Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

272 Chapter 10 Force and Force-Related Parameters

Example 10.8 Most of you may have seen water towers in and around small towns. The function of a water

tower is to create a desirable municipal water pressure for household and other usage in a

town. To achieve this purpose, water is stored in large quantities in elevated tanks. You may

also have noticed that sometimes the water towers are placed on top of hills or at high points

in a town. The municipal water pressure may vary from town to

town, but it generally falls somewhere between 50 psi and 80 psi.

We are interested in developing a table that shows the relation-

ship between the height of water aboveground in the water tower

and the water pressure in a pipeline located at the base of the

water tower, as shown in Figure 10.22. We will calculate the

water pressure, in psi, in a pipe located at the base of the water

tower as we vary the height of water in increments of 10 ft. We

will create a table showing our results up to 100 psi. And using

the height – pressure table, we will answer the question, “What

should be the water level in the water tower to create a 50-psi

water pressure in a pipe at the base of the water tower?” The rela-

tionship between the height of water aboveground in the water

tower and the water pressure in a pipeline located at the base of

the water tower is given by Equation (10.15):

where

Pis the water pressure at the base of the water tower (lb/ft

2

)

ris the density of water (equal to 1.94 slugs /ft

3

)

gis the acceleration due to gravity (g32.2 ft /s

2

)

his the height of water aboveground (in ft)

Substituting the known values into Equation (10.15) leads to

Recall that to convert the pressure from lb/ft

2

to lb/in

2

, we take the following step:

And performing the conversion,

Note that the factor 0.4338 has the proper units that give the pressure in lb/in

2

when the valueh

is input in feet. Next, we generate Table 10.3 by substituting forhin increments of 10 ft in the

preceding equation. From Table 10.3, we can see that in order to create a 50-psi water pressure

in a pipeline at the base of the tower, the water level in the water tower should be approxi-

mately 120 ft.

P a

lb

in

2 b1.94a

slugs

ft

3 ba32.2

ft

s

2 b3h^1 ft24a

1 ft

2

144 in

2 b^1 0.4338^23 h^1 ft^24

P a

lb

in

2 bP^ a

lb

ft

2 ba

1 ft

2

144 in

2 b

P a

lb

ft

2 b1.94a

slugs

ft

3 ba32.2

ft

s

2 b3h^1 ft^24

Prgh

■Figure 10.22

The water tower of Example 10.8.

62080_10_ch10_p251-302.qxd 5/22/10 12:32 AM Page 272

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