Pressure and motion of dry sand: translation of Hagen’s paper from 1852

Abstract

In a remarkable paper from 1852, Gotthilf Heinrich Ludwig Hagen measured and explained two fundamental aspects of granular matter: The first effect is the saturation of pressure with depth in a static granular system confined by silo walls -generally known as the Janssen effect. The second part of his paper describes the dynamics observed during the flow out of the container -today often called the Beverloo law -and forms the foundation of the hourglass theory. The following is a translation of the original German paper from 1852.

Cohesive, frictional powders: contact models for tension

“…(If the walls would be frictional, the pressure from a certain wall would not be transferred completely to the respective opposite wall, since frictional forces carry part of the load-an effect that is known since the early work of Janssen [23,77,86].) Pressure-sintering is stopped when the kinetic energy of the sample is many orders of magnitude smaller than the potential energy-typically ten orders of magnitude.…”

Velocity and density scaling at the outlet of a silo and its role in the expression of the mass flow rate

“…The scale factor √ 2gR can be justified assuming the existence of a region, above the orifice, below which the grains fall freely under the gravity. This hypothetical region scales with the outlet aperture R and it was early introduced by Hagen [10] and lately developed by Brown & Richards [11] under the name of "free fall arch". Following the original idea of Hagen, the scaled expression (Eq.…”

Discharge flow of a granular media from a silo: effect of the packing fraction and of the hopper angle

“…One of the simplest and widely used expression is the one proposed by Berverloo [2] for flat-bottomed silos. Following the experimental observation that the flow rate is mainly controlled by the outlet diameter D, it is based on dimensional analysis with a concept of a free fall arch at the outlet [1] and of an "empty annulus" [6] considering a reduced outlet length due to the particle size. More recent works proposed a continuous modeling with a mu(I) granular rheology which gives good results for a large amount of beads at the aperture [3], [4].…”