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figure 2.11 Bernoulli's principle.
Note: During the early design phase of a treatment plant, it is important
to establish the hydraulic grade line across the plant because both the
proper selection of the plant site elevation and the suitability of the site
depend on this consideration.
Note: Changes in the piezometric surface occur when water is flowing.
2.7.4 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 fluid system in the 1700s. Before discussing Bernoulli's
energy equation, it is important to understand the basic principle behind
Bernoulli's equation. Water (or any other hydraulic fluid) in a hydraulic
system possesses kinetic energy and potential energy. kinetic energy
is present when the water is in motion; the faster the water moves, the
more kinetic energy is used. Potential energy is a result of the water
pressure. The total energy of the water is the sum of the kinetic energy
and potential energy. Bernoulli's principle states that the total energy of
the water (fluid) always remains constant; therefore, when the water flow
in a system increases, the pressure must decrease. When water starts to
flow in a hydraulic system, the pressure drops. When the flow stops, the
pressure rises again. The pressure gauges shown in Figure 2.11 indicate
this balance more clearly.
Note: The basic principle explained above ignores friction losses from
point to point in a fluid system employing steady-state flow.
2.7.4.1 Bernoulli's Equation
In a hydraulic system, total energy head is equal to the sum of
three individual energy heads. This can be expressed as:
Total Energy Head = Elevation Head + Pressure Head + Velocity Head
where the elevation head is the pressure due to the elevation of the water,
the pressure head is the height of a column of water that a given hydro-
static pressure in a system could support, and the velocity head is the
* This section is adapted from Nathanson, J.A., Basic environmental Technology: Water
Supply, Waste management, and Pollution Control , 2nd ed., Prentice Hall, Upper Saddle
River, NJ, 1997, pp. 29-30.
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