We will explain how to decide the shape of the powder storage hopper.
When designing a hopper, volume calculations are the main focus, but it is better to have a variety of options regarding the shape.
If you only handle powders whose properties will not change over time, you can continue to use the installed hopper, but the physical properties of raw materials often change.
In particular, the angle of repose is a factor directly connected to hopper design.
It can be difficult in unexpected places.
Once you understand how difficult it is, you can say you have a pretty good understanding of hopper design.
angle of repose
The angle of repose is an important indicator of powder physical properties in hopper design.
Especially when it comes to powder, characteristics such as how the powder clogs and slides are one indicator.
When powder is dropped onto a flat surface to form a mountain, the angle of the cone is called the “angle of repose,” as shown in the diagram below.
This depends on the physical properties of the powder.
Approximately 40° is a medium angle of repose, and powders from batch chemical plants often have values around this.
Concentric hopper
When calculating the capacity of a hopper, cases can be classified based on the shape of the hopper.
Let’s start with concentricity, which is easy to calculate.
spatial volume
Spatial volume is a matter of simple arithmetic.
Let’s consider the conical part and the linear part separately.
The conical part
$$ V_1=\frac{1}{3}\frac{π}{4}({D_1}^2*(H_1+\frac{D_2}{D_1-D_2}H_1)-{D_2}^2*\frac{D_2}{D_1-D_2}H_1) $$
It can be expressed as It is a shape that subtracts two cones.
If you fix this a little
$$ V_1=\frac{π}{12}({D_1}^2+D_1D_2+{D_2}^2)*H_1 $$
It becomes.
The linear motion part is the same as the cylinder formula,
$$ V_2=\frac{π}{4}{D_1}^2H_2 $$
It becomes.
This total value is the space volume of the concentric hopper .
powder volume
The area where powder can actually be stored in the hopper is less than the space volume.
This is because powder has an angle of repose.
However, the calculation is simple.
The height of the linear motion part is reduced and calculated as a cone.
$$ V_3=\frac{π}{12}{D_1}^2H_3 $$
If the angle of repose is Θ1, then
$$ \frac{D_1}{2}tanΘ_1=H_3 $$
There is a relationship.
This calculation assumes that the nozzle at the top of the hopper is concentric with the hopper. This is the limit for the powder volume in the conical part considering the angle of repose. If the inlet nozzle is offset from the center of the hopper, it is difficult to determine the powder volume considering the angle of repose. And it doesn’t make much sense.
eccentric hopper
Next to concentricity, let’s look at eccentricity.
space capacity
The calculation itself for eccentric capacitance is the same as for concentric capacitance.
If the diameter of the hopper bottom is small and can be ignored, the formula is simpler.
The space capacity of the eccentric conical part is calculated by setting D 2 =0 in the calculation formula for the concentric conical part.
$$ V_3=\frac{π}{12}{D_1}^2H_1 $$
It can be written as Simple.
powder capacity
Powder capacity can be calculated by assuming that the hopper is filled to capacity.
It is also assumed that the inlet nozzle at the top of the hopper is concentric with the hopper.
Calculations when storing capacity halfway in the conical part are as complicated as calculations for the upper conical part, and have almost no meaning.
How to determine hopper capacity
How is the capacity of the hopper determined?
This depends on the powder being stored.
powder weight
bulk density
Processing amount per batch
Weight and bulk density are specific to the powder used.
On the other hand, the processing amount can be adjusted.
Let’s say that the plant has a throughput of 2m3 per batch, and the hopper space capacity is about 1.5m3.
If you calculate the powder capacity using the above calculation, and you can only store about 1.1m3, consider dividing the operation into two.
This is possible because it is a batch process.
Although it is preferable to have a larger hopper capacity, there are still some aspects that can be accommodated by changing the operating method even if this is not possible.
reference
lastly
We introduced an example of calculating the capacity of a powder storage hopper.
There is a difference between space capacity and powder capacity, and the angle of repose of the powder is involved.
Cases are divided into concentric and eccentric. In practice, there is no big difference.
The difficulty of the calculation will vary depending on whether the inlet nozzle is the same as the center of the hopper, but in practice it will not make much of a difference even if you calculate it assuming that the inlet nozzle is the same as the center of the hopper.
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