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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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 4-corner
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 5-sections
(1-rectangle & 4-circular segments, 2-large/2-small).
3. Calculate the area of the rectangle, 1- large circular
segment and 1-small 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 cross-section is a triangle whose
2-vertices lies on the rectangular outlet and 1-vertex 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