Pump Ed 101
Joe Evans, Ph.D
members of that family of machines known as "dynamic pumps"
are very different than the cousins that make up the "displacement"
branch of the tree . Unlike the displacement pump, which adds
energy to a fluid only intermittently, dynamic pumps continuously
impart energy into a flowing liquid. One of the primary members
of this family is the centrifugal pump and, although centrifugal force
is actually a farce, this group is still able to meet the
requirements of the definition.
Mechanics is the study of forces and motion. Hydraulics is the
branch of mechanics that focuses this study on liquids. And, dynamics
is the branch of mechanics and hydraulics that deals with the motion
equilibrium of systems under the action of forces related to
motion. Motion and equilibrium are the key words here and they
will be our focus. In this short tutorial, we will investigate
the "dynamics" that occur within the
centrifugal pump from the time a liquid enters the suction until
it exits the discharge. I have chosen to present this tutorial in
html format so that I can utilize some imbedded animations and also
link to several other web sites that offer some additional learning
tools that may help clarify certain points. It is also available
in pdf format but all of the images will be seen in still life.
Before we enter the world of dynamic pumps lets take a quick look at
the displacement pump. The animation to the right is that of a single acting
piston pump and is borrowed from Animated Software
Company. As you can see, one complete operation
(cycle) consists of a suction stroke (piston moves to the left) and a
discharge stroke (piston moves to the right). The suction and
discharge check valves open and close in accordance with the direction
of the piston and liquid movement. This results in the discharge
of a volume of liquid equal to that of the "displacement" of the
cylinder. Although external energy (atmospheric pressure etc.) is
required to bring liquid into the cylinder during the suction stroke, energy is added to the liquid "only"
during the discharge stroke.
The flow produced by this simple piston pump is f = d/t where f is flow, d is the volume displaced
during the discharge stroke, and t
is the unit of time. If d
is one gallon and t is
one second then
flow is equal to 1 gps or 60 gpm. The amount of pressure
generated, however, is dictated by the system and it is virtually
impossible to calculate the maximum
pressure that can be
generated. For example, if this pump is filling a tank 231 feet
above it, the
total system pressure would be 100 psi (elevation) plus the friction
generated by the piping. But, suppose that someone closes a valve
half way up - - how would the system pressure change? It is
totally unpredictable, as it would depend upon the power of the driver
and the strength of the materials. In other words, pressure would
increase until the driver stalls, the pipe bursts, or some other
The Role of the Impeller
The centrifugal pump,
on the other hand, adds energy continuously via its rotating
impeller. The animation to the left, borrowed from Light My Pump, shows a
view. As the
impeller rotates, water enters the vanes where it is accelerated to its maximum
velocity just as it exits at the periphery of the impeller. The
kinetic energy added by the impeller is then transformed into pressure
energy as water flows through the ever increasing geometry of the
volute. It usually reaches its maximum pressure at the volute
throat where the cutwater directs flow into the discharge.
Now, some would lead you to believe that this energy is added via a
quantity known as centrifugal force.
This force is defined as "center fleeing" and is said to outwardly
accelerate any object that happens to be
traveling in a circle or through an arc. The example to the right
someone swinging a can in a circle. If it is
released, at the exact point shown in the example, centrifugal force
should carry it directly to the right. But in real life, it does
not - - it travels tangent to the circle in which it was swinging.
animation on the left,
borrowed from Science Joy
clear this up a bit. It shows two views of a car as it begins to
curve to the left. The bottom view is one from the passenger seat
and the top one is a "bird's eye" view from above. As the car
enters the curve the passenger sees the tape cartridge on the dash
begin to slide to the right and eventually fly out the window.
Upon seeing this the passenger would assume that centrifugal force is
the culprit because he, too would feel some force pulling him to the
right. The bird, however, would notice something quite
different. The bird would see the dash sliding under the tape
as the tape maintained its original direction of travel. Unlike
the car's tires and the road, the light weight tape and the dash
develop very little
friction between them so the tape continues in the same direction it
was traveling before
the car entered the curve. Centrifugal force is one of three
"false" forces found in nature. It's "existence" depends upon
one's point of reference. The force you feel when rounding a
curve is caused by your body trying to act exactly as the tape and the
can did - -
its original direction of travel.
Well, if centrifugal force is not responsible for adding kinetic energy
- - what is? Just how does that impeller add energy in the form
of velocity? We will get to that in a minute but, first, lets
outline the steps a liquid encounters as it moves from suction to
1 Rotation of the
impeller and the shape of the vane entrances forces liquid to move from
of the impeller into its vanes.
2 During rotation
the curved shape
of the vanes causes liquid to continue to flow towards
the vane exits.
3 This flow causes
a partial vacuum at the eye which allows
atmospheric or some other, outside pressure to force more liquid into
the eye thus regenerating the entire process.
4 As liquid flows
through the vanes, it gains velocity and reaches
its maximum velocity just as it exits the vanes.
5 Upon exiting the
vanes, liquid enters the volute where most of its
kinetic energy of motion is transformed into pressure energy.
Now, getting back to our question - - how does the impeller add
velocity? Well it is has to do with the ever changing rotational velocity of points
along the radius of a spinning disc. Linear velocity is a very
straight (pun intended) forward quantity - - when an object moves in a
its velocity is simply distance traveled divided by the time it took to
get there (v=d/t). Another characteristic is that every part of
that object moves at the same velocity. Take an automobile for
example - - even though the front bumper will get there first, the back
bumper is traveling at the same velocity! This is not the case
with rotational motion. When we talk about rotational velocity we
usually use the term "rpm" or rotations per minute. That is
because every point along the radius of a rotating disc will complete
one rotation in the same amount of time. But the distance any
point will travel depends upon its location on the radius. The
link that you see a couple of lines below will bring up an animation
that will put this in perspective. I would like to provide
a link to the developer's site but I cannot remember where I found
it. I find that, sometimes, my memory is not as good as it used
to be. Also, my memory is not as good as it used to be.
Anyway, after you click on the link,
click on the "line" or "?"
button to the left. Then click on the
After you have viewed the animation click on your
browser's back arrow to return to the tutorial. Click here to see the animation.
What you saw was two lady bugs sitting on a phonograph disc - - one at
some distance "R" from the center of the disc and the other at twice
that distance. When you hit the play button the disc began to
spin and both bugs crossed the "finish" line at the very same
time. Their trips, however, were quite different. The
circumference of the circle described by the lady bug at point R is
equal to 2πR. If we assume that R is
one foot then the circumference and the equivalent "straight line"
distance traveled is 6.28 feet. At 2R the other lady bug will
travel twice that distance or 12.56 feet. Since both complete one
rotation in the same amount of time, the bug at point 2R must travel at
twice the velocity.
Although simple, rotational motion is more complex that linear motion
because the equivalent velocity is always proportional the the radius -
- double the radius and the velocity doubles. The same thing
happens in a centrifugal pump. As water flows through the vanes of
impeller, it encounters an ever increasing radius that causes velocity
to increase proportionally. Its final and also maximum
velocity is reached just as it exits the vanes at the periphery or
outer most diameter of the impeller. It is in this simple manner
that the impeller adds velocity energy to water.
The head produced by a centrifugal pump is proportional to the velocity
attained by the water as it exits the vanes at the periphery of the
impeller (peripheral velocity).
If you double the rotational speed or the diameter of the impeller you
double its peripheral velocity. Cut either in half and you reduce
the peripheral velocity by one half. The peripheral velocity
produced by an impeller is always Cw
where C is the
circumference and w is
rpm. Since head is based entirely
upon velocity, we can easily compute the maximum head that can be
produced by an impeller by rearranging the "falling body" equation (v2=2gh).
This equation states that the velocity at which an object will strike
the ground, near the surface of the earth, is equal to 2gh - - where g is the universal
gravitational constant (32ft/sec/sec) and h is the height of the object
when it was released. This assumes that the object is falling in
a vacuum and encounters no wind resistance.
If we rearrange the equation to solve for height we get h=v2/2g. Lets take a look at
practical example. Suppose we have
an impeller that is 9" in diameter and is rotating at 1800 rpm.
What is the maximum head it can produce? First we need the
circumference of the impeller in feet:
C = πd = 3.14
x 9" = 28.3" = 2.36'
Then we can compute the
velocity of the water as it exits the vanes:
v = Cw = 2.36' x 1800 rpm = 4248
ft/min = 70.8 ft/sec
Now we can replace v in our equation with the computed velocity and
solve for h:
h= v2/2g = (70.8)2 / (2 x 32) = 5012.64 / 64 = 78.32'
The maximum head that can be produced by a 9" diameter impeller
rotating at 1800 rpm is just a tad over 78'. Head varies as the
square of a change in rotational speed or impeller diameter (peripheral
velocity). Double the speed or diameter and head increases by
four. Reduce either by one half and head is reduced to one
fourth. One of the interesting things about the equation we just
used is that there is no
mention of mass or weight. Just as all objects, regardless of
their weight, fall at the same rate those same bodies will also reach
the same height given the same initial velocity. In the case of
the centrifugal pump this means that all liquids, regardless of their
weight (specific gravity) will reach the same head in feet even though
their pressures in PSI will vary substantially.
The flow produced by an
impeller is also proportional to the velocity
it attains at the periphery. But, unlike the piston pump there is
no simple equation that we can use to calculate it. Flow depends
upon the design and dimensions of the vanes. But, once it has
been determined by testing, changes will always be directly
proportional to a change in rotational speed or impeller diameter
(peripheral velocity). Double the rotational speed or diameter
and flow doubles - - reduce either by one half and flow is reduced by
The Role of the Volute
The volute houses the impeller and
is the "receptacle" for the water exiting the impeller vanes. Its
volume is many times that of the
impeller and its
nearly circular geometry guides the flow from the vane exits to its
discharge. During this trip, the flow encounters an ever
increasing volume and a corresponding reduction in velocity.
The illustration to the left is a cross section of an end suction pump
showing the volute and the impeller. The area just above the
discharge, where the volute begins, (about 7 o'clock) is known as the
cutwater. Its purpose is to guide water into the discharge and
reduce recirculation back into the volute. The colors indicate
velocity of the water at various areas of the volute. Red equates
to the highest velocity while blue is the lowest. You will note
that the areas of highest velocity occur near the vane exits and the
narrow portion of the volute from the cut water to about 10
o'clock. Velocity decreases as the volute volume increases and
reaches its lowest level in the area of the discharge. The
the volute is to convert the kinetic energy of velocity to that of
pressure. But how does it do this? After all there no
moving parts! Well, it has to do with its ever increasing volume
and the corresponding decrease in velocity of the water moving through
Water can possess three forms of hydraulic energy - - potential energy
due to elevation, kinetic energy due to velocity, and pressure energy
due to weight or force. In physics we say that energy can
be created nor destroyed - - it can only change its state or
Therefore these three forms of energy must be able to live in
harmony and their quantities, at a given point in time, will follow a
simple law known as The
Conservation of Energy. Now, for our purposes, we can
pretty much eliminate
because there is little or no elevation change from a pump's suction to
its discharge. But as we saw above, a liquid's velocity undergoes
large change as it moves through the impeller and volute. Since
velocity is, in fact, energy it must be replaced by some other form as
it decreases. That other form of energy is pressure and it arises
of it own accord as the volute volume increases and velocity decreases.
The figure to
the right shows a pipe with water flowing from left ot right at 100
gpm. As water reaches the center of the pipe it encounters a
section that has a reduced diameter but a short distance away the pipe
returns to its original diameter. Notice the three pressure
- - the one on the left points to 12 o'clock while the one in the
center is at 10 o'clock. The gauge on the right displays just a
little less than the one on the far left. In other words pressure
drops as water enters the constricted area of the pipe but it returns
to nearly its original pressure as it exits the constricted area.
What is happening here?
Well, if flow is to remain constant (100 gpm) the velocity of the water
must increase as it travels through the constricted area of the
pipe. We see this in nature when a slow moving river enters and
exits a narrow gorge. And, it confirms our statement about energy
- - as one form (velocity) increases, another form (pressure) must
decrease and vice versa. Bernoulli's
theorem states that during steady flow the energy at any point in a
conduit is the sum of the velocity energy, pressure energy, and the
potential energy due to elevation. It also says the the sum will
remain constant if there are no losses.
example above, the small loss in pressure seen in the right hand
portion of the pipe is due to increased friction in the narrow
section. Depending upon the circumstances, pressure loss due to
friction may be a result of the generation and dissipation of heat or
it could be due to a
small increase in velocity due to a change in laminar flow.
As friction increases laminar flow becomes less symmetrical which,
essentially, reduces the diameter of the conduit. Click here
and you will be directed to Mark
Mitchell's web site that illustrates the Bernoulli
Principle. It will allow you to vary pipe
diameters and see the resulting changes in velocity and pressure.
You can drag the yellow boxes to make any kind of conduit you desire
including the one in our example above. After you have finished
click on your browser's back arrow to return to the tutorial.
The Java code for this animation is also available on Mark's site but,
I have never been able to get it to compile correctly. For some
reason the flowing "dots" are omitted. If you have a suggestion
as to what I am doing wrong, drop me an email. I would like to
use it in one of my Power Point presentations. OK, lets put those
five steps, we outlined earlier, into perspective.
chart to the left shows the relationship of velocity and pressure as
water moves from a pump's suction to its discharge. The light
blue area is velocity energy and the dark blue area is pressure
energy. The total energy of the system is represented by the
upper edge of the light blue area. These quantities will differ
from pump to pump and application to application but, the trends will
always remain the same.
The energy at the pump's suction is almost entirely that of pressure
because the velocity in the suction piping is typically low. As
liquid enters the more restricted area of the impeller eye velocity
increases in order to maintain flow. As a result pressure
decreases but the total energy remains unchanged. The change in
total energy occurs in the next step. As water traverses the ever
increasing radius of the impeller vanes, velocity increases and
pressure remains relatively constant. And, it is this increase in
velocity that increases the total energy of the flowing water. As
water exits the vanes it reaches its maximum velocity and the maximum
total energy of the system is achieved. In the volute total
energy remains unchanged but the velocity decreases due to its
increasing volume. Bernoulli keeps the system honest by replacing
this loss in velocity energy with an equivalent increase in pressure
energy which reaches its maximum as flow nears the discharge.
Once in the discharge we have a pressure / velocity relationship that
is similar to that of the suction with one big exception. That
exception is that the total energy has increased as a result of the
velocity energy added by the impeller.
Well, that pretty much sums up the dynamics (motion and equilibrium) of
the centrifugal pump. It is all about energy conservation and the
rise and fall of the various forms of energy depending upon the
conditions within the system. Even the energy added by the
impeller was not "created". It simply transformed the mechanical
energy of the driver which transformed electrical energy which may have
transformed the energy of flowing water - - and so on. It never
ends. Energy cannot be created or destroyed - - it can only
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