of 1 inch, the volume of fluid in the left cylinder
will decrease by 2 cubic inches. At the same time,
the volume in the right cylinder will increase by
2 cubic inches. Since the diameter of the right
cylinder cannot change, the piston must move
upward to allow the volume to increase. The
piston will move a distance equal to the volume
increase divided by the surface area of the piston
(equal to the surface area of the cylinder). In this
example, the piston will move one-tenth of an inch
(2 cu. in. ÷ 20 sq. in.). This leads to the second
basic rule for a fluid power system that contains
two pistons: The distances the pistons move are
inversely proportional to the areas of the pistons.
Or more simply, if one piston is smaller than the
other, the smaller piston must move a greater
distance than the larger piston any time the pistons
move.
LIQUIDS IN MOTION
In the operation of fluid power systems, there
must be a flow of fluid. The amount of flow will
vary from system to system. To understand fluid
power systems in action, it is necessary to
understand some of the characteristics of liquids
in motion.
Liquids in motion have characteristics dif-
ferent from liquids at rest. Frictional resistances
within a fluid (viscosity) and inertia contribute to
these differences. (Viscosity is discussed in chapter
3.) Inertia, which means the resistance a mass
offers to being set in motion, will be discussed
later in this section. There are other relationships
of liquids in motion with which you must become
familiar. Among these are volume and velocity
of flow, flow rate and speed, laminar and
turbulent flow, and more importantly, the force
and energy changes which occur in flow.
VOLUME AND VELOCITY OF FLOW
The volume of a liquid passing a point in a
given time is known as its volume of flow or flow
rate. The volume of flow is usually expressed in
gallons per minute (gpm) and is associated with
relative pressures of the liquid, such as 5 gpm at
40 psi.
The velocity of flow or velocity of the fluid
is defined as the average speed at which the fluid
moves past a given point. It is usually expressed
in feet per second (fps) or feet per minute (fpm).
Velocity of flow is an important consideration in
sizing the hydraulic lines. (Hydraulic lines are
discussed in chapter 5.)
Volume and velocity of flow are often
considered together.
With other conditions
unaltered—that is,
with volume of input
unchanged—the velocity of flow increases as the
cross section or size of the pipe decreases, and the
velocity of flow decreases as the cross section
increases. For example, the velocity of flow is slow
at wide parts of a stream and rapid at narrow
parts, yet the volume of water passing each part
of the stream is the same.
In figure 2-13, if the cross-sectional area of
the pipe is 16 square inches at point A and 4
square inches at point B, we can calculate the
relative velocity of flow using the flow equation
Q = v A
Equation 2-7.
where Q is the volume of flow, v is the velocity
of flow and A is the cross-sectional area of the
liquid. Since the volume of flow at point A, Q1,
is equal to the volume of flow at point B, Q2, we
can use equation 2-7 to determine the ratio of the
Figure 2-13.—Volume and velocity of flow.
2-9
