## Cone Of Flowing Solids

Figure 4. Illustrates angle of internal friction.

The angle of repose is sensitive to the conditions of the supporting surface; the smoother the surface, the smaller the angle. The angle may also be reduced by vibrating the supporting surface.

When handling slow moving materials having large angles of repose, well-designed, bunkers and hoppers are provided with highly polished internal surfaces and low amplitude vibrators. The angle is also sensitive to moisture. Specifically, moisture tends to increase the angle of repose. The variation of p with moisture content is likely due to the surface layer of moisture that surrounds each particle and surface tension effects which bind aggregates of solids together.

The angle of internal friction, a, is defined as the equilibrium angle between flowing particles and bulk or stationary solids in a bin. Figure 4 illustrates the definition. The angle of internal friction is greater than the angle of repose.

The angle of slide is defined as the angle from the horizontal of an inclined surface on which an amount of material will slide downward due to the influence of gravity. This angle is important in the sizing and operation of chutes and hoppers as well as pneumatic conveying systems. It provides a measure of the relative adhesiveness of a dry material to a dissimilar surface. This angle depends on the type or nature of solids, the physical and surface properties of equipment (e.g., roughness, cleanliness, dryness), the surface configuration (e.g., the degree of curvature), the manner in which solids are placed onto surfaces, and the rate of change of the slope of the surface during measurements.

Table 7 provides some literature reported measurements of the properties discussed for common filter media and aids as loose materials. You might try an experiment and measure the various angles. In developing your data base, obtain the measurements in triplicate, and calculate a standard deviation for each angle measurement.

 (g/cm3) Angle of Repose (degress) Friction Coefficient Inside Outside on Steel Phosphate powder

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