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Specialist article
01.09.2021  |  73x
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Gully or valley angle of a rectangular hopper

About the gully angle of pyramid shaped hoppers

Recommendations for proper flow from rectangular or pyramid shaped hoppers, in view of the corners of the hopper that are less steep.
Rectangular hoppers are widely used to store bulk solids. Although convenient to fabricate they have process drawbacks in that large flat sides are prone to deflection, so often require stiffening, and the converging faces form gully angles that offer poor flow and self-clearing properties. Some small compensation is given by the rectangular outlets being somewhat easier to fit with slide valves. ​​

The gully angle of a symmetrical, pyramid shaped hopper is roughly 10 degrees less steep than sides and is prone to retention of product unless it is radiused.

For Mass Flow design purposes, the inclination of the gullies should be considered as a cone. For Funnel Flow hoppers the gully angle should exceed the wall friction angle by at least 10 degrees. Some product retention in the corners is almost inevitable unless the corner is radiused or significantly increased in inclination.

Mass flow is much more practical and residue much less likely if the end walls are made vertical. This can be done in two stages to transform to a square outlet. Both stages could be inclined for Mass or Funnel flow, or the first stage Funnel flow and the second Mass flow, to produce a form of expanded flow, with the slot transition giving compensating flow benefits, compared with the final square outlet in mass flow.

The ratio of length to width of an outlet must exceed 3:1 to secure the full flow benefits of a slot outlet and provide reliable discharge similar to a circular outlet diameter that is twice the slot width.

Two opposing walls must be longer than the ‘critical rathole diameter’ and sufficiently steep to permit mass flow to ensure that the hopper will not ‘rathole’. The ends must still be considered as parts of a cone to guarantee mass flow, otherwise the end sections will only self-clear according to the ‘drained repose’ angle.

Calculation
Gully or valley angle c = arctan [ ( tan(a)^2 + tan(b)^2 )^0.5 ]
Where a and b are the inclination of the two sides of the hopper.
Follow the link to find a practical tool to Program to calculate the volume, surface area and weight of a pyramid shaped hopper.

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