How to Design and Implement Chutes in Bulk Solids Handling Systems
How to Design and Implement Chutes in Bulk Solids Handling Systems
7. Design Principles For Chute Design
7.1. Design Principle 1 – Prevent Plugging At Impact Points
The chute face must be sufficiently smooth and steep to allow sliding and hence cleanoff of the stickiest material that it has to handle.
The impact pressure at any point that the material stream impacts the chute face is presented in Fig. 14
The velocity following an impact with the chute surface may be calculated from Fig. 15.
Stagnation and hence plugging will occur when V_{2} = 0 m/s.
It is critical that the velocity at the point in question be accurately estimated.
Fig. 14: Formular for impact pressure.
Fig. 15: Velocity after impact.
As the material moves through the chute it may be subjected to different acceleration forces such as sliding along the chute plates or free falling through the vertical section of a chute.
The acceleration along a face of the chute is calculated as
(12)
And the velocity is calculated as
(13)
where:
V_{0} = velocity at the start of the incline
S = length of the incline.
For free fall the velocity is calculated as
(14)
where:
S = height of the free fall
g = acceleration due to gravity.
For a section of the chute at a slightly different inclination, the starting velocity
(15)
where:
β is the inclination of the section.
Acceleration over this section is
(16)
so that the exit velocity
(17)
The stream velocity in the belt direction:
(18)
The vertical component is
(19)
The impact pressure of the stream with the belt
(20)
7.2. Design Principle 2 – Ensure Sufficient CrossSectional Area
Always ensure that there is sufficient belt crosssectional area to allow for the free flow of material through different sections of the chute.
Eq. (1) given in Section 4.2. must be valid at all sections through the chute.
7.3. Design Principle 3 – Control Stream of Particles
It is critical to retain control of the material flow through the chute in order to ensure efficient transfer.
The following figures and formulae give the design principles employed with both a material stream falling under gravity as well as that where material exits the chute with significant velocity.
The case illustrated in Fig. 16 shows slow moving particles exiting the discharge chute and falling through a freefall vertical portion of the chute onto the curved 'spoon' chute.
Fig. 16: Chute flow configuration – inline transfer.
The flow into the curved bottom section of the chute may be illustrated by the free body diagram in Fig. 17.
Fig. 17: Spoon chute flow model.
For a chute of rectangular crosssection we find
(21)
where:
V_{0} = initial velocity at entry to stream
H_{0} = initial stream thickness
Analysing the dynamic equilibrium conditions of Fig. 16 leads to the following differential equation:
(22)
On conditon that the curved section of the chute is of constant radius R and assuming that μ_{E} remains constant at an average value for whole of the stream, it may be shown that the solution of the above equation leads to Eq. 23 for the velocity at any location
(23)
For v = v_{0} at θ = θ_{0}
(24)
Special case:
when θ_{0} = 0 and v = v_{0}, then
(25)
Eq. 23 then becomes
(26)
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