Science of Water : Concepts and Applications

Water Hydraulics 59
With regard to fl ow, continuity of fl ow and the continuity equation have been discussed (i.e.,
Equation 3.15). Along with the continuity of fl ow principle and continuity equation, the law of conservation
of energy, piezometric surface, and Bernoulli’s theorem (or principle) are also important
to our study of water hydraulics.
CONSERVATION OF ENERGY
Many of the principles of physics are important for the study of hydraulics. When applied to problems
involving the fl ow of water, few principles of physical science are more important and useful to
us than the law of conservation of energy. Simply put, the law of conservation of energy states that
energy can neither be created nor destroyed, but it can be converted from one form into another. In
a given closed system, the total energy is constant.
ENERGY HEAD
Two types of energy—kinetic and potential—and three forms of mechanical energy—potential
energy due to elevation, potential energy due to pressure, and kinetic energy due to velocity—exist
in hydraulic systems. Energy has the unit of foot pounds (ft-lb). It is convenient to express hydraulic
energy in terms of energyhead, in feet of water. This is equivalent to foot-pounds per pound of water
(ft-lb/lb = ft).
PIEZOMETRIC SURFACE
As mentioned earlier, we have seen that when a vertical tube, open at the top, is installed onto 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 piezometric 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).
The surface of water that is in contact with the atmosphere is known as free water surface.
Many important hydraulic measurements are based on the difference in height between the free
water surface and some point in the water system. The piezometric surface is used to locate this free
water surface in a vessel, where it cannot be observed directly.
To understand how a piezometer actually measures pressure, consider the following example.
If a clear, see-through pipe is connected to the side of a clear glass or plastic vessel, the water will
rise in the pipe to indicate the level of the water in the vessel. Such a see-through pipe, the piezometer,
allows you to see the level of the top of the water in the pipe; this is the piezometric surface.
In practice, a piezometer is connected to the side of a tank or pipeline. If the water-containing
vessel is not under pressure (as is the case in Figure 3.8), the piezometric surface will be the same
Free water
surface
Open end
Piezometric surface
Piezometer
FIGURE 3.8 A container not under pressure where the piezometric surface is the same as the free water
surface in the vessel.