Lyons W.C. (ed.). Standard handbook of petroleum and natural gas engineering.2001- Volume 1
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2
General Engineering
and
Science
Gordon
R.
Bopp, Ph.D.
Phillip W. Johnson, Ph.D., P.E.
Environmental Technology and Educational
Department
of
Mineral Engineering
Services Company
University of Alabama
Richland, Washington
Tuscaloosa, Alabama
Ronald
M.
Brimhall, Ph.D., P.E.
Texas A&M University
College Station, Texas
B.
J.
Gallaher, P.E.
Consultant
Soils and Geological Engineering
I.as
Cruces, New Mexico
Murty
Kuntamukkula, Ph.D.
Westinghouse Savannah River Company
Aiken, South Carolina
William
C.
Lyons,
Ph.D., P.E.
New Mexico Institute of Mining and Technology
Socorro,
New Mexico
Basic Mechanics (Statics and Dynamics)
..............................................
137
Fluid Mechanics
....................................................................................
168
Strength
of
Materials
............................................................................
185
Thermodynamics
..................................................................................
209
Definitions, Laws, and Units 137. Statics 139. Dynamics
149.
Fluid Statics 168. Fluid Dynamics 170.
Stress and Strain 185. Elementary Loading Configurations 188. Prediction of Failure 194.
Units of Energy 209. The First Law of Thermodynamics 210. Entropy Production: Flow
Systems 214. Application of the Second Law 216. Summary of Thermodynamic Equations 223.
Thermal Properties for Selected Systems 223.
Geological Engineering
........................................................................
240
General Rock Types 240. Historical Geology 241. Petroleum Geology 242. Source Rocks 243.
Migration 244. Accumulation 245. Structural Geology 246. Traps 251. Basic Engineering Rock
Properties 254. Basic Engineering Soil Properties 266.
Electricity
..............................................................................................
278
Electrical Units 278. Electrical Circuit Elements 281. Transient and AC Circuits 284. AC Power 285.
Magnetism 286. Transformers 288. Rotating Machines 289. Polyphase Circuits 293. Power
Transmission and Distribution Systems 294.
Chemistry
..............................................................................................
297
Characteristics of Chemical Compounds 297. Petroleum Chemistry 299. Physical Chemistry 325.
Thermochemistry 351.
Engineering Design
..............................................................................
365
Scientific and Engineering Philosophies 367. The "Art" of Engineering Design 369. Design in the
Petroleum Industry 379. Engineering Ethics 380. Intellectual Property.
References
.............................................................................................
386
135
2
General Engineering and Science
BASIC MECHANICS (STATICS AND DYNAMICS)
Mechanics is the physical science that deals with the effects of forces on the state
of motion or rest of solid, liquid, or gaseous bodies. The field may be divided into
the mechanics of rigid bodies, the mechanics of deformable bodies, and the mechanics
of fluids.
A rigid body is one that does not deform. True rigid bodies do not exist in nature;
however, the assumption of rigid body behavior
is
usually an acceptable accurate
simplification for examining the state
of
motion or rest of structures and elements of
structures. The rigid body assumption is not useful in the study of structural failure.
Rigid body mechanics is further subdivided into the study of bodies at rest, statics,
and the study of bodies in motion, dynamics.
Definitions, Laws, and Units
Fundamental Quantities
All of Newtonian mechanics
is
developed from the independent and absolute
concepts ofspace, time, and mass. These quantities cannot be exactly defined, but they
may be functionally defined as follows:
Space. Some fixed reference system in which the position
of
a body can be uniquely
defined. The concept of space is generally handled by imposition of a coordinate
system, such as the Cartesian system, in which the position of a body can be stated
mathematically.
Time. Physical events generally occur in some causal sequence. Time is a measure
of this sequence and is required in addition to position in space in order to fully
specify an event.
Derived Quantities
Muss.
A measure
of
the resistance of a body to changes in its state of motion.
The concepts
of
space, time, and mass may be combined to produce additional
useful measures and concepts.
Particle. An entity which has mass, but can be considered to occupy a point in
space. Rigid bodies that are not subject to the action of an unbalanced couple often
may be treated as particles.
Body. A collection
of
particles.
A
rigid body
is
a rigidly connected collection of
particles.
Force. The action of one body on another. This action will cause a change in the
motion of the first body unless counteracted by an additional force or forces. A force
may be produced either by actual contact or remotely (gravitation, electrostatics,
magnetism, etc.). Force is a vector quantity.
Couple.
If two forces
of
equal magnitude, opposite direction, and different lines of
action act on a body, they produce a tendency for rotation, but no tendency for
translation. Such a pair of forces is called a couple. The magnitude of the moment
137
138
General Engineering and Science
produced by a couple is calculated by multiplying the magnitude of one of the two
forces times the perpendicular distance between them. Moment is a vector quantity,
and its sense of direction is considered to be outwardly perpendicular to the plane of
counterclockwise rotation of the couple. The moment of a single force about some
point
A
is the magnitude
of
the force times the perpendicular distance between A
and the line of action of the force.
Velocity.
A
measure of the instantaneous rate of change of position in space with
respect to time. Velocity is a vector quantity.
Acceleration.
A measure of the instantaneous rate
of
change in velocity with respect
to time. Acceleration
is
a vector quantity.
Gravitational acceleration.
Every body falling in a vacuum at a given position above
and near the surface of the earth
will
have the same acceleration,
g.
While this
acceleration varies slightly over the earth’s surface due
to
local variations in its shape
and density, it is sufficiently accurate for most engineering calculations to assume
that g
=
32.2
ft/s2 or
9.81
m/sp at the surface of the earth.
Weight.
A
measure of the force exerted on a body
of
mass
M
by the gravitational
attraction of the earth. The magnitude of this force is
W=Mg
where
W
is the weight of the body. Strictly speaking, weight is a vector quantity since
it is a force acting in the direction of the gravitational acceleration.
General Laws
The foregoing defined quantities interact according to the following fundamental
laws, which are based upon empirical evidence.
Conservation
of
mass.
The mass of a system of particles remains unchanged during
the course of ordinary physical events.
Parallelogram law
for
the addition
of
forces.
Two forces,
F,
and
F,,
acting on a particle
may be replaced by a single force,
R,
called their resultant. If the two forces are
represented
as
the adjacent sides of a parallelogram, the diagonal of the parallelogram
will represent the resultant (Figure
2-1).
Principle
of
transmissibility.
A
force acting at a point on a body can be replaced by a
second force acting at a different point on the body without changing the state of
equilibrium or motion of the body as long as the second force has the same magnitude
and line
of
action as the first.
Newton’s
Laws
of
Motion
1.
A
particle at rest
will
remain at rest, and
a
particle in motion will remain in
motion along a straight line with no acceleration unless acted upon by an
unbalanced system of forces.
FI
Figure
2-1. Parallelogram law for addition of forces.
Basic Mechanics (Statics and Dynamics)
139
2.
If
an
unbalanced system of forces acts upon
a
particle, it will accelerate in the
direction of the resultant force at
a
rate proportional to the magnitude of the
resultant force. This law expresses the relationship between force, mass, and
acceleration and may be written
as
F=Ma
(2-2)
where
F
is the resultant force, M is the mass of the particle, and
a
is the
acceleration
of
the particle.
3.
Contact forces between two bodies have the same magnitude, the same line of
action, and opposite direction.
Gmuitution.
Two particles in space are attracted toward each other by
a
force that
is proportional to the product of their masses and inversely proportional to the square
of
the distance between them. Mathematically this may be stated as
where
I
F
1
is the magnitude of the force of gravitational attraction,
G
is the universal
gravitational constant (6.673
x
10-"m3/kg
-
s2
or
3.44
x
10.' ft4/lb
-
s4),
m, and m2
are
the masses of particles
1
and 2, and r is the distance between the two particles.
Systems
of
Units
Two systems of units are in common usage in mechanics. The first, the
SI
system.
is an absolute system based
on
the fundamental quantities of space, time, and mass.
All
other quantities, including force, are derived.
In
the SI system the basic unit of
mass is the kilogram (kg), the basic unit of length (space) is the meter (m), and the
basic unit of time is the second
(s).
The derived unit of force is the Newton (N),
which is defined
as
the force required to accelerate a mass of
1
kg at
a
rate of
1
m/s'.
The
US.
customary
or
English system
of
units is a gravitational system based upon
the quantities of space, time, and force (weight).
All
other quantities including mass
are derived. The basic unit of length (space) is the foot (ft), the basic unit of time is
the second
(s),
and the basic unit of force is the pound (Ib). The derived unit of mass
is the
slug,
which is the unit
of
mass that will be accelerated by
a
force of one pound
at
a rate
of
1
ft/s2. To apply the slug in practice,
as
in Equation 2-2, the weight in
pounds
mass must first be divided by g
=
32.2 ft/s2, thus generating
a
working mass in
units of
lb
-
s2/ft, or slugs.
Statics
If there are
no
unbalanced forces acting
on
a
particle,
the particle is said to be in
static equilibrium, and Newton's second law reduces to
Thus, solving
a
problem in particle statics reduces to finding the unknown force
or forces such that the resultant force will be zero. To facilitate this process it is useful
to
draw
a
diagram showing the particle of interest and
all
the forces acting upon
it.
This is called
afree-body diagram.
Next
a
coordinate system (usually Cartesian) is
superimposed
on
the free-body diagram, and the forces are decomposed into their
140
General Engineering and Science
components along the coordinate axes. For the particle to be in equilibrium, the sum
of the force components along each of the axes must be zero.
This
yields an algebraic
equation to be solved for the forces in each coordinate direction.
Example
2-1
Block W, weighing
100
Ib (see Figure
2-2)
is attached at point
A
to
a
cable, which is,
in turn, attached to vertical walls at points
B
and
C.
What are the tensions in segments
AB and BC?
Breaking down the diagram into the various forces (Figure 2-2b):
Force balance in the
y
direction:
F,
=
-100
+
T,
sin
45"
+
TAB sin 15"
=
0
0.707T,
+
0.259TA,
=
100
Force balance in the x direction:
F,
=
T, cos 45"
-
TAB cos 15"
=
0
0.707TA,
-
0.966TA,
=
0
and solving Example Equations a and b simultaneously yields
TAB
=
81.6 lb
T,,
=
111.5
lb
If there are no unbalanced forces and no unbalanced moments acting on a
rigid
body,
the rigid body is said to be in static equilibrium. That is, Equation 2-4 must be
satisfied just as for particles, and furthermore:
L
TAB
y
(b)
100
Ib
Figure
2-2.
Diagram for Example
2-1.
Basic Mechanics (Statics and Dynamics)
141
where
XM4
is the sum of the vector moments of all the forces acting on the body
about any arbitrarily selected point
A.
In two dimensions this constitutes an algebraic
equation because all moments must act about an axis perpendicular to the plane of
the forces. In three dimensions the moments must be decomposed into components
parallel
to
the principal axes, and the components along each axis must sum
algebraically to zero.
Example
2-2
A
weightless beam 10 ft in length (see Figure 2-3a) supports a 10-lb weight, W,
suspended by a cable at point
C.
The beam
is
inclined at an angle of 30" and rests
against a step at point
A
and a frictionless fulcrum at point
B,
a distance of
L,
=
6 ft
from point
A.
What are the reactions at points
A
and B?
Breaking the diagram down into the various forces (Figure 2-3b):
Force balance in the x direction:
Fx
=
RA,
-
10 cos 60"
=
0
R<\
=
5
lb
Moment balance about point
A:
'ZM,
=
(10)(10)sin6O0-6R,,
=
0
RI%,
=
14.43 lb
Force balance in the
y
direction:
Fy
=
R,,
+
R,\\
-
10 sin 60"
=
0
R,,
-
10 sin
60"
=
-R,,
R,
=
-4.43 Ib
Note that although the direction assumed for R,4, was incorrect, the sign of the result
indicates the correct direction.
Whenever the weight of a body is significant
in
comparison to the external forces,
the weight, or body force, must be considered in both the force and moment balances.
Figure 2-3.
Diagram for Example
2-2.
142
General Engineering and Science
The weight W of the body acts at the
center
ofgruuity,
the Cartesian coordinates of
which are found by:
7
=
-jydw
1
W"
1
W
Z
=
-
zdw
The foregoing are volume integrals evaluated over the entire volume of the rigid
body and dw is an infinitesimal element of weight. If the body is of uniform density,
then the center of gravity is also called the
centroid.
Centroids of common lines,
areas, and volumes are shown in Tables
2-1, 2-2,
and
2-3.
For a composite body made
up
of elementary shapes with known centroids and known weights the center
of
gravity can be found from
Table
2-1
Centroids
of
Common Lines
[2]
(2-10)
(2-1
1)
Basic Mechanics (Statics and Dynamics)
143
Panbolic
area
L
Ppnbolic
span-
13
Table
2-2
Centroids
of
Common Areas
[2]
f
ji
Arm
Example
2-3
A
mallet is composed of a section
of
a right circular cylinder welded to a cylindrical
shaft, as shown in Figure 24a and b. Both components are steel, and the density
is
uniform throughout. Find the centroid of the mallet.
r
=
2 in.
L,
=
6 in.
L,
=
1.5
in.
d
=
1
in.
L,
=
5
in.
y
=
0.283
Ib/k3
144
General Engineering and Science
Table
2-3
Centroids
of
Common Volumes
[2]
Hemisphere
Semiellipsoid
of
revolution
Paraboloid
of
revolution
Cone
Pyramid