Calculating volumes of solids in piles as they are poured into various shaped containers can be important information for solids-handling applications. The following set of equations represents guidance to help determine solids volume in these cases.
Solids in containers
Solids fed through a nozzle into a cylindrical or rectangular silo normally form a partial cone of a complex shape when the material is loaded off-center (eccentrically). Few articles have been published to estimate the volume of material in such cones, and those that have are limited [1,2]. In Ref.1, a graph is given to find the volume in a cylindrical silo. The article in Ref. 2 mentions shortcut methods for various types of containers to calculate the volume ratio with imaginary reference cones. These equations aim to provide more exact analytical methods to calculate the volume of material of solids heaps, characterized by their angles of repose α.
To find the effective volume of the silo, first the remaining cylindrical volume of the silo should be calculated and the total added to the volume of the bottom cone and of the heap.
In the case of concentric loading in a cylindrical silo with radius Rs, the height of the heap, h, is equal to…