Science of Water : Concepts and Applications

Water Hydraulics 61
or hydraulic gradient of the system. (Note: It is important to point out that in a static water system,
the HGL is always horizontal.) The HGL is a very useful graphical aid when analyzing pipe fl ow
problems.
√ Important Point: During the early design phase of a treatment plant, it is important to establish
the HGL across the plant because both the proper selection of the plant site elevation and the
suitability of the site depend on this consideration. Typically, most conventional water treatment
plants required 16–17 ft of head loss across the plant.
√ Key Point: Changes in the piezometric surface occur when water is fl owing.
BERNOULLI’S THEOREM *
Swiss physicist and mathematician Samuel Bernoulli developed the calculation for the total energy
relationship from point to point in a steady-state fl uid system in the 1700s. Before discussing Bernoulli’s
energy equation, it is important to understand the basic principle behind Bernoulli’s equation.
Water (and any other hydraulic fl uid) in a hydraulic system possesses two types of energy—
kinetic and potential. Kinetic energy is present when the water is in motion. The faster the water
moves, the more the kinetic energy used. Potential energy is a result of the water pressure. The
total energy of the water is the sum of the kinetic and potential energy. Bernoulli’s principle states
that the total energy of the water (fl uid) always remains constant. Therefore, when the water fl ow
in a system increases, the pressure must decrease. When water starts to fl ow in a hydraulic system,
the pressure drops. When the fl ow stops, the pressure rises again. The pressure gauges shown in
Figure 3.11 indicate this balance more clearly.
√ Note: The basic principle explained above ignores friction losses from point to point in a fl uid
system employing steady-state fl ow.
BERNOULLI’S EQUATION
Piezometric surface
1 2 3
HGL
Piezometric surface
1 2
Closed valve Open valve
(a) (b)
FIGURE 3.10 Shows head loss and piezometric surface changes when water is fl owing.
In a hydraulic system, total energy head is equal to the sum of three individual energy heads. This
can be expressed as
Total head = elevation head + pressure head + velocity head
* The section is adapted from Nathanson, J.A. (1997), Basic Environmental Technology: Water Supply, Waste Management,
and Pollution Control, 2nd ed., Prentice-Hall, Upper Saddle River, NJ.
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HGL