Fluid Mechanics-Elementary Fluid Dynamics—The Bernoulli Equation

As was discussed in the previous chapter, there are many situations involving fluids in which
the fluid can be considered as stationary. In general, however, the use of fluids involves motion
of some type. In fact, a dictionary definition of the word “fluid” is “free to change in
form.” In this chapter we investigate some typical fluid motions 1fluid dynamics2 in an elementary
way.
To understand the interesting phenomena associated with fluid motion, one must consider
the fundamental laws that govern the motion of fluid particles. Such considerations include
the concepts of force and acceleration. We will discuss in some detail the use of Newton’s
second law 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 effectively used 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.