Circumference, Area, and Volume - Basic Mathematics for Water and Wastewater Operators - page 167

TABLE 11.1
Volume Formulas
Sphere volume

=

(π/6) × (Diameter) 3

Cone volume =

1/3 × Volume of a cylinder

Rectangular tank volume =

=

Area of rectangle × H (or depth)
L × W × H (or depth)

Cylinder volume =

=

Area of cylinder × H (or depth)
π × r 2 × H (or depth)

■ Example 11.13
Problem: A unit rectangular process basin has a length of 15 ft, width of 7 ft, and
depth of 9 ft. What is the volume of the basin?

Solution:

V = L × W × D = 15 ft × 7 ft × 9 ft = 945 ft 3

■ Example 11.14
Problem: A sedimentation tank is 60 ft long, 40 ft wide, and 12 ft deep. What is the
volume of the tank in cubic feet?

Solution:

60 ft × 40 ft × 12 ft = 28,800 ft 3

For wastewater operators, representative surface areas are most often rectangles,
triangles, circles, or a combination of these. Practical volume formulas used in water/
wastewater calculations are given in Table 11.1.

v oluMe of r ound p ipe and r ound s urfaCe a reas
To determine the volume of round pipe and round surface areas, the following exam-
ples are helpful.

■ Example 11.15
Problem: Find the volume of a 3-in. round pipe that is 300 ft long.

Solution:

1. Change the diameter of the duct from inches to feet by dividing 3 in. by 12:

3 in. ÷ 12 in./ft = 0.25 ft

2. Find the radius ( r ) by dividing the diameter by 2:

0.25 ft ÷ 2 = 0.125