Page 194 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

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156 Chapter 5 Water Hydraulics, Transmission, and Appurtenances
The moment of inertia of the most common rectangular shape (width b and height h)
can be calculated by the following equation:
I (1>12)Ah 2
cg
(1>12)(bh) h 2
(1>12)bh 3 (5.9)

EXAMPLE 5.1 WATER, SPECIFIC WEIGHT, FORCE AND MOMENT OF INERTIA
Water rises to level E in the pipe attached to water storage tank ABCD in Fig. 5.1. Neglecting the
weight of the tank and riser pipe, determine (a) the resultant force acting on area AB, which is 8 ft
wide (2.4 m); (b) the location of the resultant force acting on area AB; (c) the pressure on the bot-
tom BC; and (d) the total weight of the water.

Figure 5.1 Water Tank for E
Example 5.1.
A 1 ft 2 12 ft (3.7 m)
2
(0.093 m )

6 ft (1.8 m) A D

B C

20 ft (6.1 m)

Solution 1 (U.S. Customary System):
a. The resultant force, P f , acting on area AB:
P f ( h cg ) A
3
(62.4 lb/ft )(12 ft 3 ft)(6 ft 8 ft)
45,000 lb
b. The location of the resultant force acting on area AB:
y cp [I cg >y cg A] y cg
I cg (1>12)bh 3
3
y cp [8(6) >12]>[15(6 8)] 15
0.20 15
15.2 ft