Friction angle

Wall Friction Angles. Wall friction values, important when characterizing the dow properties of a bulk soHd, are expressed as the wall friction angle or coefficient of sliding friction. The lower the friction, the less steep the hopper walls need to be to achieve mass dow. 

Fig. 5. Wall friction test (a) apparatus for measurement, and (b) results, where is the wall friction angle.

A material s flow function is usually measured on the same tester as the wall friction angle, although the cell arrangement is somewhat different (Fig. 6). ConsoHdation values are easily controUed, and the cohesive strength of the bulk soHd is determined by measuring interparticle shear stresses while some predeterrnined normal pressure is being appHed. 

Conica.1 Hoppers. Design charts for conical hoppers typically are plots of wall friction angles, ( ), vs hopper angle, 9. Charts such as that in... 

Roll friction angle deg deg (Sr Pow der compaction normal stress kg/cm psf... 

Microdeval abrasion loss (%) Magnesium sulfate soundness loss (%) Friction angle (°)... 

The primary FML must be able to support its own weight on the side slopes. In order to calculate self-weight, the FML-specific gravity, friction angle, FML thickness, and FML yield stress must be known. 

Waste settlement is another consideration. As waste settles in the landfill, a downward force will act on the primary FML. A low friction component between the FML and underlying material prevents that force from being transferred to the underlying material, putting tension on the primary FML. A 12-in. direct shear test is used to measure the friction angle between the FML and underlying material. 

The internal friction angle is also important for slugging beds (Zenz and Othmer, 1960). DiFelice et al. (1992 a, b) did not report their values it could be that the disagreement they found in their slugging bed tests was due to mismatches of the internal friction angle. 

Figure 33. Dimensionless spoutdiametersasafunctionof dimensionless height for small columns. Case A test case Case B all dimensionless parameters matched, bed diameter halved Case C particle Reynolds number mismatched Case D Froude number mismatched Case E density ratio, Reynolds number mismatched Case F bed Reynolds number mismatched Case G internal friction angle, loose packed voidage mismatched. (From He et al., 1995.)...

The developed model for the simulation of the dynamic flow rate in a rotary kiln has been validated for varied experimental conditions filling phases, transient responses after a step in the rotation speed or in the feed rate (not presented here). It is shown that this dynamic model, based on the Sae-man equation developed for rolling mode, works with the slipping mode too the replacement of the angle of repose by the wall friction angle is sufficient. 

A pressure dependence of the internal angle of friction is known to represent the quantification of the pore space dependence of internal friction [3], Such a dependence has also been observed in wall friction experiments for the bed friction angle [5, 13] of soil. So, we must assume 6 = 6(p) and pressure dependence of with pressure [3,5,13], the simplest parameterisation is linear and we choose... 

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