Environmental Engineering Reference
In-Depth Information
3. Find the volume (
V
):
V
=
L
× π ×
r
2
V
= 300 ft × 3.14 × 0.0156 = 14.7 ft
2
■
Example 11.16
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
= 96 in. × 3.14 × (12 i in.2
2
= 96 in. × 3.14 × 14 4 in.
2
= 43,407 ft
3
■
Example 11.17
Problem:
A sedimentation basin is 80 ft in diameter and 12 ft deep. What is the
volume of the tank?
Solution:
V
=
H
× π ×
r
2
= 12 ft × 3.14 × (40 ft × 40 ft) = 60,403 ft
3
v
oluMe
of
a
C
one
and
s
phere
The following equations and examples show how to determine the volume of a cone,
a sphere, and a tank.
Volume of a Cone
Volume of a cone = (π/12) × (Diameter)
2
× Height
(11.8)
(π/12) = (3.14/12) = 0.262
Note:
The diameter used in the formula is the diameter of the base of the cone.
■
Example 11.18
Problem:
The bottom section of a circular settling tank has the shape of a cone. How
many cubic feet of water are contained in this section of the tank if the tank has a
diameter of 120 ft and the cone portion of the unit has a depth of 6 ft?
Solution:
V
= 0.262 × (120 ft)
2
× 6 ft = 22,637 ft
3
Volume of a Sphere
Volume of a sphere = (π/6) × (Diameter)
3
(11.9)
(π/6) = (3.14/6) = 0.524
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