Science of Water : Concepts and Applications

58 The Science of Water: Concepts and Applications
Solution:
Using the equation, A1V1 = A2V2 , we need to determine the area of each pipe:
The continuity equation now becomes
Solving for V 2
12in.:
A
4
D
2
314 1ft
.
4
0. 785
2
ft 2
6 3 14 05 ( . )
in.:
A .
4
0. 196
ft 2
(0.785 ft ) 3 ft 2 ⎛ ⎞
2
ft
⎝
⎜
s ⎠
⎟ ( 0. 196 ) V
V 2 2
(0.785ft )(3ft/s)
2
(0.196ft )
12ft/s
or fps
PRESSURE/VELOCITY
In a closed pipe fl owing full (under pressure), the pressure is indirectly related to the velocity of the
liquid. This principle, when combined with the principle discussed in the previous section, forms
the basis for several fl ow measurement devices (Venturi meters and rotameters) as well as the injector
used for dissolving chlorine into water:
or
Velocity pressure velocity pressure
1 1 2 2
2
2
VP 1 1 VP 2 2
(3.15)
PIEZOMETRIC SURFACE AND BERNOULLI’S THEOREM
They will take your hand and lead you to the pearls of the desert, those secret wells swallowed by oyster
crags of wadi, underground caverns that bubble rusty salt water you would sell your own mothers to
drink.
—S. Holman (1998)
To keep the systems in waterworks operating properly and effi ciently, the operators must understand
the basics of hydraulics—the laws of force, motion, and others. As stated previously, most
applications of hydraulics in water treatment systems involve water in motion—in pipes under
pressure or in open channels under the force of gravity. The volume of water fl owing past any given
point in the pipe or channel per unit time is called the fl ow rate or discharge—or just fl ow.