Hopper volume
Hopper volume
(OP)
Does anyone know the formula for the volume of a hopper which has a round top and a rectangular outlet. Rather like the frustrum of a cone except the bottom is rectangular.
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Hopper volume

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RE: Hopper volume
RE: Hopper volume
the larger dimension of the rectangular outlet equal to
or more than 50% the diameter of the hopper top? Usually
for the kind of hopper you've described, it is a common
practice (for ease in fabrication) to use a frustrum of a cone and provide a transition outlet (round to rectangular),
unless your case is what was described previously described.
RE: Hopper volume
RE: Hopper volume
Regards
Brian
RE: Hopper volume
Sorry a picture is not available and a drawing would be a bit impractical at this stage.
Regards
Brian21
RE: Hopper volume
2m diameter tranforming to 600mm X 2m rectangle
My Solid model shows a volume of 3.611 cubic meters. Now, I also took the liberty of accepting the defaults that control the lofted shape so this could be off a little based on your design.
Hope it helps.
jackboot
RE: Hopper volume
Regards
Brian21
RE: Hopper volume
If you can't visualize what I'm describing, post your addy
and I'll send you the solution.
Try this and determine the volume of each commponent:
1. Draw a the top circle (2.00 m) and the bottom
rectangular section. For simplicity, set the 4corner
points of the rectangle on the circumference of the
circle (rectangle length is now less than 2.00m).
2. Now looking at your drawing, there are 5sections
(1rectangle & 4circular segments, 2large/2small).
3. Calculate the area of the rectangle, 1 large circular
segment and 1small circular segment. Use any method
you are familiar with.
4. The volume of the hopper will be the sum of the 3
areas multiplied by the height of the hopper.
The volume calculations is based on the premise that the
volume of a sliced circular segment (slicing plane is such
that the resulting sliced crosssection is a triangle whose
2vertices lies on the rectangular outlet and 1vertex on
the quadrant of the circle) is half of the unsliced circular
segment.
RE: Hopper volume
In my last post, the premise on the sliced volume is incorrect. You have to calculate the sliced volume (a portion of a cylinder using the formulas shown in page 64 of the Machinery Hanbook 24), add all the 4 sliced volume
and subtract the total from the volume of the cylinder.
By 3D modelling, the volume is 3.932427 cu.m. By calcs,
the volume is approx. 0.02% less.
Estassoc
RE: Hopper volume
Regards
Brian