the angle of repose for the each type of sand.
5) Angle of repose for each type of sand was calculated.
6) 15% of magnesium stearate was measured and each type of sand was added to it until it reach 100g.
7) Step 2 until 5 was repeated
RESULTS AND CALCULATION:
Angle of repose : tan θ = height/width
Angle of repose without glidant:
150 mm : tan θ = (2.20 cm)/(2.23 cm)
= 43.11°
355 mm : tan θ = (2.00 cm)/(2.23 cm)
= 40.40°
500mm : tan θ = (1.90 cm)/(2.23 cm)
= 38.96°
850mm : tan θ = (1.80 cm)/(2.23 cm)
= 37.45°
Various size : tan θ = (2.30 cm)/(2.23 cm)
= 44.38°
Angle of repose with glidant:
150mm : tan θ = (3.80 cm)/(2.23 cm)
= 58.27°
355mm : tan θ = (2.30 cm)/(2.23 cm)
= 44.38°
500mm : tan θ = (2.10 cm)/(2.23 cm)
= 41.78°
850mm : tan θ = (2.10 cm)/(2.23 cm)
= 41.78°
Various sizes : tan θ = (2.20 cm)/(2.23 cm)
= 43.11°
150 mm : tan θ = (3.90 cm)/(2.50 cm)
θ = 57.34 °
355 mm : tan θ = (2.20 cm)/(2.50 cm)
θ = 41.35 °
500 mm : tan θ = (1.90 cm)/(2.50 cm)
θ = 37.75 °
850 mm : tan θ = (1.80 cm)/(2.50 cm)
θ = 35.75 °
Various sizes : tan θ = (2.40 cm)/(2.50 cm)
θ = 43.83 °
Angle of repose with glidant
150 mm : tan θ = (4.10 cm)/(2.50 cm)
θ = 58.63 °
355 mm : tan θ = (3.50 cm)/(2.50 cm)
θ = 54.46 °
500 mm : tan θ = (2.40 cm)/(2.50 cm)
θ = 43.83 °
850 mm : tan θ = (2.80 cm)/(2.50 cm)
θ = 48.23 °
Various sizes : tan θ = (3.00 cm)/(2.50 cm)
θ = 50.19 °
Angle of repose without glidant
150 mm : tan θ = (3.65 cm)/(2.40 cm)
= 56.67 °
355 mm : tan θ = (1.90 cm)/(2.40 cm)
= 38.37 °
500 mm : tan θ = (1.75 cm)/(2.40 cm)
= 36.10 °
850 mm : tan θ = (1.75 cm)/(2.40 cm)
= 36.10 °
Various sizes : tan θ = (2.00 cm)/(2.40 cm)
= 39.81 °
Angle of repose with glidant
150 mm : tan θ = (4.60 cm)/(2.40 cm)
= 62.45 °
355 mm : tan θ = (4.30 cm)/(2.40 cm)
= 60.83 °
500 mm : tan θ = (3.50 cm)/(2.40 cm)
= 55.56 °
850 mm : tan θ = (3.40 cm)/(2.40 cm)
= 54.78 °
Various sizes : tan θ = (4.15 cm)/(2.40 cm)
= 59.96 °
Angle of repose without glidant
150 mm : tan θ = (2.20 cm)/(2.30 cm)
= 43.73 °
355 mm : tan θ = (2.00 cm)/(2.30 cm)
= 41.00 °
500 mm : tan θ = (1.90 cm)/(2.30 cm)
= 39.56 °
850 mm : tan θ = (1.80 cm)/(2.30 cm)
= 38.05 °
Various sizes : tan θ = (2.30 cm)/(2.30 cm)
= 45.00 °
Angle of repose with glidant
150 mm : tan θ = (3.80 cm )/(2.30 cm)
= 58.82 °
355 mm : tan θ = (3.70 cm)/(2.30 cm)
= 58.13 °
500 mm : tan θ = (3.50 cm)/(2.30 cm)
= 56.69 °
850 mm : tan θ = (3.00 cm)/(2.30 cm)
= 52.52 °
Various sizes : tan θ = (3.30 cm)/(2.30 cm)
= 55.12 °
QUESTIONS:
1) What is the angle of repose for each of the substances?
2. What is the factors may influence the angle of repose for each of substances?
- Particle size, coarser particles have high angles of repose than fine particles.
- Particle shape
- Cohesiveness, fine particles may reveal cohesiveness owing to spherical particles having a greater tendency to roll.
- Presence of other components example glidants.
- Moisture, Angle of repose of loose dry powder increases by compacting as well as by introducing by moisture. Moist sand has a much higher angle of repose than dry sand.
- The individual material will affect the angle of repose, a reflection of the different coefficients of friction between different substances.
3. What other method can be used to calculate the angle of repose for each substances?
Tilting box method - This method is appropriate for fine-grained, non-cohesive materials, with individual particle size less than 10 mm. The material is placed within a box with a transparent side to observe the granular test material. It should initially be level and parallel to the base of the box. The box is slowly tilted at a rate of approximately .3 degrees/second. Tilting is stopped when the material begins to slide in bulk, and the angle of the tilt is measured.
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. Stop pouring the material when the pile reaches a predetermined height or the base a predetermined width. Rather than attempt to measure the angle of the resulting cone directly, divide the height by half the width of the base of the cone. The inverse tangent of this ratio is the angle of repose.
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. The effect is similar to watching clothes tumble over one another in a slowly rotating clothes dryer. The granular material will assume a certain angle as it flows within the rotating cylinder. This method is recommended for obtaining the dynamic angle of repose, and may vary from the static angle of repose measured by other methods. When describing the angle of repose for a substance, always specify the method used
DISCUSSION:
One of the methods for testing powder flow is angle of repose. Angle of repose can be influenced by many different factors. Density, particle shape and size, moisture content, and texture of the particles all have a profound effect on an object’s ability to flow. If a material flows easily it has a low angle of repose and if it does not, it has a high angle of repose. As we can see from the section of results and calculation above, the smallest size of sand (150 mm) without glidant having high angle of repose. Meanwhile, for the largest size of sand which is 850 mm has low angle of repose. This is because the angle of repose is influenced by the particle size of material. From the result, it can be seen that the material of uniform size (150 mm, 355mm, 500 mm, 850 mm) have low angle of repose than the material of various sizes. This is because particles of uniform size will flow easily, hence low angle of repose. In addition, particles of irregular shape have showed high angle of repose because of the interlocking do not flow easily. Other factor that influences the angle of repose is the moisture content in the solids. Angle of repose of loose dry powder increases by compacting as well as by introducing by moisture. Moist sand has a much higher angle of repose than dry sand. Solid materials of different structure like granular and fibres which show different flowabilty characteristics also influenced the angle of repose. It can be seen when we mix magnesium stearate (glidant) with the sand. The angle of repose become higher as we mix more magnesium stearate with the sand. The individual material will affect the angle of repose, a reflection of the different coefficients of friction between different substances. Each particulate material has its own unique angle of repose, and will interact with outside influences differently because of it. Every granulated or powder solid uses friction to “hold together” against the force of gravity.
CONCLUSION:
Particles size and shape will influence the angle of repose of the material. Also affect the angle of repose is moisture and the density of material. All of this will give effect to the angle of repose and their flowability. A material which flows easily has a low angle of repose and it will has a high angle of repose when the flowability of the material is decrease.
REFERENCES:
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