<p>CHAPTER 2
_________________________________________________________________________
REVIEW OF FUNDAMENTALS
This chapter will review the fundamental concepts and principles upon which the
hydraulics of pipeline systems is based. The review is intended to be sufficiently complete
that readers who have taken a good first course in elementary fluid mechanics, but not
necessarily recently, will be reminded of, and updated in, the essential conceptual building
blocks that are the foundation of the material in this book. We will begin with an
introduction to the fundamental equations that are the foundation of most of the subsequent
developments in the book. Because the concept of the energy grade line (EGL or simply
EL) and the hydraulic grade line (HGL) is so useful, we shall look at this idea separately.
Next we look at some length at various head loss formulas. How turbomachines with
rotating impellers, particularly pumps, function is vitally important to the understanding
of many parts of this book, so their theory of operation and basic characteristics will be
examined. The chapter will conclude with several steady-flow examples and a range of
problems that will allow readers to test their readiness for the coming chapters. If a
thorough review is desired, one might consult Miller (1984).
2.1 THE FUNDAMENTAL PRINCIPLES
2.1.1. THE BASIC EQUATIONS
Conservation of mass is the most basic principle. In general, the fluid density ρ may
vary in response to changes in the fluid temperature and/or pressure. For a fixed control
volume V enclosed by a surface S, a general statement of mass conservation is
∂
∂t
ρ dV
V∫
+ ρ
r
v ⋅
r
n
S∫
dS = 0
(2.1)
in which
r
v is a velocity at a point and
r
n is an outer normal unit vector to the surface
S , and t is time. The first term represents the accumulation of mass over time in the
control volume; for steady flows it is zero. At a surface point the dot product
r
v ⋅
r
n gives
the component of the velocity which crosses the surface, so the second te