Hopper angle

Compressibility. The bulk density of a soHd is an essential value used in the analysis of its flow properties, such as when calculating mass flow hopper angles, opening sizes, bin loads, etc. Loose and/or packed density values ate not sufficient. Bulk soHds exhibit a range of densities that vary as a function of consoHdating pressure. This range of densities, called the compressibiHty of the soHd, can often be expressed on a log—log plot as a line or relationship. 

Conica.1 Hoppers. Design charts for conical hoppers typically are plots of wall friction angles, ( ), vs hopper angle, 9. Charts such as that in... 

Wed e Hoppers. Different design charts are used for wedge hoppers (Fig. 7b) than for conical hoppers. Values of hopper angle 0 (measured... 

B = outlet diameter or width, g = acceleration owing to gravity, m = 1 for circular opening and 0 for slotted opening, and 0 = hopper angle (measured from vertical) in degrees. A modification of this equation takes particle size into account. This modification is only important if the particle size is a significant fraction of the outlet size (8). 

The key to solving these problems is to design the vessel for a mass flow pattern. This involves consideration of both the hopper angle and surface finish, the effect of inserts used to introduce gas and control the soHds flow pattern, and sizing the outlet valve to avoid arching and discharge rate limitations. In addition, the gas or Hquid must be injected such that the soHd particles ate uniformly exposed to it, and flow instabiHties such as fluidization in localized regions are avoided. 

Until Jenike developed the rationale for storage-vessel design, a common criterion was to measure the angle of repose, use this value as the hopper angle, and then fit the bin to whatever space was available. Too often, bins were designed from an architectural or structural-engineering viewpoint rather than from the role they were to play in a process. Economy of space is certainly one vahd criterion in bin design, but others must be considered equally as well. Table 21-14 compares the principal characteristics of mass-flow and funnel-flow bins. 

When considering scale effects, the implication of the foregoing analysis is that the hopper angle required for mass flow is principally dependent on the outlet size selected for the hopper under consideration. Note that the... 

Of course, mass flow is highly dependent upon conditions below the hopper a throttled valve, a lip or other protrusion, or anything that can initiate a zone of stagnant powder can convert any hopper into funnel flow, regardless of the hopper angle or surface finish. 

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