Janssen equation
The stresses in a silo can be described with the Janssen equation (after HA Janssen, 1895) . It describes the equilibrium of forces in the vertical direction and is a special case of the general equation of hydrostatic equilibrium , taking into account the silo wall.
For a disk-shaped volume element (radius r) of height dz , which spans the entire cross-section of the silo with circumference , applies
- ,
in which
- the vertical tension
- the mean density of the bulk material
- g is the gravitational acceleration
- the wall shear stress
- z denotes the depth from the upper edge of the bulk material.
The weight of the bulk material acts in the disk
- the difference in stresses (pressure gradient ) on the top and bottom of the disc (the first terms on both sides) as well
- against the thrust exerted by the silo wall .
The Janssen equation can be transformed into an ordinary differential equation :
The solution of the like. can be found by choosing suitable boundary and initial conditions .
literature
- ↑ Janssen, HA: Experiments on grain pressure in silo cells . In: Z. Ver. German Ing. Band 39 , 1895, p. 1045-1049 ( duke.edu [PDF] scan of the article (memento in the web archive from October 30, 2011)). Experiments using grain pressure in silo cells ( memento of the original from March 3, 2011 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice.