Announcement

Announcement Module
Collapse
No announcement yet.

Cubic ft

Page Title Module
Move Remove Collapse
X
Conversation Detail Module
Collapse
  • Filter
  • Time
  • Show
Clear All
new posts

  • Cubic ft

    I have a square to round funnel shaped hopper the 4 sides are 60" at the top by 6" on the bottom and the unit is 60" tall...I need to calculate what the cubic ft capacity is of the hopper

    Thanks

  • #2
    Re: Cubic ft

    Originally posted by Unregistered View Post
    I have a square to round funnel shaped hopper the 4 sides are 60" at the top by 6" on the bottom and the unit is 60" tall...I need to calculate what the cubic ft capacity is of the hopper

    Thanks
    Given the change in shape, any calculation will be an approximation, not exact. Are the sides essentially straight, or a constant taper from bottom to top? I'm assuming this below. If there is a midpoint with sharp change in flare angle, it needs to be broken into two problems.

    The volume of a frustrum of a cone or pyramid is given by the height and the areas of the upper and lower bases as
    V = (1/3)*H*(B1 + B2 + sqrt(B1*B2)
    B1 = 60" x 60" = 3600 in²
    B2 = (pi/4) x 6" x 6" = 28.3 in²
    sqrt(B1*B2) = 319 in²

    V= 78946 in³
    1 ft³ = 1728 in³, so 45.7ft³

    For comparison, a full pyramid tapering to a point, with 5' base and height is 41.7 ft³

    Comment


    • #3
      Re: Cubic ft

      Thanks for the quick response but I still don't understand the answer @ 47.ft3 is that telling me the capacity of the cone shaped funnel is 47 cubic feet of grain...this is a grain hopper

      Comment


      • #4
        Re: Cubic ft

        Originally posted by Unregistered View Post
        Thanks for the quick response but I still don't understand the answer @ 47.ft3 is that telling me the capacity of the cone shaped funnel is 47 cubic feet of grain...this is a grain hopper
        Yes, ft³ is cubic feet. But note my assumptions/questions about shape.

        Comment


        • #5
          Re: Cubic ft

          OK new problem... I need to get the capacity of this hopper up to 90 Cubic Ft but I have height restrictions in the bldg so I can't go higher than 60" so if I make the top part 60" X 60" and go straight down 36" (+- 75 Cubic Ft) then form the pyramid into a 60 X 60 by 24" tall by 6" on the bottom what does that figure out to be in cubic feet

          Comment


          • #6
            Re: Cubic ft

            Originally posted by Unregistered View Post
            OK new problem... I need to get the capacity of this hopper up to 90 Cubic Ft but I have height restrictions in the bldg so I can't go higher than 60" so if I make the top part 60" X 60" and go straight down 36" (+- 75 Cubic Ft) then form the pyramid into a 60 X 60 by 24" tall by 6" on the bottom what does that figure out to be in cubic feet
            The answer above, 45.7 ft³, can be corrected to the new lower section height by multiplying by 24/60, thus 18.3 ft³. To this add the 75 ft³ of the new upper section for a total of 93.3 ft³.

            I'm not sure the grain will flow well with the hopper so shallow.

            Comment


            • #7
              Re: Cubic ft

              OK so what is the total cubic ft if the hopper is 60 X 60 X 24 at the top and then 60 x 60 x 36 tall down to 6"..... I don't understand the formula you provided...what do the asteriscks mean etc

              Comment


              • #8
                Re: Cubic ft

                Originally posted by Unregistered View Post
                OK so what is the total cubic ft if the hopper is 60 X 60 X 24 at the top and then 60 x 60 x 36 tall down to 6"..... I don't understand the formula you provided...what do the asteriscks mean etc
                Many computer languages (Basic, Fortran, etc) use the asteric as the multiplication symbol, so we tend to use it here in formulas. Note that B1 and B2 remain unchanged in the revisions you have asked about, only the height of the funnel section changes, with a rectangular solid above it. The slash "/" is the symbol for division. The parentheses group operations that have to be done before other operations.

                In the latest, you have 50 ft³ in the upper box, and 27.4 ft³ in the funnel part for 77.4 ft³ total.

                Comment


                • #9
                  Re: Cubic ft

                  OK so we can't make it work at 60" sq on top and I can't go any higher than 60"tall so now I'm at 72 X 72 X 60....it can be 72 X 72 X 18 -24 with the base pyramid being 36 -42 height hopefully this will work as I need to be more than 90 cubic ft I look forward to your response

                  Comment


                  • #10
                    Re: Cubic ft

                    Originally posted by Unregistered View Post
                    OK so we can't make it work at 60" sq on top and I can't go any higher than 60"tall so now I'm at 72 X 72 X 60....it can be 72 X 72 X 18 -24 with the base pyramid being 36 -42 height hopefully this will work as I need to be more than 90 cubic ft I look forward to your response
                    OK, so I'm switching to feet. Max 5' high, max 6'x6' across the top, 0.5' circular opening at the bottom, part of the 5' height is a rectangular bin, part is a funnel. Do you want it exactly 90 cubic feet, or a little over 90 cubic feet? I'm assuming latter.

                    For the funnel section, using new dimensions in feet
                    B1 = 36 ft²
                    B2 = 0.1965 ft²
                    Sqrt(B1*B2) = 2.6587 ft²
                    (B1 + B2 + sqrt(B1*B2))/3 = 12.9517 ft² the mean area of the funnel
                    The area of the box part at the top is B1, 36 ft²

                    Lets try height of box part 1.25' (15") and funnel part 3.75' (45")

                    Total volume is 36 ft² * 1.25 ft + 12.9517 ft² * 3.75 ft = 93.57 ft³
                    I think we are there.

                    Comment


                    • #11
                      Re: Cubic ft

                      Many Thanks for your help

                      Comment

                      Working...
                      X