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					         PDHengineer.com
                    Course № M-3005

                    Centrifugal Pumps




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                              Centrifugal Pumps (3 PDH)

                                    Course No. M-3005

Introduction
The centrifugal pump is second only to the electric motor as the most widely used type of rotating
mechanical equipment in the world. It is not surprising that this is true in the typical nuclear or
fossil fuel power plant, refinery, petrochemical, or chemical complex, where the use of centrifugal
pumps is so prevalent. Since this is where the process design engineer plies his or her wares, it
is necessary that engineers be familiar with the theory and application of centrifugal pumps.

The portion of this lesson on pump system curves was adapted from "A Pump Handbook for
Salesmen", written by D. B. Barta, now retired from the Ingersoll Rand Company. This handbook
was never published, and was informally distributed within the Ingersoll Rand Company as part of
a training program.

You may notice some inconsistencies in the symbol definitions in different parts of the text. For
instance, the symbol ω is used for rotational speed (rpm) in some cases, while the symbol N is
used for rpm in conjunction with the pump affinity laws, because the affinity laws always seem to
use that symbol. I have tried to define, or possibly redefine, the symbols used for each set of
equations.

The Centrifugal Pump
Centrifugal pumps offer important advantages over other types of pumps. Since they operate at
considerably higher speeds, they are smaller and lighter. The suction and discharge flows are
smooth and relatively free from pulsations. Because there is a maximum differential pressure
which they can develop known as the shutoff differential pressure, discharge piping can be
designed without the necessity of relief valves and the pump can be started against closed
discharge shutoff or check valves. Since there are not as many wearing parts, maintenance and
downtime are lower than for other types of pumps.

On the other hand, centrifugal pumps do not perform well at low flows or high viscosities. For
applications under these conditions, it is frequently better to use a rotary or reciprocating pump.
The centrifugal pump consists of a casing to contain the liquid being pumped, an impeller which
rotates thus transferring energy to the pumped liquid, a shaft to which the impeller is attached, a
stuffing box containing a mechanical seal or packing to prevent leakage at the point where the
shaft passes through the casing, bearings to support the shaft, a coupling to connect the pump
shaft to the driver shaft and a driver, which is normally either an electric motor or a steam turbine,
although engines and gas turbines are occasionally used to drive pumps. Sometimes a gear
increaser or decreaser is used between the pump and drive to obtain a desired pump speed.
Liquid enters the casing through the suction nozzles and is propelled outward toward the
discharge nozzle by the rotating impeller. As the liquid passes from the center of the impeller to
the periphery, its angular momentum is increased. After leaving the impeller, the velocity, which
was created in the impeller, is converted or diffused into a pressure increase by decelerating the
liquid in the outer zone of the casing known as the diffuser, or volute.




                                               Page 1
Performance Parameters
When specifying a centrifugal pump, it is necessary to provide information on its performance
characteristics in units that are universally understood and agreed upon. Generally speaking,
these are as follows:

Flow
Flow through a pump is generally understood as the volumetric Flow, rather than the weight or
mass flow, and normally is expressed in U. S. gallons per minute (gpm). cubic meters per second
(1 cu.m/min = 4.4 gal/sec), or on large capacity pumps in cubic feet per second (cfs) (one cfs =
449gpm).

Specific gravity
Specific gravity is the standard method of expressing the density of the liquid being pumped, and
is generally understood to be the ratio of the density of the liquid to the density of the water at
standard conditions.

Suction Pressure
Suction pressure is the pressure at the suction nozzle of the pump expressed in pounds per
square inch gauge.

Discharge Pressure
Discharge pressure is the pressure at the discharge nozzle of the pump expressed in pounds per
square inch gauge.

Differential Pressure
Differential pressure is the difference between the discharge pressure and the suction pressure
measured in pounds per square inch.

Differential Head (Also known as Total Dynamic Head or TDH)
Differential head is the energy per unit weight necessary to create the pump differential pressure.
Its true unit of measure is foot-pounds per pound; however, if one cancels out the pounds in both
the numerator and denominator, the result is the generally accepted unit of measure for head
which is simply feet. From this it can be deduced that the head could also be interpreted as the
height of a static column of liquid which would have a pressure at its base equal to the differential
pressure of the pump.

A formula relating the differential pressure, the specific gravity and the differential head can be
derived by applying the first law of thermodynamics as follows:

h1 + v12 /2g + p1/γ + Q + w = h2 + v22 /2g + p2 /γ
where:
h =elevation
v = velocity



                                                Page 2
g = gravitational constant
w = work per unit weight which by definition is the differential head.
Q = heat transfer
p = pressure
γ = specific weight

Subscripts 1 and 2 indicate suction and discharge conditions respectively.

If we assume that the elevation and velocity at the suction and discharge are the same and that
the heat transfer, Q, is negligible, the first law can be simplified to the following:

w = (p2 - p1) / γ = H

where H is the differential head. Since we wish to express H in feet, (p2 - p1) must be in pounds
per square foot, and the specific weight must be in pounds per cubic foot. Noting from our
previous definition of specific gravity, that the specific weight equals the specific gravity times the
specific weight of water at standard conditions, we have:

H = ∆p lb/in2 x 144 in2/ ft2
Specific gravity x 62.4 lb/cu ft

H=      2.31 ∆p
Specific gravity (sg)
Where H is in feet and p1 and p2 are in psig.

Net Positive Suction Head (NPSH)
The suction pressure, expressed in feet of liquid, required at the eye of the impeller to prevent
cavitation. This required NPSH (NPSHr) is usually determined by a test performed by the pump
manufacturer. The available NPSH (NPSHa) is a function of the system design and operation,
and must exceed the NPSHr or else cavitation will occur.

Hydraulic Horsepower
The hydraulic horsepower of a pump is the work which would ideally be required to produce the
pressure rise in the pumped liquid. Recalling our definition of head as the energy per unit mass
necessary to create the pump differential pressure, we can easily calculate the horsepower for a
given flow and differential head by multiplying the head times the flow in pounds per minute and
dividing the result by 33,000 foot pounds per minute per horsepower.

Noting that the flow in pounds per minute is 8.33 lb per gal x sg. x gpm (where 8. 33 lb per gal is
the density of water at standard conditions), we have:

Hydraulic Horsepower = 8.33 lb per gal.x sg x gpm x feet of head
                             33,000 ft lb per HP min

Hydraulic Horsepower = sg x gpm x head
                          3,960

If we substitute 2.31 (p1- p2)/sg for the head, we have:




                                                Page 3
(4) Hydraulic Horsepower = gpm (p1- p2)
                             1,714




Brake Horsepower
Brake horsepower is the actual horsepower transmitted to the pump by the driver through the
shaft coupling. In order to accurately measure the brake horsepower, it is necessary to measure
the speed (rpm) and torque at the coupling. If these two values are known, the brake horsepower
can then be calculated as follows:

Brake horsepower = work in foot pounds per minute / 33,000
Work = Force x Distance
Force = Torque / Radius
Distance = 2π Radius x rpm x time
Work = (Torque / Radius) x 2π Radius x rpm x time
Work per min. = 2π x torque x rpm
Brake HP = (2π x torque x rpm) / 33,000

Brake HP = (torque x rpm) / 5,250

Since instruments to measure torque at shaft couplings are expensive and rarely available except
in test facilities, brake horsepower is frequently approximated by measuring the energy
consumption of the driver. For a steam turbine, this would be the steam flow; for an electric
motor, the amps, and for an engine or gas turbine, the fuel consumption.

Efficiency
Efficiency is the ratio of the hydraulic horsepower to the brake horsepower.

Efficiency (η) = hydraulic HP / brake HP, therefore:

Brake horsepower BHP = ( sg x gpm x head) / 3,690 x η

Specific Speed
It is obviously not possible in this short summary to discuss the theory of dimensionless
parameters in great depth. For our purposes it is sufficient to state that it seems intuitively logical
that if any complex natural phenomenon can be described by a parameter calculated from
variables, which could logically affect it, then it should be dimensionless, since nature should be
completely oblivious to the man made concept of dimensions. If we apply this principal to
centrifugal pumps we can see that the flow, the differential head and the speed are the variables
which could be expected to describe pump performance. One could argue that a dimension
describing the pump size should be added to this list. We will therefore recognize the validity of
this argument by stipulating that the dimensionless parameters which result from flow, differential
head and speed should be applied to dimensionally similar machines. The parameter which
follows from this reasoning is known as the specific speed and is calculated as follows:

Ns = N Q1/2/ H3/4

Where



                                                Page 4
Q = flow in gpm
H = head in feet
N = pump speed

The number that results from this formula is not the same number which would result if the
dimensions were consistent. In order to make the dimensions consistent, we would multiply by
the appropriate constants. Therefore, the conclusions drawn from specific speed calculated with
standard parameters and inconsistent units would be the same as if the dimensions were
consistent. Follow that? Words can be tricky as well as math!

The concept of specific speed was originally defined as the speed which is required to produce a
head of one foot at a flow of one gallon per minute in a machine that is dimensionally similar, but
smaller. The concept is extended to state that at a given value of specific speed, the operating
conditions are such that similar flow conditions can exist in geometrically similar machines. This
is analogous to the concept of using the Reynolds number to predict fluid flow characteristics. As
a result of empirical tests which have been performed on a number of pumps, the curves shown
in Figure 2 have developed. These curves show a plot of efficiency versus specific speed for
various types of centrifugal pumps.




Figure 2

Two points can be drawn from Figure 2; first, low specific speed pumps have very high radial flow
components and high specific speed pumps have high or totally axial flow components.

Second, the most efficient pumps fall in the specific speed range of 2000 to 2500. Although,
strictly speaking, only the pumps with predominately radial flow components should be classified
as centrifugal; in practice all pumps with rotating impellers, regardless of specific speed, are



                                              Page 5
categorized as centrifugal pumps.

Performance Curves
The essence of the pump application to an engineer's work is to select the optimum commercially
available pump for a given set of hydraulic conditions. Of fundamental importance to this task is
the understanding of how to use and interpret the pump performance curves which are found in
manufacturers’ catalogs. A typical catalog performance curve will consist of curves of head
versus flow for various impeller diameters, lines of constant horsepower and efficiency
superimposed on the head/flow coordinates and a plot of net positive suction head required
(NPSHr) versus flow.




Figure 3

A typical example of such curves is shown in Figure 3. It should be noted that the pump curves
which we are discussing here, and which comprise the vast majority of curves normally
encountered, are drawn for a fixed speed which usually coincides with a standard motor speed.




                                             Page 6
An understanding of the theoretical basis for these performance curves will prove a valuable
asset in solving pump application problems. Let us begin our discussion of performance curves
with the equation which is the theoretical basis for the performance of all turbo machines, the
Euler turbine equation. Consider the generalized turbo machine rotor in Figure 4.The rotor
rotates about its axis with an angular velocity N.




Figure 4

Fluid enters the impeller at a point near the axis, travels through the impeller following an
undefined path and exits at the periphery of the impeller. Let us assume that steady state
conditions apply; that is, that the angular velocity and flow through the impeller are constant,
there is no heat transfer and fluid velocity magnitudes and directions do not change with time.
Let us also assume that the velocity at any point at a given radius from the rotor axis is the same
at any point on the circumference described by that radius. This means that at any radius the
velocity of the fluid can be described by a vector at a point. Consider now the velocity of the fluid
at the point where it enters the impeller near its axis and at the point where it exits the impeller at
its periphery. In both cases the velocity can be resolved into three components, one parallel to
the axis (the axial component) one perpendicular to the axis (the radial component) and one in
the plane of the impeller and perpendicular to the axial and radial components, (the tangential
component).

Recall from Newton's law that a change in momentum (in this case velocity since the mass is a
constant) results in a force being exerted in the direction of the change of momentum. Thus, we
see that if there is a change in axial momentum as the fluid travels through the impeller, then an
axial force will result. Similarly, a change in radial momentum will result in a radial force.

In an actual pump, the two forces just mentioned do not contribute to energy transfer but rather
produce forces which must be absorbed by bearings; the axial force by a thrust bearing and the
radial force by journal bearings.



                                                Page 7
The tangential component of the momentum (velocity) vector is the one which is most significant
in describing pump performance since it is the increase in tangential momentum, created by
torque, exerted on the fluid by the impeller which causes the increase in pressure.

Recalling that momentum is the product of mass and velocity we would have:
M = mV
Where:
M = tangential momentum
m = mass
V = tangential velocity
m = Qt/g
where:
Q = weight flow (Ib/sec)

g = 32.2 ft/sec
t = time (sec)
then: M = (Qt x V) /g

From Newton's law, force is equal to the time rate of change of momentum

Force= (Qt x V) / g x t
Force= QV / g
Torque = Force x Radius
Force = Torque / Radius = QV / g
Torque = (QV/g) x Radius
Work = Force x Distance
Work = Force x 2π Radius x ωt, where ω is rpm
Work = 2πωt x Torque
Work = 2πωt x QV / g x Radius

Notice that 2πωt x radius is the tangential velocity of the impeller, or U.

Then Work = (UVQt) / g, noting that head was defined as the energy (or work per unit mass) to
create the pressure rise. Thus,

Work = (UVQt) / g.

And since mass = Qt, (Work / Mass) = head = UV/g.

In order to develop a relationship between the head and the flow, we must consider a diagram
relating the fluid and impeller velocity vectors at the point where the fluid exits from the impeller.




                                                Page 8
Figure 5

Referring to Figure 5 we see that V, the tangential component of the fluid velocity is equal to U,
the tangential velocity of the rotor, minus the tangential component of the velocity of the fluid
relative to the impeller, Vru

Head = (U/g) x (U-Vru)

We also note from the vector diagram that Vru equals the radial component of the relative velocity,
Vr(radial) times the cotangent of β, the angle between a tangent to the impeller vane and a tangent
to the periphery of the impeller.

Vru = Vr(radial) x cot β

Then H = ( U / g ) ( U – Vr cot β )

We now note that the flow through the pump, from the law of continuity, is equal to the discharge
area (A) at the periphery of the impeller times the radial component of the relative velocity:

Q = AVr(radial) Then Vr(radial) =Q/A

Substituting into our formula above for head we have:

H = (U2/g) – (U cot β/ g A) Q

Note that for a given pump operating at a particular rpm, U, β/g A

We then have finally:
Head = K1- K2Q

where K1 = U2/g,




                                               Page 9
and K2 = U cot β/ area x g

K1 and K2 are constants.

Note that K2 determines the slope of the head capacity curve and is dependent on the cotangent
of β.

If β is equal to 90o, cot β equals zero and the head is a constant.


This of course is an idealized treatment; in actual practice the hydraulic losses must also be
subtracted. This is the reason for the characteristic head-capacity curve as shown in Figure 3.
instead of the straight line. ~~ This explains the very flat performance curves that straight vaned
pumps normally have. On the other hand as β decreases cot β increases, therefore so does the
slope of the head capacity curve. Curve slopes for several values of β are shown in Figure 6.




Figure 6

Affinity Laws
As we mentioned at the beginning of our discussion of performance curves, most pump
performance curves are drawn for a constant speed, usually a standard motor speed. Frequently,
it is necessary to predict the performance of a pump at a speed other than that shown in the
catalog performance curve. The affinity laws are relationships between the flow, head and power
and the RPM for the same pump operating at different speeds, or for geometrically similar pumps
operating at the same specific speed, which permits us to predict performance at different
speeds. Using dimensionless parameter once again, it can be shown that:

1. With impeller diameter, D, held constant:

Q1 / Q2 = N1 / N2

H1 / H2 = (N1 / N2)2

BHP1 / BHP2 = (N1 / N2)3




                                               Page 10
2. With Speed held constant:

Q1 / Q2 = D1 / D2

H1 / H2 =(D1 / D2)2

(BHP1 / BHP2) = (D1 / D2)3


Where: Q = Flow rate of the fluid


When the performance (Q1, H1, and BHP1) is known at some Particular speed (N1) or impeller
diameter (D1), the affinity formulas can be used to estimate the performance at some other speed
or diameter. The efficiency remains nearly constant for speed changes and for small changes in
impeller diameter.

Net Positive Suction Head
A pump characteristic which is of equal importance to the head-capacity curve is the NPSH or net
positive suction head. In order to understand NPSH, we must first discuss the phenomenon of
cavitation. Cavitation occurs when the pressure at the suction eye of the pump impeller drops
below the vapor pressure of the liquid being pumped. This pressure drop causes gas bubbles to
form which suddenly collapse as they flow into higher-pressure regions of the pump. The sudden
collapse of the gas bubbles results in mechanical shock, which can cause severe pitting of the
impeller vanes. Cavitation is normally characterized by noise, vibration and a reduction in head.
The noise and vibration are obviously a result of the mechanical shock caused by the collapsing
gas bubbles; however, the explanation for the drop in head is not so obvious. As the pressure at
the eye of the impeller of a low or medium specific speed pump reaches the vapor pressure of the
liquid being pumped, a band of vapor starts to form at the back side of the vane, and rapidly
extends across the entire channel formed by the two adjacent impeller vanes. When this
happens, the flow through the pump impeller for a given suction pressure cannot be increased by
reducing the discharge pressure, since the pressure differential (and therefore the flow) between
the suction and the area where vaporization is taking place is fixed. It is interesting to note that
pumps with very high specific speeds (i.e. axial flow pumps) do not experience a sharp drop in
head when cavitation takes place, but do experience a gradual drop off in head which increases
as the cavitation becomes more severe. This is due to the fact that the blades do not overlap,
and therefore do not form a definite channel which can be blocked by a band of the vaporized
liquid.

Cavitation has eluded a simple, elegant theoretical description which would allow calculating the
conditions under which cavitation will take place without relying on empirical test data. However,
there have been theoretical analyses made which use some empirical data and which do aid in
understanding qualitatively the mechanism by which cavitation takes place. The most well known
of these analyses is that using Thoma's cavitation constant. In order to develop
Thoma's theory, we begin with Bernoulli's equation for a pump that is about to experience
cavitation:

Ha + hs = hL + hv + (c2/2g) + λ (w2/2g) , where:

Ha = pressure head of the liquid in the suction tank

Hs = static head of the liquid in the suction tank and piping above the pump suction nozzle



                                               Page 11
hL = head loss in suction piping and pump suction

hv = vapor pressure of pumped liquid expressed as head

c = average absolute velocity of liquid through the impeller eye.

λ (w2/2g ) = the local pressure drop below average pressure in the eye of the impeller when
cavitation takes place (w is the average relative velocity and λ is an experimental coefficient).

The local pressure drop is frequently referred to as the dynamic depression, and results from the
fact that there is a pressure differential between the two faces of an impeller vane. This pressure
differential is a result of the reaction of the liquid being pumped to the torque being exerted on it
by the impeller vanes.

Thoma theorized that the sum of the velocity head and the dynamic depressions is proportional to
the total head:

(c2/2g) + (w2/2g) = Hσ

where σ is known as Thoma's cavitation constant, and is less than one. If we assume the suction
losses are negligible and substitute H for c2/2g + λ(w2/2g) in Bernoulli's equation we have:

σ = (Ha + hs- hv) / H

Since, as we have seen from the affinity laws, the head H varies as the square of the speed for
the same pump at different speeds, or similar pumps at the same specific speed:

σ = 1 /[2gH (c2 + 2w2)] = a constant

This relationship is used primarily to determine the conditions at which very large pumps and
hydraulic turbines will cavitate from model test results. Another approach that has been used to
describe and study cavitation is the so-called suction specific speed:

Suction specific speed = N (gpm)1/2 / [(c2/2g) + σ (w2/2g)]3/4

The principal of suction specific speed was arrived at using the principle of dimensionless
parameters in a fashion similar to the reasoning used to develop the concept of specific speed,
which was discussed earlier in this section. By combining the formulas for specific speed, suction
specific speed and Thoma cavitation constant we have:

Specific speed / suction specific speed = (Thoma cavitation constant)3/4

It has been shown by correlating the results of tests done on single suction pumps at their best
efficiency point, that the Thoma cavitation constant is related to the specific speed as follows:

σ = 6.3 (specific speed)4/3 / 106

If σ values for moderate specific speeds are calculated using the above formula, and then
substituted into the formula:

Specific speed / suction specific speed = σ 3/4



                                               Page 12
It will be seen that the suction specific speed will be approximately equal to 8000.

Now return to the original subject of our discussion, NPSH. Consider Bernoulli's equation for a
system that includes the suction vessel and piping as well as the inlet eye of the pump impeller:

Ha +hs = h1 + Hp + (c2/2g) + σ (w2/2g)

This equation is the same as the one used to start our discussion of Thoma's cavitation constant
with the exception that Hp has been substituted for hv, where hp is defined as the pressure at the
impeller inlet eye expressed as head. As was stated previously, if hp equals hv, cavitation will
result. Therefore, the pumping system should be designed so that hp is always greater than hv.
Rearranging the Bernoulli equation, which we have just written we have:

hp = (Ha + hs - h1) - (c2/2g) + σ (w2/2g)

If cavitation is to be avoided, Hp must be greater than hv therefore:

(Ha + hs - h1) - (c2/2g) + σ (w2/2g) > hv

or, (Ha + hs - h1) - hv > (c2/2g) + σ (w2/2g)

In a practical pump system design problem, the term on the left is called the Net Positive Suction
Head Available (NPSHa), and is calculated just as shown in the left side of the inequality above.
That is, the sum of the pressure head in the suction vessel and the static head of the liquid above
the pump suction minus the suction system losses minus the vapor pressure. The term on the
right is known as the net Positive Suction Head Required (NPSHr), and is a characteristic of the
pump. In practice, no attempt is made to calculate the NPSHr by estimating fluid velocities inside
the pump. Rather, the NPSHr is determined by testing each pump and noting the NPSH at which
cavitation begins for flows throughout the operating range of the pump. The curve of NPSHr
versus flow, which can be found in pump catalogs superimposed on the head capacity curve, is
then plotted. Noting that:

c2/2g + σ (w2/2g) = NPSHr, we have:

(Ha + hs - h1) - hv > NPSHr See figure 7.




                                                Page 13
Figure 7

Following the definition of NPSHr above, we can now rewrite the expression for suction specific
speed as:

Suction Specific Speed (Nss) =N (Q)1/2 / NPSHr3/4

For a properly designed commercially available pump, the suction specific speed will normally be
between 8,000 and 12,000. The margin of NPSHa over NPSHr is a complicated decision and
depends on many factors, including the liquid properties, size and h.p. of the pump, system
operation, and control.

Radial Thrust
Any discussion of radial thrust must begin with a discussion of the flow space in the casing
around the periphery of the impeller. Most centrifugal pumps have a volute casing, shown in
Figure 8.




                                             Page 14
Figure 8

Notice that the outer boundary of the casing starts at point A, where it is separated from the
impeller by a small clearance. From there it winds around the impeller in such a fashion that the
flow area available to the liquid discharging from the impeller is constantly increasing. At Point B,
it joins the diffuser section leading to the pump discharge. Point A, the close clearance point, is
known as the tongue, or cut water. The flow passage A-B just before the diffuser and discharge
is called the throat.

There are two schools of thought regarding the layout of the actual volute curve. One says that
the volute should be laid out in such a fashion that the angular momentum of the liquid pumped is
a constant at any point in the area around the periphery of the impeller.

That is; velocity x radius = constant

In practice, it has been found that this approach leads to excessive velocities at the smaller
section areas of the volute, and that a better approach is to lay the volute out in such a way that
the average velocity throughout the entire zone around the impeller is constant. This approach
has been found to yield higher efficiencies and obviously implies that the curve be constructed in
such a fashion that the flow area increases directly proportional to the angular displacement from
the cutwater.

The radial thrust on a pump impeller is the resultant of the pressure force acting on the impeller
from the liquid in the volute. If the volute is designed so that the velocity is constant throughout,
then in theory the pressure should be constant as well. In practice this is approximately true, at
the best efficiency point, but not true at flows other than best efficiency. As the flow varies from
shutoff to the end of the curve, the direction and magnitude of the radial thrust change constantly,
passing through a minimum magnitude at the best efficiency point. Normally, the largest thrust




                                              Page 15
loads are at shut off and low flow conditions. It is for this reason, among others, that it is not
desirable to operate centrifugal pumps at very low flows, or at shut off.

In order to reduce some of the radial forces which act on a centrifugal pump impeller, double-
volute casings are frequently used. Such a casing is illustrated in Figure 9.




Figure 9

In a double volute casing, a flow divider is introduced with its cutwater 1800 from the principal
pump casing cut water. In this way the radial forces which build up in one half of the casing
should be balanced by similar forces in the opposite half of the casing. In practice, complete
radial balance is never achieved; however a substantial reduction in unbalanced radial force can
be realized.

Axial Thrust
Of equal importance to the radial thrust is the axial thrust. Every pump from the smallest general
service water pump to the largest multistage boiler feed pump must have some provision for
restraining the shaft against axial movement, and counterbalancing axial force. In a simple single
stage pump, shown diagrammatically in Figure 10, the axial forces are due to two causes:

    1.   The pressure difference across the back shroud of the impeller at the suction eye.
    2.   The dynamic effect of the liquid entering the impeller in an axial direction, and turning 90o as it changes
         direction to flow in a radial direction through the impeller.




                                                       Page 16
Figure 10

Therefore, the thrust could be calculated as follows:
Thrust = (eye area - shaft area)x (shroud pressure - suction pressure) minus [(Eye area) (
density) x (axial velocity)2/2g

Two things should be noted about the above expression for thrust. First, the dynamic force acts in
the opposite direction to the force caused by the pressure difference, and secondly the shroud
pressure normally lies between the suction and discharge pressure and must be determined by
testing.

There are three traditional methods of reducing or counterbalancing the residual axial thrust on a
centrifugal pump impeller. The most common method is to drill holes in the back shroud of the
impeller in the area of the suction eye. This has the effect of relieving the pressure on the back
shroud. However, it also permits liquid to flow from the discharge of the impeller, through the
clearance between the back shroud and the pump casing, through the balance holes and back
into the suction of the pump. It therefore results in inefficiencies due to recirculation and due to
flow disturbances caused by the leakage flow from the balance holes mixing with the flow
entering the suction of the pump.

Another method of achieving axial balance frequently used on single stage overhung pumps is
the use of radial ribs on the back shroud of the impeller. Without such ribs, the angular velocity of
the liquid in the space between the back shroud of the impeller and the pump casing has been
shown by testing to be one half the angular velocity of the impeller. The addition of radial ribs on
the back shroud of the impeller increases the angular velocity of the liquid and thus decreases the
pressure. There is a theoretical basis for this effect, however it is omitted here since it is very
long and complex and not useful or necessary for pump application work .

The last commonly used method of axial balance is the use of a balance piston and chamber.
This type of axial balance is used almost exclusively on multistage pumps and is illustrated in
Figure 11.



                                              Page 17
Figure 11

A solid plate or "piston" which rotates with the shaft is mounted on the shaft at the discharge end
of the pump. There is a close clearance labyrinth seal between the circumference of the balance
piston and the pump casing, and a low-pressure chamber outboard of the balance piston. Since
there is a leakage across the labyrinth from the high-pressure inboard side of the balance piston
to the outboard low-pressure chamber, the chamber is normally piped either to the pump suction
vessel or the pump suction itself, thus permitting the leakage to flow back into the pump suction.
If the labyrinth seal is good, this will also serve to maintain the pressure in the chamber at a level
slightly above pump suction pressure. Since the resultant force on the balance piston opposes
the resultant pressure differential forces on the pump impellers, the balance piston serves as a
very effective axial thrust balancing device. Another version utilizes a balance drum and bushing
where the pressure breakdown is done in the vertical close clearance between the rotating
balance drum face and the stationary balance drum bushing.


System Curves
A centrifugal pump always operates at the intersection of its Head-Capacity curve and the system
curve. The system curve is a curve which shows how much head is required to make liquid flow
through the system of piping, valves, etc. The head in the system is made up of three
components:

    1.   Static Head
    2.   Pressure Head
    3.   Friction from entrance and exit head losses.




                                                        Page 18
Figure 12

In Figure 12, the static head is 70 feet, the pressure head is 60 feet, (26-0) x 2.31. The friction
head through all the piping, valves and fittings is 18.9 feet when the flow is 1500 gpm.

In drawing the system curve, Figure 13, the static head will not change with flow, so it is
represented as a horizontal line AB. The pressure head does not change with flow either, so it is
added to the static head and shown as a horizontal line CD. The friction head through a piping
system, however, varies approximately as the square of the flow.

So the friction at 500 gpm will be: (500 /1500)2 x 18.9 = 2.1 feet.(Point E),
and the friction at 1000 GPM will be: (1000/1500) 2 x 18.9 = 8.4 ft (Point F)




Figure 13

These determine the system curve, CEFG. All system curves are drawn the same way. The



                                               Page 19
pump curve has been overlaid on the system curve in Figure 12. Unless something is done to
change either the pump curve or the system curve, the pump will operate at 1500 GPM (Point G)
indefinitely.
If the throttle valve in the pump discharge line is closed partially, it will add head loss to the
system and the pump can be forced to operate at Point H, (1000GPM), Point J (500 GPM), or any
other point on its curve. This is essentially bending the system curve by adding head loss, and is
known as throttling control. It is the most common form of pump control, but is wasteful of power
since the pressure throttled out across the valve (FH or EJ) is lost.

Minimum Flow Requirements
All centrifugal pumps have minimum flow requirements that must be met to prevent damage to
the pump and/or the system. There are six distinct effects that an engineer applying centrifugal
pumps must be aware of so that the system has adequate protection to prevent or minimize the
consequences of operating at flows below the minimum requirement.

1. Excess heating of the pump due to its inefficiency. This is best illustrated by considering the
operation against a closed discharge valve. In this case, all of the pump energy is added to the
fluid inside the pump. It will eventually flash to a vapor, usually with detrimental effects to the
pump. There is some minimum flow, above which this will not occur, and the pump will continue
to operate satisfactorily. It is common, however, to start centrifugal pumps against a closed
discharge valve to stabilize the pump as it comes up to speed. The discharge valve should be
opened automatically or manually as soon as the pump is up to full speed. Care must be taken
with high specific speed not to exceed the motor horsepower rating, because the horsepower vs.
capacity curve rises sharply toward shut off.
 2. Radial and axial thrust usually both increase as the flow is reduced, and there are limits set by
the manufacturer to prevent shaft breakage and bearing failure.
 3. Pumps with high suction specific speeds, usually above 12,000, have NPSH requirements that
increase rather than continuing to decrease with decreasing flow. Since these pumps are
normally applied where the NPSHa is marginal, it is possible to reach the point where the NPSHr
exceeds the NPSHa and the pump begins to cavitate at low flows.
4. All pumps have a flow at which there is internal recirculation on the suction and discharge
sides of the impeller. Depending on the size, HP, and service of the pump, this can be
detrimental to the pump and/or the piping system.
5. On some pumps, in some systems, the suction and discharge pulsations increase at low
flows. These can cause excessive piping motion and system upsets. These pulsations usually
occur at a frequency equal to the number of impeller vanes x the running speed or some
harmonic of this frequency.

6. There is usually noise associated with pump cavitation. Also the noise level usually increases
as the flow is decreased because of the added turbulence and recirculation. Many times this is
unacceptable because of its effect on personnel. It also manifests itself as increased vibration
which can exceed acceptable limits. Each of the six areas may result in a different minimum flow
requirement, so the pump manufacturer must specify what the minimum flow requirement is, so
the system engineer can design a bypass or recirculation system that has adequate flow
capacity.

Centrifugal Pump Drives
Centrifugal pumps lend themselves to direct connected drives. The great majority of them are
driven by induction motors at speeds from 3600 RPM (2 pole-60HZ) down to as low as 300 RPM
(24 pole-60HZ), and even lower on very large pumps. The second most common direct
connected drives are steam turbines, especially in power plants, refineries, and chemical plants.
Also widely used are diesel and gasoline engines, particularly where electric service is



                                              Page 20
unavailable or very expensive, for example irrigation pumps.
The low starting torque and lack of torque fluctuations generally make direct connected drives
simple to engineer and relatively trouble free.

Speed increasers are used many times with induction motors where speeds above two-pole
speed (3600RPM @ 60HZ) are desirable, generally because of high system head requirements.
A few manufacturers have single stage high speed (up to 25,000 RPM) pumps available with the
speed increaser as an integral part of the pump. Speed decreasers are also used with induction
motors and steam turbines, generally on larger low speed pumps where it is desirable to use
lower cost higher speed motors, or mechanical drive turbines that operate most efficiently at
speeds greater than 3000 RPM. When gasoline or diesel engines are used to drive vertical
turbine pumps, they have right angle gears between the engine and pump, many times with a 1.1
ratio.

For variable speed applications, fluid drives, eddy current couplings, wound rotor motors, variable
voltage and frequency motors are available. On rubber lined and hard metal slurry pumps, it is
common to use V-belt drives to obtain optimum pump speeds while using two or four pole
electrical motors. Of course, steam turbines have the inherent advantage of variable speed, as
do gas turbines.


Conclusion
Much of today's engineering at the design and production levels is performed by computers using
commercially-developed programs. This has taken much of the day-to-day "dog work" out of
engineering, and has freed up engineers to do more challenging and creative tasks beyond
computations. However, it is essential for an engineer to understand what the computer
programs actually do, and even more enlightening to be able to trace the origins of a computer
calculation back to the basics of F=MA and the first and second laws of thermodynamics. Only
then does one really understand, for instance, why a pump performs at it does.

Fortunately, the derivations illustrated in this course are not performed every time an engineer
specifies a pump! But once having studied these derivations, an engineer can use the
streamlined computer solutions with some increased degree of confidence that he or she knows
what the solutions are based upon.

Perhaps the most practical and useful tools to the mechaical engineer presented herein are:
 (1) The pump affinity laws
 (2) Understanding the significance of and how to calculate NPSH
 (3) Interpreting pump performance curves




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