Civil Engineering Reference
In-Depth Information
8
CHAPTER
Applications in Fluid
Mechanics
8.1 INTRODUCTION
The general topic of fluid mechanics encompasses a wide range of problems of
interest in engineering applications. The most basic definition of a
fluid
is to state
that a fluid is a material that conforms to the shape of its container. Thus, both
liquids and gases are fluids. Alternately, it can be stated that a material which,
in itself, cannot support shear stresses is a fluid. The reader familiar with the dis-
tortion energy theory of solids will recall that geometric distortion is the result of
shear stress while normal stress results in volumetric change. Thus, a fluid read-
ily distorts, since the resistance to shear is very low, and such distortion results
in flow.
The physical behavior of fluids and gases is very different. The differences in
behavior lead to various subfields in fluid mechanics. In general, liquids exhibit
constant density and the study of fluid mechanics of liquids is generally referred
to as
incompressible flow.
On the other hand, gases are highly compressible
(recall Boyle's law from elementary physics [1]) and temperature dependent.
Therefore, fluid mechanics problems involving gases are classified as cases of
compressible flow
.
In addition to considerations of compressibility, the relative degree to which
a fluid can withstand some amount of shear leads to another classification of fluid
mechanics problems. (Regardless of the definition, all fluids can support
some
shear.) The resistance of a fluid to shear is embodied in the material property
known as viscosity. In a very practical sense, viscosity is a measure of the “thick-
ness” of a fluid. Consider the differences encountered in stirring a container
of water and a container of molasses. The act of stirring introduces shearing
stresses in the fluid. The “thinner,” less
viscous,
water is easy to stir; the “thicker,”
more viscous, molasses is harder to stir. The physical effect is represented by
the shear stresses applied to the “stirrer” by the fluid. The concept of viscosity is
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