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Design of Mass Flow Hoppers

Calculation of aperture size This program for the design of mass flow hoppers is based on the method of Jenike, as described in Storage and Flow of Solids by A.W. Jenike (Bulletin No. 123 of the Utah Eng. Exp. Station, Univ. of Utah, Salt Lake City, USA). The program takes in the results of shear cell tests and determines the minimum diameter at the bottom of a conical hopper or the minimum width of a slot outlet together with, in either case, the semi-included angle of the hopper to ensure uninterrupted discharge with no dead spaces inside the hopper.

The first part of the three-part program asks for the test data and processes it to obtain the material flow function and the effective angle of internal friction. For each yield locus the points are plotted and the best fit parabolic curves are drawn.

The two Mohr circles are then drawn, giving one point on the material flow function and one value of the effective angle of internal friction. The second part of the program will determine the limiting value of the wall slope for a conical hopper and the recommended slope for a slot outlet hopper; the value of the flow factor is then obtained. This is done by solving numerically two simultaneous differential equations. The program will either use the value of the effective angle of internal friction (delta) obtained in part one, or if preferred, the value of delta can be obtained manually by drawing the yield loci and fed in at this point.

Worked example The program will also ask for the angle of wall friction, which must have been measured. The third part of the program will draw the material flow function of the powder, using the data obtained in part one or results obtained manually. The flow factor line is then drawn and a recommended value for the critical applied stress is obtained. The program will then calculate the critical opening size for mass flow. A test is carried out, particularly necessary in the case of free-flowing materials, to ensure that the outlet is large enough to prevent mechanical blocking of the hopper opening. Finally, for conical hoppers, various permissible hopper geometries will be printed out after the program has asked for the capacity in tonnes and the angle of repose of the powder, which determines the amount of waste space at the top of the hopper. A mass flow hopper which best fits the available space can then be selected. Note that, for a mean particle size of 60 microns or greater, this program now includes calculation of the discharge rate from the minimum opening. If this rate is not sufficient, a revised opening size is calculated.

Flow factor chart