fluid_mechanics

3Elementary Fluid
Dynamics—The
Bernoulli Equation
CHAPTER OPENING PHOTO: Flow past a blunt body: On any object placed in a moving fluid there is a stagnation
point on the front of the object where the velocity is zero. This location has a relatively large pressure
and divides the flow field into two portions—one flowing to the left, and one flowing to the right of
the body. 1Dye in water.2 1Photograph by B. R. Munson.2
Learning Objectives
After completing this chapter, you should be able to:
■ discuss the application of Newton’s second law to fluid flows.
■ explain the development, uses, and limitations of the Bernoulli equation.
■ use the Bernoulli equation (stand-alone or in combination with the continuity
equation) to solve simple flow problems.
■ apply the concepts of static, stagnation, dynamic, and total pressures.
■ calculate various flow properties using the energy and hydraulic grade lines.
The Bernoulli equation
may be the most
used and abused
equation in fluid
mechanics.
In this chapter we investigate some typical fluid motions (fluid dynamics) in an elementary way.
We will discuss in some detail the use of Newton’s second law (F ma) as it is applied to fluid
particle motion that is “ideal” in some sense. We will obtain the celebrated Bernoulli equation
and apply it to various flows. Although this equation is one of the oldest in fluid mechanics and
the assumptions involved in its derivation are numerous, it can be used effectively to predict and
analyze a variety of flow situations. However, if the equation is applied without proper respect
for its restrictions, serious errors can arise. Indeed, the Bernoulli equation is appropriately called
“the most used and the most abused equation in fluid mechanics.”
A thorough understanding of the elementary approach to fluid dynamics involved in this chapter
will be useful on its own. It also provides a good foundation for the material in the following
chapters where some of the present restrictions are removed and “more nearly exact” results are
presented.
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