Geoscience Reference
In-Depth Information
TABLE 2.1
Volume Formulas
Sphere volume
=
(π/6) × (diameter)
3
Cone volume
=
1/3 × (volume of a cylinder)
Rectangular tank volume
=
(Area of rectangle) × (
D
or
H
)
=
(
L
×
W
) × (
D
or
H
)
Cylinder volume
=
(Area of cylinder) × (
D
or
H
)
=
π
r
2
× (
D
or
H
)
Solution:
V
=
L
×
W
×
D
= 15 ft × 7 ft × 9 ft = 945 ft
3
For wastewater operators, representative surface areas are most often rectangles, triangles, cir-
cles, or a combination of these. Practical volume formulas used in water/wastewater calculations
are given in Table 2.1.
When determining the volume of round pipe and round surface areas, the following examples
are helpful.
■
EXAMPLE 2.49
Problem:
Find the volume of a 3-in. round pipe that is 300 ft long.
Solution:
1. Change the diameter (
D
) of the duct from inches to feet by dividing by 12:
D
= 3 ÷ 12 = 0.25 ft
2. Find the radius (
r
) by dividing the diameter by 2:
r
= 0.25 ft ÷ 2 = 0.125
3. Find the volume (
V
):
V
=
L
× π ×
r
2
V
= 300 ft × 3.14 × 0.0156 = 14.72 ft
2
■
EXAMPLE 2.50
Problem:
Find the volume of a smokestack that is 24 in. in diameter (entire length) and 96 in. tall.
Solution:
First find the radius of the stack. The radius is one half the diameter, so 24 in. ÷ 2 = 12 in.
Now find the volume:
V
=
H
× π ×
r
2
V
= 96 in. × π × (12 i in.)2
2
V
= 96 in. × π × (14 4 in.
2
) = 43,407 ft
3
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