Circumference, Area, and Volume - Basic Mathematics for Water and Wastewater Operators - page 169

■ Example 11.19
Problem: What is the volume in cubic feet of a gas storage container that is spherical
and has a diameter of 60 ft?

Solution:

V = 0.524 × (60 ft) 3 = 113,184 ft 3

Volume of a Circular or Cylindrical Tank
Circular process and various water and chemical storage tanks are commonly found
in water/wastewater treatment. A circular tank consists of a circular floor surface
with a cylinder rising above it (see Figure 11.10). The volume of a circular tank is
calculated by multiplying the surface area times the height of the tank walls.

■ Example 11.20
Problem: If a tank is 20 ft in diameter and 25 ft deep, how many gallons of water
will it hold?

Hint: In this type of problem, calculate the surface area first, multiply by the height,
and then convert to gallons.

Solution:

r = D ÷ 2 = 20 ft ÷ 2 = 10 ft

A = π × r 2 = 3.14 × (10 ft) 2 = 314 ft 2

V = A × H = 314 ft 2 × 25 ft = 7850 ft 3

7850 ft 3 × 7.48 gal l /f ft3 3 = 58,718 gal

v oluMe in g allons
It is often necessary to calculate a volume of a tank or pipe in gallons rather than
cubic feet. In most cases the volume must be calculated in cubic feet and then con-
verted into gallons. This is determined by multiplying cubic feet by 7.48.

Volume in gallons = Cubic feet × 7.48 ga l /f t 3

FIGURE 11.10 Cylindrical tank.