Truncated Rectangle Hopper Volume
This Truncated Hopper Volume and Slope Angle Calculator is designed to calculate the volume and slope angles of a rectangular hopper with a larger inlet and a smaller outlet, commonly referred to as a truncated frustum. The calculator helps users quickly determine the volume of material that can be stored or passed through the hopper and the angles of the hopper walls, which are critical for material flow and hopper design.
Truncated Rectangle Hopper Volume Calculator
Calculator
- inlet length A in inches
- inlet width B in inches
- outlet length a in inches
- outlet length b in inches
- the height in inches
Results
- hopper volume in cubic inches
- in cubic feet
- in litres
- angle c located on side A (the slope angle in degrees for the longer side of the hopper)
- angle d located on side B (the slope angle in degrees for the shorter side of the hopper)
- the valley angle (the overall slope angle in degrees (represents the combined steepness of both sides (side A and side B) of the hopper)
Formula
H/3A+B+√AB
where H is the height
A the area of the inlet side
B the outlet area
Conversions
one cubic inch (in³) = 0.016387064 litres (L) one cubic inch (in³) = 0.000578703703703704 cubic feet (ft³)
Example Calculation
inlet-A length = 24 inches inlet-B width = 9 inches outlet-a = 4 inches outlet-b = 4 inches height-H = 20 inches
First, calculate the area of the inlet and the outlet;
24 * 9 = 216
Inlet-A has an area of 216 square inches.
4 * 4 = 16
Outlet-B has an area of 16 square inches.
Plug the values into the formula;
20 ÷ 3 * ( 216 + 16 + √216 * 16)
6.666666666666667 * (216 + 16 + 58.78775)
6.666666666666667 * 290.78775 = 1938.585
This hopper has a volume of 1938.585 cubic inches.
This tool is ideal for engineers, designers, and individuals in industries where hopper design and material flow are critical. The results help inform decisions about space, capacity, and material handling.
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