13-08-2012, 11:45 AM
Fluid Mechanics
1Fluid Mechanics.pdf (Size: 4.46 MB / Downloads: 275)
INTRODUCTION
Fluid mechanics is encountered in almost every area of our physical lives. Blood flows through our veins
and arteries, a ship moves through water and water flows through rivers, airplanes fly in the air and air
flows around wind machines, air is compressed in a compressor and steam expands around turbine
blades, a dam holds back water, air is heated and cooled in our homes, and computers require air to cool
components. All engineering disciplines require some expertise in the area of fluid mechanics.
In this book we will present those elements of fluid mechanics that allow us to solve problems
involving relatively simple geometries such as flow through a pipe and a channel and flow around
spheres and cylinders. But first, we will begin by making calculations in fluids at rest, the subject of fluid
statics. The math requirement is primarily calculus but some differential equation theory will be used.
The more complicated flows that usually are the result of more complicated geometries will not be
presented in this book.
In this first chapter, the basic information needed in our study will be presented. Much of it has been
included in previous courses so it will be a review. But, some of it should be new to you. So, let us get
started.
DIMENSIONS, UNITS, AND PHYSICAL QUANTITIES
We finish this section with comments on significant figures. In every calculation, well, almost every
one, a material property is involved. Material properties are seldom known to four significant figures
and often only to three. So, it is not appropriate to express answers to five or six significant figures. Our
calculations are only as accurate as the least accurate number in our equations. For example, we use
gravity as 9.81 m=s2, only three significant figures. It is usually acceptable to express answers using four
significant figures, but not five or six. The use of calculators may even provide eight. The engineer does
not, in general, work with five or six significant figures. Note that if the leading numeral in an answer is
1, it does not count as a significant figure, e.g., 1248 has three significant figures.
GASES AND LIQUIDS
The substance of interest in our study of fluid mechanics is a gas or a liquid. We restrict ourselves to
those liquids that move under the action of a shear stress, no matter how small that shearing stress may
be. All gases move under the action of a shearing stress but there are certain substances, like ketchup,
that do not move until the shear becomes sufficiently large; such substances are included in the subject of
rheology and are not presented in this book.
A force acting on an area is displayed in Fig. 1.1. A stress vector is the force vector divided by
the area upon which it acts. The normal stress acts normal to the area and the shear stress acts tangent
to the area. It is this shear stress that results in fluid motions. Our experience of a small force parallel
to the water on a rather large boat confirms that any small shear causes motion.
1Fluid Mechanics.pdf (Size: 4.46 MB / Downloads: 275)
INTRODUCTION
Fluid mechanics is encountered in almost every area of our physical lives. Blood flows through our veins
and arteries, a ship moves through water and water flows through rivers, airplanes fly in the air and air
flows around wind machines, air is compressed in a compressor and steam expands around turbine
blades, a dam holds back water, air is heated and cooled in our homes, and computers require air to cool
components. All engineering disciplines require some expertise in the area of fluid mechanics.
In this book we will present those elements of fluid mechanics that allow us to solve problems
involving relatively simple geometries such as flow through a pipe and a channel and flow around
spheres and cylinders. But first, we will begin by making calculations in fluids at rest, the subject of fluid
statics. The math requirement is primarily calculus but some differential equation theory will be used.
The more complicated flows that usually are the result of more complicated geometries will not be
presented in this book.
In this first chapter, the basic information needed in our study will be presented. Much of it has been
included in previous courses so it will be a review. But, some of it should be new to you. So, let us get
started.
DIMENSIONS, UNITS, AND PHYSICAL QUANTITIES
We finish this section with comments on significant figures. In every calculation, well, almost every
one, a material property is involved. Material properties are seldom known to four significant figures
and often only to three. So, it is not appropriate to express answers to five or six significant figures. Our
calculations are only as accurate as the least accurate number in our equations. For example, we use
gravity as 9.81 m=s2, only three significant figures. It is usually acceptable to express answers using four
significant figures, but not five or six. The use of calculators may even provide eight. The engineer does
not, in general, work with five or six significant figures. Note that if the leading numeral in an answer is
1, it does not count as a significant figure, e.g., 1248 has three significant figures.
GASES AND LIQUIDS
The substance of interest in our study of fluid mechanics is a gas or a liquid. We restrict ourselves to
those liquids that move under the action of a shear stress, no matter how small that shearing stress may
be. All gases move under the action of a shearing stress but there are certain substances, like ketchup,
that do not move until the shear becomes sufficiently large; such substances are included in the subject of
rheology and are not presented in this book.
A force acting on an area is displayed in Fig. 1.1. A stress vector is the force vector divided by
the area upon which it acts. The normal stress acts normal to the area and the shear stress acts tangent
to the area. It is this shear stress that results in fluid motions. Our experience of a small force parallel
to the water on a rather large boat confirms that any small shear causes motion.