Example Calculation

Inlet Length/Side A (la): 1 metres
Inlet Width/Side B (lb): 1.5 metres
Outlet Length/Side A (lao): 0.3 metres
Outlet Width/Side B (lbo): 0.3 metres
Hopper Height (H): 1 metres

Calculate the Top and Bottom Areas

Top Area (At): This is the area of the top of the hopper (inlet), which is a rectangle or square.

At = la * lb = 1 * 1.5 = 1.5 m²

Bottom Area (Ab): This is the area at the bottom of the hopper (outlet), which is also a rectangle or a square.

Ab = lao * lbo = 0.3 * 0.3 = 0.09 m²

Calculate the Volume of the Truncated Pyramid (Frustum Volume):

The volume of a truncated pyramid is given by:

Va = H/3 * (At + Ab + √At * Ab)

Substituting the values:

Va = 3 * 1(1.5 + 0.09 + √1.5 * 0.09

First, calculate the square root term:

√1.5 * 0.09 = √0.135 = 0.367

Now, substitute the values:

Va = 1/3 * (1.5 + 0.09 + 0.367) = 1/3 * 1.957 = 0.652m³

Slope Angle Calculation

The slope angles are calculated using trigonometry (arc tangent) for both the longer side (Side A) and the shorter side (Side B).
Side A Slope Angle (Aang): The difference between the top and bottom lengths (du) along Side A:

du= (la-lao) ÷ 2 = (1 - 0.3) ÷ 2 = 0.35 m

The slope angle is calculated using:

Aang = arctan(du ÷ H) = arctan(0.35 ÷ 1) = 19.29°

Side B Slope Angle (Bang): The difference between the top and bottom widths (db) along Side B:

db= (lb-lbo) ÷ 2 = (1.5 - 0.3) ÷ 2 = 0.6 m

Bang = arctan(db ÷ H) = arctan(0.6 ÷ 1) = 30.96°

Combined Slope Angle

The combined slope angle is an average representation of the steepness on both sides:

c = arctan(√tan²(Aang) + tan²(Bang) 

First, calculate the tangent of each angle:

tan (19.29°) = 0.349 and tan (30.96°) = 0.601

Now, calculate the combined slope angle:

c = arctan(√0.349² + 0.601²) = arctan(√0.122 + 0.362) = arctan(0.75 = 05 = 34.78°

Covert Volume to Other Units:

Litres: 1m³ = 1000L

0.652 * 1000 = 652.47 L

Cubic Feet: 1m³ = 35.3147 ft³

0.652 * 35.3147 = 23.04 ft³

Results:

Volume of Hopper: 0.652 m³
Volume in Cubic Feet: 23.04 ft³
Volume in Liters: 652.47 L
Slope Angle on Side A: 19.29°
Slope Angle on Side B: 30.96°
Combined Slope Angle: 34.78°

Farming Calculators

Main Page