The ‘slip angle’ for a mass flow hopper depends mainly upon the wall friction between the bulk material and the material of construction of the converging section of the hopper wall. It is also influenced to an extent by the internal angle of friction of the bulk material. The relationships are given in Jenike’s Bull. 123, Univ. of Utah experimental station 1964 and also in the British Materials Handling Board Guide to the design of hoppers, silos bins and bunkers, published by BSI.

Simplified charts showing this information for Conical and Vee hoppers are given in an Ajax Equipment technical paper – ‘Storage and Feeding of Particulate Solids’. This publication also includes a crude ‘rule of thumb’ formulae for conical, pyramid and Vee hoppers, based on wall friction measurements only, that is normally within 2 or 3 degrees of the value derived from a more detailed investigation. This is useful as a quick guide to the requirements for basic evaluation and site planning. If you care to send your postal or email address to lyn@ajax.co.uk, a copy of these items will be sent forward.

I would emphasise the importance of securing representative samples of both the wall contact material and of the range of condition of the product to be stored, to determine the upper and lower bounds of friction. It is also good practice to employ a wall friction measuring tool that can record, if necessary, static friction under instantaneous and time consolidated conditions and dynamic friction at various slip velocities as the hopper has to accommodate all circumstances of product and operational variations. The test machine should preferably have a long stroke so that all the readings in a series can be taken at one ‘run’. One such device with these facilities can be seen on the web site of www.ajax.co.uk.

Lyn Bates ■