Educ. Reso. for Part. Techn. 992Q-Tardos
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Copyright © 1999 ERC at the Univ. of Florida

Stresses in Bins and Hoppers, by Gabriel I. Tardos

-- Appendix: Flow Factor Calculations
Using Plane and Cylindrical Slices --

The expressions for the average plane and radial hopper stresses given by Eqs. 15 and 16 have to be converted to principal stresses before they can be used for flow factor calculations. These read

where = arcsin [sin W / sin ]. Combining the above equations with Eqs. 15 and 16 and using the definition of the flow factor, ff, in Eq. 28, one obtains for the plane slice

Fig. 15 illustrates the dependence of ff in a plane slice, with m = 1 for both the 2D hopper and for the plane hopper and m = 2 for the conical hopper.


Fig. 15 - Lines of equal flow factor as a function of powder-wall friction angle (ordinate)
and angle of hopper wall from the vertical (abscissa), for a material
with an angle of internal friction of = 40o based on Eq. A.3 [after Drescher, 1991]

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