Angle of internal friction

The angle of internal friction can be measured indirectly, in shear cells for example, or directly, by the grooved plate method. There 

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In addition to the physical properties just described there are those properties which affect the flowability of the material. Specifically, these properties are the material s angle of repose, angle of internal friction, and the angle of slide. 

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. 

Angle of Internal Friction—a. Angle of internal friction, or angle of shear, is the angle of solid against solid. It is the angle at which a catalyst will flow on itself in the nonfluidized state. For an FCC catalyst, this is about 80°. 

If the fluid stream is a gas, the last term in the above equation is essentially unity. Unless the cyclone itself is rotating or, for example, located on another planet, g can be taken as 32.2. If the bulk solids angle of internal friction is unknown, then taking an average value of 62 degrees, the equation reduces to ... 

The influence of consolidation load on the flowability of sucrose is shown in Fig. 8. For this material, the effective angle of internal friction is nearly constant yet the shear index is seen to change with state of consolidation. Apparently, for sucrose, increased consolidation results in a somewhat more free flowing although still cohesive material. As such, sucrose can be considered a complex powder [49] with perhaps somewhat better flow characteristics when consolidated (as might occur in a hopper). 

Podczeck, F., Miah, Y. The influence of particle size and shape on the angle of internal friction and the flow factor of unlubricated and lubricated powders. Int. J. Pharm., 144, 1996, 187-194. 

Figure 10 Mass flow/funnel flow design chart for a conical hopper handling a bulk material with a 40 effective angle of internal friction.

The angle of repose of a powder blend, effective angle of internal friction (EAIF) from shear cell measurements, and the mean time to avalanche (MTA) in powder cohesivity tests are useful for assessing the flow of a tableting mixture at various scales (15 18). 

Solution The kinematic angle of internal friction can be determined from the Mohr circle, which is tangential to the yield locus at the end point. This Mohr circle yields the major consolidating stress o and minor consolidating stress <73. Thus, % is found to be 30°, either from Eq. (8.27) or from a tangent of the Mohr circle which passes through the origin, as shown in Fig. E8.1. 

Mr Gas radial velocity component Vs Static angle of internal friction... 

A cohesionless material of weight density 12 kN/m3 and an angle of internal friction of 30° is stored in a tall cylindrical bin of diameter 1.8 m and an angle of wall friction 22°. Use Janssen s formula to determine the depths at which the radial stress in the material reaches 70 percent of its maximum value for both active and passive cases. 

A conical hopper of a half angle 20° and an angle of wall friction 25° is used to store a cohesionless material of bulk density 1,900 kg/m3 and an angle of internal friction 45°. The top surface of the material lies at a level 3.0 m above the apex and is free of loads. Apply Walker s method to determine the normal and shear stresses on the wall at a height of 1.2 m above the apex if the angle between the major principal plane at that height and the hopper wall is 30°. Assume a distribution factor of 1.1. 

It is required to design a mass flow conical hopper with the volume capacity of 100 m3 to store a cohesionless material of bulk density 1,700 kg/m3 and an angle of internal friction 40°. Four sets of shear tests have been conducted on the material and results for the unconfined yield strength and the corresponding consolidating stress are as follows ... 

A force balance over a differential element (Fig. 4.5) simply using pressure P instead of the compressive stress, with shear stress at the wall xw = aw tan fiw + cw, where [lw is the angle of internal friction and cw is the coefficient of cohesion at the wall... 

Angle of Spatula and Angle of Internal Friction. The angle of spatula is a quick measurement of the angle of internal friction. This is the angle, measured from the horizontal, that a material assumes on a... 

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