Page 131 - Nutrient Management Planning Guide

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Chapter 4.1

Calculating the Volume of a Rounded Windrow

A pile of manure resembles a rounded windrow (Figure 4.1.2). The rounded manure windrow has the following dimensions top length = 24 m, bottom length 31 m, width 3.4 m and height 2.6 m (Figure 4.1.6).

Figure 4.1.6 Windrow of Cattle Manure with Estimated Dimensions

The estimated volume of this pile is:

Volume of partial cylinder (V

cylinder

) = 0.785 × H

windrow

× L

top

× W

windrow

= 0.785 × 2.6 m × 24 m × 3.4 m

= 166.5 m 3 is the volume of the partial cylinder

Diameter of the partial sphere (D

sphere

) = (L

bottom

– L

top

+ W

windrow

) ÷ 2 = (31 m – 24 m+ 3.4 m) ÷ 2

= 5.2 m is the diameter of the partial sphere

Volume of partial sphere (V

sphere

) = 0.131 × H

windrow

× [(4 × H

windrow

× H

windrow

) + (3 × D x D)] = 0.131 × 2.6 m × [(4 × 2.6 x 2.6) + (3 × 5.2 x 5.2)] = 0.3406 m × [(4 × 6.76 m 2 )+ (3 × 27.04 m 2 )] = 0.3406 m × [27.04 m 2 + 81.12 m 2 ] = 0.3406 m × 108.16 m 2

= 36.8 m 3 is the volume of the partial sphere

The volume of the pile is:

Total windrow volume (V

windrow

) = V

cylinder

+ V

sphere

= 166.5 m 3 + 36.8 m 3

= 203.3 m 3 is the total volume of the rounded windrow