Use Of Base Plate In Angle Of Repose

Fixed base cone

Fig. 22 Four methods used to measure the angle of repose. Source: Ref 30

Brown (Ref 31) reported three methods to measure the drained angle of repose (Fig. 23) and a rotating drum method to measure the dynamic angle of repose, as follows:

• Ledge: Material is first charged into a rectangular Perspex box that is 30 cm (12 in.) in height with a 10 by 10 cm (4 by 4 in.) base. A slot at the base of one vertical wall can be closed by a board. The closure board is then removed to allow the material to flow slowly through the narrow slot. The angle with the horizontal of the surface of the material remaining when the flow stops is measured as the angle of repose.

• Crater: A circular Perspex tube with a 14.5 cm (5.7 in.) diam is place vertically on a flat, horizontal base plate having a 1.5 cm (0.59 in.) diam orifice in the center. The powder is discharged through the orifice. The height of the remaining material resting against the wall of the tube is measured at eight equidistant points around the circumference to determine the angle of repose.

• Circular heap: A circular platform 7.6 cm (3 in.) in diameter is supported horizontally over a circular hole in a flat base plate and surrounded by a cylindrical tube having 17.8 cm (7 in.) diam and sufficient height (35 cm, or 13.8 in.) to ensure that when it is filled with powder the platform and any heap that may form on it is completely immersed in the powder. The powder in the cylindrical tube is then allowed to flow slowly out of the circular hole in the base plate. The height of the resulting heap on the circular platform is then obtained. The tangent of the angle of repose is calculated as in the fixed height methods.

• Dynamic angle of repose: A drum 15 or 30 cm (6 or 12 in.) in diameter and 10.2 cm (4 in.) long with Perspex end faces and roughened internal surfaces is half filled with powder and slowly rotated counterclockwise, with its axis horizontal. Within a certain range of rotation speeds (usually 2.5 to 6 rpm), the surface of the powder in the drum becomes substantially steady. The angle of inclination of the surface to the horizontal is measured at various speeds to determine the angle of repose.

The Vehicle Angle Repose
Fig. 23 Apparatus used to measure the drained angle of repose. Source: Ref 30

Table 7 lists the angles of repose measured using these methods. Henein et al. (Ref 32, 33) used a method similar to that used by Brown to determine the dynamic angle of repose and lower angle of repose (shear angle) of several materials. Rotating cylinders of 40 and 106 cm (16 and 42 in.) diam were lined with 24-3 grit type E silicon carbide abrasive paper. One of the two end plates of each cylinder were made of plexiglas to observe and photograph the bed. The maximum angle of bed inclination just before slump occurred was measured with a long-arm protractor, and this angle was designated the upper angle of repose, or the dynamic angle of repose. The angle relative to the horizontal of the shear plane that separated the slumping solids of the bed surface from the material moving with the cylinder wall was considered the lower angle of repose, or shear angle (see Fig. 24). Table 8 summarizes the upper and lower angles of repose of several materials.

Table 7 Drained angles of repose (degrees to the horizontal)

Descriptive class

Material

Circular heap (±1 2 ft

(±2°), ft

Dynamic1^, ft

Smooth, spherical

Beads

17;2

25

27

25 '

Beads

20

23

21 '

24

Rough, nearly spherical

Sand

32 2 ,b)

34

35-35 2

34 '

Tapioca

30

34

37 2

32

Rice

35

37

42

Angular

Sand

37

37

39

36 '

Sand

35 '

37

38 '

38 '

Sand

35 '

36

37 '

38 '

Durite

37

40

41

Charcoal

38

Charcoal

38 '

Charcoal

42 '

Charcoal

42 '

Coal

37 '

37

41

34

Coal

35 '

37 '

Coal

36

38

Coal

36 '

38 2 . . . . . .

Coal

38 '

38 2 . . . . . .

Containing fine particles Coal

52 . . . . . .

Coal

54

59-61 . . . . . .

Coal

47 '

Fine coal

67 ... ...

Limestone

64 . . . . . .

Source: Ref 30

(b) On a 5.1 cm (2 in.) diam platform in a 12.7 cm (5 in.) diam cylinder.

Table 8 Upper and lower angles of repose of several materials

Material

Average size

Particle shape

Particle density,

Loose bulk

Dense bulk

Statistic angle of

Dynamic angle of

Cylinder diameter

Shear angle,

mm

in.

kg/m3

density, kg/m3

density, kg/m3

repose, degrees

repose, degrees

m

ft

degrees

Gravel

3.0

0.12

Angular

2870

1560

1690

40.7

37.5

0.40

1.3

34.7

37.0

1.06

3.5

34.4

Iron oxide

11.6

0.46

Spherical

31.5

35.2

0.40

1.3

33.3

Limestone

4.3

0.17

Irregular

2700

1450

1610

40.3

39.6

0.40

1.3

37.7

B

36.5

1.06

3.5

34.5

Limestone

1.5

0.06

Irregular

2690

1520

1600

37.8

36.0

0.40

1.3

33.6

C

1.06

3.5

32.5

Limestone D

0.58

0.02

Irregular

2680

1490

1570

35.6

34.9

0.40

1.3

33.5

Limestone F

8.1

0.32

Angular

2690

42.8

41.5

1.06

3.5

38.5

Nickel oxide

4.9

0.19

Spherical

870

900

32.5

30.2

0.40

1.3

29.9

Sand B

0.50

0.02

Nodular

2660

1640

1740

33.4

33.6

0.40

1.3

32.2

Fig. 24 Dynamic angle of repose and shear angle of material in a rotating cylinder. B, shear plane; upper angle of repose (dynamic angle of repose). Angle 0s, is lower angle of repose.

Riley et al. (Ref 34) reported methods to measure the angles of repose of cohesive powders. They used both tilting box and fixed bed methods to measure the angle of repose of mixtures of glass ballotini and cohesive powders of different compositions and then extrapolated the results to obtain the angles of repose of pure cohesive material. Figure 25 shows a sample plot and gives the angle of repose of several cohesive powders.

Eieema P100, %

Powder

Tilting box

Fixed bed

Calcium carbonate

83.0

78.0

Eleema P100 (microfine cellulose)

64.5

68.0

Avieel PH101 (microcrystalline cellulose)

57.5

51.5

Methylcellulose 20 BPC

50.0

52.0

Methylcellulose 450 BP

63.0

55.0

Hydroxypropyl methylcellulose 4500

64.5

Hydroxypropyl methylcellulose 5000

59.5

58.5

Hydroxyethyl methylcellulose 3500

61.0

61.0

Magnesium stearate

69.0

66.0

Stearic acid

Source: Ref 34

Fig. 25 Typical plot of mixture composition versus angle of repose. Curve extrapolated to determine angle of pure material. Source: Ref 34

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