Water Hydraulics - Wastewater Operators - page 62

Velocity 1 × Pressure 1 = Velocity 2 × Pressure 2 (2.15)

or

v 1 P 1 = v 2 P 2

2.7 PiezoMeTriC surfaCe and bernoulli's TheoreM

To keep the systems in your plant operating properly and effi-
ciently, you must understand the basics of hydraulics—the laws of force,
motion, and others. As stated previously, most applications of hydrau-
lics in water/wastewater treatment systems involve water in motion—in
pipes under pressure or in open channels under the force of gravity. The
volume of water flowing past any given point in the pipe or channel per
unit time is called the flow rate or discharge , or just low . The continu-
ity of flow and the continuity equation have already been discussed (see
Equation 2.15). Along with the continuity of flow principle and conti-
nuity equation, the law of conservation of energy, piezometric surface,
and Bernoulli's theorem (or principle) are also important to our study of
water hydraulics.

2.7.1 Conservation of energy

Many of the principles of physics are important to the study of
hydraulics. When applied to problems involving the flow of water, few of
the principles of physical science are more important and useful to us
than the law of conservation of energy . Simply, the law of conservation
of energy states that energy can neither be created nor destroyed, but it
can be converted from one form to another. In a given closed system, the
total energy is constant.

2.7.2 energy head

In addition to the kinetic and potential energy in hydraulic systems
are three forms of mechanical energy: potential energy due to elevation,
potential energy due to pressure, and kinetic energy due to velocity.
Energy has the units of foot-pounds (ft-lb). It is convenient to express
hydraulic energy in terms of energy head in feet of water. This is equiva-
lent to foot-pounds per pound of water (ft-lb/lb = ft).

2.7.3 Piezometric surface *

We have seen that when a vertical tube, open at the top, is inserted
into a vessel of water, the water will rise in the tube to the water level in
the tank. The water level to which the water rises in a tube is the piezo-
metric surface . That is, the piezometric surface is an imaginary surface
that coincides with the level of the water to which water in a system
would rise in a piezometer (an instrument used to measure pressure).

* This section is adapted from Spellman, F.R., The Science of Water: Concepts &
applications , Technomic, Lancaster, PA, 1998, pp. 92-93.