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FACTORS INVOLVED IN FLOW
An understanding of the behavior of fluids in
motion,
or solids for that matter, requires an understanding
of the term inertia. Inertia is the term
used by scientists to describe the property possessed
by all forms of matter that makes the matter
resist being moved if it is at rest, and likewise,
resist any change in its rate of motion if
it is moving.
The basic statement covering inertia is
Newton’s
first law of motion—inertia. Sir Isaac Newton
was a British philosopher and mathematician. His
first law states: A body at rest tends to
remain at rest, and a body in motion tends to remain
in motion at the same speed and direction, unless
acted on by some unbalanced force. This
simply says what you have learned by experience—that
you must push an object to start it
moving and push it in the opposite direction to
stop it again.
A familiar illustration is the effort a pitcher
must
exert to make a fast pitch and the opposition the
catcher must put forth to stop the ball. Similarly,
considerable work must be performed by
the engine to make an automobile begin to
roll; although, after it has attained a certain velocity,
it will roll along the road at uniform speed
if just enough effort is expended to overcome
friction, while brakes are necessary to stop
its motion. Inertia also explains the kick or recoil
of guns and the tremendous striking force of
projectiles.
Inertia
and Force
To overcome the tendency of an object to
resist
any change in its state of rest or motion, some
force that is not otherwise canceled or unbalanced
must act on the object. Some unbalanced
force must be applied whenever fluids are
set in motion or increased in velocity; while conversely,
forces are made to do work elsewhere whenever
fluids in motion are retarded or stopped.
There is a direct relationship between the
magnitude
of the force exerted and the inertia against
which it acts. This force is dependent on
two factors: (1) the mass of the object (which
is proportional to its weight), and (2) the
rate at which the velocity of the object is
changed. The rule is that the force in pounds
required to overcome inertia is equal to
the weight of the object multiplied by the change
in velocity, measured in feet per second, and
divided by 32 times the time in seconds required
to accomplish the change. Thus, the rate of
change in velocity of an object is proportional to
the force applied. The number 32 appears because
it is the conversion factor between weight and
mass.
There are five physical factors that can act on
a
fluid to affect its behavior. All of the physical actions
of fluids in all systems are determined by the
relationships of these five factors to each other.
Summarizing, these five factors are as follows:
1. Gravity, which acts at all times on all
bodies,
regardless of other forces
2. Atmospheric pressure, which acts on
any
part of a system exposed to the open air
3. Specific applied forces, which mayor may
not
be present, but which, in any event, are entirely
independent of the presence or absence of
motion
4. Inertia, which comes into play
whenever there is a change from
rest to motion or the opposite, or
whenever there is a change in direction
or in rate of motion
5. Friction, which is always present
whenever there is
motion
Figure 2-16 illustrates a possible relationship of these factors with respect to a particle of fluid
(P) in a system. The different forces are shown in terms of head, or in other words, in terms of
vertical columns of fluid required to provide the forces. At the particular moment under
consideration, a particle of water (P) is being acted on by applied force (A), by atmospheric pressure
(B), and by gravity (C) produced by the weight of the fluid standing over it. The particle possesses
sufficient inertia or velocity head to rise to level P1, since head equivalent to F was lost in friction
as P passed through the system. Since atmospheric pressure (B) acts downward on both sides of the
system, what is gained on one side is lost on the other.
If all the pressure acting on P to force it through the nozzle could be recovered in the form
of elevation head, it would rise to level Y. If account is taken of the balance in atmospheric
pressure, in a frictionless system, P would rise to level X, or precisely as high as the sum of the
gravity head and the head equivalent to the applied force.
Kinetic Energy
It was previously pointed out that a force must be
applied to an object in order to give it a velocity or
to increase the velocity it already has. Whether the
force begins or changes velocity, it acts over a
certain distance. A force acting over a certain distance
is work. Work and all forms into which it
can be changed are classified as energy. Obviously
then, energy is required to give an object
velocity. The greater the energy used, the greater
the velocity will be.
Disregarding friction, for an object to be brought
to rest or for its motion to be slowed down,
a force opposed to its motion must be applied
to it. This force also acts over some distance.
In this way energy is given up by the object
and delivered in some form to whatever opposes
its continuous motion. The moving object is
therefore a means of receiving energy at one place
(where its motion is increased) and delivering it
to another point (where it is stopped or retarded).
While it is in motion, it is said to contain
this energy as energy of motion or kinetic energy.
Since energy can never be destroyed, it follows that
if friction is disregarded the energy delivered to
stop the object will exactly equal the energy that
was required to increase its speed. At all times the
amount of kinetic energy possessed by an object
depends on its weight and the velocity at which
it is moving.
Figure 2-16.—Physical factors governing fluid flow.
The mathematical relationship for kinetic energy
is stated in the rule: "Kinetic energy in foot-pounds
is equal to the force in pounds which created
it, multiplied by the distance through which
it was applied, or to the weight of the moving
object in pounds, multiplied by the square of
its velocity in feet per second, and divided by 64.s"
The relationship between inertia forces, velocity,
and kinetic energy can be illustrated by analyzing
what happens when a gun fires a projectile
against the armor of an enemy ship. (See fig.
2-17.) The explosive force of the powder in the
breach pushes the projectile out of the gun, giving
it a high velocity. Because of its inertia, the
projectile offers opposition to this sudden velocity
and a reaction is set up that pushes the gun
backward (kick or recoil). The force of the explosion
acts on the projectile throughout its movement
in the gun. This is force acting through a
distance producing work. This work appears as kinetic
energy in the speeding projectile. The resistance
of the air produces friction, which uses some
of the energy and slows down the projectile. Eventually,
however, the projectile hits its target and,
because of the inertia, tries to continue moving.
The target, being relatively stationary, tends
to remain stationary because of its inertia. The
result is that a tremendous force is set up that either
leads to the penetration of the armor or the
shattering of the projectile. The projectile is
simply a means of transferring energy, in this
instance for destructive purpose, from the gun
to the enemy ship. This energy is transmitted in
the form of energy of motion or kinetic energy.
A similar action takes place in a fluid power system
in which the fluid takes the place of the projectile.
For example, the pump in a hydraulic
Figure 2-17.—Relationship of inertia, velocity, and kinetic energy.
system imparts energy to the fluid, which overcomes
the inertia of the fluid at rest and causes
it to flow through the lines. The fluid flows against
some type of actuator that is at rest. The fluid
tends to continue flowing, overcomes the inertia
of the actuator, and moves the actuator to
do work. Friction uses up a portion of the energy
as the fluid flows through the lines and components.
